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 Main {

	public static void main(String[] args) throws Exception{
		MemeProblem res = new MemeProblem();
		res.resolve();
	}
	
	static class MemeProblem {
		
		public void resolve () {
			Scanner scan = new Scanner(System.in);
			int t = scan.nextInt();
			while(t!=0){
				t = t - 1;
				int d = scan.nextInt();
				int res = (d * d) - (4 * d);
				if(res < 0){
					System.out.println("N");
				}else{
					double a = (d + Math.sqrt(res))/2.0;
					double b = d - a;
					System.out.println("Y " + a + " " + b);
				}
			}
			scan.close();
		}
	}

}