Problem Statement

You are given a positive integer $N$ and a string $S$ of length $N$ consisting of +, 0, and -.

An integer sequence $A$ of length $N$ is called a happy sequence if the following conditions are satisfied for every $i ~ (1 \leq i \leq N)$.

• If the $i$-th character of $S$ is +, then $A_i > 0$.
• If the $i$-th character of $S$ is 0, then $A_i = 0$.
• If the $i$-th character of $S$ is -, then $A_i < 0$.

Find the maximum possible length of a longest increasing subsequence of a happy sequence of length $N$.

Here, a longest increasing subsequence of a sequence $X$ is a subsequence of $X$ (not necessarily contiguous) that is strictly increasing and has the maximum length among such subsequences.

Constraints

• $1 \leq N \leq 3 \times 10^5$
• $N$ is an integer.
• $S$ is a string of length $N$ consisting of +, 0, and -.

Input

The input is given from Standard Input in the following format.

$N$
$S$

Output

Output the maximum possible length of a longest increasing subsequence of a happy sequence of length $N$.

Sample

5
-+-+0

3

3
+0-

1

12
+-+-00+-+-00

5