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

list:=
[
rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 
            2, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 
            2, 2, 2, 2 ],
        \[ 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 2, 1, 2, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 
            0, 0, 2, 0 ],
        \[ 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 2, 0, 1, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 
            2, 2, 0, 0 ],
        \[ 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 2, 2, 0, 0, 1, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 
            0, 2, 0, 0 ],
        \[ 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 2, 0, 2, 2, 0, 1, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 
            2, 2, 0, 0 ],
        \[ 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 2, 2, 0, 0, 2, 0, 1, 2, 0, 0, 0, 2, 0, 0, 2, 2, 
            0, 2, 0, 2 ],
        \[ 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 2, 2, 2, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 2, 0, 
            2, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 2, 2, 0, 0, 0, 0, 2, 0, 1, 2, 2, 2, 2, 0, 0, 0, 
            2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 2, 2, 0, 0, 2, 2, 2, 0, 0, 1, 0, 0, 2, 0, 2, 0, 
            0, 2, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 1, 0, 0, 0, 0, 2, 
            0, 0, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 1, 2, 0, 0, 2, 
            2, 2, 0, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 1, 0, 2, 0, 
            0, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 1, 2, 0, 
            2, 0, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 1, 0, 
            0, 2, 0, 0 ],
        \[ 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 1, 
            0, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 
            1, 0, 0, 2 ],
        \[ 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 
            2, 1, 2, 0 ],
        \[ 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 
            2, 0, 1, 2 ],
        \[ 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 
            0, 2, 0, 1 ]
    ],
    dtb := \[ 34992, 0 ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 
            2, 0, 2, 0 ],
        \[ 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 
            2, 0, 2, 0 ],
        \[ 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 
            0, 0, 0, 2 ],
        \[ 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 
            2, 0, 0, 2 ],
        \[ 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 
            2, 0, 0, 2 ],
        \[ 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 2, 1, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 
            0, 2, 2, 0 ],
        \[ 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 2, 1, 2, 2, 0, 0, 2, 0, 0, 0, 0, 
            0, 2, 2, 0 ],
        \[ 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 2, 0, 2, 2, 0, 2, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 
            0, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 2, 0, 0, 2, 2, 0, 0, 2, 1, 2, 0, 2, 0, 0, 2, 0, 
            0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 2, 0, 0, 2, 2, 0, 2, 2, 0, 1, 0, 0, 2, 2, 2, 2, 
            0, 2, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 
            0, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, 1, 0, 2, 0, 2, 
            0, 2, 0, 0 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 1, 0, 0, 0, 
            2, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 1, 0, 0, 
            2, 0, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 1, 2, 
            0, 0, 0, 0 ],
        \[ 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 1, 
            0, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 
            1, 2, 0, 0 ],
        \[ 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 
            0, 1, 2, 2 ],
        \[ 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 
            2, 0, 1, 2 ],
        \[ 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, 
            2, 0, 0, 1 ]
    ],
    dtb := \[ 34850, 0 ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 
            2, 0, 2, 2 ],
        \[ 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 2, 
            0, 2, 2, 0 ],
        \[ 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 2, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 
            2, 0, 2, 0 ],
        \[ 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 2, 1, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, 
            0, 0, 2, 0 ],
        \[ 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 
            0, 2, 2, 2 ],
        \[ 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 2, 0, 2, 0, 2, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 
            2, 2, 2, 0 ],
        \[ 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 2, 2, 2, 2, 1, 2, 2, 0, 2, 2, 0, 2, 2, 2, 
            2, 0, 2, 0 ],
        \[ 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 2, 2, 0, 1, 2, 2, 2, 0, 0, 0, 0, 0, 
            0, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 2, 0, 0, 0, 0, 2, 0, 0, 1, 2, 2, 2, 2, 0, 2, 2, 
            0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 2, 0, 0, 2, 2, 0, 0, 1, 0, 0, 2, 2, 0, 2, 
            0, 0, 2, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 1, 2, 2, 0, 2, 0, 
            0, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 1, 0, 2, 2, 2, 
            0, 0, 0, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 1, 0, 0, 0, 
            2, 2, 2, 0 ],
        \[ 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 1, 2, 0, 
            2, 0, 0, 2 ],
        \[ 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 1, 2, 
            0, 2, 2, 0 ],
        \[ 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 1, 
            2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 
            1, 2, 2, 0 ],
        \[ 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 
            0, 1, 2, 0 ],
        \[ 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 
            0, 0, 1, 0 ],
        \[ 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 
            2, 2, 2, 1 ]
    ],
    dtb := \[ 34596, 0 ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 
            2, 0, 2, 2 ],
        \[ 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 2, 1, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 
            2, 0, 2, 2 ],
        \[ 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 2, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 
            2, 0, 0, 0 ],
        \[ 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 2, 0, 2, 1, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 
            2, 2, 2, 2 ],
        \[ 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 
            0, 2, 0, 2 ],
        \[ 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2, 
            0, 0, 2, 2 ],
        \[ 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 0, 
            0, 2, 2, 2 ],
        \[ 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 0, 2, 2, 2, 1, 2, 2, 2, 0, 2, 2, 2, 0, 
