UVA1626 DP经典

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.
Input
The input begins with a single positive integer on a line by itself indicating the number of the cases
following, each of them as described below.
This line is followed by a blank line, and there is also a blank line between two consecutive inputs.
The input file contains at most 100 brackets (characters ‘(’, ‘)’, ‘[’ and ‘]’) that are situated on a
single line without any other characters among them.
Output
For each test case, the output must foll