RF1:=recformat<mat:SeqEnum,dtb:SeqEnum>;
 list:=

[ PowerStructure(Rec) |
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 3, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 1, 0, 0, 2, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 2, 1, 2, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 0, 1, 2, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 3, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 3, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 3, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 3, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48152>, <20, 1048576>, <24, 8440672>, <28, 36700160>, 
            <32, 150655740>, <36, 286261248>, <40, 566887712>, <44, 749731840>, <48, 757578120>, <52, 749731840>, <56, 
            472110016>, <60, 286261248>, <64, 157691910>, <68, 36700160>, <72, 30325824>, <76, 1048576>, <80, 3496808>, 
            <88, 237280>, <96, 11132>, <104, 160>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 3, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 3, 0, 2, 2, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 3, 2, 2, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 3, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 1, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 1, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48568>, <20, 1048576>, <24, 8441472>, <28, 36700160>, 
            <32, 150642140>, <36, 286261248>, <40, 566925952>, <44, 749731840>, <48, 757536712>, <52, 749731840>, <56, 
            472111360>, <60, 286261248>, <64, 157731782>, <68, 36700160>, <72, 30287104>, <76, 1048576>, <80, 3511688>, 
            <88, 235648>, <96, 10972>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 3, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 3, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 3, 2, 2, 0, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 3, 0, 2, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0, 2, 3, 2, 0, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 3, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 3, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 3, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 1, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48184>, <20, 1048576>, <24, 8444928>, <28, 36700160>, 
            <32, 150628316>, <36, 286261248>, <40, 566958208>, <44, 749731840>, <48, 757488328>, <52, 749731840>, <56, 
            472159744>, <60, 286261248>, <64, 157699526>, <68, 36700160>, <72, 30300928>, <76, 1048576>, <80, 3508232>, 
            <88, 236032>, <96, 10972>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 3, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 3, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 1, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 3, 0, 0, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 2, 3, 0, 2, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 2, 1, 0, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 3, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 1, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 3, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 3, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 2, 2, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48248>, <20, 1048576>, <24, 8435520>, <28, 36700160>, 
            <32, 150685468>, <36, 286261248>, <40, 566815680>, <44, 749731840>, <48, 757662536>, <52, 749731840>, <56, 
            472076416>, <60, 286261248>, <64, 157662790>, <68, 36700160>, <72, 30367616>, <76, 1048576>, <80, 3477320>, 
            <88, 240704>, <96, 11036>, <104, 192>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 2, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 3, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 1, 2, 0, 0, 2, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 2, 1, 0, 2, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2, 1, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 3, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 3, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47928>, <20, 1048576>, <24, 8447360>, <28, 36700160>, 
            <32, 150617948>, <36, 286261248>, <40, 566984320>, <44, 749731840>, <48, 757445320>, <52, 749731840>, <56, 
            472208128>, <60, 286261248>, <64, 157661894>, <68, 36700160>, <72, 30320896>, <76, 1048576>, <80, 3501320>, 
            <88, 237440>, <96, 10844>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 3, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 1, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 2, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2, 3, 2, 2, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 1, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 3, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 3, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 1, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47960>, <20, 1048576>, <24, 8452000>, <28, 36700160>, 
            <32, 150587068>, <36, 286261248>, <40, 567068640>, <44, 749731840>, <48, 757323272>, <52, 749731840>, <56, 
            472306240>, <60, 286261248>, <64, 157621126>, <68, 36700160>, <72, 30328256>, <76, 1048576>, <80, 3498920>, 
            <88, 239648>, <96, 10300>, <104, 96>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 3, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 0, 1, 2, 2, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 0, 3, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 3, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0, 0, 1, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 1, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 3, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47688>, <20, 1048576>, <24, 8452048>, <28, 36700160>, 
            <32, 150592716>, <36, 286261248>, <40, 567050288>, <44, 749731840>, <48, 757346664>, <52, 749731840>, <56, 
            472297504>, <60, 286261248>, <64, 157611942>, <68, 36700160>, <72, 30339168>, <76, 1048576>, <80, 3495512>, 
            <88, 239376>, <96, 10508>, <104, 112>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 2, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 1, 2, 2, 0, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 1, 2, 2, 0, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 3, 2, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 1, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 3, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 3, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 3, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48168>, <20, 1048576>, <24, 8442800>, <28, 36700160>, 
            <32, 150642028>, <36, 286261248>, <40, 566922960>, <44, 749731840>, <48, 757533224>, <52, 749731840>, <56, 
            472134880>, <60, 286261248>, <64, 157695718>, <68, 36700160>, <72, 30313376>, <76, 1048576>, <80, 3502520>, 
            <88, 236656>, <96, 11052>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 3, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 1, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 2, 2, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 3, 0, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 2, 3, 0, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 3, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 3, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 3, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 1, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47784>, <20, 1048576>, <24, 8446640>, <28, 36700160>, 
            <32, 150624748>, <36, 286261248>, <40, 566969040>, <44, 749731840>, <48, 757452584>, <52, 749731840>, <56, 
            472231648>, <60, 286261248>, <64, 157615078>, <68, 36700160>, <72, 30359456>, <76, 1048576>, <80, 3485240>, 
            <88, 240496>, <96, 10668>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 3, 0, 2, 2, 2, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 0, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 2, 1, 0, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 3, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 1, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 3, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48344>, <20, 1048576>, <24, 8439136>, <28, 36700160>, 
            <32, 150660924>, <36, 286261248>, <40, 566878496>, <44, 749731840>, <48, 757586184>, <52, 749731840>, <56, 
            472110016>, <60, 286261248>, <64, 157683846>, <68, 36700160>, <72, 30335040>, <76, 1048576>, <80, 3491624>, 
            <88, 238816>, <96, 10940>, <104, 160>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 1, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 1, 2, 0, 0, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0, 3, 2, 0, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 0, 3, 2, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 1, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 2, 3, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 3, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 1, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47608>, <20, 1048576>, <24, 8449920>, <28, 36700160>, 
            <32, 150609308>, <36, 286261248>, <40, 566999680>, <44, 749731840>, <48, 757431880>, <52, 749731840>, <56, 
            472208128>, <60, 286261248>, <64, 157675334>, <68, 36700160>, <72, 30305536>, <76, 1048576>, <80, 3509960>, 
            <88, 234880>, <96, 11164>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 1, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 1, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 1, 2, 0, 0, 0, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 3, 2, 0, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 0, 3, 2, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 3, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 3, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 1, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 3, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48072>, <20, 1048576>, <24, 8439312>, <28, 36700160>, 
            <32, 150665420>, <36, 286261248>, <40, 566864752>, <44, 749731840>, <48, 757598824>, <52, 749731840>, <56, 
            472117408>, <60, 286261248>, <64, 157658534>, <68, 36700160>, <72, 30356704>, <76, 1048576>, <80, 3483608>, 
            <88, 239696>, <96, 11020>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 3, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 3, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 3, 2, 2, 2, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 0, 3, 2, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 3, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 3, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 1, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 1, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 1, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48392>, <20, 1048576>, <24, 8436240>, <28, 36700160>, 
            <32, 150678668>, <36, 286261248>, <40, 566830960>, <44, 749731840>, <48, 757655272>, <52, 749731840>, <56, 
            472052896>, <60, 286261248>, <64, 157709606>, <68, 36700160>, <72, 30329056>, <76, 1048576>, <80, 3493400>, 
            <88, 237648>, <96, 11212>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 1, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 3, 2, 2, 0, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 0, 1, 2, 2, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 0, 0, 3, 2, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 3, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 1, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 3, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47752>, <20, 1048576>, <24, 8441744>, <28, 36700160>, 
            <32, 150657932>, <36, 286261248>, <40, 566875504>, <44, 749731840>, <48, 757596136>, <52, 749731840>, <56, 
            472101280>, <60, 286261248>, <64, 157688102>, <68, 36700160>, <72, 30330592>, <76, 1048576>, <80, 3496856>, 
            <88, 235984>, <96, 11468>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 1, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 2, 1, 0, 0, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2, 3, 2, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 2, 0, 1, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 3, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 3, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 3, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47960>, <20, 1048576>, <24, 8442720>, <28, 36700160>, 
            <32, 150645948>, <36, 286261248>, <40, 566915360>, <44, 749731840>, <48, 757527048>, <52, 749731840>, <56, 
            472174528>, <60, 286261248>, <64, 157635462>, <68, 36700160>, <72, 30359616>, <76, 1048576>, <80, 3483560>, 
            <88, 240352>, <96, 10812>, <104, 160>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 3, 2, 0, 2, 2, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 3, 2, 2, 2, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 3, 2, 2, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 0, 0, 3, 0, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 3, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 1, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 3, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 1, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48632>, <20, 1048576>, <24, 8422144>, <28, 36700160>, 
            <32, 150763932>, <36, 286261248>, <40, 566607104>, <44, 749731840>, <48, 757968456>, <52, 749731840>, <56, 
            471815680>, <60, 286261248>, <64, 157790022>, <68, 36700160>, <72, 30331392>, <76, 1048576>, <80, 3488456>, 
            <88, 235264>, <96, 12188>, <104, 256>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 1, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 3, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 3, 0, 0, 2, 0, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 0, 3, 2, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 3, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 3, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 3, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2, 1, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48120>, <20, 1048576>, <24, 8436672>, <28, 36700160>, 
            <32, 150680860>, <36, 286261248>, <40, 566826432>, <44, 749731840>, <48, 757646408>, <52, 749731840>, <56, 
            472092544>, <60, 286261248>, <64, 157652038>, <68, 36700160>, <72, 30372224>, <76, 1048576>, <80, 3476168>, 
            <88, 240832>, <96, 11036>, <104, 192>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 1, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 3, 0, 0, 0, 0, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 2, 3, 0, 0, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 3, 2, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 3, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 3, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 3, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 1, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48216>, <20, 1048576>, <24, 8430880>, <28, 36700160>, 
            <32, 150716348>, <36, 286261248>, <40, 566731360>, <44, 749731840>, <48, 757784584>, <52, 749731840>, <56, 
            471978304>, <60, 286261248>, <64, 157703558>, <68, 36700160>, <72, 30360256>, <76, 1048576>, <80, 3479720>, 
            <88, 238496>, <96, 11580>, <104, 224>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 1, 2, 2, 0, 2, 2, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 3, 0, 0, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 2, 1, 2, 2, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2, 0, 1, 0, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 3, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 1, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 1, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 1, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48168>, <20, 1048576>, <24, 8433648>, <28, 36700160>, 
            <32, 150699756>, <36, 286261248>, <40, 566774288>, <44, 749731840>, <48, 757726248>, <52, 749731840>, <56, 
            472019296>, <60, 286261248>, <64, 157693926>, <68, 36700160>, <72, 30355488>, <76, 1048576>, <80, 3482552>, 
            <88, 238512>, <96, 11436>, <104, 208>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 1, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 1, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 3, 2, 2, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 0, 1, 2, 0, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 0, 0, 3, 2, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 1, 0, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 1, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0, 1, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 3, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47656>, <20, 1048576>, <24, 8447408>, <28, 36700160>, 
            <32, 150623596>, <36, 286261248>, <40, 566965968>, <44, 749731840>, <48, 757468712>, <52, 749731840>, <56, 
            472199392>, <60, 286261248>, <64, 157652710>, <68, 36700160>, <72, 30331808>, <76, 1048576>, <80, 3497912>, 
            <88, 237168>, <96, 11052>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 3, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 3, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 1, 2, 0, 0, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0, 1, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 3, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, 1, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48264>, <20, 1048576>, <24, 8437008>, <28, 36700160>, 
            <32, 150677516>, <36, 286261248>, <40, 566827888>, <44, 749731840>, <48, 757671400>, <52, 749731840>, <56, 
            472020640>, <60, 286261248>, <64, 157747238>, <68, 36700160>, <72, 30301408>, <76, 1048576>, <80, 3506072>, 
            <88, 234320>, <96, 11596>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 3, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 3, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 1, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 3, 0, 0, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 1, 2, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 3, 0, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 3, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 1, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 1, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47464>, <20, 1048576>, <24, 8458608>, <28, 36700160>, 
            <32, 150556076>, <36, 286261248>, <40, 567142288>, <44, 749731840>, <48, 757224616>, <52, 749731840>, <56, 
            472379488>, <60, 286261248>, <64, 157598054>, <68, 36700160>, <72, 30323488>, <76, 1048576>, <80, 3504632>, 
            <88, 238384>, <96, 10348>, <104, 80>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 3, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 3, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 3, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 3, 0, 2, 0, 0, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 2, 3, 2, 2, 0, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 3, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 3, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 1, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 1, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47080>, <20, 1048576>, <24, 8461936>, <28, 36700160>, 
            <32, 150543404>, <36, 286261248>, <40, 567169936>, <44, 749731840>, <48, 757186984>, <52, 749731840>, <56, 
            472411744>, <60, 286261248>, <64, 157581926>, <68, 36700160>, <72, 30326560>, <76, 1048576>, <80, 3505784>, 
            <88, 237616>, <96, 10476>, <104, 80>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 3, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 3, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 1, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 3, 0, 2, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 2, 3, 0, 2, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 1, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 1, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 3, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 1, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48264>, <20, 1048576>, <24, 8437648>, <28, 36700160>, 
            <32, 150671756>, <36, 286261248>, <40, 566850928>, <44, 749731840>, <48, 757617640>, <52, 749731840>, <56, 
            472101280>, <60, 286261248>, <64, 157666598>, <68, 36700160>, <72, 30355168>, <76, 1048576>, <80, 3483032>, 
            <88, 240080>, <96, 10956>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 3, 2, 0, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 3, 2, 2, 2, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 0, 1, 2, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 3, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 1, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 1, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48664>, <20, 1048576>, <24, 8417632>, <28, 36700160>, 
            <32, 150790780>, <36, 286261248>, <40, 566542752>, <44, 749731840>, <48, 758039432>, <52, 749731840>, <56, 
            471798208>, <60, 286261248>, <64, 157747462>, <68, 36700160>, <72, 30380864>, <76, 1048576>, <80, 3466088>, 
            <88, 239328>, <96, 12028>, <104, 288>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 3, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 3, 2, 0, 2, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 0, 3, 0, 2, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 2, 2, 1, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 3, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 3, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 3, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 1, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48232>, <20, 1048576>, <24, 8442416>, <28, 36700160>, 
            <32, 150642604>, <36, 286261248>, <40, 566924496>, <44, 749731840>, <48, 757525160>, <52, 749731840>, <56, 
            472151008>, <60, 286261248>, <64, 157676902>, <68, 36700160>, <72, 30327200>, <76, 1048576>, <80, 3496184>, 
            <88, 238320>, <96, 10860>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 3, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 1, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 3, 0, 0, 2, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 3, 2, 2, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 2, 0, 1, 0, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 1, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 3, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 3, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48520>, <20, 1048576>, <24, 8434704>, <28, 36700160>, 
            <32, 150686732>, <36, 286261248>, <40, 566806384>, <44, 749731840>, <48, 757703656>, <52, 749731840>, <56, 
            471988384>, <60, 286261248>, <64, 157768742>, <68, 36700160>, <72, 30292192>, <76, 1048576>, <80, 3508376>, 
            <88, 234064>, <96, 11596>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 3, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 3, 0, 2, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 2, 3, 2, 2, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 3, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 1, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 1, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48168>, <20, 1048576>, <24, 8433392>, <28, 36700160>, 
            <32, 150702060>, <36, 286261248>, <40, 566765072>, <44, 749731840>, <48, 757747752>, <52, 749731840>, <56, 
            471987040>, <60, 286261248>, <64, 157726182>, <68, 36700160>, <72, 30333984>, <76, 1048576>, <80, 3491768>, 
            <88, 236208>, <96, 11692>, <104, 208>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 1, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 1, 2, 0, 0, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 3, 0, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 2, 3, 0, 0, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 1, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 1, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 1, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 3, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48648>, <20, 1048576>, <24, 8433808>, <28, 36700160>, 
            <32, 150689036>, <36, 286261248>, <40, 566804848>, <44, 749731840>, <48, 757698280>, <52, 749731840>, <56, 
            472004512>, <60, 286261248>, <64, 157747238>, <68, 36700160>, <72, 30309088>, <76, 1048576>, <80, 3500312>, 
            <88, 236240>, <96, 11340>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 3, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 1, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 3, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 3, 0, 0, 0, 2, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 3, 2, 0, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 0, 1, 0, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 3, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 1, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 3, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 3, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2, 2, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47944>, <20, 1048576>, <24, 8449744>, <28, 36700160>, 
            <32, 150601932>, <36, 286261248>, <40, 567028784>, <44, 749731840>, <48, 757378920>, <52, 749731840>, <56, 
            472265248>, <60, 286261248>, <64, 157633446>, <68, 36700160>, <72, 30329952>, <76, 1048576>, <80, 3497816>, 
