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 C(int n, int m) {
  return (n & m) == m;
}

int main() {
  int n;
  string s;
  cin >> n >> s;
  n = s.size();
  int one = 0;
  for (int i = 0; i < n; ++i) {
    s[i] -= '1';
    one += s[i] == 1;
  }
  int target = 2;
  if (one) {
    target = 1;
  }
  int ans = 0;
  for (int i = 0; i < n; ++i) {
    if (s[i] == target)
      ans ^= C(n-1, i);
  }
  ans *= target;
  printf("%d\n", ans);
  return 0;
}