## Day 1, Problem 1 - Transformed Sequence

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}. ∀x, y ∈ {0, 1, …, N−1}, define the distance between x and y to be D(x, y) = min{|xy|, N − |xy|}. Given the distance D(i, Ti) 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.

### Input Format

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.

### Output Format

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.

```5
1 1 2 2 1
```

### Sample Output

```1 2 4 0 3
```

### Constraints

For 20% of the test data, N ≤ 50.
For 60% of the test data, N ≤ 500.
For 100% of the test data, N ≤ 10000.

Point Value: 20 (partial)
Time Limit: 1.00s
Memory Limit: 256M