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)


#[allow(dead_code)]
const MOD: usize = 1_000000000 + 7;

fn main() {
    let mut cin = Scanner::new();
    let n = cin.next_usize();
    let m = cin.next_usize();
    let inf = 1<<29;
    let mut edges = vec![(0,0); m];
    for i in 0..m {
        let a = cin.next_usize() - 1;
        let b = cin.next_usize() - 1;
        edges[i] = (a,b);
    }
    let mut ans = 0;
    for e in 0..m {
        let mut dist = vec![vec![inf; n]; n];
        for i in 0..n { dist[i][i] = 0; }
        for i in 0..m {
            if i != e {
                let a = edges[i].0;
                let b = edges[i].1;
                dist[a][b] = 1;
                dist[b][a] = 1;
            }
        }
        for k in 0..n {
            for i in 0..n {
                for j in 0..n {
                    dist[i][j] = std::cmp::min(dist[i][j], dist[i][k] + dist[k][j])
                }
            }
        }
        let mut b = 0;
        for i in 0..n {
            for j in 0..n {
                if dist[i][j] == inf {
                    b = 1;
                }
            }
        }
        ans += b;
    }
    println!("{}", ans);
}


struct Scanner {
    reader: std::io::Stdin,
    tokens: std::collections::VecDeque<String>,
}

impl Scanner {
    fn new() -> Self {
        Scanner {
            reader: std::io::stdin(),
            tokens: std::collections::VecDeque::new(),
        }
    }

    fn next(&mut self) -> String {
        if self.tokens.is_empty() {
            let mut s = String::new();
            loop {
                self.reader.read_line(&mut s).ok();
                let s = s.trim();
                if s.len() != 0 {
                    for it in s.split_whitespace() {
                        self.tokens.push_back(it.into())
                    }
                    break;
                }
            }
        }
        self.tokens.pop_front().unwrap()
    }

    fn next_generics<T>(&mut self) -> T where
        T: std::str::FromStr + std::marker::Copy,
        <T as std::str::FromStr>::Err: std::fmt::Debug
    {
        self.next().parse().unwrap()
    }
    
    #[allow(dead_code)] fn next_i32(&mut self) -> i32 { self.next_generics::<i32>() }
    #[allow(dead_code)] fn next_i64(&mut self) -> i64 { self.next_generics::<i64>() }
    #[allow(dead_code)] fn next_u64(&mut self) -> u64 { self.next_generics::<u64>() }
    #[allow(dead_code)] fn next_usize(&mut self) -> usize { self.next_generics::<usize>() }
    #[allow(dead_code)] fn next_isize(&mut self) -> isize { self.next_generics::<isize>() }
}