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.Text;
using System.Linq;

class Program
{
    static void Main(string[] args) {
#if DEBUG
        System.Diagnostics.Debug.WriteLine("-----TextFile1");
        System.Diagnostics.Debug.WriteLine(process("../TextFile1.txt"));
        System.Diagnostics.Debug.WriteLine("-----TextFile2");
        System.Diagnostics.Debug.WriteLine(process("../TextFile2.txt"));
        System.Diagnostics.Debug.WriteLine("-----TextFile3");
        System.Diagnostics.Debug.WriteLine(process("../TextFile3.txt"));
#endif

#if !DEBUG
        String ret = process(new System.IO.StreamReader(Console.OpenStandardInput()));
        Console.WriteLine(ret);
#endif
    }

    static string process(string filePath) {
        using (var input = new System.IO.StreamReader(filePath)) {
            if(input.EndOfStream) return "NO PROC";
            return process(input);
        }
    }

    static string process(System.IO.TextReader input) {
        var s     = input.ReadLine();
        var spl   = s.Split(' ');
        int n     = int.Parse(spl[0]);
        int d     = int.Parse(spl[1]);

        int[][] ary  = new int[n][];

        for(int i=0; i<n; i++) {
            ary[i] = ToIntArray(input.ReadLine(), d);
        }

        int count = 0;
        for(int i=0; i<n; i++) {
            for(int j=i; j<n; j++) {
                if (i == j) continue;
                if (calc(ary[i], ary[j], d)) count++;
            }
        }

        return count.ToString();
    }

    static bool calc(int[] xi, int[] xj, int size) {
        int v = 0;
        for(int i=0; i<size; i++) {
            int k = xi[i] - xj[i];
            v += k * k;
        }
        for(int i=0; ; i++) {
            int ii = i * i;
            if (ii == v) return true;
            if (ii > v) return false;
        }
    }
    
    static int[] ToIntArray(string strs, int n) {
        int[] ret = new int[n];
        var spl =strs.Split(' ');
        for (int i = 0; i < n; i++) ret[i] = int.Parse(spl[i]);
        return ret;
    }
}