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;
int n,ans=0x3f3f3f3f,cnt1,cnt2;
string str;
int main()
{
	scanf("%d",&n);
	cin>>str;
	for(int i=0;i<n;i++)
		if(str[i]=='.') cnt2++;
	for(int i=0;i<n;i++)
	{
		ans=min(ans,cnt1+cnt2);
		if(str[i]=='#') cnt1++;
		else cnt2--;
	}
	ans=min(ans,cnt1+cnt2);
	printf("%d",ans);
	return 0;
}