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The bound is polynomial in n and the largest absolute value of a sub-determinant of A, denoted by \\Delta. More precisely, we show that the diameter of P is bounded by O(\\Delta^2 n^4 log n\\Delta). If P is bounded, then we show that the diameter of P is at most O(\\Delta^2 n^3.5 log n\\Delta).\n  For the special case in which A is a totally unimodular matrix, the bounds are O(n^4 log n) and O(n^3.5 log n) respectively. 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