#include<bits/stdc++.h>
using namespace std;
const int N=1e6+5;
int n,i,j,a[N];
char c[N];
bool ck1(){
	int tot=0;
	for(i=1;i<=n;++i)tot^=a[i]&1&(((n-1)&(i-1))==i-1);
	return tot==1;
}
bool ck2(){
	int tot=0;
	for(i=1;i<=n;++i)if(a[i]&1)return 0;
	for(i=1;i<=n;++i)tot^=(a[i]&2?1:0)&(((n-1)&(i-1))==i-1);
	return tot==1;
}
int main(){
	scanf("%d%s",&n,c+1);for(i=1;i<n;++i)a[i]=abs(c[i]-c[i+1]);--n;
	printf("%d\n",ck1()?1:ck2()?2:0);
}
### Prompt

Please formulate 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<bits/stdc++.h>
using namespace std;
const int N=1e6+5;
int n,i,j,a[N];
char c[N];
bool ck1(){
	int tot=0;
	for(i=1;i<=n;++i)tot^=a[i]&1&(((n-1)&(i-1))==i-1);
	return tot==1;
}
bool ck2(){
	int tot=0;
	for(i=1;i<=n;++i)if(a[i]&1)return 0;
	for(i=1;i<=n;++i)tot^=(a[i]&2?1:0)&(((n-1)&(i-1))==i-1);
	return tot==1;
}
int main(){
	scanf("%d%s",&n,c+1);for(i=1;i<n;++i)a[i]=abs(c[i]-c[i+1]);--n;
	printf("%d\n",ck1()?1:ck2()?2:0);
}
```