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;

public class C {

    /*

7
69
0
1
4
5
999
1000
     */
    public static void main(String args[]) {
        Scanner in = new Scanner(System.in);

        int tests = in.nextInt();

        for (int t = 0; t < tests; t++) {
            int d = in.nextInt();

            double b = (d - Math.sqrt(d * d - 4 * d)) / 2.0;
            double a = d / b;

            if (Double.isNaN(a) && Double.isNaN(b)) {
                System.out.println("N");
            } else if (Double.isNaN(a)) {
                if (Double.compare(b, 0.0) == 0) {
                    System.out.printf("Y %.9f %.9f\n", 0.0, 0.0);
                }
            } else {
                System.out.printf("Y %.9f %.9f\n", a, b);
            }
        }

    }
}