Score : $300$ points

Problem Statement

There are $N$ stones arranged in a row. Every stone is painted white or black. A string $S$ represents the color of the stones. The $i$-th stone from the left is white if the $i$-th character of $S$ is ., and the stone is black if the character is #.

Takahashi wants to change the colors of some stones to black or white so that there will be no white stone immediately to the right of a black stone. Find the minimum number of stones that needs to be recolored.

Constraints

• $1 \leq N \leq 2\times 10^5$
• $S$ is a string of length $N$ consisting of . and #.

Input

Input is given from Standard Input in the following format:

$N$

$S$

Output

Print the minimum number of stones that needs to be recolored.

3
#.#

1

It is enough to change the color of the first stone to white.

5
#.##.

2

9
.........

0