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.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;

public class Main {

	public static void main(String[] args) throws Exception {
		// TODO 自動生成されたメソッド・スタブ
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		String W = in.readLine();
		String[] D = W.split(" ");

		int n = Integer.parseInt(D[0]);
		int d = Integer.parseInt(D[1]);

		ArrayList<ArrayList<Integer>> x = new ArrayList<ArrayList<Integer>>();
		for(int i=0;i<n;i++){
			W = in.readLine();
			ArrayList<Integer> tmp = new ArrayList<Integer>();
			D = W.split(" ");
			for(int k=0;k<D.length;k++){
				tmp.add(Integer.parseInt(D[k]));
			}
			x.add(tmp);
		}

		int ans =0;
		for(int i=0;i<x.size();i++){
			for(int k=i+1;k<x.size();k++){
				if(calc(x.get(i),x.get(k))){
					ans++;
				}

			}
		}

		System.out.println(ans);
	}

	public static boolean calc(ArrayList<Integer> y , ArrayList<Integer> z ){
		long ans = 0;
		for(int i=0;i<y.size();i++){
			ans += Math.pow((y.get(i)-z.get(i)), 2);
		}
		double sqrt = Math.sqrt(ans);
		long c = (long)sqrt;
		return ans == Math.pow(c,2);
	}

}