            <88, 239120>, <96, 10508>, <104, 112>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 3, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 1, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 1, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 1, 2, 2, 0, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 1, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 3, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 3, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 1, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47176>, <20, 1048576>, <24, 8465808>, <28, 36700160>, 
            <32, 150516556>, <36, 286261248>, <40, 567241968>, <44, 749731840>, <48, 757089128>, <52, 749731840>, <56, 
            472477600>, <60, 286261248>, <64, 157570726>, <68, 36700160>, <72, 30315488>, <76, 1048576>, <80, 3510872>, 
            <88, 238032>, <96, 10124>, <104, 48>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 3, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 1, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 1, 2, 0, 2, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 3, 0, 0, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 3, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 3, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 3, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 1, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 49144>, <20, 1048576>, <24, 8399360>, <28, 36700160>, 
            <32, 150896668>, <36, 286261248>, <40, 566271360>, <44, 749731840>, <48, 758408264>, <52, 749731840>, <56, 
            471536128>, <60, 286261248>, <64, 157813318>, <68, 36700160>, <72, 30407936>, <76, 1048576>, <80, 3448520>, 
            <88, 239616>, <96, 12828>, <104, 384>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2, 3, 0, 0, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 0, 2, 3, 0, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 1, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 3, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48200>, <20, 1048576>, <24, 8428752>, <28, 36700160>, 
            <32, 150730060>, <36, 286261248>, <40, 566696112>, <44, 749731840>, <48, 757829480>, <52, 749731840>, <56, 
            471953440>, <60, 286261248>, <64, 157699750>, <68, 36700160>, <72, 30372704>, <76, 1048576>, <80, 3474008>, 
            <88, 239120>, <96, 11660>, <104, 240>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 3, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 3, 0, 0, 0, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 2, 1, 0, 0, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 2, 3, 2, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 3, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 1, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 1, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48040>, <20, 1048576>, <24, 8453488>, <28, 36700160>, 
            <32, 150576236>, <36, 286261248>, <40, 567096208>, <44, 749731840>, <48, 757291816>, <52, 749731840>, <56, 
            472314976>, <60, 286261248>, <64, 157638374>, <68, 36700160>, <72, 30308128>, <76, 1048576>, <80, 3507512>, 
            <88, 238384>, <96, 10284>, <104, 80>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 3, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 1, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 3, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 1, 2, 2, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 2, 3, 2, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 3, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 3, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 3, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47848>, <20, 1048576>, <24, 8446128>, <28, 36700160>, 
            <32, 150626476>, <36, 286261248>, <40, 566965968>, <44, 749731840>, <48, 757455272>, <52, 749731840>, <56, 
            472231648>, <60, 286261248>, <64, 157612390>, <68, 36700160>, <72, 30362528>, <76, 1048576>, <80, 3483512>, 
            <88, 241008>, <96, 10604>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 1, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 1, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 1, 2, 0, 0, 2, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0, 3, 0, 0, 2, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 2, 1, 0, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 1, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 1, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 1, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 1, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48408>, <20, 1048576>, <24, 8429088>, <28, 36700160>, 
            <32, 150723836>, <36, 286261248>, <40, 566712928>, <44, 749731840>, <48, 757814152>, <52, 749731840>, <56, 
            471946048>, <60, 286261248>, <64, 157727750>, <68, 36700160>, <72, 30347968>, <76, 1048576>, <80, 3483752>, 
            <88, 237728>, <96, 11644>, <104, 224>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 3, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 3, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 3, 0, 0, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 2, 1, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 1, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 3, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48472>, <20, 1048576>, <24, 8428832>, <28, 36700160>, 
            <32, 150723260>, <36, 286261248>, <40, 566719072>, <44, 749731840>, <48, 757795336>, <52, 749731840>, <56, 
            471978304>, <60, 286261248>, <64, 157692806>, <68, 36700160>, <72, 30372544>, <76, 1048576>, <80, 3472808>, 
            <88, 240544>, <96, 11324>, <104, 224>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 1, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 3, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 3, 0, 0, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 1, 2, 0, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 0, 3, 2, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 1, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 3, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 1, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 3, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47720>, <20, 1048576>, <24, 8456432>, <28, 36700160>, 
            <32, 150564140>, <36, 286261248>, <40, 567125392>, <44, 749731840>, <48, 757246120>, <52, 749731840>, <56, 
            472363360>, <60, 286261248>, <64, 157603430>, <68, 36700160>, <72, 30325024>, <76, 1048576>, <80, 3502328>, 
            <88, 239280>, <96, 10220>, <104, 80>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 2, 2, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 1, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 3, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 3, 0, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 2, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 1, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 3, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 0, 0, 1, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 1, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48008>, <20, 1048576>, <24, 8439952>, <28, 36700160>, 
            <32, 150662540>, <36, 286261248>, <40, 566872432>, <44, 749731840>, <48, 757585384>, <52, 749731840>, <56, 
            472133536>, <60, 286261248>, <64, 157645094>, <68, 36700160>, <72, 30364384>, <76, 1048576>, <80, 3480728>, 
            <88, 240336>, <96, 10956>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 3, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 3, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 3, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 3, 2, 0, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 3, 2, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 3, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 3, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 1, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 1, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47976>, <20, 1048576>, <24, 8454256>, <28, 36700160>, 
            <32, 150572204>, <36, 286261248>, <40, 567108496>, <44, 749731840>, <48, 757267624>, <52, 749731840>, <56, 
            472347232>, <60, 286261248>, <64, 157608806>, <68, 36700160>, <72, 30326560>, <76, 1048576>, <80, 3500024>, 
            <88, 240176>, <96, 10092>, <104, 80>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 3, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 1, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 3, 2, 2, 0, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 1, 2, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 0, 0, 3, 2, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 1, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 3, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 3, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 3, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48088>, <20, 1048576>, <24, 8441440>, <28, 36700160>, 
            <32, 150651708>, <36, 286261248>, <40, 566900000>, <44, 749731840>, <48, 757553928>, <52, 749731840>, <56, 
            472142272>, <60, 286261248>, <64, 157662342>, <68, 36700160>, <72, 30344256>, <76, 1048576>, <80, 3489320>, 
            <88, 239072>, <96, 10940>, <104, 160>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 3, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 3, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 2, 3, 2, 0, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 3, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 3, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 3, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48104>, <20, 1048576>, <24, 8434288>, <28, 36700160>, 
            <32, 150696876>, <36, 286261248>, <40, 566781968>, <44, 749731840>, <48, 757712808>, <52, 749731840>, <56, 
            472035424>, <60, 286261248>, <64, 157680486>, <68, 36700160>, <72, 30363168>, <76, 1048576>, <80, 3479672>, 
            <88, 239152>, <96, 11372>, <104, 208>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 3, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 3, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 3, 2, 0, 2, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 3, 2, 2, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 2, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 3, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 3, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 3, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 3, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48248>, <20, 1048576>, <24, 8434880>, <28, 36700160>, 
            <32, 150691228>, <36, 286261248>, <40, 566792640>, <44, 749731840>, <48, 757716296>, <52, 749731840>, <56, 
            471995776>, <60, 286261248>, <64, 157743430>, <68, 36700160>, <72, 30313856>, <76, 1048576>, <80, 3500360>, 
            <88, 234944>, <96, 11676>, <104, 192>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 3, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 1, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 1, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 3, 2, 2, 0, 0, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 1, 2, 2, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1, 2, 0, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 1, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 1, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 1, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 1, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48200>, <20, 1048576>, <24, 8437648>, <28, 36700160>, 
            <32, 150674636>, <36, 286261248>, <40, 566835568>, <44, 749731840>, <48, 757657960>, <52, 749731840>, <56, 
            472036768>, <60, 286261248>, <64, 157733798>, <68, 36700160>, <72, 30309088>, <76, 1048576>, <80, 3503192>, 
            <88, 234960>, <96, 11532>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 1, 2, 0, 0, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 3, 2, 2, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 2, 0, 1, 0, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 1, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 1, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 3, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48168>, <20, 1048576>, <24, 8442928>, <28, 36700160>, 
            <32, 150640876>, <36, 286261248>, <40, 566927568>, <44, 749731840>, <48, 757522472>, <52, 749731840>, <56, 
            472151008>, <60, 286261248>, <64, 157679590>, <68, 36700160>, <72, 30324128>, <76, 1048576>, <80, 3497912>, 
            <88, 237808>, <96, 10924>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 1, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 1, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 3, 2, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 0, 3, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 0, 3, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 1, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48344>, <20, 1048576>, <24, 8420576>, <28, 36700160>, 
            <32, 150778684>, <36, 286261248>, <40, 566571936>, <44, 749731840>, <48, 757993736>, <52, 749731840>, <56, 
            471846592>, <60, 286261248>, <64, 157712518>, <68, 36700160>, <72, 30397760>, <76, 1048576>, <80, 3460904>, 
            <88, 240224>, <96, 11964>, <104, 288>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 3, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 3, 0, 0, 0, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 2, 1, 0, 0, 0, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 2, 3, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, 3, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 1, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 3, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48872>, <20, 1048576>, <24, 8418352>, <28, 36700160>, 
            <32, 150781100>, <36, 286261248>, <40, 566573392>, <44, 749731840>, <48, 757991848>, <52, 749731840>, <56, 
            471839200>, <60, 286261248>, <64, 157727078>, <68, 36700160>, <72, 30388384>, <76, 1048576>, <80, 3462008>, 
            <88, 241392>, <96, 11628>, <104, 272>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 3, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 1, 0, 2, 0, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 2, 2, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 2, 1, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 3, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 3, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 1, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 3, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48472>, <20, 1048576>, <24, 8428320>, <28, 36700160>, 
            <32, 150727868>, <36, 286261248>, <40, 566700640>, <44, 749731840>, <48, 757838344>, <52, 749731840>, <56, 
            471913792>, <60, 286261248>, <64, 157757318>, <68, 36700160>, <72, 30329536>, <76, 1048576>, <80, 3491240>, 
            <88, 235936>, <96, 11836>, <104, 224>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 1, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 3, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 1, 2, 0, 2, 0, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 3, 2, 0, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2, 0, 1, 2, 0, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 1, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 3, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 3, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47896>, <20, 1048576>, <24, 8442976>, <28, 36700160>, 
            <32, 150646524>, <36, 286261248>, <40, 566909216>, <44, 749731840>, <48, 757545864>, <52, 749731840>, <56, 
            472142272>, <60, 286261248>, <64, 157670406>, <68, 36700160>, <72, 30335040>, <76, 1048576>, <80, 3494504>, 
            <88, 237536>, <96, 11132>, <104, 160>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 3, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 1, 0, 2, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2, 1, 2, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 3, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 3, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 3, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 1, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48072>, <20, 1048576>, <24, 8448592>, <28, 36700160>, 
            <32, 150606540>, <36, 286261248>, <40, 567018032>, <44, 749731840>, <48, 757395048>, <52, 749731840>, <56, 
            472249120>, <60, 286261248>, <64, 157644198>, <68, 36700160>, <72, 30325344>, <76, 1048576>, <80, 3498968>, 
            <88, 238992>, <96, 10508>, <104, 112>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 3, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 3, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 3, 0, 2, 0, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 1, 0, 2, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 2, 1, 0, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 1, 0, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 0, 3, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 1, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47928>, <20, 1048576>, <24, 8437952>, <28, 36700160>, 
            <32, 150677980>, <36, 286261248>, <40, 566826432>, <44, 749731840>, <48, 757659848>, <52, 749731840>, <56, 
            472060288>, <60, 286261248>, <64, 157692358>, <68, 36700160>, <72, 30341504>, <76, 1048576>, <80, 3490568>, 
            <88, 236992>, <96, 11484>, <104, 192>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 3, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 1, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 1, 2, 2, 2, 0, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 2, 3, 2, 0, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 3, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 1, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 1, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48376>, <20, 1048576>, <24, 8433984>, <28, 36700160>, 
            <32, 150693532>, <36, 286261248>, <40, 566791104>, <44, 749731840>, <48, 757710920>, <52, 749731840>, <56, 
            472011904>, <60, 286261248>, <64, 157721926>, <68, 36700160>, <72, 30330752>, <76, 1048576>, <80, 3492296>, 
            <88, 237120>, <96, 11420>, <104, 192>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 3, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 3, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 1, 2, 0, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 0, 3, 2, 2, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 3, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 1, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 1, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 3, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48536>, <20, 1048576>, <24, 8427936>, <28, 36700160>, 
            <32, 150728444>, <36, 286261248>, <40, 566702176>, <44, 749731840>, <48, 757830280>, <52, 749731840>, <56, 
            471929920>, <60, 286261248>, <64, 157738502>, <68, 36700160>, <72, 30343360>, <76, 1048576>, <80, 3484904>, 
            <88, 237600>, <96, 11644>, <104, 224>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 1, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 3, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 2, 1, 0, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 2, 1, 0, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 3, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 3, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 1, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 1, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 0, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48040>, <20, 1048576>, <24, 8443824>, <28, 36700160>, 
            <32, 150638572>, <36, 286261248>, <40, 566929104>, <44, 749731840>, <48, 757527848>, <52, 749731840>, <56, 
            472134880>, <60, 286261248>, <64, 157701094>, <68, 36700160>, <72, 30307232>, <76, 1048576>, <80, 3505976>, 
            <88, 235632>, <96, 11180>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 3, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 1, 0, 2, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 1, 2, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 3, 0, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 3, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 3, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 3, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48680>, <20, 1048576>, <24, 8419504>, <28, 36700160>, 
            <32, 150779372>, <36, 286261248>, <40, 566568784>, <44, 749731840>, <48, 758016040>, <52, 749731840>, <56, 
            471790816>, <60, 286261248>, <64, 157783526>, <68, 36700160>, <72, 30346912>, <76, 1048576>, <80, 3481016>, 
            <88, 236400>, <96, 12204>, <104, 272>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 1, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 1, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2, 3, 0, 2, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 2, 1, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 3, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2, 1, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 2, 3, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48200>, <20, 1048576>, <24, 8438416>, <28, 36700160>, 
            <32, 150667724>, <36, 286261248>, <40, 566863216>, <44, 749731840>, <48, 757593448>, <52, 749731840>, <56, 
            472133536>, <60, 286261248>, <64, 157637030>, <68, 36700160>, <72, 30373600>, <76, 1048576>, <80, 3475544>, 
            <88, 241872>, <96, 10764>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 3, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 3, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 3, 2, 2, 2, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 0, 1, 2, 2, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 0, 0, 3, 0, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 3, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 1, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 3, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 3, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47800>, <20, 1048576>, <24, 8439616>, <28, 36700160>, 
            <32, 150668764>, <36, 286261248>, <40, 566855616>, <44, 749731840>, <48, 757600712>, <52, 749731840>, <56, 
            472140928>, <60, 286261248>, <64, 157617094>, <68, 36700160>, <72, 30389120>, <76, 1048576>, <80, 3470984>, 
            <88, 241728>, <96, 10972>, <104, 192>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 3, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 3, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 3, 2, 2, 2, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 0, 3, 0, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 2, 3, 2, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 3, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 1, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 1, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47752>, <20, 1048576>, <24, 8451408>, <28, 36700160>, 
            <32, 150595596>, <36, 286261248>, <40, 567042608>, <44, 749731840>, <48, 757360104>, <52, 749731840>, <56, 
            472281376>, <60, 286261248>, <64, 157625382>, <68, 36700160>, <72, 30331488>, <76, 1048576>, <80, 3498392>, 
            <88, 238736>, <96, 10572>, <104, 112>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 1, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 3, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 1, 0, 2, 2, 0, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 3, 0, 2, 2, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 0, 2, 3, 2, 0, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 1, 2, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 1, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 3, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47528>, <20, 1048576>, <24, 8458352>, <28, 36700160>, 
            <32, 150555500>, <36, 286261248>, <40, 567148432>, <44, 749731840>, <48, 757205800>, <52, 749731840>, <56, 
            472411744>, <60, 286261248>, <64, 157563110>, <68, 36700160>, <72, 30348064>, <76, 1048576>, <80, 3493688>, 
            <88, 241200>, <96, 10028>, <104, 80>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 3, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 1, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 1, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 1, 0, 2, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 3, 2, 0, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 3, 0, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 1, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 3, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 3, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 1, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48056>, <20, 1048576>, <24, 8418496>, <28, 36700160>, 
            <32, 150798044>, <36, 286261248>, <40, 566518336>, <44, 749731840>, <48, 758062024>, <52, 749731840>, <56, 
            471812992>, <60, 286261248>, <64, 157699526>, <68, 36700160>, <72, 30421120>, <76, 1048576>, <80, 3451784>, 
