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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;//リストの使用
using System.Collections.Generic;
using System.Text;//テキストの高速出力に必要
class Program
{
	static void Main()
	{
    string[] input = Console.ReadLine().Split(' ');
    int h = int.Parse(input[0]);//行の長さ
    int w = int.Parse(input[1]);//列の長さ
    long[,] matrix = new long[h,w];//行列
    long answer = 0;
    
    for(int i = 0; i < h; i++)//それぞれの行
    {
  	  long[] nums = Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);
  	  for(int j = 0; j < w; j++) matrix[i,j] = nums[j];//行の全ての成分
    }

    for(int i = 0; i < h; i++)
    {
      for(int j = i+1; j < h; j++)
      {
        long length = 0;
        for(int k = 0; k < w; k++)
        {
          length += (matrix[i,k]-matrix[j,k])*(matrix[i,k]-matrix[j,k]);
        }
        for(long k = 0; k < 1000; k++)
        {
          if(length == k*k) answer++;
        }
      }
    }

		Console.WriteLine(answer);
	}
}