Problem Statement

A string consisting of $0$ and $1$ is called a good string $X$ when the following condition is satisfied.

• For every contiguous substring $Y$ of $X$ with length at least 2, the number of $0$ in $Y$ is less than or equal to the number of $1$ in $Y$.

For example, $101$ is a good string. On the other hand, $10011$ contains $00$ as a substring, and the number of $0$ in this string (2) is greater than the number of $1$ (0), so it is not a good string.

You are given a string $S$ of length $N$ consisting of $0$ and $1$. In one operation, you can choose one $0$ in $S$ and change it to $1$.

Find the minimum number of operations required to make $S$ a good string.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $S$ is a string of length $N$ consisting only of $0$ and $1$
• $N$ is an integer

Input

The input is given from standard input in the following format.

$N$
$S$

Output

Print on one line the minimum number of operations required to make $S$ a good string, followed by a newline.

Sample

5
01001

1

6
111111

0

10
1010010001

3