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 $f?$