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 ] are 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

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