Problem: The statement of this problem is the same as the statement of problem C2. The only difference is that, in problem C1, n is always even, and in C2, n is always odd.

You are given a regular polygon with 2 ⋅ n vertices (it's convex and has equal sides and equal angles) and all its sides have length 1. Let's name it as 2n-gon.

Your task is to find the square of the minimum size such that you can embed 2n-gon in the square. Embedding 2n-gon in the square means that you need to place 2n-gon in the square in such way that each point which lies inside or on a border of 2n-gon should also lie inside or on a border of the square.

You can rotate 2n-gon and/or the square.

Input

The first line contains a single integer T (1 ≤ T ≤ 200) — the number of test cases.

Next T lines contain descriptions of test cases — one per line. Each line contains single even integer n (2 ≤ n ≤ 200). Don't forget you need to embed 2n-gon, not an n-gon.

Output

Print T real numbers — one per test case. For each test case, print the minimum length of a side of the square 2n-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}.

Example

Input


3
2
4
200


Output


1.000000000
2.414213562
127.321336469

Solution (in JAVA):

Solution:
import java.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class C {		
	static class FastReader 
	{ 
		BufferedReader br; 
			StringTokenizer st; 

			public FastReader() 
			{ 
				br = new BufferedReader(new
						InputStreamReader(System.in)); 
			} 

			String next() 
			{ 
				while (st == null || !st.hasMoreElements()) 
				{ 
					try
					{ 
						st = new StringTokenizer(br.readLine()); 
					} 
					catch (IOException e) 
					{ 
						e.printStackTrace(); 
					} 
				} 
				return st.nextToken(); 
			} 

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

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

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

			String nextLine() 
			{ 
				String str = ""; 
			try
			{ 
				str = br.readLine(); 
			} 
			catch (IOException e) 
			{ 
				e.printStackTrace(); 
			} 
			return str; 
			}
	}
	
	public static void main(String args[]) {
		OutputStream outputStream = System.out;
        PrintWriter out = new PrintWriter(outputStream);
        FastReader in = new FastReader();
		Main(in, out);
		out.close();
	}

	static void Main(FastReader in, PrintWriter out) {
		int t = in.nextInt();
		final double PI = 3.14159265;
		while(t-->0){
			double n = in.nextDouble();
			double arg = (PI/(2*n));
			double tanVal = Math.tan(arg);
			out.println(1.0/tanVal);
		}
	}	
}