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.