Brackets Sequence

Time Limit: 2 Seconds
Memory Limit: 65536 KB
Special Judge

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 a1 a2 ... an is called a subsequence
of the string b1 b2 ... bm, if there exist such indices 1 = i1 < i2 <
... < in = m, that aj = bij for all 1 = j = n.

**Input**

The input file contains at most 100 brackets (characters '(', ')', '[' and ']')
that are situated on a single line without any other characters among them.

**Output**

Write to the output file a single line that contains some regular brackets sequence
that has the minimal possible length and contains the given sequence as a subsequence.

**This problem contains multiple test cases!**

The first line of a multiple input is an integer N, then a blank line followed
by N input blocks. Each input block is in the format indicated in the problem
description. There is a blank line between input blocks.

The output format consists of N output blocks. There is a blank line between
output blocks.

**Sample Input**

1

([(]

**Sample Output**

()[()]

Source:

**Northeastern Europe 2001**
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