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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
int main(){
    int N,M;
    cin>>N>>M;
    vector<int> a(M),b(M),c(M);
    vector<vector<int>> d(N, vector<int>(N,2000000000));
    for(int i=0;i<M;i++){
        cin>>a[i]>>b[i]>>c[i];
        a[i]--, b[i]--;
    }
    for(int i=0;i<N;i++) d[i][i]=0;
    for(int i=0;i<M;i++){
        d[a[i]][b[i]]=min(d[a[i]][b[i]], c[i]);
        d[b[i]][a[i]]=min(d[b[i]][a[i]], c[i]);
    }
    for(int i=0;i<N;i++){
        for(int j=0;j<N;j++){
            for(int k=0;k<N;k++){
                d[i][j]=min(d[i][j], d[i][k]+d[k][j]);
            }
        }
    }
  int ans=M;
    for(int i=0;i<M;i++){
        for(int j=0;j<N;j++){
            if(d[j][a[i]]+c[i]==d[j][b[i]]) goto minus;
        }
        continue;
        minus: ans--;
    }
    cout<<ans<<endl;
}