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: Wrong Answer)

fn conn(adjl: &Vec<Vec<usize>>, v: usize, mut used: usize) -> bool {
    if used == (1 << adjl.len()) - 1 {
        return true;
    }
    for &u in &adjl[v] {
        if (1usize << u) & used == 0 {
            used |= 1usize << u;
            if conn(adjl, u, used) {
                return true;
            }
        }
    }
    return false;
}
fn solve() {
    let (n, m): (usize, usize) = (read::<usize>(), read::<usize>());
    let mut edges = vec![];
    for i in 0..m {
        let (u, v): (usize, usize) = (read::<usize>() - 1, read::<usize>() - 1);
        edges.push((u, v))
    }
    let mut res = 0;
    for i in 0..m {
        let mut adjl = vec![vec![]; n];
        for j in 0..m {
            if j == i {
                continue;
            }
            adjl[edges[j].0].push(edges[j].1);
            adjl[edges[j].1].push(edges[j].0);
        }
        if !conn(&adjl, 0, 1) {
            res += 1;
        }
    }
    println!("{}", res);
}

fn main() {
    let stack_size = 104_857_600;
    let thd = std::thread::Builder::new().stack_size(stack_size);
    thd.spawn(|| solve()).unwrap().join().unwrap();
}

// =========
#[allow(unused_imports)]
use std::cmp::{max, min, Reverse};
#[allow(unused_imports)]
use std::collections::{BinaryHeap, HashMap, HashSet};
#[allow(unused_imports)]
use std::process::exit;

#[allow(dead_code)]
const MOD: usize = 1000000007;

fn read<T: std::str::FromStr>() -> T {
    use std::io::Read;
    let stdin = std::io::stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

// =========