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...a_n is called a subsequence of the string b_1b_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.

Examples