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)

from collections import defaultdict, Counter
from itertools import product, groupby, count, permutations, combinations
from math import pi, sqrt
from collections import deque
from bisect import bisect, bisect_left, bisect_right
from string import ascii_lowercase
from functools import lru_cache
import sys
sys.setrecursionlimit(10000)
INF = float("inf")
YES, Yes, yes, NO, No, no = "YES", "Yes", "yes", "NO", "No", "no"
dy4, dx4 = [0, 1, 0, -1], [1, 0, -1, 0]
dy8, dx8 = [0, -1, 0, 1, 1, -1, -1, 1], [1, 0, -1, 0, 1, 1, -1, -1]


def inside(y, x, H, W):
    return 0 <= y < H and 0 <= x < W


def ceil(a, b):
    return (a + b - 1) // b


# 初項s, 交差dのn個の数列の和
def sum_of_arithmetic_progression(s, d, n):
    return n * (2 * s + (n - 1) * d) // 2


# aとbの最大公約数
def gcd(a, b):
    if b == 0:
        return a
    return gcd(b, a % b)


# aとbの最小公倍数
def lcm(a, b):
    g = gcd(a, b)
    return a / g * b


def main():
    N = int(input())
    S = input()

    total_b = S.count("#")
    total_w = S.count(".")
    ans = min(total_b, total_w)
    b, w = 0, 0
    for i in range(N):
        left_b = b
        right_w = total_w - w
        ans = min(ans, left_b + right_w)

        if S[i] == "#":
            b += 1
        else:
            w += 1

    print(ans)


if __name__ == '__main__':
    main()