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.*;
import java.lang.*;

public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        Locale.setDefault(Locale.US);
        long t = in.nextLong();
        for (int i = 0; i < t; ++i) {
            double d = in.nextDouble();
            if (d * (d - 4) < 0) {
                System.out.print("N\n");
                continue;
            }
            double a = (d + Math.sqrt(d * (d - 4))) / 2;
            double b = d - a;
            System.out.format("Y %.20f %.20f\n", a, b);
        }
    }
}