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

list:=
[
rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 1, 2, 0, 2, 0, 0, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 1, 2, 0, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 1, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 1, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 1, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 1, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 1, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 113128>, <24, 16321520>, <32, 269838508>, <40, 
        1091934608>, <48, 1600710568>, <56, 997143392>, <64, 276916582>, <72, 38161696>, <80, 3580536>, <88, 235952>, 
        <96, 10604>, <104, 80>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 1, 2, 0, 0, 2, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 1, 2, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 1, 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, 2, 2, 0, 0, 0, 0, 1, 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, 0, 2, 0, 1, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 1, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 1, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 1, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 113816>, <24, 16294944>, <32, 269991292>, <40, 
        1091549792>, <48, 1601214088>, <56, 996822848>, <64, 276944134>, <72, 38249152>, <80, 3534312>, <88, 241312>, 
        <96, 11260>, <104, 224>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 1, 2, 2, 0, 2, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 0, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 1, 0, 0, 0, 2, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 1, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 1, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 1, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 1, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 1, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47656>, <20, 1048576>, <24, 8457072>, <28, 36700160>, <32,
        150561260>, <36, 286261248>, <40, 567133072>, <44, 749731840>, <48, 757232680>, <52, 749731840>, <56, 
        472379488>, <60, 286261248>, <64, 157589990>, <68, 36700160>, <72, 30332704>, <76, 1048576>, <80, 3499448>, <88,
        239920>, <96, 10156>, <104, 80>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 1, 0, 0, 2, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 1, 0, 0, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 1, 0, 0, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 1, 0, 2, 0, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 1, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 1, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, 1, 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, 0, 2, 0, 1, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 1, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48072>, <20, 1048576>, <24, 8438928>, <28, 36700160>, <32,
        150668876>, <36, 286261248>, <40, 566850928>, <44, 749731840>, <48, 757631080>, <52, 749731840>, <56, 
        472069024>, <60, 286261248>, <64, 157706918>, <68, 36700160>, <72, 30324448>, <76, 1048576>, <80, 3497432>, <88,
        236240>, <96, 11404>, <104, 176>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 1, 2, 2, 0, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 1, 2, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 1, 2, 0, 0, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 1, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 1, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 1, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 1, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 1, 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, 2, 0, 2, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 113400>, <24, 16321984>, <32, 269828252>, <40, 
        1091971392>, <48, 1600644168>, <56, 997216640>, <64, 276861254>, <72, 38193792>, <80, 3565512>, <88, 240832>, 
        <96, 9884>, <104, 64>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 1, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 1, 2, 0, 2, 0, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 1, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 1, 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, 2, 0, 0, 2, 2, 1, 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, 0, 0, 2, 0, 2, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 112984>, <24, 16320800>, <32, 269845308>, <40, 
        1091919328>, <48, 1600717832>, <56, 997166912>, <64, 276869766>, <72, 38200256>, <80, 3564456>, <88, 239008>, 
        <96, 10428>, <104, 96>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 1, 2, 2, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 1, 2, 2, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 1, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 1, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2, 1, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 1, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 1, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 1, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 47928>, <20, 1048576>, <24, 8447232>, <28, 36700160>, <32,
        150619100>, <36, 286261248>, <40, 566979712>, <44, 749731840>, <48, 757456072>, <52, 749731840>, <56, 
        472192000>, <60, 286261248>, <64, 157678022>, <68, 36700160>, <72, 30310144>, <76, 1048576>, <80, 3505928>, <88,
        236288>, <96, 10972>, <104, 128>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 1, 2, 2, 2, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 2, 2, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 2, 0, 2, 0, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 1, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 1, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 1, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 1, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 1, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 61304>, <20, 974592>, <24, 8076864>, <28, 41000704>, <32, 
        135226780>, <36, 313644544>, <40, 545499968>, <44, 740070400>, <48, 800673608>, <52, 700150272>, <56, 
        498499712>, <60, 289839616>, <64, 138448198>, <68, 55271424>, <72, 19088512>, <76, 6018048>, <80, 1782856>, <84,
        489216>, <88, 119104>, <92, 24320>, <96, 6556>, <100, 512>, <104, 64>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 1, 2, 2, 2, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 1, 0, 2, 0, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 2, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 1, 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, 2, 2, 0, 0, 2, 1, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 1, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 114024>, <24, 16295024>, <32, 269987372>, <40, 
