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

list:=
[
rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0 ],
        \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 2, 1, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 1, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 0 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 2, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 1, 2, 0, 0, 0, 2, 2, 2, 2, 2 ],
        \[ 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 1, 2, 2, 2, 0, 2, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 1, 2, 2, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 1, 2, 2, 2, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 1, 0, 2, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110918>, <24, 16381156>, <32, 268387564>, <40, 
        1094807324>, <48, 1601702006>, <56, 991400424>, <64, 280143638>, <72, 38817720>, <80, 3060370>, <88, 150004>, 
        <96, 6012>, <104, 108>, <112, 50>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 1, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 1, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 2, 0, 2, 1, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 2, 0, 0, 1, 0, 0, 2, 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, 2, 0, 2, 2, 1, 0, 0, 2, 0, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 1, 0, 2, 0, 0, 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, 1, 0, 2, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, 1, 2, 2, 2, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 1, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110546>, <24, 16393264>, <32, 268318432>, <40, 
        1094984432>, <48, 1601459054>, <56, 991578336>, <64, 280091390>, <72, 38806752>, <80, 3069262>, <88, 150256>, 
        <96, 5472>, <104, 48>, <112, 50>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 2, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 1, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 2, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 2, 0, 0, 1, 2, 2, 2, 0, 2, 2, 0, 0, 2, 0 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 2, 2, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0 ],
        \[ 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 1, 0, 2, 0, 2, 2, 0, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 1, 0, 2, 2, 2, 0, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 1, 0, 0, 2, 0, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 1, 0, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 1, 2, 0, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110574>, <24, 16389932>, <32, 268339460>, <40, 
        1094927700>, <48, 1601541382>, <56, 991510968>, <64, 280120902>, <72, 38800424>, <80, 3071194>, <88, 148828>, 
        <96, 5812>, <104, 68>, <112, 50>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 2, 1, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 1, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 1, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 2, 0, 1, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 2, 2, 0, 2, 1, 0, 0, 2, 0, 2, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 1, 0, 2, 2, 0, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 1, 0, 0, 0, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 1, 2, 0, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 1, 2, 2, 0, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 1, 2, 2, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 1, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110714>, <24, 16392856>, <32, 268317624>, <40, 
        1094987464>, <48, 1601459454>, <56, 991566576>, <64, 280110766>, <72, 38792080>, <80, 3074710>, <88, 149496>, 
        <96, 5464>, <104, 40>, <112, 50>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0 ],
        \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 2, 1, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 2, 1, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 0, 0, 1, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 0, 0, 0, 1, 2, 2, 2, 0, 2, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 1, 0, 2, 2, 2, 2, 0, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 1, 0, 0, 2, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 1, 2, 2, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 1, 0, 0, 2, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 1, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110626>, <24, 16388016>, <32, 268349744>, <40, 
        1094905104>, <48, 1601561614>, <56, 991516512>, <64, 280091166>, <72, 38828960>, <80, 3058270>, <88, 151536>, 
        <96, 5616>, <104, 80>, <112, 50>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 2, 1, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 1, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 0, 1, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 0, 2, 2, 1, 0, 2, 2, 0, 2, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 1, 2, 0, 0, 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, 2, 0, 0, 1, 2, 2, 2, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 1, 0, 0, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 1, 2, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 1, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 1, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110374>, <24, 16392948>, <32, 268324396>, <40, 
        1094965676>, <48, 1601486006>, <56, 991559688>, <64, 280095254>, <72, 38808408>, <80, 3069298>, <88, 149444>, 
        <96, 5692>, <104, 60>, <112, 50>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0 ],
        \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 2, 1, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 1, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 0, 2, 0, 1, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 1, 0, 0, 2, 2, 2, 2, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 1, 2, 0, 2, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 1, 2, 2, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 1, 2, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 1, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110770>, <24, 16391280>, <32, 268326208>, <40, 
        1094966768>, <48, 1601484590>, <56, 991554144>, <64, 280106174>, <72, 38801376>, <80, 3070126>, <88, 150320>, 
        <96, 5440>, <104, 48>, <112, 50>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2 ],
        \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ],
        \[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 1, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 2 ],
        \[ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2 ],
        \[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 2, 0, 0, 0, 0, 2, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0 ],
        \[ 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 1, 2, 0, 2, 2, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 1, 0, 0, 2, 0, 2, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 1, 0, 0, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 1, 0, 2, 2, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 1, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 1, 2, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110346>, <24, 16398440>, <32, 268290088>, <40, 
        1095054968>, <48, 1601366174>, <56, 991639824>, <64, 280082318>, <72, 38793456>, <80, 3076966>, <88, 149256>, 
        <96, 5384>, <104, 24>, <112, 50>, <128, 1> ]>

];