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.text.DecimalFormat;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        // a=d-b b^2-db+d=0 a^2+a-2=0 
        int num = sc.nextInt();
        String[] res = new String[num];
        int d;
        double a, b;
        DecimalFormat dFormat = new DecimalFormat("0.000000000");
        for (int i = 0; i < num; ++i) {
            d = sc.nextInt();
            b = (d + Math.sqrt(d * d - 4 * d)) / 2;
            if(b<0) b = (d - Math.sqrt(d * d - 4 * d)) / 2;
            a = d - b;
            if (Math.abs((a + b) - a * b) <= 10e-6 && Math.abs((a + b) - d) <= 10e-6) {
                res[i] = "Y " + dFormat.format(b) + " " + dFormat.format(a);
            } else {
                res[i] = "N";
            }
        }
        for (String i : res) {
            System.out.println(i);
        }
        sc.close();
    }
}