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 *a*_{1}*a*_{2} … *a _{n}*, your goal is to find the length of the longest regular brackets sequence that is a subsequence of

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 “end” and should not be processed.

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
```