Problem:
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.

Sample Input 1

3
#.#

Sample Output 1

1

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

Sample Input 2

5
#.##.

Sample Output 2

2

Sample Input 3

9
.........

Sample Output 3

0

Solution in Python (3.4.3) (judge verdict: Accepted)

N = int(input())
S = input()
d = [0] * (N+1)
s = [0] * (N+1)
for i, c in enumerate(S):
    if c=="#":
        s[i + 1] = s[i] + 1
        d[i+1] = d[i]
    else:
        s[i + 1] = s[i]
        d[i + 1] = d[i] + 1
#print(s, d)
ans = float("inf")
ddd = d[-1]
for ss, dd in zip(s[:-1],d[1:]):
    ans = min(ans, ss+(ddd-dd))

print(ans)