CF852C Property

Bill is a famous mathematician in BubbleLand. Thanks to his revolutionary math discoveries he was able to make enough money to build a beautiful house. Unfortunately, for not paying property tax on time, court decided to punish Bill by making him lose a part of his property. Bill’s property can be observed as a convex regular $ 2n $ -sided polygon $ A_{0}\ A_{1}...\ A_{2n-1}\ A_{2n},\ A_{2n}=\ A_{0} $ , with sides of the exactly 1 meter in length. Court rules for removing part of his property are as follows: - Split every edge $ A_{k}\ A_{k+1},\ k=0...\ 2n-1 $ in $ n $ equal parts of size $ 1/n $ with points $ P_{0},P_{1},...,P_{n-1} $ - On every edge $ A_{2k}\ A_{2k+1},\ k=0...\ n-1 $ court will choose one point $ B_{2k}=\ P_{i} $ for some $ i=0,...,\ n-1 $ such that  - On every edge $ A_{2k+1}A_{2k+2},\ k=0...n-1 $ Bill will choose one point $ B_{2k+1}=\ P_{i} $ for some $ i=0,...,\ n-1 $ such that  - Bill gets to keep property inside of $ 2n $ -sided polygon $ B_{0}\ B_{1}...\ B_{2n-1} $ Luckily, Bill found out which $ B_{2k} $ points the court chose. Even though he is a great mathematician, his house is very big and he has a hard time calculating. Therefore, he is asking you to help him choose points so he maximizes area of property he can keep.

The first line contains one integer number $ n\ (2

Output contains $ n $ distinct integers separated by a single space representing points $ B_{1},B_{3},...,B_{2n-1} $ Bill should choose in order to maximize the property area. If there are multiple solutions that maximize the area, return any of them.

To maximize area Bill should choose points: $ B_{1}=P_{0} $ , $ B_{3}=P_{2} $ , $ B_{5}=P_{1} $