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>

const int MAX_N = 200000;

int main() {
	int N;
	std::string S;

	std::cin >> N >> S;

	static int black[MAX_N + 1] = {};
	for(int i = 1; i <= N; ++i) {
		if(S[i - 1] == '#') black[i] = black[i - 1] + 1;
		else black[i] = black[i - 1];
	}

	int ans = MAX_N;
	for(int i = 0; i <= N; ++i) {
		ans = std::min(ans, black[i] + N - i - black[N] + black[i]);
	}

	std::cout << ans << std::endl;
}