Complex Integer Solutions

Let $f(x) = a_0 + a_1 x + a_2 x^2 + \cdots + a_d x^d$, where each $a_i$ ($0 \le i \le d$) is an integer constant and $a_d \ne 0$. Write a program that finds all complex integer solutions of $f(x) = 0$. A complex integer is a complex number whose real and imaginary parts are both integers.

The input consists of two lines. The first line contains $d$, the degree of $f(x)$. The second line contains $d+1$ integers $a_0, a_1, \ldots, a_d$. The following are guaranteed: $1 \le d \le 10$, $|a_i| \le 10^6$, and $a_d \ne 0$.

Print two lines. On the first line, print the number $m$ of complex integer solutions. On the second line, print the $m$ solutions separated by spaces. Count and print each solution exactly once even if it is a multiple root. Sort the solutions in ascending order of real part, then imaginary part, and print them in the following format: 0, -2, i, -3i, 2+i, 3-4i.