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 main()
{
	int N;
	string S;
	cin >> N >> S;

	vector<int> bv( N );
	vector<int> wv( N );
	int w = 0;
	int b = 0;
	for( int i = 0; i < N; i++ ) {
		bv[i] = b;
		if( S[i] == '#' ) b++;
	}
	for( int i = N - 1; i >= 0; i-- ) {
		wv[i] = w;
		if( S[i] == '.' ) w++;
	}
	int ans = N;
	for( int i = 0; i < N; i++ ) {
		ans = min( ans, bv[i] + wv[i] );
	}

	cout << ans << endl;
}