100 Degree Function

Suppose \(f(x)\) is a polynomial with integer coefficients of degree \(100\). Find the biggest possible number of pairs of integers \(n<m\), such that \(f(n)=m\) and \(f(m)=n\).

Details and assumptions

You are asked to find the biggest possible number of pairs, not the biggest pair. Hence, your answer is just an integer, not a pair of integers.

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