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.io.InputStream;
import java.io.PrintStream;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.List;
import java.util.Scanner;
import java.util.Set;
import java.util.stream.IntStream;

public class Main {

  static Set<Long> squareNumber = new HashSet<>();

  static {
    int max = 20 * 20 * 10;
    for (int i = 0; i < max; i++) {
      long pow = i * i;
      if (pow > max) {
        break;
      }
      squareNumber.add(pow);
    }
  }

  public static void main(String[] args) {
    resolve(System.in, System.out);
  }


  static void resolve(InputStream is, PrintStream pw) {
    Scanner sc = new Scanner(is);
    int n = Integer.parseInt(sc.next());
    int d = Integer.parseInt(sc.next());
    sc.nextLine();
    List<Point> points = new ArrayList<>();
    int result = 0;
    for (int i = 0; i < n; i++) {
      Point pointN = Point.of(d, sc.nextLine());
      result += points.stream().filter(p -> p.isIntegerDistance(pointN)).count();
      points.add(pointN);
    }
    pw.println(result);
  }

  static class Point {

    int d;
    int x[];

    Point(int d, int[] x) {
      this.d = d;
      this.x = x;
    }

    static Point of(int d, String line) {
      return new Point(d,
        Arrays.stream(line.split(" ", -1)).map(Integer::parseInt).mapToInt(Integer::intValue)
          .toArray());
    }

    boolean isIntegerDistance(Point other) {
      long powDistance = (int) IntStream.range(0, d)
        .mapToLong(i -> (this.x[i] - other.x[i]) * (this.x[i] - other.x[i])).sum();
      return squareNumber.contains(powDistance);
    }
  }
}