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 (1.15.1) (judge verdict: Accepted)

pub fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

pub fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

pub fn read_vec2<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

pub fn read_col<T: std::str::FromStr>(n: usize) -> Vec<T> {
    (0..n).map(|_| read()).collect()
}

use std::collections::BTreeSet;

fn check(
    u: usize,
    goal: usize,
    edge: &Vec<BTreeSet<usize>>,
    checked: &mut BTreeSet<usize>,
) -> bool {
    if checked.contains(&u) {
        return false;
    }
    if u == goal {
        return true;
    }

    checked.insert(u);

    for v in &edge[u] {
        if check(*v, goal, &edge, checked) {
            return true;
        }
    }
    false
}

fn main() {
    let nm: Vec<usize> = read_vec();
    let n = nm[0];
    let m = nm[1];
    let ab: Vec<Vec<usize>> = read_vec2(m);
    let mut edge: Vec<BTreeSet<usize>> = vec![BTreeSet::new(); n];

    for tmp in &ab {
        let a = tmp[0] - 1;
        let b = tmp[1] - 1;
        edge[a].insert(b);
        edge[b].insert(a);
    }

    let mut ans: usize = 0;
    for tmp in &ab {
        let a = tmp[0] - 1;
        let b = tmp[1] - 1;

        edge[a].remove(&b);
        edge[b].remove(&a);
        let mut checked = BTreeSet::new();
        if !check(a, b, &edge, &mut checked) {
            ans += 1;
        }
        edge[a].insert(b);
        edge[b].insert(a);
    }
    println!("{}", ans);
}