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 q3
{
	public static void main(String ar[])
	{
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		for(int T =0 ;T<t;T++)
		{
			int d = sc.nextInt();
			double d1 = 1.000000000001 * d;
			if(d>0 && d<4)
			{
				System.out.println("N");
			}
			else
			{
				double dis = Math.sqrt(Math.pow(d1, 2) - 4.000000000001*d1);
				double a = (d + dis)/2.000000000001;
				double b = (d - dis)/2.000000000001;
				if(Math.abs((a+b)-a*b) <= 0.000001 && Math.abs((a+b)-d1) <=0.000001)
				{
					System.out.printf("Y %.9f %.9f\n",a,b);
				}
				else
				{
					System.out.println("N");
				}
			}
		}
	}
}