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, e[300010], w[300010], pe=0, pw=0;

int main(void){
    string s;
    cin >> n >> s;
    for(int i=0;i<n;++i){
        if(s[i]=='#') ++pw;
        w[i] = pw;
    }
    for(int i=n-1;i>=0;--i){
        if(s[i]=='.') ++pe;
        e[i] = pe;
    }
    int min = 800010;
    for(int i=0;i<n;++i){
        if(min > (w[i]+e[i]-1)) min = w[i]+e[i]-1;
    }
    cout << min << endl;
}