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
#include <stdio.h>

int max(int a, int b) {
	return a > b ? a : b;
}

char s[501010];
int next[501010] = {};
int back[501010] = {};
int f[501010] = {};

int main() {
	int n;


	scanf("%d", &n);
	scanf("%s", s);

	int bk = -1;
	int i;
	for (i = 0; i < n; i++) {
		back[i] = bk;
		if (s[i] == '0') bk = i;
	}

	int nx = n;
	for (i = n - 1; i >= 0; i--) {
		next[i] = nx;

		if (s[i] == '0') nx = i;
	}

	for (i = 0; i < n; i++) {
		f[i] = max(f[i - 1], f[i]);

		if (s[i] == '1') {
			if (back[i] >= 1 && s[back[i] - 1] == '1') {
				int c = i - back[i];
				f[i] = max(f[i], f[back[i] - 2] + c);
			}

			if (next[i] < n - 1 && s[next[i] + 1] == '1') {
				int c = next[i] - i;
				f[next[i] + 1] = max(f[next[i] + 1], f[i - 1] + c);
			}
		}
	}

	printf("%d", f[n - 1]);

	getchar(); getchar();

}