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<algorithm>
#define RI register int
#define CI const int&
using namespace std;
const int N=1e6+5;
int n,b[N],ret; char a[N]; bool one;
int main()
{
	RI i,j; for (scanf("%d%s",&n,a),--n,i=0;i<n;++i) b[i]=abs(a[i]-a[i+1]);
	for (i=0;i<n;++i) if (b[i]==1) one=1;
	if (!one) { for (i=0;i<n;++i) if (b[i]==2) b[i]=1; }
	else for (i=0;i<n;++i) b[i]%=2;
	//for (i=0;i<n;++i) printf("%d",b[i]);
	for (i=0;i<n;++i) if (((n-1)^i)==n-1-i) ret^=b[i];
	return printf("%d",ret*(one?1:2)),0;
}