We give the following inductive definition of a “regular brackets” sequence:</p>

• the empty sequence is a regular brackets sequence,
• if s is a regular brackets sequence, then (s) and [s] are regular brackets sequences, and
• if a and b are regular brackets sequences, then 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 a₁a₂...a_n, your goal is to find the length of the longest regular brackets sequence that is a subsequence of s. That is, you wish to find the largest m such that for indices i₁, i₂, . . . , i_m where 1 ≤ i₁ < i₂ < . . . < i_m ≤ n, a_i1 ai2</sub> . . . aim</sub> is a regular brackets sequence.</sub>

입력 형식

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 형식

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

힌트

Given the initial sequence ([([]])], the longest regular brackets subsequence is [([])].