Problem: Given is a sequence of N digits a_1a_2\ldots a_N, where each element is 1, 2, or 3. Let x_{i,j} defined as follows:

* x_{1,j} := a_j \quad (1 \leq j \leq N)
* x_{i,j} := | x_{i-1,j} - x_{i-1,j+1} | \quad (2 \leq i \leq N and 1 \leq j \leq N+1-i)



Find x_{N,1}.

Constraints

* 2 \leq N \leq 10^6
* a_i = 1,2,3 (1 \leq i \leq N)

Input

Input is given from Standard Input in the following format:


N
a_1a_2\ldotsa_N


Output

Print x_{N,1}.

Examples

Input

4
1231


Output

1


Input

10
2311312312


Output

0

Solution (in CPP):

Solution:
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int N=1e6+10;
int n,cnt[N],sum[N],tmp=2,ans;
char a[N];
int main() {
	scanf("%d",&n); n--;scanf("%s",a);
	for(int i=0;i<=n;i++) {
		a[i]-='1';
		if(a[i]==1) tmp=1;
	}
	for(int i=1;i<=n;i++) 
		sum[i]=sum[i-1]+(cnt[i]=(i&1?0:cnt[i>>1]+1));
	for(int i=0;i<=n;i++)
		if(sum[n]==sum[i]+sum[n-i])
			(ans+=a[i]/tmp)&=1;
	printf("%d\n",ans*tmp); return 0;
}