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

list:=
[
rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 1, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 1, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 1, 2, 2, 2, 2, 0, 2, 2, 0, 0 ],
        \[ 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 1, 2, 2, 0, 2, 2, 2, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 1, 2, 2, 0, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 1, 2, 0, 2, 0, 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, 2, 0, 0, 1, 2, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 1, 0, 2, 0, 0 ],
        \[ 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, 0, 2, 2, 1, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110756>, <24, 16389164>, <32, 268436464>, <40, 
        1094752436>, <48, 1601362496>, <56, 992063160>, <64, 279838958>, <72, 38728680>, <80, 3123364>, <88, 155740>, 
        <96, 5984>, <104, 36>, <112, 56>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 2, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 1, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 2, 1, 0, 2, 2, 0, 0, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 1, 0, 0, 0, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 1, 0, 0, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 1, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 1, 2, 2, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 1, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110808>, <24, 16384832>, <32, 268462332>, <40, 
        1094688064>, <48, 1601441736>, <56, 992023680>, <64, 279824902>, <72, 38756992>, <80, 3110056>, <88, 157760>, 
        <96, 6012>, <104, 64>, <112, 56>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 2, 0, 1, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 1, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 1, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 2, 0, 2, 1, 2, 2, 2, 0, 2, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 1, 0, 2, 2, 0, 2, 2, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 1, 0, 2, 2, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 1, 2, 2, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 1, 2, 2, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110844>, <24, 16382692>, <32, 268475352>, <40, 
        1094653564>, <48, 1601490864>, <56, 991984872>, <64, 279840190>, <72, 38755192>, <80, 3110236>, <88, 157172>, 
        <96, 6184>, <104, 76>, <112, 56>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 1, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 1, 0, 2, 2, 2, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 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, 2, 0, 0, 2, 2, 2, 2, 2, 0, 1, 0, 0, 2, 2, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 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, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 1, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 1, 0, 0, 0 ],
        \[ 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, 2, 2, 0, 0, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110708>, <24, 16387484>, <32, 268447584>, <40, 
        1094725636>, <48, 1601389920>, <56, 992062488>, <64, 279812302>, <72, 38755720>, <80, 3111604>, <88, 157836>, 
        <96, 5904>, <104, 52>, <112, 56>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 2, 1, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 1, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2 ],
        \[ 1, 1, 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, 2, 0, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 2, 2, 1, 2, 2, 2, 2, 0, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 1, 2, 0, 2, 2, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 1, 0, 2, 2, 0, 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, 0, 2, 1, 0, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 1, 0, 2, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 1, 2, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 111424>, <24, 16368792>, <32, 268551252>, <40, 
        1094461864>, <48, 1601753304>, <56, 991790832>, <64, 279899830>, <72, 38765392>, <80, 3100336>, <88, 157432>, 
        <96, 6644>, <104, 136>, <112, 56>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 2 ],
        \[ 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 1, 0, 0, 2, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 1, 0, 2, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 1, 2, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 1, 0, 2, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 1, 2, 0, 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, 2, 0, 2, 2, 2, 1, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110664>, <24, 16383888>, <32, 268471148>, <40, 
        1094664720>, <48, 1601467816>, <56, 992018976>, <64, 279806310>, <72, 38776736>, <80, 3102040>, <88, 158800>, 
        <96, 6060>, <104, 80>, <112, 56>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 2, 2, 1, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 1, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 1, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 1, 2, 2, 0, 2, 2, 0, 2, 2, 0 ],
        \[ 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 1, 0, 2, 0, 2, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 1, 2, 2, 0, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 1, 2, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 1, 2, 2, 2, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 1, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110800>, <24, 16385832>, <32, 268456772>, <40, 
        1094699544>, <48, 1601434744>, <56, 992011920>, <64, 279851670>, <72, 38733872>, <80, 3120256>, <88, 155592>, 
        <96, 6180>, <104, 56>, <112, 56>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 2, 1, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 2, 1, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 1, 0, 2, 2, 2, 2, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 1, 2, 2, 0, 0, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 1, 2, 0, 2, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 1, 2, 2, 0, 2, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 1, 2, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 1, 2, 2, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 1, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110980>, <24, 16382700>, <32, 268472240>, <40, 
        1094663892>, <48, 1601476480>, <56, 991993272>, <64, 279840750>, <72, 38752424>, <80, 3110788>, <88, 157596>, 
        <96, 6048>, <104, 68>, <112, 56>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 2, 1, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 1, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 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, 2, 0, 0, 0, 0, 2, 0, 2, 1, 0, 0, 2, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 1, 0, 0, 2, 0, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 1, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 1, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 1, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110632>, <24, 16391008>, <32, 268426988>, <40, 
        1094777760>, <48, 1601321704>, <56, 992105664>, <64, 279808998>, <72, 38743616>, <80, 3117880>, <88, 157152>, 
        <96, 5804>, <104, 32>, <112, 56>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 1, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 1, 2, 2, 0, 0, 0, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 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, 0, 2, 0, 2, 2, 2, 1, 2, 0, 2, 0, 2, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 1, 2, 2, 2, 2, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 1, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 1, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 1, 0, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 1, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110772>, <24, 16384588>, <32, 268464608>, <40, 
        1094681940>, <48, 1601448928>, <56, 992021496>, <64, 279821262>, <72, 38761256>, <80, 3108340>, <88, 157948>, 
        <96, 6032>, <104, 68>, <112, 56>, <128, 1> ]>
,

rec<RF | 
    mat := [ PowerSequence(IntegerRing()) |
        \[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 1, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2 ],
        \[ 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0 ],
        \[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0, 0 ],
        \[ 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 1, 0, 0, 2, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 1, 0, 0, 2, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 1, 0, 2, 0, 0, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 1, 2, 0, 2, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 1, 2, 0, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 2, 2, 0, 1, 0, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 1, 2, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 1, 0 ],
        \[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 1 ]
    ],
    dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 110948>, <24, 16380540>, <32, 268486960>, <40, 
        1094623652>, <48, 1601534144>, <56, 991948248>, <64, 279857774>, <72, 38750664>, <80, 3111268>, <88, 156652>, 
        <96, 6304>, <104, 84>, <112, 56>, <128, 1> ]>


];