#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
signed main() { 
  ios::sync_with_stdio(false); cin.tie(0);
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; i++) {
    char ch;
    cin >> ch;
    a[i] = ch - '1';
  }
  bool ones = false;
  for (auto& i : a) if (i == 1) ones = true;
  if (ones) {
    for (auto& i : a) if (i == 2) i = 0;
  } else {
    for (auto& i : a) if (i == 2) i = 1;
  }
  auto doit = [] (int n, const vector<int>& a) {
    int res = 0;
    for (int i = 0; i < n; i++) {
      if (((n - 1) & i) == i) res ^= a[i];
    }
    return res;
  };
  cout << (ones ? doit(n, a) : 2 * doit(n, a)) << endl;
  return 0;
}
### Prompt

Your challenge is to write 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
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
signed main() { 
  ios::sync_with_stdio(false); cin.tie(0);
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; i++) {
    char ch;
    cin >> ch;
    a[i] = ch - '1';
  }
  bool ones = false;
  for (auto& i : a) if (i == 1) ones = true;
  if (ones) {
    for (auto& i : a) if (i == 2) i = 0;
  } else {
    for (auto& i : a) if (i == 2) i = 1;
  }
  auto doit = [] (int n, const vector<int>& a) {
    int res = 0;
    for (int i = 0; i < n; i++) {
      if (((n - 1) & i) == i) res ^= a[i];
    }
    return res;
  };
  cout << (ones ? doit(n, a) : 2 * doit(n, a)) << endl;
  return 0;
}
```