National Olympiad in Informatics, China, 2009

For ~N~ integers ~0, 1, \dots, N-1~, a transformed sequence ~T~ can change ~i~ to ~T_i~, where ~T_i \in \{0, 1, \dots, N-1\}~ and ~\bigcup_{i=0}^{N-1} \{T_i\} =\{0, 1, \dots, N-1\}~. ~\forall x,y \in \{0, 1, \dots, N-1\}~, define the distance between ~x~ and ~y~ to be ~D(x, y) = \min\{|x-y|, N-|x-y|\}~. Given the distance ~D(i, T_i)~ between each ~i~ and ~T_i~, you must determine a transformed sequence ~T~ that satisfies 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 ~S_i = T_i~ and ~S_p < T_p~ for ~i = 0, 1, \dots, p-1~, then we say that ~S~ is lexicographically smaller than ~T~.

Input Specification

The first line of input contains a single integer ~N~, the length of the sequence. The following line contains ~N~ integers ~D_i~, where ~D_i~ is the distance between ~i~ and ~T_i~.

Output Specification

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.

Note: Pairs of adjacent numbers in the output must be separated by a single space, and there cannot be trailing spaces.

Sample Input

5
1 1 2 2 1

Sample Output

1 2 4 0 3

Constraints

For 20% of the test data, ~N \le 50~.
For 60% of the test data, ~N \le 500~.
For 100% of the test data, ~N \le 10\,000~.

Problem translated to English by Alex.