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

list:=
[
rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2 ],
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 2, 1, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 2, 1, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 2, 0, 2, 0, 0, 2, 1, 2, 2, 2, 2, 2, 0, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 2, 0, 0, 0, 2, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 2, 2, 0, 0, 0, 2, 1, 0, 0, 2, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 2, 2, 2, 2, 0, 0, 2, 1, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 1, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 1, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0, 2, 1, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 1, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 1, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110784>, <24, 16390792>, <32, 268425172>, <40, 
        1094783864>, <48, 1601316056>, <56, 992101968>, <64, 279820982>, <72, 38733552>, <80, 3121456>, <88, 156840>, 
        <96, 5748>, <104, 24>, <112, 56>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0 ],
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 2, 1, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 2, 0, 0, 0, 0, 2, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2, 1, 2, 2, 2, 0, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 0, 2, 2, 2, 2, 0, 1, 0, 0, 2, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 2, 2, 2, 2, 2, 0, 2, 1, 2, 2, 0, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 1, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 1, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 1, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110888>, <24, 16376848>, <32, 268512108>, <40, 
        1094555440>, <48, 1601630184>, <56, 991876512>, <64, 279880678>, <72, 38752096>, <80, 3110200>, <88, 155472>, 
        <96, 6700>, <104, 112>, <112, 56>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0 ],
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 2, 0, 1, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 0, 1, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 2, 0, 0, 1, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 2, 0, 0, 0, 1, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 2, 0, 2, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 2, 0, 2, 2, 0, 2, 2, 1, 0, 0, 2, 2, 2, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 2, 0, 2, 0, 0, 2, 2, 1, 2, 0, 0, 2, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 1, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1, 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, 0, 0, 2, 2, 2, 0, 2, 1, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 1, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 111032>, <24, 16378208>, <32, 268499548>, <40, 
        1094593760>, <48, 1601569160>, <56, 991933632>, <64, 279846854>, <72, 38767296>, <80, 3103240>, <88, 158176>, 
        <96, 6236>, <104, 96>, <112, 56>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2 ],
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 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, 2, 0, 0, 2, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 2, 1, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 2, 2, 2, 1, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 2, 2, 1, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 2, 0, 2, 2, 2, 1, 2, 2, 0, 2, 0, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 2, 0, 2, 2, 0, 0, 2, 1, 0, 0, 0, 2, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 2, 0, 0, 0, 2, 2, 2, 1, 2, 0, 0, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 1, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 1, 0, 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, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 1, 2, 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, 0, 2, 0, 2, 0, 1, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 1, 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, 2, 2, 2, 2, 2, 0, 2, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110440>, <24, 16390224>, <32, 268436524>, <40, 
        1094748656>, <48, 1601364584>, <56, 992072736>, <64, 279820646>, <72, 38742240>, <80, 3119224>, <88, 155792>, 
        <96, 6124>, <104, 48>, <112, 56>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 2, 2, 1, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 2, 0, 0, 2, 1, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 2, 0, 0, 2, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 2, 0, 0, 0, 2, 2, 1, 2, 0, 2, 0, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 2, 2, 2, 0, 0, 0, 0, 1, 2, 2, 2, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2, 0, 1, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 1, 0, 0, 0, 0, 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, 2, 1, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 1, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 0, 1, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 1, 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, 2, 2, 2, 2, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 111016>, <24, 16371376>, <32, 268543276>, <40, 
        1094479568>, <48, 1601721320>, <56, 991834848>, <64, 279858278>, <72, 38790048>, <80, 3092152>, <88, 158576>, 
        <96, 6636>, <104, 144>, <112, 56>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0 ],
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 2, 2, 1, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 0, 0, 2, 1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 0, 2, 1, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 2, 0, 0, 2, 2, 0, 1, 2, 0, 0, 2, 2, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 2, 0, 2, 0, 0, 2, 0, 1, 2, 0, 2, 0, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 2, 2, 0, 2, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 2, 1, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 1, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 1, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 2, 1, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 1, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110784>, <24, 16381640>, <32, 268482900>, <40, 
