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

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

### Output

Write a single line that contains some regular brackets sequence
that has the minimal possible length and contains the given sequence as a
subsequence.

### Sample

**Problem Author: **Andrew Stankevich

**Problem Source: **2001-2002 ACM Northeastern European Regional Programming Contest