Description

Original source: CTU Open 2004

Given an undirected graph, determine the maximum number of connected components after deleting one vertex.

Input Format

Multiple test cases. The first line contains two integers $P$ and $C$, representing the number of vertices and edges, respectively.
The next $C$ lines each contain two integers $p1$ and $p2$, indicating an edge between $p1$ and $p2$. There are no duplicate edges. Input ends with 0 0.

Output Format

Output the result for each test case on a separate line.

Sample 1

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

1
2
2

Constraints and Hints

$1 \le P \le 10000, C \ge 0, 0 \le p1, p2 < P$