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) {
    int N, D;
    int[][] X;
    try(Scanner sc = new Scanner(System.in)) {
      N = sc.nextInt();
      D = sc.nextInt();
      X = new int[N][D];
      for(int i = 0; i < N; i++) {
        X[i] = new int[D];
        for(int d = 0; d < D; d++) {
          X[i][d] = sc.nextInt();
        }
      }
    }
    int count = 0;
    for(int i = 0; i < N; i++) {
      for(int j = i+1; j < N; j++) {
        int rSquared = 0;
        for(int d = 0; d < D; d++) {
          int diff = X[i][d] - X[j][d];
          rSquared += diff * diff;
        }
        double r = Math.sqrt(rSquared);
        if ( isOk(r) ) {
          count++;
        }
      }
    }
    System.out.println(count);
  }
  
  private static boolean isOk(double value) {
    int intValue = (int)Math.floor(value);
    return value == (double)intValue;
  }
}