The Unique Topological Sort

An unweighted directed graph is given. Determine whether it has a unique topological sort.

Input

The first line contains the number of vertices $n(1\le n\le 2\cdot 10^5)$ and the number of edges $m(1\le m\le 10^5)$ in the graph. The following $m$ lines describe the edges of the graph, each represented by a pair of integers — the indices of the start and end vertices.

Output

Print "YES" if there is a unique topological sort of the vertices, and "NO" if there are multiple valid sorts. If a topological sort is impossible, print $-1$.

Examples