            <88, 240576>, <96, 12252>, <104, 320>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 3, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 3, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 3, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 1, 0, 2, 2, 0, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 2, 3, 0, 2, 2, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 3, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0, 1, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 1, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 3, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47928>, <20, 1048576>, <24, 8447616>, <28, 36700160>, 
            <32, 150615644>, <36, 286261248>, <40, 566993536>, <44, 749731840>, <48, 757423816>, <52, 749731840>, <56, 
            472240384>, <60, 286261248>, <64, 157629638>, <68, 36700160>, <72, 30342400>, <76, 1048576>, <80, 3492104>, 
            <88, 239744>, <96, 10588>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 1, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 1, 0, 0, 0, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 3, 0, 0, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 2, 2, 1, 0, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 3, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 3, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 1, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48328>, <20, 1048576>, <24, 8428240>, <28, 36700160>, 
            <32, 150728908>, <36, 286261248>, <40, 566708400>, <44, 749731840>, <48, 757791848>, <52, 749731840>, <56, 
            472017952>, <60, 286261248>, <64, 157629862>, <68, 36700160>, <72, 30421856>, <76, 1048576>, <80, 3452120>, 
            <88, 244752>, <96, 11020>, <104, 240>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 3, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 3, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 3, 0, 2, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 1, 0, 2, 0, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 2, 1, 2, 2, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 3, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 3, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 3, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 3, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48040>, <20, 1048576>, <24, 8444080>, <28, 36700160>, 
            <32, 150636268>, <36, 286261248>, <40, 566938320>, <44, 749731840>, <48, 757506344>, <52, 749731840>, <56, 
            472167136>, <60, 286261248>, <64, 157668838>, <68, 36700160>, <72, 30328736>, <76, 1048576>, <80, 3496760>, 
            <88, 237936>, <96, 10924>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 3, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 3, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 3, 2, 2, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 1, 2, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 3, 0, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 3, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 1, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 3, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48456>, <20, 1048576>, <24, 8416912>, <28, 36700160>, 
            <32, 150800460>, <36, 286261248>, <40, 566512112>, <44, 749731840>, <48, 758087016>, <52, 749731840>, <56, 
            471757216>, <60, 286261248>, <64, 157767846>, <68, 36700160>, <72, 30373344>, <76, 1048576>, <80, 3470168>, 
            <88, 237264>, <96, 12428>, <104, 304>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 3, 2, 0, 0, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 3, 0, 2, 2, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2, 2, 1, 2, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 3, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 3, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 1, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 3, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47432>, <20, 1048576>, <24, 8454352>, <28, 36700160>, 
            <32, 150583500>, <36, 286261248>, <40, 567071792>, <44, 749731840>, <48, 757314408>, <52, 749731840>, <56, 
            472329760>, <60, 286261248>, <64, 157590438>, <68, 36700160>, <72, 30348384>, <76, 1048576>, <80, 3493208>, 
            <88, 239632>, <96, 10508>, <104, 112>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 3, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 1, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 3, 0, 2, 2, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 1, 2, 0, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 0, 0, 3, 0, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 1, 0, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 3, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 1, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 3, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47544>, <20, 1048576>, <24, 8460608>, <28, 36700160>, 
            <32, 150540636>, <36, 286261248>, <40, 567188288>, <44, 749731840>, <48, 757150152>, <52, 749731840>, <56, 
            472452736>, <60, 286261248>, <64, 157550790>, <68, 36700160>, <72, 30346368>, <76, 1048576>, <80, 3494792>, 
            <88, 241728>, <96, 9820>, <104, 64>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 1, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 3, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 1, 2, 2, 2, 0, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 3, 2, 0, 2, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 1, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 1, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 3, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0, 1, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47608>, <20, 1048576>, <24, 8459200>, <28, 36700160>, 
            <32, 150550428>, <36, 286261248>, <40, 567152960>, <44, 749731840>, <48, 757228104>, <52, 749731840>, <56, 
            472339840>, <60, 286261248>, <64, 157660998>, <68, 36700160>, <72, 30274176>, <76, 1048576>, <80, 3525320>, 
            <88, 234176>, <96, 10652>, <104, 64>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 3, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 1, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 1, 2, 2, 2, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 3, 2, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 1, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 3, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 3, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 3, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47720>, <20, 1048576>, <24, 8437744>, <28, 36700160>, 
            <32, 150683052>, <36, 286261248>, <40, 566814224>, <44, 749731840>, <48, 757664424>, <52, 749731840>, <56, 
            472083808>, <60, 286261248>, <64, 157648230>, <68, 36700160>, <72, 30376992>, <76, 1048576>, <80, 3476216>, 
            <88, 239536>, <96, 11372>, <104, 208>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 2, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 1, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 1, 2, 0, 0, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 1, 2, 0, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 0, 3, 0, 0, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 3, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 3, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 3, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 3, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48024>, <20, 1048576>, <24, 8451104>, <28, 36700160>, 
            <32, 150592252>, <36, 286261248>, <40, 567051744>, <44, 749731840>, <48, 757358216>, <52, 749731840>, <56, 
            472257856>, <60, 286261248>, <64, 157666822>, <68, 36700160>, <72, 30299072>, <76, 1048576>, <80, 3511016>, 
            <88, 236704>, <96, 10620>, <104, 96>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 3, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 1, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 1, 0, 0, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 1, 2, 0, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 2, 0, 3, 2, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 3, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 3, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 1, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 3, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47592>, <20, 1048576>, <24, 8456944>, <28, 36700160>, 
            <32, 150565292>, <36, 286261248>, <40, 567113104>, <44, 749731840>, <48, 757283752>, <52, 749731840>, <56, 
            472298848>, <60, 286261248>, <64, 157673318>, <68, 36700160>, <72, 30275872>, <76, 1048576>, <80, 3524216>, 
            <88, 233648>, <96, 10860>, <104, 80>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 3, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 3, 0, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 2, 1, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 3, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 1, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 3, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 1, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48296>, <20, 1048576>, <24, 8442032>, <28, 36700160>, 
            <32, 150643180>, <36, 286261248>, <40, 566926032>, <44, 749731840>, <48, 757517096>, <52, 749731840>, <56, 
            472167136>, <60, 286261248>, <64, 157658086>, <68, 36700160>, <72, 30341024>, <76, 1048576>, <80, 3489848>, 
            <88, 239984>, <96, 10668>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 3, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 3, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 1, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 1, 2, 0, 2, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 1, 2, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2, 0, 3, 2, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 3, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 1, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47880>, <20, 1048576>, <24, 8440720>, <28, 36700160>, 
            <32, 150661388>, <36, 286261248>, <40, 566869360>, <44, 749731840>, <48, 757601512>, <52, 749731840>, <56, 
            472101280>, <60, 286261248>, <64, 157682726>, <68, 36700160>, <72, 30336736>, <76, 1048576>, <80, 3493400>, 
            <88, 237008>, <96, 11340>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 3, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 3, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 2, 1, 2, 2, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 0, 3, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 3, 2, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 3, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 3, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 1, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47704>, <20, 1048576>, <24, 8444896>, <28, 36700160>, 
            <32, 150637884>, <36, 286261248>, <40, 566932256>, <44, 749731840>, <48, 757505544>, <52, 749731840>, <56, 
            472190656>, <60, 286261248>, <64, 157630086>, <68, 36700160>, <72, 30358080>, <76, 1048576>, <80, 3485864>, 
            <88, 239456>, <96, 10940>, <104, 160>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 1, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 3, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 2, 1, 2, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 0, 3, 2, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 3, 2, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 1, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 1, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 3, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48408>, <20, 1048576>, <24, 8429472>, <28, 36700160>, 
            <32, 150720380>, <36, 286261248>, <40, 566726752>, <44, 749731840>, <48, 757781896>, <52, 749731840>, <56, 
            471994432>, <60, 286261248>, <64, 157679366>, <68, 36700160>, <72, 30380224>, <76, 1048576>, <80, 3469928>, 
            <88, 241184>, <96, 11260>, <104, 224>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 3, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 1, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 3, 2, 2, 0, 2, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 0, 3, 0, 0, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 2, 3, 0, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 1, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 1, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 3, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48424>, <20, 1048576>, <24, 8431216>, <28, 36700160>, 
            <32, 150710124>, <36, 286261248>, <40, 566748176>, <44, 749731840>, <48, 757769256>, <52, 749731840>, <56, 
            471970912>, <60, 286261248>, <64, 157731558>, <68, 36700160>, <72, 30335520>, <76, 1048576>, <80, 3489464>, 
            <88, 237104>, <96, 11564>, <104, 208>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 3, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 3, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 3, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 1, 0, 2, 2, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 3, 0, 2, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 2, 1, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 3, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 0, 3, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 3, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 1, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47816>, <20, 1048576>, <24, 8442000>, <28, 36700160>, 
            <32, 150652748>, <36, 286261248>, <40, 566900080>, <44, 749731840>, <48, 757534312>, <52, 749731840>, <56, 
            472198048>, <60, 286261248>, <64, 157588646>, <68, 36700160>, <72, 30398176>, <76, 1048576>, <80, 3467480>, 
            <88, 243408>, <96, 10636>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 3, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 3, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 1, 2, 2, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 3, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 3, 2, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 1, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 3, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48728>, <20, 1048576>, <24, 8416480>, <28, 36700160>, 
            <32, 150798268>, <36, 286261248>, <40, 566516640>, <44, 749731840>, <48, 758095880>, <52, 749731840>, <56, 
            471717568>, <60, 286261248>, <64, 157825414>, <68, 36700160>, <72, 30330176>, <76, 1048576>, <80, 3487400>, 
            <88, 234080>, <96, 12604>, <104, 288>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 3, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 3, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 3, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 1, 0, 2, 0, 0, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 3, 2, 0, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 0, 0, 3, 0, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 3, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 1, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 3, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 3, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47800>, <20, 1048576>, <24, 8448768>, <28, 36700160>, 
            <32, 150611036>, <36, 286261248>, <40, 567004288>, <44, 749731840>, <48, 757407688>, <52, 749731840>, <56, 
            472256512>, <60, 286261248>, <64, 157618886>, <68, 36700160>, <72, 30347008>, <76, 1048576>, <80, 3490952>, 
            <88, 239872>, <96, 10588>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 1, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 3, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 3, 2, 2, 2, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 1, 2, 2, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 0, 0, 3, 2, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 1, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 3, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 1, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 3, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47752>, <20, 1048576>, <24, 8451536>, <28, 36700160>, 
            <32, 150594444>, <36, 286261248>, <40, 567047216>, <44, 749731840>, <48, 757349352>, <52, 749731840>, <56, 
            472297504>, <60, 286261248>, <64, 157609254>, <68, 36700160>, <72, 30342240>, <76, 1048576>, <80, 3493784>, 
            <88, 239888>, <96, 10444>, <104, 112>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 1, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 3, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 3, 0, 0, 2, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 2, 3, 2, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 0, 3, 2, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 3, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 3, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 3, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 1, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47720>, <20, 1048576>, <24, 8437872>, <28, 36700160>, 
            <32, 150681900>, <36, 286261248>, <40, 566818832>, <44, 749731840>, <48, 757653672>, <52, 749731840>, <56, 
            472099936>, <60, 286261248>, <64, 157632102>, <68, 36700160>, <72, 30387744>, <76, 1048576>, <80, 3471608>, 
            <88, 240688>, <96, 11244>, <104, 208>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 3, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 1, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 3, 2, 2, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 0, 3, 0, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 3, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 3, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 3, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47928>, <20, 1048576>, <24, 8447104>, <28, 36700160>, 
            <32, 150620252>, <36, 286261248>, <40, 566975104>, <44, 749731840>, <48, 757466824>, <52, 749731840>, <56, 
            472175872>, <60, 286261248>, <64, 157694150>, <68, 36700160>, <72, 30299392>, <76, 1048576>, <80, 3510536>, 
            <88, 235136>, <96, 11100>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 3, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 3, 0, 2, 2, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 1, 0, 0, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 2, 1, 0, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 1, 2, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 3, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 3, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 3, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48456>, <20, 1048576>, <24, 8435344>, <28, 36700160>, 
            <32, 150683852>, <36, 286261248>, <40, 566814064>, <44, 749731840>, <48, 757690216>, <52, 749731840>, <56, 
            472004512>, <60, 286261248>, <64, 157755302>, <68, 36700160>, <72, 30299872>, <76, 1048576>, <80, 3505496>, 
            <88, 234704>, <96, 11532>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 3, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 3, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 3, 0, 2, 2, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 3, 0, 0, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 2, 1, 0, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 1, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 1, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48088>, <20, 1048576>, <24, 8450592>, <28, 36700160>, 
            <32, 150593980>, <36, 286261248>, <40, 567048672>, <44, 749731840>, <48, 757360904>, <52, 749731840>, <56, 
            472257856>, <60, 286261248>, <64, 157664134>, <68, 36700160>, <72, 30302144>, <76, 1048576>, <80, 3509288>, 
            <88, 237216>, <96, 10556>, <104, 96>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 3, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 1, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 3, 0, 2, 0, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 3, 0, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 2, 3, 0, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 3, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, 1, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 3, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47720>, <20, 1048576>, <24, 8456176>, <28, 36700160>, 
            <32, 150566444>, <36, 286261248>, <40, 567116176>, <44, 749731840>, <48, 757267624>, <52, 749731840>, <56, 
            472331104>, <60, 286261248>, <64, 157635686>, <68, 36700160>, <72, 30303520>, <76, 1048576>, <80, 3511544>, 
            <88, 236976>, <96, 10476>, <104, 80>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 1, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 3, 0, 2, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 2, 1, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 1, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 3, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 3, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 3, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48440>, <20, 1048576>, <24, 8423808>, <28, 36700160>, 
            <32, 150757596>, <36, 286261248>, <40, 566620928>, <44, 749731840>, <48, 757949640>, <52, 749731840>, <56, 
            471831808>, <60, 286261248>, <64, 157781958>, <68, 36700160>, <72, 30332928>, <76, 1048576>, <80, 3489032>, 
            <88, 234880>, <96, 12252>, <104, 256>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 3, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 3, 2, 2, 2, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 1, 0, 2, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 1, 0, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 2, 3, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 2, 2, 1, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 1, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48616>, <20, 1048576>, <24, 8429936>, <28, 36700160>, 
            <32, 150713004>, <36, 286261248>, <40, 566748176>, <44, 749731840>, <48, 757755816>, <52, 749731840>, <56, 
            472003168>, <60, 286261248>, <64, 157691238>, <68, 36700160>, <72, 30366240>, <76, 1048576>, <80, 3475064>, 
            <88, 240944>, <96, 11116>, <104, 208>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 3, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 2, 3, 2, 0, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 2, 0, 3, 0, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, 1, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 1, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 1, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 1, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47864>, <20, 1048576>, <24, 8447872>, <28, 36700160>, 
            <32, 150616220>, <36, 286261248>, <40, 566987392>, <44, 749731840>, <48, 757442632>, <52, 749731840>, <56, 
            472208128>, <60, 286261248>, <64, 157664582>, <68, 36700160>, <72, 30317824>, <76, 1048576>, <80, 3503048>, 
            <88, 236928>, <96, 10908>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 1, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 3, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 3, 2, 0, 2, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 3, 0, 0, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 2, 1, 2, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 1, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 1, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 1, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48504>, <20, 1048576>, <24, 8433088>, <28, 36700160>, 
            <32, 150695836>, <36, 286261248>, <40, 566789568>, <44, 749731840>, <48, 757705544>, <52, 749731840>, <56, 
            472028032>, <60, 286261248>, <64, 157700422>, <68, 36700160>, <72, 30347648>, <76, 1048576>, <80, 3484232>, 
            <88, 239296>, <96, 11164>, <104, 192>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 1, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 3, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 3, 0, 2, 2, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 1, 2, 0, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 0, 1, 2, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 1, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 1, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 3, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48168>, <20, 1048576>, <24, 8443568>, <28, 36700160>, 
            <32, 150635116>, <36, 286261248>, <40, 566950608>, <44, 749731840>, <48, 757468712>, <52, 749731840>, <56, 
            472231648>, <60, 286261248>, <64, 157598950>, <68, 36700160>, <72, 30377888>, <76, 1048576>, <80, 3474872>, 
            <88, 243568>, <96, 10284>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 1, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 1, 0, 2, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 2, 3, 2, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 1, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 3, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 1, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 1, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48584>, <20, 1048576>, <24, 8424784>, <28, 36700160>, 
            <32, 150748492>, <36, 286261248>, <40, 566645424>, <44, 749731840>, <48, 757920872>, <52, 749731840>, <56, 
            471840544>, <60, 286261248>, <64, 157796518>, <68, 36700160>, <72, 30315872>, <76, 1048576>, <80, 3495896>, 
