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 Main {

    public static void main(String[] args) {
	// write your code here
/*
        Scanner in = new Scanner(System.in);
        long n = in.nextLong();
        long ans ;
        if (n%2 == 0) ans = n/2;
        else {
            for(long i=3; ;i+=2){
                if (n%i == 0) {
                    ans = n/i;
                    break;
                }
            }
        }
        System.out.println(ans);

    */
        int t;
        Scanner in = new Scanner(System.in);
        t = in.nextInt();
        double d;
        for(int i=0;i<t;i++){
            d = in.nextDouble();
            double delta = d*d-4*d ;
            if (delta >= 0) {
                double x1, x2;
                x1 = (d - Math.sqrt( delta)) / 2;
                x2 = (d + Math.sqrt( delta)) / 2;
                //if (x1 < 0) System.out.println("N");
                System.out.println("Y " + x2 + " " + x1);
                //}
            }
            else System.out.println("N");
        }


    }
}