We give the following inductive definition of a ˇ°regular bracketsˇ± sequence:
• the empty sequence is a regular brackets sequence,
• if s is a regularbrackets 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 ...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 ˇÜ n, ai1ai2 ...aim is a regular brackets sequence.
Given the initial sequence ([(])], the longest regular brackets subsequence is [()].
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 ˇ°endˇ± and should not be processed. For example:
((())) ()()() (]) )[)( ([) end
For each input case, the program should print the length of the longest possible regular brackets subsequence on a single line. For example:
6 6 4 0 6