Title
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 ai and vertex bi with a distance of ci.
Here, a self-loop is an edge where ai = bi (1≤i≤M), and double edges are two edges where (ai,bi)=(aj,bj) or (ai,bi)=(bj,aj) (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≤ai,bi≤N
- 1≤ci≤1000
- ci 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
a1 b1 c1
a2 b2 c2
:
aM bM cM
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.