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.io.*;

public class Solution
{
    public static int MIN(int a,int b)
    {
        if(a<b)
            return a;
        return b;
    }
    public static void main(String[] args) throws IOException
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        int t = Integer.parseInt(br.readLine());
        while(t-->0)
        {
            int n = Integer.parseInt(br.readLine());
            n = 2*n;
            double d = 1/(2*Math.tan(Math.PI/n));
            double len = 2*d;
            double r = Math.sqrt(0.25+d*d);
            double len2 = 2*r;
            if((len<len2)&&((Math.sqrt(2)*len)>=len2))
                bw.write(len+"\n");
            else
                bw.write(len2+"\n");
        }
        bw.flush();
    }
}