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.io.FileNotFoundException;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) throws FileNotFoundException {

		//    	File file = new File("src/in.txt");
		//    	Scanner sc = new Scanner(file);

		Scanner sc = new Scanner(System.in);

		int N = sc.nextInt();
		int D = sc.nextInt();

		int[][] X = new int[N][D];

		for(int i=0;i<N;i++) {
			for(int j=0;j<D;j++) {
				X[i][j]= sc.nextInt();
			}
		}
		int ans = 0;
		for(int i=0;i<N-1;i++) {
			for(int j=i+1;j<N;j++) {
				int[] a = X[i];
				int[] b = X[j];
				int d2  = d2(a,b,D);
				if(isSquareNumber(d2)) {
					ans ++;
				}
			}
		}
		System.out.println(ans);
	}
	public static int d2(int[] y, int[] z,int D) {
		int d2 = 0;

		int sum = 0;
		for(int i=0;i<D;i++) {
			sum += (y[i]-z[i])*(y[i]-z[i]);
		}
		d2 = sum;

		return d2;
	}
    // 平方数かどうかを調べる。
    public static boolean isSquareNumber (int number) {
        if (number < 0) {
            throw new IllegalArgumentException("Argument must be 0 and over.");
        }
        double sqrtOfNumber = Math.sqrt(number);
        return (isInteger(sqrtOfNumber));
    }

    // 整数かどうかを調べる。
    public static boolean isInteger (double number) {
        return (number == Math.floor(number));
    }
}