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 debug(String str) {
        boolean debug = false;
        if (debug = false) {
            return;
        }
        System.out.println(str);
    }

    //木構造
    public static void main(String[] args) {

        int N;
        int D;
        int[][] xList;
        try (Scanner sc = new Scanner(System.in)) {
            N = sc.nextInt();
            D = sc.nextInt();
            xList = new int[N][D];
            for(int i = 0;i < N; i++){
                for(int j = 0;j < D; j++){
                    xList[i][j] = sc.nextInt();
                }
            }
        }
        int result = 0;
        for(int i = 0;i < N; i++){
            for(int j = i;j < N; j++){
                if(i == j){
                    continue;
                }
                if(check(xList[i] , xList[j]))
                    result++;
            }
        }

        System.out.println(result);
    }

    private static  boolean check(int i[] , int j[]){
        int length = i.length;
        int dis = 0;
        for(int d = 0; d < length;d++){
            int temp = j[d]- i[d];
            dis += temp * temp;
        }
        double t = Math.sqrt(dis);
        int ii = (int) (t / 1);
        return (double)ii == t;
    }

}