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:
/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

import java.io.*;

/**
 *
 * @author arvin
 */
public class sum_eq_mul {
    public static void main(String args[]) throws Exception
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        int n=Integer.parseInt(br.readLine());
        while(n--!=0)
        {
            int x=Integer.parseInt(br.readLine());
            double check=(double)(x*x)-(4*x);
            if(check>=0)
            {
                double ans1=(double)((double)x+(double)Math.sqrt(check))/2;
                double ans2=(double)((double)x-(double)Math.sqrt(check))/2;
                System.out.println("Y "+ans1+" "+ans2);
            }
            else
                System.out.println("N");
        }
        br.close();
    }
}