Problem Statement

You are given an integer $X$.

Find all integers $n$ such that $\displaystyle \sqrt{n^2+n+X}$ is an integer.

Constraints

• $-10^{14} \le X\le 10^{14}$
• The input value is an integer.

Input

The input is given from Standard Input in the following format:

X

Output

Let $N_1,N_2,\ldots,N_K$ be the integers $n$ such that $\displaystyle \sqrt{n^2+n+X}$ is an integer, listed in ascending order (where $K$ is the number of $n$ satisfying the condition). Output in the following format:

K
N_1 N_2 \ldots N_K