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: Wrong Answer)

<?php
fscanf(STDIN, "%d %d", $n, $m);
for ($i = 0; $i < $m; $i++) {
	fscanf(STDIN, "%d %d", $a[$i], $b[$i]);
	$g[$a[$i]][$b[$i]] = $g[$b[$i]][$a[$i]] = 1;
}
$x = 0;
for ($i = 0; $i < $m; $i++) {
	$tmp[] = $a[$i];
	$f = [$a[$i] => 1];
	while ($tmp) {
		$p = array_shift($tmp);
		foreach ($g[$p] as $q => $r) {
			if ($p != $a[$i] && $q == $b[$i]) {
				$x++;
				break 2;
			} elseif ($q != $b[$i] && !isset($f[$q])) {
				$tmp[] = $q;
				$f[$q] = 1;
			}
		}
	}
}
echo $m - $x;