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.io.*;
import java.util.*;
public class code 
{
	public static void main(String []args) throws IOException
    {
    	BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    	PrintWriter pw=new PrintWriter(System.out);
    	int t=Integer.parseInt(br.readLine());
    	while(t--!=0)
    	{
    		double d=Double.parseDouble(br.readLine());
    		double delta=d*d-(4*d);
    		if(delta<0)
    		{
    			pw.println("N");
    			continue;
    		}
    		delta=Math.sqrt(delta);
    		double valOne=(d-delta)/2,valTwo=(d+delta)/2,A,B;
    		if(valOne<0)
    		{
    			A=valTwo;
    			B=d-A;
    		}
    		else
    		{
    			A=Math.min(valOne,valTwo);
    			B=d-A;
    		}
    		pw.printf("Y %.10f %.10f\n",A,B);
    	}
    	pw.flush();
    }
}