            <88, 234128>, <96, 12172>, <104, 240>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 3, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 1, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 3, 2, 2, 2, 0, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 0, 3, 2, 0, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 3, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 1, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 3, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 1, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48680>, <20, 1048576>, <24, 8419760>, <28, 36700160>, 
            <32, 150777068>, <36, 286261248>, <40, 566578000>, <44, 749731840>, <48, 757994536>, <52, 749731840>, <56, 
            471823072>, <60, 286261248>, <64, 157751270>, <68, 36700160>, <72, 30368416>, <76, 1048576>, <80, 3471800>, 
            <88, 238704>, <96, 11948>, <104, 272>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 3, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 3, 0, 2, 0, 0, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 3, 2, 0, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 1, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 1, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 3, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47992>, <20, 1048576>, <24, 8437824>, <28, 36700160>, 
            <32, 150676252>, <36, 286261248>, <40, 566837184>, <44, 749731840>, <48, 757630280>, <52, 749731840>, <56, 
            472108672>, <60, 286261248>, <64, 157641286>, <68, 36700160>, <72, 30376832>, <76, 1048576>, <80, 3475016>, 
            <88, 240960>, <96, 11036>, <104, 192>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 3, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 1, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 1, 2, 0, 0, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 0, 1, 0, 2, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 2, 1, 0, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 1, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 1, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 1, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 3, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48264>, <20, 1048576>, <24, 8437392>, <28, 36700160>, 
            <32, 150674060>, <36, 286261248>, <40, 566841712>, <44, 749731840>, <48, 757639144>, <52, 749731840>, <56, 
            472069024>, <60, 286261248>, <64, 157698854>, <68, 36700160>, <72, 30333664>, <76, 1048576>, <80, 3492248>, 
            <88, 237776>, <96, 11212>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 1, 2, 0, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 0, 3, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 1, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 1, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2, 0, 0, 1, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 3, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48104>, <20, 1048576>, <24, 8443824>, <28, 36700160>, 
            <32, 150635692>, <36, 286261248>, <40, 566944464>, <44, 749731840>, <48, 757487528>, <52, 749731840>, <56, 
            472199392>, <60, 286261248>, <64, 157633894>, <68, 36700160>, <72, 30353312>, <76, 1048576>, <80, 3485816>, 
            <88, 240752>, <96, 10604>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 3, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 3, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 3, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 1, 2, 0, 2, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 3, 0, 2, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 2, 2, 1, 2, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 1, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 3, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 3, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 3, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47928>, <20, 1048576>, <24, 8447744>, <28, 36700160>, 
            <32, 150614492>, <36, 286261248>, <40, 566998144>, <44, 749731840>, <48, 757413064>, <52, 749731840>, <56, 
            472256512>, <60, 286261248>, <64, 157613510>, <68, 36700160>, <72, 30353152>, <76, 1048576>, <80, 3487496>, 
            <88, 240896>, <96, 10460>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 3, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 0, 3, 0, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 3, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 1, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 3, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48088>, <20, 1048576>, <24, 8431776>, <28, 36700160>, 
            <32, 150714044>, <36, 286261248>, <40, 566732896>, <44, 749731840>, <48, 757789960>, <52, 749731840>, <56, 
            471962176>, <60, 286261248>, <64, 157725062>, <68, 36700160>, <72, 30343360>, <76, 1048576>, <80, 3487784>, 
            <88, 236320>, <96, 11836>, <104, 224>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 3, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 3, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 2, 0, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 3, 0, 2, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 2, 3, 2, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 3, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 1, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 3, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48568>, <20, 1048576>, <24, 8413888>, <28, 36700160>, 
            <32, 150816476>, <36, 286261248>, <40, 566475328>, <44, 749731840>, <48, 758126536>, <52, 749731840>, <56, 
            471748480>, <60, 286261248>, <64, 157742534>, <68, 36700160>, <72, 30402688>, <76, 1048576>, <80, 3456392>, 
            <88, 240064>, <96, 12252>, <104, 320>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 1, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 1, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 3, 0, 2, 2, 0, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 1, 0, 0, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 2, 3, 0, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 1, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 3, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 3, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 1, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48216>, <20, 1048576>, <24, 8430624>, <28, 36700160>, 
            <32, 150718652>, <36, 286261248>, <40, 566722144>, <44, 749731840>, <48, 757806088>, <52, 749731840>, <56, 
            471946048>, <60, 286261248>, <64, 157735814>, <68, 36700160>, <72, 30338752>, <76, 1048576>, <80, 3488936>, 
            <88, 236192>, <96, 11836>, <104, 224>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 3, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 3, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 3, 0, 0, 0, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 2, 3, 0, 0, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 1, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 3, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 3, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 3, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 3, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48120>, <20, 1048576>, <24, 8445824>, <28, 36700160>, 
            <32, 150623132>, <36, 286261248>, <40, 566975104>, <44, 749731840>, <48, 757453384>, <52, 749731840>, <56, 
            472208128>, <60, 286261248>, <64, 157653830>, <68, 36700160>, <72, 30330112>, <76, 1048576>, <80, 3496136>, 
            <88, 238976>, <96, 10652>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 3, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 3, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 3, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 3, 2, 0, 0, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 3, 0, 2, 0, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 3, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 3, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 3, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 3, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47832>, <20, 1048576>, <24, 8453280>, <28, 36700160>, 
            <32, 150581308>, <36, 286261248>, <40, 567084000>, <44, 749731840>, <48, 757296392>, <52, 749731840>, <56, 
            472338496>, <60, 286261248>, <64, 157594246>, <68, 36700160>, <72, 30343616>, <76, 1048576>, <80, 3493160>, 
            <88, 240928>, <96, 10172>, <104, 96>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 3, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 3, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 1, 0, 0, 2, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 2, 1, 0, 0, 0, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 2, 3, 2, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 3, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 1, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 1, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 3, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48440>, <20, 1048576>, <24, 8424448>, <28, 36700160>, 
            <32, 150751836>, <36, 286261248>, <40, 566643968>, <44, 749731840>, <48, 757895880>, <52, 749731840>, <56, 
            471912448>, <60, 286261248>, <64, 157701318>, <68, 36700160>, <72, 30386688>, <76, 1048576>, <80, 3465992>, 
            <88, 240640>, <96, 11612>, <104, 256>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 1, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 3, 0, 2, 2, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 1, 0, 0, 0, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 2, 1, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 1, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 1, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 3, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48312>, <20, 1048576>, <24, 8434624>, <28, 36700160>, 
            <32, 150690652>, <36, 286261248>, <40, 566798784>, <44, 749731840>, <48, 757697480>, <52, 749731840>, <56, 
            472028032>, <60, 286261248>, <64, 157708486>, <68, 36700160>, <72, 30338432>, <76, 1048576>, <80, 3489416>, 
            <88, 237760>, <96, 11356>, <104, 192>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 3, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 1, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 3, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 1, 0, 0, 2, 0, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 1, 2, 0, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 0, 3, 0, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 1, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 1, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 1, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 3, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47528>, <20, 1048576>, <24, 8457840>, <28, 36700160>, 
            <32, 150560108>, <36, 286261248>, <40, 567130000>, <44, 749731840>, <48, 757248808>, <52, 749731840>, <56, 
            472347232>, <60, 286261248>, <64, 157627622>, <68, 36700160>, <72, 30305056>, <76, 1048576>, <80, 3512120>, 
            <88, 236592>, <96, 10540>, <104, 80>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 3, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 3, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 3, 2, 2, 0, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 0, 3, 0, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 1, 2, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 3, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 3, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 1, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48136>, <20, 1048576>, <24, 8447824>, <28, 36700160>, 
            <32, 150610572>, <36, 286261248>, <40, 567005744>, <44, 749731840>, <48, 757419240>, <52, 749731840>, <56, 
            472216864>, <60, 286261248>, <64, 157673766>, <68, 36700160>, <72, 30306912>, <76, 1048576>, <80, 3506456>, 
            <88, 237200>, <96, 10700>, <104, 112>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 3, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 3, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 3, 0, 0, 0, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2, 3, 2, 2, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 3, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 3, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2, 1, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 3, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48008>, <20, 1048576>, <24, 8439568>, <28, 36700160>, 
            <32, 150665996>, <36, 286261248>, <40, 566858608>, <44, 749731840>, <48, 757617640>, <52, 749731840>, <56, 
            472085152>, <60, 286261248>, <64, 157693478>, <68, 36700160>, <72, 30332128>, <76, 1048576>, <80, 3494552>, 
            <88, 236880>, <96, 11340>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 1, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 1, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 3, 2, 2, 2, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 0, 2, 3, 0, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 1, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 1, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 3, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48216>, <20, 1048576>, <24, 8440288>, <28, 36700160>, 
            <32, 150656316>, <36, 286261248>, <40, 566889248>, <44, 749731840>, <48, 757570056>, <52, 749731840>, <56, 
            472126144>, <60, 286261248>, <64, 157673094>, <68, 36700160>, <72, 30339648>, <76, 1048576>, <80, 3490472>, 
            <88, 238944>, <96, 10940>, <104, 160>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 3, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 3, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 1, 0, 2, 2, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 2, 1, 0, 2, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 2, 1, 0, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 1, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 1, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 3, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48104>, <20, 1048576>, <24, 8434032>, <28, 36700160>, 
            <32, 150699180>, <36, 286261248>, <40, 566772752>, <44, 749731840>, <48, 757734312>, <52, 749731840>, <56, 
            472003168>, <60, 286261248>, <64, 157712742>, <68, 36700160>, <72, 30341664>, <76, 1048576>, <80, 3488888>, 
            <88, 236848>, <96, 11628>, <104, 208>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 3, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 3, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 3, 0, 2, 2, 2, 2, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 3, 2, 0, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 0, 1, 0, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 3, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 1, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 1, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 3, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48040>, <20, 1048576>, <24, 8443696>, <28, 36700160>, 
            <32, 150639724>, <36, 286261248>, <40, 566924496>, <44, 749731840>, <48, 757538600>, <52, 749731840>, <56, 
            472118752>, <60, 286261248>, <64, 157717222>, <68, 36700160>, <72, 30296480>, <76, 1048576>, <80, 3510584>, 
            <88, 234480>, <96, 11308>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 3, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 3, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 1, 2, 2, 0, 2, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 0, 3, 0, 2, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 0, 2, 1, 2, 0, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 3, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 3, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 3, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48152>, <20, 1048576>, <24, 8440544>, <28, 36700160>, 
            <32, 150656892>, <36, 286261248>, <40, 566883104>, <44, 749731840>, <48, 757588872>, <52, 749731840>, <56, 
            472093888>, <60, 286261248>, <64, 157708038>, <68, 36700160>, <72, 30315072>, <76, 1048576>, <80, 3501416>, 
            <88, 236128>, <96, 11260>, <104, 160>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 1, 2, 2, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 0, 0, 3, 0, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 1, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 1, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 3, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 1, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48216>, <20, 1048576>, <24, 8431520>, <28, 36700160>, 
            <32, 150710588>, <36, 286261248>, <40, 566754400>, <44, 749731840>, <48, 757730824>, <52, 749731840>, <56, 
            472058944>, <60, 286261248>, <64, 157622918>, <68, 36700160>, <72, 30414016>, <76, 1048576>, <80, 3456680>, 
            <88, 244256>, <96, 10940>, <104, 224>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 3, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 3, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 1, 0, 2, 0, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 2, 1, 0, 0, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 2, 1, 0, 0, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 1, 2, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 1, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47736>, <20, 1048576>, <24, 8449536>, <28, 36700160>, 
            <32, 150607004>, <36, 286261248>, <40, 567016576>, <44, 749731840>, <48, 757383496>, <52, 749731840>, <56, 
            472288768>, <60, 286261248>, <64, 157589318>, <68, 36700160>, <72, 30365440>, <76, 1048576>, <80, 3483464>, 
            <88, 241664>, <96, 10396>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 3, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 1, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 3, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 3, 2, 0, 2, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 2, 1, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 3, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 2, 3, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 3, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 1, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48680>, <20, 1048576>, <24, 8438448>, <28, 36700160>, 
            <32, 150658156>, <36, 286261248>, <40, 566889168>, <44, 749731840>, <48, 757576232>, <52, 749731840>, <56, 
            472102624>, <60, 286261248>, <64, 157706470>, <68, 36700160>, <72, 30316448>, <76, 1048576>, <80, 3497912>, 
            <88, 238448>, <96, 10796>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 3, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 1, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 1, 0, 2, 2, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 2, 3, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 3, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 3, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 0, 1, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 3, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48024>, <20, 1048576>, <24, 8441952>, <28, 36700160>, 
            <32, 150649980>, <36, 286261248>, <40, 566903072>, <44, 749731840>, <48, 757551240>, <52, 749731840>, <56, 
            472142272>, <60, 286261248>, <64, 157665030>, <68, 36700160>, <72, 30341184>, <76, 1048576>, <80, 3491048>, 
            <88, 238560>, <96, 11004>, <104, 160>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 3, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 1, 2, 0, 2, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 3, 2, 0, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 0, 1, 0, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 1, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2, 3, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 1, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47720>, <20, 1048576>, <24, 8446512>, <28, 36700160>, 
            <32, 150628780>, <36, 286261248>, <40, 566949072>, <44, 749731840>, <48, 757503656>, <52, 749731840>, <56, 
            472151008>, <60, 286261248>, <64, 157698406>, <68, 36700160>, <72, 30302624>, <76, 1048576>, <80, 3510008>, 
            <88, 234224>, <96, 11372>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 3, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 3, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 1, 2, 0, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 3, 0, 0, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 2, 3, 2, 2, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 1, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 1, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 1, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47912>, <20, 1048576>, <24, 8445104>, <28, 36700160>, 
            <32, 150632812>, <36, 286261248>, <40, 566944464>, <44, 749731840>, <48, 757500968>, <52, 749731840>, <56, 
            472167136>, <60, 286261248>, <64, 157674214>, <68, 36700160>, <72, 30322592>, <76, 1048576>, <80, 3500216>, 
            <88, 236912>, <96, 11052>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 1, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 3, 2, 0, 0, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 0, 1, 0, 2, 0, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 2, 3, 0, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 3, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 3, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 3, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 0, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48312>, <20, 1048576>, <24, 8434368>, <28, 36700160>, 
            <32, 150692956>, <36, 286261248>, <40, 566789568>, <44, 749731840>, <48, 757718984>, <52, 749731840>, <56, 
            471995776>, <60, 286261248>, <64, 157740742>, <68, 36700160>, <72, 30316928>, <76, 1048576>, <80, 3498632>, 
            <88, 235456>, <96, 11612>, <104, 192>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 1, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 3, 2, 2, 0, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 3, 0, 2, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 3, 0, 2, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 1, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 3, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 3, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0, 1, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48488>, <20, 1048576>, <24, 8439728>, <28, 36700160>, 
            <32, 150655276>, <36, 286261248>, <40, 566889168>, <44, 749731840>, <48, 757589672>, <52, 749731840>, <56, 
            472070368>, <60, 286261248>, <64, 157746790>, <68, 36700160>, <72, 30285728>, <76, 1048576>, <80, 3512312>, 
            <88, 234608>, <96, 11244>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 1, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 3, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 3, 2, 0, 0, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 3, 0, 0, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 2, 2, 3, 2, 2, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 3, 2, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 3, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 3, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 3, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47528>, <20, 1048576>, <24, 8458224>, <28, 36700160>, 
            <32, 150556652>, <36, 286261248>, <40, 567143824>, <44, 749731840>, <48, 757216552>, <52, 749731840>, <56, 
            472395616>, <60, 286261248>, <64, 157579238>, <68, 36700160>, <72, 30337312>, <76, 1048576>, <80, 3498296>, 
            <88, 240048>, <96, 10156>, <104, 80>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 3, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 1, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 3, 2, 2, 0, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 3, 0, 2, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 2, 1, 2, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 3, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 1, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 3, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 1, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47816>, <20, 1048576>, <24, 8451024>, <28, 36700160>, 
            <32, 150596172>, <36, 286261248>, <40, 567044144>, <44, 749731840>, <48, 757352040>, <52, 749731840>, <56, 
            472297504>, <60, 286261248>, <64, 157606566>, <68, 36700160>, <72, 30345312>, <76, 1048576>, <80, 3492056>, 
            <88, 240400>, <96, 10380>, <104, 112>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 1, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 3, 2, 0, 2, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 3, 2, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 2, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 1, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 3, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 1, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47768>, <20, 1048576>, <24, 8453536>, <28, 36700160>, 
            <32, 150581884>, <36, 286261248>, <40, 567077856>, <44, 749731840>, <48, 757315208>, <52, 749731840>, <56, 
            472306240>, <60, 286261248>, <64, 157629190>, <68, 36700160>, <72, 30319040>, <76, 1048576>, <80, 3504104>, 
