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>
#define ll long long
#define pb push_back
using namespace std;
const int N=2e5+5;
int ans=1e9,n,dpa[N],dpb[N];
string s;
int main()
{
	ios::sync_with_stdio(false);
	cin>>n;
	cin>>s;
	for(int i=0;i<n;i++)
	{
		dpa[i+1]=dpa[i]+(s[i]=='.');
		dpb[i+1]=dpb[i]+(s[i]=='#');
	}
	for(int i=0;i<=n;i++)
	{
		int pnt=dpb[i]+dpa[n]-dpa[i];
		ans=min(ans,pnt);
	}
	cout<<ans<<endl;
	return 0;
}