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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
#![allow(unused_imports)]
use itertools::Itertools;
use proconio::{input, marker::*};
use std::cmp::*;
use std::collections::*;
use superslice::*;

fn main() {
    input! {
        n: usize,
        m: usize,
        g: [[Usize1;2];m],
    }

    let mut ans = 0;

    for i in 0..m {
        let mut uf = UnionFind::new(n);

        for j in 0..m {
            if j == i {
                continue;
            }
            uf.unite(g[j][0], g[j][1]);
        }

        if uf.size(0) != n {
            ans += 1;
        }
    }

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

struct UnionFind {
    par: Vec<usize>,
    size: Vec<usize>,
}

impl UnionFind {
    fn new(i: usize) -> Self {
        UnionFind {
            par: (0..i).collect(),
            size: vec![1; i],
        }
    }

    fn root(&mut self, i: usize) -> usize {
        if self.par[i] == i {
            return i;
        } else {
            self.par[i] = self.root(self.par[i]);
            return self.par[i];
        }
    }

    fn same(&mut self, x: usize, y: usize) -> bool {
        self.root(x) == self.root(y)
    }

    fn size(&mut self, i: usize) -> usize {
        let root = self.root(i);
        self.size[root]
    }

    fn unite(&mut self, x: usize, y: usize) {
        let x = self.root(x);
        let y = self.root(y);

        if x == y {
            return;
        }

        if self.size[x] < self.size[y] {
            self.par[x] = y;
            self.size[y] += self.size[x];
        } else {
            self.par[y] = x;
            self.size[x] += self.size[y];
        }
    }
}
*/

fn main() {
    let exe = "/tmp/bin00BABE6C";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";