RF:=recformat<mat:SeqEnum,dtb:SeqEnum>;

list:=
[
rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 2, 2, 2, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 1, 2, 2, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 2, 0, 0, 2, 1, 2, 0, 0, 0, 0, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 1, 0, 2, 2, 0, 0 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 1, 2, 0, 2, 0 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 1, 2, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 1, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 113384>, <24, 16310832>, <32, 269898796>, <40, 
        1091790032>, <48, 1600878504>, <56, 997077984>, <64, 276857446>, <72, 38244768>, <80, 3542392>, <88, 242416>, 
        <96, 10476>, <104, 144>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 2, 2, 2, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 1, 2, 2, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 2, 0, 0, 2, 1, 2, 0, 0, 0, 0, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 1, 0, 2, 2, 0, 0 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 1, 2, 0, 2, 0 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 1, 2, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 1, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47848>, <20, 1048576>, <24, 8446512>, <28, 36700160>, <32,
        150623276>, <36, 286261248>, <40, 566977744>, <44, 749731840>, <48, 757430184>, <52, 749731840>, <56, 
        472265696>, <60, 286261248>, <64, 157581926>, <68, 36700160>, <72, 30380448>, <76, 1048576>, <80, 3476856>, <88,
        242416>, <96, 10476>, <104, 144>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 1, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 1, 0, 2, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 1, 2, 0, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 1, 0, 2, 2, 2, 0, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 1, 2, 2, 2, 0, 0 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 1, 0, 0, 2, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 1, 0, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47432>, <20, 1048576>, <24, 8454736>, <28, 36700160>, <32,
        150580300>, <36, 286261248>, <40, 567083568>, <44, 749731840>, <48, 757289320>, <52, 749731840>, <56, 
        472363808>, <60, 286261248>, <64, 157559974>, <68, 36700160>, <72, 30366304>, <76, 1048576>, <80, 3486552>, <88,
        241040>, <96, 10380>, <104, 112>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 1, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 1, 0, 0, 2, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 1, 2, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0, 0, 2, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 1, 2, 0, 0, 0, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 1, 2, 2, 2, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 1, 2, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 1, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47832>, <20, 1048576>, <24, 8453024>, <28, 36700160>, <32,
        150583868>, <36, 286261248>, <40, 567072736>, <44, 749731840>, <48, 757325064>, <52, 749731840>, <56, 
        472291904>, <60, 286261248>, <64, 157644422>, <68, 36700160>, <72, 30307776>, <76, 1048576>, <80, 3509544>, <88,
        236576>, <96, 10684>, <104, 96>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 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, 2, 2, 0, 2, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 1, 0, 0, 2, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 1, 2, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 0, 0, 2, 0, 1, 0, 0, 2, 2, 0, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 2, 0, 0, 0 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 0, 2, 0, 0 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 1, 0, 0, 0 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 1, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48536>, <20, 1048576>, <24, 8428320>, <28, 36700160>, <32,
        150725244>, <36, 286261248>, <40, 566713952>, <44, 749731840>, <48, 757805192>, <52, 749731840>, <56, 
        471963968>, <60, 286261248>, <64, 157708038>, <68, 36700160>, <72, 30361280>, <76, 1048576>, <80, 3478248>, <88,
        239008>, <96, 11516>, <104, 224>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 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, 2, 2, 0, 2, 1, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 1, 2, 0, 0, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 1, 2, 2, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 1, 0, 0, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 2, 0, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 1, 0, 0, 0, 0, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 1, 2, 2, 0, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 1, 2, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 1, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 1, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48248>, <20, 1048576>, <24, 8444800>, <28, 36700160>, <32,
        150626844>, <36, 286261248>, <40, 566966912>, <44, 749731840>, <48, 757465928>, <52, 749731840>, <56, 
        472193792>, <60, 286261248>, <64, 157666374>, <68, 36700160>, <72, 30321920>, <76, 1048576>, <80, 3499848>, <88,
