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

list:=
[
rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 2, 2, 0, 2, 0, 2, 2, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 1, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 1, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 1, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 61192>, <20, 1011520>, <24, 7809248>, <28, 40576640>, <32,
        140527324>, <36, 309891392>, <40, 540779168>, <44, 741117440>, <48, 798653720>, <52, 707106432>, <56, 
        499374784>, <60, 289052416>, <64, 137791558>, <68, 52814976>, <72, 19752768>, <76, 5426688>, <80, 2413176>, <84,
        459328>, <88, 289376>, <92, 26240>, <96, 29020>, <100, 576>, <104, 2080>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 2, 0, 0, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 2, 2, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 1, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 1, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 1, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 116712>, <24, 16129408>, <32, 272994428>, <40, 
        1084517760>, <48, 1603958744>, <56, 1002002176>, <64, 273366406>, <72, 37378816>, <80, 4060376>, <88, 408448>, 
        <96, 31868>, <104, 1920>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 2, 2, 0, 2, 2, 2, 0, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 2, 2, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 1, 0, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 1, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 60872>, <20, 1004480>, <24, 7805536>, <28, 41303424>, <32,
        137610908>, <36, 313752512>, <40, 540558240>, <44, 737059328>, <48, 802875032>, <52, 704276352>, <56, 
        501127104>, <60, 289046784>, <64, 136569286>, <68, 54162816>, <72, 18596672>, <76, 6185472>, <80, 2042424>, <84,
        642240>, <88, 212960>, <92, 48512>, <96, 22556>, <100, 1728>, <104, 1824>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 2, 0, 0, 2, 0, 0, 0, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 2, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 1, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 58792>, <20, 1021952>, <24, 8008896>, <28, 38717440>, <32,
        146912188>, <36, 299360256>, <40, 547167552>, <44, 747577344>, <48, 782222680>, <52, 722292736>, <56, 
        492612480>, <60, 287797248>, <64, 143099910>, <68, 47276032>, <72, 23627392>, <76, 3317760>, <80, 3347864>, <84,
        120832>, <88, 390080>, <92, 2048>, <96, 33468>, <104, 2112>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 0, 0, 2, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 1, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 1, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 1, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 57480>, <20, 1031168>, <24, 7997344>, <28, 38732800>, <32,
        146903260>, <36, 299192320>, <40, 547402592>, <44, 747876352>, <48, 781680152>, <52, 722135040>, <56, 
        493086784>, <60, 287741952>, <64, 142996038>, <68, 47337472>, <72, 23551680>, <76, 3321856>, <80, 3382264>, <84,
        113664>, <88, 390688>, <92, 1024>, <96, 33116>, <104, 2016>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 0, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 1, 0, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 1, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 1, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 116328>, <24, 16142400>, <32, 272919420>, <40, 
        1084712512>, <48, 1603685080>, <56, 1002214528>, <64, 273287558>, <72, 37382784>, <80, 4063064>, <88, 410432>, 
        <96, 31100>, <104, 1856>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 2, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 2, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 1, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 1, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 58088>, <20, 1022464>, <24, 8050496>, <28, 38716928>, <32,
        146661884>, <36, 299350016>, <40, 547818048>, <44, 747620352>, <48, 781331416>, <52, 722213888>, <56, 
        493252224>, <60, 287876096>, <64, 142930566>, <68, 47233024>, <72, 23572096>, <76, 3328000>, <80, 3383768>, <84,
        121344>, <88, 391744>, <92, 1536>, <96, 31228>, <104, 1856>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 0, 2, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 1, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 1, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 1, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 50600>, <20, 1048576>, <24, 8298304>, <28, 36700160>, <32,
        153519804>, <36, 286261248>, <40, 560220608>, <44, 749731840>, <48, 759810392>, <52, 749731840>, <56, 
        477681792>, <60, 286261248>, <64, 153975302>, <68, 36700160>, <72, 29457280>, <76, 1048576>, <80, 4028824>, <88,
        408640>, <96, 30140>, <104, 1728>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 0, 2, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 1, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 1, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 1, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 116136>, <24, 16162624>, <32, 272795324>, <40, 
        1085032896>, <48, 1603258712>, <56, 1002494080>, <64, 273250822>, <72, 37321600>, <80, 4094360>, <88, 408640>, 
        <96, 30140>, <104, 1728>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 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 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 1, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 1, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 1, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 115912>, <24, 16159776>, <32, 272818716>, <40, 
        1084967008>, <48, 1603351192>, <56, 1002428224>, <64, 273267398>, <72, 37326528>, <80, 4092728>, <88, 407200>, 
        <96, 30620>, <104, 1760>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 2, 0, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 1, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 1, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 1, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 65192>, <20, 958464>, <24, 7977216>, <28, 41244672>, <32, 
        136907324>, <36, 314640384>, <40, 541283968>, <44, 735289344>, <48, 803264856>, <52, 705339392>, <56, 
        500097024>, <60, 289378304>, <64, 136921862>, <68, 53686272>, <72, 18751232>, <76, 6201344>, <80, 2002072>, <84,
        688128>, <88, 191232>, <92, 55296>, <96, 19772>, <100, 2048>, <104, 1664>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 0, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 2, 0, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 1, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 1, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 50376>, <20, 1048576>, <24, 8295456>, <28, 36700160>, <32,
        153543196>, <36, 286261248>, <40, 560154720>, <44, 749731840>, <48, 759902872>, <52, 749731840>, <56, 
        477615936>, <60, 286261248>, <64, 153991878>, <68, 36700160>, <72, 29462208>, <76, 1048576>, <80, 4027192>, <88,
        407200>, <96, 30620>, <104, 1760>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 2, 0, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 1, 0, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 1, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 58120>, <20, 1013760>, <24, 8117536>, <28, 38701056>, <32,
        146346076>, <36, 299507712>, <40, 548414432>, <44, 747364352>, <48, 780754712>, <52, 722292736>, <56, 
        493549376>, <60, 288010240>, <64, 142874950>, <68, 47128576>, <72, 23533504>, <76, 3334144>, <80, 3416184>, <84,
        129024>, <88, 387488>, <92, 2048>, <96, 29404>, <104, 1632>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 2, 0, 2, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 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, 0, 0, 2, 0, 0, 2, 0, 1, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 1, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 56808>, <20, 1039872>, <24, 7973312>, <28, 38748672>, <32,
        146959356>, <36, 299034624>, <40, 547477696>, <44, 748132352>, <48, 781350360>, <52, 722056192>, <56, 
        493413248>, <60, 287607808>, <64, 142924422>, <68, 47441920>, <72, 23498624>, <76, 3315712>, <80, 3400920>, <84,
        105984>, <88, 393920>, <92, 512>, <96, 32764>, <104, 1984>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 2, 0, 2, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 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, 0, 0, 2, 0, 0, 2, 0, 1, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 1, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 51688>, <20, 1048576>, <24, 8250816>, <28, 36700160>, <32,
        153799676>, <36, 286261248>, <40, 559495360>, <44, 749731840>, <48, 760810968>, <52, 749731840>, <56, 
        476945280>, <60, 286261248>, <64, 154196614>, <68, 36700160>, <72, 29495168>, <76, 1048576>, <80, 3997912>, <88,
        405184>, <96, 32764>, <104, 1984>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 0, 2, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 0, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 1, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 1, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 1, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 51560>, <20, 1048576>, <24, 8233792>, <28, 36700160>, <32,
