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:
/*
use proconio::input;
use proconio::marker::Usize1;

pub struct UnionFind {
  n: usize,
  root: Vec<usize>,
  rank: Vec<usize>,
  size: Vec<usize>,
}

impl UnionFind {
  pub fn new(n: usize) -> Self {
    let root = (0..n).into_iter().collect();
    let rank = vec![0; n];
    let size = vec![1; n];
    Self {
      n,
      root,
      rank,
      size,
    }
  }

  pub fn find(&mut self, x: usize) -> usize {
    if x >= self.n {
      panic!();
    }
    if self.root[x] == x {
      x
    } else {
      let root = self.find(self.root[x]);
      self.root[x] = root;
      root
    }
  }

  pub fn unite(&mut self, x: usize, y: usize) {
    if x >= self.n || y >= self.n {
      panic!();
    }
    let x_root = self.find(x);
    let y_root = self.find(y);
    if x_root == y_root {
      return;
    }
    if self.rank[x_root] < self.rank[y_root] {
      self.root[x_root] = y_root;
      self.size[y_root] += self.size[x_root];
    } else {
      self.root[y_root] = x_root;
      self.size[x_root] += self.size[y_root];
      if self.rank[x_root] == self.rank[y_root] {
        self.rank[x_root] += 1;
      }
    }
  }

  pub fn size(&mut self, x: usize) -> usize {
    if x >= self.n {
      panic!();
    }
    let x_root = self.find(x);
    self.size[x_root]
  }

  pub fn is_same(&mut self, x: usize, y: usize) -> bool {
    if x >= self.n || y >= self.n {
      panic!();
    }
    self.find(x) == self.find(y)
  }
}

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

  let mut res = 0;
  for skip in 0..m {
    let mut uf = UnionFind::new(n);
    for (i, &(u, v)) in edges.iter().enumerate() {
      if i == skip {
        continue;
      }
      uf.unite(u, v);
    }
    for u in 0..n {
      if uf.size(u) != n {
        res += 1;
        break;
      }
    }
  }
  println!("{}", res);
}
*/

fn main() {
    let exe = "/tmp/binB9E7AAC8";
    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>";