        237952>, <96, 10780>, <104, 128>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 1, 2, 0, 0, 2, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 1, 2, 2, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 2, 0, 2, 0, 1, 2, 2, 2, 0, 0, 0 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 1, 0, 2, 0, 2, 0 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 1, 0, 0, 0, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 2, 1, 0, 2, 0 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 1, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48296>, <20, 1048576>, <24, 8442544>, <28, 36700160>, <32,
        150638828>, <36, 286261248>, <40, 566942416>, <44, 749731840>, <48, 757481256>, <52, 749731840>, <56, 
        472217312>, <60, 286261248>, <64, 157611494>, <68, 36700160>, <72, 30369696>, <76, 1048576>, <80, 3478584>, <88,
        242544>, <96, 10412>, <104, 144>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 2, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 1, 0, 2, 2, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 1, 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, 2, 2, 0, 0, 2, 0, 2, 1, 0, 2, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 0, 0, 0, 2, 1, 0, 2, 0, 2, 0, 0 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 1, 2, 0, 2, 2, 0 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 0, 1, 0, 2, 0, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 1, 2, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 1, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 1, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47896>, <20, 1048576>, <24, 8452640>, <28, 36700160>, <32,
        150584444>, <36, 286261248>, <40, 567074272>, <44, 749731840>, <48, 757317000>, <52, 749731840>, <56, 
        472308032>, <60, 286261248>, <64, 157625606>, <68, 36700160>, <72, 30321600>, <76, 1048576>, <80, 3503208>, <88,
        238240>, <96, 10492>, <104, 96>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 1, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 1, 2, 2, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 1, 0, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 1, 0, 0, 2, 0, 2, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 1, 2, 2, 0, 0, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 1, 0, 2, 0, 0 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 1, 0, 2, 0 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 1, 0, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 1, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47784>, <20, 1048576>, <24, 8455920>, <28, 36700160>, <32,
        150566124>, <36, 286261248>, <40, 567120272>, <44, 749731840>, <48, 757255976>, <52, 749731840>, <56, 
        472349024>, <60, 286261248>, <64, 157618662>, <68, 36700160>, <72, 30313760>, <76, 1048576>, <80, 3507768>, <88,
        237744>, <96, 10412>, <104, 80>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 2, 2, 0, 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, 0, 0, 0, 0, 1, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 2, 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, 0, 2, 0, 2, 1, 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, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 2, 0, 0, 0, 1, 2, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 2, 2, 0, 1, 2, 2, 0, 0, 2, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 1, 2, 0, 0, 2, 0 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 1, 2, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 1, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 1, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 114408>, <24, 16273392>, <32, 270115756>, <40, 
        1091230352>, <48, 1601651112>, <56, 996505440>, <64, 277034854>, <72, 38269728>, <80, 3519352>, <88, 240048>, 
        <96, 12396>, <104, 336>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 1, 2, 2, 2, 2, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 1, 2, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 0, 0, 2, 0, 1, 0, 2, 0, 0, 0, 0 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 1, 0, 2, 0, 0, 0 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 1, 2, 2, 0, 0 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 1, 2, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 1, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 1, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48392>, <20, 1048576>, <24, 8436624>, <28, 36700160>, <32,
        150675468>, <36, 286261248>, <40, 566842736>, <44, 749731840>, <48, 757630184>, <52, 749731840>, <56, 
        472086944>, <60, 286261248>, <64, 157679142>, <68, 36700160>, <72, 30346976>, <76, 1048576>, <80, 3486744>, <88,
        239056>, <96, 11084>, <104, 176>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 1, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 1, 2, 2, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 0, 0, 0, 2, 1, 2, 0, 0, 0, 2, 0 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 1, 0, 2, 0, 0, 0 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 1, 2, 0, 0, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 1, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48040>, <20, 1048576>, <24, 8443952>, <28, 36700160>, <32,
