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>
#define rep(i,n) for (int i = 0; i < (n); ++i)
using namespace std;
typedef long long ll;
const int INT_INF = 2147483647;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }

int main(){
  int n;
  cin >> n;
  char s[n];
  rep(i,n)cin >> s[i];
  vector<int>v;
  rep(i,n){
    if(s[i]=='#')v.push_back(i);
  }
  vector<int> ans;
  rep(i,v.size()){
    int t=0;
    t+=i;
    t+=n-v[i]-1-(v.size()-(i+1));
    ans.push_back(t);
  }
  ans.push_back(v.size());
  ans.push_back(n-v.size());
  int res = 1000000;
  rep(i,ans.size()){
    //cout << ans[i] << endl;
    chmin(res,ans[i]);
  }
  cout << res << endl;
}