Line Up

Problem Description

Determine whether there is a way to arrange the $N$ people numbered from $1$ to $N$ in a single line, such that $M$ given requirements are all satisfied.

Each requirement gives two integers $A_i$ and $B_i$, meaning that person $A_i$ and person $B_i$ must be adjacent.

It is guaranteed that all requirements are distinct — for example, once $1, 5$ is given, neither $1, 5$ nor $5, 1$ will be given again.

Input Format

The first line contains two integers $N$ and $M$, the number of people and the number of requirements.

Output Format

If there is a way to line these people up in a row satisfying all conditions, output Yes; otherwise output No.

Sample Input 1

4 2
1 3
2 3

Sample Output 1

Yes

Sample Input 2

4 3
1 4
2 4
3 4

Sample Output 2

No

Sample Input 3

3 3
1 2
1 3
2 3

Sample Output 3

No

Constraints

For all data: $2 \leq N \leq 10^5$, $0 \leq M \leq 10^5$, $1 \leq A_i < B_i \leq N$.