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: Wrong Answer)

import java.util.Scanner;
import java.lang.Math;
 
class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int d = sc.nextInt();
    int[] x = new int[n * d];
    double[] powerBox = new double[n * 2];
    double[] resultBox = new double[n];
    if(d == 1){
        System.out.println(n*2);
    }else if(d < 6){
        for(int i = 0;i < n * d;i++){
            x[i] = sc.nextInt();
        }

        for(int i = 0;i < n * 2 - d;i++){
            powerBox[i] = Math.pow((x[i] - x[i + 2]),2);

        }

        int count = 0;
        for(int i = n * 2 - d;i < n * 2;i++){
            powerBox[i] = Math.pow((x[i] - x[count]),2);
            count++;
        }

        int CorrectCount = 0;
        int intBox = 0;
        for(int i = 0;i < n;i += 2){
            resultBox[i] = Math.sqrt(powerBox[i] + powerBox[i + 1]);
            intBox = (int)resultBox[i];
            if((resultBox[i] - intBox) == 0.0){
                CorrectCount++;
            }
        }
        System.out.println(CorrectCount);
    }else{
        System.out.println(0);
    }
  }
}