            <88, 238112>, <96, 10492>, <104, 96>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 3, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 3, 0, 0, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 1, 0, 0, 2, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 2, 2, 3, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 3, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 1, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 3, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 3, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48136>, <20, 1048576>, <24, 8420112>, <28, 36700160>, 
            <32, 150786060>, <36, 286261248>, <40, 566550512>, <44, 749731840>, <48, 758019816>, <52, 749731840>, <56, 
            471837856>, <60, 286261248>, <64, 157700646>, <68, 36700160>, <72, 30411744>, <76, 1048576>, <80, 3455768>, 
            <88, 240464>, <96, 12108>, <104, 304>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 2, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 3, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 3, 2, 2, 0, 0, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 3, 2, 0, 2, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 0, 0, 1, 2, 2, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 1, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 3, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48280>, <20, 1048576>, <24, 8439648>, <28, 36700160>, 
            <32, 150659196>, <36, 286261248>, <40, 566881568>, <44, 749731840>, <48, 757583496>, <52, 749731840>, <56, 
            472110016>, <60, 286261248>, <64, 157686534>, <68, 36700160>, <72, 30331968>, <76, 1048576>, <80, 3493352>, 
            <88, 238304>, <96, 11004>, <104, 160>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 3, 2, 0, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2, 2, 3, 2, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 3, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 3, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 3, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 1, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48088>, <20, 1048576>, <24, 8441568>, <28, 36700160>, 
            <32, 150650556>, <36, 286261248>, <40, 566904608>, <44, 749731840>, <48, 757543176>, <52, 749731840>, <56, 
            472158400>, <60, 286261248>, <64, 157646214>, <68, 36700160>, <72, 30355008>, <76, 1048576>, <80, 3484712>, 
            <88, 240224>, <96, 10812>, <104, 160>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 3, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 3, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 3, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 2, 2, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 2, 1, 0, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 2, 3, 2, 0, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 1, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 1, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 3, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 3, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47704>, <20, 1048576>, <24, 8454560>, <28, 36700160>, 
            <32, 150575548>, <36, 286261248>, <40, 567099360>, <44, 749731840>, <48, 757269512>, <52, 749731840>, <56, 
            472370752>, <60, 286261248>, <64, 157567366>, <68, 36700160>, <72, 30358976>, <76, 1048576>, <80, 3487400>, 
            <88, 242208>, <96, 10044>, <104, 96>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 2, 2, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 2, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 3, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 1, 2, 2, 2, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 0, 3, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 3, 0, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 1, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 1, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 1, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48296>, <20, 1048576>, <24, 8422960>, <28, 36700160>, 
            <32, 150765548>, <36, 286261248>, <40, 566601040>, <44, 749731840>, <48, 757967656>, <52, 749731840>, <56, 
            471839200>, <60, 286261248>, <64, 157751270>, <68, 36700160>, <72, 30360736>, <76, 1048576>, <80, 3477560>, 
            <88, 236784>, <96, 12204>, <104, 272>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 3, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 3, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 3, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 3, 2, 2, 0, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 2, 1, 2, 0, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 1, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 1, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 1, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 3, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48040>, <20, 1048576>, <24, 8435184>, <28, 36700160>, 
            <32, 150691692>, <36, 286261248>, <40, 566798864>, <44, 749731840>, <48, 757677864>, <52, 749731840>, <56, 
            472083808>, <60, 286261248>, <64, 157634790>, <68, 36700160>, <72, 30392352>, <76, 1048576>, <80, 3467576>, 
            <88, 242096>, <96, 11052>, <104, 208>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 1, 0, 2, 2, 2, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 3, 2, 2, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 1, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 1, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 0, 3, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47512>, <20, 1048576>, <24, 8455584>, <28, 36700160>, 
            <32, 150574972>, <36, 286261248>, <40, 567090144>, <44, 749731840>, <48, 757304456>, <52, 749731840>, <56, 
            472306240>, <60, 286261248>, <64, 157639942>, <68, 36700160>, <72, 30306752>, <76, 1048576>, <80, 3511016>, 
            <88, 236064>, <96, 10748>, <104, 96>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 1, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 3, 2, 0, 2, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 2, 2, 1, 0, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 1, 0, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 3, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 1, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 3, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48344>, <20, 1048576>, <24, 8448032>, <28, 36700160>, 
            <32, 150605500>, <36, 286261248>, <40, 567017952>, <44, 749731840>, <48, 757414664>, <52, 749731840>, <56, 
            472193344>, <60, 286261248>, <64, 157717894>, <68, 36700160>, <72, 30271424>, <76, 1048576>, <80, 3520808>, 
            <88, 234656>, <96, 10812>, <104, 96>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 3, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 1, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 1, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 1, 2, 2, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 0, 3, 2, 0, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 1, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0, 3, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 3, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47960>, <20, 1048576>, <24, 8442464>, <28, 36700160>, 
            <32, 150648252>, <36, 286261248>, <40, 566906144>, <44, 749731840>, <48, 757548552>, <52, 749731840>, <56, 
            472142272>, <60, 286261248>, <64, 157667718>, <68, 36700160>, <72, 30338112>, <76, 1048576>, <80, 3492776>, 
            <88, 238048>, <96, 11068>, <104, 160>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 3, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 3, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 1, 2, 2, 2, 0, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 1, 2, 2, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 3, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 1, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 3, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48168>, <20, 1048576>, <24, 8452336>, <28, 36700160>, 
            <32, 150580844>, <36, 286261248>, <40, 567085456>, <44, 749731840>, <48, 757307944>, <52, 749731840>, <56, 
            472298848>, <60, 286261248>, <64, 157649126>, <68, 36700160>, <72, 30303520>, <76, 1048576>, <80, 3508664>, 
            <88, 238256>, <96, 10284>, <104, 80>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 3, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 1, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 3, 0, 2, 2, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2, 3, 0, 0, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 2, 3, 2, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 1, 2, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 1, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 3, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 3, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47848>, <20, 1048576>, <24, 8454768>, <28, 36700160>, 
            <32, 150573356>, <36, 286261248>, <40, 567096208>, <44, 749731840>, <48, 757305256>, <52, 749731840>, <56, 
            472282720>, <60, 286261248>, <64, 157678694>, <68, 36700160>, <72, 30277408>, <76, 1048576>, <80, 3521912>, 
            <88, 234544>, <96, 10732>, <104, 80>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 3, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 1, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 1, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 3, 2, 2, 2, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 0, 1, 2, 2, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 1, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 1, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 1, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 3, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48056>, <20, 1048576>, <24, 8436800>, <28, 36700160>, 
            <32, 150682588>, <36, 286261248>, <40, 566815680>, <44, 749731840>, <48, 757675976>, <52, 749731840>, <56, 
            472044160>, <60, 286261248>, <64, 157703110>, <68, 36700160>, <72, 30336896>, <76, 1048576>, <80, 3491720>, 
            <88, 236864>, <96, 11484>, <104, 192>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 1, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 3, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 3, 2, 2, 0, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 0, 3, 2, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 3, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, 3, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 3, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 1, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47848>, <20, 1048576>, <24, 8445744>, <28, 36700160>, 
            <32, 150629932>, <36, 286261248>, <40, 566952144>, <44, 749731840>, <48, 757487528>, <52, 749731840>, <56, 
            472183264>, <60, 286261248>, <64, 157660774>, <68, 36700160>, <72, 30330272>, <76, 1048576>, <80, 3497336>, 
            <88, 237552>, <96, 10988>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 3, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 3, 2, 0, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 2, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 3, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, 1, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 3, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 3, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48568>, <20, 1048576>, <24, 8432576>, <28, 36700160>, 
            <32, 150697564>, <36, 286261248>, <40, 566786496>, <44, 749731840>, <48, 757708232>, <52, 749731840>, <56, 
            472028032>, <60, 286261248>, <64, 157697734>, <68, 36700160>, <72, 30350720>, <76, 1048576>, <80, 3482504>, 
            <88, 239808>, <96, 11100>, <104, 192>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 3, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 1, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 1, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 3, 0, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 2, 1, 0, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 1, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 3, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 1, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 1, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48088>, <20, 1048576>, <24, 8432032>, <28, 36700160>, 
            <32, 150711740>, <36, 286261248>, <40, 566742112>, <44, 749731840>, <48, 757768456>, <52, 749731840>, <56, 
            471994432>, <60, 286261248>, <64, 157692806>, <68, 36700160>, <72, 30364864>, <76, 1048576>, <80, 3478568>, 
            <88, 238624>, <96, 11580>, <104, 224>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 3, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 3, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 3, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 3, 2, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 1, 0, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 3, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 1, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 1, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48152>, <20, 1048576>, <24, 8440800>, <28, 36700160>, 
            <32, 150654588>, <36, 286261248>, <40, 566892320>, <44, 749731840>, <48, 757567368>, <52, 749731840>, <56, 
            472126144>, <60, 286261248>, <64, 157675782>, <68, 36700160>, <72, 30336576>, <76, 1048576>, <80, 3492200>, 
            <88, 238432>, <96, 11004>, <104, 160>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 3, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 3, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 3, 2, 2, 0, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 3, 0, 0, 0, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 1, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 1, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 3, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48008>, <20, 1048576>, <24, 8439824>, <28, 36700160>, 
            <32, 150663692>, <36, 286261248>, <40, 566867824>, <44, 749731840>, <48, 757596136>, <52, 749731840>, <56, 
            472117408>, <60, 286261248>, <64, 157661222>, <68, 36700160>, <72, 30353632>, <76, 1048576>, <80, 3485336>, 
            <88, 239184>, <96, 11084>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 3, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 1, 2, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 0, 3, 0, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 1, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 1, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 3, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 1, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48168>, <20, 1048576>, <24, 8443056>, <28, 36700160>, 
            <32, 150639724>, <36, 286261248>, <40, 566932176>, <44, 749731840>, <48, 757511720>, <52, 749731840>, <56, 
            472167136>, <60, 286261248>, <64, 157663462>, <68, 36700160>, <72, 30334880>, <76, 1048576>, <80, 3493304>, 
            <88, 238960>, <96, 10796>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 3, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 1, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 3, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 3, 2, 0, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 0, 1, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 1, 0, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 3, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 3, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 3, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47560>, <20, 1048576>, <24, 8462608>, <28, 36700160>, 
            <32, 150528076>, <36, 286261248>, <40, 567218928>, <44, 749731840>, <48, 757116008>, <52, 749731840>, <56, 
            472461472>, <60, 286261248>, <64, 157570726>, <68, 36700160>, <72, 30323168>, <76, 1048576>, <80, 3505112>, 
            <88, 239952>, <96, 9868>, <104, 48>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 3, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 3, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 1, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 1, 2, 0, 0, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 3, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, 1, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, 0, 3, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 1, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48728>, <20, 1048576>, <24, 8416864>, <28, 36700160>, 
            <32, 150794812>, <36, 286261248>, <40, 566530464>, <44, 749731840>, <48, 758063624>, <52, 749731840>, <56, 
            471765952>, <60, 286261248>, <64, 157777030>, <68, 36700160>, <72, 30362432>, <76, 1048576>, <80, 3473576>, 
            <88, 237536>, <96, 12220>, <104, 288>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 1, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 3, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 3, 2, 0, 2, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 0, 3, 2, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 1, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 1, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 1, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 1, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48184>, <20, 1048576>, <24, 8435904>, <28, 36700160>, 
            <32, 150684892>, <36, 286261248>, <40, 566814144>, <44, 749731840>, <48, 757670600>, <52, 749731840>, <56, 
            472060288>, <60, 286261248>, <64, 157681606>, <68, 36700160>, <72, 30353792>, <76, 1048576>, <80, 3483656>, 
            <88, 239040>, <96, 11228>, <104, 192>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 3, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 3, 0, 0, 2, 0, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 2, 3, 2, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 3, 0, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 1, 2, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 3, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 1, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 3, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48456>, <20, 1048576>, <24, 8426320>, <28, 36700160>, 
            <32, 150740428>, <36, 286261248>, <40, 566670000>, <44, 749731840>, <48, 757872488>, <52, 749731840>, <56, 
            471905056>, <60, 286261248>, <64, 157737382>, <68, 36700160>, <72, 30352736>, <76, 1048576>, <80, 3480920>, 
            <88, 237712>, <96, 11788>, <104, 240>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 3, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 1, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 1, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 3, 0, 0, 2, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 2, 2, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 1, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 1, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 3, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48264>, <20, 1048576>, <24, 8428368>, <28, 36700160>, 
            <32, 150730636>, <36, 286261248>, <40, 566697648>, <44, 749731840>, <48, 757821416>, <52, 749731840>, <56, 
            471969568>, <60, 286261248>, <64, 157680934>, <68, 36700160>, <72, 30386528>, <76, 1048576>, <80, 3467672>, 
            <88, 240784>, <96, 11468>, <104, 240>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 1, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 2, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 2, 1, 0, 2, 0, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 3, 2, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 1, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 3, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 3, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 3, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48024>, <20, 1048576>, <24, 8460512>, <28, 36700160>, 
            <32, 150532220>, <36, 286261248>, <40, 567209632>, <44, 749731840>, <48, 757143688>, <52, 749731840>, <56, 
            472405696>, <60, 286261248>, <64, 157636358>, <68, 36700160>, <72, 30278464>, <76, 1048576>, <80, 3521768>, 
            <88, 237152>, <96, 9980>, <104, 32>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 1, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 3, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 1, 2, 2, 0, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 2, 1, 2, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 1, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 1, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 1, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0, 1, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47992>, <20, 1048576>, <24, 8437312>, <28, 36700160>, 
            <32, 150680860>, <36, 286261248>, <40, 566818752>, <44, 749731840>, <48, 757673288>, <52, 749731840>, <56, 
            472044160>, <60, 286261248>, <64, 157705798>, <68, 36700160>, <72, 30333824>, <76, 1048576>, <80, 3493448>, 
            <88, 236352>, <96, 11548>, <104, 192>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 3, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 3, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 3, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 1, 2, 0, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 3, 2, 0, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 1, 0, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 3, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 2, 3, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 3, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 1, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48696>, <20, 1048576>, <24, 8421632>, <28, 36700160>, 
            <32, 150765660>, <36, 286261248>, <40, 566604032>, <44, 749731840>, <48, 757971144>, <52, 749731840>, <56, 
            471815680>, <60, 286261248>, <64, 157787334>, <68, 36700160>, <72, 30334464>, <76, 1048576>, <80, 3486728>, 
            <88, 235776>, <96, 12124>, <104, 256>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 2, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 3, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 1, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 1, 2, 2, 0, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 1, 2, 2, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 3, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 1, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 1, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47784>, <20, 1048576>, <24, 8446384>, <28, 36700160>, 
            <32, 150627052>, <36, 286261248>, <40, 566959824>, <44, 749731840>, <48, 757474088>, <52, 749731840>, <56, 
            472199392>, <60, 286261248>, <64, 157647334>, <68, 36700160>, <72, 30337952>, <76, 1048576>, <80, 3494456>, 
            <88, 238192>, <96, 10924>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 3, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 3, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 1, 0, 2, 0, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 2, 3, 0, 0, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 2, 1, 2, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 1, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 1, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 3, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, 0, 1, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47944>, <20, 1048576>, <24, 8440464>, <28, 36700160>, 
            <32, 150660812>, <36, 286261248>, <40, 566875504>, <44, 749731840>, <48, 757582696>, <52, 749731840>, <56, 
            472133536>, <60, 286261248>, <64, 157647782>, <68, 36700160>, <72, 30361312>, <76, 1048576>, <80, 3482456>, 
            <88, 239824>, <96, 11020>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 3, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 3, 0, 2, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 1, 2, 0, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0, 3, 2, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 3, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 1, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 1, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48168>, <20, 1048576>, <24, 8442544>, <28, 36700160>, 
            <32, 150644332>, <36, 286261248>, <40, 566913744>, <44, 749731840>, <48, 757554728>, <52, 749731840>, <56, 
            472102624>, <60, 286261248>, <64, 157727974>, <68, 36700160>, <72, 30291872>, <76, 1048576>, <80, 3511736>, 
            <88, 234352>, <96, 11308>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 3, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 3, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 1, 0, 0, 2, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 3, 0, 2, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 2, 3, 2, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 1, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 3, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 3, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47880>, <20, 1048576>, <24, 8440592>, <28, 36700160>, 
            <32, 150662540>, <36, 286261248>, <40, 566864752>, <44, 749731840>, <48, 757612264>, <52, 749731840>, <56, 
            472085152>, <60, 286261248>, <64, 157698854>, <68, 36700160>, <72, 30325984>, <76, 1048576>, <80, 3498008>, 
            <88, 235856>, <96, 11468>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 3, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 3, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 1, 2, 2, 0, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0, 1, 2, 2, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 0, 3, 0, 0, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2, 1, 2, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 3, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 1, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 3, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48424>, <20, 1048576>, <24, 8431728>, <28, 36700160>, 
