22636번 - Complex Integer Solutions 다국어

문제

Let f(x) = a₀ + a₁x + a₂x² + ... + a_dx^d be the function where each a_i (0 ≤ i ≤ d) is a constant integer (and a_d is non-zero) and x is a variable. Your task is to write a program that finds all complex integer solutions of the equation f(x) = 0 for a given f(x). Here, by complex integers, we mean complex numbers whose real and imaginary parts are both integers.

입력

The input consists of two lines. The first line of the input contains d, the degree of f(x). The second line contains (d + 1) integers a₀, ... , a_d, the coeffcients of the equation. You may assume all the following: 1 ≤ d ≤ 10, |a_i| ≤ 10⁶ and a_d ≠ 0.

출력

There should be two lines in the output. In the first line, print the number m of complex integer solutions. In the second line, print m solutions separated by space. Each solution should be counted and printed exactly once even if it is a multiple root. The solutions should be printed in ascending order of their real parts then their imaginary parts, and in the following fashion: 0, -2, i, -3i, 2+i, and 3-4i.

제한

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