# [BalticOI 2011 Day2] Tree Mirroring

## 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.

## 输入输出格式

### 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.

## 输入输出样例

### 输入样例 #1

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

### 输出样例 #1

``NO``

### 输入样例 #2

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

### 输出样例 #2

``YES``

### 输入样例 #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``````

### 输出样例 #3

``YES``