Xyene really likes the organic compound xylene, also known as dimethylbenzene. He has received an organic molecule as a present, and would like to know if there exists a dimethylbenzene somewhere in it.

However, organic chemistry is a struggle for Xyene, so he'll settle for knowing whether or not his molecule contains **six** carbons atoms arranged in a ring, or **cycle**. There may be multiple cycles in Xyene's present, but he's only interested in finding out if there is **at least one** that is six atoms long.

Xyene has numbered the carbon atoms in his present from , and has given you **distinct** pairs of the form , representing a bond between atoms and .

Does his present contain at least one cycle of length six?

#### Input Specification

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

The next lines will contain two integers and , defining a bond.

#### Output Specification

`YES`

if the given molecule contains a cycle that is six carbon atoms long, `NO`

otherwise.

#### Sample Input 1

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

#### Sample Output 1

`YES`

#### Explanation for Sample 1

This is a ring of six carbons: .

#### Sample Input 2

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

#### Sample Output 2

`NO`

#### Explanation for Sample 2

Though this may be a cycle, it is only of length three.

#### Sample Input 3

```
2 1
1 2
```

#### Sample Output 3

`NO`

#### Explanation of Sample 3

This is not a cycle!

#### Sample Input 4

```
8 8
1 2
2 3
3 4
4 5
5 6
6 1
6 7
7 8
```

#### Sample Output 4

`YES`

#### Sample Input 5

```
8 9
1 2
2 3
3 4
4 5
5 6
6 1
6 7
7 8
8 1
```

#### Sample Output 5

`YES`

## Comments

can there be lines in between the circles? what would this output: 6 7 1 2 2 3 3 4 4 5 5 6 6 1 1 4

I noticed that the ladderane structure is possible, but I'm confused on whether a ladderane contains a 'simple cycle' of length 6.

Example Case:

What is the proper answer? Do the AC submissions disagree over this?

aren't the carbon atoms supposed to be placed in increasing order?

1 2, 2 3, 3 5, 5 6, 6 4, and 4 1 gives a simple cycle of length 6.

Cycle means simple cycle)