#include<bits/stdc++.h>
using namespace std;

typedef long long LL;

const int N=1000000;

int n;
char s[N+9];

void into(){
  scanf("%d%s",&n,s+1);
}

int Lucas(int n,int m){
  if (n<m||m<0) return 0;
  return n<2?1:(n&1)>=(m&1)&&Lucas(n>>1,m>>1);
}

int a[N+9],c1;

void Get_a(){
  for (int i=1;i<=n;++i) c1+=(a[i]=s[i]-'1')==1;
}

int ans;

void Get_ans(){
  for (int i=1;i<=n;++i) a[i]=a[i]>>!c1&1;
  for (int i=1;i<=n;++i) ans^=a[i]&Lucas(n-1,i-1);
  ans<<=!c1;
}

void work(){
  Get_a();
  Get_ans();
}

void outo(){
  printf("%d\n",ans);
}

int main(){
  into();
  work();
  outo();
  return 0;
}
### Prompt

Develop a solution in Cpp 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;

typedef long long LL;

const int N=1000000;

int n;
char s[N+9];

void into(){
  scanf("%d%s",&n,s+1);
}

int Lucas(int n,int m){
  if (n<m||m<0) return 0;
  return n<2?1:(n&1)>=(m&1)&&Lucas(n>>1,m>>1);
}

int a[N+9],c1;

void Get_a(){
  for (int i=1;i<=n;++i) c1+=(a[i]=s[i]-'1')==1;
}

int ans;

void Get_ans(){
  for (int i=1;i<=n;++i) a[i]=a[i]>>!c1&1;
  for (int i=1;i<=n;++i) ans^=a[i]&Lucas(n-1,i-1);
  ans<<=!c1;
}

void work(){
  Get_a();
  Get_ans();
}

void outo(){
  printf("%d\n",ans);
}

int main(){
  into();
  work();
  outo();
  return 0;
}
```