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 PHP (5.6.30) (judge verdict: Accepted)

<?php
error_reporting(0);
//$A = explode(" ",trim(fgets(STDIN)));
list($N,$M) = explode(" ",trim(fgets(STDIN)));
//頂点フラグ
$used = new SplFixedArray($N);
//接続状態を保存する
$connected = new SplFixedArray($N);
//初期化
for($i=0;$i<$N;$i++) {
  $used[$i]=0;
  //接続状態はconnected[頂点数=N][頂点数=N]
  $connected[$i]=new SplFixedArray($N);
  for($j=0;$j<$N;$j++) {
    $connected[$i][$j]=0;
  }
}
for($i=0;$i<$M;$i++) {
  list($P1[],$P2[]) = explode(" ",trim(fgets(STDIN)));
}
$ret=0;
for($i=0;$i<$M;$i++) {
  $used=array_fill(0,$N,0);
  for($j=0;$j<$M;$j++) {
    if ($j==$i) {
      $connected[$P1[$j]-1][$P2[$j]-1] = 0;
      $connected[$P2[$j]-1][$P1[$j]-1] = 0;
      continue;
    }
    $connected[$P1[$j]-1][$P2[$j]-1] = 1;
    $connected[$P2[$j]-1][$P1[$j]-1] = 1;
  }
  dfs(0);
  $v=0;
  foreach($used as $u) {
    $v+=$u;
  }
  if ($v!=$N) {
    $ret++;
  }
}
printf("%d\n",$ret);

function dfs($now) {
  global $used,$connected,$M,$N;
  if ($used[$now]==1) return 0;
  $used[$now]=1;
  for($i=0;$i<$N;$i++) {
    if ($connected[$now][$i]) {
      dfs($i);
    }
  }
}