# Check if a Graph Is a Linked List

Given an undirected graph with

`v`

vertices and `e`

edges, you are asked to determine if the graph is actually a linked list. Input

The first line of the input contains two integers

`v`

(1 ≤ v ≤ 100 000) and `e`

(1 ≤ e ≤ 100 000).The following

`e`

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 a linked list and `No`

otherwise. Examples

Input | Output |

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

6 4
3 2
2 1
5 6
4 6 | No |

#### Constraints

Time limit: 1 seconds

Memory limit: 512 MB

Output limit: 1 MB