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 Python (3.4.3) (judge verdict: Runtime Error)

import math
n,d=input().split()
n=int(n)
d=int(d)
def combinations(n, r):
    return math.factorial(n)/(math.factorial(n-r)*math.factorial(r))
x=[]
for i in range(n):
  xa=[int(s) for s in input().split()]
  x.append(xa)
a=[]
if d==1:
  count=combinations(n,2)
  count=int(count)
else:
  for i in range(n-1):
    for j in range(i+1,n):
      t=[]
      for k in range(d):
        c=(x[i][k]-x[j][k])*(x[i][k]-x[j][k])
        t.append(c)
        if k==d-1:
          a.append(sum(t))
  answer=list(map(lambda x:pow(x,1/2),a))
  count=0
  for l in range(n):
    if answer[l].is_integer()==True:
      count=count+1
print(count)