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()

b = [0] * N
w = [0] * N

for i, s in enumerate(S):
    if s == "#":
        b[i] += 1
    elif s == ".":
        w[i] += 1

def accmulate(arr):
    N = len(arr)
    cs = [0]*(N+1)
    for i in range(N):
        cs[i+1] = cs[i] + arr[i]
    return cs

# [l,r)
def query(cs, l, r):
    return cs[r] - cs[l]

b = accmulate(b)
w = accmulate(w)
ans = N

for k in range(N+1):
    res = b[k] + (w[N] - w[k])
    ans = min(ans, res)
    
print(ans)