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# (.NET Core 3.1.201) (judge verdict: Accepted)

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

namespace Tasks
{
    public class D
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var NM = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
            var (N, M) = (NM[0], NM[1]);
            var infinity = (int)1e9;
            var nodes = new (int A, int B, int C)[M];
            var graph = new int[N][].Select(x => x = Enumerable.Repeat(infinity, N).ToArray()).ToArray();
            for (var i = 0; i < N; i++)
            {
                graph[i][i] = 0;
            }
            for (var i = 0; i < M; i++)
            {
                var abc = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
                var a = abc[0] - 1;
                var b = abc[1] - 1;
                var c = abc[2];
                graph[a][b] = Math.Min(graph[a][b], c);
                graph[b][a] = Math.Min(graph[b][a], c);
                nodes[i] = (a, b, c);
            }

            for (var k = 0; k < N; k++)
            {
                for (var i = 0; i < N; i++)
                {
                    for (var j = 0; j < N; j++)
                    {
                        graph[i][j] = Math.Min(graph[i][j], graph[i][k] + graph[k][j]);
                    }
                }
            }

            var answer = M;
            for (var i = 0; i < M; i++)
            {
                var ok = false;
                for (var j = 0; j < N; j++)
                {
                    if (graph[j][nodes[i].A] + nodes[i].C == graph[j][nodes[i].B]) ok = true;
                }
                if (ok) answer--;
            }
            Console.WriteLine(answer);
        }
    }
}