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 2_n_-sided polygon _A_0 _A_1... A_2_n - 1 A_2_n,  A_2_n =  _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... 2_n_ - 1 in n equal parts of size 1 / n with points _P_0, _P_1, ..., P__n - 1
• On every edge A_2_k A_2_k + 1,  k = 0... n - 1 court will choose one point B_2_k =  P__i for some i = 0, ...,  n - 1 such that
• On every edge A_2_k + 1_A_2_k_ + 2,  k = 0...n - 1 Bill will choose one point B_2_k + 1 =  P__i for some i = 0, ...,  n - 1 such that
• Bill gets to keep property inside of 2_n_-sided polygon _B_0 _B_1... B_2_n - 1

Luckily, Bill found out which B_2_k 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.

比尔是泡泡国（BubbleLand）一位著名的数学家。得益于他革命性的数学发现，他赚到了足够的钱建造了一座美丽的房子。不幸的是，由于未能及时缴纳房产税，法院裁定对比尔进行处罚——剥夺他部分房产。

比尔的房产可视为一个凸正 $2n$ 边形 $A_0 A_1 \dots A_{2n-1} A_{2n}$，其中 $A_{2n} = A_0$，且所有边长恰好为 $1$ 米。

法院制定的房产剥夺规则如下：

• 将每条边 $A_k A_{k+1}$（其中 $k = 0, 1, \dots, 2n-1$）等分为 $n$ 段，每段长度为 $\frac{1}{n}$，分点记为 $P_0, P_1, \dots, P_{n-1}$；
• 在每条边 $A_{2k} A_{2k+1}$（其中 $k = 0, 1, \dots, n-1$）上，法院将选定一个点 $B_{2k} = P_i$（其中 $i \in \{0, 1, \dots, n-1\}$），满足条件：
  
• 在每条边 $A_{2k+1} A_{2k+2}$（其中 $k = 0, 1, \dots, n-1$）上，比尔将选定一个点 $B_{2k+1} = P_i$（其中 $i \in \{0, 1, \dots, n-1\}$），满足条件：
  
• 比尔得以保有的房产，即为以 $2n$ 边形 $B_0 B_1 \dots B_{2n-1}$ 为边界的内部区域。

幸运的是，比尔已提前获知法院所选定的所有点 $B_{2k}$。尽管他是一位杰出的数学家，但他的房子实在太大，难以手动完成相关计算。因此，他请求你帮助他选择各 $B_{2k+1}$ 点，以使他所能保留的房产面积最大化。

The first line contains one integer number n (2 ≤ n ≤ 50000), representing number of edges of 2_n_-sided polygon.

The second line contains n distinct integer numbers B_2_k (0 ≤ B_2_k ≤ n - 1,  k = 0... n - 1) separated by a single space, representing points the court chose. If B_2_k = i, the court chose point P__i on side A_2_k A_2_k + 1.

第一行包含一个整数 $ n $（$ 2 \leq n \leq 50000 $），表示一个 $ 2n $ 边形的边数。

第二行包含 $ n $ 个互不相同的整数 $ B_{2k} $（$ 0 \leq B_{2k} \leq n - 1 $，其中 $ k = 0, \dots, n - 1 $），由单个空格分隔，表示法庭所选的点。若 $ B_{2k} = i $，则法庭在边 $ A_{2k}A_{2k+1} $ 上选择了点 $ P_i $。

Output contains n distinct integers separated by a single space representing points _B_1, _B_3, ..., B_2_n - 1 Bill should choose in order to maximize the property area. If there are multiple solutions that maximize the area, return any of them.

输出包含 n 个互不相同的整数，以单个空格分隔，表示比尔应选择的点 _B_₁, _B_₃, ..., _B_₂ₙ ₋ ₁，以最大化地块面积。若存在多个能最大化面积的解，则返回其中任意一个即可。

To maximize area Bill should choose points: _B_1 = _P_0, _B_3 = _P_2, _B_5 = _P_1

为使面积最大，比尔应选择以下点：$B_1 = P_0$，$B_3 = P_2$，$B_5 = P_1$