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


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

	Scanner std = new Scanner(System.in);

	int N = std.nextInt();
	//List<Integer> list = new ArrayList<>();
	List<List<Integer>> list = new ArrayList<>();
	int D = std.nextInt();
	//int B = std.nextInt();
	//int C = std.nextInt();
	//int temp = 0;
	//int[][] X = new int[D][];

	for(int i = 0; i < N; i++) {
		List<Integer> list2 = new ArrayList<>();
		for(int j = 0; j < D; j++) {
		int a = std.nextInt();
		list2.add(a);
		}
		list.add(list2);
	}

	System.out.println(nCombination2(list));

	//for(int i = 0; i < N; i++) {
	//	for(int j = 0; j < D; j++) {
	//	int b = list.get(i).get(j) - list.get(i).get(j+1)  ;
	//	}
	//}


	}


	public static int nCombination2(List<List<Integer>> list) {
        int count = list.size();
        int num = 0;
        double a = 0;
        for (int i = 0; i < count - 1; i++) {
            for (int j = i + 1; j < count; j++) {
            	for(int k = 0; k < list.get(0).size(); k++) {
              a = a + Math.pow(list.get(i).get(k) - list.get(j).get(k),2); //num++;
            	}
            double b = Math.pow(a, 2);
              if(b == (int)b) {
            	  num++;
              }

              }
               // System.out.print(num + " {" + list[i] + ", " + list[j] + "}\t");
            }
            //System.out.println();
        return num;}
        //System.out.println("[answer] " + count + "C2 : " + num);
    }