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 Python (3.4.3) (judge verdict: Accepted)

def main():
	INF = 10**9+7
	N, M = map(int, input().split())
	dist = [[INF for _ in range(N+1)] for _ in range(N+1)]
	for i in range(1, N+1):
		for j in range(1, N+1):
			if i == j:
				dist[i][j] = 0
	a, b, c = [0]*M, [0]*M, [0]*M
	for i in range(M):
		a[i], b[i], c[i] = map(int, input().split())
		dist[a[i]][b[i]] = min(dist[a[i]][b[i]], c[i])
		dist[b[i]][a[i]] = min(dist[b[i]][a[i]], c[i])
	for k in range(1, N+1):
		for i in range(1, N+1):
			for j in range(1, N+1):
				dist[i][j] = min(dist[i][j], dist[i][k]+dist[k][j])
	ans = M
	for i in range(M):
		shrotest = False
		for j in range(1, N+1):
			if dist[j][a[i]]+c[i] == dist[j][b[i]]:
				shrotest = True
		if shrotest:
			ans -= 1
	print(ans)

if __name__ == '__main__':
    main()