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문제

For N integers 0, 1, …, N−1, a transformed sequence T can change i to Ti, where Ti ∈ {0, 1, …, N−1} and ∪i = 0N−1 { Ti } = {0, 1, …, N−1}. ∀xy ∈ {0, 1, …, N−1}, define the distance between x and y to be D(xy) = min{|x − y|, N − |x − y|}. Given the distance D(iTi) between each i and Ti, you must determine a transformed sequence T that satisfy the requirements. If many sequences satisfy the requirements, then output the lexicographically smallest one.

Note: For two transformed sequences S and T, if there exists a p < N that satisfies Si = Ti and Sp < Tp for i = 0, 1, …, p−1, then we say that S is lexicographically smaller than T.

입력

The first line of input contains a single integer N, the length of the sequence.

The following line contains N integers Di, where Di is the distance between i and Ti.

출력

If there exists at least one transformed sequence T, then output one line containing N integers, representing the lexicographically smallest transformed sequence T. Otherwise, output "No Answer" (without quotes). Note: Pairs of adjacent numbers in the output must be separated by a single space, and there cannot be trailing spaces.

제한

N ≤ 10000

예제 입력 1

5
1 1 2 2 1

예제 출력 1

1 2 4 0 3