        153909372>, <36, 286261248>, <40, 559213376>, <44, 749731840>, <48, 761170136>, <52, 749731840>, <56, 
        476746368>, <60, 286261248>, <64, 154166150>, <68, 36700160>, <72, 29594752>, <76, 1048576>, <80, 3952216>, <88,
        410176>, <96, 33404>, <104, 2112>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 2, 0, 0, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 2, 0, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 2, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 1, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 1, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 57352>, <20, 1031168>, <24, 8007776>, <28, 38732800>, <32,
        146839772>, <36, 299192320>, <40, 547566624>, <44, 747876352>, <48, 781460248>, <52, 722135040>, <56, 
        493234624>, <60, 287741952>, <64, 142970950>, <68, 47337472>, <72, 23524928>, <76, 3321856>, <80, 3396472>, <84,
        113664>, <88, 390112>, <92, 1024>, <96, 32604>, <104, 1952>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 0, 2, 0, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 2, 0, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 1, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 1, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 1, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 1, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 116552>, <24, 16135072>, <32, 272962972>, <40, 
        1084592864>, <48, 1603871640>, <56, 1002035776>, <64, 273398214>, <72, 37333952>, <80, 4081592>, <88, 404512>, 
        <96, 32028>, <104, 1888>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 0, 2, 0, 0, 2, 2, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 2, 0, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 1, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 1, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 1, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 1, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 51016>, <20, 1048576>, <24, 8270752>, <28, 36700160>, <32,
        153687452>, <36, 286261248>, <40, 559780576>, <44, 749731840>, <48, 760423320>, <52, 749731840>, <56, 
        477223488>, <60, 286261248>, <64, 154122694>, <68, 36700160>, <72, 29469632>, <76, 1048576>, <80, 4016056>, <88,
        404512>, <96, 32028>, <104, 1888>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 2, 2, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 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, 0, 0, 0, 0, 0, 2, 1, 2, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 1, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 1, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 117128>, <24, 16101856>, <32, 273162076>, <40, 
        1084077728>, <48, 1604571672>, <56, 1001543872>, <64, 273513798>, <72, 37391168>, <80, 4047608>, <88, 404320>, 
        <96, 33756>, <104, 2080>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 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, 0, 2, 2, 0, 1, 2, 2, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 2, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 1, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 1, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 59592>, <20, 1014400>, <24, 7793120>, <28, 41336576>, <32,
        137535132>, <36, 313619584>, <40, 540939552>, <44, 737129472>, <48, 802377880>, <52, 704326912>, <56, 
        501315264>, <60, 289085952>, <64, 136615366>, <68, 54060288>, <72, 18567744>, <76, 6206464>, <80, 2047288>, <84,
        653440>, <88, 209248>, <92, 48896>, <96, 21532>, <100, 1664>, <104, 1696>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 0, 0, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 1, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 1, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 116968>, <24, 16117696>, <32, 273063676>, <40, 
        1084338368>, <48, 1604205528>, <56, 1001822080>, <64, 273418374>, <72, 37390208>, <80, 4051928>, <88, 407744>, 
        <96, 32508>, <104, 1984>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 0, 0, 2, 0, 0, 0, 2, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 2, 0, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 0, 2, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 1, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 116936>, <24, 16112928>, <32, 273095708>, <40, 
        1084249440>, <48, 1604338328>, <56, 1001707840>, <64, 273475270>, <72, 37372096>, <80, 4058936>, <88, 404384>, 
        <96, 33180>, <104, 2016>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 2, 0, 2, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 0, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 1, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 1, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 1, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 116296>, <24, 16137632>, <32, 272951452>, <40, 
        1084623584>, <48, 1603817880>, <56, 1002100288>, <64, 273344454>, <72, 37364672>, <80, 4070072>, <88, 407072>, 
        <96, 31772>, <104, 1888>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 0, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 0, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 0, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 1, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 1, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 1, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 60648>, <20, 1005440>, <24, 7812288>, <28, 41321216>, <32,
        137503484>, <36, 313782144>, <40, 540797888>, <44, 736846848>, <48, 802816984>, <52, 704466688>, <56, 
        500877696>, <60, 289141248>, <64, 136753286>, <68, 54016768>, <72, 18603392>, <76, 6185984>, <80, 2025432>, <84,
        665984>, <88, 209344>, <92, 49920>, <96, 21244>, <100, 1408>, <104, 1728>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 0, 2, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 2, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 0, 2, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 2, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 2, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 1, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 1, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 58760>, <20, 1013760>, <24, 8074528>, <28, 38701056>, <32,
        146605788>, <36, 299507712>, <40, 547742944>, <44, 747364352>, <48, 781661208>, <52, 722292736>, <56, 
        492925760>, <60, 288010240>, <64, 143002182>, <68, 47128576>, <72, 23625152>, <76, 3334144>, <80, 3365112>, <84,
        129024>, <88, 388512>, <92, 2048>, <96, 31580>, <104, 1888>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 2, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 2, 0, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 2, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 1, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 62696>, <20, 975360>, <24, 7950848>, <28, 41276928>, <32, 
        136906876>, <36, 314335232>, <40, 541712896>, <44, 735758336>, <48, 802227672>, <52, 705260544>, <56, 
        501026816>, <60, 289031168>, <64, 136696198>, <68, 53938176>, <72, 18626560>, <76, 6178816>, <80, 2056664>, <84,
        672256>, <88, 196096>, <92, 54784>, <96, 18556>, <100, 2048>, <104, 1536>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 0, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 1, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 1, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 1, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 51240>, <20, 1048576>, <24, 8254272>, <28, 36700160>, <32,
        153788732>, <36, 286261248>, <40, 559512256>, <44, 749731840>, <48, 760802904>, <52, 749731840>, <56, 
        476929152>, <60, 286261248>, <64, 154231558>, <68, 36700160>, <72, 29462912>, <76, 1048576>, <80, 4014616>, <88,
        400448>, <96, 33340>, <104, 1984>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 0, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 1, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 1, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 1, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 116776>, <24, 16118592>, <32, 273064252>, <40, 
        1084324544>, <48, 1604251224>, <56, 1001741440>, <64, 273507078>, <72, 37327232>, <80, 4080152>, <88, 400448>, 
        <96, 33340>, <104, 1984>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 0, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 1, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 1, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 1, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 57384>, <20, 1031680>, <24, 8000320>, <28, 38732288>, <32,
        146886972>, <36, 299182080>, <40, 547441344>, <44, 747919360>, <48, 781635160>, <52, 722056192>, <56, 
        493104256>, <60, 287820800>, <64, 143012614>, <68, 47294464>, <72, 23527808>, <76, 3332096>, <80, 3394072>, <84,
        114176>, <88, 388160>, <92, 512>, <96, 33340>, <104, 1984>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 2, 2, 2, 2, 0, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 0, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 2, 2, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 2, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 1, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 1, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 51240>, <20, 1048576>, <24, 8245120>, <28, 36700160>, <32,
