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Language:
Brackets
 Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 7832 Accepted: 4158

Description

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

• 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 a1a2an, 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 < … < imn, ai1ai2aim is a regular brackets sequence.

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

Input

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.

Output

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

Sample Input

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

Sample Output

```6
6
4
0
6```

Source

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