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.*;
import java.io.*;
public class MemeProblem
{
	public static void main(String[] f)
	{
		int t,i;
		double D,b,d;
		double root1,root2;
		Scanner sc=new Scanner(System.in);
		t=sc.nextInt();
		for(i=0;i<t;i++)
		{
			d=sc.nextDouble();
			D=((d*d)-(4*d));
			if(D<0)
			{
				System.out.println("N");
			}
			else
			{
				root1=((d+Math.sqrt(D))/2);
				root2=((d-Math.sqrt(D))/2);
				System.out.println("Y"+" "+root1+" "+root2);
			}
		}		
	}
}