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.*;

public class Main {
    static BufferedReader br;

    public static void main(String[] args) throws Exception {
        br = new BufferedReader(new InputStreamReader(System.in));
        int tc=cinI();
        while (tc-->0) {
            double n = Double.parseDouble(br.readLine());

            double x = Math.tan(Math.PI / (2 * n));
            double ans = 1 / x;
            cout(ans + " ");
        }

    }




    public  static  void  init(int[] arr,String[] str) throws Exception{
        for(int j=0;j<str.length;j++){
            arr[j+1]=getI(str[j]);

        }
    }
    public  static  void update(int index,int[] bit,int  val){


        while (index < bit.length) {
            bit[index]+=val;
            index = index + (index&(-index));
        }

    }

    public  static int evensum(int index,int[] bit){



        int sum=0;
        while (index>0){
            sum+=bit[index];
            index=  index- (index&(-index));
        }
        return sum;
    }

    public static String ToString(Long x) {
        return Long.toBinaryString(x);
    }

    public static void cout(String s) {
        System.out.println(s);
    }

    public static Integer cinI() throws Exception {
        return Integer.parseInt(br.readLine());
    }

    public static int getI(String s) throws Exception {
        return Integer.parseInt(s);
    }


    public static String cin() throws Exception {
        return br.readLine();
    }

    public static String[] cinA() throws Exception {
        return br.readLine().split(" ");
    }



    public static long getL(String s) throws Exception {
        return Long.parseLong(s);
    }

    public static int max(int a, int b) {
        return Math.max(a, b);
    }

    public static void coutI(int x) {
        System.out.println(String.valueOf(x));
    }

    public static void coutI(long x) {
        System.out.println(String.valueOf(x));
    }

    public static Long cinL() throws Exception {
        return Long.parseLong(br.readLine());
    }



}
class ob{
    int left;
    int length;

    public ob(int l,int length){
        this.left  =l;
        this.length=length;
    }
}
class sort implements Comparator<ob>{

    @Override
    public int compare(ob ob, ob t1) {
        return ob.length-t1.length;
    }
}