Cycling Through The Polynomial Shuffle

Suppose \(f(x)\) is a polynomial with integer coefficients which is bijective modulo \(49\), which means that \(x\not \equiv y \pmod {49} \Leftrightarrow f(x)\not \equiv f(y) \pmod {49}.\) We define the composition powers \(f^{(i)}(x)\) by setting \(f^{(1)}=f\) and \(f^{(i+1)}(x)=f(f^{(i)}(x)).\) For a given \(f,\) its order (in modulo 49) is defined as the smallest positive integer \(n,\) such that \(f^{(n)}(x)\equiv x \pmod {49}\) for all integers \(x.\)

What is the largest possible order of \(f?\)

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