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 Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub

		Scanner s=new Scanner(System.in) ;
		int test=s.nextInt() ;
		for(int tc=0;tc<test;tc++)
		{
		    
		    int t=s.nextInt() ;
		    int n=t*t-4*t ;
		    if(n<0)
		    {
		        System.out.println("N") ;
		    }
		    else
		    {
		       double d=Math.pow(n,0.5) ;
		       double d1=(t+d)/2 ;
		       double d2=(t-d)/2 ;
		        System.out.print("Y ") ;
		        System.out.format("%.9f",d1);
		        System.out.print(" ");
		        System.out.format("%.9f",d2);
		        System.out.println();
		    }
		}
}
}