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: Accepted)

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cassert>
#include<climits>
#include<algorithm>
#include<vector>
#include<deque>
#include<map>
#include<set>
#include<sstream>
#include<cstring>

#define REP(i,s,n) for(int i=s;i<n;++i)
#define rep(i,n) REP(i,0,n)

using namespace std;

#define MAX_V 110
#define MAX_E 1010
int V, E, fw[MAX_V][MAX_V], a[MAX_E], b[MAX_E], c[MAX_E];

int main() {
  cin >> V >> E;
  rep(i,V) rep(j,V) fw[i][j] = INT_MAX;
  rep(i,V) fw[i][i] = 0;
  rep(i,E) {
    cin >> a[i] >> b[i] >> c[i];
    --a[i], --b[i];
    fw[a[i]][b[i]] = fw[b[i]][a[i]] = c[i];
  }
  rep(k,V) rep(i,V) rep(j,V) if( fw[i][k] != INT_MAX && fw[k][j] != INT_MAX ) fw[i][j] = min(fw[i][j],fw[i][k]+fw[k][j]);
  int cnt = 0;
  rep(i,E) {
    bool found = false;
    rep(s,V) rep(t,V) {
      if( fw[s][a[i]] + c[i] + fw[b[i]][t] == fw[s][t]  ) {
	found = true;
	break;
      }
    }
    if( !found ) ++cnt;
  }
  cout << cnt << endl;
  return 0;
}