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>
 
#define BIG 2000000007
 
#define MOD 1000000007
typedef unsigned long long ull;
typedef   signed long long sll;

#define N_MAX 100
#define M_MAX 100
 
typedef struct {
	int a;
	int b;
} hw;
 
 
const hw vector8[8] = {
	{-1, -1},
	{-1,  0},
	{-1, +1},
	{ 0, -1},
	{ 0, +1},
	{+1, -1},
	{+1,  0},
	{+1, +1}
};
 
ull n, m;
ull h, w;
ull k;
ull va, vb, vc, vd, ve, vf;
// ull a[N_MAX];
// sll a[N_MAX];
// ull b[M_MAX];
// ull dp[N_MAX][M_MAX + 1];
// char s[N_MAX + 1];
// char t[N_MAX + 1];
// char s[N_MAX][M_MAX + 1];
hw arr[N_MAX];
// hw brr[M_MAX];
// ull digitdp[102][   2][    2];
//          pos  less  carry
 
void swap_adj(ull *a, ull *b){
	ull tmp = *b;
	*b = *a;
	*a = tmp;
	return;
}
 
ull divide(ull a, ull b){
	ull x = MOD - 2;
	ull ans = 1;
	while (x) {
		if (x & 1) ans = (ans * b) % MOD;
		b = (b * b) % MOD;
		x /= 2;
	}
	return (a * ans) % MOD;
}
 
int digits(ull x){
	int i = 1;
	while (x >= 10) {
		x /= 10;
		i++;
	}
	return i;
}
 
int min(ull x, ull y){
	return (x < y) ? x : y;
}
 
ull gcd(ull x, ull y){
	if (x < y) {
		return gcd(y, x);
	} else if (y == 0) {
		return x;
	} else {
		return gcd(y, x % y);
	}
}
 
ull bitpow(ull a, ull x){
	ull result = 1;
	while (x) {
		if (x & 1) {
			result *= a;
			result %= MOD;
		}
		x /= 2;
		a = (a * a) % MOD;
	}
	return result;
}
 
// int nextroute(int arr[]){
// 	int i = n - 1;
// 	int j, x;
// 	while (arr[i - 1] > arr[i]) i--;
 
// 	x = n;
// 	for (j = i; j < n; j++) {
// 		if (arr[j] < arr[i - 1]) continue;
// 		if (x == n || arr[x] > arr[j]) x = j;
// 	}
// 	arr[i - 1] ^= arr[x];
// 	arr[x] ^= arr[i - 1];
// 	arr[i - 1] ^= arr[x];
 
// 	qsort(&arr[i], n - i, sizeof(int), comp);
// 	return 0;
// }
 
int nibutan_target(ull target){
	ull maxdist = (target * (target + 1) / 2); // 時刻targetまでに到着できる距離は[-maxdist, maxdist]
	return (n <= maxdist);
}
 
int targetdig(ull x, int index /* 1-indexed */){
	// static...?
	int posmax = digits(x);
	if (posmax < index) return -1;
	while (posmax > index) {
		posmax--;
		x /= 10;
	}
	return x % 10;
}
 
int intcomp(const void *left, const void *right){
	if ((*(int*)left) < (*(int*)right)) {
		return -1;
	} else if ((*(int*)left) > (*(int*)right)) {
		return +1;
	} else {
		return 0;
	}
}
 
int ullcomp(const void *left, const void *right){
	if ((*(ull*)left) < (*(ull*)right)) {
		return -1;
	} else if ((*(ull*)left) > (*(ull*)right)) {
		return +1;
	} else {
		return 0;
	}
}
 
int hwAcomp(const void *left, const void *right){
	return intcomp(&(((hw*)left)->a), &(((hw*)right)->a));
}
 
int hwBcomp(const void *left, const void *right){
	return intcomp(&(((hw*)left)->b), &(((hw*)right)->b));
}
 
int hwABcomp(const void *left, const void *right){
	int x = hwAcomp(left, right);
	if (x) return x;
	return hwBcomp(left, right);
}

ull solve(){
	int i, j, k;
	int path[N_MAX][N_MAX];
	int ans = m;

	for (i = 0; i < n; i++) {
		for (j = 0; j < n; j++) {
			path[i][j] = (i == j ? 1 : 0);
		}
	}

	for (i = 0; i < m; i++) {
		path[arr[i].a][arr[i].b] = path[arr[i].b][arr[i].a] = 1;
	}

	for (i = 0; i < m; i++) {
		int isreachable[N_MAX] = {1}; // 1, 0, 0, ...
		int stack[N_MAX] = {0};
		int stackend = 0;
		for (j = 0; j <= stackend; j++) {
			// printf("%d:: %d/%d: [%d]\n", i, j, stackend, stack[j]);

			for (k = 0; k < m; k++) {
				if (k == i) continue;
				if (arr[k].a == stack[j] && isreachable[arr[k].b] == 0)  {
					isreachable[arr[k].b] = 1;
					stackend++;
					stack[stackend] = arr[k].b;
				}
				if (arr[k].b == stack[j] && isreachable[arr[k].a] == 0)  {
					isreachable[arr[k].a] = 1;
					stackend++;
					stack[stackend] = arr[k].a;
				}
			}
			if (stackend >= n - 1) {
				ans--;
				break;
			}
		}
	}

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

	return 0;
}
 
int main(void){
	int i, j, k;

	scanf("%llu%llu", &n, &m);
	for (i = 0; i < m; i++) {
		scanf("%d%d", &arr[i].a, &arr[i].b);
		arr[i].a--;
		arr[i].b--;
	}

	solve();
 
	return 0;
}