# 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, 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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