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 Towers {
    public static void main(String args[]) {
      Scanner input = new Scanner(System.in);
      int t = input.nextInt();
      for ( int i = 0; i < t; i++){
      int n = input.nextInt();
      double a,b;
	  if ( n < 4 && n != 0 ) {
		  System.out.println("N");
		  continue;
      }
	  double r = Math.sqrt( n * n - (double)4 * n );
	  
	  a = ( n - r ) / 2;
	  b = ( n + r ) / 2;
	  System.out.println("Y " + a + " " + b);
	  }
	}	  
}