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<bits/stdc++.h>
#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define pii pair<int,int>
#define C 0.5772156649
#define pi acos(-1.0)
#define ll long long
#define mod 1000000007
#define ls l,m,rt<<1
#define rs m+1,r,rt<<1|1

using namespace std;

const double g=10.0,eps=1e-9;
const int N=500000+10,maxn=1000000+10,inf=0x3f3f3f;

char s[N];
int dp[N];
int main()
{
    int n,last=0;
    scanf("%d%s",&n,s);
    for(int i=2;i<n;i++)
    {
        dp[i]=max(dp[i],dp[i-1]);
        if(s[i-2]=='1'&&s[i-1]=='0'&&s[i]=='1')
        {
            last=i;
            for(int j=i-2;j>=0&&s[j]=='1';j--)dp[i]=max(dp[i],dp[j-1]+i-j-1);
        }
        if(s[i]=='0')last=0;
        if(last!=0)dp[i]=max(dp[i],dp[last-3]+i-last+1);
       // cout<<last<<endl;
    }
    printf("%d\n",dp[n-1]);
    return 0;
}
/****************
6
101011
****************/
