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.

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.

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