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 Go (1.6) (judge verdict: Accepted)

package main

import "fmt"

const Limit = 50

var matrix [Limit][Limit]bool
var a [Limit]int
var b [Limit]int
var visited [Limit]bool
var n, k int

func check(node int) {
	if visited[node] {
		return
	} else {
		visited[node] = true
		for i := 0; i < n; i++ {
			if matrix[node][i] {
				check(i)
			}
		}
	}
}

func main() {
	fmt.Scan(&n, &k)
	//
	for i := 0; i < k; i++ {
		fmt.Scan(&a[i], &b[i])
		a[i]--
		b[i]--
		matrix[a[i]][b[i]] = true
		matrix[b[i]][a[i]] = true
	}
	//
	//
	bridge := 0
	for i := 0; i < k; i++ {
		matrix[a[i]][b[i]] = false
		matrix[b[i]][a[i]] = false
		for j := 0; j < n; j++ {
			visited[j] = false
		}

		check(0)
		true_cnt := 0
		for j := 0; j < n; j++ {
			if visited[j] {
				true_cnt++
			}
		}
		if true_cnt != n {
			bridge++
		}

		matrix[a[i]][b[i]] = true
		matrix[b[i]][a[i]] = true
	}

	fmt.Println(bridge)
}