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.Collections.Generic;

public class CSharp
{
    public static void Main()
    {
        Kyopuro chokudai = new Kyopuro();
        chokudai.AtCoder();
    }
}

public class Kyopuro
{

    int n, d;
    int[][] x;

    public void AtCoder()
    {
        string[] input;
        input = Console.ReadLine().Split(' ');
        n = int.Parse(input[0]);
        d = int.Parse(input[1]);
        x = new int[n][];
        int ans = 0;
        int tmp = 0;
        int y = 0;

        for(int i=0; i<n; i++)
        {
            x[i] = new int[d];
            input = Console.ReadLine().Split(' ');
            for(int j=0; j<d; j++)
            {
                x[i][j] = int.Parse(input[j]);
            }
        }

        for(int i=0; i<n; i++)
        {
            for(int j=i+1; j<n; j++)
            {
                tmp = 0;
                for(int k=0; k<d; k++)
                {
                    y = x[i][k] - x[j][k];
                    tmp += y * y;
                }
                for(int k=0; k<200; k++)
                {
                    if (k * k == tmp) ans++;
                }
            }
        }

        Console.WriteLine(ans);
    }
    public static void DebugWL(object x) { System.Diagnostics.Debug.WriteLine(x); }
}