C1. Simple Polygon Embedding
binary search; geometry; math; ternary search
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.
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.
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 \(10^{-6}\).