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 PHP (5.6.30) (judge verdict: Wrong Answer)

<?php
fscanf(STDIN,"%d %d",$N,$M);

for($i=1;$i<=$M;$i++){  
  ${"array".$i} = explode(" ",fgets(STDIN));
}

if($N-1 === $M){
  echo 0;
}else{
  $arrayResult = array();
  $arrayNumber = array();
  $arrayResult[1] = 0;
//  $arrayNumber[1] = 1;
  $result = 0;
  for($i=1;$i<=$M;$i++){
    $x = ${"array".$i}[0];
    $y = ${"array".$i}[1];
    $z = ${"array".$i}[2];
    if(array_key_exists($y,$arrayResult)){      
      if($z >= $arrayResult[$x]+$arrayResult[$y]){
//        $arrayResult[$y] = $arrayResult[$x]+$arrayResult[$y];
        $result++;
      }elseif(${"array".$arrayNumber[$y]}[2] >= ${"array".$arrayNumber[$y]}[0]+$arrayResult[$x]+$z){
        $result++;
      }else{
//        $arrayResult[$y] = $arrayResult[$x]+$z;
      }
      //☆　>=対応
      if($arrayResult[${"array".$arrayNumber[$y]}[0]]+${"array".$arrayNumber[$y]}[2] > $arrayResult[$x]+$z){
        $arrayResult[$y] = $arrayResult[$x]+$z;
        $arrayNumber[$y] = $x;
      }
    }else{
      $arrayResult[$y] = $arrayResult[$x]+$z;
      $arrayNumber[$y] = $x;
    }
  }
  echo $result;
}