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.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;
import java.io.*;
public class j19 {
    public static void main(String[] args) throws Exception{
      BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
     int t = Integer.parseInt(br.readLine());
    while(t-->0){
        double d = Double.parseDouble(br.readLine());
        double dis = (double)(Math.pow(d,2)-4*d);
        double disroot = (double)(Math.sqrt(dis));
        if(dis<0){
            System.out.println("N");
        }
        else{
            double a = 0.0;
            double b = 0.0;
                a = (double)((double)((d+disroot)/2.0));
                b = (double)((double)((d-disroot)/2.0));
                System.out.printf("Y %.9f %.9f\n",a,b);
        }
    }
   }
}