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.math.*;
import java.text.*;

import java.util.*;


public class Solving {
    public static Scanner in =new Scanner(System.in);
    public static boolean canSolve(int c){
        int d=(int)(Math.pow(c,2)-(4*c));
        if(d>0)
        return true;
        else
            return false;
    }
    public static void solve(int c){
        NumberFormat fm=new DecimalFormat("#.#########");
        int d=(int)(Math.pow(c,2)-(4*c));
        double sqrtD=(double)Math.sqrt(d);
        double b=(double)((c+sqrtD)/2.0);
        double a=c-b;
        String c1=fm.format(b);
        String c2=fm.format(a);
        System.out.println("Y "+c1+" "+c2);
    }
    public static void main(String[] args){
        int T=in.nextInt();
        for(int t=0;t<T;t++){
             int c=in.nextInt();
        if(c==0)
            System.out.println("Y "+"0.000000000 "+"0.000000000");
        else if(canSolve(c)){
          solve(c);
        }
        else if(c==4)
            System.out.println("Y "+"2.000000000 "+"2.000000000");
        else
                System.out.println("N");
        }
    }
    
   
}