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: Time Limit Exceeded)

n, m = map(int, input().split())

nd = [[] for _ in range(n + 1)]
eg = [True] * m
for i in range(m):
    a, b, c = map(int, input().split())
    nd[a].append([b, c, i])
    nd[b].append([a, c, i])

for i in range(1, n):
    for j in range(i + 1, n + 1):
        tr = [10 * 10] * (n + 1)
        fg = [False] * (n + 1)
        fr = [[] for _ in range(n + 1)]
        tr[i] = 0
        while True:
            mi = 0
            for k in range(1, n + 1):
                if fg[k]:
                    continue
                if mi == 0 or tr[k] < tr[mi]:
                    mi = k
            if mi == 0:
                break
            fg[mi] = True
            for xc in nd[mi]:
                x, c, e = xc
                nc = c + tr[mi]
                if nc < tr[x]:
                    tr[x] = nc
                    fr[x] = [mi, e]
        mi, e = fr[j]
        eg[e] = False
        while len(fr[mi]) > 0:
            mi, e = fr[mi]
            eg[e] = False

ans = 0
for f in eg:
    if f:
        ans += 1
print(ans)