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 D {

	public static void main(String[] args) {
		Scanner sc =  new Scanner(System.in);
		int n= sc.nextInt();
		int[] main =  new int[n];
		for (int i=0; i<main.length; i++) {
			main[i]=sc.nextInt();
		}
		for (int i=0; i<main.length; i++) {
		int d =  main[i];
		double a=0;
		double b=0;
		double D=d*d-4*d;
		if (D<0) {
			System.out.println("N");
		} else {
			a=(d+Math.sqrt(D))/2;
			b=d-a;
			System.out.println("Y "+a+" "+b);
		}

	}}

}