Problem:
Score : 300 points

Problem Statement

You are given an undirected connected graph with N vertices and M edges that does not contain self-loops and double edges.

The i-th edge (1 \leq i \leq M) connects Vertex a_i and Vertex b_i.

An edge whose removal disconnects the graph is called a bridge.

Find the number of the edges that are bridges among the M edges.

Notes

A self-loop is an edge i such that a_i=b_i (1 \leq i \leq M).

Double edges are a pair of edges i,j such that a_i=a_j and b_i=b_j (1 \leq i<j \leq M).

An undirected graph is said to be connected when there exists a path between every pair of vertices.

Constraints

2 \leq N \leq 50

N-1 \leq M \leq min(N(N−1)⁄2,50)

1 \leq a_i<b_i \leq N

The given graph does not contain self-loops and double edges.

The given graph is connected.

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
a_2 b_2
:
a_M b_M

Output

Print the number of the edges that are bridges among the M edges.

Sample Input 1

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

Sample Output 1

4

The figure below shows the given graph:

The edges shown in red are bridges. There are four of them.

Sample Input 2

3 3
1 2
1 3
2 3

Sample Output 2

0

It is possible that there is no bridge.

Sample Input 3

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

Sample Output 3

5

It is possible that every edge is a bridge.

Solution in JavaScript (node.js v5.12) (judge verdict: Accepted)

process.stdin.resume();
process.stdin.setEncoding('utf8');

var g_input = '';
process.stdin.on('data', function(chunk) {
    g_input += chunk;
});

process.stdin.on('end', function() {
    Main(g_input.split(/\r?\n/));
});

function Main(input) {

    var size = input[0].split(' ');
    var n = parseInt(size[0], 10);
    var m = parseInt(size[1], 10);
    var a = new Array(m);
    var b = new Array(m);
    var graph = new Array(n);
    for (var i = 0; i < n; i++) {
        graph[i] = new Array(n);
        for (var j = 0; j < n; j++) {
            graph[i][j] = false;
        }
    }
    for (var i = 0; i < m; i++) {
        var link = input[i + 1].split(' ');
        a[i] = parseInt(link[0], 10);
        b[i] = parseInt(link[1], 10);
        graph[a[i] - 1][b[i] - 1] = true;
        graph[b[i] - 1][a[i] - 1] = true;
    }

    var bridge = 0;
    for (var i = 0; i < m; i++) {
        graph[a[i] - 1][b[i] - 1] = false;
        graph[b[i] - 1][a[i] - 1] = false;

        var visited = new Array(n);
        for (var j = 0; j < n; j++) {
            visited[j] = false;
        }

        dfs(1, graph, visited);
        for (var j = 0; j < n; j++) {
            if (!visited[j]) {
                bridge++;
                break;
            }
        }

        graph[a[i] - 1][b[i] - 1] = true;
        graph[b[i] - 1][a[i] - 1] = true;
    }

    console.log(bridge);

    return 0;
}

function dfs(pos, graph, visited) {
    visited[pos - 1] = true;

    for (var i = 0; i < graph.length; i++) {
        if (visited[i]) {
            continue;
        }
        if (graph[pos - 1][i]) {
            dfs(i + 1, graph, visited);
        }
    }
}