**18 人解决**，22 人已尝试。

**32 份提交通过**，共有 64 份提交。

**4.3** EMB 奖励。

**单点时限: **2.0 sec

**内存限制: **256 MB

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 $a_1a_2\ldots a_n$ is called a subsequence of the string $b_1b_2 \ldots b_m$, if there exist such indices $1 \le i_1 < i_2 < \cdots < i_n \le m$, that $a_j=b_{i_j}$ for all $1 \le j \le n$.

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

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.

Input

([(]

Output

()[()]