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 n,i,j,b[1000100],r;
char a[1000100];
bool ok=false;
int main() {
  scanf("%d",&n);
  scanf("%s",a);
  for (i=0; i<n; i++) {
    a[i]=a[i]-'1';
    if (a[i]==1) ok=true;
    b[i+1]=b[i];
    for (j=i+1; j%2==0; j/=2) b[i+1]++;
  }
  if (!ok) for (i=0; i<n; i++) a[i]/=2;
  for (i=0; i<n; i++) if (a[i]==1 && b[n-1]==b[i]+b[n-1-i]) r^=1;
  if (!ok) r*=2;
  printf("%d\n",r);
  return 0;
}