Roads of Potokolandiya

In Potokoland, there are $n$ cities and $n$ two-way roads. The $i$-th road connects cities $i$ and $(i+i)$ (if $i+i>n$, then $i+i-n$).

For example, if $n=5$, the roads will be $(1,2)$, $(2,4)$, $(3,1)$, $(4,3)$, and $(5,5)$.

Determine if it is possible to travel from any city to any other city using the roads. If not, find a pair of cities that are not connected.

Input

The first line contains one integer $n$ ($1\le n\le 10^6$).

Output

Output YES if it is possible to travel from any city to any other city.

Otherwise, output NO on the first line. On the second line, output any two cities $a$ and $b$ ($1\le a,b\le n$; $a\ne b$) such that it is impossible to travel from $a$ to $b$ using the roads.

Examples