Problem Statement

You are given a simple undirected graph with N vertices and M edges. The vertices are numbered $1, 2, \dots, N$, and the edges are numbered $1, 2, \dots, M$.
Edge i $, (i = 1, 2, \dots, M) connects vertices u_i$ and v_i.
Determine if this graph is a path graph.

What is a simple undirected graph?
A simple undirected graph is a graph without self-loops or multiple edges whose edges do not have a direction.

What is a path graph?
A graph with $N vertices numbered 1, 2, \dots, N$ is said to be a path graph if and only if there is $a sequence (v_1, v_2, \dots, v_N)$ that is a permutation of $(1, 2, \dots, N)$ and satisfies the following conditions:

• For all $i = 1, 2, \dots, N-1,$ there is an edge connecting vertices v_i and v_{i+1}.
• If integers i and $j satisfies 1 \leq i, j \leq N$ and $|i - j| \geq 2$, then there is no edge that connects vertices v_i and v_j.

Input

The input is given from Standard Input in the following format:
N M
u_1 v_1
u_2 v_2
$\vdots$
u_M v_M

Output

Print Yes if the given graph is a path graph; print No otherwise.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $0 \leq M \leq 2 \times 10^5$
• $1 \leq u_i, v_i \leq N$ $, (i = 1, 2, \dots, M)$
• All values in the input are integers.
• The graph given in the input is simple.

Sample Input 1

4 3
1 3
4 2
3 2

Sample Output 1

Yes

Illustrated below is the given graph, which is a path graph.

Sample Input 2

2 0

Sample Output 2

No

Illustrated below is the given graph, which is not a path graph.

Sample Input 3

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

Sample Output 3

No

Illustrated below is the given graph, which is not a path graph.

见题面 Input 部分

见题面 Output 部分