Making a Monochrome String

You are given a binary string $S$ of length $N$. A binary string is a string whose every character is either $`0`$ or $`1`$.

In one operation, you may choose a non-empty contiguous substring $T$ of the current string such that the number of $`0`$s in $T$ is equal to the number of $`1`$s in $T$, and delete it. After deletion, the remaining prefix and suffix are concatenated.

A string is called monochrome if it satisfies one of the following conditions.

• The string is empty.
• Every character of the string is $`0`$.
• Every character of the string is $`1`$.

Find the minimum number of operations required to make $S$ monochrome.

The input is given in the following format.

$N$

$S$

Print the minimum number of operations required to make $S$ monochrome.

• $1 \le N \le 200\,000$.
• $S$ is a binary string of length $N$.