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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
   public static void main (String[] args) throws java.lang.Exception
	{
	    
// -----------------------------Fast IO using BufferedReader-----------------------------------------------------------------	    

		 BufferedReader br = new BufferedReader( 
                              new InputStreamReader(System.in)); 
  
        StringTokenizer st = new StringTokenizer(br.readLine());
         PrintWriter out = new PrintWriter(System.out); 
        int T = Integer.parseInt(st.nextToken()); 
        
// ----------------------------------------------------------------------------------------------------------	    
    
		while(T-- >0)
		{
		   double n=Double.parseDouble(br.readLine());
		   double d=3.1415926535897/(2*n);
		   double ans=1.0/(Math.tan(d));
		   out.println(ans);
		}
		out.close();   
	}
}