P10472 Bracket Painter

Candela is a cartoonist. She has a strange hobby: drawing brackets on paper. One day, right after getting up, Candela drew a sequence of brackets in a row, containing parentheses `()` , square brackets `[]` , and curly braces `{}` , with total length $N$. This randomly drawn bracket sequence looks messy, so Candela defines what kinds of bracket sequences are “beautiful”: 1. The empty bracket sequence is beautiful. 2. If bracket sequence $A$ is beautiful, then `(A)` , `[A]` , and `{A}` are also beautiful. 3. If bracket sequences $A$ and $B$ are both beautiful, then `AB` is also beautiful. For example, `[(){}]()` is a beautiful bracket sequence, while `)({)[}](` is not. Now Candela wants to find a continuous segment in the bracket sequence she drew such that this substring is beautiful and its length is as large as possible. Can you help her?

The first line contains a bracket sequence of length $N$.

Output one integer, the length of the longest beautiful continuous substring.

Constraints: the testdata guarantees $5 \leq N \leq 10^4$. The values of $N$ in each test point are: $5, 10, 50, 100, 100, 1000, 1000, 10000, 10000, 10000$. Translated by ChatGPT 5