RF1:=recformat<mat:SeqEnum,dtb:SeqEnum>;
 list:=

[ PowerStructure(Rec) |
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 3, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0 ],
            \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 3, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 1, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 3, 0, 2, 2, 0, 0, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 2, 2, 2, 1, 0, 2, 0, 0, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 2, 2, 0, 2, 3, 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, 2, 2, 0, 2, 2, 0, 1, 2, 2, 0, 2, 2 ],
            \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 1, 0, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 3, 2, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 1, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 3, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 1 ],
            \[ 2, 2, 0, 0, 0, 0, 0, 0, 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, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 59288>, <20, 996800>, <24, 8073888>, <28, 40417152>, 
            <32, 137580412>, <36, 309808576>, <40, 547465184>, <44, 742758912>, <48, 795060360>, <52, 704932736>, <56, 
            496435264>, <60, 289381632>, <64, 140215558>, <68, 53471616>, <72, 20331968>, <76, 5331456>, <80, 2095336>, 
            <84, 370368>, <88, 157472>, <92, 14208>, <96, 8700>, <100, 192>, <104, 96>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0 ],
            \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 3, 2, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 2, 0, 0, 2, 2, 2, 2, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 1, 2, 2, 2, 2, 0, 2, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 2, 0, 2, 1, 2, 2, 0, 2, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 3, 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, 2, 2, 2, 2, 0, 2, 2, 1, 2, 0, 0, 2, 0 ],
            \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 3, 2, 0, 2, 2 ],
            \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 3, 0, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 3, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 1, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 3 ],
            \[ 2, 2, 0, 0, 0, 0, 0, 0, 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, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 60744>, <20, 977856>, <24, 8144272>, <28, 40386944>, 
            <32, 137323852>, <36, 310154688>, <40, 547693808>, <44, 742117888>, <48, 795212136>, <52, 705326976>, <56, 
            496117664>, <60, 289413376>, <64, 140310182>, <68, 53391744>, <72, 20372448>, <76, 5313024>, <80, 2088792>, 
            <84, 384192>, <88, 152016>, <92, 16768>, <96, 7564>, <100, 192>, <104, 48>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 3, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
            \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 3, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 3, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 1, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 3, 0, 2, 2, 0, 0, 0, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 3, 0, 0, 0, 0, 2, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 3, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 2, 0, 2, 2, 3, 2, 0, 0, 2, 2, 2 ],
            \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 3, 0, 0, 0, 2, 0 ],
            \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 3, 0, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 3, 2, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 0, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 1, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 3 ],
            \[ 2, 2, 0, 0, 0, 0, 0, 0, 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, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 60568>, <20, 986144>, <24, 8097504>, <28, 40403136>, 
            <32, 137513724>, <36, 310005408>, <40, 547425056>, <44, 742340864>, <48, 795349128>, <52, 705304128>, <56, 
            496112832>, <60, 289229952>, <64, 140324358>, <68, 53516352>, <72, 20347456>, <76, 5306624>, <80, 2090984>, 
            <84, 374176>, <88, 153184>, <92, 16576>, <96, 8572>, <100, 288>, <104, 160>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 3, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2 ],
            \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 3, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 3, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 1, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 3, 0, 0, 2, 2, 0, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2, 3, 0, 2, 0, 2, 0, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 2, 2, 2, 2, 3, 0, 2, 2, 2, 0, 2 ],
            \[ 0, 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, 1, 2, 0, 0, 2, 2 ],
            \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 3, 2, 0, 2, 0 ],
            \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 1, 2, 0, 2 ],
            \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 0, 1, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 1 ],
            \[ 2, 2, 0, 0, 0, 0, 0, 0, 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, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 60024>, <20, 987136>, <24, 8102400>, <28, 40402176>, 
            <32, 137493916>, <36, 309985536>, <40, 547472512>, <44, 742423552>, <48, 795274568>, <52, 705154048>, <56, 
            496193024>, <60, 289377792>, <64, 140264774>, <68, 53437952>, <72, 20377344>, <76, 5323776>, <80, 2081608>, 
            <84, 375808>, <88, 154624>, <92, 15616>, <96, 8604>, <100, 256>, <104, 128>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 3, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 0 ],
            \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 3, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 3, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 3, 0, 2, 0, 2, 0, 2, 0, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 3, 0, 0, 0, 2, 0, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 3, 2, 2, 0, 0, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 3, 2, 2, 0, 2, 2, 2 ],
            \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 3, 0, 0, 0, 2, 2 ],
            \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 3, 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, 0, 2, 2, 1, 2, 0, 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, 2, 2, 2, 0, 0, 1, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 1, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 3 ],
            \[ 2, 2, 0, 0, 0, 0, 0, 0, 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, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 60488>, <20, 987072>, <24, 8090768>, <28, 40402304>, 
            <32, 137558732>, <36, 309986752>, <40, 547304816>, <44, 742416896>, <48, 795513192>, <52, 705169280>, <56, 
            496001952>, <60, 289358080>, <64, 140341158>, <68, 53453184>, <72, 20371168>, <76, 5317120>, <80, 2077784>, 
            <84, 377024>, <88, 154320>, <92, 15744>, <96, 8972>, <100, 192>, <104, 176>, <112, 120>, <128, 1> ]>,
    rec<RF1 | 
        mat := [ PowerSequence(IntegerRing()) |
            \[ 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2 ],
            \[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 3, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 3, 2, 2, 2, 2, 2, 2, 0, 0, 0 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 3, 0, 0, 2, 2, 2, 2, 2 ],
            \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 2, 3, 2, 0, 0, 0, 0, 2 ],
            \[ 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 3, 0, 0, 0, 2, 0 ],
            \[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 3, 2, 2, 0, 2 ],
            \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 1, 2, 2, 0 ],
            \[ 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 3, 2, 2 ],
            \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 1, 0 ],
            \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 3 ],
            \[ 2, 2, 0, 0, 0, 0, 0, 0, 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, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
        ],
        dtb := [ car<IntegerRing(), IntegerRing()> | <0, 1>, <16, 59768>, <20, 986848>, <24, 8105600>, <28, 40402496>, 
            <32, 137479452>, <36, 309991264>, <40, 547505792>, <44, 742398720>, <48, 795231560>, <52, 705201088>, <56, 
            496223488>, <60, 289328512>, <64, 140255814>, <68, 53467072>, <72, 20375808>, <76, 5315328>, <80, 2082888>, 
            <84, 376160>, <88, 154752>, <92, 15936>, <96, 8476>, <100, 224>, <104, 128>, <112, 120>, <128, 1> ]>
]
;