        150637676>, <36, 286261248>, <40, 566931664>, <44, 749731840>, <48, 757524264>, <52, 749731840>, <56, 
        472136672>, <60, 286261248>, <64, 157702886>, <68, 36700160>, <72, 30303648>, <76, 1048576>, <80, 3508536>, <88,
        234736>, <96, 11308>, <104, 144>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 1, 2, 2, 0, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 0, 0, 0, 2, 1, 2, 0, 2, 0, 2, 0 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 1, 0, 2, 0, 2, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, 1, 0, 0, 2, 0 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 1, 2, 2, 0 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 1, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48456>, <20, 1048576>, <24, 8445264>, <28, 36700160>, <32,
        150619468>, <36, 286261248>, <40, 566988336>, <44, 749731840>, <48, 757439848>, <52, 749731840>, <56, 
        472202528>, <60, 286261248>, <64, 157678246>, <68, 36700160>, <72, 30307936>, <76, 1048576>, <80, 3504984>, <88,
        237712>, <96, 10636>, <104, 112>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 2, 2, 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, 0, 2, 2, 0, 1, 2, 2, 0, 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, 2, 2, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 1, 2, 0, 0, 0, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 2, 2, 2, 1, 0, 0, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 0, 2, 0, 2, 1, 2, 2, 2, 0, 2, 0 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 1, 0, 2, 0, 2, 0 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 1, 2, 0, 0, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 0, 0 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 1, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 1, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 0, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47160>, <20, 1048576>, <24, 8463808>, <28, 36700160>, <32,
        150529372>, <36, 286261248>, <40, 567209280>, <44, 749731840>, <48, 757130440>, <52, 749731840>, <56, 
        472454528>, <60, 286261248>, <64, 157568710>, <68, 36700160>, <72, 30324352>, <76, 1048576>, <80, 3507720>, <88,
        237760>, <96, 10332>, <104, 64>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 1, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 1, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 1, 0, 2, 2, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 1, 0, 0, 2, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 1, 0, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 2, 1, 2, 0, 2, 0, 2, 0 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 1, 2, 2, 2, 0, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 1, 2, 2, 2, 0 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 0, 1, 2, 2, 0 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48392>, <20, 1048576>, <24, 8436880>, <28, 36700160>, <32,
        150673164>, <36, 286261248>, <40, 566851952>, <44, 749731840>, <48, 757608680>, <52, 749731840>, <56, 
        472119200>, <60, 286261248>, <64, 157646886>, <68, 36700160>, <72, 30368480>, <76, 1048576>, <80, 3477528>, <88,
        241360>, <96, 10828>, <104, 176>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 1, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 2, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 1, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 1, 2, 2, 0, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 1, 2, 2, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 1, 2, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 0, 2, 0, 0, 1, 0, 2, 2, 0, 0, 0 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 1, 2, 0, 0, 2, 0 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 1, 0, 0, 2, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 1, 0, 0, 0 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 1, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 1, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 113832>, <24, 16297328>, <32, 269975532>, <40, 
        1091592208>, <48, 1601154856>, <56, 996865632>, <64, 276933606>, <72, 38243872>, <80, 3537976>, <88, 240944>, 
        <96, 11180>, <104, 208>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 1, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 2, 2, 2, 2, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 1, 2, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 1, 2, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 2, 0, 2, 0, 1, 2, 0, 2, 2, 2, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 1, 2, 2, 0, 0, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 1, 2, 2, 2, 0 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 1, 2, 2, 0 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 1, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 113400>, <24, 16312832>, <32, 269886236>, <40, 
        1091820672>, <48, 1600844360>, <56, 997086720>, <64, 276877382>, <72, 38221568>, <80, 3552712>, <88, 240640>, 
