\[ \large \min{\left|\frac{x_i-x_j}{1+x_ix_j}\right|} \leq C\]

For all 7-tuples of real numbers \((x_1, x_2,...,x_7)\), the following inequality holds, where the minimum is taken over all \(1 \leq i < j \leq 7\). Let \(D\) be the smallest possible value of \(C\). If we can have \(\min{\left|\dfrac{x_i-x_j}{1+x_ix_j}\right|} = D\), submit your answer as \(\dfrac{1}{D^2} + 2017\). If not, then submit your answer as \(\dfrac{1}{D^2} + 1\).

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