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<queue>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
typedef long long ll;
const int maxn=5e5+10;
const int INF=1e9;
char str[maxn];
int dp[maxn];
inline int read(){
	int x=0,flag=1;
	char ch=getchar();
	while(!isdigit(ch) && ch!='-')ch=getchar();
	if(ch=='-')flag=-1,ch=getchar();
	while(isdigit(ch))x=(x<<3)+(x<<1)+ch-'0',ch=getchar();
	return x*flag;
}
int main(){
	int i,j,k,m,n;
	n=read();
	scanf("%s",str+1);
	int flag=-1;
	for(i=3;i<=n;i++) {
		dp[i]=dp[i-1];
		if(str[i]=='1' && str[i-1]=='0' && str[i-2]=='1'){
			flag=i;
			for(j=i-2;str[j]=='1' && j>=1;j--)
				dp[i]=max(dp[i],dp[j-1]+i-j-1);
		}
		if(str[i]=='0')flag=-1;
		if(str[i]=='1' && flag!=-1)
			dp[i]=max(dp[i],dp[flag-3]+i-flag+1);
	}
	printf("%d\n", dp[n]);
	return 0;
}