        <96, 10524>, <104, 128>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 1, 0, 0, 2, 0, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 1, 2, 0, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 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, 0, 0, 2, 2, 1, 2, 2, 0, 0, 0, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 1, 2, 2, 2, 0, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 1, 0, 0, 0, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 1, 0, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 1, 2, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 1, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47528>, <20, 1048576>, <24, 8458224>, <28, 36700160>, <32,
        150556908>, <36, 286261248>, <40, 567141776>, <44, 749731840>, <48, 757223720>, <52, 749731840>, <56, 
        472381280>, <60, 286261248>, <64, 157597158>, <68, 36700160>, <72, 30322976>, <76, 1048576>, <80, 3505464>, <88,
        238000>, <96, 10412>, <104, 80>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 1, 0, 2, 2, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 2, 0, 0, 0, 2, 1, 0, 2, 0, 2, 2, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 1, 2, 0, 2, 0, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, 1, 2, 0, 2, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 1, 0, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 1, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 113720>, <24, 16300736>, <32, 269956060>, <40, 
        1091642816>, <48, 1601083080>, <56, 996922752>, <64, 276910534>, <72, 38246784>, <80, 3537928>, <88, 241600>, 
        <96, 10972>, <104, 192>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 1, 0, 0, 2, 0, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 1, 0, 0, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 1, 2, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 2, 0, 2, 0, 1, 2, 2, 2, 0, 0, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 1, 0, 2, 2, 0, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 1, 0, 2, 2, 0 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 1, 0, 0, 0 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 1, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 1, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 113576>, <24, 16308656>, <32, 269909740>, <40, 
        1091757776>, <48, 1600940328>, <56, 996997344>, <64, 276930022>, <72, 38200224>, <80, 3560248>, <88, 238192>, 
        <96, 10924>, <104, 144>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 1, 2, 0, 0, 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, 2, 2, 2, 0, 1, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 1, 2, 2, 2, 0, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 1, 2, 2, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 1, 2, 0, 0, 2, 2, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 1, 2, 0, 0, 0, 0 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 1, 2, 0, 2, 0 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 1, 2, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 1, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 114216>, <24, 16302512>, <32, 269936236>, <40, 
        1091690192>, <48, 1601053224>, <56, 996868320>, <64, 277032166>, <72, 38144928>, <80, 3579832>, <88, 234096>, 
        <96, 11308>, <104, 144>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 1, 0, 0, 2, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2, 1, 2, 0, 0, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 2, 0, 2, 0, 1, 0, 0, 2, 0, 2, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 1, 2, 0, 0, 2, 0 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 1, 0, 2, 0 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 1, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 113544>, <24, 16303632>, <32, 269944076>, <40, 
        1091659632>, <48, 1601094632>, <56, 996850848>, <64, 277019174>, <72, 38160608>, <80, 3576472>, <88, 232528>, 
        <96, 11852>, <104, 176>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 1, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 1, 0, 0, 0, 0, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 1, 0, 2, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 2, 2, 2, 1, 0, 2, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, 2, 0, 2, 1, 2, 2, 0, 0, 0, 0 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 1, 0, 2, 2, 2, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 1, 0, 0, 0, 0 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 1, 2, 0, 0 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 1, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48216>, <20, 1048576>, <24, 8431008>, <28, 36700160>, <32,
        150715452>, <36, 286261248>, <40, 566733920>, <44, 749731840>, <48, 757781000>, <52, 749731840>, <56, 
        471980096>, <60, 286261248>, <64, 157705350>, <68, 36700160>, <72, 30356672>, <76, 1048576>, <80, 3482280>, <88,
        237600>, <96, 11708>, <104, 224>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 1, 2, 0, 2, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 1, 2, 2, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 2, 0, 2, 0, 1, 0, 2, 2, 2, 2, 0 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 1, 2, 2, 0, 0, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 1, 2, 0, 2, 0 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 1, 0, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 1, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 113672>, <24, 16312144>, <32, 269886348>, <40, 
