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.*;
public class q3 {
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int test = scan.nextInt();
        while(test-->0){
            int n = scan.nextInt();
            if(n==2){
                System.out.println("1.000000000");
                continue;
            }
            double val = (double)360/(double)(2*n);
            
            double r1 = 90 - (double)val/(double)2;
            r1 = Math.toRadians(r1);
            double a = Math.tan(r1)/2;
            double r2 = 90 -  val;
            r2 = Math.toRadians(r2);
            double  b = a/(Math.tan(r2));
            //System.out.println(val+" "+a+" "+b+" ");
            System.out.println(2*a);

        }
    }
}