            <32, 150705516>, <36, 286261248>, <40, 566766608>, <44, 749731840>, <48, 757726248>, <52, 749731840>, <56, 
            472035424>, <60, 286261248>, <64, 157667046>, <68, 36700160>, <72, 30378528>, <76, 1048576>, <80, 3471032>, 
            <88, 241712>, <96, 11052>, <104, 208>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 3, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 1, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 1, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 3, 2, 0, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 1, 2, 0, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 0, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 1, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 1, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 1, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48440>, <20, 1048576>, <24, 8423936>, <28, 36700160>, 
            <32, 150756444>, <36, 286261248>, <40, 566625536>, <44, 749731840>, <48, 757938888>, <52, 749731840>, <56, 
            471847936>, <60, 286261248>, <64, 157765830>, <68, 36700160>, <72, 30343680>, <76, 1048576>, <80, 3484424>, 
            <88, 236032>, <96, 12124>, <104, 256>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 3, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 3, 2, 0, 0, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 3, 0, 2, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 2, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 3, 2, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 1, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 3, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48520>, <20, 1048576>, <24, 8425808>, <28, 36700160>, 
            <32, 150742156>, <36, 286261248>, <40, 566666928>, <44, 749731840>, <48, 757875176>, <52, 749731840>, <56, 
            471905056>, <60, 286261248>, <64, 157734694>, <68, 36700160>, <72, 30355808>, <76, 1048576>, <80, 3479192>, 
            <88, 238224>, <96, 11724>, <104, 240>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 1, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 1, 2, 0, 0, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 1, 0, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 2, 3, 2, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 1, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 1, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 1, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 1, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47976>, <20, 1048576>, <24, 8444464>, <28, 36700160>, 
            <32, 150635692>, <36, 286261248>, <40, 566936784>, <44, 749731840>, <48, 757514408>, <52, 749731840>, <56, 
            472151008>, <60, 286261248>, <64, 157687654>, <68, 36700160>, <72, 30314912>, <76, 1048576>, <80, 3503096>, 
            <88, 236272>, <96, 11116>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 1, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 1, 2, 2, 0, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 3, 2, 2, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 3, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 3, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48072>, <20, 1048576>, <24, 8448336>, <28, 36700160>, 
            <32, 150608844>, <36, 286261248>, <40, 567008816>, <44, 749731840>, <48, 757416552>, <52, 749731840>, <56, 
            472216864>, <60, 286261248>, <64, 157676454>, <68, 36700160>, <72, 30303840>, <76, 1048576>, <80, 3508184>, 
            <88, 236688>, <96, 10764>, <104, 112>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 1, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 1, 2, 2, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 3, 2, 0, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 1, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 1, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 1, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47912>, <20, 1048576>, <24, 8454128>, <28, 36700160>, 
            <32, 150576236>, <36, 286261248>, <40, 567088528>, <44, 749731840>, <48, 757318696>, <52, 749731840>, <56, 
            472266592>, <60, 286261248>, <64, 157692134>, <68, 36700160>, <72, 30269728>, <76, 1048576>, <80, 3524792>, 
            <88, 233904>, <96, 10796>, <104, 80>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 3, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 3, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 2, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 0, 2, 1, 2, 2, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 3, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 3, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 3, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47736>, <20, 1048576>, <24, 8449408>, <28, 36700160>, 
            <32, 150608156>, <36, 286261248>, <40, 567011968>, <44, 749731840>, <48, 757394248>, <52, 749731840>, <56, 
            472272640>, <60, 286261248>, <64, 157605446>, <68, 36700160>, <72, 30354688>, <76, 1048576>, <80, 3488072>, 
            <88, 240512>, <96, 10524>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 3, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 3, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 3, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 1, 2, 2, 0, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 3, 0, 0, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 3, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 1, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, 1, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 3, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48648>, <20, 1048576>, <24, 8415248>, <28, 36700160>, 
            <32, 150806796>, <36, 286261248>, <40, 566498288>, <44, 749731840>, <48, 758105832>, <52, 749731840>, <56, 
            471741088>, <60, 286261248>, <64, 157775910>, <68, 36700160>, <72, 30371808>, <76, 1048576>, <80, 3469592>, 
            <88, 237648>, <96, 12364>, <104, 304>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 2, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 3, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 1, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 3, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 1, 2, 2, 2, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0, 3, 2, 0, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0, 1, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 3, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 3, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 1, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 1, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48360>, <20, 1048576>, <24, 8441648>, <28, 36700160>, 
            <32, 150643756>, <36, 286261248>, <40, 566927568>, <44, 749731840>, <48, 757509032>, <52, 749731840>, <56, 
            472183264>, <60, 286261248>, <64, 157639270>, <68, 36700160>, <72, 30354848>, <76, 1048576>, <80, 3483512>, 
            <88, 241648>, <96, 10476>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 3, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 3, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 1, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 3, 0, 0, 2, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 1, 2, 2, 0, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 0, 1, 2, 2, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 1, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 3, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 1, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 1, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47976>, <20, 1048576>, <24, 8444592>, <28, 36700160>, 
            <32, 150634540>, <36, 286261248>, <40, 566941392>, <44, 749731840>, <48, 757503656>, <52, 749731840>, <56, 
            472167136>, <60, 286261248>, <64, 157671526>, <68, 36700160>, <72, 30325664>, <76, 1048576>, <80, 3498488>, 
            <88, 237424>, <96, 10988>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 3, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 1, 0, 2, 0, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 1, 0, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 0, 2, 3, 2, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 1, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 3, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 1, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 1, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48184>, <20, 1048576>, <24, 8435776>, <28, 36700160>, 
            <32, 150686044>, <36, 286261248>, <40, 566809536>, <44, 749731840>, <48, 757681352>, <52, 749731840>, <56, 
            472044160>, <60, 286261248>, <64, 157697734>, <68, 36700160>, <72, 30343040>, <76, 1048576>, <80, 3488264>, 
            <88, 237888>, <96, 11356>, <104, 192>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 3, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 1, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 3, 0, 0, 0, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 1, 0, 2, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 2, 1, 0, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 3, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 1, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 3, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 3, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48088>, <20, 1048576>, <24, 8441312>, <28, 36700160>, 
            <32, 150652860>, <36, 286261248>, <40, 566895392>, <44, 749731840>, <48, 757564680>, <52, 749731840>, <56, 
            472126144>, <60, 286261248>, <64, 157678470>, <68, 36700160>, <72, 30333504>, <76, 1048576>, <80, 3493928>, 
            <88, 237920>, <96, 11068>, <104, 160>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 3, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 3, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 1, 2, 2, 0, 0, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 1, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 3, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 1, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 1, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48360>, <20, 1048576>, <24, 8431856>, <28, 36700160>, 
            <32, 150707244>, <36, 286261248>, <40, 566755856>, <44, 749731840>, <48, 757755816>, <52, 749731840>, <56, 
            471987040>, <60, 286261248>, <64, 157718118>, <68, 36700160>, <72, 30343200>, <76, 1048576>, <80, 3486584>, 
            <88, 237744>, <96, 11500>, <104, 208>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 3, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 3, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 3, 2, 0, 0, 0, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 2, 1, 0, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 1, 2, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 1, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 3, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 1, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47832>, <20, 1048576>, <24, 8452896>, <28, 36700160>, 
            <32, 150584764>, <36, 286261248>, <40, 567070176>, <44, 749731840>, <48, 757328648>, <52, 749731840>, <56, 
            472290112>, <60, 286261248>, <64, 157642630>, <68, 36700160>, <72, 30311360>, <76, 1048576>, <80, 3506984>, 
            <88, 237472>, <96, 10556>, <104, 96>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 3, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 3, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 1, 0, 0, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 1, 2, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 3, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 3, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 1, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 1, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48056>, <20, 1048576>, <24, 8446336>, <28, 36700160>, 
            <32, 150621404>, <36, 286261248>, <40, 566978176>, <44, 749731840>, <48, 757450696>, <52, 749731840>, <56, 
            472208128>, <60, 286261248>, <64, 157656518>, <68, 36700160>, <72, 30327040>, <76, 1048576>, <80, 3497864>, 
            <88, 238464>, <96, 10716>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 3, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 3, 0, 2, 2, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 1, 2, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 0, 0, 3, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 2, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 3, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 3, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 3, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47864>, <20, 1048576>, <24, 8438848>, <28, 36700160>, 
            <32, 150672796>, <36, 286261248>, <40, 566843328>, <44, 749731840>, <48, 757624904>, <52, 749731840>, <56, 
            472108672>, <60, 286261248>, <64, 157646662>, <68, 36700160>, <72, 30370688>, <76, 1048576>, <80, 3478472>, 
            <88, 239936>, <96, 11164>, <104, 192>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 3, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 3, 0, 2, 0, 0, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 3, 0, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 0, 2, 3, 0, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 1, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 3, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 1, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47848>, <20, 1048576>, <24, 8446256>, <28, 36700160>, 
            <32, 150625324>, <36, 286261248>, <40, 566970576>, <44, 749731840>, <48, 757444520>, <52, 749731840>, <56, 
            472247776>, <60, 286261248>, <64, 157596262>, <68, 36700160>, <72, 30373280>, <76, 1048576>, <80, 3478904>, 
            <88, 242160>, <96, 10476>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 3, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0, 3, 0, 0, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 2, 1, 0, 2, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 3, 2, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48024>, <20, 1048576>, <24, 8442080>, <28, 36700160>, 
            <32, 150648828>, <36, 286261248>, <40, 566907680>, <44, 749731840>, <48, 757540488>, <52, 749731840>, <56, 
            472158400>, <60, 286261248>, <64, 157648902>, <68, 36700160>, <72, 30351936>, <76, 1048576>, <80, 3486440>, 
            <88, 239712>, <96, 10876>, <104, 160>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 1, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 3, 2, 2, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 2, 1, 0, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 3, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 3, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 3, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 1, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48120>, <20, 1048576>, <24, 8436288>, <28, 36700160>, 
            <32, 150684316>, <36, 286261248>, <40, 566812608>, <44, 749731840>, <48, 757678664>, <52, 749731840>, <56, 
            472044160>, <60, 286261248>, <64, 157700422>, <68, 36700160>, <72, 30339968>, <76, 1048576>, <80, 3489992>, 
            <88, 237376>, <96, 11420>, <104, 192>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 1, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 3, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 3, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 3, 0, 0, 2, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 3, 0, 2, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 2, 2, 1, 2, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 3, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 3, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, 3, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 3, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47816>, <20, 1048576>, <24, 8441744>, <28, 36700160>, 
            <32, 150655052>, <36, 286261248>, <40, 566890864>, <44, 749731840>, <48, 757555816>, <52, 749731840>, <56, 
            472165792>, <60, 286261248>, <64, 157620902>, <68, 36700160>, <72, 30376672>, <76, 1048576>, <80, 3476696>, 
            <88, 241104>, <96, 10892>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 2, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 3, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 3, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 3, 2, 0, 2, 2, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 3, 2, 0, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 1, 0, 0, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 3, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 1, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 1, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47400>, <20, 1048576>, <24, 8459376>, <28, 36700160>, 
            <32, 150552044>, <36, 286261248>, <40, 567154576>, <44, 749731840>, <48, 757200424>, <52, 749731840>, <56, 
            472411744>, <60, 286261248>, <64, 157568486>, <68, 36700160>, <72, 30341920>, <76, 1048576>, <80, 3497144>, 
            <88, 240176>, <96, 10156>, <104, 80>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 3, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 3, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 3, 2, 2, 0, 0, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 3, 0, 2, 0, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 2, 3, 2, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 3, 0, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 3, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, 1, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 3, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 0, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47448>, <20, 1048576>, <24, 8465632>, <28, 36700160>, 
            <32, 150512060>, <36, 286261248>, <40, 567255712>, <44, 749731840>, <48, 757076488>, <52, 749731840>, <56, 
            472470208>, <60, 286261248>, <64, 157596038>, <68, 36700160>, <72, 30293824>, <76, 1048576>, <80, 3518888>, 
            <88, 237152>, <96, 10044>, <104, 32>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 1, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 1, 2, 0, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 2, 0, 3, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 1, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 1, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 3, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 3, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47816>, <20, 1048576>, <24, 8441232>, <28, 36700160>, 
            <32, 150659660>, <36, 286261248>, <40, 566872432>, <44, 749731840>, <48, 757598824>, <52, 749731840>, <56, 
            472101280>, <60, 286261248>, <64, 157685414>, <68, 36700160>, <72, 30333664>, <76, 1048576>, <80, 3495128>, 
            <88, 236496>, <96, 11404>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 1, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 1, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 3, 0, 0, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 1, 0, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 2, 1, 2, 2, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 1, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 1, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0, 3, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48056>, <20, 1048576>, <24, 8436928>, <28, 36700160>, 
            <32, 150681436>, <36, 286261248>, <40, 566820288>, <44, 749731840>, <48, 757665224>, <52, 749731840>, <56, 
            472060288>, <60, 286261248>, <64, 157686982>, <68, 36700160>, <72, 30347648>, <76, 1048576>, <80, 3487112>, 
            <88, 238016>, <96, 11356>, <104, 192>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 3, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 0, 3, 2, 2, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 0, 3, 0, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 0, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 3, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 3, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 1, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47608>, <20, 1048576>, <24, 8450304>, <28, 36700160>, 
            <32, 150605852>, <36, 286261248>, <40, 567013504>, <44, 749731840>, <48, 757399624>, <52, 749731840>, <56, 
            472256512>, <60, 286261248>, <64, 157626950>, <68, 36700160>, <72, 30337792>, <76, 1048576>, <80, 3496136>, 
            <88, 238336>, <96, 10780>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 3, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 3, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 3, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 3, 2, 0, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 1, 2, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 3, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 1, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48376>, <20, 1048576>, <24, 8434112>, <28, 36700160>, 
            <32, 150692380>, <36, 286261248>, <40, 566795712>, <44, 749731840>, <48, 757700168>, <52, 749731840>, <56, 
            472028032>, <60, 286261248>, <64, 157705798>, <68, 36700160>, <72, 30341504>, <76, 1048576>, <80, 3487688>, 
            <88, 238272>, <96, 11292>, <104, 192>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 3, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 1, 2, 0, 2, 2, 0, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 1, 2, 0, 0, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 0, 3, 0, 0, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 2, 1, 0, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 3, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 3, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 3, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 3, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47848>, <20, 1048576>, <24, 8427056>, <28, 36700160>, 
            <32, 150748844>, <36, 286261248>, <40, 566640976>, <44, 749731840>, <48, 757905832>, <52, 749731840>, <56, 
            471903712>, <60, 286261248>, <64, 157705574>, <68, 36700160>, <72, 30382240>, <76, 1048576>, <80, 3471224>, 
            <88, 237808>, <96, 12140>, <104, 272>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 3, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 1, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 1, 2, 2, 0, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 3, 0, 2, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 2, 1, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 3, 0, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 3, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 3, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 3, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48008>, <20, 1048576>, <24, 8448848>, <28, 36700160>, 
            <32, 150607116>, <36, 286261248>, <40, 567011888>, <44, 749731840>, <48, 757413864>, <52, 749731840>, <56, 
            472216864>, <60, 286261248>, <64, 157679142>, <68, 36700160>, <72, 30300768>, <76, 1048576>, <80, 3509912>, 
            <88, 236176>, <96, 10828>, <104, 112>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 3, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 3, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 1, 2, 2, 0, 0, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 3, 2, 2, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 0, 3, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 2, 3, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 3, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 1, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48136>, <20, 1048576>, <24, 8447696>, <28, 36700160>, 
            <32, 150611724>, <36, 286261248>, <40, 567001136>, <44, 749731840>, <48, 757429992>, <52, 749731840>, <56, 
            472200736>, <60, 286261248>, <64, 157689894>, <68, 36700160>, <72, 30296160>, <76, 1048576>, <80, 3511064>, 
            <88, 236048>, <96, 10828>, <104, 112>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 3, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 1, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 3, 0, 2, 2, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 3, 2, 2, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 3, 2, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 3, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 1, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48312>, <20, 1048576>, <24, 8443648>, <28, 36700160>, 
            <32, 150634076>, <36, 286261248>, <40, 566942848>, <44, 749731840>, <48, 757515208>, <52, 749731840>, <56, 
            472127488>, <60, 286261248>, <64, 157726406>, <68, 36700160>, <72, 30285568>, <76, 1048576>, <80, 3513992>, 
            <88, 234752>, <96, 11100>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 3, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 1, 2, 0, 2, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 3, 0, 2, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 1, 0, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 1, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 1, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 1, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47752>, <20, 1048576>, <24, 8451280>, <28, 36700160>, 
