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, marker::Usize1};

struct Graph {
    size: usize,
    mat: Vec<Vec<bool>>,
    visited: Vec<bool>,
    ab: Vec<(usize, usize)>,
}

impl Graph {
    fn new(n: usize, ab: Vec<(usize, usize)>) -> Self {
        let mut mat = vec![vec![false; n]; n];
        let visited = vec![false; n];
        let size = n;
        for &(a, b) in ab.iter() {
            mat[a][b] = true;
            mat[b][a] = true;
        }
        Self { size, mat, visited, ab }
    }

    fn dfs(&mut self, x: usize) {
        self.visited[x] = true;
        for i in 0..self.size {
            if !self.visited[i] && self.mat[x][i] {
                self.dfs(i);
            }
        }
    }

    fn solve(&mut self) -> usize {
        let mut count = 0;
        for i in 0..self.ab.len() {
            for e in self.visited.iter_mut() {
                *e = false;
            }
            self.mat[self.ab[i].0][self.ab[i].1] = false;
            self.mat[self.ab[i].1][self.ab[i].0] = false;
            self.dfs(0);

            if self.visited.iter().any(|&x| x == false) {
                count += 1;
            }
    
            self.mat[self.ab[i].0][self.ab[i].1] = true;
            self.mat[self.ab[i].1][self.ab[i].0] = true;
        }
        count
    }
}

fn main() {
    input! {
        n: usize,
        m: usize,
        ab: [(Usize1, Usize1); m],
    }

    let mut graph = Graph::new(n, ab);

    let ans = graph.solve();

    println!("{}", ans);
}