LogiQuest

286. Is the Graph Bipartite?

MediumBFSColouring

Print YES if the undirected graph can be 2-coloured so every edge joins different colours, else NO.

Input format

Line 1: n m Next m lines: u v

Output format

YES or NO

Example 1

Input

4 4
1 2
2 3
3 4
4 1

Output

YES

Example 2

Input

3 3
1 2
2 3
3 1

Output

NO

Constraints

1 ≤ n ≤ 10⁵

Read input from standard input and print the answer to standard output. Your code is judged against 4 test cases, most of them hidden.

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