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Problem 1073. -- Servicing Stations

Servicing Stations

Time Limit: 1 Sec  Memory Limit: 64 MB
Submit: 8  Solved: 2


A company offers personal computers for sale in N towns ( 3<=N<=35), denoted by 1, 2,..., N. There are direct routes connecting M pairs among these towns. The company decides to build servicing stations to ensure that for any town X, there will be a station located either in X or in some immediately neighboring town of X. Write a program to find the minimum number of stations the company has to build.


The input consists of multiple problem descriptions. Every description starts with number of towns N and number of town-pairs M, separated by a space. Each of the next M lines contains a pair of integers representing connected towns, at one pair per line with each pair separated by a space. The input ends with N = 0 and M = 0.


For each input case, print a line reporting the minimum number of servicing stations needed.

Sample Input

8 12
1 2
1 6
1 8
2 3
2 6
3 4
3 5
4 5
4 7
5 6
6 7
6 8
0 0

Sample Output




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