# Check if a Graph is Complete

A graph is complete if all the vertices are connected to all the other vertices.

Given an undirected graph with

`n`

vertices and `m`

edges, you are asked to check if it’s a complete graph. Input

The first line of the input contains two integers

`n`

(1 ≤ v ≤ 500) and `m`

(1 ≤ e ≤ 100 000).The following

`m`

lines contain pairs of integers `v1`

, `v2`

(1 ≤ v1, v2 ≤ v) which means that the vertex `v1`

is connected to the vertex `v2`

and vice versa. Output

The program should print

`Yes`

if the graph is complete and `No`

otherwise. Examples

Input | Output |

3 2
1 2
2 3
| No |

3 3
1 2
2 3
3 1 | Yes |

7 21
1 2
1 3
1 4
1 5
1 6
1 7
2 3
2 4
2 5
2 6
2 7
3 4
3 5
3 6
3 7
4 5
4 6
4 7
5 6
5 7
6 7 | Yes |

#### Constraints

Time limit: 1 seconds

Memory limit: 512 MB

Output limit: 1 MB