        153846460>, <36, 286261248>, <40, 559363584>, <44, 749731840>, <48, 760995928>, <52, 749731840>, <56, 
        476813568>, <60, 286261248>, <64, 154229766>, <68, 36700160>, <72, 29505024>, <76, 1048576>, <80, 3994648>, <88,
        402304>, <96, 33724>, <104, 2048>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 2, 2, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 1, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 1, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 116328>, <24, 16151552>, <32, 272861692>, <40, 
        1084861184>, <48, 1603492056>, <56, 1002330112>, <64, 273289350>, <72, 37340672>, <80, 4083032>, <88, 408576>, 
        <96, 30716>, <104, 1792>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 2, 2, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 1, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 116552>, <24, 16125920>, <32, 273020700>, <40, 
        1084444192>, <48, 1604064664>, <56, 1001920192>, <64, 273396422>, <72, 37376064>, <80, 4061624>, <88, 406368>, 
        <96, 32412>, <104, 1952>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 1, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 1, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 59720>, <20, 1014656>, <24, 7787744>, <28, 41336576>, <32,
        137569564>, <36, 313614208>, <40, 540838176>, <44, 737145856>, <48, 802548120>, <52, 704308992>, <56, 
        501139648>, <60, 289085952>, <64, 136728262>, <68, 54078208>, <72, 18523712>, <76, 6190080>, <80, 2057144>, <84,
        658816>, <88, 207968>, <92, 48896>, <96, 21660>, <100, 1408>, <104, 1696>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 0, 2, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 0, 0, 2, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 2, 2, 0, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 1, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 1, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 50088>, <20, 1048576>, <24, 8311552>, <28, 36700160>, <32,
        153448252>, <36, 286261248>, <40, 560393856>, <44, 749731840>, <48, 759595864>, <52, 749731840>, <56, 
        477797376>, <60, 286261248>, <64, 153998598>, <68, 36700160>, <72, 29390592>, <76, 1048576>, <80, 4062616>, <88,
        402688>, <96, 30268>, <104, 1664>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 2, 2, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 2, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 1, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 58152>, <20, 1012736>, <24, 8117248>, <28, 38702080>, <32,
        146347196>, <36, 299528192>, <40, 548412032>, <44, 747278336>, <48, 780757592>, <52, 722450432>, <56, 
        493548032>, <60, 287852544>, <64, 142873606>, <68, 47214592>, <72, 23536384>, <76, 3313664>, <80, 3413784>, <84,
        128000>, <88, 388608>, <92, 3072>, <96, 29116>, <104, 1664>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 0, 2, 2, 2, 2, 0, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 2, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 117352>, <24, 16104704>, <32, 273138684>, <40, 
        1084143616>, <48, 1604479192>, <56, 1001609728>, <64, 273497222>, <72, 37386240>, <80, 4049240>, <88, 405760>, 
        <96, 33276>, <104, 2048>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 2, 2, 2, 2, 2, 0, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 2, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 51816>, <20, 1048576>, <24, 8240384>, <28, 36700160>, <32,
        153863164>, <36, 286261248>, <40, 559331328>, <44, 749731840>, <48, 761030872>, <52, 749731840>, <56, 
        476797440>, <60, 286261248>, <64, 154221702>, <68, 36700160>, <72, 29521920>, <76, 1048576>, <80, 3983704>, <88,
        405760>, <96, 33276>, <104, 2048>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 2, 2, 2, 0, 0, 2, 2, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 2, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 2, 0, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 1, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 1, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 117320>, <24, 16081632>, <32, 273286172>, <40, 
        1083757344>, <48, 1604998040>, <56, 1001264320>, <64, 273550534>, <72, 37452352>, <80, 4016312>, <88, 406112>, 
        <96, 34716>, <104, 2208>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 2, 2, 2, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 2, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 2, 0, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 1, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 1, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 56840>, <20, 1039360>, <24, 7942496>, <28, 38749184>, <32,
        147155164>, <36, 299044864>, <40, 546963744>, <44, 748089344>, <48, 782047000>, <52, 722135040>, <56, 
        492936128>, <60, 287528960>, <64, 143018054>, <68, 47484928>, <72, 23570496>, <76, 3305472>, <80, 3363192>, <84,
        105472>, <88, 393440>, <92, 1024>, <96, 34652>, <104, 2208>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 0, 2, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 0, 0, 2, 2, 0, 2, 0, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 0, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 0, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 1, 2, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 50888>, <20, 1048576>, <24, 8281184>, <28, 36700160>, <32,
        153623964>, <36, 286261248>, <40, 559944608>, <44, 749731840>, <48, 760203416>, <52, 749731840>, <56, 
        477371328>, <60, 286261248>, <64, 154097606>, <68, 36700160>, <72, 29442880>, <76, 1048576>, <80, 4030264>, <88,
        403936>, <96, 31516>, <104, 1824>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 0, 2, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 0, 0, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 1, 0, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 1, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 116520>, <24, 16121152>, <32, 273052732>, <40, 
        1084355264>, <48, 1604197464>, <56, 1001805952>, <64, 273453318>, <72, 37357952>, <80, 4068632>, <88, 403008>, 
        <96, 33084>, <104, 1984>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 2, 2, 2, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 2, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 1, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 57128>, <20, 1031168>, <24, 8004928>, <28, 38732800>, <32,
        146863164>, <36, 299192320>, <40, 547500736>, <44, 747876352>, <48, 781552728>, <52, 722135040>, <56, 
        493168768>, <60, 287741952>, <64, 142987526>, <68, 47337472>, <72, 23529856>, <76, 3321856>, <80, 3394840>, <84,
        113664>, <88, 388672>, <92, 1024>, <96, 33084>, <104, 1984>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 0, 0, 2, 2, 2, 2, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 2, 0, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 2, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 1, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 1, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 59752>, <20, 1040064>, <24, 7672832>, <28, 40621952>, <32,
        141093628>, <36, 309369536>, <40, 539964672>, <44, 742087168>, <48, 799080152>, <52, 706506112>, <56, 
        499365888>, <60, 289004800>, <64, 137796230>, <68, 52943744>, <72, 19720704>, <76, 5446144>, <80, 2397272>, <84,
        441280>, <88, 297984>, <92, 22400>, <96, 31996>, <100, 448>, <104, 2304>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 2, 0, 0, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 0, 0, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 1, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 1, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 116968>, <24, 16126848>, <32, 273005948>, <40, 
        1084487040>, <48, 1604012504>, <56, 1001937664>, <64, 273420166>, <72, 37348096>, <80, 4071896>, <88, 405888>, 
        <96, 32124>, <104, 1920>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 2, 0, 2, 0, 0, 0, 0, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 1, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 1, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 1, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 64616>, <20, 968704>, <24, 7926784>, <28, 41226240>, <32, 
        137251836>, <36, 314353664>, <40, 540723968>, <44, 736165888>, <48, 803206360>, <52, 704663552>, <56, 
        500856832>, <60, 289120256>, <64, 136483974>, <68, 54153216>, <72, 18687488>, <76, 6127616>, <80, 2055000>, <84,
        649216>, <88, 203776>, <92, 53248>, <96, 20988>, <100, 2048>, <104, 1792>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 2, 2, 2, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 1, 2, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 56488>, <20, 1039360>, <24, 7987712>, <28, 38749184>, <32,
        146874940>, <36, 299044864>, <40, 547693440>, <44, 748089344>, <48, 781061464>, <52, 722135040>, <56, 
        493609472>, <60, 287528960>, <64, 142887686>, <68, 47484928>, <72, 23466240>, <76, 3305472>, <80, 3418776>, <84,
