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 (1.42.0) (judge verdict: Accepted)

use std::io::*;
use std::str::FromStr;

pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

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

impl UnionFind {
    fn new(n: usize) -> UnionFind {
        // initialize
        let mut v: Vec<usize> = vec![];
        for i in 0..n + 1 {
            v.push(i)
        }
        let mut s: Vec<usize> = vec![1; n + 1];

        UnionFind { parent: v, size: s }
    }

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

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

    fn unite(&mut self, a: usize, b: usize) {
        let mut ra = self.root(a);
        let mut rb = self.root(b);
        if ra == rb {
            return;
        }
        if self.size[ra] < self.size[rb] {
            std::mem::swap(&mut ra, &mut rb)
        };
        self.size[ra] += self.size[rb];
        self.parent[rb] = ra;
    }

    fn same(&self, a: usize, b: usize) -> bool {
        let ra = self.root(a);
        let rb = self.root(b);
        self.parent[a] == self.parent[b]
    }
}

fn main() {
    let n: usize = read();
    let m: usize = read();
    let mut edges: Vec<(usize, usize)> = vec![];
    let mut ans = 0;

    for _ in 0..m {
        let a: usize = read();
        let b: usize = read();
        edges.push((a, b))
    }

    for i in 0..m {
        let mut uf = UnionFind::new(n);
        for j in 0..m {
            let mi = edges[j];
            if i == j {
                continue;
            }
            uf.unite(mi.0, mi.1)
        }
        if uf.size(1) == n {
            ans += 1;
        }
    }
    println!("{}", m - ans);
}