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(unused_imports)]
use std::io::{ self, Write };
use std::str::FromStr;
use std::cmp::{ min, max };
use std::collections::{ BinaryHeap, VecDeque };

#[allow(unused_macros)]
macro_rules! trace {
    ($var:expr) => {
        let _ = writeln!(&mut std::io::stderr(), ">>> {} = {:?}", stringify!($var), $var);
    };
    ($($args:expr),*) => {
        let _ = writeln!(&mut std::io::stderr(), ">>> {} = {:?}", stringify!($($args),*), ($($args),*));
    };
}

const M: usize = 1_000_000_007;

fn main() {
    let mut sc = Scanner::new();

    let n: usize = sc.cin();
    let m: usize = sc.cin();

    let INF: i32 = 100000000;
    let mut d = vec![vec![INF; n]; n];
    for i in 0..n {
        d[i][i] = 0;
    }
    let mut edges = vec![];

    for _ in 0..m {
        let a = sc.cin::<usize>() - 1;
        let b = sc.cin::<usize>() - 1;
        d[a][b] = 1;
        d[b][a] = 1;
        edges.push((a, b));
    }

    let mut ans = 0;
    for e in edges.iter() {

        let mut c = vec![vec![INF; n]; n];
        for i in 0..n {
            for j in 0..n {
                c[i][j] = d[i][j];
            }
        }
        c[e.0][e.1] = INF;
        c[e.1][e.0] = INF;

        for k in 0..n {
            for i in 0..n {
                for j in 0..n {
                    c[i][j] = min::<i32>(
                        c[i][j],
                        c[i][k] + c[k][j]
                    );
                }
            }
        }

        if c[e.0][e.1] == INF {
            ans += 1;
        }

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

}

#[allow(dead_code)]
struct Scanner { stdin: io::Stdin, buffer: VecDeque<String>, }
#[allow(dead_code)]
impl Scanner {
    fn new() -> Scanner { Scanner { stdin: io::stdin(), buffer: VecDeque::new() } }
    fn reserve(&mut self) {
        while self.buffer.len() == 0 {
            let mut line = String::new();
            let _ = self.stdin.read_line(&mut line);
            for w in line.split_whitespace() {
                self.buffer.push_back(String::from(w));
            }
        }
    }
    fn cin<T: FromStr>(&mut self) -> T {
        self.reserve();
        match self.buffer.pop_front().unwrap().parse::<T>() {
            Ok(a) => a,
            Err(_) => panic!("parse err")
        }
    }
}