Problem: Try guessing the statement from this picture: 

<image>

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.Scanner;
import java.util.HashMap;
import java.util.Arrays;
public class Codechef{
 

  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
      int t=sc.nextInt();
      for(int i=0;i<t;i++){
          int d=sc.nextInt();
          if((d*d-4*d)>=0){
                      double a=((double)d+Math.sqrt(d*d-4*d))/2;
                    double b=((double)d-Math.sqrt(d*d-4*d))/2;
                    String s1=String.valueOf(a);
                    String s2=String.valueOf(b);

                    if(s1.charAt(s1.length()-1)=='0'){
                      s1=s1+"0000";
                    }
                    if(s2.charAt(s2.length()-1)=='0'){
                      s2=s2+"0000";
                    }
                System.out.print("Y "+s1+" "+s2+" \n");

          }else{
            System.out.println("N");
          }

      }
   
        
     
  }
}