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 $v_j$.

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.

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.

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.