13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T737,

You are given a positive integer $$$n$$$.

Find a sequence of fractions $$$\frac{a_i}{b_i}$$$, $$$i = 1 \ldots k$$$ (where $$$a_i$$$ and $$$b_i$$$ are positive integers) for some $$$k$$$ such that:

$$$$$$ \begin{cases} \text{$b_i$ divides $n$, $1 \lt b_i \lt n$ for $i = 1 \ldots k$} \\ \text{$1 \le a_i \lt b_i$ for $i = 1 \ldots k$} \\ \text{$\sum\limits_{i=1}^k \frac{a_i}{b_i} = 1 - \frac{1}{n}$} \end{cases} $$$$$$

Input

The input consists of a single integer $$$n$$$ ($$$2 \le n \le 10^9$$$).

Output

In the first line print "YES" if there exists such a sequence of fractions or "NO" otherwise.

If there exists such a sequence, next lines should contain a description of the sequence in the following format.

The second line should contain integer $$$k$$$ ($$$1 \le k \le 100\,000$$$) — the number of elements i

Fractions

Examples