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: Wrong Answer)

N = int(input())
S = input()
dp = [0 for i in range(N)]
b = 0
w = 0
flag1 = True
flag2 = True
for i in range(N):
    if flag1 and S[i] == '.':
        pass
    elif flag1:
        flag1 = False
        b += 1
    elif S[i] == '.':
        dp[i] = b
    else:
        b += 1

for i in reversed(range(N)):
    if flag2 and S[i] == '#':
        pass
    elif flag2:
        flag2 = False
        w += 1
    elif S[i] == '#':
        dp[i] = w
    else:
        w += 1
ans = float('inf')
for i in range(N-1):
    if (S[i] == '.' and S[i+1] == '#') or (S[i] == '#' and S[i+1] == '.'):
        if dp[i] == 0 or dp[i+1] == 0:
            ans = min(ans,dp[i]+dp[i+1])
        else:
            ans = min(ans,min(dp[i],dp[i+1]))
if ans == float('inf'):
    print(0)
else:
    print(ans)