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;
using ll = int64_t;
#define rep(i,n) for(int i = 0; i < ((int)(n)); i++)   // 0-indexed昇順

int main() {
    int N; cin >> N;
    string S; cin >> S;
    int L = 0, R = 0;
    rep(i,N) if (S[i] == '.') R++;
    ll mi = L + R;
    rep(i,N) {
        if (S[i] == '#') L++;
        else R--;
        if (mi > L+R) {
            mi = L+R;
        }
    }
    cout << mi << endl;
}