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

Solution (in CPP):

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

int main(){
  int n;
  int check = 0;
  char c;
  cin >> n;
  vector<int> ans(0);
  for (int i = 0; i < n; i++) {
    cin >> c;
    ans.push_back(c - '0');
  }
  while(ans.size() > 1){
    n = ans.size();
    if(n % 2 == 0 && check == 0){
      for(int i = 0; i < n/2; i++){
        ans.at(i) = abs(ans.at(i*2) - ans.at(i*2 + 1));
      }
      ans.erase(ans.begin() + n/2, ans.end());
      check = 1;
    }
    else{
      for(int i = 0; i < n - 1; i++){
        ans.at(i) = abs(ans.at(i) - ans.at(i+1));
      }
      ans.pop_back();
      check = 0;
    }
  }
  cout << ans.at(0) << endl;
}