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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;
#[allow(unused_imports)]
use proconio::marker::{Bytes, Chars};
#[allow(unused_imports)]
use std::cmp::{min, max};
use std::collections::VecDeque;

fn main() {
	input! {
		n: usize,
		m: usize,
		ab: [(usize, usize); m]
	}

	let inf: usize = 9999999999999;
	let mut ans = 0;

	for x in 0..m {
		// グラフを生成
		let mut v: Vec<Vec<usize>> = vec![vec![]; n];
		for i in 0..m {
			if i == x {
				continue;
			}
			v[ab[i].0-1].push(ab[i].1-1);
			v[ab[i].1-1].push(ab[i].0-1);
		}

		let mut d = vec![inf; n];
		let mut q = VecDeque::new();
		d[0] = 0;
		q.push_back((0usize, 0usize));	// スタートノード, 距離

		while q.len() > 0 {
			let tmp = q.pop_front().unwrap();
			for i in 0..v[tmp.0].len() {
				if d[v[tmp.0][i]] != inf {
					continue;
				}
				d[v[tmp.0][i]] = tmp.1 + 1;
				q.push_back((v[tmp.0][i], tmp.1 + 1));
			}
		}
		// 全ノードに到達したか確認
		for i in 0..n {
			if d[i] == inf {
				ans += 1;
				break;
			}
		}
	}
	println!("{}", ans);
}