题目描述

Let $T$ be a rooted tree (a connected undirected acylic 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.

输入格式

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.

输出格式

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

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

NO

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

YES

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

YES

提示

对于 $30\%$ 的数据，$3 \le N,M \le 300$。

对于 $60\%$ 的数据，$3 \le N,M \le 3500$。

对于所有数据，$3 \le N,M \le 10^5$。