Property

0ms

262144K

Description:

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 A₀ A₁... A_2n - 1 A_2n, A_2n = A₀, 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 P₀, P₁, ..., 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 $\text{[math]}$
On every edge A_2k + 1A_2k + 2, k = 0...n - 1 Bill will choose one point B_2k + 1 = P_i for some i = 0, ..., n - 1 such that $\text{[math]}$
Bill gets to keep property inside of 2n-sided polygon B₀ B₁... 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.

Input:

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.

Output:

Output contains n distinct integers separated by a single space representing points B₁, B₃, ..., 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.

Sample Input:

3
0 1 2

Sample Output:

0 2 1

Note:

To maximize area Bill should choose points: B₁ = P₀, B₃ = P₂, B₅ = P₁

$\text{[math]}$

Informação

Provedor Codeforces

Código CF852C