Integer Solution:

triple [1,1,18] - Cost: 4
triple [2,3,25] - Cost: 4
triple [3,21,15] - Cost: 3
triple [4,13,27] - Cost: 4
triple [5,11,11] - Cost: 4
triple [6,32,29] - Cost: 4
triple [7,25,30] - Cost: 4
triple [8,6,24] - Cost: 4
triple [9,30,9] - Cost: 4
triple [10,5,13] - Cost: 4
triple [11,27,21] - Cost: 4
triple [12,29,28] - Cost: 4
triple [13,16,3] - Cost: 4
triple [14,8,31] - Cost: 4
triple [15,19,22] - Cost: 4
triple [16,23,12] - Cost: 4
triple [17,2,23] - Cost: 4
triple [18,10,16] - Cost: 4
triple [19,4,20] - Cost: 4
triple [20,24,33] - Cost: 4
triple [21,17,1] - Cost: 4
triple [22,31,19] - Cost: 4
triple [23,22,17] - Cost: 4
triple [24,33,26] - Cost: 4
triple [25,14,10] - Cost: 4
triple [26,28,4] - Cost: 4
triple [27,18,5] - Cost: 4
triple [28,9,6] - Cost: 4
triple [29,12,32] - Cost: 4
triple [30,15,7] - Cost: 4
triple [31,7,14] - Cost: 4
triple [32,26,2] - Cost: 5
triple [33,20,8] - Cost: 3
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Total Costs: 131