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----- 3 3 1 2 1 1 3 1 2 3 3

-----Sample Output----- 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.