#include <cstdio>

int n,a[1000001];
int main(){
	scanf("%d",&n);
	bool cando=0;
	for(int i=1;i<=n;i++)scanf("%1d",a+i),--a[i],cando|=(a[i]==1);
	for(int i=1;i<=n;i++)if(a[i]==2)a[i]=!cando;
	int ans=0;
//	for(int i=1;i<=n;i++)printf("%d ",a[i]);putchar('\n');
	for(int i=1;i<=n;i++)if(((n-i)&(i-1))==0)ans^=a[i];
	printf("%d\n",ans?(cando?1:2):0);
}
### Prompt

Your challenge is to write a cpp solution to the following 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

### Response

```cpp
#include <cstdio>

int n,a[1000001];
int main(){
	scanf("%d",&n);
	bool cando=0;
	for(int i=1;i<=n;i++)scanf("%1d",a+i),--a[i],cando|=(a[i]==1);
	for(int i=1;i<=n;i++)if(a[i]==2)a[i]=!cando;
	int ans=0;
//	for(int i=1;i<=n;i++)printf("%d ",a[i]);putchar('\n');
	for(int i=1;i<=n;i++)if(((n-i)&(i-1))==0)ans^=a[i];
	printf("%d\n",ans?(cando?1:2):0);
}
```