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)

# coding: utf-8

N = int(input())
S = input().strip()

def stone_cnt(idx):
  return S[:idx].count("#") + S[idx:].count(".")

left = 0
right = len(S)

while left <= right:
  mid = (left + right) // 2
  if stone_cnt(left) > stone_cnt(right):
    left = mid + 1
  else:
    right = mid - 1

print(stone_cnt(mid))