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
(), , (()), (), (), ()[()]
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
Problem Author: Andrew Stankevich
Problem Source: 2001-2002 ACM Northeastern European Regional Programming Contest