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 <iostream>
#include <string>
#include <algorithm>
#include <vector>
#include <stack>
#include <queue>
#include <list>
#include <set>
#include <map>
#include <numeric>
#include <regex>
#include <tuple>
#include<iomanip>
using namespace std;

typedef long long ll;
typedef pair<int, int> P;
#define MOD 1000000007 // 10^9 + 7
#define INF 1000000000 // 10^9
#define LLINF 1LL<<60

int a[200009]; // a[i] : 1～i番目までの石のうち黒の個数

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);

	int N; cin >> N;
	a[0] = 0;
	for (int i = 1; i <= N; i++) {
		a[i] = a[i - 1];
		char tmp; cin >> tmp;
		if (tmp == '#') a[i]++;
	}


	int ans = INF;
	// すべて同じ色なら0
	if (a[N] == N) ans = 0;
	if (a[N] == 0) ans = 0;

	// i番目以降すべて黒
	for (int i = 1; i <= N+1; i++) {
		int tmp = a[i - 1] + N - i + 1 - (a[N] - a[i - 1]);
		ans = min(ans, tmp);
	}
	cout << ans << endl;

	return 0;
}