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 Bhaskara{
	public static void main(String[] args){
		Scanner scan = new Scanner(System.in);
		int t = scan.nextInt();
		int d;
		double b1, b2;
		double a;
		double delta;
		boolean solution;
		while(t > 0){
			solution = false;
			d = scan.nextInt();
			delta =  Math.sqrt(d*d-4*d);
			b1 = (-d + delta)/-2;
			b2 = (-d - delta)/-2;
			//System.out.println(b1);
			//System.out.println(b2);
			if(b1 >= 0){
				a = d - b1;
				if(a >= 0){
					System.out.println("Y "+a+" "+b1);
					solution = true;
				}
			}		
			if(!solution && b2 >= 0){
				a = d - b2;
				if(a >= 0){
					System.out.println("Y "+a+" "+b2);
					solution = true;
				}
			}
			else if(!solution) System.out.println("N");
			t--;
		}
		scan.close();
	}
}