Problem Statement

Given is a string $S$ of length $N$ consisting of lowercase English letters. Snuke can do this operation any number of times: remove fox occurring as a substring from $s$ and concatenate the remaining parts of $s$.

What is the minimum possible length of $s$ after some number of operations by Snuke?

Constraints

• $1 \leq N \leq 2 \times 10^{5}$
• $s$ is a string of length $N$ consisting of lowercase English letters.

Input

Input is given from Standard Input in the following format:

N
s

Print

Print the minimum possible length of $s$ after some number of operations by Snuke.