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;
#define ll long long

int main(){
    int N;
    string S;
    cin >> N >> S;
    int b = count(S.begin(), S.end(), '#');
    int ans = N-b;
    int bcnt = 0;
    for (int i = 0; i < N; i++) {
        if (S[i] == '#') bcnt++;
        ans = min(ans, bcnt+(N-1-i-(b-bcnt)));
    }
    cout << ans << endl;
    return 0;
}