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.util.Scanner;
import java.io.*;

public class CodeForces {
    public static void main(String[] args) throws IOException {
        Scanner in=new Scanner(System.in);

        int runs=Integer.parseInt(in.nextLine());

        for(int i=0;i<runs;i++) {
            double num=Integer.parseInt(in.nextLine());
            double min=num-Math.pow(10, -6);
            double max=num+Math.pow(10,6);

            int counter=0;

            double low=0;
            double high=num;

            double num1=num/2;
            double num2=num-num1;

            boolean flag=false;

            while(!flag) {
                counter++;
                if (Math.abs((num1+num2)-num1*num2)<=Math.pow(10, -6) && Math.abs((num1+num2)-num)<=Math.pow(10, -6)) {
                    System.out.println("Y " + num1 + " " + num2);
                    flag=true;
                }else {
                    if(num1*num2>num) {
                        low=num1;
                        num1=(low+high)/2;
                        num2=num-num1;
                    }else {
                        high=num1;
                        num1=(low+high)/2;
                        num2=num-num1;
                    }
                }

                if(counter==80) {
                    System.out.println("N");
                    flag = true;
                }
            }





        }

    }
}