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: Runtime Error)

object Main extends App {

  // 入力値から座標の配列を生成
  def generateCoordinates: Array[Array[Int]] = {
    var coordinates = scala.collection.mutable.ListBuffer.empty[Array[Int]]
    io.Source.stdin.getLines().zipWithIndex.foreach {
      case (line, index) if index != 0  =>
        val coordinate = line.split(" ").map(_.toInt)
        coordinates += coordinate
    }
    coordinates.toArray
  }

  def isIntegerDistance(a1: Array[Int], a2: Array[Int]): Boolean = {
    val squareSum = a1.zip(a2).map {
      case (p1, p2) =>
        val diff = math.abs(p1 - p2)
        diff * diff
    }.sum
    val d = math.sqrt(squareSum)
    d == d.toInt
  }

  val coordinates = generateCoordinates
  val lastCoordinateIndex = coordinates.size - 1
  var result: Int = 0

  coordinates.zipWithIndex.foreach {
    case (c, selfIndex) =>
      var targetIndex = selfIndex + 1
      while (targetIndex <= lastCoordinateIndex) {
        val t = coordinates(targetIndex)
        if (isIntegerDistance(c, t)) result += 1
        targetIndex += 1
      }
  }

  println(result)

}