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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import Data.Graph.Inductive
import Control.Monad
import Data.List(foldl')
import qualified Data.List as L
import Data.Set
import qualified Data.Set as S

main = do
    [n_, m_] <- return . L.map read . words =<< getLine
    let readEdge = do
	    [a,b,c] <- return . L.map read . words =<< getLine
	    return (a,b,c)
    edges <- replicateM m_ readEdge
    let nodes = L.map (\i->(i,())) [1..n_]
	gr = mkGraph nodes edges	::Gr () Int
	edgeSet:: Set (Node,Node) -> LPath Int ->  Set (Node,Node)
	edgeSet set (LP []) = set
	edgeSet set (LP [node]) = set
	edgeSet set (LP ((nodeId1,_):(nodeId2,_):path)) =
	    edgeSet (insert (nodeId1,nodeId2) set) $ LP ((nodeId2,0::Int):path)
	rltree = msTree (undir gr)
	lastSet = L.foldl' edgeSet S.empty rltree
    print $ m_ - (size lastSet)