$\sqrt{f}(x)$

A polynomial $f(x) = a_n x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0$ with integer coefficients, defined for all real $x$, is given.

If a polynomial $g(x) = b_m x^m + b_{m-1} x^{m-1} + \cdots + b_1 x + b_0$ satisfies $g(g(x)) = f(x)$ for all $x$, then $g$ is called a square root of $f$.

Determine whether $f$ has a square root $g$ in which every coefficient $b_i$ is an integer between $-100$ and $100$ inclusive. If one exists, print any such $g$.

The first line contains the degree $n$ of $f(x)$.

The second line contains the coefficients $a_n, a_{n-1}, \cdots, a_1, a_0$ of $f(x)$, separated by spaces.

If a polynomial $g(x) = b_m x^m + b_{m-1} x^{m-1} + \cdots + b_1 x + b_0$ ($b_m \neq 0$) satisfying the conditions exists, print $m$ on the first line. Then print $b_m, b_{m-1}, \cdots, b_1, b_0$ in that order, separated by spaces, on the second line. If several answers exist, print any one of them.

If $g(x)$ does not exist, print -1 on the first line.

• $1 \le n \le 25$
• $-10^{15} \le a_i \le 10^{15}$, $a_n \neq 0$