Integer Solution:

triple [1,26,2] - Cost: 5
triple [2,11,60] - Cost: 6
triple [3,53,53] - Cost: 4
triple [4,20,25] - Cost: 5
triple [5,65,24] - Cost: 5
triple [6,45,35] - Cost: 4
triple [7,4,11] - Cost: 4
triple [8,57,65] - Cost: 4
triple [9,10,7] - Cost: 4
triple [10,15,26] - Cost: 4
triple [11,23,3] - Cost: 5
triple [12,33,17] - Cost: 4
triple [13,38,15] - Cost: 5
triple [14,66,46] - Cost: 4
triple [15,52,36] - Cost: 4
triple [16,35,30] - Cost: 5
triple [17,44,43] - Cost: 4
triple [18,31,49] - Cost: 5
triple [19,34,9] - Cost: 5
triple [20,60,13] - Cost: 4
triple [21,7,22] - Cost: 4
triple [22,30,54] - Cost: 4
triple [23,16,27] - Cost: 4
triple [24,12,12] - Cost: 4
triple [25,58,56] - Cost: 4
triple [26,62,40] - Cost: 4
triple [27,40,63] - Cost: 3
triple [28,6,51] - Cost: 6
triple [29,22,31] - Cost: 4
triple [30,64,48] - Cost: 5
triple [31,39,45] - Cost: 3
triple [32,25,23] - Cost: 5
triple [33,3,47] - Cost: 4
triple [34,43,58] - Cost: 5
triple [35,9,37] - Cost: 4
triple [36,17,10] - Cost: 4
triple [37,56,1] - Cost: 4
triple [38,42,32] - Cost: 4
triple [39,32,28] - Cost: 4
triple [40,63,55] - Cost: 5
triple [41,2,44] - Cost: 5
triple [42,48,6] - Cost: 5
triple [43,5,52] - Cost: 5
triple [44,54,42] - Cost: 4
triple [45,46,20] - Cost: 4
triple [46,51,61] - Cost: 4
triple [47,41,8] - Cost: 3
triple [48,21,41] - Cost: 4
triple [49,29,64] - Cost: 4
triple [50,50,66] - Cost: 4
triple [51,36,59] - Cost: 6
triple [52,27,4] - Cost: 4
triple [53,19,33] - Cost: 4
triple [54,14,62] - Cost: 4
triple [55,49,21] - Cost: 4
triple [56,24,38] - Cost: 4
triple [57,61,34] - Cost: 4
triple [58,8,19] - Cost: 6
triple [59,1,18] - Cost: 4
triple [60,28,5] - Cost: 4
triple [61,47,39] - Cost: 5
triple [62,18,14] - Cost: 4
triple [63,55,57] - Cost: 4
triple [64,37,50] - Cost: 4
triple [65,59,16] - Cost: 4
triple [66,13,29] - Cost: 5
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Total Costs: 286