D. Binary Sorting
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Given a binary string of length $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$). You can peform and operation which involves choosing $$$l$$$ and $$$r$$$ ($$$1 \le l \le r \le n$$$) and reversing the substring from $$$l$$$ to $$$r$$$. What is the minimum number of moves to sort the binary string (all $$$0$$$s should be before all $$$1$$$s)?

Input

First line contains a single number $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$).

Second line contains a string with $$$n$$$ characters, each either $$$0$$$ or $$$1$$$.

Output

Output a single number $$$X$$$, the minimum number of moves to sort the inputted binary string.

Example
Input
5
11010
Output
2
Note

We can first choose the range ($$$1, 5$$$), giving us the string $$$01011$$$ after the reversing operation. We then choose the range $$$(2, 3)$$$, giving us $$$00111$$$ which is fully sorted. There is no way to get to a fully sorted binary string in less operations.