Problem Description

Input format

The first line consists of two integers, $n$ and $m$, representing the number of points and edges in a given graph.

Next, in the $m$ rows, two numbers $u$ and $v$ represent an edge in the graph, ensuring that there are no duplicate edges or self loops.

Output format

Output a string YES or NO to indicate whether the image is a tree-mirrored graph.

Samples

7 7
1 2
2 3
3 4
4 5
5 6
6 7
7 1

NO

Data scale and agreement

For $30\%$ of the data:$3\le n,m\le 300$;

For $60\%$ of the data:$3\le n,m\le 3.5\times 10^3$;

For all of the data:$3\le n,m\le 10^5$.