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

list:=
[
rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 
            0, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 2, 1, 0, 2, 0, 0, 2, 0, 2, 2, 0, 
            0, 2, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 
            2, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 2, 2, 1, 0, 0, 0, 2, 2, 2, 2, 
            0, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 2, 2, 2, 0, 1, 0, 0, 2, 0, 2, 2, 
            2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 2, 2, 2, 0, 1, 0, 2, 2, 0, 2, 
            2, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 2, 0, 2, 0, 0, 1, 2, 0, 2, 2, 
            0, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 0, 1, 0, 2, 2, 
            0, 0, 0, 0 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 1, 0, 2, 
            2, 0, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 1, 0, 
            0, 2, 2, 0 ],
        \[ 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 1, 
            2, 0, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, 0, 
            1, 0, 2, 2 ],
        \[ 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 
            0, 1, 0, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 
            2, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 
            0, 0, 2, 1 ],
        \[ 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 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, 34733>, <24, 37536964>, <32, 2587353827>, <40, 
        36984571432>, <48, 174941611982>, <56, 346506969916>, <64, 327834321720>, <72, 160708323120>, <80, 42918082688>,
        <88, 6419637500>, <96, 545094788>, <104, 26982696>, <112, 1041026>, <120, 60292>, <128, 4831>, <136, 256>, <144,
        3>, <160, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 
            2, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 2, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 
            2, 0, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 2, 2, 0, 2, 2, 0, 2, 0, 
            0, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 2, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 
            2, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 2, 2, 2, 0, 1, 2, 2, 0, 0, 2, 2, 
            0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 2, 0, 2, 1, 2, 2, 2, 0, 0, 
            0, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 2, 0, 2, 2, 2, 1, 0, 2, 0, 2, 
            0, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 1, 2, 2, 2, 
            2, 2, 0, 0 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 1, 2, 2, 
            0, 2, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 1, 2, 
            2, 0, 0, 2 ],
        \[ 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 1, 
            2, 0, 0, 2 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 
            1, 0, 0, 2 ],
        \[ 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 
            0, 1, 0, 0 ],
        \[ 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 
            0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 
            0, 2, 2, 1 ],
        \[ 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 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, 34779>, <24, 37538400>, <32, 2587338397>, <40, 
        36984636800>, <48, 174941458156>, <56, 346507188704>, <64, 327834140658>, <72, 160708381440>, <80, 42918124442>,
        <88, 6419578912>, <96, 545124354>, <104, 26975872>, <112, 1041436>, <120, 60320>, <128, 4845>, <136, 256>, <144,
        3>, <160, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 
            0, 2, 0, 0 ],
        \[ 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 2, 0, 2, 2, 2, 2, 2, 2, 0, 
            2, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 2, 2, 1, 0, 2, 0, 2, 0, 2, 0, 0, 
            0, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 2, 1, 0, 2, 2, 0, 0, 2, 2, 
            2, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 2, 0, 1, 2, 0, 0, 2, 2, 0, 
            2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 2, 0, 2, 1, 0, 2, 0, 0, 2, 
            0, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, 2, 2, 2, 2, 
            2, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 0, 2, 
            0, 2, 0, 0 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 1, 0, 0, 
            2, 2, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 1, 2, 
            0, 0, 2, 0 ],
        \[ 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 1, 
            0, 2, 0, 2 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 
            1, 2, 0, 2 ],
        \[ 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 2, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 
            2, 1, 2, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 
            0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 
            0, 0, 2, 1 ],
        \[ 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 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, 34685>, <24, 37540764>, <32, 2587321211>, <40, 
        36984699256>, <48, 174941325966>, <56, 346507354372>, <64, 327834039840>, <72, 160708353552>, <80, 42918237200>,
        <88, 6419473892>, <96, 545177580>, <104, 26960376>, <112, 1043810>, <120, 60156>, <128, 4855>, <136, 256>, <144,
        3>, <160, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 
            0, 2, 0, 0 ],
        \[ 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 
            0, 0, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 2, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 
            0, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 2, 1, 0, 0, 2, 2, 2, 2, 0, 
            2, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 2, 2, 2, 0, 1, 0, 2, 2, 2, 2, 0, 
            2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 2, 2, 2, 0, 1, 2, 2, 0, 0, 2, 
            2, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 2, 2, 0, 2, 2, 1, 0, 2, 2, 2, 
            2, 0, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 1, 2, 0, 2, 
            2, 0, 0, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 1, 2, 0, 
