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>
#define all(x) begin(x), end(x)
#define dbg(x) cerr << #x << " = " << x << endl
#define _ << ' ' <<
using namespace std;
using ll = long long;
using vi = vector<int>;

int n;
string s;
int a[200001];
int dp[200001][3];

int f(int k, int p)
{
    if (k == n)
        return 0;
    if (dp[k][p] != -1)
        return dp[k][p];

    int sol = 1e9;
    if (p != 1) sol = min(sol, (a[k] != 0) + f(k + 1, 0));
    sol = min(sol, (a[k] != 1) + f(k + 1, 1));
    return dp[k][p] = sol;
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin >> n;
    cin >> s;
    for (int i = 0; i < n; ++i)
        a[i] = s[i] == '#';

    memset(dp, -1, sizeof dp);
    cout << f(0, 2);
}