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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;

public class C1076 {
	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
		int n = Integer.parseInt(in.readLine());
		for(int i = 0;i<n;i++) {
			double k = Double.parseDouble(in.readLine());
			if(k <= 0) {
				out.write("Y 0.000000 0.000000\n" );
			}
			else if(k < 4) {
				out.write("N\n");
			} else if(k == 4) {
				out.write("Y ");
				out.write("2.0000000" + " " + "2.0000000\n");
			} else {
				double l = 1;
				double r = 2;
				while(l <= r) {
					double mid = (l+r) / 2;
					double o = k - mid;
					double pp = mid * o;
					if(Math.abs(pp - k) <= 0.000001) {
						out.write("Y ");
						out.write(o + " " + mid + "\n");
						break;
					} else if (pp > k) {
						r = mid;
					} else {
						l = mid;
					}
				}
				
			}
			
			
		}
		out.flush();
	}
}