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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
int acs(const void *a, const void *b) { 
  return *(int*)a - *(int*)b;
} /* 1,2,3,4.. */
int des(const void *a, const void *b) {
  return *(int*)b - *(int*)a;
} /* 8,7,6,5.. */
int cmp_char(const void *a, const void *b) { 
  return *(char*)a - *(char*)b;
} /* a,b,c,d.. */
int cmp_str(const void *a, const void *b) {
  return strcmp(*(const char **)a, *(const char **)b);
} /* aaa,aab.. */
#define min(a,b) (a < b ? a : b)
#define max(a,b) (a > b ? a : b)
#define rep(i, l, r) for (int i = l; i < r; i++)
#define MAX 100001
#define MOD 1000000007
#define INF 1000000009
typedef long long int lli;

int bridge[51][51] = {0};
int visited[51];

void dfs(int n) {
  visited[n] = 1;
  rep(i, 1, 51) {
    if ( visited[i] ) continue;
    if ( bridge[i][n] == 0 ) continue;
    dfs(i);
  }
}

int main(void) {
  int N, M;
  scanf("%d %d", &N, &M);

  int a[51], b[51];
  rep(i, 0, M) {
    scanf("%d %d", &a[i], &b[i]);
    bridge[a[i]][b[i]] = bridge[b[i]][a[i]] = 1;
  }

  int ans = 0;
  rep(i, 0, M) {
    bridge[a[i]][b[i]] = bridge[b[i]][a[i]] = 0;
    rep(j, 1, 51) visited[j] = 0;
    dfs(1);
    int ok = 1;
    rep(j, 1, N+1) {
      if ( visited[j] ) continue;
      ok = 0;
      break;
    }
    if ( ok == 0 ) ans++;
    bridge[a[i]][b[i]] = bridge[b[i]][a[i]] = 1;
  }
  printf("%d\n", ans);
  return 0;
}