Ainz is a master player of the DMMORPG Yggdrasil. Currently, he is preparing to class up!

The classes in Yggdrasil form a forest: that is, there exists at most 1 path between each pair of nodes. However, Ainz finds that someone has used a world item to add some number of extra edges!

Ainz can use the skill «Wish Upon a Star» to remove at most a single edge. He then asks you: is it possible to restore the graph to a forest?

#### Constraints

##### Subtask 1 [20%]

##### Subtask 2 [80%]

#### Input Specification

The first line of input will contain two space separated integers, and , respectively.

The next lines will each contain two space separated integers, and , indicating there exists a bidirectional edge from to .

#### Output Specification

Output `YES`

if the graph can be restored to a forest by removing at most one edge, and `NO`

otherwise.

#### Sample Input 1

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

#### Sample Output 2

`YES`

#### Explanation for Sample Output 1

Removing the edge makes the graph a forest.

#### Sample Input 2

```
4 2
1 2
3 4
```

#### Sample Output 2

`YES`

#### Explanation for Sample Output 2

The graph is already a forest.

## Comments