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 $a_1{a}_2\dots a_n$ is called a subsequence of the string $b_1{b}_2\dots b_m$, if there exist such indices $1\le i_1<i_2<\cdots <i_n\le m$, that $a_j=b_{i_j}$ for all $1\le j\le n$.