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 <bits/stdc++.h>
using namespace std;

//repetition
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i, n) for(int i = 0; i < (int)(n); i++)

//container util
#define all(x) (x).begin(),(x).end()

//typedef
typedef long long ll;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<ll> VLL;
typedef vector<VLL> VVLL;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef pair<ll, ll> PLL;


//conversion
inline int toInt(string s) {int v; istringstream sin(s);sin>>v;return v;}
template<class T> inline string toString(T x) {ostringstream sout;sout<<x;return sout.str();}


int main(){
  int n;
  string s;
  cin >> n >> s;
  bool flag = true;
  int cnt = 0;
  int a[n];
  rep(i,n){
    if(s[i] == '.') a[i] = 1;
    else a[i]= 0;
  }
  rep(i,n-1) a[i+1] += a[i];


  rep(i,n){
    if(flag == false){
      if(s[i] == '.') cnt++;
      //cout << 3 << endl;
      continue;
    }
    if(s[i] == '#'){
      if((n-i) - (a[n-1] - a[i]) >= (n-i)/2 ){
        flag = false;
      //  cout << 1 << endl;
      }else{
        cnt++;
    //    cout << 2 << endl;
      }
    }
  }

  cout << cnt << endl;
  return 0;
}