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 $\cup_{i = 0}^{n - 1} B_{2i} = \cup_{i = 0}^{n - 1} P_{i}$  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 $\cup_{i = 0}^{n - 1} B_{2 i + 1} = \cup_{i = 0}^{n - 1} P_{i}$  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.


-----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 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.


-----Example-----
Input
3
0 1 2

Output
0 2 1



-----Note-----

To maximize area Bill should choose points: B_1 = P_0, B_3 = P_2, B_5 = P_1

[Image]

Difficulty: interview

Starter code:

Solutions:
n = int(input())
a = input().split()
for i in range(n):
    a[i] = int(a[i])
b = []
for i in range(0, n-1):
    b.append((a[i]-(n-a[i+1]), i))
b.append((a[n-1]-(n-a[0]), n-1))
b = sorted(b)
ans = n*[0]
for i in range(n):
    # the line segment at index b[i][1]
    ans[b[i][1]] = i
for i in range(n):
    print(ans[i], end = ' ')