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: Time Limit Exceeded)

#include <stdio.h>
#define REP(i, n) for(i = 0; i < n; ++i)
#define FOR(i, a, b) for(i = a; i < b; ++i)

void yes_or_no(char boolean){
    if(boolean){
        printf("Yes\n");
    }else{
        printf("No\n");
    }
}

typedef struct{
    char checked[50];
}checklist;

 char isConnected(int a, int b, int N, char matrix[N][N], checklist chk){
     chk.checked[a] = 1, chk.checked[b] = 1;

     if(matrix[a][b]){
         return 1;
     }

     int c;
     char flag = 0;

     REP(c, N){
         if(chk.checked[c] != 1){
             char f = isConnected(a, c, N, matrix, chk);
             char g = isConnected(c, b, N, matrix, chk);
             chk.checked[c] = 0;

             flag |= (f & g);
         }
         if(flag){
             return 1;
         }
     }

     return 0;
}

int main(){
    int N, M;
    scanf("%d %d", &N, &M);
    char matrix[N][N];
    checklist chk;
    int list_p[M], list_q[M];
    int x, y;
    int i;
    int ans = 0;

    REP(x, N){
        chk.checked[x] = 0;
        REP(y, N){
            matrix[x][y] = (x == y)? 1 : 0;
        }
    }

    REP(i, M){
        scanf("%d %d", &list_p[i], &list_q[i]);
        x = list_p[i] - 1, y = list_q[i] - 1;
        matrix[x][y] = 1;
        matrix[y][x] = 1;
    }

    REP(i, M){
        x = list_p[i] - 1, y = list_q[i] - 1;
        matrix[x][y] = 0;
        matrix[y][x] = 0;

        char ret = isConnected(x, y, N, matrix, chk);
        if(ret == 0){
            ans++;
        }

        matrix[x][y] = 1;
        matrix[y][x] = 1;         
    }
    printf("%d\n", ans);
    return 0;
}