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>
using namespace std;
typedef long long ll;

int main() {
    int N;
    string S;
    cin >> N >> S;
    
    vector<int> white(N + 1, 0);
    for (int i = 1; i <= N; ++i) {
        white[i] = white[i - 1] + (S[i - 1] == '.' ? 1 : 0);
    }
    int ans = N;
    for (int i = 0; i <= N; ++i) {
        ans = min(ans, white[N] + i - 2 * white[i]);
    }

    cout << ans << endl;

    return 0;
}