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.BufferedWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.IOException;
import java.io.FileOutputStream;
import java.util.StringTokenizer;
public class PolygonEmbed{
	public static void main(String[] args) throws IOException{
		FastReader sc = new FastReader();
		BufferedWriter out = new BufferedWriter(new OutputStreamWriter(new FileOutputStream(java.io.FileDescriptor.out),"ASCII"),512);
		int t = sc.nextInt();
		while(t-- > 0){
			int n = sc.nextInt()<<1;
			double angle = Math.PI/n;
			double a = 1/(Math.tan(angle)*2);
			double l = a*2;
			out.write(l + "");
			out.write('\n');
			out.flush();
		}
		
	}
}
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; 
    }
}