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.lang.*;

/**
 *
 * @author Sameep
 */
public class Day29a {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        // TODO code application logic here
        Scanner sc = new Scanner(System.in);
        double t = sc.nextDouble();
        while(t-->0)
        {
            double d = sc.nextDouble();
            double temp = Math.pow(d, 2);
            double temp2 = temp - (4*d);
            double temp3 = Math.sqrt(temp2);
            if(temp >= (4*d))
            {
                double a = (d + temp3)/2;
                double b = (d - temp3)/2;
                if(b<0)
                {
                    System.out.println("N");
                }
                else
                {
                    System.out.print("Y ");
                    System.out.printf("%.9f %.9f",a,b);
                    System.out.println();
                }
            }
            else
            {
                System.out.println("N");
            }
        }
    }
    
}