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

public class test
{
	public static void main (String[] args) throws java.lang.Exception
	{
		inputs in=new inputs (System.in);
		// double a = 45;
		// double b = Math.toRadians(a); 
        // System.out.println(Math.cos(b));
		// double cos = Math.cos(b);
		int t = in.nextInt();
		while(--t>=0)
		{
			int n = in.nextInt();
			int cnt = ((n*2)-4)/4;
			double sum = 0;
			double div = 90.0/(cnt+1);
			double a = 0;
			for(int i=0;i<cnt;i++)
			{
				a = a+div;
				double b = Math.toRadians(a); 
				sum+=Math.sin(b);

			}
			System.out.println(1+sum*2);
			
			
		}
		
	}
}

class inputs
{
    public BufferedReader reader;
    public StringTokenizer token;

    inputs(InputStream str)
    {
        reader=new BufferedReader(new InputStreamReader(str));
        token=null;
    }

    int nextInt()
    {
        while(token==null||!token.hasMoreTokens())
        {
            try { token=new StringTokenizer(reader.readLine());   }
            catch(IOException e){  throw new RuntimeException(e); }
        }
        return Integer.parseInt(token.nextToken());
    }

    long nextLong()
    {
        while(token==null||!token.hasMoreTokens())
        {
            try { token=new StringTokenizer(reader.readLine());   }
            catch(IOException e){  throw new RuntimeException(e); }
        }
        return Long.parseLong(token.nextToken());
    }

    String next()
    {
        while(token==null||!token.hasMoreTokens())
        {
            try { token=new StringTokenizer(reader.readLine());   }
            catch(IOException e){  throw new RuntimeException(e); }
        }
        return token.nextToken();
    }

}