Semi-complete graph

A directed graph is called semi-complete if there is at least one edge between any pair of its distinct vertices.

For a graph given by a list of edges, check if it is semi-complete.

Input

Contains the number of vertices n (1 ≤ n ≤ 100) and the number of edges m (1 ≤ m ≤ ** n** * (n - 1)) in the graph. Then follows m pairs of numbers - the edges of the graph.

Output

Print YES if the graph is semi-complete and NO otherwise.

Examples