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

[ PowerStructure(Rec) |
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0 ],
            \[ 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0 ],
            \[ 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 3, 0, 0, 0, 0, 2, 2, 2, 0, 2 ],
            \[ 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 3, 0, 0, 0, 2, 0, 0, 2, 2 ],
            \[ 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 3, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 1, 2, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 0, 3, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 0, 3, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 3 ],
            \[ 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 2, 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 ],
            \[ 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 61160>, <20, 986624>, <24, 7970432>, <28, 40676352>, 
            <32, 139238780>, <36, 310701568>, <40, 543447168>, <44, 738070528>, <48, 797265368>, <52, 710253568>, <56, 
            498290944>, <60, 288655360>, <64, 138717062>, <68, 52022272>, <72, 19898624>, <76, 5509120>, <80, 2336728>, 
            <84, 562688>, <88, 233600>, <92, 44032>, <96, 21884>, <100, 1536>, <104, 1664>, <112, 232>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 2, 2, 2, 0, 2, 2, 0, 0, 2, 2, 2 ],
            \[ 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 3, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0 ],
            \[ 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 2, 2, 0, 0, 2, 0, 2, 2, 2 ],
            \[ 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 2, 0, 0, 2, 2, 0, 0, 0 ],
            \[ 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 3, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 3, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 3, 0, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 2, 1, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 3 ],
            \[ 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 2, 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 ],
            \[ 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 59400>, <20, 1016832>, <24, 7825440>, <28, 40720384>, 
            <32, 139869020>, <36, 310146048>, <40, 542451936>, <44, 739172352>, <48, 797954328>, <52, 709429248>, <56, 
            498083136>, <60, 288804864>, <64, 138776390>, <68, 52070400>, <72, 19890624>, <76, 5529600>, <80, 2300280>, 
            <84, 553984>, <88, 245920>, <92, 38912>, <96, 25052>, <100, 1024>, <104, 1888>, <112, 232>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 3, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 3, 0, 2, 0, 0, 2, 0, 2, 2 ],
            \[ 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 2, 2, 0, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 3, 0, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 3, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 0, 0, 1, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 3 ],
            \[ 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 2, 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 ],
            \[ 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 61544>, <20, 986624>, <24, 7948288>, <28, 40676352>, 
            <32, 139371516>, <36, 310701568>, <40, 543103744>, <44, 738070528>, <48, 797732056>, <52, 710253568>, <56, 
            497963008>, <60, 288655360>, <64, 138794118>, <68, 52022272>, <72, 19936768>, <76, 5509120>, <80, 2314072>, 
            <84, 562688>, <88, 233472>, <92, 44032>, <96, 23036>, <100, 1536>, <104, 1792>, <112, 232>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2 ],
            \[ 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2 ],
            \[ 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 0, 2, 0, 2, 0, 2, 2, 2 ],
            \[ 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 2, 0, 2, 2, 2, 2, 0, 0 ],
            \[ 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 2, 0, 0, 2, 0 ],
            \[ 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 3, 2, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 3, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 0, 1, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 0, 0, 3, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 3 ],
            \[ 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 2, 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 ],
            \[ 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 60072>, <20, 1008256>, <24, 7869312>, <28, 40704256>, 
            <32, 139684668>, <36, 310301312>, <40, 542721280>, <44, 738929664>, <48, 797797720>, <52, 709477632>, <56, 
            498124032>, <60, 288978432>, <64, 138729734>, <68, 51935488>, <72, 19931136>, <76, 5549056>, <80, 2294936>, 
            <84, 559232>, <88, 244608>, <92, 39168>, <96, 24124>, <100, 1152>, <104, 1792>, <112, 232>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0 ],
            \[ 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 3, 0, 0, 0, 2, 2, 2, 0, 0, 0 ],
            \[ 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 3, 2, 0, 2, 0, 0, 2, 2, 0 ],
            \[ 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 3, 2, 0, 0, 0, 2, 0, 2 ],
            \[ 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 2, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 1, 2, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 3, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 1 ],
            \[ 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 2, 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 ],
            \[ 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 59720>, <20, 1008256>, <24, 7876896>, <28, 40704256>, 
            <32, 139644572>, <36, 310301312>, <40, 542819424>, <44, 738929664>, <48, 797670296>, <52, 709477632>, <56, 
            498206016>, <60, 288978432>, <64, 138721222>, <68, 51935488>, <72, 19909312>, <76, 5549056>, <80, 2307512>, 
            <84, 559232>, <88, 242592>, <92, 39168>, <96, 24092>, <100, 1152>, <104, 1760>, <112, 232>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2 ],
            \[ 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 3, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0 ],
            \[ 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 3, 0, 2, 0, 0, 2, 2, 0, 2, 2 ],
