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;

public class MemeProblem {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();

        while(t-- != 0) {
            int d = sc.nextInt();

            //Discriminant = b2 - 4ac
            int D = d*d - 4*d;
            if(D < 0){
                //roots are imaginary
                System.out.println("N");
            } else {
                //x1 = (-b +- sqrt(D))/ 2a
                double b = d + Math.sqrt(D);
                b /= 2;

                double a = 0;
                if(b!=0){
                    a = (double) d/b;
                }

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