        1091815984>, <48, 1600874728>, <56, 997014816>, <64, 276967206>, <72, 38156896>, <80, 3579160>, <88, 235152>, 
        <96, 10956>, <104, 112>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 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, 0, 2, 0, 2, 1, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 1, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, 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, 2, 2, 0, 0, 0, 1, 2, 2, 2, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 2, 2, 0, 1, 0, 2, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 2, 2, 0, 2, 1, 0, 2, 0, 2, 0, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 1, 2, 0, 0, 2, 0 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 0, 1, 2, 2, 2, 0 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 1, 0, 0, 0 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 1, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 1, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 113752>, <24, 16295328>, <32, 269990972>, <40, 
        1091546208>, <48, 1601229320>, <56, 996792384>, <64, 276980870>, <72, 38220992>, <80, 3547816>, <88, 237600>, 
        <96, 11708>, <104, 224>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 1, 0, 0, 2, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 1, 0, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 0, 2, 2, 1, 2, 2, 0, 0, 2, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 0, 2, 0, 0 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 1, 0, 0, 2, 0 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 1, 2, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 113576>, <24, 16308912>, <32, 269907436>, <40, 
        1091766992>, <48, 1600918824>, <56, 997029600>, <64, 276897766>, <72, 38221728>, <80, 3551032>, <88, 240496>, 
        <96, 10668>, <104, 144>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 1, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 1, 2, 0, 0, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 1, 0, 2, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 1, 2, 2, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 2, 0, 0, 1, 2, 2, 0, 0, 0, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 1, 0, 2, 0, 2, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 1, 0, 0, 0, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 1, 2, 2, 0 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 1, 2, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48248>, <20, 1048576>, <24, 8435648>, <28, 36700160>, <32,
        150684572>, <36, 286261248>, <40, 566818240>, <44, 749731840>, <48, 757658952>, <52, 749731840>, <56, 
        472078208>, <60, 286261248>, <64, 157664582>, <68, 36700160>, <72, 30364032>, <76, 1048576>, <80, 3479880>, <88,
        239808>, <96, 11164>, <104, 192>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 1, 0, 2, 0, 0, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 1, 2, 0, 2, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 0, 2, 2, 2, 1, 2, 0, 0, 2, 2, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 0, 0 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 1, 2, 0, 0, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 1, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 114184>, <24, 16298512>, <32, 269961356>, <40, 
        1091628912>, <48, 1601121512>, <56, 996850848>, <64, 276992294>, <72, 38191328>, <80, 3559192>, <88, 237648>, 
        <96, 11212>, <104, 176>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 1, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 1, 2, 0, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 1, 0, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 0, 0, 2, 2, 1, 0, 2, 0, 0, 0, 0 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 2, 2, 0, 2, 0 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 1, 0, 2, 0, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 1, 0, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 1, 2, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 1, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48216>, <20, 1048576>, <24, 8449056>, <28, 36700160>, <32,
        150602300>, <36, 286261248>, <40, 567022048>, <44, 749731840>, <48, 757416456>, <52, 749731840>, <56, 
        472179008>, <60, 286261248>, <64, 157741190>, <68, 36700160>, <72, 30250944>, <76, 1048576>, <80, 3531432>, <88,
        231584>, <96, 11196>, <104, 96>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 1, 2, 0, 0, 2, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 1, 2, 2, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 1, 0, 2, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 2, 2, 0 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 1, 2, 2, 2, 0, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 1, 2, 2, 0, 0 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 1, 0, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 1, 2, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 0, 1, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48280>, <20, 1048576>, <24, 8439264>, <28, 36700160>, <32,
        150662908>, <36, 286261248>, <40, 566865696>, <44, 749731840>, <48, 757622920>, <52, 749731840>, <56, 
        472047296>, <60, 286261248>, <64, 157752838>, <68, 36700160>, <72, 30285376>, <76, 1048576>, <80, 3514344>, <88,
