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.io.*;

public class CF1076C {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(System.out);
		int t = Integer.parseInt(br.readLine());
		while (t-- > 0) {
			int d = Integer.parseInt(br.readLine());
			// x * x - d * x + d = 0
			// d * d - 4 * d = (d - 4) * d >= 0
			// d == 0 || d >= 4
			// (d \pm sqrt((d - 4) * d)) / 2
			if (d > 0 && d < 4)
				pw.println("N");
			else {
				double r = Math.sqrt((d - 4) * d);
				pw.println("Y " + (d + r) / 2.0 + " " + (d - r) / 2.0);
			}
		}
		pw.close();
	}
}