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:
/* package codechef; // don't place package name! */

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

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{


         
	public static void main (String[] args) throws java.lang.Exception
	{
            Scanner in=new Scanner(System.in);
            int t=in.nextInt();
            while(t-->0)
            {
            double d=in.nextDouble();

            double a1=(d+Math.sqrt((d*d)-(4*d)))/2;
            double a2=(d-Math.sqrt((d*d)-(4*d)))/2;

            double b1=d-a1;
            double b2=d-a2;

            if(Math.abs((a1+b1)-(a1*b1))<=0.000001)
            {
                if(Math.abs((a1+b1)-d)<=0.000001)
                {
                    System.out.printf("Y %.9f %.9f \n",a1,b1);
                }
            }
            else if(Math.abs((a2+b2)-(a2*b2))<=0.000001)
            {
                if(Math.abs((a2+b2)-d)<=0.000001)
                {
                    System.out.printf("Y %.9f %.9f \n",a2,b2);
                }
            }
            else 
            {
                System.out.println("N");
            }
        }
    }

}