CF1354C2.Not So Simple Polygon Embedding

The statement of this problem is the same as the statement of problem C1. 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.

本题的题面与问题 C1 完全相同，唯一区别在于：在问题 C1 中，$n$ 恒为偶数；而在问题 C2 中，$n$ 恒为奇数。

给定一个具有 $2 \cdot n$ 个顶点的正多边形（即它是凸的，且所有边长相等、所有内角相等），其所有边长均为 $1$。我们称其为 $2n$-边形。

你的任务是求出能够嵌入该 $2n$-边形的最小正方形的面积（即边长的平方）。所谓将 $2n$-边形嵌入正方形，是指将 $2n$-边形置于正方形内部（含边界），使得 $2n$-边形内部或边界上的任意一点，也都位于该正方形的内部或边界上。

你可以对 $2n$-边形和/或正方形进行任意角度的旋转。

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 odd integer $n$ ($3 \le n \le 199$). Don't forget you need to embed $2n$-gon, not an $n$-gon.

第一行包含一个整数 $T$（$1 \le T \le 200$）—— 表示测试用例的数量。

接下来的 $T$ 行每行描述一个测试用例。每行包含一个奇数 $n$（$3 \le n \le 199$）。请注意，你需要嵌入的是一个 $2n$ 边形，而非 $n$ 边形。

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 $10^{-6}$.

输出 $T$ 个实数——每个测试用例输出一个。对于每个测试用例，输出能嵌入该正 $2n$ 边形的正方形的最短边长。若你的答案的绝对或相对误差不超过 $10^{-6}$，则视为正确。