"Brackets sequence"

Time Limit: 1000MS Memory Limit: 65536KB

Problem Description

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.


Each line of input contains a single testcase. Testcase consists of at most 200 brackets (characters '(', ')', '[' and ']') that are situated on a single line without any other characters among them.


For each input line write to the output a single line that contains some regular brackets sequence that has the minimal possible length and contains the given sequence as a subsequence.

Example Input


Example Output