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.*;
import java.util.*;

public class Main {

	public static void main(String[] args) throws IOException {
		InputReader scan = new InputReader(System.in);
		int t = scan.nextInt();
		StringBuilder res = new StringBuilder();
		while (t-->0) {
			int n = scan.nextInt();
			if (n == 0) {
				res.append("Y 0 0\n");
				continue;
			}
			double a = (n + Math.sqrt(n*n - 4*n))/2.0;
			if (Double.isNaN(a)) {
				res.append("N\n");
			} else {
				double b = n / a;
				res.append("Y "+a+" "+b+"\n");
			}
		}
		System.out.println(res);
	}

	static class InputReader {
		StringTokenizer tokenizer;
		BufferedReader reader;
		String temp;
		String token;

		public InputReader(InputStream stream) {
			tokenizer = null;
			reader = new BufferedReader(new InputStreamReader(stream));
		}

		public InputReader(FileInputStream stream) {
			tokenizer = null;
			reader = new BufferedReader(new InputStreamReader(stream));
		}

		public String nextLine() throws IOException {
			return reader.readLine();
		}

		public String next() {
			if (temp != null) {
				String s = temp;
				temp = null;
				return s;
			}

			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					return null;
				}
			}
			return tokenizer.nextToken();
		}

		public boolean hasNext() {
			return (temp = next()) != null;
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}
	}
}