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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

from collections import deque
import heapq
N,M=map(int,input().split())
R=[]
G=[[] for i in range(N)]
for i in range(M):
    a,b,c=map(int,input().split())
    a,b=a-1,b-1
    G[a].append((b,c))
    G[b].append((a,c))
    R.append((a,b,c))
Q=[[0]*N for i in range(N)]
INF=10**9
for i in range(N):
    stack=[]
    g=[INF for i in range(N)]
    g[i]=0
    n=1
    for b,c in G[i]:
        heapq.heappush(stack,(g[i]+c,i,b))
    used=[[0]*N for i in range(N)]
    while(stack):
        if n==N:
            break
        c,a,b=heapq.heappop(stack)
        g[b]=c
        n+=1
        used[a][b]=1
        used[b][a]=1
        for j in G[b]:
            if used[b][j[0]] or g[j[0]]!=INF:
                continue
            heapq.heappush(stack,(g[b]+j[1],b,j[0]))
    for j in range(i+1,N):
        Q[i][j]=g[j]
ans=0
for a,b,c in R:
    if b<a:
        a,b=b,a
    if Q[a][b]<c:
        ans+=1
print(ans)