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Задачі

Brackets Sequence

Brackets Sequence

Ліміт часу 1 секунда
Ліміт використання пам'яті 16 MiB

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 1i_1 < i_2 < ... < i_nm, that a_j=b_ij for all 1jn.

Вхідні дані

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

Вихідні дані

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

Приклад

Вхідні дані #1
([(]
Вихідні дані #1
()[()]
Автор Andrew Stankevich
Джерело 2001-2002 ACM Northeastern European Regional Programming Contest