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;
using ll = long long;
#define rep(i, n) for(int i=0; i < n; i++)

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);
	int n;
	cin>>n;
	string s;
	cin>>s;
	vector<int> a(n+1), b(n+1);
	rep(i,n)a[i+1]=s[i]=='#';
	rep(i,n)b[i+1]=s[i]=='.';
	rep(i,n)a[i+1]+=a[i];
	rep(i,n)b[i+1]+=b[i];
	int ans = n;
	rep(i,n+1)ans = min(ans, a[i] + b[n]-b[i]);
	cout<<ans<<endl;
}