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.Scanner;

public class Meme_Problem {

    public static void main(String[] args) {

        Scanner s=new Scanner(System.in);
        int t =s.nextInt();

        while(t-->0){

            int d=s.nextInt();

            double sq=Math.sqrt((d*d)-(4*d));
            double a1=(d+sq)/2,b1=d-a1;
            double a2=(d-sq)/2,b2=d-a2;

            if( Math.abs((a1+b1)-(a1*b1)) <=1e-6  &&  ((a1+b1)-d) <= 1e-6){
                System.out.println("Y "+a1+" "+b1);
                continue;
            }


            if( Math.abs((a2+b2)-(a2*b2)) <=1e-6  &&  ((a2+b2)-d) <= 1e-6){
                System.out.println("Y "+a2+" "+b2);
                continue;
            }


            System.out.println("N");


        }
    }
}