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.