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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Threading.Tasks;

class Program {
    static void Main (string[] args) {
          //1000000007

        //int n = int.Parse(Console.ReadLine ());
        string[] p = Console.ReadLine ().Split(' ');
        int n = int.Parse(p[0]);
        int d = int.Parse(p[1]);
        int[] A0= new int[d];
        int[] A1= new int[d];
        int[] A2= new int[d];
                int[] A4= new int[n];
        double[] A3= new double[d];

        Double o = 0;
        double s = 0;
        int ans = 0;

        for(int i=0;i<n;i++){
            if(d > 1){
            string[] ten1 = Console.ReadLine ().Split(' ');
            
            for(int j=0;j<d;j++){
                A2[j] = int.Parse(ten1[j]);
            }
            if(i > 0){
                for(int j=0;j<d;j++){
                    A3[j] = System.Math.Pow((Double)A1[j] - (Double)A2[j],2);
                }
                for(int k=0;k<d;k++){
                    o = o + A3[k];
                }
                s = System.Math.Sqrt(o);

                if((int)s == s){
                    ans++;
                }

            }else{
                Array.Copy(A2,A0,d);
            }
            if(i == n -1){
                o = 0;
                for(int j=0;j<d;j++){
                    A3[j] = System.Math.Pow((Double)A2[j] - (Double)A0[j],2);
                }
                for(int k=0;k<d;k++){
                    o = o + A3[k];
                }
                s = System.Math.Sqrt(o);

                if((int)s == s){
                    ans++;
                }
            }
            Array.Copy(A2,A1,d);
            o = 0;
            }else{

            }

        }
        if(d == 1){
        for(int i=0;i<n;i++){
            A4[i] = int.Parse(Console.ReadLine ());
        }
                int sum = 0;
                for(int l=1;l<n;l++){
                    sum = sum + n -l;
                    
                }
                ans = sum;
        }

        Console.WriteLine(ans);

    }
}