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(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N; string S; cin >> N >> S;
    vector<int> cntb(N+1,0),cntw(N+1,0);
    for (int i=0;i<N;++i) cntb[i+1]=cntb[i]+(S[i]=='#');
    for (int i=N-1;i>=0;--i) cntw[i]=cntw[i+1]+(S[i]=='.');
    int ans=N;
    for (int i=0;i<=N;++i) ans=min(ans,cntb[i]+cntw[i]);
    cout << ans << '\n';
}