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;

/**
 * Created by Mach on 13.11.2018.
 */
public class round54c {

    public static void main(String[] args) {
        Scanner input=new Scanner(System.in);
        String s=input.nextLine();
        int n=Integer.parseInt(s);
        int[] nums= new int[n];

        for (int i=0; i<n; i++) solve(Integer.parseInt(input.nextLine()));
        

    }

    private static void solve(int d){
        double a=0, b=0;
        if (d==0) {
            System.out.println("Y "+a+" "+b);
            return;
        }
        if (d<4) {
            System.out.println("N");
            return;
        }
        int dis=d*d-4*d;
        a=(d+Math.sqrt(dis))/2;
        b=(d-Math.sqrt(dis))/2;

        System.out.println("Y "+a+" "+b);

    }


}