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.lang.String;
import java.io.*;
import java.util.*;
import java.util.StringTokenizer;
//class Main    //AtCoder
//class Solution // Codechef
public class Solution2 //Codeforces
{
    public static void main(String args[])
    {
        try {
            FastReader sc = new FastReader();
            int TT = sc.nextInt();
            for(int hehe=1 ; hehe  <= TT ; hehe++){
                int N=sc.nextInt();
                double d=(Math.tan((Math.PI - (Math.PI/N))/(2*1.0)));
                sopln(d);
            }
            out.flush();
        }catch (Exception e) {
            sopln(e.toString());
        }
    }
    public final static int d = 256;
    static int MOD = 1000000007;
    static final double PI = Math.PI;
    private static BufferedReader in = new BufferedReader (new InputStreamReader (System.in));
    private static PrintWriter out = new PrintWriter (new OutputStreamWriter (System.out));
    static 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());
        }

        char nextChar()
        {
            try {
                return (char) (br.read());
            }catch (IOException e){
                return '~';
            }
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
    static void sop(Object o){System.out.print(o);}
    static double ceil(double d){
        return Math.ceil(d);
    }
    static double floor(double d){
        return Math.floor(d);
    }
    static double round(double d){
        return Math.round(d);
    }
    static void sopln(Object o){System.out.println(o);}
    static void printArray(char arr[]){
        for(char L:arr)
            sop(L+" ");
        sopln("");
    }

}