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 C {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        for (int i = 0; i < n; i++) {
            int k = sc.nextInt();
            if (k == 0) System.out.println("Y 0 0");
            else if (k < 4) System.out.println("N");
            else if (k == 4) System.out.println("Y 2 2");
            else {
                double step = (double)k / 4;
                double a = step;
                double b = k - a;
                double mult = a * b;
                while (Math.abs(mult - k) > 0.000001) {
                    step /= 2;
                    a += mult > k ? -step : step;
                    b = k - a;
                    mult = a * b;
                }
                System.out.println("Y " + a + " " + b);
            }
        }
    }
}