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<iostream>
#include<string>

using namespace std;

int main()
{
	int N;
	string S;

	cin >> N >> S;

	int *w,*b;

	w = new int[N+1];
	b = new int[N+1];

	int ans = N;

	int cntw = 0,cntb = 0;

	w[0] = 0;
	b[0] = 0;

	for(int i=1;i<=N;i++)
	{
		if(S[i-1] == '#')cntb++;
		if(S[i-1] == '.')cntw++;
		b[i] = cntb;
		w[i] = cntw;
	}

	for(int i=0;i<N+1;i++)
	{	
		ans = min(ans,b[i]+w[N]-w[i]);
	}

	cout << ans << endl;

	return 0;
}