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;

#define watch(x) cerr << (#x) << ": " << (x) << endl
#define int long long

int solve(vector<int>& nums, int i, int white_count) {
    int n = nums.size();
    if(i == n) return 0;

    int cand1 = nums[i] + solve(nums, i+2, white_count - nums[i+1]);
    return min(cand1, white_count);
}

int32_t main() {

    int n; cin >> n;
    string s; cin >> s;

    vector<int> nums;
    if(s[0] == '.') nums.push_back(0);

    int count = 1;
    for(int i = 1; i < n; ++i) {
        if(s[i] != s[i-1]) {
            nums.push_back(count);
            count = 1;
        } else {
            count++;
        }
    }
    nums.push_back(count);

    if(s.back() == '#') nums.push_back(0);
    int white_count = 0;
    for(int i = 1; i < (int)nums.size(); i+=2) {
        white_count += nums[i];
    }

    int ans = solve(nums, 0, white_count);

    cout << ans << endl;
    
    return 0;
}