#include<bits/stdc++.h>
using namespace std;
const int maxn=1001000;
inline int C(int n,int m)
{
	if(n<m) return 0;
	if(n<=1) return 1;
	return C(n%2,m%2)&C(n/2,m/2);
}
int n,flag=0,v[maxn];
int main()
{
	cin>>n;char c;int ans=0;
	for(int i=1;i<=n;i++) cin>>c,v[i]=c-'0'-1;
	for(int i=1;i<=n;i++) if(v[i]==1) {flag=1;break;}
	if(flag) {for(int i=1;i<=n;i++) if(v[i]==1&&C(n-1,i-1)) ans^=1;}
	else {for(int i=1;i<=n;i++) if(v[i]==2&&C(n-1,i-1)) ans^=2;}
	printf("%d\n",ans);
}
### Prompt

Please provide a CPP coded solution to the problem described below:

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<bits/stdc++.h>
using namespace std;
const int maxn=1001000;
inline int C(int n,int m)
{
	if(n<m) return 0;
	if(n<=1) return 1;
	return C(n%2,m%2)&C(n/2,m/2);
}
int n,flag=0,v[maxn];
int main()
{
	cin>>n;char c;int ans=0;
	for(int i=1;i<=n;i++) cin>>c,v[i]=c-'0'-1;
	for(int i=1;i<=n;i++) if(v[i]==1) {flag=1;break;}
	if(flag) {for(int i=1;i<=n;i++) if(v[i]==1&&C(n-1,i-1)) ans^=1;}
	else {for(int i=1;i<=n;i++) if(v[i]==2&&C(n-1,i-1)) ans^=2;}
	printf("%d\n",ans);
}
```