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.*;
import java.math.*;	
	public class Main {
		static boolean prime[];
		static ArrayList<Integer>pi;
		static void siv(int n)
		{
		    prime=new boolean [n+1];
		    for(int i=0;i<n;i++) {
		    	prime[i]=true;
		    }
		    pi=new ArrayList<Integer>();
		    for (int p=2; p*p<=n; p++)
		    {
		        if (prime[p] == true)
		        {
		            for (int i = p*2; i<=n; i += p)
		            prime[i] = false;
		        }
		    }
		    int x = 1;
		    for(int k = 2; k <= n; k++)
		    {
		        if(prime[k] == true)
		        {
		            pi.add(k);
		            x++;
		        }
		    }
		}

		static final int MAX=1000000007 ;
	    public static void main(String[] args) {
			Scanner s=new Scanner(System.in);
			int t=s.nextInt();
			for(int i=0;i<t;i++) {
				int d=s.nextInt();
				double b=(d*d)-(4*d);
				
				
				if(b<0) {
					System.out.println("N");
					
				}
				else {
					b=Math.sqrt(b);
				System.out.print("Y ");
				b=(d-b)/2;
				System.out.println((d-b)+" "+b);
				}
				
			}
			
			
			
			
	    }
	}