Problem Statement

You are given an undirected graph with N vertices numbered 1 to N and M edges numbered 1 to M. Edge i connects vertex u_i and vertex v_i.
Determine whether every connected component in this graph satisfies the following condition.

• The connected component has the same number of vertices and edges.

Input

The input is given from Standard Input in the following format:
N M
u_1 v_1
$\vdots$
u_M v_M

Output

If every connected component satisfies the condition, print Yes; otherwise, print No.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $0 \leq M \leq 2 \times 10^5$
• $1 \leq u_i \leq v_i \leq N$
• All values in the input are integers.

Sample Input 1

3 3
2 3
1 1
2 3

Sample Output 1

Yes

The graph has a connected component formed from just vertex 1, and another formed from vertices 2 and 3.
The former has one edge (edge 2), and the latter has two edges (edges 1 and 3), satisfying the condition.

Sample Input 2

5 5
1 2
2 3
3 4
3 5
1 5

Sample Output 2

Yes

Sample Input 3

13 16
7 9
7 11
3 8
1 13
11 11
6 11
8 13
2 11
3 3
8 12
9 11
1 11
5 13
3 12
6 9
1 10

Sample Output 3

No

见题面 Input 部分

见题面 Output 部分