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.math.BigInteger;
import java.nio.charset.IllegalCharsetNameException;
import java.util.*;

public class Main {
    public static void main(String[] args) throws IOException {
        OutputStream outputStream = System.out;
        PrintWriter out = new PrintWriter(outputStream);
        FastReader in = new FastReader();
        test a=new test();
        a.solve(in,out);
        out.close();
    }
}

class test {
    public void solve(FastReader in, PrintWriter out) {
        int t = in.nextInt();
        while (t-->0) {
            int n =in.nextInt();
            int a =1;

            System.out.format("%.9f",2*ap(2*n,a));
           System.out.println();
        }

    }
    double ap(double n, double a)
    {


        if (a < 0 && n < 0)
            return -1;


        return (a / (2 * java.lang.Math.tan((180 / n)
                * 3.14159265358979323846264338327950288419716939 / 180)));
    }

}


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;
    }
}