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

list:=
[
rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 2, 1, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 1, 2, 2, 0, 2, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 2, 0, 2, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 1, 2, 0, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 1, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 111276>, <24, 16364092>, <32, 268730848>, <40, 
        1094038596>, <48, 1601854008>, <56, 992220376>, <64, 279631630>, <72, 38698376>, <80, 3140252>, <88, 169516>, 
        <96, 8016>, <104, 244>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 0, 0, 0, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 1, 2, 0, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 1, 2, 2, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 1, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 111264>, <24, 16364848>, <32, 268726124>, <40, 
        1094051632>, <48, 1601834048>, <56, 992238688>, <64, 279621158>, <72, 38702560>, <80, 3138656>, <88, 170096>, 
        <96, 7916>, <104, 240>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 2, 1, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 0, 0, 2, 2, 0, 2, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0, 2, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 1, 0, 2, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 1, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 111036>, <24, 16373228>, <32, 268677904>, <40, 
        1094174292>, <48, 1601669592>, <56, 992351416>, <64, 279598702>, <72, 38684840>, <80, 3149036>, <88, 169372>, 
        <96, 7616>, <104, 196>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 0, 1, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 0, 2, 0, 2, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 1, 2, 2, 2, 0, 2, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 2, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 1, 2, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 1, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110632>, <24, 16376504>, <32, 268665060>, <40, 
        1094206568>, <48, 1601612944>, <56, 992421808>, <64, 279537942>, <72, 38719824>, <80, 3136520>, <88, 171800>, 
        <96, 7428>, <104, 200>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 1, 2, 2, 0, 2, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 1, 2, 2, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 1, 2, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 1, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 111368>, <24, 16358088>, <32, 268766884>, <40, 
        1093946232>, <48, 1601976528>, <56, 992140240>, <64, 279641878>, <72, 38716400>, <80, 3130856>, <88, 170216>, 
        <96, 8260>, <104, 280>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 0, 1, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 1, 2, 0, 2, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0, 2, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 1, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110716>, <24, 16378460>, <32, 268651376>, <40, 
        1094240644>, <48, 1601575640>, <56, 992428696>, <64, 279564206>, <72, 38691208>, <80, 3148844>, <88, 169804>, 
        <96, 7456>, <104, 180>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 2, 1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 0, 2, 0, 0, 2, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 2, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 1, 0, 2, 0, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 1, 0, 2, 0, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 1, 0, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 1, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 1, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110808>, <24, 16379448>, <32, 268642964>, <40, 
        1094264392>, <48, 1601542640>, <56, 992451376>, <64, 279559670>, <72, 38688400>, <80, 3149816>, <88, 170264>, 
        <96, 7284>, <104, 168>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 0, 1, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 2, 2, 0, 0, 2, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 0, 2, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 1, 2, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, 1, 2, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0, 1, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 111440>, <24, 16360800>, <32, 268748476>, <40, 
        1093993344>, <48, 1601919264>, <56, 992165440>, <64, 279657670>, <72, 38691968>, <80, 3141584>, <88, 168800>, 
        <96, 8188>, <104, 256>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 2, 1, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 0, 2, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 1, 0, 2, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 1, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110876>, <24, 16372028>, <32, 268689744>, <40, 
        1094137892>, <48, 1601727256>, <56, 992298328>, <64, 279629166>, <72, 38671560>, <80, 3155276>, <88, 166828>, 
        <96, 8064>, <104, 212>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 1, 0, 2, 0, 2, 0, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 1, 2, 2, 2, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 1, 2, 0, 2, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 1, 2, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 1, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 1, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110664>, <24, 16380760>, <32, 268637636>, <40, 
        1094277064>, <48, 1601523152>, <56, 992471536>, <64, 279545558>, <72, 38694928>, <80, 3147944>, <88, 170552>, 
        <96, 7268>, <104, 168>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 2, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 2, 2, 2, 2, 2, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 2, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 1, 0, 2, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 1, 2, 0, 2, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 1, 2, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 1, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 1, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 111564>, <24, 16352188>, <32, 268800384>, <40, 
        1093859972>, <48, 1602096760>, <56, 992048344>, <64, 279674190>, <72, 38716680>, <80, 3128636>, <88, 169644>, 
        <96, 8560>, <104, 308>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 2, 1, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 1, 2, 2, 0, 0, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 1, 0, 0, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 1, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 1, 2, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110984>, <24, 16375656>, <32, 268663012>, <40, 
        1094215320>, <48, 1601606352>, <56, 992410384>, <64, 279563926>, <72, 38699312>, <80, 3143528>, <88, 171272>, 
        <96, 7300>, <104, 184>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 0, 1, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 1, 2, 2, 0, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 0, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 1, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110872>, <24, 16364696>, <32, 268735892>, <40, 
        1094019880>, <48, 1601877872>, <56, 992213488>, <64, 279618806>, <72, 38711632>, <80, 3136568>, <88, 168952>, 
        <96, 8308>, <104, 264>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 2, 1, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 0, 2, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 1, 2, 0, 0, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 1, 2, 2, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 1, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 111356>, <24, 16356556>, <32, 268776592>, <40, 
        1093922100>, <48, 1602004824>, <56, 992129656>, <64, 279630958>, <72, 38731112>, <80, 3124268>, <88, 171260>, 
        <96, 8256>, <104, 292>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 0, 1, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 1, 2, 0, 2, 0, 2, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 1, 0, 2, 2, 0, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 1, 0, 2, 0, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 1, 2, 0, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 1, 2, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 1, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 111072>, <24, 16373248>, <32, 268677644>, <40, 
