Problems
Transitivity of a graph
Transitivity of a graph
Undirected graph without loops and multiple edges is called transitive, if from conditions that vertices u and v are connected with an edge, vertices v and w are connected with an edge and all three vertices u, v and w are different, implies that vertices u and w are connected with an edge.
Verify that a given undirected graph is transitive.
Input data
The first line contains the number of vertices n and edges m~(3 \le n \le 100, 0 \le m \le (n \cdot (n - 1)) / 2) of the graph. Then m lines are given - the list of edges.
Output data
Print "YES" or "NO" — the answer to the question about transitivity of a graph.
Examples
Input example #1
3 3 1 2 2 3 1 3
Output example #1
YES
Input example #2
3 2 1 2 1 3
Output example #2
NO