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>
using std::max;

const int MAXN=5e5+5;

int n;

char s[MAXN];
int f[MAXN],g[MAXN];

int main()
{
	int i;
	scanf("%d%s",&n,s+1);
	for(i=1;i<=n;i++)
		if(s[i]=='0') g[i]=i;
		else g[i]=g[i-1];
	for(i=3;i<=n;i++)
	{
		f[i]=f[i-1];
		if(s[i]=='0') continue;
		if(s[i-2]=='1'&&s[i-1]=='0')
		{
			f[i]=max(f[i],f[g[i-2]]+(i-2)-g[i-2]);
			f[i]=max(f[i],f[g[i-2]+1]+(i-2)-(g[i-2]+1));
		}else if(g[i]>1) if(s[g[i]-1]=='1')
			f[i]=max(f[i],f[g[i]-2]+i-g[i]);
	}
	printf("%d\n",f[n]);
	return 0;
}