        105472>, <88, 393216>, <92, 1024>, <96, 32060>, <104, 1920>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 0, 0, 0, 2, 0, 0, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 2, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 1, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 1, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 117096>, <24, 16097088>, <32, 273194108>, <40, 
        1083988800>, <48, 1604704472>, <56, 1001429632>, <64, 273570694>, <72, 37373056>, <80, 4054616>, <88, 400960>, 
        <96, 34428>, <104, 2112>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 0, 0, 0, 2, 2, 0, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 2, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 1, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 1, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 51560>, <20, 1048576>, <24, 8232768>, <28, 36700160>, <32,
        153918588>, <36, 286261248>, <40, 559176512>, <44, 749731840>, <48, 761256152>, <52, 749731840>, <56, 
        476617344>, <60, 286261248>, <64, 154295174>, <68, 36700160>, <72, 29508736>, <76, 1048576>, <80, 3989080>, <88,
        400960>, <96, 34428>, <104, 2112>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 0, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0, 0, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 2, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 1, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 57608>, <20, 1021952>, <24, 8061408>, <28, 38717440>, <32,
        146603740>, <36, 299360256>, <40, 547960224>, <44, 747577344>, <48, 781148440>, <52, 722292736>, <56, 
        493366464>, <60, 287797248>, <64, 142923846>, <68, 47276032>, <72, 23536960>, <76, 3317760>, <80, 3402872>, <84,
        120832>, <88, 388960>, <92, 2048>, <96, 31068>, <104, 1824>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 2, 0, 0, 2, 0, 0, 0, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 2, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0, 0, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 1, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 50632>, <20, 1048576>, <24, 8292896>, <28, 36700160>, <32,
        153554716>, <36, 286261248>, <40, 560124000>, <44, 749731840>, <48, 759956632>, <52, 749731840>, <56, 
        477551424>, <60, 286261248>, <64, 154045638>, <68, 36700160>, <72, 29431488>, <76, 1048576>, <80, 4038712>, <88,
        404640>, <96, 30876>, <104, 1760>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 1, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 1, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 1, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 51496>, <20, 1048576>, <24, 8243584>, <28, 36700160>, <32,
        153848764>, <36, 286261248>, <40, 559369728>, <44, 749731840>, <48, 760963672>, <52, 749731840>, <56, 
        476878080>, <60, 286261248>, <64, 154154502>, <68, 36700160>, <72, 29560320>, <76, 1048576>, <80, 3969304>, <88,
        408960>, <96, 32956>, <104, 2048>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 2, 0, 0, 0, 2, 2, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 2, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 1, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 51016>, <20, 1048576>, <24, 8261600>, <28, 36700160>, <32,
        153745180>, <36, 286261248>, <40, 559631904>, <44, 749731840>, <48, 760616344>, <52, 749731840>, <56, 
        477107904>, <60, 286261248>, <64, 154120902>, <68, 36700160>, <72, 29511744>, <76, 1048576>, <80, 3996088>, <88,
        406368>, <96, 32412>, <104, 1952>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 2, 2, 2, 0, 0, 0, 2, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 2, 0, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 1, 2, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 1, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 1, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 1, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 116584>, <24, 16139840>, <32, 272930940>, <40, 
        1084681792>, <48, 1603738840>, <56, 1002150016>, <64, 273341318>, <72, 37352064>, <80, 4074584>, <88, 407872>, 
        <96, 31356>, <104, 1856>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 2, 2, 0, 2, 0, 0, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 0, 2, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 1, 2, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 1, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 1, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 116392>, <24, 16140736>, <32, 272931516>, <40, 
        1084667968>, <48, 1603784536>, <56, 1002069376>, <64, 273430022>, <72, 37289088>, <80, 4102808>, <88, 400576>, 
        <96, 32188>, <104, 1856>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 1, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 1, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 1, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 60392>, <20, 1017920>, <24, 7780480>, <28, 40594560>, <32,
        140615292>, <36, 309780032>, <40, 540772992>, <44, 741185024>, <48, 798425048>, <52, 707360896>, <56, 
        499645696>, <60, 288602880>, <64, 137718150>, <68, 53073536>, <72, 19713280>, <76, 5395968>, <80, 2431192>, <84,
        444224>, <88, 289408>, <92, 27776>, <96, 29308>, <100, 832>, <104, 2176>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 0, 0, 2, 2, 2, 0, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 2, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 2, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 1, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 57480>, <20, 1021952>, <24, 8071840>, <28, 38717440>, <32,
        146540252>, <36, 299360256>, <40, 548124256>, <44, 747577344>, <48, 780928536>, <52, 722292736>, <56, 
        493514304>, <60, 287797248>, <64, 142898758>, <68, 47276032>, <72, 23510208>, <76, 3317760>, <80, 3417080>, <84,
        120832>, <88, 388384>, <92, 2048>, <96, 30556>, <104, 1760>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 2, 2, 2, 2, 2, 0, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 0, 0, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 2, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 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 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 1, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 116168>, <24, 16148064>, <32, 272887964>, <40, 
        1084787616>, <48, 1603597976>, <56, 1002248128>, <64, 273319366>, <72, 37337920>, <80, 4084280>, <88, 406496>, 
        <96, 31260>, <104, 1824>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 2, 2, 2, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 2, 0, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 1, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 61320>, <20, 997056>, <24, 7856160>, <28, 41286528>, <32, 
        137391324>, <36, 313884352>, <40, 540905440>, <44, 736905728>, <48, 802639896>, <52, 704179584>, <56, 
        501182784>, <60, 289338624>, <64, 136564294>, <68, 53990272>, <72, 18600896>, <76, 6195712>, <80, 2044664>, <84,
        656320>, <88, 214176>, <92, 48000>, <96, 20828>, <100, 1472>, <104, 1632>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 2, 2, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 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, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 1, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 51400>, <20, 1048576>, <24, 8239456>, <28, 36700160>, <32,
        153877916>, <36, 286261248>, <40, 559288480>, <44, 749731840>, <48, 761083032>, <52, 749731840>, <56, 
        476779968>, <60, 286261248>, <64, 154197958>, <68, 36700160>, <72, 29549888>, <76, 1048576>, <80, 3973432>, <88,
        406240>, <96, 33564>, <104, 2080>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 0, 2, 2, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 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, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 1, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 56904>, <20, 1039872>, <24, 7948960>, <28, 38748672>, <32,
        147112604>, <36, 299034624>, <40, 547076064>, <44, 748132352>, <48, 781896088>, <52, 722056192>, <56, 
        493035584>, <60, 287607808>, <64, 143004614>, <68, 47441920>, <72, 23549376>, <76, 3315712>, <80, 3373752>, <84,
        105984>, <88, 392992>, <92, 512>, <96, 34332>, <104, 2144>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 2, 0, 0, 2, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 2, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 1, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 1, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 1, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 61160>, <20, 1006080>, <24, 7779200>, <28, 41247232>, <32,
        137992060>, <36, 313572352>, <40, 539633024>, <44, 738039808>, <48, 803435992>, <52, 703155200>, <56, 
        501451520>, <60, 289197056>, <64, 136278918>, <68, 54480896>, <72, 18510592>, <76, 6133760>, <80, 2076632>, <84,
        608768>, <88, 237952>, <92, 41472>, <96, 24444>, <100, 1024>, <104, 1920>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 2, 0, 0, 2, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 2, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 1, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 1, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 1, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 60744>, <20, 1011008>, <24, 7834080>, <28, 40577152>, <32,
