Let \(\pi\) be a permutation of \(\{1, 2, . . . , 2000\}\).

Find the maximum possible number of ordered pairs \((i, j)\in\{1, 2, . . . , 2000\}^2\) with \(i < j\) such that \(\pi(i).\pi(j)> i. j\).

This problem is adapted from HMMT.

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