C. Property
time limit per test
0.5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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... A2n - 1 A2n,  A2n =  A0, with sides of the exactly 1 meter in length.

Court rules for removing part of his property are as follows:

• Split every edge Ak Ak + 1,  k = 0... 2n - 1 in n equal parts of size 1 / n with points P0, P1, ..., Pn - 1
• On every edge A2k A2k + 1,  k = 0... n - 1 court will choose one point B2k =  Pi for some i = 0, ...,  n - 1 such that
• On every edge A2k + 1A2k + 2,  k = 0...n - 1 Bill will choose one point B2k + 1 =  Pi for some i = 0, ...,  n - 1 such that
• Bill gets to keep property inside of 2n-sided polygon B0 B1... B2n - 1

Luckily, Bill found out which B2k 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 B2k (0 ≤ B2k ≤ n - 1,  k = 0... n - 1) separated by a single space, representing points the court chose. If B2k = i, the court chose point Pi on side A2k A2k + 1.

Output

Output contains n distinct integers separated by a single space representing points B1, B3, ..., B2n - 1 Bill should choose in order to maximize the property area. If there are multiple solutions that maximize the area, return any of them.

Example
Input
30 1 2
Output
0 2 1
Note

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