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.Scanner;

public class C_Meme_Problem_1076 {

	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);
		int n = input.nextInt();
		for (int i = 0; i < n; i++) {
			int d= input.nextInt();
			if(d!=0 && d<4) {
				System.out.println("N");
				continue;
			}
			System.out.print("Y ");
			double a,b;
			double temp=(d*d)-(4*d);
			temp=Math.sqrt(temp);
			a=(temp+d)/2;
			b=(d-temp)/2;
			
			
			
			
			System.out.println(a+" "+b);
		}
		
		
	}
}