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 petgraph::unionfind::UnionFind;
use proconio::input;
use proconio::marker::Usize1;

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

    let mut count = 0;
    'outer: for i in 0..m {
        let mut uf = UnionFind::new(n);
        for j in 0..m {
            if i != j {
                uf.union(e[j].0, e[j].1);
            }
        }
        let representative = uf.find(0);
        for j in 1..n {
            if representative != uf.find(j) {
                count += 1;
                continue 'outer;
            }
        }
        //println!("i: {}", i);
    }
    println!("{}", count);
}