Problem:
Score : 400 points

Problem Statement

You are given an undirected connected weighted graph with N vertices and M edges that contains neither self-loops nor double edges.

The i-th (1≤i≤M) edge connects vertex a_i and vertex b_i with a distance of c_i.

Here, a self-loop is an edge where a_i = b_i (1≤i≤M), and double edges are two edges where (a_i,b_i)=(a_j,b_j) or (a_i,b_i)=(b_j,a_j) (1≤i<j≤M).

A connected graph is a graph where there is a path between every pair of different vertices.

Find the number of the edges that are not contained in any shortest path between any pair of different vertices.

Constraints

2≤N≤100

N-1≤M≤min(N(N-1)/2,1000)

1≤a_i,b_i≤N

1≤c_i≤1000

c_i is an integer.

The given graph contains neither self-loops nor double edges.

The given graph is connected.

Input

The input is given from Standard Input in the following format:

N M
a_1 b_1 c_1
a_2 b_2 c_2
:
a_M b_M c_M

Output

Print the number of the edges in the graph that are not contained in any shortest path between any pair of different vertices.

Sample Input 1

3 3
1 2 1
1 3 1
2 3 3

Sample Output 1

1

In the given graph, the shortest paths between all pairs of different vertices are as follows:

The shortest path from vertex 1 to vertex 2 is: vertex 1 → vertex 2, with the length of 1.

The shortest path from vertex 1 to vertex 3 is: vertex 1 → vertex 3, with the length of 1.

The shortest path from vertex 2 to vertex 1 is: vertex 2 → vertex 1, with the length of 1.

The shortest path from vertex 2 to vertex 3 is: vertex 2 → vertex 1 → vertex 3, with the length of 2.

The shortest path from vertex 3 to vertex 1 is: vertex 3 → vertex 1, with the length of 1.

The shortest path from vertex 3 to vertex 2 is: vertex 3 → vertex 1 → vertex 2, with the length of 2.

Thus, the only edge that is not contained in any shortest path, is the edge of length 3 connecting vertex 2 and vertex 3, hence the output should be 1.

Sample Input 2

3 2
1 2 1
2 3 1

Sample Output 2

0

Every edge is contained in some shortest path between some pair of different vertices.

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
class Program{
	static void Main(){
		int[] s=Array.ConvertAll(Console.ReadLine().Split(),int.Parse);
		int[,] dp=new int[s[0]+1,s[0]+1];
		int[][] arr=new int[s[1]][];
		int ans=0;

		for(int i=1;i<=s[0];i++){
			for(int j=1;j<=s[0];j++){
				if(i!=j){dp[i,j]=int.MaxValue/2;}
			}
		}
		for(int i=0;i<s[1];i++){
			arr[i]=Array.ConvertAll(Console.ReadLine().Split(),int.Parse);
			dp[arr[i][0],arr[i][1]]=arr[i][2];
			dp[arr[i][1],arr[i][0]]=arr[i][2];
		}
		for(int i=1;i<=s[0];i++){
			for(int j=1;j<=s[0];j++){
				for(int k=1;k<=s[0];k++){
					dp[j,k]=Math.Min(dp[j,k],dp[j,i]+dp[i,k]);
				}
			}
		}
		for(int i=0;i<s[1];i++){
			if(dp[arr[i][0],arr[i][1]]<arr[i][2]){ans++;}
		}
		Console.WriteLine(ans);
	}
}