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()
ans1 = 0
ans2 = 0
DP = [0 for i in range(N)]
s = s[::-1]
if s[0] == ".":
    DP[0] = 1

for i in range(1, N):
    DP[i] = DP[i - 1]
    if s[i] == ".":
        DP[i] += 1

ans = N * 20
DP = DP[::-1]


DP2 = [0 for i in range(N)]
s = s[::-1]
if s[0] == "#":
    DP2[0] = 1

for i in range(1, N):
    DP2[i] = DP2[i - 1]
    if s[i] == "#":
        DP2[i] += 1

ans = DP[0]
for i in range(1, N):
    #print(ans, DP[i] + DP2[i - 1])
    ans = min(ans, DP[i] + DP2[i - 1])
ans = min(ans, DP2[N - 1])
print(ans)