Problem Statement

You are given a string $S$ of length $N$ consisting of +,-,?. You will create an integer sequence $A$ of length $N$ according to the following rules.

Here, $S_i$ denotes the $i$-th character of the string $S$, and $A_i$ denotes the $i$-th element of the integer sequence $A$.

• If $S_i=$+, set $A_i=1$.
• If $S_i=$-, set $A_i=-1$.
• If $S_i=$?, set $A_i=1$ or $A_i=-1$.

For the created $A$, let $f(A)$ be the answer to the following problem.

There is an integer sequence $A$ of length $N$, and you can perform the following operation on $A$.

• Choose integers $l,r \ (1 \leq l \leq r \leq N)$ and multiply each of the values $A_l, A_{l+1}, \cdots , A_r$ by $-1$.

Find the minimum number of operations required to achieve the following condition.

• Condition: Let $B_i= \sum_{j=1}^{i} A_j$. For all $i$, $B_i \geq 0$ holds.

Find the minimum value of $f(A)$.

Input

$N$
$S$

• $1 \leq N \leq 2 \times 10^5$
• $S$ is a string of length $N$ consisting of +,-,?
• $N$ is an integer.

Output

Print the minimum value of $f(A)$ as an integer.

Sample

5
+--?-

1

4
??--

0

13
-?+++---?----

2