Background

Translated from Problem F of NERC 2018.

Problem Description

You are given an integer $n$. You need to construct several proper fractions of the form $\dfrac{a_i}{b_i}$ such that $\sum^k_{i=1} \frac{a_i}{b_i} = 1 - \frac{1}{n}$, and each $b_i$ can divide $n$.

Input Format

A positive integer $n$ $(2 \leq n \leq 10^9)$.

Output Format

If it is impossible to construct, output one line NO.

Otherwise, output one valid solution. Output YES, and make $\sum^k_{i=1} \frac{a_i}{b_i} = 1 - \frac{1}{n}$. On the second line output an integer $k$, then in the next $k$ lines output two integers $a_i$ and $b_i$ $(b_i \neq n)$.

Note that the range of $k$ you output must satisfy $2 \leq k \leq 10^5$.

2

NO

6

YES
2
1 2
1 3

Hint

For all testdata, it is guaranteed that $2 \leq n \leq 10^9$.

For the first sample, there is no solution whose sum equals $\frac{1}{2}$.

For the second sample, $\frac{1}{2} + \frac{1}{3} = \frac{5}{6}$.

Translated by ChatGPT 5