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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.List;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;

/**
 * http://abc075.contest.atcoder.jp/tasks/abc075_c
 */
public class Main {

	static Point[] points;
	static Set<Integer> g = new HashSet<Integer>();
	static Set<Integer> v = new HashSet<Integer>();
	
	public static void main(String[] args) {
		
		Scanner sc = new Scanner(System.in);
		final int N = sc.nextInt();
		final int M = sc.nextInt();
		points = new Point[N];
		for(int i=0; i<N; i++) points[i] = new Point(i);
		for(int i=0; i<M; i++){
			int x = sc.nextInt()-1;
			int y = sc.nextInt()-1;
			points[x].neighbor.add(y);
			points[y].neighbor.add(x);
		}
		sc.close();
		dfs(0, 0, new ArrayList<Integer>());
		int m = 0;
		for(int i:g){
			for(int n:points[i].neighbor){
				if(g.contains(n)){
					m++;
				}
			}
		}
		System.out.println(M-m/2);
	}
	
	
	private static void dfs(int current, int previous, List<Integer> route) {
		if(route.contains(current)){
			int d = route.indexOf(current);
			for(int i=d; i<route.size(); i++) g.add(route.get(i));
			return;
		}
		v.add(current);
		for(int n: points[current].neighbor){
			if(n==previous) continue;
			List<Integer> newRoute = new ArrayList<Integer>();
			for(int r: route) newRoute.add(r);
			newRoute.add(current);
			dfs(n, current, newRoute);
		}
	}

	static class Point{
		public Point(int id) {
			this.id = id;
		}
		int id;
		Set<Integer> neighbor = new HashSet<>();
	}

}