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.io.*;
import java.util.*;

public class meme
{
	public static void main(String[] args) throws IOException
	{
		Scanner s = new Scanner(System.in);
		
		int t = Integer.parseInt(s.nextLine());
		int input[] = new int[t];
		
		for (int i = 0; i < t; i++)
		{
			input[i] = Integer.parseInt(s.nextLine());
		}
		
		for (int i = 0; i < t; i++)
		{
			double d = input[i];
			double a = (d + Math.sqrt(d * (d - 4))) / 2;
			double b = d - a;
			
			if (a >= 0 && b >= 0)
			{	
				System.out.println("Y" + " " + a + " " + b);

			}
			else
			{
				System.out.println("N");
			}
		}
		s.close();
	}
}