1255. 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 ‘]’ is given. You are to find the shortest possible regular brackets sequence, that contains the given character sequence as a subsequence. Here, a string $a_1a_2\ldots a_n$ is called a subsequence of the string $b_1b_2 \ldots b_m$, if there exist such indices $1 \le i_1 < i_2 < \cdots < i_n \le m$, that $a_j=b_{i_j}$ for all $1 \le j \le n$.