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.*;
import java.util.*;
import java.lang.Math.*;

public class main{
	static Scanner in;

	private static void solve(){

		double n = in.nextDouble();
		n *=2;

		double ang = 360/(n*2);
		ang = 180-(90+ang);
		ang = Math.toRadians(ang);
		double ans = Math.tan(ang);

		System.out.println(String.format("%.9f",ans));

	}

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

	private static class Read{
		BufferedReader br;
		StringTokenizer st;
		public Read(){
			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();
		}
		String line(){
			String ans = "";
			try { ans = br.readLine(); }
			catch (IOException e) { e.printStackTrace(); }
			return ans;
		}
		int nextInt(){return Integer.parseInt(next());}
		double nextDouble(){return Double.parseDouble(next());}
		long nextLong(){return Long.parseLong(next());}
	}

}