An unweighted directed acyclic graph is given. Determine whether it has a unique topological sort.
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 lines describe the edges of the graph, each represented by a pair of integers — the indices of the start and end vertices.
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 .

Example 1
Example 2