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;
  string M;
  bool a=false,b=false,c=false;
  cin>>N>>M;
  for(int i=0;i<N;i++)
  {
    a|=M.at(i)=='2';
    b^=M.at(i)=='2'&&((N-1)&i)==i;
    c^=M.at(i)=='3'&&((N-1)&i)==i;
  }
  if(b)
    return cout<<1<<endl,0;
  if(a)
    return cout<<0<<endl,0;
  if(c)
    return cout<<2<<endl,0;
  else
    return cout<<0<<endl,0;
}