Order Of A Polynomial Shuffle

For how many possible values of nn, can one find a polynomial with integer coefficients f(x)f(x) and pair-wise distinct integers x1,x2,...,xn,x_1,x_2,...,x_n, such that 0xi240\leq x_i \leq 24 for all ii and {f(x1)x2(mod25)f(x2)x3(mod25) ...f(xn)x1(mod25) ?\begin{cases}f(x_1)\equiv x_2 \pmod {25}\\ f(x_2)\equiv x_3 \pmod {25}\\ \ ...\\ f(x_n)\equiv x_1 \pmod {25} \ ?\end{cases}

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