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 f(int n,int k){
  return (n&k)==k;
}

signed main(){
  int n;cin>>n;
  string s;cin>>s;
  int a=2;
  for(int i=0;i<n;i++)if(s[i]=='2')a=1;
  for(int i=0;i<n;i++){
    if(a==1&&s[i]=='3')s[i]='1';
    if(a==2&&s[i]=='3')s[i]='2';
  }
  int od=0;
  for(int i=0;i<n;i++){
    if(s[i]=='2'){
      od^=f(n-1,i);
    }
  }
  cout<<od*a<<endl;
}