Problem Description

Let $T$ be a rooted tree (a connected undirected acyclic graph), and let $S$ be a perfect copy of $T$. Construct a new graph by taking the union of $T$ and $S$, and merging the corresponding leaf nodes (but never the root). We call such a graph a tree-mirrored graph.

Input Format

The first line of input contains two integers $N$ and $M$, the number of vertices and edges of a graph $G$. The vertices in $G$ are labeled from $1$ to $N$. The following $M$ lines describe the edges. Each such line contains two integers $x$ and $y (x≠y; 1 \le x,y \le N)$, describing one edge. There will be at most one edge between any pair of vertices.

Output Format

The first and only line of output should contain the string "YES" if the graph $G$ is a tree-mirrored graph, and "NO" otherwise.

Sample Input and Output

Sample Input #1

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

Sample Output #1

NO

Sample Input #2

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

Sample Output #2

YES

Sample Input #3

22 28
13 8
8 1
1 22
1 12
1 14
13 18
13 4
4 20
20 7
13 15
15 3
15 9
9 16
9 19
22 5
12 5
14 5
5 11
11 6
18 6
7 10
10 17
17 6
3 21
21 6
16 2
19 2
2 21

Sample Output #3

YES

Notes

For 30% of the data, $3 \le N,M \le 300$.

For 60% of the data, $3 \le N,M \le 3500$.

For all data, $3 \le N,M \le 10^5$.

见题面 Input 部分

见题面 Output 部分