Problem Statement

A correct parenthesis sequence is defined as follows.

・The empty string is a correct parenthesis sequence.
・If a string $s$ is a correct parenthesis sequence, then '(' $+\ s\ +$ ')' is a correct parenthesis sequence.
・If strings $s,t$ are correct parenthesis sequences, then $s+t$ is a correct parenthesis sequence.

For example, "(())()", "(((())))", and so on are correct parenthesis sequences.

You are given a string $S$ of length $N$ consisting of '(' and ')'. For $1\le i\le N$, let $S_i$ denote the contiguous subsequence of $S$ from the $1$-st character to the $i$-th character. Let $T$ be a string obtained by concatenating $S_1,S_2,\cdots ,S_N$ in any order of your choice. Let $f(T)$ be the maximum length of a string that is a subsequence of $T$ and is a correct parenthesis sequence. Find the maximum value of $f(T)$.

※A subsequence of $S$ means a string obtained by deleting some characters from $S$ and joining the remaining characters without changing their order.

Input

$N$
$S$

$1\le N\le 10^5$
$S$ is a string of length $N$ consisting of '(' and ')'

Output

Find the maximum value of $f(T)$. Print a newline at the end.

Sample

3
)((

4

5
)))))

0

10
(((()))()(

34