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{
  static char arr[][];
  public static void main(String[] args) throws IOException {
    Scanner in=new Scanner(System.in);
    int t=in.nextInt();
    int d;
    double det;
    double a,b;
    while(t-->0){
      d=in.nextInt();
      det=d*d-4.0*d;
      if(det<0){
        System.out.println("N");
      }
      else{
        System.out.print("Y ");
        det=Math.sqrt(det);
        a=(d+det)/2;
        b=(d-det)/2;
        System.out.println(a+" "+b);
      }
    }
  }
}