#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i = 0; i < (int)n; i++)
using ll = long long;

int main(){  
  int n;
  cin >> n;
  string s;
  cin >> s;
  vector<int> a(n);
  bool one = false;
  rep(i,n) {
    a[i] = s[i] - '1';
    if(a[i] == 1) one = true;
  }
  if(!one) {
    rep(i,n) a[i] /= 2;
  }
  int m = 0;
  rep(i,n) {
    if(n-1 == (i | (n-1-i))) m += a[i]; 
  }
  if(one && (m % 2)) cout << 1 << endl;
  else if(one && !(m % 2)) cout << 0 << endl;
  else if(!one && (m % 2)) cout << 2 << endl;
  else cout << 0 << endl;
  return 0;
}

### 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;
#define rep(i,n) for(int i = 0; i < (int)n; i++)
using ll = long long;

int main(){  
  int n;
  cin >> n;
  string s;
  cin >> s;
  vector<int> a(n);
  bool one = false;
  rep(i,n) {
    a[i] = s[i] - '1';
    if(a[i] == 1) one = true;
  }
  if(!one) {
    rep(i,n) a[i] /= 2;
  }
  int m = 0;
  rep(i,n) {
    if(n-1 == (i | (n-1-i))) m += a[i]; 
  }
  if(one && (m % 2)) cout << 1 << endl;
  else if(one && !(m % 2)) cout << 0 << endl;
  else if(!one && (m % 2)) cout << 2 << endl;
  else cout << 0 << endl;
  return 0;
}

```