Problem:
Problem Statement

You are given two integers a and b (a≤b). Determine if the product of the integers a, a+1, …, b is positive, negative or zero.

Constraints

a and b are integers.

-10^9≤a≤b≤10^9

Partial Score

In test cases worth 100 points, -10≤a≤b≤10.

Input

The input is given from Standard Input in the following format:

a b

Output

If the product is positive, print Positive. If it is negative, print Negative. If it is zero, print Zero.

Sample Input 1

1 3

Sample Output 1

Positive

1×2×3=6 is positive.

Sample Input 2

-3 -1

Sample Output 2

Negative

(-3)×(-2)×(-1)=-6 is negative.

Sample Input 3

-1 1

Sample Output 3

Zero

(-1)×0×1=0.

Solution in Scala (2.13.1) (judge verdict: Accepted)

object Main extends App {
  val Array(a, b) = io.StdIn.readLine.split(" ").map(_.toInt)

  def nega_zero_posi(n: Long): String = n match {
    case v if v < 0  => "Negative"
    case v if v == 0 => "Zero"
    case v if 0 < v  => "Positive"
  }

  // a, a+1, ..., b の数列が
  val result = (nega_zero_posi(a),nega_zero_posi(b)) match {
    case ("Positive", "Positive")  => "Positive" // 正の整数のみ含むとき
    case ("Zero", _) | (_, "Zero") => "Zero"     // 0を含むとき
    case ("Negative", "Positive")  => "Zero"     // 0を含むとき
    case ("Negative", "Negative")  => { // 負の整数のみ含み、かつ
      if ((b-a+1)%2 == 0) "Positive"      // - 負の整数が偶数個あるとき
      else "Negative"                   // - 負の整数が奇数個あるとき
    }
  }

  println(result)
}