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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>
#include<vector>
using namespace std;

int main(void){
  long n;
  string s;
  cin >> n >> s;
  long  ans = n;
  long n_b = 0;
  long n_all_b = 0;
  for( string::iterator itr=s.begin(); itr!=s.end(); ++itr){
    if( *itr == '#') n_all_b++;
  }
  for( long i=0; i<n; ++i){
    if( s[i] == '#') n_b++;
    if( ans > n_b + ( (n - (i+1)) - (n_all_b - n_b) ) ){
      ans = n_b + ( (n - (i+1)) - (n_all_b - n_b) );
    }
  }
  cout << ans << endl;
  return 0;
}