Problem:
Score : 200 points

Problem Statement

There are N points in a D-dimensional space.

The coordinates of the i-th point are (X_{i1}, X_{i2}, ..., X_{iD}).

The distance between two points with coordinates (y_1, y_2, ..., y_D) and (z_1, z_2, ..., z_D) is \sqrt{(y_1 - z_1)^2 + (y_2 - z_2)^2 + ... + (y_D - z_D)^2}.

How many pairs (i, j) (i < j) are there such that the distance between the i-th point and the j-th point is an integer?

Constraints

All values in input are integers.

2 \leq N \leq 10

1 \leq D \leq 10

-20 \leq X_{ij} \leq 20

No two given points have the same coordinates. That is, if i \neq j, there exists k such that X_{ik} \neq X_{jk}.

Input

Input is given from Standard Input in the following format:

N D
X_{11} X_{12} ... X_{1D}
X_{21} X_{22} ... X_{2D}
\vdots
X_{N1} X_{N2} ... X_{ND}

Output

Print the number of pairs (i, j) (i < j) such that the distance between the i-th point and the j-th point is an integer.

Sample Input 1

3 2
1 2
5 5
-2 8

Sample Output 1

1

The number of pairs with an integer distance is one, as follows:

The distance between the first point and the second point is \sqrt{|1-5|^2 + |2-5|^2} = 5, which is an integer.

The distance between the second point and the third point is \sqrt{|5-(-2)|^2 + |5-8|^2} = \sqrt{58}, which is not an integer.

The distance between the third point and the first point is \sqrt{|-2-1|^2+|8-2|^2} = 3\sqrt{5}, which is not an integer.

Sample Input 2

3 4
-3 7 8 2
-12 1 10 2
-2 8 9 3

Sample Output 2

2

Sample Input 3

5 1
1
2
3
4
5

Sample Output 3

10

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

(defun next (i.j N)
  (let ((i (car i.j))
	(j (cdr i.j)) )
    (if (< (1+ j) N)
	(cons i (1+ j)) (cons (1+ i) (+ i 2)) )))

(let ((N (read))
      (D (read))
      (counter 0) )

  (setf array (make-array N))

  (dotimes (x N)
    (setf (aref array x) (loop :repeat D :collect (read))))

  (do ((i.j '(0 . 1) (next i.j N)))
      ((>= (car i.j) (1- N)))

    (let ((i (car i.j))
	  (j (cdr i.j)) )
      (let ((d^2 (reduce #'+
			 (mapcar #'(lambda (x y) (expt (- x y) 2))
				 (aref array i)  (aref array j) ))))
	(if (= d^2 (expt (isqrt d^2) 2))
	    (setf counter (1+ counter)) ))
      ;(princ (cons i j))
      ))
  (princ counter) )