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

$input = explode(' ', trim(fgets(STDIN)));
$n = (int)$input[0];
$m = (int)$input[1];

$edges = [];
for ($i=0; $i < $m; $i++) { 
	$input = explode(' ', trim(fgets(STDIN)));
	$edges[] = [(int)$input[0], (int)$input[1]];
}

$cnt = 0;
// 全辺について、のぞいた場合のUnionFindをする
foreach ($edges as $k_not => $e_not) {
	$parents = initNodes($n);
	foreach ($edges as $k => $e) {
		if ($k == $k_not) {
			continue;
		}
		$p1 = getParent($parents, $e[0]);
		$p2 = getParent($parents, $e[1]);
		if ($p1 !== $p2) {
			$parents[max($p1, $p2)] = $parents[min($p1, $p2)];
		}
	}
	for ($i=1; $i < $n; $i++) { 
		if (getParent($parents, $i) != getParent($parents, $i+1)) {
			$cnt += 1;
			break;
		}
	}
}
echo $cnt;

//互いに素な集合
function initNodes($n){
	$g = [];
	for ($i=1; $i <= $n; $i++) { 
		$g[$i] = $i;
	}
	return $g;
}

function getParent($parents, $i){
	if ($parents[$i] != $i) {
		$parents[$i] = getParent($parents, $parents[$i]);
	}
	return $parents[$i];
}