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)

#create environment
import numpy as pd
num = 1
i = 1
k = 1
df = pd.DataFrame()
count_num = 0
f = lambda x: (x**2)

#input1 N D (numeric)
N, D = map(int, input().split())
#input2
for l in (1, N):
  a = map(int, input().split())
  if a is none:
    break
  df[l] = a

#for num > 2:
#  a = map(int, input().split())
#  if a is none:
#    break
#  df[i] = a
#  i = i + 1

# make combination
df_new = df.T
#a_new = a.T
print(df_new)
for i in range(0, len(df_new.index)):
  for j in range(k, len(df_new.index)):
    print_str = str(i) + '-' + str(j)
    print(print_str)
    k = k + 1
    df_new_ij = df_new.loc[[i,j],:]
    obj_num = np.sqrt(df_new_ij.apply(f).cumsum().iloc[1,:].cumsum()[len(df['a'])-1])
    
    if obj_num == round(obj_num):
      count_num = count_num + 1

print(count_num)