Problem: Try guessing the statement from this picture: 

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You are given a non-negative integer d. You have to find two non-negative real numbers a and b such that a + b = d and a ⋅ b = d.

Input

The first line contains t (1 ≤ t ≤ 10^3) — the number of test cases.

Each test case contains one integer d (0 ≤ d ≤ 10^3).

Output

For each test print one line.

If there is an answer for the i-th test, print "Y", and then the numbers a and b.

If there is no answer for the i-th test, print "N".

Your answer will be considered correct if |(a + b) - a ⋅ b| ≤ 10^{-6} and |(a + b) - d| ≤ 10^{-6}.

Example

Input


7
69
0
1
4
5
999
1000


Output


Y 67.985071301 1.014928699
Y 0.000000000 0.000000000
N
Y 2.000000000 2.000000000
Y 3.618033989 1.381966011
Y 997.998996990 1.001003010
Y 998.998997995 1.001002005

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
public class test {
   public static double[] quadratic(int d) {
      
      if (d * (d-4) < 0) return null;
      //x^2-dx+d
      //a = d + sqrt(d^2-4d), b = d - sqrt(d^2-4d)
      
      
      double a = d + Math.sqrt(d * (d-4)), b = d - Math.sqrt(d * (d-4));
      a /= 2;
      b /= 2;
      double[] results = {a, b};
      return results;
   }
   public static void main(String[] args) {
      Scanner sc = new Scanner(System.in);
      int n = sc.nextInt();
      for (int i = 0; i < n; i++) {
         sc.nextLine();
         int k = sc.nextInt();
         double[] results = quadratic(k);
         if (results == null) System.out.println("N");
         else {
            System.out.println("Y " + results[0] + " " + results[1]);
         }
      }
   }
}