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

namespace Program
{
    public class ABC051D
    {
        static class Console_
        {
            private static Queue<string> param = new Queue<string>();
            public static int NextInt() => int.Parse(NextString());
            public static long NextLong() => long.Parse(NextString());
            public static string NextString()
            {
                if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item);
                return param.Dequeue();
            }
        }
        static public void Main(string[] args)
        {
            var N = Console_.NextInt();
            var M = Console_.NextInt();
            var dist = new int[N, N];
            var checkPath = new List<Tuple<int, int, int>>();
            for (int i = 0; i < M; ++i)
            {
                var a = Console_.NextInt();
                var b = Console_.NextInt();
                var c = Console_.NextInt();
                dist[a - 1, b - 1] = c;
                dist[b - 1, a - 1] = c;
                checkPath.Add(Tuple.Create(a - 1, b - 1, c));
            }
            for (int k = 0; k < N; ++k)
            {
                for (int i = 0; i < N; ++i)
                {
                    for (int j = 0; j < N; ++j)
                    {
                        if (dist[i, k] != 0 && dist[k, j] != 0)
                        {
                            if (dist[i, j] == 0 || dist[i, j] > dist[i, k] + dist[k, j])
                            {
                                dist[i, j] = dist[i, k] + dist[k, j];
                            }
                        }
                    }
                }
            }
            var sum = 0;
            foreach (var item in checkPath)
            {
                if (dist[item.Item1, item.Item2] < item.Item3)
                {
                    ++sum;
                }
            }
            Console.WriteLine(sum);
        }
    }
}