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

ini_set('error_reporting', E_ALL & ~E_NOTICE & ~E_WARNING);
ini_set('display_errors', 'Off');

// define('DEBUG', true);
define('DEBUG', false);

fscanf(STDIN, "%d %d", $N, $M);

$ans = 0;
$v = array();
$sum = array();

for ($i = 0; $i < $M; $i++) {
    fscanf(STDIN, "%d %d", $a, $b);
    $v[$a][$b] = 1;
    $v[$b][$a] = 1;
}
if (DEBUG) var_dump($v);

$flag = true;
while($flag) {
    $flag = false;
    foreach ($v as $key => $val) {
        if (DEBUG) echo "no.{$key} " . count($val) . PHP_EOL;
        if (count($v[$key]) == 1) {
            $ans++;
            $flag = true;
            foreach ($v[$key] as $no => $one) {
                if (DEBUG) echo "X: no:{$no} one:{$one}\n";
                unset($v[$key][$no]);
                unset($v[$no][$key]);
            }
        } 
    }
    // sleep(1);
}
echo $ans . PHP_EOL;