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

[ PowerStructure(Rec) |
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2 ],
            \[ 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 3, 2, 0, 2, 0, 2, 2, 2, 2, 0 ],
            \[ 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 2, 2, 2, 2, 0, 2, 0 ],
            \[ 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 3, 2, 2, 2, 2, 0, 2, 0 ],
            \[ 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 3, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 2, 3, 2, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 0, 0, 3, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 3, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 3, 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, 0, 2, 0, 0, 0, 3, 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, 0, 2, 0, 2, 0, 2, 2, 1 ],
            \[ 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, 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, 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 ],
            \[ 2, 0, 2, 0, 0, 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 ],
            \[ 2, 2, 0, 0, 0, 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, 0, 2, 2, 0, 2, 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, 0 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 61384>, <20, 980736>, <24, 8059232>, <28, 40547840>, 
            <32, 138041948>, <36, 310507264>, <40, 546126624>, <44, 739756032>, <48, 796192600>, <52, 708095488>, <56, 
            496501696>, <60, 289129472>, <64, 139896134>, <68, 52487680>, <72, 20284480>, <76, 5457920>, <80, 2125752>, 
            <84, 490240>, <88, 180448>, <92, 30208>, <96, 12508>, <100, 768>, <104, 672>, <112, 168>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 2, 1, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 2, 3, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0 ],
            \[ 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 1, 2, 2, 0, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 2, 3, 0, 2, 2, 2, 2, 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, 2, 0, 1, 2, 2, 0, 0, 2, 2, 2 ],
            \[ 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 1, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2, 1, 0, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 2, 1, 2, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 1, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 3, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 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, 2, 2, 0, 2, 0, 0, 2, 1 ],
            \[ 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, 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, 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 ],
            \[ 2, 0, 2, 0, 0, 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 ],
            \[ 2, 2, 0, 0, 0, 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, 0, 2, 2, 0, 2, 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, 0 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 60744>, <20, 988928>, <24, 8013536>, <28, 40564224>, 
            <32, 138236124>, <36, 310359808>, <40, 545836448>, <44, 739969024>, <48, 796366424>, <52, 708095488>, <56, 
            496466624>, <60, 288916480>, <64, 139919942>, <68, 52635136>, <72, 20261184>, <76, 5441536>, <80, 2126648>, 
            <84, 482048>, <88, 181344>, <92, 30208>, <96, 13660>, <100, 768>, <104, 800>, <112, 168>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 3, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0 ],
            \[ 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 3, 2, 2, 0, 2, 0, 0, 0, 2, 2 ],
            \[ 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 2, 3, 0, 2, 2, 0, 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, 0, 3, 2, 2, 0, 0, 0, 2, 2 ],
            \[ 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 3, 0, 2, 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, 2, 2, 2, 0, 3, 0, 2, 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, 0, 0, 0, 2, 2, 3, 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, 0, 2, 0, 2, 0, 0, 3, 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, 0, 2, 0, 2, 0, 0, 0, 3, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 1 ],
            \[ 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, 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, 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 ],
            \[ 2, 0, 2, 0, 0, 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 ],
            \[ 2, 2, 0, 0, 0, 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, 0, 2, 2, 0, 2, 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, 0 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 62248>, <20, 972544>, <24, 8088448>, <28, 40531456>, 
            <32, 137949052>, <36, 310654720>, <40, 546148480>, <44, 739543040>, <48, 796398360>, <52, 708095488>, <56, 
            496242432>, <60, 289342464>, <64, 139981190>, <68, 52340224>, <72, 20301056>, <76, 5474304>, <80, 2123416>, 
            <84, 498432>, <88, 175488>, <92, 30208>, <96, 12668>, <100, 768>, <104, 640>, <112, 168>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 2, 1, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 2, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2 ],
            \[ 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 1, 2, 0, 2, 0, 0, 2, 0, 0, 2 ],
            \[ 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 1, 0, 0, 0, 0, 2, 0, 0, 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, 0, 0, 2, 2, 0 ],
            \[ 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 2, 0, 0, 1, 0, 2, 2, 0, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 3, 0, 0, 2, 0, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 2, 3, 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, 2, 2, 0, 2, 2, 2, 3, 0, 0, 2 ],
            \[ 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, 0, 0, 2, 2, 1, 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, 2, 0, 2, 2, 3, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 1 ],
            \[ 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, 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, 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 ],
            \[ 2, 0, 2, 0, 0, 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 ],
            \[ 2, 2, 0, 0, 0, 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, 0, 2, 2, 0, 2, 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, 0 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 60328>, <20, 988928>, <24, 8050240>, <28, 40564224>, 
            <32, 138010748>, <36, 310359808>, <40, 546425152>, <44, 739969024>, <48, 795560472>, <52, 708095488>, <56, 
            497040512>, <60, 288916480>, <64, 139774342>, <68, 52635136>, <72, 20206720>, <76, 5441536>, <80, 2159384>, 
            <84, 482048>, <88, 183616>, <92, 30208>, <96, 11388>, <100, 768>, <104, 576>, <112, 168>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 2, 1, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 2, 0, 3, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0 ],
            \[ 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 3, 2, 0, 0, 2, 2, 2, 0, 0, 2 ],
            \[ 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 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, 2, 2, 2, 0, 2, 1, 2, 0, 2, 0, 2, 0, 2 ],
            \[ 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 2, 2, 1, 0, 2, 0, 0, 2, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 1, 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, 2, 2, 2, 2, 2, 2, 1, 0, 0, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 3, 0, 0, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 3, 2, 0 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 3, 2 ],
            \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 3 ],
            \[ 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, 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, 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 ],
            \[ 2, 0, 2, 0, 0, 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 ],
            \[ 2, 2, 0, 0, 0, 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, 0, 2, 2, 0, 2, 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, 0 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 61192>, <20, 980736>, <24, 8070304>, <28, 40547840>, 
            <32, 137975580>, <36, 310507264>, <40, 546298336>, <44, 739756032>, <48, 795959256>, <52, 708095488>, <56, 
            496665664>, <60, 289129472>, <64, 139857606>, <68, 52487680>, <72, 20265408>, <76, 5457920>, <80, 2137080>, 
            <84, 490240>, <88, 180512>, <92, 30208>, <96, 11932>, <100, 768>, <104, 608>, <112, 168>, <128, 1> ]>
]
;