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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define rep(i,l,r) for(int i=l; i<(int)(r); i++)
#define rep_eq(i,l,r) for(int i=l; i<=(int)(r); i++)
#define all(vec) vec.begin(),vec.end()
#define allr(vec) vec.rbegin(),vec.rend()
using namespace std;

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

using ll=int64_t;

using vb=vector<bool>;
using vc=vector<char>;
using vs=vector<string>;
using vi=vector<int>;
using vll=vector<ll>;
using vvi=vector<vi>;

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);

  int N; string S; cin >>N >>S;
  vi left(N+1);
  vi right(N+1);
  rep(i,0,N) {
    if (S[i]=='#') {
      left[i+1]=left[i]+1;
    } else {
      left[i+1]=left[i];
    }
    if (S[N-i-1]=='.') {
      right[N-i-1]=right[N-i]+1;
    } else {
      right[N-i-1]=right[N-i];
    }
  }

  int ans=INT_MAX;
  rep(i,0,N+1) {
    chmin(ans,left[i]+right[i]);
  }

  cout <<ans <<'\n';
  return 0;
}