        140379420>, <36, 309901632>, <40, 541158944>, <44, 741074432>, <48, 798144920>, <52, 707185280>, <56, 
        499718848>, <60, 288973568>, <64, 137729734>, <68, 52857984>, <72, 19693632>, <76, 5416448>, <80, 2445240>, <84,
        458816>, <88, 288096>, <92, 26752>, <96, 27804>, <100, 576>, <104, 1952>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 0, 0, 2, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 2, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 2, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 1, 0, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 1, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 1, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 51496>, <20, 1048576>, <24, 8281216>, <28, 36700160>, <32,
        153608636>, <36, 286261248>, <40, 560001280>, <44, 749731840>, <48, 760105560>, <52, 749731840>, <56, 
        477469440>, <60, 286261248>, <64, 154032646>, <68, 36700160>, <72, 29477888>, <76, 1048576>, <80, 4012312>, <88,
        410752>, <96, 30396>, <104, 1792>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 2, 0, 2, 2, 2, 2, 0, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 0, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 0, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 1, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 117480>, <24, 16075968>, <32, 273317628>, <40, 
        1083682240>, <48, 1605085144>, <56, 1001230720>, <64, 273518726>, <72, 37497216>, <80, 3995096>, <88, 410048>, 
        <96, 34556>, <104, 2240>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 2, 0, 2, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 0, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 0, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 1, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 51944>, <20, 1048576>, <24, 8211648>, <28, 36700160>, <32,
        154042108>, <36, 286261248>, <40, 558869952>, <44, 749731840>, <48, 761636824>, <52, 749731840>, <56, 
        476418432>, <60, 286261248>, <64, 154243206>, <68, 36700160>, <72, 29632896>, <76, 1048576>, <80, 3929560>, <88,
        410048>, <96, 34556>, <104, 2240>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 1, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 1, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 117320>, <24, 16090784>, <32, 273228444>, <40, 
        1083906016>, <48, 1604805016>, <56, 1001379904>, <64, 273552326>, <72, 37410240>, <80, 4036280>, <88, 404256>, 
        <96, 34332>, <104, 2144>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 1, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 1, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 51784>, <20, 1048576>, <24, 8226464>, <28, 36700160>, <32,
        153952924>, <36, 286261248>, <40, 559093728>, <44, 749731840>, <48, 761356696>, <52, 749731840>, <56, 
        476567616>, <60, 286261248>, <64, 154276806>, <68, 36700160>, <72, 29545920>, <76, 1048576>, <80, 3970744>, <88,
        404256>, <96, 34332>, <104, 2144>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 0, 0, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 2, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 2, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 1, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 50728>, <20, 1048576>, <24, 8287872>, <28, 36700160>, <32,
        153583292>, <36, 286261248>, <40, 560056576>, <44, 749731840>, <48, 760030296>, <52, 749731840>, <56, 
        477533952>, <60, 286261248>, <64, 154000390>, <68, 36700160>, <72, 29484032>, <76, 1048576>, <80, 4014616>, <88,
        409216>, <96, 30652>, <104, 1792>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 0, 2, 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, 0, 0, 2, 0, 1, 0, 0, 2, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 2, 0, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 1, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 1, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 116808>, <24, 16124384>, <32, 273023004>, <40, 
        1084450336>, <48, 1604032408>, <56, 1001984704>, <64, 273321158>, <72, 37431360>, <80, 4036280>, <88, 413024>, 
        <96, 31644>, <104, 1952>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 2, 0, 2, 2, 0, 2, 0, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 2, 2, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 2, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 57160>, <20, 1030656>, <24, 8002592>, <28, 38733312>, <32,
        146876572>, <36, 299202560>, <40, 547469664>, <44, 747833344>, <48, 781584280>, <52, 722213888>, <56, 
        493167424>, <60, 287663104>, <64, 142957510>, <68, 47380480>, <72, 23561408>, <76, 3311616>, <80, 3380152>, <84,
        113152>, <88, 391840>, <92, 1536>, <96, 32796>, <104, 2016>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 2, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 1, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 1, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 60840>, <20, 1004864>, <24, 7807360>, <28, 41303168>, <32,
        137601084>, <36, 313744704>, <40, 540579072>, <44, 737089024>, <48, 802857816>, <52, 704227968>, <56, 
        501121280>, <60, 289086208>, <64, 136592134>, <68, 54150272>, <72, 18579456>, <76, 6182400>, <80, 2046872>, <84,
        645184>, <88, 213376>, <92, 48256>, <96, 22332>, <100, 1600>, <104, 1792>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 0, 2, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 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, 0, 0, 0, 0, 2, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 1, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 56808>, <20, 1038848>, <24, 7959104>, <28, 38749696>, <32,
        147050236>, <36, 299055104>, <40, 547237696>, <44, 748046336>, <48, 781679064>, <52, 722213888>, <56, 
        493182080>, <60, 287450112>, <64, 142978182>, <68, 47527936>, <72, 23525504>, <76, 3295232>, <80, 3385560>, <84,
        104960>, <88, 393536>, <92, 1536>, <96, 33532>, <104, 2112>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 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, 0, 0, 0, 2, 0, 2, 2, 1, 0, 0, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 1, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 1, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 1, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 51144>, <20, 1048576>, <24, 8251168>, <28, 36700160>, <32,
        153808668>, <36, 286261248>, <40, 559467872>, <44, 749731840>, <48, 760836248>, <52, 749731840>, <56, 
        476960064>, <60, 286261248>, <64, 154145990>, <68, 36700160>, <72, 29538496>, <76, 1048576>, <80, 3981880>, <88,
        406944>, <96, 32924>, <104, 2016>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 0, 0, 2, 2, 0, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 0, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 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 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 1, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 61704>, <20, 1002944>, <24, 7858784>, <28, 40560512>, <32,
        140311516>, <36, 310046656>, <40, 541123616>, <44, 740874752>, <48, 798410008>, <52, 707154816>, <56, 
        499449280>, <60, 289225984>, <64, 137776710>, <68, 52680064>, <72, 19748416>, <76, 5446144>, <80, 2429048>, <84,
        464576>, <88, 284128>, <92, 26496>, <96, 28252>, <100, 704>, <104, 1952>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 0, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 2, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 1, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 1, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 117384>, <24, 16109472>, <32, 273106652>, <40, 
        1084232544>, <48, 1604346392>, <56, 1001723968>, <64, 273440326>, <72, 37404352>, <80, 4042232>, <88, 409120>, 
        <96, 32604>, <104, 2016>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 2, 0, 0, 0, 2, 0, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 1, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 1, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 51560>, <20, 1048576>, <24, 8242944>, <28, 36700160>, <32,
        153851644>, <36, 286261248>, <40, 559362048>, <44, 749731840>, <48, 760977112>, <52, 749731840>, <56, 
        476861952>, <60, 286261248>, <64, 154167942>, <68, 36700160>, <72, 29552640>, <76, 1048576>, <80, 3972184>, <88,
        408320>, <96, 33020>, <104, 2048>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 0, 0, 2, 0, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 0, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 1, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 1, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 50760>, <20, 1048576>, <24, 8273312>, <28, 36700160>, <32,
        153675932>, <36, 286261248>, <40, 559811296>, <44, 749731840>, <48, 760369560>, <52, 749731840>, <56, 
        477288000>, <60, 286261248>, <64, 154068934>, <68, 36700160>, <72, 29500352>, <76, 1048576>, <80, 4004536>, <88,
