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.*;
import java.util.*;

public class X {

	public static void main(String[] args) {
		FastScanner in=new FastScanner();
		PrintWriter out=new PrintWriter(System.out);
		int t=in.nextInt();
		while(t-->0)
		solve(in,out);
		out.close();
	}
   

    static void solve(FastScanner in,PrintWriter out){
      int N=in.nextInt();
    
      double val = N * N - 4.0 * N; 
  
    // Not possible 
    if (val < 0) { 
        out.println("N"); 
        return; 
    } 
  
   
    double a = (N + Math.sqrt(val)) / 2.0; 
    double b = (N - Math.sqrt(val)) / 2.0; 
     out.println("Y "+a+" "+b);
    }                      
    

 
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		
	

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