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.io.*;

public class Main{



   public static long primeFactors(long n) 
{ 
    
    // Print the number of 2s that divide n 
  
    while (n%2 == 0) 
    { 
        return 2;
      
    } 
  
    // n must be odd at this point.  So we can skip  
    // one element (Note i = i +2) 
    for (long i = 3; i <= Math.sqrt(n); i = i+2) 
    { 
        // While i divides n, print i and divide n 
        while (n%i == 0) 
        { 
            return i;
            
             
        } 
    } 
  
    // This condition is to handle the case when n  
    // is a prime number greater than 2 
    if (n > 2) 
        return n;

    return 0;
       
} 

    

    public static boolean isPrime(long n) 
    { 
        // Corner cases 
        if (n <= 1) return false; 
        if (n <= 3) return true; 
      
        // This is checked so that we can skip  
        // middle five numbers in below loop 
        if (n % 2 == 0 || n % 3 == 0) return false; 
      
        for (long i = 5; i * i <= n; i = i + 6) 
            if (n % i == 0 || n % (i + 2) == 0) 
            return false; 
      
        return true; 
    } 

    public static void main(String[] args) {

        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader inp = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver();
        solver.solve(inp, out);
        out.close();
        
          }




    static class Solver {
        private void solve(InputReader inp, PrintWriter out1) {
         
            Scanner sc = new Scanner(System.in);
           int t = sc.nextInt();
           for(int i=0;i<t;i++)
           {
               double d = sc.nextDouble();

               if(d*d-(4*d)<0)
               {
                   out1.println("N");

               }
               else
               {
                   double temp = (d*d)-(4*d);
                   temp=Math.sqrt(temp);
                   temp+=d;
                   temp/=2;
                   double temp2=d-temp;
                   out1.println("Y "+temp+" "+temp2);
               }

            }
            
            

    }


    
}






    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }
    }
}
class ele{
    long value;
    long i;
    boolean flag;
    public ele(long value,long i)
    {
        this.value = value;
        this.i=i;
        this.flag = false;
    }
}