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>
using namespace std;
const int maxn=1000005;
int n,a[maxn],ans,chk;char s[maxn];
int main(){
	scanf("%d%s",&n,s+1);
	for (int i=1;i<=n;i++) a[i]=s[i]-'0';
	if(n==1){printf("%d\n",a[1]);return 0;}
	n--;
	for (int i=1;i<=n;i++){
		a[i]-=a[i+1];
		if(a[i]<0) a[i]=-a[i];
		if(a[i]==1&&(i-1&n-1)==i-1) ans^=1;
		if(a[i]==1) chk=1;
	}
	if(ans==1){puts("1");return 0;}
	if(chk==1){puts("0");return 0;}
	for (int i=1;i<=n;i++) a[i]>>=1;
	for (int i=1;i<=n;i++)
	if(a[i]==1&&(i-1&n-1)==i-1) ans^=1;
	puts(ans?"2":"0");
	return 0;
}