Simple Polygon Embedding

题意翻译

该题题意和$\rm CF1354C2$相同，只是保证$n$为偶数。 求边长为$1$的正$(2\times n)$边形的最小外接正方形的边长。 $T$组数据。$T\le 200,n\le 200$，且$\bf{n}$**为偶数**。

题目描述

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 \cdot 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.

输入输出格式

输入格式

The first line contains a single integer $ T $ ( $ 1 \le T \le 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 \le n \le 200 $ ). Don't forget you need to embed $ 2n $ -gon, not an $ n $ -gon.

输出格式

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} $ .

输入输出样例

输入样例 #1

3
2
4
200

输出样例 #1

1.000000000
2.414213562
127.321336469