Problem: Try guessing the statement from this picture: 

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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 Main {
    public void run() {
        Scanner scanner = new Scanner(System.in);
        int t = scanner.nextInt();
        for (int i = 0; i < t; i++) {
            double d = scanner.nextDouble();
            double a;
            double b;
            double l = 0;
            double r = d;
            double diff = 10e-20;
            String result = "N";
            while (true) {
                a = l + (r - l) / 2;
                b = d - a;
                if (a + b == d && Math.abs(a * b - a - b) <= 10e-9 && Math.abs(a + b - d) <= 10e-9) {
                    result = "Y";
                    break;
                }
                if (Math.abs(diff - Math.abs(a * b - a - b)) < 10e-20) {
                    break;
                }
                diff = Math.abs(a * b - a - b);
                if (a * b > a + b) {
                    r = l + (r - l) / 2;
                } else {
                    l = l + (r - l) / 2;
                }
            }
            if (result.equals("Y")) {
                result += " " + a + " " + b;
            }
            System.out.println(result);
        }


    }
    public static void main(String[] args) {
        new Main().run();
    }
}