            <32, 150596748>, <36, 286261248>, <40, 567038000>, <44, 749731840>, <48, 757370856>, <52, 749731840>, <56, 
            472265248>, <60, 286261248>, <64, 157641510>, <68, 36700160>, <72, 30320736>, <76, 1048576>, <80, 3503000>, 
            <88, 237584>, <96, 10700>, <104, 112>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 3, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 3, 0, 0, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 1, 0, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 1, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 1, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 1, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48904>, <20, 1048576>, <24, 8431632>, <28, 36700160>, 
            <32, 150697100>, <36, 286261248>, <40, 566787952>, <44, 749731840>, <48, 757719784>, <52, 749731840>, <56, 
            471988384>, <60, 286261248>, <64, 157752614>, <68, 36700160>, <72, 30310624>, <76, 1048576>, <80, 3498008>, 
            <88, 237136>, <96, 11212>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 1, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 3, 2, 0, 2, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 0, 3, 2, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 2, 0, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 3, 0, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 3, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 3, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 1, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48712>, <20, 1048576>, <24, 8424016>, <28, 36700160>, 
            <32, 150749644>, <36, 286261248>, <40, 566648496>, <44, 749731840>, <48, 757904744>, <52, 749731840>, <56, 
            471872800>, <60, 286261248>, <64, 157758886>, <68, 36700160>, <72, 30343520>, <76, 1048576>, <80, 3483224>, 
            <88, 237456>, <96, 11788>, <104, 240>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 3, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 0, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 3, 2, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 3, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 1, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 3, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48088>, <20, 1048576>, <24, 8440928>, <28, 36700160>, 
            <32, 150656316>, <36, 286261248>, <40, 566881568>, <44, 749731840>, <48, 757596936>, <52, 749731840>, <56, 
            472077760>, <60, 286261248>, <64, 157726854>, <68, 36700160>, <72, 30301248>, <76, 1048576>, <80, 3507752>, 
            <88, 234464>, <96, 11452>, <104, 160>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 3, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 3, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 1, 0, 0, 2, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 2, 3, 0, 0, 0, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 2, 1, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 3, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 3, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 1, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47624>, <20, 1048576>, <24, 8452560>, <28, 36700160>, 
            <32, 150590988>, <36, 286261248>, <40, 567053360>, <44, 749731840>, <48, 757343976>, <52, 749731840>, <56, 
            472297504>, <60, 286261248>, <64, 157614630>, <68, 36700160>, <72, 30336096>, <76, 1048576>, <80, 3497240>, 
            <88, 238864>, <96, 10572>, <104, 112>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 3, 0, 2, 2, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 2, 1, 2, 2, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 0, 3, 0, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 3, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, 1, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 1, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 3, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47864>, <20, 1048576>, <24, 8448640>, <28, 36700160>, 
            <32, 150609308>, <36, 286261248>, <40, 567015040>, <44, 749731840>, <48, 757378120>, <52, 749731840>, <56, 
            472304896>, <60, 286261248>, <64, 157567814>, <68, 36700160>, <72, 30382336>, <76, 1048576>, <80, 3475400>, 
            <88, 243840>, <96, 10140>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 3, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 1, 0, 0, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2, 1, 2, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2, 0, 1, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 1, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 1, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 3, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 3, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47992>, <20, 1048576>, <24, 8447232>, <28, 36700160>, 
            <32, 150616220>, <36, 286261248>, <40, 566995072>, <44, 749731840>, <48, 757415752>, <52, 749731840>, <56, 
            472256512>, <60, 286261248>, <64, 157610822>, <68, 36700160>, <72, 30356224>, <76, 1048576>, <80, 3485768>, 
            <88, 241408>, <96, 10396>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 1, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 3, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 3, 2, 2, 0, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 3, 2, 2, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 1, 2, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 3, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 1, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 1, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48552>, <20, 1048576>, <24, 8430064>, <28, 36700160>, 
            <32, 150714732>, <36, 286261248>, <40, 566737424>, <44, 749731840>, <48, 757785384>, <52, 749731840>, <56, 
            471954784>, <60, 286261248>, <64, 157742310>, <68, 36700160>, <72, 30330912>, <76, 1048576>, <80, 3490616>, 
            <88, 236976>, <96, 11564>, <104, 208>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 3, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 3, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 3, 0, 2, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 3, 2, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 3, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 1, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 3, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 1, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48072>, <20, 1048576>, <24, 8439056>, <28, 36700160>, 
            <32, 150667724>, <36, 286261248>, <40, 566855536>, <44, 749731840>, <48, 757620328>, <52, 749731840>, <56, 
            472085152>, <60, 286261248>, <64, 157690790>, <68, 36700160>, <72, 30335200>, <76, 1048576>, <80, 3492824>, 
            <88, 237392>, <96, 11276>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 3, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 3, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 2, 0, 2, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 0, 1, 2, 2, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 0, 3, 2, 0, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 3, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 3, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 0, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47672>, <20, 1048576>, <24, 8449792>, <28, 36700160>, 
            <32, 150607580>, <36, 286261248>, <40, 567010432>, <44, 749731840>, <48, 757402312>, <52, 749731840>, <56, 
            472256512>, <60, 286261248>, <64, 157624262>, <68, 36700160>, <72, 30340864>, <76, 1048576>, <80, 3494408>, 
            <88, 238848>, <96, 10716>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 3, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 3, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 1, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 3, 0, 2, 0, 0, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 1, 2, 2, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 0, 3, 0, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 3, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48488>, <20, 1048576>, <24, 8421552>, <28, 36700160>, 
            <32, 150769580>, <36, 286261248>, <40, 566596432>, <44, 749731840>, <48, 757964968>, <52, 749731840>, <56, 
            471855328>, <60, 286261248>, <64, 157727078>, <68, 36700160>, <72, 30380704>, <76, 1048576>, <80, 3467768>, 
            <88, 239472>, <96, 11884>, <104, 272>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 3, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 1, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 3, 0, 2, 0, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 0, 0, 3, 2, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 1, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 1, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 3, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 3, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47768>, <20, 1048576>, <24, 8453664>, <28, 36700160>, 
            <32, 150580732>, <36, 286261248>, <40, 567082464>, <44, 749731840>, <48, 757304456>, <52, 749731840>, <56, 
            472322368>, <60, 286261248>, <64, 157613062>, <68, 36700160>, <72, 30329792>, <76, 1048576>, <80, 3499496>, 
            <88, 239264>, <96, 10364>, <104, 96>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 1, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 1, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 1, 0, 2, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 0, 2, 3, 2, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 3, 2, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 1, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 3, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48408>, <20, 1048576>, <24, 8429728>, <28, 36700160>, 
            <32, 150718076>, <36, 286261248>, <40, 566735968>, <44, 749731840>, <48, 757760392>, <52, 749731840>, <56, 
            472026688>, <60, 286261248>, <64, 157647110>, <68, 36700160>, <72, 30401728>, <76, 1048576>, <80, 3460712>, 
            <88, 243488>, <96, 11004>, <104, 224>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 2, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 3, 2, 2, 2, 2, 0, 2, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 1, 0, 2, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 2, 1, 2, 0, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 0, 1, 2, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 3, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 3, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 2, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48264>, <20, 1048576>, <24, 8437520>, <28, 36700160>, 
            <32, 150672908>, <36, 286261248>, <40, 566846320>, <44, 749731840>, <48, 757628392>, <52, 749731840>, <56, 
            472085152>, <60, 286261248>, <64, 157682726>, <68, 36700160>, <72, 30344416>, <76, 1048576>, <80, 3487640>, 
            <88, 238928>, <96, 11084>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 3, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 1, 2, 2, 2, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 1, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 1, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 3, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 1, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48504>, <20, 1048576>, <24, 8433344>, <28, 36700160>, 
            <32, 150693532>, <36, 286261248>, <40, 566798784>, <44, 749731840>, <48, 757684040>, <52, 749731840>, <56, 
            472060288>, <60, 286261248>, <64, 157668166>, <68, 36700160>, <72, 30369152>, <76, 1048576>, <80, 3475016>, 
            <88, 241600>, <96, 10908>, <104, 192>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 3, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 3, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 1, 2, 2, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 0, 1, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 1, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 3, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 1, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 1, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47816>, <20, 1048576>, <24, 8460304>, <28, 36700160>, 
            <32, 150537292>, <36, 286261248>, <40, 567197424>, <44, 749731840>, <48, 757148264>, <52, 749731840>, <56, 
            472429216>, <60, 286261248>, <64, 157592230>, <68, 36700160>, <72, 30313952>, <76, 1048576>, <80, 3507416>, 
            <88, 239696>, <96, 9868>, <104, 48>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 3, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 3, 2, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 3, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 1, 2, 2, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 0, 0, 1, 2, 0, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 3, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 3, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 1, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 1, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48312>, <20, 1048576>, <24, 8443904>, <28, 36700160>, 
            <32, 150631772>, <36, 286261248>, <40, 566952064>, <44, 749731840>, <48, 757493704>, <52, 749731840>, <56, 
            472159744>, <60, 286261248>, <64, 157694150>, <68, 36700160>, <72, 30307072>, <76, 1048576>, <80, 3504776>, 
            <88, 237056>, <96, 10844>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 1, 2, 0, 0, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 0, 3, 0, 0, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 1, 2, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 1, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 3, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 1, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 1, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47800>, <20, 1048576>, <24, 8457792>, <28, 36700160>, 
            <32, 150554460>, <36, 286261248>, <40, 567148352>, <44, 749731840>, <48, 757225416>, <52, 749731840>, <56, 
            472355968>, <60, 286261248>, <64, 157636806>, <68, 36700160>, <72, 30294144>, <76, 1048576>, <80, 3515528>, 
            <88, 236864>, <96, 10332>, <104, 64>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 3, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 1, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 3, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 1, 2, 0, 2, 2, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 0, 1, 2, 2, 0, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 2, 0, 3, 0, 2, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 1, 0, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 3, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 1, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48072>, <20, 1048576>, <24, 8429904>, <28, 36700160>, 
            <32, 150725452>, <36, 286261248>, <40, 566706864>, <44, 749731840>, <48, 757813352>, <52, 749731840>, <56, 
            471969568>, <60, 286261248>, <64, 157688998>, <68, 36700160>, <72, 30377312>, <76, 1048576>, <80, 3472856>, 
            <88, 239248>, <96, 11660>, <104, 240>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 3, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 3, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 3, 2, 2, 0, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 3, 2, 0, 0, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 3, 0, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 1, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 3, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 1, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47768>, <20, 1048576>, <24, 8453408>, <28, 36700160>, 
            <32, 150583036>, <36, 286261248>, <40, 567073248>, <44, 749731840>, <48, 757325960>, <52, 749731840>, <56, 
            472290112>, <60, 286261248>, <64, 157645318>, <68, 36700160>, <72, 30308288>, <76, 1048576>, <80, 3508712>, 
            <88, 236960>, <96, 10620>, <104, 96>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 3, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 1, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 3, 0, 2, 0, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 3, 2, 0, 0, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 3, 2, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 1, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 3, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 3, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 3, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48456>, <20, 1048576>, <24, 8426448>, <28, 36700160>, 
            <32, 150739276>, <36, 286261248>, <40, 566674608>, <44, 749731840>, <48, 757861736>, <52, 749731840>, <56, 
            471921184>, <60, 286261248>, <64, 157721254>, <68, 36700160>, <72, 30363488>, <76, 1048576>, <80, 3476312>, 
            <88, 238864>, <96, 11660>, <104, 240>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 3, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 3, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 1, 2, 2, 2, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 1, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 1, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 1, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 1, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48632>, <20, 1048576>, <24, 8421760>, <28, 36700160>, 
            <32, 150767388>, <36, 286261248>, <40, 566593280>, <44, 749731840>, <48, 758000712>, <52, 749731840>, <56, 
            471767296>, <60, 286261248>, <64, 157838406>, <68, 36700160>, <72, 30299136>, <76, 1048576>, <80, 3502280>, 
            <88, 231808>, <96, 12572>, <104, 256>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 3, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 2, 3, 0, 2, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 2, 2, 3, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 1, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 1, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 3, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 1, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47320>, <20, 1048576>, <24, 8457632>, <28, 36700160>, 
            <32, 150565180>, <36, 286261248>, <40, 567117792>, <44, 749731840>, <48, 757253384>, <52, 749731840>, <56, 
            472370752>, <60, 286261248>, <64, 157583494>, <68, 36700160>, <72, 30340544>, <76, 1048576>, <80, 3497768>, 
            <88, 239136>, <96, 10428>, <104, 96>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 1, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 3, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 1, 2, 2, 0, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 1, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 3, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 1, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 3, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47976>, <20, 1048576>, <24, 8444720>, <28, 36700160>, 
            <32, 150633388>, <36, 286261248>, <40, 566946000>, <44, 749731840>, <48, 757492904>, <52, 749731840>, <56, 
            472183264>, <60, 286261248>, <64, 157655398>, <68, 36700160>, <72, 30336416>, <76, 1048576>, <80, 3493880>, 
            <88, 238576>, <96, 10860>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 3, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 3, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 3, 2, 2, 2, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 2, 1, 2, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 3, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 1, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 1, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 3, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47896>, <20, 1048576>, <24, 8452768>, <28, 36700160>, 
            <32, 150583036>, <36, 286261248>, <40, 567080928>, <44, 749731840>, <48, 757299080>, <52, 749731840>, <56, 
            472338496>, <60, 286261248>, <64, 157591558>, <68, 36700160>, <72, 30346688>, <76, 1048576>, <80, 3491432>, 
            <88, 241440>, <96, 10108>, <104, 96>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 3, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 3, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 3, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 3, 2, 0, 0, 0, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 0, 3, 0, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 1, 2, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 3, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2, 3, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 0, 1, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47864>, <20, 1048576>, <24, 8429696>, <28, 36700160>, 
            <32, 150730524>, <36, 286261248>, <40, 566694656>, <44, 749731840>, <48, 757817928>, <52, 749731840>, <56, 
            471993088>, <60, 286261248>, <64, 157644870>, <68, 36700160>, <72, 30412800>, <76, 1048576>, <80, 3458504>, 
            <88, 241792>, <96, 11548>, <104, 256>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 3, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 1, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 1, 2, 2, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 0, 3, 2, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 1, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 3, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 1, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47832>, <20, 1048576>, <24, 8443232>, <28, 36700160>, 
            <32, 150647100>, <36, 286261248>, <40, 566903072>, <44, 749731840>, <48, 757564680>, <52, 749731840>, <56, 
            472110016>, <60, 286261248>, <64, 157705350>, <68, 36700160>, <72, 30310464>, <76, 1048576>, <80, 3505448>, 
            <88, 234720>, <96, 11452>, <104, 160>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 3, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 1, 2, 2, 0, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 3, 0, 2, 0, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 3, 0, 2, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 1, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 1, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 1, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47496>, <20, 1048576>, <24, 8453328>, <28, 36700160>, 
            <32, 150589836>, <36, 286261248>, <40, 567050288>, <44, 749731840>, <48, 757360104>, <52, 749731840>, <56, 
            472265248>, <60, 286261248>, <64, 157652262>, <68, 36700160>, <72, 30308448>, <76, 1048576>, <80, 3509912>, 
            <88, 235536>, <96, 10956>, <104, 112>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 3, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 3, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 3, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 1, 0, 0, 0, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2, 1, 2, 2, 2, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 0, 1, 0, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 3, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 3, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 3, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47784>, <20, 1048576>, <24, 8437104>, <28, 36700160>, 
            <32, 150685932>, <36, 286261248>, <40, 566806544>, <44, 749731840>, <48, 757677864>, <52, 749731840>, <56, 
            472067680>, <60, 286261248>, <64, 157661670>, <68, 36700160>, <72, 30369312>, <76, 1048576>, <80, 3479096>, 
            <88, 238896>, <96, 11436>, <104, 208>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 3, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 3, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 3, 0, 2, 2, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 2, 3, 0, 2, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 1, 0, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 1, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 1, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 1, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 3, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48616>, <20, 1048576>, <24, 8429040>, <28, 36700160>, 
            <32, 150721068>, <36, 286261248>, <40, 566715920>, <44, 749731840>, <48, 757831080>, <52, 749731840>, <56, 
            471890272>, <60, 286261248>, <64, 157804134>, <68, 36700160>, <72, 30290976>, <76, 1048576>, <80, 3507320>, 
            <88, 232880>, <96, 12012>, <104, 208>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 1, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 3, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 3, 0, 0, 2, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 2, 3, 0, 0, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 1, 0, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 3, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 1, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 3, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 3, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48568>, <20, 1048576>, <24, 8414016>, <28, 36700160>, 
            <32, 150815324>, <36, 286261248>, <40, 566479936>, <44, 749731840>, <48, 758115784>, <52, 749731840>, <56, 
            471764608>, <60, 286261248>, <64, 157726406>, <68, 36700160>, <72, 30413440>, <76, 1048576>, <80, 3451784>, 
