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>
#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");
    }
}

void traverse(int now,int N, char chk[N], char matrix[N][N]){
     chk[now] = 1;
     int next;

     REP(next, N){
         if(matrix[now][next] == 1 && chk[next] != 1){
             traverse(next, N, chk,  matrix);
         }
     }
}

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

    REP(x, N){
        chk[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;


        traverse(0, N, chk, matrix);

        int k;
        char bridge = 0;

        REP(k, N){
            if(chk[k] == 0){
                bridge = 1;
            }else{
                chk[k] = 0;
            }
        }


        if(bridge) ans++;

        matrix[x][y] = 1;
        matrix[y][x] = 1;         
    }

    printf("%d\n", ans);

    return 0;
}