Let us define a regular brackets sequence in the following way:
- Empty sequence is a regular sequence.
- If S is a regular sequence, then (S) and [S] are both regular sequences.
- 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 ≤
i2 < ... <
in ≤ m that
bij for all 1 ≤ j ≤ n.
Contains at most 100 brackets (characters (, ), [ and ]) that are situated on a single line without any other characters among them.
Write a single line that contains some regular brackets sequence that has the minimal possible length and contains the given sequence as a subsequence.