N cells are arranged in a row. Some of them may contain tokens. You are given a string s that consists of `0`s and `1`s. If the i-th character of s is `1`, the i-th cell (from left) contains a token. Otherwise, it doesn't contain a token.

Snuke wants to perform the following operation as many times as possible. In each operation, he chooses three consecutive cells. Let's call the cells X, Y, Z from left to right. In order for the operation to be valid, both X and Z must contain tokens and Y must not contain a token. Then, he removes these two tokens and puts a new token on Y.

How many operations can he perform if he performs operations in the optimal way?

Constraints

* 1 \leq N \leq 500,000
* |s| = N
* Each character in s is either `0` or `1`.

Input

Input is given from Standard Input in the following format:


N
s


Output

Print the answer.

Examples

Input

7
1010101


Output

2


Input

50
10101000010011011110001001111110000101010111100110


Output

10

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;

public class Main {

	static PrintWriter out;
	static InputReader ir;

	static void solve() {
		int n = ir.nextInt();
		char[] s = ir.next().toCharArray();
		ArrayList<Integer> l = new ArrayList<>();
		int res = 0;
		for (int i = 0; i < n; i++) {
			if (s[i] == '1') {
				int pre = i;
				while ((i < n && s[i] == '1') || (i < n - 1 && s[i] == '0' && s[i - 1] == '1' && s[i + 1] == '1')) {
					if (s[i] == '0') {
						l.add(i - pre);
						pre = i + 1;
					}
					i++;
				}
				l.add(i - pre);
				int[][] dp = new int[l.size()][4];
				for (int j = 0; j < l.size(); j++)
					Arrays.fill(dp[j], -(1 << 30));
				dp[0][0] = 0;
				for (int j = 1; j < l.size(); j++) {
					dp[j][0] = Math.max(Math.max(dp[j - 1][0], Math.max(dp[j - 1][1], dp[j - 1][2])), dp[j - 1][3]);
					if (l.get(j) != 1) {
						dp[j][1] = Math.max(Math.max(dp[j - 1][0] + l.get(j - 1), dp[j - 1][1] + l.get(j - 1) - 1),
								dp[j - 1][3] + 1);
						dp[j][2] = Math.max(Math.max(dp[j - 1][0] + l.get(j), dp[j - 1][1] + l.get(j)),
								dp[j - 1][3] + l.get(j));
						dp[j][3] = Math.max(Math.max(dp[j - 1][0] + l.get(j) - 1, dp[j - 1][1] + l.get(j) - 1),
								dp[j - 1][3] + l.get(j) - 1);
					} else {
						dp[j][2] = Math.max(
								Math.max(dp[j - 1][0] + l.get(j - 1), dp[j - 1][1] + Math.max(1, l.get(j - 1) - 1)),
								dp[j][3] + 1);
					}
				}
				// tr(dp);
				res += Arrays.stream(dp[l.size() - 1]).max().getAsInt();
				l.clear();
			}
		}
		out.println(res);
	}

	public static void main(String[] args) {
		ir = new InputReader(System.in);
		out = new PrintWriter(System.out);
		solve();
		out.flush();
	}

	static class InputReader {

		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;

		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}

		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}

		private int readByte() {
			if (hasNextByte())
				return buffer[curbuf++];
			else
				return -1;
		}

		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}

		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}

		public boolean hasNext() {
			skip();
			return hasNextByte();
		}

		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (!isSpaceChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}

		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}

		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public long[] nextLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}

	static void tr(Object... o) {
		out.println(Arrays.deepToString(o));
	}
}
