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(unused_macros)]
macro_rules! input {
    ( source = $ s : expr , $ ( $ r : tt ) * ) => { let mut iter = $ s . split_whitespace ( ) ; let mut next = || { iter . next ( ) . unwrap ( ) } ; input_inner ! { next , $ ( $ r ) * } };
    ( $ ( $ r : tt ) * ) => { let stdin = std :: io :: stdin ( ) ; let mut bytes = std :: io :: Read :: bytes ( std :: io :: BufReader :: new ( stdin . lock ( ) ) ) ; let mut next = move || -> String { bytes . by_ref ( ) . map ( | r | r . unwrap ( ) as char ) . skip_while ( | c | c . is_whitespace ( ) ) . take_while ( | c |! c . is_whitespace ( ) ) . collect ( ) } ; input_inner ! { next , $ ( $ r ) * } };
}
#[allow(unused_macros)]
macro_rules! input_inner {
    ( $ next : expr ) => { };
    ( $ next : expr , ) => { };
    ( $ next : expr , $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let $ var = read_value ! ( $ next , $ t ) ; input_inner ! { $ next $ ( $ r ) * } };
}
#[allow(unused_macros)]
macro_rules! read_value {
    ( $ next : expr , ( $ ( $ t : tt ) ,* ) ) => { ( $ ( read_value ! ( $ next , $ t ) ) ,* ) };
    ( $ next : expr , [ $ t : tt ; $ len : expr ] ) => { ( 0 ..$ len ) . map ( | _ | read_value ! ( $ next , $ t ) ) . collect ::< Vec < _ >> ( ) };
    ( $ next : expr , chars ) => { read_value ! ( $ next , String ) . chars ( ) . collect ::< Vec < char >> ( ) };
    ( $ next : expr , usize1 ) => { read_value ! ( $ next , usize ) - 1 };
    ( $ next : expr , $ t : ty ) => { $ next ( ) . parse ::<$ t > ( ) . expect ( "Parse error" ) };
}

fn main() {
    input! {
        n: usize, m: usize,
        ab: [(usize1, usize1); m]
    }
    let mut ret = 0u64;
    for i in 0..m {
        let mut utree = Utree::new(n);
        for j in 0..m {
            if i == j {continue;}
            utree.unite(ab[j].0, ab[j].1);
        }
        if !utree.is_same(ab[i].0, ab[i].1) {
            ret += 1;
        }
    }
    println!("{}", ret);
}

#[allow(dead_code)]
pub struct Utree {
    n: usize,
    par: Vec<usize>,
    rank: Vec<usize>,
    size: Vec<usize>,
}
#[allow(dead_code)]
impl Utree {
    pub fn new(n: usize) -> Utree {
        Utree {
            n: n,
            par: (0..n).collect(),
            rank: vec![0; n],
            size: vec![1; n],
        }
    }
    pub fn find(&mut self, x: usize) -> usize {
        if self.par[x] == x {
            x
        } else {
            let parent = { self.par[x] };
            let ret = self.find(parent);
            self.par[x] = ret;
            ret
        }
    }
    pub fn unite(&mut self, mut x: usize, mut y: usize) {
        x = self.find(x);
        y = self.find(y);
        if x == y {
            return;
        };
        if self.rank[x] < self.rank[y] {
            self.par[x] = y;
            self.size[y] += self.size[x];
        } else {
            self.par[y] = x;
            self.size[x] += self.size[y];
            if self.rank[x] == self.rank[y] {
                self.rank[x] += 1;
            }
        }
    }
    pub fn is_same(&mut self, mut x: usize, mut y: usize) -> bool {
        x = self.find(x);
        y = self.find(y);
        x == y
    }
    pub fn get_size(&mut self, mut x: usize) -> usize {
        x = self.find(x);
        self.size[x]
    }
}