# Property

## 题目描述

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 ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF852C/e71ce7d28e76a9d68c876b746b3556061957b614.png) - 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 ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF852C/7095d055aa9dac0eea6c740c3e32d5c3310f8624.png) - 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.

## 输入输出格式

### 输入格式

The first line contains one integer number \$ n\ (2<=n<=50000) \$ , representing number of edges of \$ 2n \$ -sided polygon. The second line contains \$ n \$ distinct integer numbers \$ B_{2k}\ (0<=B_{2k}<=n-1,\ k=0...\ n-1) \$ separated by a single space, representing points the court chose. If \$ B_{2k}=i \$ , the court chose point \$ P_{i} \$ on side \$ A_{2k}\ A_{2k+1} \$ .

### 输出格式

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.

## 输入输出样例

### 输入样例 #1

``````3
0 1 2
``````

### 输出样例 #1

``````0 2 1
``````

## 说明

To maximize area Bill should choose points: \$ B_{1}=P_{0} \$ , \$ B_{3}=P_{2} \$ , \$ B_{5}=P_{1} \$ ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF852C/56dafbdba9c3350fcbc41412bc74c64b71c99fdf.png)