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 Scala (2.11.7) (judge verdict: Accepted)

import java.util.Scanner


object Main {


  def read() = {
    val sc = new Scanner(System.in)
    val n, d = sc.nextInt()
    val x = IndexedSeq.fill(n, d)(sc.nextInt())
    (n, d, x)
  }

  def solve(n: Int, d: Int, x: IndexedSeq[IndexedSeq[Int]]): Long = {
    def dist(y:IndexedSeq[Int], z:IndexedSeq[Int]):Double ={
      math.sqrt((y,z).zipped.map((yi,zi)=> (yi-zi)*(yi-zi)).sum)
    }
    val eps = 1e-6
    (for (i1 <- 0 until n; i2 <- i1 + 1 until n) yield {
      val y = x(i1)
      val z = x(i2)
      val d = dist(y,z)
        d.%(1) <= eps || d.%(1) >= 1 - eps
    }).count(identity)
  }

  def main(args: Array[String]): Unit = {
    val (n, d, x) = read()
    println(solve(n, d, x))
  }
}