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>

typedef long long ll;

using namespace std;

const ll MOD = 1e9 + 7;

string s;
int c1, c2, ans, n;

int main()
{
    cin >> n >> s; ans = n;
    for (int i = 0; i < n; i++) c2 += (s[i] == '.');
    ans = min(ans, c1 + c2);
    for (int i = 0; i < n; i++)
    {
        c1 += (s[i] == '#');
        c2 -= (s[i] == '.');
        ans = min(ans, c1 + c2);
    }
    cout << ans;
}