#include<bits/stdc++.h>
using namespace std;
int N, a[1001000], b[1001000];
string s;

void solve(int x) {
  if( x == 0) return;
  int k = 1;
  while(2*k <= x) k*=2;
  
  for(int i=0; i+k <= x; ++i) {
    b[i] = a[i] ^ a[i+k];
  }
  for(int i=0;i+k<=x;++i) a[i] = b[i];
  solve(x - k);
}

int main() {
  cin>>N>>s;
  int ok = 0;
  for(int i=0;i<N;++i) {
    if(s[i] == '2') ok = 1;
    a[i] = s[i] - '1'; 
  }
  if(ok) {
    for(int i=0;i<N;++i) {
      a[i] %= 2;
    }
  } else {
    for(int i=0;i<N;++i) {
      a[i] /= 2;
    }
  }
  
  solve(N-1);
  
  if(!ok) a[0] *= 2;
  cout<<a[0]<<endl;
  
  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;
int N, a[1001000], b[1001000];
string s;

void solve(int x) {
  if( x == 0) return;
  int k = 1;
  while(2*k <= x) k*=2;
  
  for(int i=0; i+k <= x; ++i) {
    b[i] = a[i] ^ a[i+k];
  }
  for(int i=0;i+k<=x;++i) a[i] = b[i];
  solve(x - k);
}

int main() {
  cin>>N>>s;
  int ok = 0;
  for(int i=0;i<N;++i) {
    if(s[i] == '2') ok = 1;
    a[i] = s[i] - '1'; 
  }
  if(ok) {
    for(int i=0;i<N;++i) {
      a[i] %= 2;
    }
  } else {
    for(int i=0;i<N;++i) {
      a[i] /= 2;
    }
  }
  
  solve(N-1);
  
  if(!ok) a[0] *= 2;
  cout<<a[0]<<endl;
  
  return 0;
}

```