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.*;


public class C
{
	static final double EPS = 1e-9;
	
	static boolean equals(double x , double y)
	{
		
		return Math.abs(x - y) <= EPS ; 
	}

	static double getB(double d)
	{
		
		double a = 1 , b = -d , c = d ;
		
		double root = b*b - 4 * a * c ; 
		
		if( Math.abs(root) < 0 )
			return Double.MAX_VALUE;
		
		return Math.max((- b + Math.sqrt(root)) / (2 * a), (- b - Math.sqrt(root)) / (2 * a)) ;
		
	}
	
	public static void main(String[] args) throws Exception
	{
		Scanner sc = new Scanner(System.in);
		PrintWriter out  = new PrintWriter(System.out);
		
		int TC = sc.nextInt(); 
		
		
		while(TC -->0)
		{
			
			double d = sc.nextInt();
			
			double b = getB(d);
			
			if(equals(b, Double.MAX_VALUE) || (new Double(b)).isNaN())
			{
				out.println("N");
			}
			else 
				out.println("Y "+(b == 0 ? 0 : d/b )+" "+b);
			
		}
		
		
		
		
		out.flush();
		out.close();
		
		

	}
	static class Scanner 
	{
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}
		
		public Scanner(String path) throws Exception{	br = new BufferedReader(new FileReader(path));}

		public String next() throws IOException 
		{
			while (st == null || !st.hasMoreTokens()) 
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {return Integer.parseInt(next());}
		
		public long nextLong() throws IOException {return Long.parseLong(next());}


		public double nextDouble() throws IOException {return Double.parseDouble(next());}

	}

	static void shuffle(int[] a)
	{
		int n = a.length;
		for(int i = 0; i < n; i++)
		{
			int r = i + (int)(Math.random() * (n - i));
			int tmp = a[i];
			a[i] = a[r];
			a[r] = tmp;
		}
	}



}