            2, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 2, 0, 2, 0, 0, 2, 2, 0, 1, 2, 2, 0, 0, 2, 0, 2, 
            0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 2, 0, 2, 2, 2, 0, 0, 0, 1, 2, 0, 0, 2, 0, 0, 
            2, 0, 0, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 
            2, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 1, 2, 0, 0, 2, 
            0, 0, 2, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 1, 2, 0, 0, 
            0, 2, 2, 0 ],
        \[ 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 0, 
            2, 0, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 1, 0, 
            0, 2, 2, 2 ],
        \[ 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 1, 
            2, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 
            1, 0, 0, 0 ],
        \[ 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 
            2, 1, 0, 0 ],
        \[ 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 
            2, 2, 1, 2 ],
        \[ 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, 
            2, 2, 0, 1 ]
    ],
    dtb := \[ 34584, 0 ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2, 
            2, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 
            2, 2, 0, 0 ],
        \[ 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 
            2, 0, 0, 2 ],
        \[ 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 
            2, 0, 0, 0 ],
        \[ 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 
            2, 0, 0, 0 ],
        \[ 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 
            0, 0, 0, 0 ],
        \[ 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 2, 1, 0, 2, 2, 2, 2, 0, 0, 0, 2, 
            0, 0, 2, 0 ],
        \[ 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 2, 2, 0, 0, 2, 2, 2, 1, 0, 2, 2, 2, 0, 0, 2, 2, 
            0, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 2, 2, 0, 0, 2, 0, 0, 2, 1, 2, 0, 2, 0, 0, 0, 2, 
            0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 2, 2, 0, 2, 2, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 
            0, 2, 2, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 1, 2, 2, 0, 0, 0, 
            2, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 2, 2, 2, 
            0, 0, 0, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 1, 0, 2, 2, 
            2, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 1, 0, 0, 
            0, 2, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 1, 2, 
            2, 2, 2, 0 ],
        \[ 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 1, 
            2, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 
            1, 2, 0, 2 ],
        \[ 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 
            0, 1, 0, 0 ],
        \[ 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 
            2, 2, 1, 2 ],
        \[ 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 
            0, 2, 0, 1 ]
    ],
    dtb := \[ 34794, 0 ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 
            2, 0, 2, 0 ],
        \[ 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 
            2, 2, 2, 0 ],
        \[ 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 2, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 
            2, 0, 0, 2 ],
        \[ 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 2, 2, 1, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 
            2, 2, 2, 0 ],
        \[ 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 
            0, 0, 2, 2 ],
        \[ 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 0, 1, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 
            0, 2, 2, 0 ],
        \[ 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 2, 2, 2, 0, 0, 
            0, 2, 0, 2 ],
        \[ 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 2, 2, 2, 2, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 
            0, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 2, 0, 2, 2, 2, 0, 2, 1, 0, 2, 0, 0, 0, 2, 2, 
            0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 2, 1, 0, 0, 0, 0, 0, 2, 
            2, 0, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 1, 0, 0, 2, 0, 2, 
            2, 2, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 1, 2, 0, 2, 2, 
            0, 0, 2, 0 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 1, 2, 2, 0, 
            2, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 1, 0, 0, 
            0, 2, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, 1, 2, 
            2, 2, 2, 2 ],
        \[ 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 1, 
            0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 
            1, 2, 0, 0 ],
        \[ 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 
            0, 1, 2, 2 ],
        \[ 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 
            2, 0, 1, 2 ],
        \[ 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 
            2, 0, 0, 1 ]
    ],
    dtb := \[ 34552, 0 ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 
            0, 0, 2, 0 ],
        \[ 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 
            2, 0, 2, 0 ],
        \[ 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 2, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 
            2, 0, 0, 2 ],
        \[ 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 2, 2, 2, 1, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 
            2, 0, 0, 2 ],
        \[ 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 2, 2, 0, 2, 1, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 
            2, 0, 2, 0 ],
        \[ 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 
            2, 2, 2, 2 ],
        \[ 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 2, 2, 2, 0, 2, 2, 1, 2, 2, 2, 2, 0, 0, 2, 2, 0, 
            0, 2, 2, 0 ],
        \[ 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 2, 2, 2, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 
            2, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 2, 0, 0, 2, 2, 2, 0, 2, 1, 2, 2, 0, 0, 0, 2, 2, 
            2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 2, 0, 0, 0, 2, 0, 0, 2, 0, 1, 0, 0, 2, 2, 0, 2, 
            2, 0, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 1, 0, 0, 0, 2, 0, 
            0, 0, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 1, 0, 0, 0, 2, 
            2, 2, 2, 2 ],
        \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 1, 2, 0, 0, 
            0, 2, 2, 0 ],
        \[ 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 2, 0, 1, 0, 0, 
            0, 0, 2, 2 ],
        \[ 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 1, 0, 
            0, 0, 2, 0 ],
        \[ 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 1, 
            0, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2, 
            1, 0, 2, 2 ],
        \[ 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 
            2, 1, 2, 2 ],
        \[ 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 
            0, 0, 1, 2 ],
        \[ 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 
            0, 0, 0, 1 ]
    ],
    dtb := \[ 34540, 0 ]>


];