##### National Olympiad in Informatics, China, 2009

For integers , a transformed sequence can change to , where and . , define the distance between and to be . Given the distance between each and , you must determine a transformed sequence that satisfies the requirements. If many sequences satisfy the requirements, then output the lexicographically smallest one.

**Note:** For two transformed sequences and , if there
exists a that satisfies and
for , then we say that is
lexicographically smaller than .

#### Input Specification

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

#### Output Specification

If there exists at least one transformed sequence , then output one
line containing integers, representing the lexicographically
smallest transformed sequence . 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, .

For 60% of the test data, .

For 100% of the test data, .

Problem translated to English by .

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