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.*;
import java.math.*;
//BigInteger A;
//A= BigInteger.valueOf(54);
//ArrayList<Integer> a=new ArrayList<>();
//TreeSet<Integer> ts=new TreeSet<>();
//HashMap<Integer,Integer> hm=new HashMap<>();
//PriorityQueue<Integer> pq=new PriorityQueue<>();
public final class CF
{
     public static void main(String[]args)throws IOException
	{
		int K=(int)Math.pow(10,9)+7;
          FastReader ob=new FastReader();
          StringBuffer sb=new StringBuffer();
          int t=ob.nextInt();
          while(t-->0)
          {
               double n=ob.nextDouble();
               double ans=1/(Math.tan(Math.toRadians(180/(2*n))));
               sb.append(ans+"\n");
          }
          System.out.println(sb);
	}
}
class Pair
{
	int x,y;
	Pair(int x,int y)
	{
		this.x=x;
		this.y=y;
	}
}
class PairComparator implements Comparator<Pair>
{
	public int compare(Pair a,Pair b)
	{
        return a.y-b.y;
	}
}
class FastReader {
    BufferedReader br;
    StringTokenizer st;
    public FastReader() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    public String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e)  {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
    public String nextLine()
    {
        String s="";
        try {
        s=br.readLine();
        } catch (IOException e)  {
                e.printStackTrace();
            }
        return s;
    }
    public int nextInt() {
        return Integer.parseInt(next());
    }
    public long nextLong() {
        return Long.parseLong(next());
    }
    public double nextDouble() {
        return Double.parseDouble(next());
    }
}