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: Accepted)

import Control.Applicative
import Control.Monad
import qualified Data.ByteString.Char8 as B
import Data.Maybe (fromJust)
import Text.Printf
import Debug.Trace
import Data.Array.IArray
import Data.Array.IO

getInts :: IO [Int]
getInts = map (fst . fromJust . B.readInt) . B.words <$> B.getLine

inf = 1000000000

solve [] _ a = a
solve ([a,b,c]:es) arr acc = solve es arr acc'
  where
    acc' = acc + (if arr!(a,b) /= c then 1 else 0)

main = do
  [n,m] <- getInts
  dt <- newArray ((1,1),(n,n)) inf :: IO (IOArray (Int,Int) Int)
  es <- replicateM m getInts
  forM_ es $ \[a,b,c] -> do
    writeArray dt (a,b) c
    writeArray dt (b,a) c
  forM_ [1..n] $ \k -> do
    forM_ [1..n] $ \i -> do
      forM_ [1..n] $ \j -> do
        a <- readArray dt (i,k)
        b <- readArray dt (k,j)
        pv <- readArray dt (i,j)
        writeArray dt (i,j) (min pv (a+b))
  arr <- freeze dt :: IO (Array (Int,Int) Int)
  print $ solve es arr 0