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>
#define N 500010
#define O 48
#define MAX(a,b) (a>(b)?a:(b))
int n,f[N];
char s[N];
signed main()
{
	scanf("%d%s",&n,s+1);int now(0),cnt(0),mn(0);
	for(register int i(1);i<=n;i++)
		f[i]=f[i-1],s[i]-O?(s[i-1]==O?f[i]=MAX(f[i],cnt+mn),cnt=mn=0:8,now>0&&s[now]-O?f[i]=MAX(f[i],f[now-1]+cnt+1):8,mn=MAX(mn,f[i-1]-cnt),++cnt):(s[i-1]==O?cnt=mn=0:8,now=i-1);
	return printf("%d\n",f[n]),0;
}