Problem Statement

Determine whether there is a way to line up N people, numbered 1 to N, in a row side by side to satisfy all of the M conditions in the following format.

• Condition: Person A_i and Person B_i are adjacent.

Input

Input is given from Standard Input in the following format:
N M
A_1 B_1
$\vdots$
A_M B_M

Output

If there is a way to line up people to satisfy the conditions, print Yes; if not, print No.

Constraints

• $2 \leq N \leq 10^5$
• $0 \leq M \leq 10^5$
• $1\leq A_i < B_i \leq N$
• All pairs (A_i,B_i) are distinct.

Sample Input 1

4 2
1 3
2 3

Sample Output 1

Yes

One way to satisfy all the conditions is to line them up in the order 4,1,3,2.

Sample Input 2

4 3
1 4
2 4
3 4

Sample Output 2

No

There is no way to line them up to satisfy all the conditions.

见题面 Input 部分

见题面 Output 部分