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>
using namespace std;
typedef long long int ll;
int n,dp[500100];
string s;
int main(){
    cin >> n >> s;
    s.resize(n+1);
    for(int i=n;i>=1;i--) s[i] = s[i-1];
    int prv = 0, prv2 = -1;
    for(int i=1;i<=n;i++){
        dp[i] = dp[i-1];
        if(s[i]=='0'){
            prv2 = prv;
            prv = i;
            continue;
        }
//        if(i<3) continue;
//        if(prv<=1) continue;
        if(prv2+1!=prv) dp[i] = max(dp[i],dp[prv-2]+i-prv);
        if(prv2+1!=prv && prv+1==i) dp[i] = max(dp[i],dp[prv2]+prv-prv2-1);
        if(prv2+2!=prv && prv+1==i) dp[i] = max(dp[i],dp[prv2+1]+prv-prv2-2);
    }
    cout << dp[n] << endl;
    return 0;
}