        407072>, <96, 31772>, <104, 1888>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 0, 2, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 0, 0, 2, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 1, 2, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 1, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 1, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 51176>, <20, 1048576>, <24, 8265088>, <28, 36700160>, <32,
        153718908>, <36, 286261248>, <40, 559705472>, <44, 749731840>, <48, 760510424>, <52, 749731840>, <56, 
        477189888>, <60, 286261248>, <64, 154090886>, <68, 36700160>, <72, 29514496>, <76, 1048576>, <80, 3994840>, <88,
        408448>, <96, 31868>, <104, 1920>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 0, 2, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 0, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 1, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 1, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 1, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 117000>, <24, 16131616>, <32, 272973916>, <40, 
        1084575968>, <48, 1603879704>, <56, 1002051904>, <64, 273363270>, <72, 37366208>, <80, 4064888>, <88, 409248>, 
        <96, 31452>, <104, 1888>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 0, 2, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 0, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 1, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 1, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 1, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 51464>, <20, 1048576>, <24, 8267296>, <28, 36700160>, <32,
        153698396>, <36, 286261248>, <40, 559763680>, <44, 749731840>, <48, 760431384>, <52, 749731840>, <56, 
        477239616>, <60, 286261248>, <64, 154087750>, <68, 36700160>, <72, 29501888>, <76, 1048576>, <80, 3999352>, <88,
        409248>, <96, 31452>, <104, 1888>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 0, 0, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 1, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 1, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 1, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 1, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 64104>, <20, 967168>, <24, 7952256>, <28, 41260544>, <32, 
        136978172>, <36, 314482688>, <40, 541316224>, <44, 735545344>, <48, 802987224>, <52, 705260544>, <56, 
        500406016>, <60, 289244160>, <64, 136826502>, <68, 53790720>, <72, 18726144>, <76, 6195200>, <80, 2010456>, <84,
        680448>, <88, 194944>, <92, 54784>, <96, 19708>, <100, 2048>, <104, 1664>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 0, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 1, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 56392>, <20, 1039872>, <24, 7981536>, <28, 38748672>, <32,
        146916380>, <36, 299034624>, <40, 547583520>, <44, 748132352>, <48, 781209496>, <52, 722056192>, <56, 
        493511360>, <60, 287607808>, <64, 142902470>, <68, 47441920>, <72, 23484480>, <76, 3315712>, <80, 3410616>, <84,
        105984>, <88, 392544>, <92, 512>, <96, 32668>, <104, 1952>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 0, 0, 2, 0, 2, 0, 2, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 0, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 0, 2, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 0, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 1, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 1, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 1, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 60744>, <20, 1011648>, <24, 7832544>, <28, 40576384>, <32,
        140388124>, <36, 309888960>, <40, 541140512>, <44, 741130752>, <48, 798159256>, <52, 707075968>, <56, 
        499726016>, <60, 289091840>, <64, 137708230>, <68, 52784512>, <72, 19707968>, <76, 5440000>, <80, 2443192>, <84,
        456896>, <88, 286560>, <92, 25984>, <96, 28316>, <100, 704>, <104, 1952>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 0, 0, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 0, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 2, 2, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 1, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 50568>, <20, 1048576>, <24, 8293536>, <28, 36700160>, <32,
        153551836>, <36, 286261248>, <40, 560131680>, <44, 749731840>, <48, 759943192>, <52, 749731840>, <56, 
        477567552>, <60, 286261248>, <64, 154032198>, <68, 36700160>, <72, 29439168>, <76, 1048576>, <80, 4035832>, <88,
        405280>, <96, 30812>, <104, 1760>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 2, 2, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 0, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 1, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 1, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 1, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 58120>, <20, 1021952>, <24, 8028832>, <28, 38717440>, <32,
        146799964>, <36, 299360256>, <40, 547452768>, <44, 747577344>, <48, 781835032>, <52, 722292736>, <56, 
        492890688>, <60, 287797248>, <64, 143025990>, <68, 47276032>, <72, 23601856>, <76, 3317760>, <80, 3366008>, <84,
        120832>, <88, 389408>, <92, 2048>, <96, 32732>, <104, 2016>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 0, 0, 0, 2, 2, 0, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 2, 2, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 1, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 51272>, <20, 1048576>, <24, 8260064>, <28, 36700160>, <32,
        153747484>, <36, 286261248>, <40, 559638048>, <44, 749731840>, <48, 760584088>, <52, 749731840>, <56, 
        477172416>, <60, 286261248>, <64, 154045638>, <68, 36700160>, <72, 29567040>, <76, 1048576>, <80, 3970744>, <88,
        413024>, <96, 31644>, <104, 1952>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 2, 0, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 1, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 1, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 57384>, <20, 1022976>, <24, 8072768>, <28, 38716416>, <32,
        146536252>, <36, 299339776>, <40, 548134336>, <44, 747663360>, <48, 780912216>, <52, 722135040>, <56, 
        493531776>, <60, 287954944>, <64, 142886662>, <68, 47190016>, <72, 23515008>, <76, 3338240>, <80, 3416600>, <84,
        121856>, <88, 387904>, <92, 1024>, <96, 30780>, <104, 1728>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 2, 2, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 51656>, <20, 1048576>, <24, 8236896>, <28, 36700160>, <32,
        153889436>, <36, 286261248>, <40, 559257760>, <44, 749731840>, <48, 761136792>, <52, 749731840>, <56, 
        476715456>, <60, 286261248>, <64, 154251718>, <68, 36700160>, <72, 29519168>, <76, 1048576>, <80, 3984952>, <88,
        403680>, <96, 33820>, <104, 2080>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 0, 2, 2, 0, 0, 0, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 0, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 2, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 1, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 115944>, <24, 16164544>, <32, 272786684>, <40, 
        1085055936>, <48, 1603218392>, <56, 1002542464>, <64, 273210502>, <72, 37344640>, <80, 4085720>, <88, 410560>, 
        <96, 29948>, <104, 1728>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 0, 2, 2, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 0, 2, 2, 2, 0, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 2, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 1, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 1, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 57704>, <20, 1021440>, <24, 8058432>, <28, 38717952>, <32,
        146620028>, <36, 299370496>, <40, 547921472>, <44, 747534336>, <48, 781193432>, <52, 722371584>, <56, 
        493348992>, <60, 287718400>, <64, 142907270>, <68, 47319040>, <72, 23560832>, <76, 3307520>, <80, 3391064>, <84,
        120320>, <88, 391488>, <92, 2560>, <96, 30844>, <104, 1856>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 0, 2, 2, 0, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 2, 0, 0, 0, 0, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 1, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 1, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 116488>, <24, 16135712>, <32, 272960092>, <40, 
        1084600544>, <48, 1603858200>, <56, 1002051904>, <64, 273384774>, <72, 37341632>, <80, 4078712>, <88, 405152>, 
        <96, 31964>, <104, 1888>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 0, 2, 2, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 0, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 1, 2, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 1, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 57480>, <20, 1030656>, <24, 8018720>, <28, 38733312>, <32,
        146766300>, <36, 299202560>, <40, 547765472>, <44, 747833344>, <48, 781179416>, <52, 722213888>, <56, 
        493446976>, <60, 287663104>, <64, 142899270>, <68, 47380480>, <72, 23524800>, <76, 3311616>, <80, 3397624>, <84,
