Problem: 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.

Examples

Input

3
#.#


Output

1


Input

3
.#


Output

1


Input

5
.##.


Output

2


Input

9
.........


Output

0

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
typedef long long ll;
using namespace std;

int main() {
    int n;
    string s;
    cin >> n >> s;
    vector<int> d(n + 1);
    for (int i = 1; i < n + 1; ++i) {
        d[i] = d[i - 1] + (s[i - 1] == '.');
    }
    int ans = 1001001001;
    for (int i = 0; i < n + 1; ++i) {
        ans = min(ans, (i - d[i]) + (d[n] - d[i]));
    }
    cout << ans << endl;
}