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;
using System.Collections.Generic;
using System.Linq;
using static AtCoder.Io;

namespace AtCoder
{
    class Program
    {
        static void Main()
        {
            var nm = ReadIntArray();
            var n = nm[0];
            var m = nm[1];
            var r = new int[n, n];
            var edge = new Tuple<int, int>[m * 2];
            for (int i = 0; i < m; i++)
            {
                var abc = ReadIntArray();
                var a = abc[0] - 1;
                var b = abc[1] - 1;
                var c = abc[2];
                r[a, b] = c;
                r[b, a] = c;
                edge[i * 2] = Tuple.Create(a, b);
                edge[i * 2 + 1] = Tuple.Create(b, a);
            }
            var count = 0;
            for (int i = 0; i < n; i++)
            {
                var cost = Enumerable.Repeat(1001, n).ToArray();
                cost[i] = 0;
                for (int j = 0; j < n; j++)
                {
                    for (int k = 0; k < edge.Length; k++)
                    {
                        if (cost[edge[k].Item1] > cost[edge[k].Item2] + r[edge[k].Item1, edge[k].Item2])
                        {
                            cost[edge[k].Item1] = cost[edge[k].Item2] + r[edge[k].Item1, edge[k].Item2];
                        }
                    }
                }
                for (int j = 0; j < n; j++)
                {
                    if (i != j && cost[j] < r[i, j])
                        count++;
                }
            }
            Console.WriteLine(count / 2);
        }
    }

    public static class Io
    {
        public static string ReadString() => Console.ReadLine();
        public static string[] ReadStringArray() => ReadString().Split(' ');
        public static int ReadInt() => int.Parse(ReadString());
        public static long ReadLong() => long.Parse(ReadString());
        public static int[] ReadIntArray() => ReadStringArray().ParseInt().ToArray();
        public static long[] ReadLongArray() => ReadStringArray().ParseLong().ToArray();
        public static IEnumerable<int> ParseInt(this IEnumerable<string> source) => source.Select(int.Parse);
        public static IEnumerable<long> ParseLong(this IEnumerable<string> source) => source.Select(long.Parse);
    }
}