            <88, 241216>, <96, 12124>, <104, 320>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 3, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 3, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 3, 0, 2, 2, 0, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 3, 0, 2, 2, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 2, 3, 0, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 3, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 1, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 1, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48328>, <20, 1048576>, <24, 8427728>, <28, 36700160>, 
            <32, 150733516>, <36, 286261248>, <40, 566689968>, <44, 749731840>, <48, 757834856>, <52, 749731840>, <56, 
            471953440>, <60, 286261248>, <64, 157694374>, <68, 36700160>, <72, 30378848>, <76, 1048576>, <80, 3470552>, 
            <88, 240144>, <96, 11532>, <104, 240>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 3, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 1, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 3, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 1, 0, 0, 2, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 2, 3, 2, 0, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 2, 0, 1, 0, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 3, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 3, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 1, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48248>, <20, 1048576>, <24, 8425984>, <28, 36700160>, 
            <32, 150746652>, <36, 286261248>, <40, 566653184>, <44, 749731840>, <48, 757887816>, <52, 749731840>, <56, 
            471912448>, <60, 286261248>, <64, 157709382>, <68, 36700160>, <72, 30377472>, <76, 1048576>, <80, 3471176>, 
            <88, 239104>, <96, 11804>, <104, 256>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 1, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 3, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 3, 0, 0, 2, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 3, 2, 0, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 0, 1, 2, 2, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 3, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 3, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 3, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 3, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48648>, <20, 1048576>, <24, 8434192>, <28, 36700160>, 
            <32, 150685580>, <36, 286261248>, <40, 566818672>, <44, 749731840>, <48, 757666024>, <52, 749731840>, <56, 
            472052896>, <60, 286261248>, <64, 157698854>, <68, 36700160>, <72, 30341344>, <76, 1048576>, <80, 3486488>, 
            <88, 239696>, <96, 10956>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 1, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 3, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 3, 0, 2, 2, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 2, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 2, 1, 2, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 1, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 1, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 3, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48376>, <20, 1048576>, <24, 8424960>, <28, 36700160>, 
            <32, 150750108>, <36, 286261248>, <40, 566647040>, <44, 749731840>, <48, 757893192>, <52, 749731840>, <56, 
            471912448>, <60, 286261248>, <64, 157704006>, <68, 36700160>, <72, 30383616>, <76, 1048576>, <80, 3467720>, 
            <88, 240128>, <96, 11676>, <104, 256>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 3, 0, 2, 2, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 1, 2, 0, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 3, 0, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 1, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 3, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0, 1, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 3, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47880>, <20, 1048576>, <24, 8450256>, <28, 36700160>, 
            <32, 150600204>, <36, 286261248>, <40, 567031856>, <44, 749731840>, <48, 757376232>, <52, 749731840>, <56, 
            472265248>, <60, 286261248>, <64, 157636134>, <68, 36700160>, <72, 30326880>, <76, 1048576>, <80, 3499544>, 
            <88, 238608>, <96, 10572>, <104, 112>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 3, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 1, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 1, 2, 0, 2, 2, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 0, 1, 2, 0, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 0, 1, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 3, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 1, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 3, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47784>, <20, 1048576>, <24, 8446128>, <28, 36700160>, 
            <32, 150629356>, <36, 286261248>, <40, 566950608>, <44, 749731840>, <48, 757495592>, <52, 749731840>, <56, 
            472167136>, <60, 286261248>, <64, 157679590>, <68, 36700160>, <72, 30316448>, <76, 1048576>, <80, 3503672>, 
            <88, 235888>, <96, 11180>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 3, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 1, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 3, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 3, 0, 2, 0, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 1, 0, 0, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 1, 0, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 1, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 3, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 1, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 3, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47960>, <20, 1048576>, <24, 8451744>, <28, 36700160>, 
            <32, 150589372>, <36, 286261248>, <40, 567059424>, <44, 749731840>, <48, 757344776>, <52, 749731840>, <56, 
            472273984>, <60, 286261248>, <64, 157653382>, <68, 36700160>, <72, 30306752>, <76, 1048576>, <80, 3508136>, 
            <88, 237344>, <96, 10556>, <104, 96>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 3, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 3, 0, 2, 2, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 2, 3, 2, 2, 2, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 1, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 1, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 2, 3, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 3, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48264>, <20, 1048576>, <24, 8446928>, <28, 36700160>, 
            <32, 150612876>, <36, 286261248>, <40, 567004208>, <44, 749731840>, <48, 757413864>, <52, 749731840>, <56, 
            472232992>, <60, 286261248>, <64, 157652262>, <68, 36700160>, <72, 30323808>, <76, 1048576>, <80, 3498392>, 
            <88, 239376>, <96, 10444>, <104, 112>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 3, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 3, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 3, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 3, 2, 2, 2, 2, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 3, 2, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 0, 1, 2, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 1, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 3, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 1, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47848>, <20, 1048576>, <24, 8445488>, <28, 36700160>, 
            <32, 150632236>, <36, 286261248>, <40, 566942928>, <44, 749731840>, <48, 757509032>, <52, 749731840>, <56, 
            472151008>, <60, 286261248>, <64, 157693030>, <68, 36700160>, <72, 30308768>, <76, 1048576>, <80, 3506552>, 
            <88, 235248>, <96, 11244>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 3, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 2, 3, 2, 2, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 2, 0, 3, 0, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 3, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 1, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 1, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 1, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48536>, <20, 1048576>, <24, 8418656>, <28, 36700160>, 
            <32, 150787324>, <36, 286261248>, <40, 566548896>, <44, 749731840>, <48, 758034056>, <52, 749731840>, <56, 
            471798208>, <60, 286261248>, <64, 157752838>, <68, 36700160>, <72, 30374720>, <76, 1048576>, <80, 3469544>, 
            <88, 238304>, <96, 12156>, <104, 288>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 3, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 1, 2, 0, 2, 2, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 1, 0, 2, 0, 0, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 3, 2, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 0, 0, 3, 0, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 1, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 3, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 3, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 1, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48312>, <20, 1048576>, <24, 8434880>, <28, 36700160>, 
            <32, 150688348>, <36, 286261248>, <40, 566808000>, <44, 749731840>, <48, 757675976>, <52, 749731840>, <56, 
            472060288>, <60, 286261248>, <64, 157676230>, <68, 36700160>, <72, 30359936>, <76, 1048576>, <80, 3480200>, 
            <88, 240064>, <96, 11100>, <104, 192>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 3, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 1, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 3, 0, 0, 2, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 1, 0, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 2, 1, 2, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 1, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 0, 3, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 3, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48104>, <20, 1048576>, <24, 8443696>, <28, 36700160>, 
            <32, 150636844>, <36, 286261248>, <40, 566939856>, <44, 749731840>, <48, 757498280>, <52, 749731840>, <56, 
            472183264>, <60, 286261248>, <64, 157650022>, <68, 36700160>, <72, 30342560>, <76, 1048576>, <80, 3490424>, 
            <88, 239600>, <96, 10732>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 1, 2, 2, 2, 0, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 1, 0, 0, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 2, 1, 2, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 1, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 1, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 1, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 1, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48440>, <20, 1048576>, <24, 8443008>, <28, 36700160>, 
            <32, 150634076>, <36, 286261248>, <40, 566950528>, <44, 749731840>, <48, 757488328>, <52, 749731840>, <56, 
            472175872>, <60, 286261248>, <64, 157672646>, <68, 36700160>, <72, 30323968>, <76, 1048576>, <80, 3496712>, 
            <88, 239232>, <96, 10588>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 3, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 1, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 3, 2, 0, 0, 0, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 2, 2, 3, 2, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 3, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 1, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 1, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 1, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48360>, <20, 1048576>, <24, 8422320>, <28, 36700160>, 
            <32, 150768428>, <36, 286261248>, <40, 566593360>, <44, 749731840>, <48, 757981096>, <52, 749731840>, <56, 
            471823072>, <60, 286261248>, <64, 157764710>, <68, 36700160>, <72, 30353056>, <76, 1048576>, <80, 3480440>, 
            <88, 236144>, <96, 12268>, <104, 272>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 1, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 3, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 3, 0, 0, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 1, 0, 2, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 1, 2, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 3, 2, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 1, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 1, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 2, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47928>, <20, 1048576>, <24, 8447488>, <28, 36700160>, 
            <32, 150616796>, <36, 286261248>, <40, 566988928>, <44, 749731840>, <48, 757434568>, <52, 749731840>, <56, 
            472224256>, <60, 286261248>, <64, 157645766>, <68, 36700160>, <72, 30331648>, <76, 1048576>, <80, 3496712>, 
            <88, 238592>, <96, 10716>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 3, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 3, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 3, 2, 0, 2, 0, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 2, 3, 2, 2, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 3, 2, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 3, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 1, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, 3, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 1, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48424>, <20, 1048576>, <24, 8431472>, <28, 36700160>, 
            <32, 150707820>, <36, 286261248>, <40, 566757392>, <44, 749731840>, <48, 757747752>, <52, 749731840>, <56, 
            472003168>, <60, 286261248>, <64, 157699302>, <68, 36700160>, <72, 30357024>, <76, 1048576>, <80, 3480248>, 
            <88, 239408>, <96, 11308>, <104, 208>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 1, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 1, 2, 0, 2, 2, 0, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 0, 3, 0, 2, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 2, 1, 0, 0, 0, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 1, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 1, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 3, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 3, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47960>, <20, 1048576>, <24, 8442208>, <28, 36700160>, 
            <32, 150650556>, <36, 286261248>, <40, 566896928>, <44, 749731840>, <48, 757570056>, <52, 749731840>, <56, 
            472110016>, <60, 286261248>, <64, 157699974>, <68, 36700160>, <72, 30316608>, <76, 1048576>, <80, 3501992>, 
            <88, 235744>, <96, 11324>, <104, 160>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 3, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 3, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 3, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 3, 0, 2, 0, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 3, 0, 2, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2, 3, 0, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 3, 0, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 3, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 1, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 1, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47880>, <20, 1048576>, <24, 8459536>, <28, 36700160>, 
            <32, 150541324>, <36, 286261248>, <40, 567185136>, <44, 749731840>, <48, 757172456>, <52, 749731840>, <56, 
            472396960>, <60, 286261248>, <64, 157621798>, <68, 36700160>, <72, 30295520>, <76, 1048576>, <80, 3514904>, 
            <88, 237904>, <96, 10060>, <104, 48>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 1, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 1, 2, 2, 2, 2, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 3, 0, 2, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0, 2, 1, 2, 0, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 3, 0, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, 3, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 1, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 1, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47384>, <20, 1048576>, <24, 8457120>, <28, 36700160>, 
            <32, 150566908>, <36, 286261248>, <40, 567114720>, <44, 749731840>, <48, 757256072>, <52, 749731840>, <56, 
            472370752>, <60, 286261248>, <64, 157580806>, <68, 36700160>, <72, 30343616>, <76, 1048576>, <80, 3496040>, 
            <88, 239648>, <96, 10364>, <104, 96>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 3, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 3, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 2, 2, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 1, 2, 2, 0, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 0, 3, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 1, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 3, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 1, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 1, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47208>, <20, 1048576>, <24, 8460784>, <28, 36700160>, 
            <32, 150548012>, <36, 286261248>, <40, 567159184>, <44, 749731840>, <48, 757203112>, <52, 749731840>, <56, 
            472395616>, <60, 286261248>, <64, 157592678>, <68, 36700160>, <72, 30321952>, <76, 1048576>, <80, 3506936>, 
            <88, 237488>, <96, 10476>, <104, 80>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 3, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 3, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 1, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 1, 2, 2, 2, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 3, 2, 0, 0, 0, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 0, 0, 1, 2, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 1, 2, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 3, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 3, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 3, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48120>, <20, 1048576>, <24, 8445568>, <28, 36700160>, 
            <32, 150625436>, <36, 286261248>, <40, 566965888>, <44, 749731840>, <48, 757474888>, <52, 749731840>, <56, 
            472175872>, <60, 286261248>, <64, 157686086>, <68, 36700160>, <72, 30308608>, <76, 1048576>, <80, 3505352>, 
            <88, 236672>, <96, 10908>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 1, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 3, 0, 2, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2, 3, 0, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0, 2, 1, 0, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 3, 0, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 3, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0, 1, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 1, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 49080>, <20, 1048576>, <24, 8418560>, <28, 36700160>, 
            <32, 150776028>, <36, 286261248>, <40, 566585600>, <44, 749731840>, <48, 757987272>, <52, 749731840>, <56, 
            471815680>, <60, 286261248>, <64, 157771206>, <68, 36700160>, <72, 30352896>, <76, 1048576>, <80, 3476360>, 
            <88, 238848>, <96, 11740>, <104, 256>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 3, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 1, 0, 2, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 2, 3, 0, 2, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 2, 3, 0, 0, 2, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 3, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 3, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 1, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 3, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48184>, <20, 1048576>, <24, 8445312>, <28, 36700160>, 
            <32, 150624860>, <36, 286261248>, <40, 566972032>, <44, 749731840>, <48, 757456072>, <52, 749731840>, <56, 
            472208128>, <60, 286261248>, <64, 157651142>, <68, 36700160>, <72, 30333184>, <76, 1048576>, <80, 3494408>, 
            <88, 239488>, <96, 10588>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 1, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 1, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 1, 2, 2, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 3, 2, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 1, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 1, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 3, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48280>, <20, 1048576>, <24, 8430624>, <28, 36700160>, 
            <32, 150715772>, <36, 286261248>, <40, 566737504>, <44, 749731840>, <48, 757765768>, <52, 749731840>, <56, 
            472010560>, <60, 286261248>, <64, 157668614>, <68, 36700160>, <72, 30384832>, <76, 1048576>, <80, 3468776>, 
            <88, 241312>, <96, 11260>, <104, 224>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 1, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 3, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 1, 0, 2, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 3, 2, 0, 0, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 1, 2, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 3, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 3, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 3, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47992>, <20, 1048576>, <24, 8438080>, <28, 36700160>, 
            <32, 150673948>, <36, 286261248>, <40, 566846400>, <44, 749731840>, <48, 757608776>, <52, 749731840>, <56, 
            472140928>, <60, 286261248>, <64, 157609030>, <68, 36700160>, <72, 30398336>, <76, 1048576>, <80, 3465800>, 
            <88, 243264>, <96, 10780>, <104, 192>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 2, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 3, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 1, 2, 2, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 3, 2, 0, 0, 2, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 3, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 1, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 1, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 3, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 1, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47880>, <20, 1048576>, <24, 8441104>, <28, 36700160>, 
            <32, 150657932>, <36, 286261248>, <40, 566883184>, <44, 749731840>, <48, 757569256>, <52, 749731840>, <56, 
            472149664>, <60, 286261248>, <64, 157634342>, <68, 36700160>, <72, 30368992>, <76, 1048576>, <80, 3479576>, 
            <88, 240464>, <96, 10956>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 1, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 3, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 3, 0, 0, 0, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 2, 3, 0, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 2, 1, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 1, 0, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 1, 2, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 1, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 3, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48024>, <20, 1048576>, <24, 8450848>, <28, 36700160>, 
            <32, 150594556>, <36, 286261248>, <40, 567042528>, <44, 749731840>, <48, 757379720>, <52, 749731840>, <56, 
            472225600>, <60, 286261248>, <64, 157699078>, <68, 36700160>, <72, 30277568>, <76, 1048576>, <80, 3520232>, 
            <88, 234400>, <96, 10876>, <104, 96>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 3, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 3, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 1, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 3, 2, 2, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 3, 2, 0, 0, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 3, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 3, 2, 2, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 3, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0, 2, 3, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 1, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 0, 1 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48040>, <20, 1048576>, <24, 8444336>, <28, 36700160>, 
            <32, 150633964>, <36, 286261248>, <40, 566947536>, <44, 749731840>, <48, 757484840>, <52, 749731840>, <56, 
            472199392>, <60, 286261248>, <64, 157636582>, <68, 36700160>, <72, 30350240>, <76, 1048576>, <80, 3487544>, 
            <88, 240240>, <96, 10668>, <104, 144>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0 ],
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 1, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 1, 0, 0, 2, 2, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2, 1, 0, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 1, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 3, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 3, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 1, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 3 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47944>, <20, 1048576>, <24, 8450000>, <28, 36700160>, 
            <32, 150599628>, <36, 286261248>, <40, 567038000>, <44, 749731840>, <48, 757357416>, <52, 749731840>, <56, 
            472297504>, <60, 286261248>, <64, 157601190>, <68, 36700160>, <72, 30351456>, <76, 1048576>, <80, 3488600>, 
            <88, 241424>, <96, 10252>, <104, 112>, <112, 120>, <128, 1> ]>
]
;