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: Runtime Error)

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

    public class Main {

    	public static void main(String[] args) throws IOException {
    		Scanner sc = new Scanner(System.in);
    		//int n = sc.nextInt();
    		//String[] array = new String[h+1];
    		//List<String> list= new ArrayList<String>(Arrays.asList(s.split("")));
    		List<Integer> list=new ArrayList<Integer>();
    		int n = sc.nextInt();
    		int d = sc.nextInt();

    		for(int i=0;n>i;i++) {
    			for(int j=0;d>j;j++) {
    				int x = sc.nextInt();
    				list.add(x);
    			}
    		}
    		int count=0;
    		//System.out.println(list);

    		for(int i=0;n*d>i;i=i+d) {
    			//System.out.println(i);
    			for(int j=i;n*d-d>j;j=j+d) {
    				//System.out.println(j);
    				int dis =0;
    				for(int ii=0;d>ii;ii++) {
    					//System.out.println(ii);
    					dis = (int) (dis+Math.pow((list.get(i+ii)
    							-list.get(j+i+ii)),2));
    				}
    				//System.out.println(dis);
    				if(Math.sqrt(dis)==(int)Math.sqrt(dis)) {
    					count++;
    				}

    			}
    		}
    		System.out.println(count);
    	}
    }