Integer Solution:

triple [1,43,66] - Cost: 17
triple [2,46,23] - Cost: 57
triple [3,9,58] - Cost: 34
triple [4,61,57] - Cost: 83
triple [5,50,63] - Cost: 78
triple [6,20,47] - Cost: 16
triple [7,57,5] - Cost: 21
triple [8,59,25] - Cost: 46
triple [9,1,15] - Cost: 23
triple [10,29,1] - Cost: 50
triple [11,30,6] - Cost: 29
triple [12,62,61] - Cost: 22
triple [13,45,45] - Cost: 105
triple [14,8,14] - Cost: 53
triple [15,19,44] - Cost: 64
triple [16,41,18] - Cost: 57
triple [17,51,36] - Cost: 31
triple [18,21,41] - Cost: 29
triple [19,53,40] - Cost: 73
triple [20,31,17] - Cost: 113
triple [21,64,26] - Cost: 10
triple [22,27,28] - Cost: 74
triple [23,37,16] - Cost: 45
triple [24,32,30] - Cost: 73
triple [25,65,9] - Cost: 46
triple [26,44,43] - Cost: 44
triple [27,17,8] - Cost: 14
triple [28,4,33] - Cost: 45
triple [29,49,19] - Cost: 42
triple [30,47,35] - Cost: 23
triple [31,22,24] - Cost: 31
triple [32,52,64] - Cost: 8
triple [33,11,56] - Cost: 58
triple [34,58,13] - Cost: 13
triple [35,40,53] - Cost: 44
triple [36,10,49] - Cost: 26
triple [37,5,12] - Cost: 8
triple [38,33,46] - Cost: 124
triple [39,66,37] - Cost: 44
triple [40,14,42] - Cost: 58
triple [41,48,32] - Cost: 48
triple [42,23,31] - Cost: 55
triple [43,36,2] - Cost: 23
triple [44,42,11] - Cost: 33
triple [45,63,59] - Cost: 6
triple [46,54,7] - Cost: 81
triple [47,24,54] - Cost: 45
triple [48,39,52] - Cost: 24
triple [49,13,10] - Cost: 36
triple [50,2,22] - Cost: 38
triple [51,28,4] - Cost: 47
triple [52,18,27] - Cost: 11
triple [53,34,21] - Cost: 28
triple [54,25,34] - Cost: 43
triple [55,6,50] - Cost: 23
triple [56,60,20] - Cost: 28
triple [57,38,51] - Cost: 70
triple [58,56,29] - Cost: 32
triple [59,15,62] - Cost: 46
triple [60,26,65] - Cost: 37
triple [61,7,48] - Cost: 29
triple [62,12,39] - Cost: 29
triple [63,55,55] - Cost: 27
triple [64,35,38] - Cost: 26
triple [65,16,60] - Cost: 8
triple [66,3,3] - Cost: 54
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Total Costs: 2758