Building the artifact

Captain America has to go back in time and collect parts to build an artifact.

Some of these parts are interconnected with a powerful force. If there’s a connection from part A to part B. Captain must collect part B before collecting A.

Sometimes a part of an artifact can be connected with itself, making it impossible to collect it.

When he collects all the parts, he can build the artifact.

Input Format

• First line contains n c the number of parts and connections
• Next c lines contain a b indicating connections from part a to part b

Output Format

Output “YES” if the artifact can be built, “NO” if it cannot be built.

Constraints

1 <= n <= 100,000

0 <= r <= 5000

Sample Input 0

2 1
1 0

Sample Output 0

YES