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>
const int INF=1e9,MOD=1e9+7;
const long long LINF=1e18;
using namespace std;
#define int long long
//template
//main
signed main(){
  int N;string s;cin>>N>>s;
  std::vector<int> v(N+1,0);
  for(int i=0;i<N;i++)v[i+1]=v[i]+(s[i]=='#');
  int ans=LINF;
  for(int i=0;i<=N;i++)ans=min(ans,v[i]-v[0]+N-i-(v[N]-v[i]));
  cout<<ans<<endl;
}