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 CodeForce {
 static ArrayList<Integer> inputarrlist(String[] str){
     ArrayList<Integer> arr=new ArrayList<>();
     for(int i=0;i<str.length;i++)
         arr.add(Integer.parseInt(str[i]));
     
     return arr;
 }
 static long[] inputarr(String[] str){
     long[] arr=new long[str.length];
     for(int i=0;i<str.length;i++)
         arr[i]=(Long.parseLong(str[i]));
     
     return arr;
 }
 
 static long gcd(long a, long b) 
    { 
      if (b == 0) 
        return a; 
      return gcd(b, a % b);  
    } 
 
 static double myfunction(double n, double a) 
    { 
  
       
        if (a < 0 && n < 0) 
            return -1; 
  
        
        return  Math.cos(Math.PI / (2 * n)) / Math.sin(Math.PI / (n)); 
    } 
 
 
    public static void main(String[] args) throws IOException {
        
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t=Integer.parseInt(br.readLine());
        while(t-->0){
       int n=Integer.parseInt(br.readLine());
       double ans=myfunction((double)2*n,(double)1);
            System.out.println(ans);
        }
}}