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)]
fn main() {
    let (n, m) = (i::u(), i::u());
    let ab = i::uv2(m);
    let mut ans = 0;
    'case: for i in 0..m {
        let mut uf = UnionFind::new(n);
        for j in 0..m {
            if i == j {
                continue;
            }
            uf.unite(ab[j].0, ab[j].1);
        }
        let root = uf.root(1);
        for j in 1..(n + 1) {
            if uf.root(j) != root {
                ans += 1;
                continue 'case;
            }
        }
    }
    println!("{}", ans);
}
#[allow(unused_imports)]
use union_find::*;

#[allow(dead_code)]
mod union_find {
    pub struct UnionFind {
        parent: Vec<usize>,
        rank: Vec<usize>,
    }

    impl UnionFind {
        pub fn new(n: usize) -> UnionFind {
            let mut parent = vec![0; n + 1];
            let rank = vec![0; n + 1];
            for i in 1..(n + 1) {
                parent[i] = i;
            }
            UnionFind {
                parent: parent,
                rank: rank,
            }
        }

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

        pub fn rank(&self, x: usize) -> usize {
            self.rank[x]
        }

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

        pub fn unite(&mut self, x: usize, y: usize) {
            let mut x = self.root(x);
            let mut y = self.root(y);
            if x == y {
                return;
            }
            if self.rank(x) < self.rank(y) {
                let tmp = y;
                y = x;
                x = tmp;
            }
            if self.rank(x) == self.rank(y) {
                self.rank[x] += 1;
            }
            self.parent[x] = y;
        }
    }
}

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::io::*;
#[allow(unused_imports)]
use std::num::*;
#[allow(unused_imports)]
use std::str::*;

#[allow(dead_code)]
mod i {
    use super::*;

    pub fn read<T: FromStr>() -> T {
        stdin()
            .bytes()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>()
            .parse::<T>()
            .ok()
            .unwrap()
    }

    pub fn str() -> String {
        read()
    }

    pub fn s() -> Vec<char> {
        str().chars().collect()
    }

    pub fn i() -> i64 {
        read()
    }

    pub fn u() -> usize {
        read()
    }

    pub fn f() -> f64 {
        read()
    }

    pub fn c() -> char {
        read::<String>().pop().unwrap()
    }

    pub fn iv(n: usize) -> Vec<i64> {
        (0..n).map(|_| i()).collect()
    }

    pub fn iv2(n: usize) -> Vec<(i64, i64)> {
        (0..n).map(|_| iv(2)).map(|a| (a[0], a[1])).collect()
    }

    pub fn uv(n: usize) -> Vec<usize> {
        (0..n).map(|_| u()).collect()
    }

    pub fn uv2(n: usize) -> Vec<(usize, usize)> {
        (0..n).map(|_| uv(2)).map(|a| (a[0], a[1])).collect()
    }

    pub fn fv(n: usize) -> Vec<f64> {
        (0..n).map(|_| f()).collect()
    }

    pub fn cmap(h: usize) -> Vec<Vec<char>> {
        (0..h).map(|_| s()).collect()
    }
}