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;

typedef long long ll;
const int INF = 1e9;
const ll INFF = 1e18;
const int MAXN = 510;
const int MOD = 1e9 + 7;

int tab[200010];

int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	vector< pair<int,int> > q;
	int n;
	cin >> n;
	for (int i = 1 ; i <= n ; i++)
	{
		char ta;
		cin >> ta;
		if (ta == '.')
			tab[i] = 0;
		else
			tab[i] = 1;
	}
	int now = tab[1];
	int cnt = 0;
	for (int i = 1 ; i <= n ; i++)
	{
		if (tab[i] != now)
		{
			q.push_back(make_pair(now,cnt));
			now = tab[i];
			cnt = 1;
		}
		else
			++cnt;
	}
	q.push_back(make_pair(now,cnt));
	int ans = 0;
	// cout << q.size() << endl;
	for (int i = 0 ; i + 1 < q.size() ; i++)
	{
		if (q[i].first == q[i + 1].first)
		{
			q[i + 1].second += q[i].second;
			continue;
		}
		if (q[i].first == 0) continue;
		if (q[i].second < q[i + 1].second)
		{
			ans += q[i].second;
			q[i].first ^= 1;
		}
		else
		{
			ans += q[i + 1].second;
			q[i + 1].first ^= 1;
		}
	}
	cout << ans << endl;
}