        113152>, <88, 394144>, <92, 1536>, <96, 31324>, <104, 1888>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 0, 0, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 0, 2, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 2, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 0, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 1, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 50472>, <20, 1048576>, <24, 8289408>, <28, 36700160>, <32,
        153580988>, <36, 286261248>, <40, 560050432>, <44, 749731840>, <48, 760062552>, <52, 749731840>, <56, 
        477469440>, <60, 286261248>, <64, 154075654>, <68, 36700160>, <72, 29428736>, <76, 1048576>, <80, 4039960>, <88,
        402560>, <96, 31420>, <104, 1792>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 2, 2, 2, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 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 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 1, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 1, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 1, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 116200>, <24, 16161984>, <32, 272798204>, <40, 
        1085025216>, <48, 1603272152>, <56, 1002477952>, <64, 273264262>, <72, 37313920>, <80, 4097240>, <88, 408000>, 
        <96, 30204>, <104, 1728>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 2, 0, 2, 2, 0, 0, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 0, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 0, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 59336>, <20, 1035968>, <24, 7673504>, <28, 41346432>, <32,
        138155548>, <36, 313171136>, <40, 539782880>, <44, 738263552>, <48, 803286168>, <52, 703276416>, <56, 
        501072960>, <60, 289353984>, <64, 136644294>, <68, 54142848>, <72, 18528192>, <76, 6210048>, <80, 2027064>, <84,
        639936>, <88, 227104>, <92, 42368>, <96, 24476>, <100, 960>, <104, 1888>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 2, 0, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 2, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 1, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 1, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 58120>, <20, 1022976>, <24, 8043040>, <28, 38716416>, <32,
        146709084>, <36, 299339776>, <40, 547692768>, <44, 747663360>, <48, 781506328>, <52, 722135040>, <56, 
        493121856>, <60, 287954944>, <64, 142972230>, <68, 47190016>, <72, 23574976>, <76, 3338240>, <80, 3381368>, <84,
        121856>, <88, 389792>, <92, 1024>, <96, 31964>, <104, 1888>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 2, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 1, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 61480>, <20, 1002304>, <24, 7876800>, <28, 40561280>, <32,
        140201532>, <36, 310059328>, <40, 541410368>, <44, 740818432>, <48, 798016088>, <52, 707264128>, <56, 
        499736448>, <60, 289107712>, <64, 137689350>, <68, 52753536>, <72, 19740800>, <76, 5422592>, <80, 2432536>, <84,
        466496>, <88, 289728>, <92, 27264>, <96, 26428>, <100, 576>, <104, 1856>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 2, 0, 2, 2, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 2, 0, 2, 2, 2, 0, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 2, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 2, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 1, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 1, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 51784>, <20, 1048576>, <24, 8217312>, <28, 36700160>, <32,
        154010652>, <36, 286261248>, <40, 558945056>, <44, 749731840>, <48, 761549720>, <52, 749731840>, <56, 
        476452032>, <60, 286261248>, <64, 154275014>, <68, 36700160>, <72, 29588032>, <76, 1048576>, <80, 3950776>, <88,
        406112>, <96, 34716>, <104, 2208>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 2, 2, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 0, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 1, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 1, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 116584>, <24, 16148992>, <32, 272873212>, <40, 
        1084830464>, <48, 1603545816>, <56, 1002265600>, <64, 273343110>, <72, 37309952>, <80, 4094552>, <88, 406016>, 
        <96, 30972>, <104, 1792>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 2, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 2, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 1, 2, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 1, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 1, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 1, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 117096>, <24, 16107264>, <32, 273127164>, <40, 
        1084174336>, <48, 1604425432>, <56, 1001674240>, <64, 273443462>, <72, 37416960>, <80, 4037720>, <88, 408320>, 
        <96, 33020>, <104, 2048>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 0, 2, 2, 0, 0, 0, 2, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 2, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 1, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 1, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 1, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 51432>, <20, 1048576>, <24, 8262528>, <28, 36700160>, <32,
        153730428>, <36, 286261248>, <40, 559674752>, <44, 749731840>, <48, 760564184>, <52, 749731840>, <56, 
        477125376>, <60, 286261248>, <64, 154144646>, <68, 36700160>, <72, 29483776>, <76, 1048576>, <80, 4006360>, <88,
        405888>, <96, 32124>, <104, 1920>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 0, 2, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 1, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 1, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 1, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 61384>, <20, 1002816>, <24, 7879776>, <28, 40560768>, <32,
        140185244>, <36, 310049088>, <40, 541449120>, <44, 740861440>, <48, 797971096>, <52, 707185280>, <56, 
        499753920>, <60, 289186560>, <64, 137705926>, <68, 52710528>, <72, 19716928>, <76, 5432832>, <80, 2444344>, <84,
        467008>, <88, 287200>, <92, 26752>, <96, 26652>, <100, 576>, <104, 1824>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 0, 2, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 2, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 1, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 116264>, <24, 16152192>, <32, 272858812>, <40, 
        1084868864>, <48, 1603478616>, <56, 1002346240>, <64, 273275910>, <72, 37348352>, <80, 4080152>, <88, 409216>, 
        <96, 30652>, <104, 1792>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 0, 2, 2, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 1, 0, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 1, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 1, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 116136>, <24, 16143296>, <32, 272919996>, <40, 
        1084698688>, <48, 1603730776>, <56, 1002133888>, <64, 273376262>, <72, 37319808>, <80, 4091288>, <88, 403136>, 
        <96, 31932>, <104, 1856>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 0, 0, 2, 0, 2, 0, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 0, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 1, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 1, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 57000>, <20, 1031680>, <24, 8022464>, <28, 38732288>, <32,
        146754236>, <36, 299182080>, <40, 547784768>, <44, 747919360>, <48, 781168472>, <52, 722056192>, <56, 
        493432192>, <60, 287820800>, <64, 142935558>, <68, 47294464>, <72, 23489664>, <76, 3332096>, <80, 3416728>, <84,
        114176>, <88, 388288>, <92, 512>, <96, 32188>, <104, 1856>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 2, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 2, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 0, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 1, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 1, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 56456>, <20, 1039360>, <24, 7973792>, <28, 38749184>, <32,
        146964700>, <36, 299044864>, <40, 547455840>, <44, 748089344>, <48, 781387288>, <52, 722135040>, <56, 
        493379648>, <60, 287528960>, <64, 142942790>, <68, 47484928>, <72, 23490240>, <76, 3305472>, <80, 3405816>, <84,
        105472>, <88, 391712>, <92, 1024>, <96, 33116>, <104, 2016>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 2, 0, 2, 2, 2, 2, 2, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 2, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0, 0, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 1, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 1, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 50600>, <20, 1048576>, <24, 8278976>, <28, 36700160>, <32,
        153644476>, <36, 286261248>, <40, 559886400>, <44, 749731840>, <48, 760282456>, <52, 749731840>, <56, 
        477321600>, <60, 286261248>, <64, 154100742>, <68, 36700160>, <72, 29455488>, <76, 1048576>, <80, 4025752>, <88,
        403136>, <96, 31932>, <104, 1856>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 2, 2, 0, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 0, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 1, 0, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 1, 2, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 59688>, <20, 1013888>, <24, 7790144>, <28, 41337088>, <32,
