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 MemProb {

	static double E = 0.0000000001;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		double mid = 0.0;
		double d2;
		double low;
		double height;
		for (int k = 0; k < t; k++) {
			int d = sc.nextInt();
			low = 0.0;
			height = d;
			mid = 0;
			while (height - low >= E * E) {
				mid = (height + low) / 2.0;
				d2 = (d - mid) * mid - d;
				if (Math.abs(d2) <= E) {
					break;
				} else if (d2 < 0) {
					height = mid;
				} else {
					low = mid;
				}
			}
			if (Math.abs((d - mid) * mid - d) <= E) {
				System.out.printf("Y %.9f %.9f%n", mid, d - mid);
			} else {
				System.out.println("N");
			}
		}
	}
}