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 ProblemC {
    public static double D = 10e-8d;
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int tc = scan.nextInt();

        while (tc-- > 0) {
            double n = scan.nextDouble();
            System.out.println(solve(n));
        }
    }

    public static String solve(double n) {
        double lo = 0;
        double hi = n / 2d;
        int iterations = 0;
        if (valid(n, lo)) {
            return String.format("Y %.10f %.10f", n, lo);
        }
        if (valid(n, hi)) {
            return String.format("Y %.10f %.10f", hi, hi);
        }
        while (lo <= hi) {
            double m = (lo + hi) / 2d;
            if (valid(n, m)) {
                return String.format("Y %.10f %.10f", Math.max(m, n - m), Math.min(m, n - m));
            } else {
                if ((m * (n - m)) > n) {
                    hi = m + D;
                } else {
                    lo = m - D;
                }
            }

            if (iterations++ > 2000) return "N";
        }

        return "N";
    }

    public static boolean valid(double n, double m) {
        double mul = (m * (n - m));

        if (Math.abs(n - mul) <= D) {
            return true;
        } else {
            return false;
        }
    }
}