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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php

$input = explode(' ', trim(fgets(STDIN)));
$n = (int)$input[0];
$m = (int)$input[1];
$infinit = 10001;

$shortest = [];
for ($i=1; $i <= $n; $i++) { 
	for ($j=1; $j <= $n; $j++) { 
		if ($i === $j) {
			$shortest[$i][$j] = 0;
		}else{
			$shortest[$i][$j] = $infinit;
		}
	}
}
$path = [];
for ($i=0; $i < $m; $i++) { 
	$input = explode(' ', trim(fgets(STDIN)));
	$fr = (int)$input[0];
	$to = (int)$input[1];
	$dist = (int)$input[2];
	$path[] = [$fr, $to, $dist];
	$shortest[$fr][$to] = $dist;
	$shortest[$to][$fr] = $dist;
}


for ($a=1; $a <= $n; $a++) { 
	for ($b=1; $b <= $n; $b++) { 
		for ($c=1; $c <= $n; $c++) { 
			$shortest[$b][$c] = min($shortest[$b][$c], $shortest[$a][$b]+$shortest[$a][$c]);
		}
	}
}

$count = 0;
foreach ($path as $v) {
	if ($shortest[$v[0]][$v[1]] < $v[2]) {
		++$count;
	}
}
echo $count;