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.io.BufferedReader;
	import java.io.IOException;
	import java.io.InputStreamReader;
	import java.io.PrintWriter;
	import java.util.Arrays;
	import java.util.HashMap;
	import java.util.Map;
	import java.util.PriorityQueue;
	import java.util.Scanner;
	import java.util.TreeMap;
	import java.util.*;
	
	public class CF_428_DIV2_B {
		
	
		public static void main(String[] args) throws IOException {
			BufferedReader input = new BufferedReader (new InputStreamReader(System.in));
			
			int t = Integer.parseInt(input.readLine());
			double d, a, b;
			double eps = 10e-6;
			while (t-- != 0) {
				d = Double.parseDouble(input.readLine());
				if (d*d - 4.0*d >= 0) {
					a = (d + Math.sqrt(d*d - 4.0*d))/2.0;
					b = d - a;
					System.out.println("Y "+ a + " " + b);
				} else {
					System.out.println("N");
				}
				
			}

			input.close();	
		}
	}