uppertraceable:=
[
    <7, []>,
    <8, []>,
    <9, []>,
    <10, [ 984, 987, 988, 990, 992, 993, 995, 996, 998, 999, 1000, 1002, 
           1003, 1240, 1241, 1242, 1243, 1244 ]>,
    <11, [ 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 
           358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 508, 509, 510, 
           511, 512, 513, 514, 515, 516, 517, 518, 519 ]>,
    <12, [ 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 149, 150, 151, 
          152, 153, 154, 155, 156, 157, 158, 159 ]>,
    <13, [ 13, 14, 15, 16, 32, 33, 34, 35, 36, 38, 39 ]>,
    <14, [ 1, 4, 5, 6 ]>,
    <15, [ 1 ]>
];

lowertraceable
[
    <11, []>,
    <10, []>,
    <9, []>
];