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.*;
public class Main
{
	public static void main(String[] args)
	{
		Scanner sc = new Scanner(System.in);
		int q=sc.nextInt();
		while(q-->0)
		{
    		int n=sc.nextInt();
    		double a=1,b=-n,c=n;
    		double d=(b*b)-4*a*c;
    		if(d<0)
    		System.out.println("N");
    		else
    		{
    		    double a1=(-b+(double)Math.sqrt(d))/(2*a);
    		    double a2=(-b-(double)Math.sqrt(d))/(2*a);
    		    if(a1>0)
    		    {
    		        double b1=(double)n/(double)a1;
    		        System.out.println("Y"+" "+String.format("%.9f",a1)+" "+String.format("%.9f",b1));
    		    }
    		    else if(a2>0)
    		    {
    		        double b2=(double)n/(double)a2;
    		        System.out.println("Y"+" "+String.format("%.9f",a2)+" "+String.format("%.9f",b2));
    		    }
    		    else
    		    System.out.println("Y 0.000000000 0.000000000");
    		}
		}
	}
}