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.Locale;
import java.util.Scanner;

/**
 *
 * @author Jakub
 */
public class Main {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in).useLocale(Locale.US);
        StringBuilder sb = new StringBuilder(1000);
        int cases = sc.nextInt();
        for (int i = 0; i < cases; i++) {
            int numero = sc.nextInt();
            int deter = (numero*numero)-4*numero;
            if (deter < 0){
                sb.append('N').append('\n');
            } else{
                double sqrt = Math.sqrt(deter);
                double n1 = (numero + sqrt)/2;
                double n2 = (numero - sqrt)/2;
                sb.append('Y');
                sb.append(' ');
                sb.append(String.format("%.9f", n1));
                sb.append(' ');
                sb.append(String.format("%.9f", n2));
                sb.append('\n');
            }
        }
        System.out.print(sb.toString().replace(',','.'));
    }
    
}