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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;
import java.util.ArrayList;

public class Main{

    public static void main(String args[]){

        Scanner scan = new Scanner(System.in);
        Integer N = Integer.parseInt(scan.next());
        Integer D = Integer.parseInt(scan.next());

        Integer array[][] = new Integer[N][D];
        double distance[] = new double[N];
        ArrayList<Double> d = new ArrayList<Double>();

        for(int i=0;i<N;i++){
            for(int j=0;j<D;j++){
                array[i][j] = Integer.parseInt(scan.next());
            }
        }
    
        for(int i=0;i<N;i++){

            for(int k=i+1;k<N;k++){

                int sum = 0;
                for(int j=0;j<D;j++){
                    if(i != N-1){
                        sum += Math.abs((array[i][j] - array[k][j]) * (array[i][j] - array[k][j]));
                    }else{
                        sum += Math.abs(  (array[i][j] - array[0][j] ) * (array[i][j] - array[0][j] )  );
                    }
                }
                d.add(Math.sqrt(sum));

            }
        }

        int count = 0;
        for(int i=0;i<d.size();i++){
            double dd = d.get(i);
            if(d.get(i) == (int)dd){
                count++;
            }
        }

        System.out.println(count);
    }
    
    static int factorial(int n){
        if(n == 0){
          return 1;
        }
        return n * factorial(n-1);
      }
}