# 1255. Brackets sequence

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 $a_1a_2\ldots a_n$ 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 $1 \le j \le n$.

### 输入格式

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

### 输出格式

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.

### 样例

Input
([(]
Output
()[()]

18 人解决，23 人已尝试。

32 份提交通过，共有 66 份提交。

4.5 EMB 奖励。