## Brackets

• 문제 ID
• 시간 제한
• 메모리 제한
• 제출 횟수
• 정답 횟수 (비율)
• 출처
• 분류

#### 문제

We give the following inductive definition of a “regular brackets” sequence:

• the empty sequence is a regular brackets sequence,
• if s$s$ is a regular brackets sequence, then (s)$(s)$ and [s]$[s]$ are regular brackets sequences, and
• if a$a$ and b$b$ are regular brackets sequences, then ab$ab$ is a regular brackets sequence.
• no other sequence is a regular brackets sequence

For instance, all of the following character sequences are regular brackets sequences:

(), [], (()), ()[], ()[()]

while the following character sequences are not:

(, ], )(, ([)], ([(]

Given a brackets sequence of characters a_1, a_2, \cdots, a_n$a_1, a_2, \cdots, a_n$, your goal is to find the length of the longest regular brackets sequence that is a subsequence of s$s$. That is, you wish to find the largest m$m$ such that for indices i_1, i_2, \cdots, i_m$i_1, i_2, \cdots, i_m$ where 1 \le i_1 < i_2 < \cdots < i_m \le n$1 \le i_1 < i_2 < \cdots < i_m \le n$, a_{i_1}, a_{i_2}, \cdots, a_{i_m}$a_{i_1}, a_{i_2}, \cdots, a_{i_m}$ is a regular brackets sequence.

For an example, given the initial sequence ([([]])], the longest regular brackets subsequence is [([])].

#### 입력

The input test file will contain multiple test cases. Each input test case consists of a single line containing only the characters (, ), [, and ]; each input test will have length between 1 and 100, inclusive. The end-of-file is marked by a line containing the word “end” and should not be processed.

#### 출력

For each input case, the program should print the length of the longest possible regular brackets subsequence on a single line.

#### 예제 입력

((()))
()()()
([]])
)[)(
([][][)
end

#### 예제 출력

6
6
4
0
6