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<cmath>
#include<cstring>
#include<cstdio>
#include<cstdlib>
#include<vector>
#include<iomanip>
#define sqr(x) (x)*(x)
using namespace std;
int n,m,i,j,dp[500005],l;
string st;
int main()
{
	cin>>st>>st;
	st=" "+st;
	for (i=3;i<st.length();i++)
	{
		dp[i]=dp[i-1];
		if (st.substr(i-3+1,3)=="101")
		{
			l=i;
			for (j=i-2;st[j]=='1'&&j>0;j--)
			{
				dp[i]=max(dp[i],dp[j-1]+i-j-1);
			}
		}
		if (st[i]=='0') l=0;
		if (st[i]=='1'&&l)
		{
			 dp[i]=max(dp[i],dp[l-3]+i-l+1);
		}
	}
	cout<<dp[st.length()-1];
	return 0;
}