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