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.util.*;

 // Compiler version JDK 11.0.2

 public class a
 {
   public static void main(String args[])
   { 
    //System.out.println("Hello, Dcoder!");
    Scanner sc=new Scanner(System.in);
    int t=sc.nextInt();
    outer:while(t-->0){
      int n=sc.nextInt();
      double D=n*n-4*n;
      if(D<0){
        System.out.println("N");
        continue outer;
      }
      else{
        D=Math.sqrt(D);
        double  a=(n+D)/2;
        double  b=n-a;
        System.out.println("Y "+a+" "+b);
      }
    }
    
    }
 }