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) {		
	
		Scanner scan = new Scanner(System.in);	
	
		int i , j , t = scan.nextInt();
		while (t > 0) {
			int d = scan.nextInt();
			if (d * d >= 4 * d) {
				double value = d;
				double a = (value + Math.sqrt(value * value - 4 * value)) / 2;
				double b = value - a;
				if (a >= 0 && b >= 0) {
					System.out.println(String.format("Y %.10f %.10f" , a , b));
				} else {					
					a = (value - Math.sqrt(value * value - 4 * value)) / 2;
					b = value - a;
					if (a >= 0 && b >= 0) {
						System.out.println(String.format("Y %.10f %.10f" , a , b));
					} else {
						System.out.println("N");
					}
				}				
			} else {
				System.out.println("N");
			}
			t --;
		}		
		
	}
	
	
	
}