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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define int long long
typedef pair<int,int> P;
int INF = 1e9+7;
int mod = 100000;
int dx[4] = {1, 0, -1, 0};
int dy[4] = {0, 1, 0, -1};
signed main() {
    int N;
    string S;
    cin >> N >> S;
    vector<P>sum(N+1);
    int A = 0,B = 0;
    for(int i = 0; i < N; i++) {
        if(S[i] == '#') {
            A++;
            sum[i+1].first = sum[i].first+1;
            sum[i+1].second = sum[i].second;
        }
        else {
            B++;
            sum[i+1].second = sum[i].second+1;
            sum[i+1].first = sum[i].first;
        }
    }
    if(A == N || B == N) {
        cout << 0 << endl;
        return 0;
    }
    int ans = INF;
    for(int i = 0; i < N; i++) {
        int cnt = sum[i+1].first;
        cnt+=(B-sum[i].second);
        ans = min(ans,cnt);
    }
    // . . . . . . # # # # # #
    cout << ans << endl;
}