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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;

namespace ABC051
{
    class Program
    {
        static void Main(string[] args)
        {

            int[,] dist = new int[100, 1000];

            string[] input;
            input = Console.ReadLine().Split(' ');
            int N = int.Parse(input[0]);
            int M = int.Parse(input[1]);

            int[] a = new int[N];
            int[] b = new int[N];
            int[] c = new int[N];
            for (int i = 0; i < N; i++)
            {
                input = Console.ReadLine().Split(' ');
                a[i] = int.Parse(input[0]) - 1;
                b[i] = int.Parse(input[1]) - 1;
                c[i] = int.Parse(input[2]);

                dist[a[i], b[i]] = c[i];
                dist[b[i], a[i]] = c[i];
            }

            // Warshall–Floyd Initialize
            for (int i = 0; i < N; i++)
            {
                for (int j = 0; j < N; j++)
                {
                    dist[i, j] = int.MaxValue;
                }
                dist[i, i] = 0;
            }

            // Warshall–Floyd
            for (int k = 0; k < N; k++)
            {
                for (int i = 0; i < N; i++)
                {
                    for (int j = 0; j < N; j++)
                    {
                        dist[i, j] = Math.Min(dist[i, j], dist[i, k] + dist[k, j]);
                    }
                }
            }

            int result = 0;
            for (int i = 0; i < N; i++)
            {
                if (c[i] > dist[a[i], b[i]]) result++;
            }
            Console.WriteLine(result);
        }
    }
}