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 Python (3.4.3) (judge verdict: Accepted)

from heapq import heappush, heappop
from itertools import permutations, accumulate, combinations
import math
import bisect
import numpy as np
from collections import defaultdict, deque
import sys
input = sys.stdin.readline
# sys.setrecursionlimit(1000000)
# MOD = 10 ** 9 + 7
# INF = float("inf")


def bfs(s, n, g):
    que = deque([])
    que.append(s)
    check = [-1] * n
    check[s] = 0
    while que:
        u = que.popleft()
        for v in g[u]:
            if check[v] == -1:
                check[v] = check[u] + 1
                que.append(v)
    if -1 in check:
        return True
    else:
        return False


def main():
    n, m = map(int, input().split())
    g = [[] for _ in range(n)]
    gg = deque([])
    for _ in range(m):
        a, b = [int(i) - 1 for i in input().split()]
        g[a].append(b)
        g[b].append(a)
        gg.append((a, b))
    ans = 0
    for i in range(m):
        a, b = gg.popleft()
        g[a].remove(b)
        g[b].remove(a)
        if bfs(0, n, g):
            ans += 1
        g[a].append(b)
        g[b].append(a)
    print(ans)


if __name__ == "__main__":
    main()