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<algorithm>
#include<string.h>
using namespace std;
int cnt[500050];
char s[500050];
int ans[500050];
int main()
{
	int n;
	cin>>n;
	for(int i=1;i<=n;i++) cin>>s[i];
	for(int i=1;i<=n;i++)if(s[i]=='0')cnt[i]=i;
		else cnt[i]=cnt[i-1];
	for(int i=1;i<=n;i++){
		ans[i]=ans[i-1];
		if(s[i]=='1'){
			if(s[i-1]=='0'&&s[i-2]=='1'){
				ans[i]=max(ans[i],ans[cnt[i-2]]+i-2-cnt[i-2]);
				ans[i]=max(ans[i],ans[cnt[i-2]+1]+i-2-cnt[i-2]-1);}
			if(s[cnt[i]-1]=='1'){
				ans[i]=max(ans[i],ans[cnt[i]-2]+i-cnt[i]);}}}
	cout<<ans[n];
	
	return 0;
 } 