# Transferring Sylla

Time Limit: 5000MS

Memory Limit: 65536K

## Description

After recapturing Sylla, the Company plans to establish a new secure system, a transferring net! The new system is designed as follows: The Company staff choose N cities around the nation which are connected by "security tunnels" directly or indirectly. Once a week, Sylla is to be transferred to another city through the tunnels. As General ordered, the transferring net must reach a certain security level that there are at least 3 independent paths between any pair of cities a, b. When General says the paths are independent, he means that the paths share only a and b in common. Given a design of a transferring net, your work is to inspect whether it reaches such security level.

## Input

The input consists of several test cases. For each test case, the first line contains two integers, N ≤ 500 and M ≤ 20000. indicating the number of cities and tunnels. The following M lines each contains two integers a and b (0 ≤ a, b < N), indicating the city a and city b are connected directly by a tunnel. The input ends by two zeroes.

## Output

For each test case output "YES" if it reaches such security level, "NO" otherwise.

4 6
0 1
0 2
0 3
1 2
1 3
2 3

4 5
0 1
0 2
0 3
1 2
1 3

7 6
0 1
0 2
0 3
1 2
1 3
2 3

0 0

YES
NO
NO

## Source

POJ Founder Monthly Contest – 2008.12.28, Dag