Cliques Y16864

Statement

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Given an undirected graph with n vertices and m edges, tell whether every connected component is a clique, that is, if all the vertices of the component are directly connected to each other.

Input

Input consists of several cases. Each case begins with n and m, followed by m pairs x y, with x ≠ y, indicating an edge between x and y. Suppose 1 ≤ n ≤ 10⁵, 0 ≤ m ≤ 5n, that the vertices are numbered between 0 and n−1, and that there are no repeated edges.

Output

For each given graph, print “SI” if every connected component is a clique, and “NO” ‍otherwise.

Observation

Even if a green light is obtained, only solutions that perform a single graph traversal will receive the maximum score.

Public test cases

Input

6 4
0 1  2 1  2 0  3 5

6 6
0 5  1 2  2 3  3 4  4 1  2 4

Output

SI
NO

Information

Author: Salvador Roura
Language: English
Translator: Salvador Roura
Original language: Catalan
Other languages: Catalan
Official solutions: C++
User solutions: C++