        1094635192>, <48, 1601509080>, <56, 991986384>, <64, 279819190>, <72, 38775664>, <80, 3101488>, <88, 158696>, 
        <96, 6132>, <104, 88>, <112, 56>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2 ],
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 2, 2, 1, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 0, 2, 1, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 2, 1, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 2, 2, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 2, 2, 0, 0, 0, 2, 1, 0, 0, 2, 2, 2, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 2, 0, 2, 2, 1, 0, 2, 0, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 0, 0, 2, 0, 0, 2, 2, 1, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 1, 0, 0, 0, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 1, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 1, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 1, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 1, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110536>, <24, 16384688>, <32, 268469708>, <40, 
        1094662800>, <48, 1601481256>, <56, 991990752>, <64, 279839910>, <72, 38751776>, <80, 3113560>, <88, 155760>, 
        <96, 6412>, <104, 80>, <112, 56>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0 ],
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 2, 2, 0, 2, 0, 0, 0, 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, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 2, 2, 1, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 2, 0, 2, 2, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 2, 0, 2, 2, 1, 2, 0, 2, 2, 0, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 2, 0, 2, 2, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 0, 0, 2, 0, 2, 0, 1, 2, 2, 0, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 2, 2, 2, 2, 0, 0, 0, 1, 2, 2, 2, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 1, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 1, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 1, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 1, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 1, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110608>, <24, 16390200>, <32, 268432260>, <40, 
        1094765512>, <48, 1601332728>, <56, 992109360>, <64, 279791638>, <72, 38759824>, <80, 3110848>, <88, 158488>, 
        <96, 5732>, <104, 40>, <112, 56>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2 ],
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 2, 2, 1, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 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, 0, 2, 0, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 2, 0, 2, 2, 1, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 2, 2, 2, 0, 0, 2, 1, 2, 2, 0, 2, 2, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 2, 2, 2, 0, 2, 2, 0, 1, 2, 2, 0, 2, 2, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2, 1, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 1, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 1, 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, 2, 2, 0, 2, 0, 2, 1, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 1, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 1, 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, 2, 0, 0, 2, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110480>, <24, 16391352>, <32, 268427652>, <40, 
        1094776264>, <48, 1601316600>, <56, 992125488>, <64, 279780886>, <72, 38764432>, <80, 3109696>, <88, 158616>, 
        <96, 5732>, <104, 40>, <112, 56>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2 ],
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 2, 2, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 0, 2, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 0, 2, 2, 1, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 0, 2, 1, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 2, 0, 0, 0, 1, 2, 0, 0, 2, 2, 2, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 2, 0, 2, 2, 0, 1, 2, 0, 2, 2, 2, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 2, 2, 2, 0, 0, 2, 2, 0, 1, 0, 0, 0, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 2, 2, 2, 0, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 1, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 1, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 1, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 1, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 111240>, <24, 16378672>, <32, 268492172>, <40, 
        1094615184>, <48, 1601543080>, <56, 991942368>, <64, 279858726>, <72, 38753312>, <80, 3108376>, <88, 157936>, 
        <96, 6092>, <104, 80>, <112, 56>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2 ],
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 2, 2, 1, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 0, 0, 0, 1, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 2, 2, 0, 2, 0, 1, 2, 2, 2, 2, 0, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 2, 2, 0, 2, 2, 2, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 2, 0, 0, 0, 0, 0, 2, 1, 2, 0, 2, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 0, 1, 0, 2, 0, 2, 2, 2 ],
        \[ 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, 0, 1, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 1, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 2, 1, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 1, 2, 2 ],
        \[ 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, 0, 2, 2, 0, 1, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 111200>, <24, 16373096>, <32, 268528756>, <40, 
        1094517848>, <48, 1601676824>, <56, 991847952>, <64, 279881462>, <72, 38762928>, <80, 3103312>, <88, 157192>, 
        <96, 6548>, <104, 120>, <112, 56>, <128, 1> ]>

];