Problem: Try guessing the statement from this picture: 

<image>

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.*;

public class cf_edu54_div2 {
	public static Scanner scn = new Scanner(System.in);
	public static double checker = Math.pow(10, -6);

	public static void main(String[] args) {
		int t = scn.nextInt();
		for (int i = 0; i < t; i++)
			Q3();

	}

	private static void Q1() {
		int n = scn.nextInt();
		String s = scn.next();
		for (int i = 0; i < s.length() - 1; i++) {
			if (s.charAt(i) > s.charAt(i + 1)) {
				String res = "";
				if (i == 0) {
					res = s.substring(1);
				} else {
					res = s.substring(0, i) + s.substring(i + 1);
				}
				System.out.println(res);
				return;
			}
		}
		System.out.println(s.substring(0, n - 1));
	}

	public static void Q3() {
		double d = scn.nextDouble();
		double x1 = 0;
		double x2 = 0;
		double y1 = 0;
		double y2 = 0;
		y1 = (d + Math.sqrt(d * d - 4 * d)) / 2;
		x1 = d - y1;
		y2 = (d - Math.sqrt(d * d - 4 * d)) / 2;
		x2 = d - y2;
		if (y1 >= 0 && x1 >= 0) {
			if (Math.abs(y1 + x1 - y1 * x1) <= checker && Math.abs(y1 + x1 - d) <= checker) {
				System.out.println("Y " + Math.max(y1, x1) + " " + Math.min(y1, x1));
				return;
			}
		}
		if (y2 >= 0 && x2 >= 0) {
			if (Math.abs(y2 + x2 - y2 * x2) <= checker && Math.abs(y2 + x2 - d) <= checker) {
				System.out.println("Y " + Math.max(y2, x2) + " " + Math.min(y2, x2));
				return;
			}

		}
		System.out.println("N");
	}

}