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 sixtynine
{
	public static void main(String ag[])
	{
		Scanner sc=new Scanner(System.in);
		double d,x1,x2,y1,y2;
		int t;
		boolean flag,go;
		t=sc.nextInt();
		while((t--)>0)
		{
			d=sc.nextDouble();
			flag=false;
			go=true;
			
				x1=(d+Math.sqrt(Math.pow(d,2)-(4*d)))/2;
				x2=(d-Math.sqrt(Math.pow(d,2)-(4*d)))/2;
				y1=d-x1;
				y2=d-x2;
				if((Math.abs((x1+y1)-(x1*y1))<=.000001))
				{
					flag=true;
					go=false;

					System.out.println("Y "+x1+" "+y1);
					
				}
				if((Math.abs((x2+y2)-(x1*y1))<=.000001)&&go==true)
				{
					flag=true;
					System.out.println("Y "+x2+" "+y2);
					
				}
			if(flag==false)
			System.out.println("N");
		}
	}
}