You are given an undirected graph that has ~n~ vertices and ~m~ edges. You should check if the given graph is a simple graph.

Input

• The first line contains two integers ~n, m~ ~(0 < n, m ≤ 10^5)~.
• Each of the next ~m~ lines contains two integers ~a, b~ representing an edge that connects vertex ~a~ and vertex ~b~ ~(0 ≤ a, b < n)~.

Output

• Print YES if the given graph is a simple graph, otherwise print NO. The output is case-sensitive.

Sample Input 1

5 4
0 0
0 1
1 2
2 1

Sample Output 1

NO

Sample Input 2

5 4
0 1
1 2
2 3
0 3

Sample Output 2

YES

Notes

• https://drive.google.com/file/d/1N1-NJnSAq7MrNJ9Oy3_f5en2PyOVNKd1/view?usp=sharing