In this task you need to check whether the given undirected graph is connected. That it is possible to go from any vertex to any other along the edges of this graph.

Input

The first line of the input are given numbers N and M are separated by

spaces – the number of vertices in the graph, respectively (1 <= N <= 10⁵, 0 <= M <= 10⁵). The following M lines contain two numbers u_i and v_i by a

space (1 <= u_i, v_i <= N); each such line means that the graph there is an edge between vertices u_i and v_i.

Output

Bring out the "YES", if the graph is connected, and "NO" otherwise.

Tayyorladi: Azat Yusupov

Text from: e-olimp.com