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We give the following inductive definition of 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 … an, 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, …, im where 1 ≤ i1 < i2 < … < im ≤ n, ai1ai2 … aim is a regular brackets sequence.
Given the initial sequence
The input test file will contain multiple test cases. Each input test case consists of a single line containing only the characters
For each input case, the program should print the length of the longest possible regular brackets subsequence on a single line.
((())) ()()() (]) )[)( ([) end
6 6 4 0 6
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