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.

Note

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

$\text{[math]}$

Idx	Name	Rating
A	Digits	2500
B	Neural Network country	2000
C	Property	2100
D	Exploration plan	2100
E	Casinos and travel	2100
F	Product transformation	2200
G	Bathroom terminal	1700
H	Bob and stages	3000
I	Dating	2300

Bubble Cup X - Finals [Online Mirror]