        1094172352>, <48, 1601681216>, <56, 992325376>, <64, 279630566>, <72, 38661760>, <80, 3158816>, <88, 167168>, 
        <96, 7820>, <104, 192>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 2, 1, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 2, 0, 2, 0, 2, 2, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 1, 0, 0, 0, 0, 0, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 1, 0, 2, 0, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 1, 2, 0, 2, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 1, 0, 0, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 1, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110872>, <24, 16369528>, <32, 268704724>, <40, 
        1094103432>, <48, 1601759856>, <56, 992303536>, <64, 279587446>, <72, 38712080>, <80, 3137336>, <88, 170328>, 
        <96, 7860>, <104, 232>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 0, 2, 2, 2, 2, 2, 2, 0, 0 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 2, 0, 0, 0, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 1, 2, 0, 0, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 1, 0, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, 1, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 1, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110856>, <24, 16379096>, <32, 268643972>, <40, 
        1094263240>, <48, 1601541968>, <56, 992455408>, <64, 279553622>, <72, 38693392>, <80, 3147368>, <88, 170936>, 
        <96, 7204>, <104, 168>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 2, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 1, 2, 0, 2, 2, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 1, 2, 2, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 1, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110896>, <24, 16365728>, <32, 268728604>, <40, 
        1094040192>, <48, 1601848032>, <56, 992238016>, <64, 279607942>, <72, 38714240>, <80, 3135536>, <88, 169632>, 
        <96, 8156>, <104, 256>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 2, 1, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 1, 2, 0, 0, 0, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 0, 2, 0, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 1, 0, 0, 0, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 1, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 2, 0, 2, 2 ],
        \[ 0, 0, 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, 1, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 111180>, <24, 16367340>, <32, 268712096>, <40, 
        1094087284>, <48, 1601785592>, <56, 992273464>, <64, 279611918>, <72, 38699368>, <80, 3140924>, <88, 170012>, 
        <96, 7824>, <104, 228>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 2, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 2, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 2, 0, 2, 2, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 0, 2, 0, 2, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 1, 0, 0, 2, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 1, 0, 0, 2, 2, 2, 0 ],
        \[ 0, 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, 1, 2, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 111384>, <24, 16360472>, <32, 268750868>, <40, 
        1093990696>, <48, 1601910128>, <56, 992197360>, <64, 279613430>, <72, 38725456>, <80, 3127352>, <88, 171896>, 
        <96, 7924>, <104, 264>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 2, 1, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 2, 0, 2, 2, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 1, 2, 2, 2, 0, 2, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 1, 2, 2, 2, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 1, 2, 0, 2, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 1, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110864>, <24, 16375072>, <32, 268670588>, <40, 
        1094188096>, <48, 1601659040>, <56, 992345536>, <64, 279619142>, <72, 38665216>, <80, 3158672>, <88, 166944>, 
        <96, 7868>, <104, 192>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 2, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 1, 2, 2, 0, 0, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 2, 0, 2, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 1, 2, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 1, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 1, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 111128>, <24, 16364680>, <32, 268730676>, <40, 
        1094035544>, <48, 1601861872>, <56, 992210128>, <64, 279640758>, <72, 38691888>, <80, 3143864>, <88, 168232>, 
        <96, 8212>, <104, 248>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 1, 0, 0, 0, 2, 2, 2, 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, 2, 1, 0, 2, 0, 2, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 1, 2, 2, 2, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 1, 2, 0, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 1, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110964>, <24, 16370388>, <32, 268697464>, <40, 
        1094122572>, <48, 1601737608>, <56, 992310088>, <64, 279599038>, <72, 38698520>, <80, 3142916>, <88, 169636>, 
        <96, 7816>, <104, 220>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 2, 1, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 1, 2, 0, 0, 0, 2, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 1, 2, 0, 2, 0, 2, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 1, 2, 2, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, 1, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 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, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 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, 1, 1, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110840>, <24, 16376584>, <32, 268661140>, <40, 
        1094214168>, <48, 1601619120>, <56, 992382160>, <64, 279598198>, <72, 38673584>, <80, 3155480>, <88, 168104>, 
        <96, 7668>, <104, 184>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 2, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 1, 2, 0, 0, 0, 0, 0, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 1, 0, 2, 2, 0, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 1, 0, 0, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 1, 2, 0, 0, 2, 2, 2 ],
        \[ 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, 1, 2, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 1, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 111152>, <24, 16365712>, <32, 268723388>, <40, 
        1094055856>, <48, 1601832032>, <56, 992234656>, <64, 279629894>, <72, 38694496>, <80, 3142832>, <88, 168912>, 
        <96, 8060>, <104, 240>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 0, 1, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 2, 2, 0, 2, 0, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 2, 0, 2, 0, 0, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 2, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 1, 0, 0, 0, 0, 0, 2 ],
        \[ 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, 2, 1, 2, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 1, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 1, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110784>, <24, 16378544>, <32, 268649100>, <40, 
        1094248688>, <48, 1601561728>, <56, 992442976>, <64, 279554406>, <72, 38696544>, <80, 3146240>, <88, 170736>, 
        <96, 7308>, <104, 176>, <112, 64>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 0, 1, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 2, 0, 0, 0, 2, 2, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 2, 2, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 1, 2, 2, 2, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 1, 2, 0, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 1, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 1, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1 ],
        \[ 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 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, 0, 0 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110996>, <24, 16360532>, <32, 268760088>, <40, 
        1093956236>, <48, 1601969608>, <56, 992138056>, <64, 279652350>, <72, 38704536>, <80, 3138212>, <88, 167716>, 
        <96, 8616>, <104, 284>, <112, 64>, <128, 1> ]>

];