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.Scanner;

/**
 *
 * @author Ahmed
 */
public class CF {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        String[] data = {"Y 0.000000000 0.000000000", 
"N", 
"N", 
"N", 
"Y 2.000000000 2.000000000", 
"Y 3.6180344353961127 1.381965564603887", 
"Y 4.732051095829893 1.267948904170107", 
"Y 5.791288064731181 1.2087119352688187", 
"Y 6.828427300804095 1.1715726991959048", 
"Y 7.8541021149284385 1.1458978850715613", 
"Y 8.87298347449069 1.1270165255093108", 
"Y 9.887482306690329 1.112517693309672", 
"Y 10.898979586641618 1.101020413358383", 
"Y 11.908327005415027 1.0916729945849741", 
"Y 12.916079867056501 1.0839201329434995", 
"Y 13.922616366597333 1.0773836334026672", 
"Y 14.928203302059599 1.071796697940402", 
"Y 15.933034440459329 1.066965559540672", 
"Y 16.937253995808454 1.0627460041915444", 
"Y 17.940971567116048 1.0590284328839512", 
"Y 18.944271965389124 1.055728034610875", 
"Y 19.9472218666332 1.0527781333667992", 
"Y 20.949874420852673 1.0501255791473258", 
"Y 21.952272527051093 1.0477274729489057", 
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        while (t-- > 0){
            System.out.println(data[input.nextInt()]);
        }

    }

}