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;

public class Main {

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);
        int N = Integer.parseInt(sc.next());
        int D = Integer.parseInt(sc.next());
        double[][] Xnd = new double[N][D];
        for (int i = 0; i < N; i++) {

            for (int j=0; j < D;j++) {

                Xnd[i][j] = Integer.parseInt(sc.next());
            }
        }

        sc.close();

        int ansCount = 0;

        //必要な計算量はNC2回,N個の座標のうちのi番目(1,2・・・N-1)
        for (int i = 0; i < N-1; i++) {

            //i番目に対してのj番目(i+1,2・・・N)の座標
            for (int j = i+1; j < N; j++) {

                double sum = 0;
                double distance = 0;

                //(Xnd[i][~]-Xnd[j][~])^2
                for (int Dindex = 0; Dindex < D; Dindex++) {

                    sum += Math.pow((Xnd[i][Dindex] - Xnd[j][Dindex]),2);
                }

                distance = Math.sqrt(sum);
                //i,j番目の座標の距離が整数ならカウント
                if (isNumber(distance)) {

                    ansCount++;
                }
            }
        }

        System.out.println(ansCount);
    }

    public static boolean isNumber(double val) {

        boolean retval = val == Math.floor(val) ? true : false;

        return retval;
    }
}