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"

func different(i, j, node, neigh int) bool {
	return !(i == node && j == neigh) && !(i == neigh && j == node)
}

func dfs(g [][]int, i, j, node int, visited []bool) {
	for _, neigh := range g[node] {
		if !visited[neigh] && different(i, j, node, neigh) {
			visited[neigh] = true
			dfs(g, i, j, neigh, visited)
		}
	}
}

func is_bridge(g [][]int, i, j int) bool {
	visited := make([]bool, len(g))
	visited[0] = true
	dfs(g, i, j, 0, visited)
	for _, b := range visited {
		if !b {
			return true
		}
	}
	return false
}

func main() {
	var n, m int
	fmt.Scan(&n, &m)
	g := make([][]int, n)
	for i := range g {
		g[i] = make([]int, 0)
	}
	for i := 0; i < m; i++ {
		var a, b int
		fmt.Scan(&a, &b)
		g[a-1] = append(g[a-1], b-1)
		g[b-1] = append(g[b-1], a-1)
	}

	cnt := 0
	for i, l := range g {
		for _, j := range l {
			if i < j && is_bridge(g, i, j) {
				cnt++
			}
		}
	}
	fmt.Println(cnt)
}