### "Brackets sequence"

#### Problem Description

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 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 a_{1}a_{2}...a_{n} is called a subsequence of the string b_{1}b_{2}...b_{m}, if there exist such indices 1 ≤ i_{1} < i_{2} < ... < i_{n} ≤ m, that a_{j}=b_{ij} for all 1 ≤ j ≤ n.

#### Input

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.

#### Output

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.

#### Sample Input

([(]

#### Sample Output

()[()]