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

    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    int D = sc.nextInt();
    int[][] m = new int[N][D];
    for (int i = 0; i < N; i++) {
      for (int j = 0; j < D; j++) {
        m[i][j] = sc.nextInt();
      }
    }
    
    // create square map
    Set<Integer> squares = new HashSet<>();
    for (int i = 0; i*i <= 16000; i++) {
      squares.add(i*i);
    }
    
    // combination(10,2)
    int ans = 0;
    for (int i = 0; i < N-1; i++) {
      for (int j = i+1; j < N; j++) {
        int dist = calc(m, i, j);
        if (squares.contains(dist)) {
          ans++;
        }
      }
    }

    System.out.println(ans);
  }
  
  private static int calc(int[][] m, int a, int b) {

    int ret = 0;
    for (int i = 0; i < m[0].length; i++) {
      int t = Math.abs(m[a][i] - m[b][i]);
      ret += t*t;
    }
    
    return ret;
  }
}