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:

//Where there is a will, there is a way!

import java.util.*;
import java.io.*;

public class Solution {
	public static void main (String[] args) throws IOException {
		
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw=new PrintWriter(System.out);
		StringTokenizer st;
                /*
                   inputCopy
inputCopy
7
69
0
1
4
5
999
1000
outputCopy
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
                */
                
                int t=Integer.parseInt(br.readLine());
                for(int ti=0;ti<t;++ti)
                {
                    double d=Double.parseDouble(br.readLine());
                    double delta=d*d - 4*d;
                    if(delta<0)
                    {
                        pw.println("N");
                        continue;
                    }
                    double a=( d+Math.sqrt(delta) )/(2e0);
                    double b=d-a;
                    if(a>=0 && b>=0)
                    {
                        pw.println("Y"+" "+a+" "+b);
                        continue;
                    }
                    else
                    {
                        a=( d-Math.sqrt(delta) )/(2e0);
                        b=d-a;
                        if(a>=0 && b>=0)
                        {
                            pw.println("Y"+" "+a+" "+b);
                        }
                        else
                        {
                            pw.println("N");
                        }
                    }
                    
                }
                pw.flush();
                pw.close();
        }
}