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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.lang.reflect.Array;
import java.util.Arrays;
import java.util.HashSet;
import java.util.StringTokenizer;

public class l {
    static  double eps=0.0000001;
    public static void main(String[]args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int tc =Integer.parseInt(br.readLine());
        while (tc-->0) {
            StringTokenizer st = new StringTokenizer(br.readLine());
            double n = Double.parseDouble(st.nextToken());
            double ds = n * n - 4 * n;
                ds= Math.sqrt(ds);
                double a1=(n+ds)/2.0;
                double a2=(n-ds)/2.0;
                double b1=n-a1;
                double b2= n-a1;
                if ((a1*b1)-n<eps) {
                    System.out.print("Y ");
                    System.out.printf("%.9f",a1);
                    System.out.print(" ");
                    System.out.printf("%.9f",b1);
                    System.out.println();
                }
                else if ((a2*b2)-n>eps){
                System.out.print("Y ");
                System.out.printf("%.9f",a2);
                System.out.print(" ");
                System.out.printf("%.9f",b2);
                System.out.println();
            }else{
                    System.out.println("N");
                }
        }
    }
}