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;

int main(){
    int N;
    int black[200002] = {};
    int n_black = 0;
    string S;
    cin >> N >> S;

    for(int i=1;i<=N;i++){
        black[i] = black[i-1];
        if(S[i-1] == '#') black[i]++;
    }
    n_black = black[N];

    int ans = 2e5 + 1;
    for(int i=0;i<=N;i++){
        ans = min(ans, black[i] + (N-i) - (n_black - black[i]));
    }
    cout << ans << endl;
    return 0;
}