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;
typedef pair<ll,ll> pll;

int main() {
  ll n;
  cin >> n;
  string s;
  cin >> s;
  vector<ll> count(n+1);
  for(ll i=0;i<n;i++) {
    if(s[i]=='#') {
      count[i+1]=count[i]+1;
    }
    else {
      count[i+1]=count[i];
    }
  }
  ll ans=n;
  for(ll i=0;i<n+1;i++) {
    ans=min(ans,count[i]+(n-i-(count[n]-count[i])));
  }
  cout << ans << endl;
}