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 <cstdio>
#include <cstring>
#include <iostream>
#include <string>
#include <cmath>
#include <bitset>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <algorithm>
using namespace std;
typedef long long int ll;
typedef pair<int, int> P;

int main()
{
	int n;
	cin>>n;
	string s;
	cin>>s;
	int dp[500001];
	dp[0]=0, dp[1]=0;
	int i0=-1;
	if(s[1]=='0') i0=1;
	for(int i=2; i<n; i++){
		dp[i]=dp[i-1];
		if(s[i]=='1'){
			if(i0==-1 || s[i0-1]=='0') continue;
			if(i0==i-1){
				for(int j=i-2; j>=0; j--){
					if(s[j]=='0') break;
					if(j>0) dp[i]=max(dp[j-1]+i-1-j, dp[i]);
                  else dp[i]=max(i-1, dp[i]);
				}
			}else{
				if(i0==1) dp[i]=max(i-1, dp[i]);
				else dp[i]=max(dp[i0-2]+i-i0, dp[i]);
			}
		}else{
			i0=i;
		}
	}
	cout<<dp[n-1]<<endl;
	return 0;
}