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 n, ans, w[1000000], b[1000000];
char s[1000000];

int main(){
    cin >> n;
    for (int i = 1; i <= n; i++) cin >> s[i];
    for (int i = 1; i <= n; i++){
        if (s[i] == '.') w[i] = w[i - 1] + 1, b[i] = b[i - 1];
        else w[i] = w[i - 1], b[i] = b[i - 1] + 1;
    }
    ans = 1e9;
    for (int i = 0; i <= n; i++){
        ans = min(ans, b[i] + w[n] - w[i]);
    }
    cout << ans;
}