        232800>, <96, 11644>, <104, 160>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 1, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 1, 0, 0, 0, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 1, 0, 0, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 2, 2, 1, 0, 2, 0, 2, 0, 0 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 1, 0, 2, 2, 0, 0 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, 1, 2, 0, 0, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 1, 0, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 1, 2, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 113592>, <24, 16310912>, <32, 269894876>, <40, 
        1091797632>, <48, 1600884680>, <56, 997038336>, <64, 276917702>, <72, 38198528>, <80, 3561352>, <88, 238720>, 
        <96, 10716>, <104, 128>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 2, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 1, 2, 0, 2, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 2, 2, 1, 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, 2, 2, 2, 0, 0, 0, 2, 1, 0, 0, 2, 0, 0, 0 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 1, 0, 0, 0, 0, 0 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 1, 2, 0, 2, 0 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 1, 0, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 1, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 113112>, <24, 16320160>, <32, 269845564>, <40, 
        1091924960>, <48, 1600698120>, <56, 997200960>, <64, 276833926>, <72, 38224320>, <80, 3554344>, <88, 241440>, 
        <96, 10172>, <104, 96>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 2, 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, 0, 0, 2, 2, 1, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 1, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 1, 0, 2, 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, 2, 0, 2, 2, 1, 2, 2, 2, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 2, 0, 2, 1, 0, 2, 2, 0, 0, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, 0, 1, 2, 0, 0, 0, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 1, 2, 2, 2, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 1, 2, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 1, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 1, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 113784>, <24, 16309120>, <32, 269902364>, <40, 
        1091779200>, <48, 1600914248>, <56, 997006080>, <64, 276941894>, <72, 38186240>, <80, 3565384>, <88, 237952>, 
        <96, 10780>, <104, 128>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 2, 2, 2, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 1, 2, 2, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2, 1, 2, 2, 0, 2, 0, 0 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 1, 0, 0, 2, 0, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 1, 2, 0, 0, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 1, 0, 0, 0 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 1, 2, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 113304>, <24, 16318368>, <32, 269853052>, <40, 
        1091906528>, <48, 1600727688>, <56, 997168704>, <64, 276858118>, <72, 38212032>, <80, 3558376>, <88, 240672>, 
        <96, 10236>, <104, 96>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 2, 2, 2, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 1, 2, 2, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2, 1, 2, 2, 0, 2, 0, 0 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 1, 0, 0, 2, 0, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 1, 2, 0, 0, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 1, 0, 0, 0 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 1, 2, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47768>, <20, 1048576>, <24, 8454048>, <28, 36700160>, <32,
        150577532>, <36, 286261248>, <40, 567094240>, <44, 749731840>, <48, 757279368>, <52, 749731840>, <56, 
        472356416>, <60, 286261248>, <64, 157582598>, <68, 36700160>, <72, 30347712>, <76, 1048576>, <80, 3492840>, <88,
        240672>, <96, 10236>, <104, 96>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 1, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 1, 2, 2, 0, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0, 1, 0, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 2, 0, 0, 2, 1, 2, 2, 2, 2, 2, 0 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 1, 0, 0, 2, 2, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 1, 2, 0, 0, 0 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 0, 1, 2, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 1, 0, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 1, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47800>, <20, 1048576>, <24, 8458176>, <28, 36700160>, <32,
        150551260>, <36, 286261248>, <40, 567160128>, <44, 749731840>, <48, 757200328>, <52, 749731840>, <56, 
        472390016>, <60, 286261248>, <64, 157606342>, <68, 36700160>, <72, 30312064>, <76, 1048576>, <80, 3508872>, <88,
