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 JavaScript (node.js v5.12) (judge verdict: Runtime Error)

"use strict"
process.stdin.resume();
process.stdin.setEncoding('utf8');
var input_string = '';

process.stdin.on('data', function (chunk) {
    input_string += chunk;
});
const space_input = function (line) {
    var arr = line.replace(/(^\s+)|(\s+$)/g, "").split(" ");
    for (var i = 0; i < arr.length; ++i) {
        arr[i] = +arr[i];
    }
    return arr;
};
const space_input_char = function (line) {
    var arr = line.replace(/(^\s+)|(\s+$)/g, "").split(" ");
    for (var i = 0; i < arr.length; ++i) {
        arr[i] = arr[i];
    }
    return arr;
};

process.stdin.on('end', function () {
    const lines = input_string.split('\n');
    const nm = space_input(lines[0])
    const N = nm[0]
    const M = nm[1]
    let ab = lines.splice(1).map(l=>space_input(l))
    let pts = new Array(N+1)
    for(let i=0;i<N+1;++i){
        pts[i]=[]
    }
    for(let e of ab){
        e[0]--
        e[1]--
        pts[e[0]].push(e[1])
        pts[e[1]].push(e[0])

    }
    let loop = []
    for(let i=0;i<N;++i){
        let next = [].concat(pts[i].map(v=>[v]))
        let done = new Set()
        while(next.length>0){
            let nextnext = []
            done.add(i)
            for(let n of next){
                const sentan = n[n.length-1]
                let nikomae = -1
                if(n.length>=2){ 
                    nikomae=n[n.length-2]
                }
                const nextsentan = pts[sentan].filter(p=>n.indexOf(p)<0&&p!==sentan&&(!done.has(p)||p===i))
                nextsentan.forEach(Nsentan=>{
                    done.add(Nsentan)
                    ttt = [].concat(n)
                    ttt.push(Nsentan)
                    if(Nsentan!==i){
                        nextnext.push(ttt)
                    }else{
                        loop.push(ttt)   
                    }
                })
            }
            next = nextnext         
        }
    }
    
    loop = loop.filter(v=>v.length>2)
    for(let l of loop){
        for(let i=0;i<l.length;++l){
            ab = ab.filter( v=> !(v[1]==l[i]&&v[0]==l[i+1%l.length])&&!(v[0]==l[i]&&v[1]==l[i+1%l.length]) )
        }
    }
    console.log(ab.length)
});