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 Common Lisp (SBCL 1.1.14) (judge verdict: Wrong Answer)

(defconstant +inf+ (ash 1 32))

(defun rep-helper (args body &optional (top nil))
  (if (null args)
      body
      (let ((arg (first args)))
        (rep-helper
         (rest args)
         (append `(loop for ,(first arg) from ,(second arg) below ,(third arg)
                        do) (if top body (list body)))))))

(defmacro rep (args &body body)
  (rep-helper (reverse args) body t))

(defun solve ()
  (let* ((n (read))
         (m (read))
         (d (make-array (list n n) :initial-element +inf+))
         (e (make-array (list n n) :initial-element +inf+)))
    (rep ((i 0 n))
      (setf (aref d i i) 0
            (aref e i i) 0))

    (loop repeat m
          do (let ((a (1- (read)))
                   (b (1- (read)))
                   (c (read)))
               (setf (aref d a b) c (aref d b a) c
                     (aref e a b) c (aref e b a) c)))

    (rep ((k 0 n) (i 0 n) (j 0 n))
      (setf (aref d i j) (min (aref d i j) (+ (aref d i k) (aref d k j)))))

    (let ((a 0))
      (rep ((i 0 n) (j 0 i))
        (when (< (aref d i j) (aref e i j))
          (incf a)))
      (princ a) (terpri))))

(solve)