        238272>, <96, 10204>, <104, 64>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 1, 2, 0, 2, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 2, 2, 1, 2, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 0, 0, 2, 0, 1, 2, 2, 2, 0, 0, 0 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 1, 0, 0, 2, 2, 0 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 1, 2, 0, 2, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, 1, 0, 2, 0 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 1, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 1, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48360>, <20, 1048576>, <24, 8441264>, <28, 36700160>, <32,
        150647468>, <36, 286261248>, <40, 566911696>, <44, 749731840>, <48, 757548456>, <52, 749731840>, <56, 
        472120544>, <60, 286261248>, <64, 157705574>, <68, 36700160>, <72, 30308256>, <76, 1048576>, <80, 3504504>, <88,
        236144>, <96, 11116>, <104, 144>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 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, 0, 0, 2, 2, 1, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 1, 2, 0, 0, 0, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 1, 2, 0, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 0, 2, 2, 0, 0, 1, 0, 2, 0, 2, 0, 0 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 1, 2, 2, 2, 0, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 1, 0, 0, 2, 0 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 1, 2, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 1, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 1, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 60328>, <20, 983040>, <24, 8049520>, <28, 41016320>, <32, 
        135313260>, <36, 313491968>, <40, 545483664>, <44, 740315136>, <48, 800479016>, <52, 700078080>, <56, 
        498727008>, <60, 289712128>, <64, 138397926>, <68, 55364608>, <72, 19050272>, <76, 6017024>, <80, 1794360>, <84,
        481280>, <88, 121136>, <92, 23552>, <96, 6956>, <100, 512>, <104, 80>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 1, 2, 2, 2, 0, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 1, 0, 0, 0, 2, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 1, 2, 2, 0, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 1, 2, 0, 0 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 1, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 1, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 113288>, <24, 16306576>, <32, 269929100>, <40, 
        1091704176>, <48, 1601008616>, <56, 996963744>, <64, 276917030>, <72, 38223584>, <80, 3551128>, <88, 238544>, 
        <96, 11212>, <104, 176>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 2, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 1, 2, 2, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 1, 0, 2, 2, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 1, 0, 2, 0, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 0, 2, 0, 2, 1, 0, 2, 2, 0, 0, 0 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 1, 0, 2, 0, 2, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 1, 0, 0, 0, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 1, 2, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 1, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 113272>, <24, 16323136>, <32, 269823900>, <40, 
        1091980096>, <48, 1600635208>, <56, 997218432>, <64, 276868422>, <72, 38184064>, <80, 3571528>, <88, 238912>, 
        <96, 10140>, <104, 64>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 2, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 1, 2, 2, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 1, 0, 2, 2, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 1, 0, 2, 0, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 0, 2, 0, 2, 1, 0, 2, 2, 0, 0, 0 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 1, 0, 2, 0, 2, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 1, 0, 0, 0, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 1, 2, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 1, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47736>, <20, 1048576>, <24, 8458816>, <28, 36700160>, <32,
        150548380>, <36, 286261248>, <40, 567167808>, <44, 749731840>, <48, 757186888>, <52, 749731840>, <56, 
        472406144>, <60, 286261248>, <64, 157592902>, <68, 36700160>, <72, 30319744>, <76, 1048576>, <80, 3505992>, <88,
        238912>, <96, 10140>, <104, 64>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 1, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 1, 2, 2, 0, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 1, 2, 0, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 0, 2, 2, 0, 1, 0, 0, 2, 2, 2, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 1, 0, 0, 0, 2, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 1, 2, 0, 0, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 1, 2, 2, 0 ],
        \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 1, 2, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 1 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 59368>, <20, 1002048>, <24, 7970224>, <28, 41047168>, <32,
        135614892>, <36, 313144384>, <40, 545143504>, <44, 740947456>, <48, 800486312>, <52, 699722880>, <56, 
        498906336>, <60, 289614592>, <64, 138376038>, <68, 55501440>, <72, 18988960>, <76, 6010368>, <80, 1802360>, <84,
        471360>, <88, 127600>, <92, 21632>, <96, 7788>, <100, 320>, <104, 144>, <112, 120>, <128, 1> ]>


];