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.*;

public class Main {


    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int t = scanner.nextInt();
        for (int i = 0; i < t; i++) {
            double d = scanner.nextInt();
            if (d < 4 && d > 0) {
                System.out.println("N");
                continue;
            }
            double D = Math.sqrt(d * d - 4 * d);
            double a = (d + D) / 2, b = (d - D) / 2;
//            double roundedOneDigitA = Math.round(a * 1000000000) / 1000000000.0;
//            double roundedOneDigitB = Math.round(b * 1000000000) / 1000000000.0;
//            System.out.println("Y " + roundedOneDigitA + " " + roundedOneDigitB);
            System.out.printf("Y %.9f %.9f\n", a, b);
        }
    }
}