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.*;
public class meme{
public static void main(String args[]){
                  Scanner sc=new Scanner(System.in);
                  int t=sc.nextInt();
            while(t>0)
            {
                              int n=sc.nextInt();
                              double d=n*n-4*n;
                              if(d<0)
                              {
                                                System.out.println("N");
                              }
                              else
                              {
                                               System.out.print("Y ");
                                               System.out.print((n+Math.sqrt(d))/2+" ");
                                               System.out.print((n-Math.sqrt(d))/2+"\n");
                              }
                              t--;
            }
}
}