            \[ 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 2, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 1, 0, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 2, 3, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 2, 3, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 1, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 3 ],
            \[ 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 2, 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 ],
            \[ 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 62504>, <20, 978432>, <24, 7982656>, <28, 40659968>, 
            <32, 139240252>, <36, 310849024>, <40, 543243712>, <44, 737857536>, <48, 797732440>, <52, 710253568>, <56, 
            497930880>, <60, 288868352>, <64, 138706694>, <68, 51874816>, <72, 20049792>, <76, 5525504>, <80, 2270744>, 
            <84, 570880>, <88, 240448>, <92, 44032>, <96, 21564>, <100, 1536>, <104, 1728>, <112, 232>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0 ],
            \[ 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 3, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2 ],
            \[ 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 3, 2, 2, 2, 0, 0, 0, 2, 0, 2 ],
            \[ 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 2, 0, 0, 2, 2, 2, 0, 2 ],
            \[ 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 2, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 3, 0, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 2, 1, 2, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 0, 3, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 1 ],
            \[ 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 2, 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 ],
            \[ 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 64520>, <20, 970240>, <24, 7945440>, <28, 40643584>, 
            <32, 139545564>, <36, 310996480>, <40, 542235296>, <44, 737644544>, <48, 799338264>, <52, 710253568>, <56, 
            496687808>, <60, 289081344>, <64, 139022918>, <68, 51727360>, <72, 20180800>, <76, 5541888>, <80, 2200440>, 
            <84, 579072>, <88, 235104>, <92, 44032>, <96, 25180>, <100, 1536>, <104, 2080>, <112, 232>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0 ],
            \[ 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 3, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2 ],
            \[ 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 3, 0, 2, 2, 2, 0, 0, 2, 0, 0 ],
            \[ 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 3, 0, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 2, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 3, 0, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 3, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 1, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 1, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 3, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 2, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 1 ],
            \[ 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 2, 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 ],
            \[ 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 62568>, <20, 978432>, <24, 7971840>, <28, 40659968>, 
            <32, 139310076>, <36, 310849024>, <40, 543050496>, <44, 737857536>, <48, 798024920>, <52, 710253568>, <56, 
            497670144>, <60, 288868352>, <64, 138847366>, <68, 51874816>, <72, 19998208>, <76, 5525504>, <80, 2290520>, 
            <84, 570880>, <88, 232448>, <92, 44032>, <96, 23036>, <100, 1536>, <104, 1792>, <112, 232>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0 ],
            \[ 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 3, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2 ],
            \[ 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 3, 2, 0, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2 ],
            \[ 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 3, 0, 2, 2, 2, 0, 2, 0 ],
            \[ 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 3, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 3, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 3, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2, 0, 1, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 2, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 1 ],
            \[ 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 2, 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 ],
            \[ 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 59144>, <20, 1016064>, <24, 7834144>, <28, 40720896>, 
            <32, 139816540>, <36, 310161664>, <40, 542597344>, <44, 739112960>, <48, 797728536>, <52, 709526016>, <56, 
            498291008>, <60, 288726016>, <64, 138665286>, <68, 52095488>, <72, 19921344>, <76, 5535744>, <80, 2296952>, 
            <84, 548096>, <88, 246432>, <92, 39424>, <96, 24796>, <100, 1280>, <104, 1888>, <112, 232>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0 ],
            \[ 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2 ],
            \[ 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 0, 0, 2, 2, 0, 0, 0, 2, 0 ],
            \[ 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 3, 0, 0, 0, 2, 0, 2, 0, 0 ],
            \[ 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 3, 2, 0, 2, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 3, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 3, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 2, 1, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 1, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 1, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 3 ],
            \[ 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 2, 0, 2, 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 ],
            \[ 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 61096>, <20, 986624>, <24, 7981248>, <28, 40676352>, 
            <32, 139168956>, <36, 310701568>, <40, 543640384>, <44, 738070528>, <48, 796972888>, <52, 710253568>, <56, 
            498551680>, <60, 288655360>, <64, 138576390>, <68, 52022272>, <72, 19950208>, <76, 5509120>, <80, 2316952>, 
            <84, 562688>, <88, 241600>, <92, 44032>, <96, 20412>, <100, 1536>, <104, 1600>, <112, 232>, <128, 1> ]>
]
;