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.
The first line contains the number of vertices n and edges m (3≤n≤100,0≤m≤(n⋅(n−1))/2) of the graph. Then m lines are given - the list of edges.
Print "YES" or "NO" — the answer to the question about transitivity of a graph.