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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
fscanf(STDIN, "%d %d", $n, $m);
$ans = 0;
for($i = 0; $i < $n; $i++){
    for($j = 0; $j < $n; $j++){
        $graph[$i][$j] = false;
    }
}

function dfs($a){
    global $vis;
    global $n;
    global $graph;

    if($vis[$a]) return;
    $vis[$a] = true;
    for($i = 0; $i < $n; $i++){
        if($graph[$a][$i]) dfs($i);
    }
}

for($i = 0; $i < $m; $i++){
    fscanf(STDIN, "%d %d", $a[$i], $b[$i]);
    $a[$i]--;
    $b[$i]--;
    $graph[$a[$i]][$b[$i]] = $graph[$b[$i]][$a[$i]] = true;
}

for($i = 0; $i < $m; $i++){
    $graph[$a[$i]][$b[$i]] = $graph[$b[$i]][$a[$i]] = false;
    for($j = 0; $j < $n; $j++) $vis[$j] = false;
    dfs(0);
    if(in_array(false, $vis, true)) $ans++;
    $graph[$a[$i]][$b[$i]] = $graph[$b[$i]][$a[$i]] = true;
}

print $ans;