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.net.Inet4Address;
import java.util.*;
import java.io.*;

public class No_I_Did_Not {

    public static void main(String[] args)throws IOException {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);

        int t = Integer.parseInt(br.readLine());

        while(t-- > 0)
        {
            double d = Double.parseDouble(br.readLine());

            if(d*d - 4*d < 0)
                out.println("N");
            else
            {
                double x = (d + Math.sqrt(d*d-4*d))/2.0;
                double y = (d - Math.sqrt(d*d-4*d))/2.0;

                out.printf("Y %.9f %.9f\n" , Math.max(x,y) , Math.min(x,y));
            }
        }
        out.flush();
        out.close();

    }

}