# 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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