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 {
    private static void testCase(int d) {
        if (d == 0) {
            System.out.println("Y 0 0");
            return;
        } else if (d < 4) {
            System.out.println("N");
            return;
        }

        double left = 0, right = Math.max(Math.sqrt(d), 1);
        for (int i = 0; i < 100; i++) {
            double a = (left + right) / 2;
            double b = d - a;
            if (a * b > d) {
                right = a;
            } else {
                left = a;
            }
        }

        double a = left, b = d - left;
        if (Math.abs(a * b - d) < 0.000001 && Math.abs(a + b - d) < 0.000001) {
            System.out.println("Y " + left + " " + (d - left));
        } else {
            System.out.println("N");
        }
    }

    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        int t = s.nextInt();
        for (int i = 0; i < t; i++) {
            testCase(s.nextInt());
        }
    }
}