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.io.PrintWriter;
import java.util.Scanner;

//import ShushiForTwo.Scanner;

public class MemeProblem {

	public static void main(String[] args) {
		// TODO Auto-generated method stub

		Scanner input = new Scanner(System.in);
		int t = input.nextInt();
		PrintWriter out = new PrintWriter(System.out);
		while(t-->0) {
			int d = input.nextInt();
			if(d==0) {
				System.out.println("Y 0 0");
				continue;
			}
			if(d<4) {
				System.out.println("N");
			}
			else {
				double  D = (Math.sqrt(d*d-4*d));
			    double a = (d+D)/2;
			    double b = (d-D)/2;
			    System.out.println("Y "+a+" "+b);
			}
			
			
		}
		out.flush();
		out.close();
	}

}