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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class MemeProblem {

	public static void main(String[] args) throws IOException {
		
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));		
		StringTokenizer st = new StringTokenizer(br.readLine());
		int t = Integer.parseInt(st.nextToken());
		
		for(int i = t; i > 0; i--){
			StringTokenizer st1 = new StringTokenizer(br.readLine());
			int d = Integer.parseInt(st1.nextToken());
			int temp = (d * d) - (4 * d);
			if(temp < 0){
				System.out.println("N");
			}
			else{
				double x1 = Math.round(((d + Math.sqrt(temp))/2.0) * Math.pow(10.0, 9.0)) / Math.pow(10.0, 9.0);
				double x2 = Math.round((d - x1)* Math.pow(10.0, 9.0)) / Math.pow(10.0, 9.0);
				System.out.println("Y " + x1 + " " + x2);
			}
		}
		
		
	}

}