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: Accepted)

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> pll;

int main() {
  ll n;
  cin >> n;
  string s;
  cin >> s;
  vector<ll> count(n+1);
  for(ll i=0;i<n;i++) {
    if(s[i]=='#') {
      count[i+1]=count[i]+1;
    }
    else {
      count[i+1]=count[i];
    }
  }
  ll ans=n;
  for(ll i=0;i<n+1;i++) {
    ans=min(ans,count[i]+(n-i-(count[n]-count[i])));
  }
  cout << ans << endl;
}