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

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

Print "YES" or "NO" — the answer to the question about transitivity of a graph.

Examples