DWITE Online Computer Programming Contest, November 2007, Problem 5

A graph is a collection of nodes, called vertices, connected to each other in some fashion by edges. A graph is called connected if it is possible to find a path along edges from every point to every other point.

Below are two graphs:

One on the left is connected, while the one on the right is not connected (there is no path from node 1 to node 3).

An edge of a graph is called a bridge if by removing that edge the graph is no longer connected.

Edge 1-2 in the following graph is a bridge, since by removing it, the graph is no longer connected (no path from node 1 to any other node):

Edge 2-3 however, is not a bridge:

You are tasked with finding the number of edges, in a graph, that are bridges. You will be given 5 connected graphs, and you will output 5 single integers for the number of bridges found in graphs.

First line will contain a single integer ~N~, number of vertices. Vertices will be numbered ~1~ to ~N~. ~1 \le N \le 100~. Second line will contain a single integer ~M~, number of edges. ~0 \le M \le 1000~. Followed by ~M~ lines, each describing an edge. An edge is described by two integers, separated by a space. All edges are valid. This format will be repeated 5 times (that is, a line after the last edge of the 1st graph, will be a single integer, describing a number of vertices in the 2nd graph).

The output will contain 5 lines, a single integer per line – the number of bridges in the described graph.

Sample Input 1

6
7
1 2
1 3
1 4
1 5
3 5
6 2
6 1

Sample Output 1

1

Problem Resource: DWITE