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 System.Text;

namespace AtCoder
{
    class Program
    {
        private const int MODULO = 1000000007;
        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }

        static int Solve(int N, List<Tuple<int, int>>[] paths)
        {
            int[][] costs = new int[N][];
            for (int i = 0; i < N; ++i)
            {
                var q = new Queue<int>();
                costs[i] = Enumerable.Repeat(int.MaxValue, N).ToArray();
                costs[i][i] = 0;
                q.Enqueue(i);
                while (q.Count > 0)
                {
                    int a = q.Dequeue();
                    foreach (var path in paths[a])
                    {
                        int b = path.Item1;
                        int c = path.Item2;
                        if (costs[i][b] > costs[i][a] + c)
                        {
                            costs[i][b] = costs[i][a] + c;
                            q.Enqueue(b);
                        }
                    }
                }
            }
            int count = 0;
            for (int a = 0; a < N; ++a)
            {
                foreach (var path in paths[a])
                {
                    int b = path.Item1;
                    int c = path.Item2;
                    if (c > costs[a][b]) { ++count; }
                }
            }
            return count / 2;
        }
        static void Main(string[] args)
        {
            int[] V1 = ReadInts();
            int N = V1[0];
            int M = V1[1];
            var paths = new List<Tuple<int, int>>[N];
            for (int i = 0; i < N; ++i) { paths[i] = new List<Tuple<int, int>>(); }
            for (int i = 0; i < M; ++i)
            {
                int[] V2 = ReadInts();
                int a = V2[0] - 1;
                int b = V2[1] - 1;
                int c = V2[2];
                paths[a].Add(new Tuple<int, int>(b, c));
                paths[b].Add(new Tuple<int, int>(a, c));
            }
            Console.WriteLine(Solve(N, paths));
        }
    }
}