Problems

# Brackets sequence

Let us define a regular brackets sequence in the following way:

1. Empty sequence is a regular sequence.
2. If S is a regular sequence, then (S) and [S] are both regular sequences.
3. If A and B are regular sequences, then AB is a regular sequence.

For example, all of the following sequences of characters are regular brackets sequences:

(), [], (()), ([]), ()[], ()[()]

And all of the following character sequences are not:

(, [, ), )(, ([)], ([(]

Some sequence of characters (, ), [ and ] are given. You are to find the shortest possible regular brackets sequence, that contains the given character sequence as a subsequence. Here, a string `a1a2...an` is called a subsequence of the string `b1b2...bm`, if there exist such indices 1`i1` < `i2` < ... < `in`m that `aj` = `bij` for all 1jn.

#### Input

Contains at most 100 brackets (characters (, ), [ and ]) that are situated on a single line without any other characters among them.

#### Output

Write a single line that contains some regular brackets sequence that has the minimal possible length and contains the given sequence as a subsequence.

Time limit 1 second
Memory limit 122.17 MiB
Input example #1
```([(]
```
Output example #1
`()[()]`