# Property

## 题意翻译

有一个正 2? 边形，在每条边上有 ? 等分点。现在已经选定了 ? 个点，? 个点分别位于第 2?+1 条边上，且这 ? 个点的序号构成了一个排列；你需要再选出 ? 个点位于第 2? 条边上，并且这 ? 个点的序号也构成一个排列，使得这些点构成的多边形面积最大。

## 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)