        1091557392>, <48, 1601220264>, <56, 996783200>, <64, 277004390>, <72, 38202912>, <80, 3553272>, <88, 237616>, 
        <96, 11500>, <104, 208>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 1, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 1, 0, 2, 0, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 1, 2, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, 1, 0, 0, 0, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 1, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 1, 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, 2, 0, 2, 2, 2, 0, 1, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 1, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 2, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 60328>, <20, 983968>, <24, 8044656>, <28, 41016000>, <32, 
        135341676>, <36, 313473312>, <40, 545417104>, <44, 740380928>, <48, 800553768>, <52, 699976000>, <56, 
        498697824>, <60, 289794176>, <64, 138375910>, <68, 55334208>, <72, 19082016>, <76, 6017280>, <80, 1779000>, <84,
        484128>, <88, 124464>, <92, 23232>, <96, 6700>, <100, 416>, <104, 80>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 1, 0, 2, 2, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 1, 0, 0, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 1, 0, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 1, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 1, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 1, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 1, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 1, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 1, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 113896>, <24, 16305712>, <32, 269921580>, <40, 
        1091730640>, <48, 1600978856>, <56, 996963296>, <64, 276947046>, <72, 38197664>, <80, 3558264>, <88, 239344>, 
        <96, 10732>, <104, 144>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 1, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 1, 0, 2, 2, 2, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 1, 2, 0, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 1, 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, 0, 0, 0, 1, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, 0, 1, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 1, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 1, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 113608>, <24, 16303632>, <32, 269940940>, <40, 
        1091677040>, <48, 1601047144>, <56, 996929696>, <64, 276934054>, <72, 38221024>, <80, 3549144>, <88, 239696>, 
        <96, 11020>, <104, 176>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 1, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 1, 0, 2, 2, 2, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 1, 2, 0, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 1, 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, 0, 0, 0, 1, 0, 0, 2, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, 0, 1, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 1, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 1, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48072>, <20, 1048576>, <24, 8439312>, <28, 36700160>, <32,
        150665420>, <36, 286261248>, <40, 566864752>, <44, 749731840>, <48, 757598824>, <52, 749731840>, <56, 
        472117408>, <60, 286261248>, <64, 157658534>, <68, 36700160>, <72, 30356704>, <76, 1048576>, <80, 3483608>, <88,
        239696>, <96, 11020>, <104, 176>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 0, 2, 0, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 1, 0, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 1, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2, 1, 0, 0, 0, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 1, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 1, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 1, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 1, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 114360>, <24, 16275904>, <32, 270101212>, <40, 
        1091266112>, <48, 1601607112>, <56, 996528512>, <64, 277039558>, <72, 38257792>, <80, 3524232>, <88, 239808>, 
        <96, 12252>, <104, 320>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 1, 0, 2, 0, 2, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 1, 2, 0, 0, 2, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 1, 2, 0, 2, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 1, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 1, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 1, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 1, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 62328>, <20, 964416>, <24, 8109504>, <28, 40985728>, <32, 
        135110684>, <36, 313831744>, <40, 545579328>, <44, 739702272>, <48, 800809288>, <52, 700417664>, <56, 
        498280832>, <60, 289803008>, <64, 138528838>, <68, 55248000>, <72, 19100288>, <76, 6010368>, <80, 1780296>, <84,
        494144>, <88, 115904>, <92, 25728>, <96, 6172>, <100, 576>, <104, 64>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 1, 0, 0, 2, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 1, 2, 0, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 1, 2, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 1, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 1, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 1, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 1, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 1, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 48216>, <20, 1048576>, <24, 8439520>, <28, 36700160>, <32,
        150663228>, <36, 286261248>, <40, 566861600>, <44, 749731840>, <48, 757634568>, <52, 749731840>, <56, 
        472029376>, <60, 286261248>, <64, 157769862>, <68, 36700160>, <72, 30275136>, <76, 1048576>, <80, 3518120>, <88,
        232032>, <96, 11708>, <104, 160>, <112, 120>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 1, 0, 0, 2, 2, 0, 0, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 1, 2, 0, 0, 0, 2, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 1, 2, 2, 0, 2, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 1, 0, 0, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 1, 0, 2, 0, 2 ],
        \[ 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 1, 0, 2, 2 ],
        \[ 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 1, 2, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 1, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 113752>, <24, 16303840>, <32, 269938748>, <40, 
        1091673888>, <48, 1601082888>, <56, 996841664>, <64, 277045382>, <72, 38139456>, <80, 3583656>, <88, 232032>, 
        <96, 11708>, <104, 160>, <112, 120>, <128, 1> ]>


];