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: Wrong Answer)

n, m = list(map(int, input().split()))
connect = {}
dist = {}
for _ in range(m):
    a, b, c = list(map(int, input().split()))
    if not a in connect.keys(): connect[a] = [b]
    else: connect[a].append(b)
    if not b in connect.keys(): connect[b] = [a]
    else: connect[b].append(a)
    
    dist[tuple(sorted([a, b]))] = c

ans = 0
for s in range(1, n):
    for t in range(s+1, n+1):
        if not (s, t) in dist.keys():
            continue
        
        dists = [1000]*(n+1)
        dists[s] = 0
        stack = [(s, sc) for sc in connect[s]]
        while len(stack) > 0:
            s0, s1 = stack[0]
            stack = stack[1:]
            if dists[s0]+dist[tuple(sorted((s0, s1)))] >= dists[s1]:
                continue
            else:
                dists[s1] = dists[s0]+dist[tuple(sorted((s0, s1)))]
                for s2 in connect[s1]:
                    stack.append((s1, s2))
        print(dists)
        if dists[t] < dist[(s, t)]:
            ans += 1

print(ans)