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.io.IOException;
import java.io.InputStream;
import java.util.InputMismatchException;

public class Main {

	public static void main(String[] args) {
		Task task = new Task();
		task.solve();
	}

	public static class Task {
		static final long MOD = (long) 1e9 + 7;

		public void solve() {
			Scan sc = new Scan();
			int n = (int) sc.scanLong();
			char[] carr = new char[n];
			int[] whites = new int[n];
			for (int i = 0; i < n; ++i) {
				carr[i] = sc.scanChar();
				whites[i] = carr[i] == '.' ? 1 : 0;
				if (i > 0)
					whites[i] += whites[i - 1];
			}
			int res = whites[n - 1];
			for (int i = 0; i < n; ++i) {
				res = Math.min(res, whites[n-1]-whites[i] + (i+1-whites[i]));
			}
			System.out.println(res);
		}
	}

	public static class Scan {
		private byte[] buf = new byte[1024];
		private int index;
		private InputStream in;
		private int total;

		public Scan() {
			in = System.in;
		}

		public int scan() {
			if (total < 0)
				throw new InputMismatchException();
			if (index >= total) {
				index = 0;
				try {
					total = in.read(buf);
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
				if (total <= 0)
					return -1;
			}
			return buf[index++];
		}

		public long scanLong() {
			long integer = 0;
			int n = scan();
			while (isWhiteSpace(n))
				n = scan();
			int neg = 1;
			if (n == '-') {
				neg = -1;
				n = scan();
			}
			while (!isWhiteSpace(n)) {
				if (n >= '0' && n <= '9') {
					integer *= 10;
					integer += n - '0';
					n = scan();
				} else
					throw new InputMismatchException();
			}
			return neg * integer;
		}

		public double scanDouble() throws IOException {
			double doub = 0;
			int n = scan();
			while (isWhiteSpace(n))
				n = scan();
			int neg = 1;
			if (n == '-') {
				neg = -1;
				n = scan();
			}
			while (!isWhiteSpace(n) && n != '.') {
				if (n >= '0' && n <= '9') {
					doub *= 10;
					doub += n - '0';
					n = scan();
				} else
					throw new InputMismatchException();
			}
			if (n == '.') {
				n = scan();
				double temp = 1;
				while (!isWhiteSpace(n)) {
					if (n >= '0' && n <= '9') {
						temp /= 10;
						doub += (n - '0') * temp;
						n = scan();
					} else
						throw new InputMismatchException();
				}
			}
			return doub * neg;
		}

		public String scanString() {
			StringBuilder sb = new StringBuilder();
			int n = scan();
			while (isWhiteSpace(n))
				n = scan();
			while (!isWhiteSpace(n)) {
				sb.append((char) n);
				n = scan();
			}
			return sb.toString();
		}

		public char scanChar() {
			int n = scan();
			while (isWhiteSpace(n))
				n = scan();
			return (char) n;
		}

		private boolean isWhiteSpace(int n) {
			if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1)
				return true;
			return false;
		}
	}
}