        137551420>, <36, 313629824>, <40, 540900800>, <44, 737086464>, <48, 802422872>, <52, 704405760>, <56, 
        501297792>, <60, 289007104>, <64, 136598790>, <68, 54103296>, <72, 18591616>, <76, 6196224>, <80, 2035480>, <84,
        652928>, <88, 211776>, <92, 49408>, <96, 21308>, <100, 1664>, <104, 1728>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 2, 0, 0, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 2, 0, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 0, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 1, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 55464>, <20, 1047552>, <24, 7955008>, <28, 38765568>, <32,
        146994108>, <36, 298897408>, <40, 547598016>, <44, 748302336>, <48, 780961624>, <52, 722135040>, <56, 
        493786752>, <60, 287315968>, <64, 142832646>, <68, 47632384>, <72, 23446912>, <76, 3289088>, <80, 3422360>, <84,
        97280>, <88, 396096>, <92, 1024>, <96, 32444>, <104, 1984>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 0, 2, 0, 2, 2, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 0, 2, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 2, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 1, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 50344>, <20, 1048576>, <24, 8310016>, <28, 36700160>, <32,
        153450556>, <36, 286261248>, <40, 560400000>, <44, 749731840>, <48, 759563608>, <52, 749731840>, <56, 
        477861888>, <60, 286261248>, <64, 153923334>, <68, 36700160>, <72, 29445888>, <76, 1048576>, <80, 4037272>, <88,
        409344>, <96, 29500>, <104, 1664>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 0, 0, 2, 0, 2, 0, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 0, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 0, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 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 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 1, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 50632>, <20, 1048576>, <24, 8283744>, <28, 36700160>, <32,
        153612444>, <36, 286261248>, <40, 559975328>, <44, 749731840>, <48, 760149656>, <52, 749731840>, <56, 
        477435840>, <60, 286261248>, <64, 154043846>, <68, 36700160>, <72, 29473600>, <76, 1048576>, <80, 4018744>, <88,
        406496>, <96, 31260>, <104, 1824>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 2, 0, 0, 2, 2, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 2, 2, 2, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 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, 2, 2, 0, 0, 0, 1, 2, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 1, 0, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 1, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 56584>, <20, 1038848>, <24, 7984736>, <28, 38749696>, <32,
        146891228>, <36, 299055104>, <40, 547654688>, <44, 748046336>, <48, 781106456>, <52, 722213888>, <56, 
        493592000>, <60, 287450112>, <64, 142871110>, <68, 47527936>, <72, 23490112>, <76, 3295232>, <80, 3406968>, <84,
        104960>, <88, 395744>, <92, 1536>, <96, 31836>, <104, 1952>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 2, 2, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 2, 2, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 0, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 1, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 1, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 117032>, <24, 16145536>, <32, 272884156>, <40, 
        1084813568>, <48, 1603553880>, <56, 1002281728>, <64, 273308166>, <72, 37342208>, <80, 4077848>, <88, 410752>, 
        <96, 30396>, <104, 1792>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 0, 0, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 2, 2, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 0, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 1, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 51144>, <20, 1048576>, <24, 8270496>, <28, 36700160>, <32,
        153683996>, <36, 286261248>, <40, 559802080>, <44, 749731840>, <48, 760364184>, <52, 749731840>, <56, 
        477320256>, <60, 286261248>, <64, 154020550>, <68, 36700160>, <72, 29540288>, <76, 1048576>, <80, 3984952>, <88,
        412448>, <96, 31132>, <104, 1888>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 2, 0, 2, 0, 0, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 2, 0, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 2, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 1, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 1, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 57128>, <20, 1031168>, <24, 8024256>, <28, 38732800>, <32,
        146738492>, <36, 299192320>, <40, 547834944>, <44, 747876352>, <48, 781080664>, <52, 722135040>, <56, 
        493528960>, <60, 287741952>, <64, 142862086>, <68, 47337472>, <72, 23531648>, <76, 3321856>, <80, 3397912>, <84,
        113664>, <88, 394176>, <92, 1024>, <96, 31292>, <104, 1856>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 0, 2, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 0, 2, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 1, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 1, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 1, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 60712>, <20, 1004672>, <24, 7817792>, <28, 41321728>, <32,
        137465404>, <36, 313797760>, <40, 540904896>, <44, 736787456>, <48, 802658392>, <52, 704563456>, <56, 
        501004928>, <60, 289062400>, <64, 136709382>, <68, 54041856>, <72, 18595712>, <76, 6192128>, <80, 2036504>, <84,
        660096>, <88, 206656>, <92, 50432>, <96, 21308>, <100, 1664>, <104, 1728>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 0, 2, 0, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 2, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 1, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 57384>, <20, 1031168>, <24, 8021696>, <28, 38732800>, <32,
        146750012>, <36, 299192320>, <40, 547804224>, <44, 747876352>, <48, 781134424>, <52, 722135040>, <56, 
        493464448>, <60, 287741952>, <64, 142915846>, <68, 47337472>, <72, 23500928>, <76, 3321856>, <80, 3409432>, <84,
        113664>, <88, 391616>, <92, 1024>, <96, 31548>, <104, 1856>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 2, 0, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 2, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 1, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 58760>, <20, 1013760>, <24, 8083680>, <28, 38701056>, <32,
        146548060>, <36, 299507712>, <40, 547891616>, <44, 747364352>, <48, 781468184>, <52, 722292736>, <56, 
        493041344>, <60, 288010240>, <64, 143003974>, <68, 47128576>, <72, 23583040>, <76, 3334144>, <80, 3385080>, <84,
        129024>, <88, 386656>, <92, 2048>, <96, 31196>, <104, 1824>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 2, 0, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 2, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 1, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 58632>, <20, 1013760>, <24, 8084960>, <28, 38701056>, <32,
        146542300>, <36, 299507712>, <40, 547906976>, <44, 747364352>, <48, 781441304>, <52, 722292736>, <56, 
        493073600>, <60, 288010240>, <64, 142977094>, <68, 47128576>, <72, 23598400>, <76, 3334144>, <80, 3379320>, <84,
        129024>, <88, 387936>, <92, 2048>, <96, 31068>, <104, 1824>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 0, 2, 2, 2, 0, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 0, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 2, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 1, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 58536>, <20, 1012736>, <24, 8095104>, <28, 38702080>, <32,
        146479932>, <36, 299528192>, <40, 548068608>, <44, 747278336>, <48, 781224280>, <52, 722450432>, <56, 
        493220096>, <60, 287852544>, <64, 142950662>, <68, 47214592>, <72, 23574528>, <76, 3313664>, <80, 3391128>, <84,
        128000>, <88, 388480>, <92, 3072>, <96, 30268>, <104, 1792>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 0, 0, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 1, 2, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 1, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 116424>, <24, 16145504>, <32, 272899484>, <40, 
        1084756896>, <48, 1603651736>, <56, 1002183616>, <64, 273373126>, <72, 37307200>, <80, 4095800>, <88, 403936>, 
        <96, 31516>, <104, 1824>, <112, 232>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 2, 0, 2, 0, 2, 2, 0, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 2, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0, 2, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 2, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 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 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 1, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 2, 2, 2, 2, 2, 2, 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 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 116168>, <24, 16157216>, <32, 272830236>, <40, 
        1084936288>, <48, 1603404952>, <56, 1002363712>, <64, 273321158>, <72, 37295808>, <80, 4104248>, <88, 404640>, 
        <96, 30876>, <104, 1760>, <112, 232>, <128, 1> ]>


];