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 <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
using namespace std;
char s[1000005];
int f[1000005],g[1000005],len,cnt;
int main() {
    scanf("%d%s",&len,s+1);
    f[0]=cnt=0;    
    for (int i=1;i<=len;i++) {
	if (s[i]=='0') cnt=0;
	else cnt++;
	g[i]=cnt;
	f[i]=f[i-1];
	if (cnt==0) continue;
	if (i-cnt-1>0&&s[i-cnt-1]=='1') f[i]=max(f[i],f[i-cnt-2]+cnt);
	if (i>1&&s[i-1]=='0')
	    for (int j=1;j<=g[i-2];j++) f[i]=max(f[i],f[i-j-2]+j);
    }
    printf("%d\n",f[len]);
    return 0;
}