            0, 0, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 0, 
            0, 2, 0, 0 ],
        \[ 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 1, 
            2, 0, 0, 2 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 
            1, 2, 2, 2 ],
        \[ 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 
            2, 1, 0, 0 ],
        \[ 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 
            2, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 
            0, 2, 0, 1 ],
        \[ 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 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, 34633>, <24, 37537500>, <32, 2587353655>, <40, 
        36984565528>, <48, 174941634058>, <56, 346506928676>, <64, 327834369228>, <72, 160708286544>, <80, 42918103796>,
        <88, 6419625828>, <96, 545101728>, <104, 26979352>, <112, 1041974>, <120, 60188>, <128, 4827>, <136, 256>, <144,
        3>, <160, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 
            0, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 2, 1, 0, 0, 2, 2, 0, 2, 2, 2, 0, 
            0, 2, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 2, 0, 1, 2, 0, 2, 2, 2, 2, 0, 0, 
            2, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 
            0, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 2, 0, 2, 2, 2, 0, 
            2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 0, 0, 0, 2, 1, 2, 2, 2, 2, 2, 
            0, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 0, 0, 2, 0, 2, 1, 2, 0, 2, 2, 
            2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 1, 0, 2, 0, 
            2, 2, 2, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 1, 2, 2, 
            2, 0, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 1, 0, 
            0, 2, 0, 2 ],
        \[ 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 1, 
            0, 0, 2, 2 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 
            1, 2, 2, 0 ],
        \[ 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 
            2, 1, 2, 0 ],
        \[ 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 
            2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 
            2, 2, 0, 1 ],
        \[ 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 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, 34869>, <24, 37534180>, <32, 2587373547>, <40, 
        36984497320>, <48, 174941783734>, <56, 346506708444>, <64, 327834587808>, <72, 160708146480>, <80, 42918151832>,
        <88, 6419627356>, <96, 545092124>, <104, 26983592>, <112, 1041146>, <120, 60260>, <128, 4823>, <136, 256>, <144,
        3>, <160, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 
            0, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 2, 1, 2, 0, 0, 0, 0, 0, 2, 0, 0, 
            0, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 2, 2, 1, 2, 2, 0, 0, 0, 2, 0, 0, 
            2, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 
            2, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 2, 2, 0, 1, 2, 2, 2, 0, 2, 0, 
            2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 2, 2, 2, 2, 1, 0, 2, 0, 2, 2, 
            0, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 2, 0, 2, 0, 1, 0, 0, 2, 0, 
            0, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 1, 2, 2, 2, 
            2, 2, 2, 0 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 1, 2, 0, 
            0, 0, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 1, 2, 
            2, 2, 2, 2 ],
        \[ 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 1, 
            0, 0, 2, 0 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 
            1, 2, 2, 0 ],
        \[ 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 
            2, 1, 0, 2 ],
        \[ 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 
            2, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 
            2, 0, 2, 1 ],
        \[ 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 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, 35015>, <24, 37529232>, <32, 2587413065>, <40, 
        36984341824>, <48, 174942149352>, <56, 346506156112>, <64, 327835131054>, <72, 160707815424>, <80, 42918251294>,
        <88, 6419635760>, <96, 545075910>, <104, 26986944>, <112, 1041584>, <120, 60144>, <128, 4801>, <136, 256>, <144,
        3>, <160, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 
            2, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 2, 1, 0, 0, 2, 2, 0, 0, 2, 2, 2, 
            2, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 
            0, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 2, 0, 2, 1, 0, 0, 2, 2, 2, 0, 0, 
            2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 2, 0, 2, 0, 1, 2, 0, 0, 2, 0, 2, 
            2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 2, 2, 1, 0, 2, 0, 0, 2, 
            0, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 
            0, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 2, 1, 0, 0, 2, 
            0, 2, 2, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 1, 2, 2, 
            0, 0, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 1, 0, 
            2, 2, 2, 0 ],
        \[ 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 1, 
            0, 0, 2, 2 ],
        \[ 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 
            1, 2, 0, 2 ],
        \[ 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 
            2, 1, 0, 0 ],
        \[ 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 
            0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 
            0, 2, 2, 1 ],
        \[ 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0 ],
        \[ 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 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, 34899>, <24, 37535696>, <32, 2587358405>, <40, 
        36984558816>, <48, 174941646628>, <56, 346506884464>, <64, 327834480666>, <72, 160708113984>, <80, 42918274370>,
        <88, 6419516848>, <96, 545145274>, <104, 26969568>, <112, 1042884>, <120, 60176>, <128, 4837>, <136, 256>, <144,
        3>, <160, 1> ]>

];