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5.1 Description
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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 a_{1}a_{2} ...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 i_{1},i_{2},...,i_{m} where 1 ≤ i_{1} < i_{2} < ...< i_{m} ˇÜ n, a_{i1}a_{i2} ...a_{im} is a regular brackets sequence.

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

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5.3 Input
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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

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5.4 Output
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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