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Problems

Graph tournament

Graph tournament

Time limit 1 second
Memory limit 128 MiB

A directed graph is called a tournament if there is exactly one edge between any pair of its different vertices. Graph is given by the list of edges. Check if it is a tournament.

Input data

The first line contains number of vertices n~(1 \le n \le 100) and number of edges m~(1 \le m \le n \cdot (n - 1)/2) in the graph. The next m lines contain the pairs of numbers — the edges of the graph.

Output data

Print "YES" if graph is tournament and "NO" otherwise.

Examples

Input example #1
4 6
1 2
1 3
4 1
2 3
4 2
4 3
Output example #1
YES