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.util.*;
import java.io.*;

public class problemB {
	
	public static void solve(int d){
		if(d == 1 || d == 2 || d == 3){
			System.out.println("N");
			return;
		}
		else{
			double delta = d*d - 4*d;
			double b = (double)(d - (double)Math.sqrt(delta))/2;
			double a = d - b;
			System.out.println("Y " + a + " " + b);
			return;
		}
	}
	
	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(br.readLine());
		for(int i = 0;i<t;i++){
			int d = Integer.parseInt(br.readLine());
			solve(d);
		}
		
	}
}