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

public class a556{
	
	public static void main(String[] args) throws Exception
    {
	   //new FileInputStream("input.txt");
		//new FileOutputStream("output.txt")
		InputReader in = new InputReader(System.in);
		OutputWriter out = new OutputWriter(System.out);		
  		int t=in.ri();
  		double d;
  		for(int it=0;it<t;it++){
			d=in.rd();
			if(d==0.0)out.pl("Y 0.000000000 0.000000000");
			else if(d>0&&d<4)out.pl("N");
			else {
				out.print("Y ");
				double a=(d-Math.sqrt(d*d-4*d))/2;
				out.pf(a);
				out.print(" ");
				double b=(d+Math.sqrt(d*d-4*d))/2;
				out.pf(b);
				out.pl();
			}
		}
		out.close();
	}
private static class InputReader
	{
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;
		 
		public InputReader(InputStream stream)
		{
			this.stream = stream;
		}
 
		public int read()
		{
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars)
			{
				curChar = 0;
				try
				{
					numChars = stream.read(buf);
				} catch (IOException e)
				{
					throw new InputMismatchException();
				}
				if (numChars <= 0)
				return -1;
			}
			return buf[curChar++];
		}
		
		public String rs()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        } 
        
		public int ri()
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-')
			{
				sgn = -1;
				c = read();
			}
			int res = 0;
			do
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
		
		public double rd() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, ri());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, ri());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
		
		public long rl() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
        
		public boolean isSpaceChar(int c)
		{
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
 
		
 
		public interface SpaceCharFilter
		{
			public boolean isSpaceChar(int ch);
		}
	}
 
	private static class OutputWriter
	{
		private final PrintWriter writer;
 
		public OutputWriter(OutputStream outputStream)
		{
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}
 
		public OutputWriter(Writer writer)
		{
			this.writer = new PrintWriter(writer);
		}
 		public void print(Object... objects)
		{
			for (int i = 0; i < objects.length; i++)
			{
				if (i != 0)
				writer.print(' ');
				writer.print(objects[i]);
			}
		}
		
		public void pf(double n)
		{
			writer.printf("%.9f", n);
		}
		public void pl(Object... objects)
		{
			print(objects);
			writer.println();
		}
 
		public void close()
		{
			writer.close();
		}
 
		public void flush()
		{
			writer.flush();
		}
 
	}
}