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 JAVA):

Solution:
import java.util.*;
class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = Integer.parseInt(sc.next());
        String S = sc.next();
        int[] blackCnt = new int[N+1];
        int[] whiteCnt = new int[N+2];
        blackCnt[0] = 0;
        whiteCnt[N+1] = 0;
        int w = 0;

        for(int i = 1; i<N+1; i++) {
            char c = S.charAt(i-1);
            blackCnt[i] = blackCnt[i-1];
            if(c == '#') blackCnt[i] += 1;
            if(c == '.') w++;
            //            System.out.println("b " + i + " " + blackCnt[i]);
        }
        whiteCnt[0] = w;
        for(int i = 1; i<N+1; i++) {
            char c = S.charAt(i-1);
            whiteCnt[i] = whiteCnt[i-1];
            if(c == '.') {
                whiteCnt[i] -= 1;
            }
            //            System.out.println("w " + i + " " + whiteCnt[i]);
        }

        int min = Integer.MAX_VALUE;
        for(int i = 1; i<N+1; i++) {
            min = Math.min(min, blackCnt[i-1]+whiteCnt[i]);
            //            System.out.println(min);
        }
        System.out.println(min);
    }
}