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1183. Brackets Sequence

Time limit: 1.0 second
Memory limit: 64 MB
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 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 1 ≤ j ≤ n.


The input 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.


Problem Author: Andrew Stankevich
Problem Source: 2001-2002 ACM Northeastern European Regional Programming Contest