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)

use std::io::{Read, stdin};
use std::str::FromStr;

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

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

    fn find(&mut self, x: usize) -> usize {
        if self.par[x] == x {
            x
        } else {
            let par = self.par[x];
            self.par[x] = self.find(par);
            self.par[x]
        }
    }

    fn unite(&mut self, x: usize, y: usize) {
        let ux = self.find(x);
        let uy = self.find(y);
        if ux != uy {
            if self.rank[ux] < self.rank[uy] {
                self.par[ux] = uy;
            } else {
                self.par[uy] = ux;
                if self.rank[ux] == self.rank[uy] { self.rank[ux] += 1; }
            }
        }
    }

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


fn main() {
    let n: usize = read();
    let m: usize = read();
    let mut edges: Vec<[usize; 2]> = Vec::new();
    for _i in 0..m {
        let a: usize = read();
        let b: usize = read();
        edges.push([a - 1, b - 1]);
    }
    let mut cnt = 0;
    for i in 0..m {
        let mut unf = UnionFind::new(n);
        for j in 0..m {
            if j != i {
                unf.unite(edges[j][0], edges[j][1]);
            }
        }
        for j in 1..n {
            if !unf.same(0, j) {
                cnt += 1;
                break;
            }
        }
    }

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


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")
}