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;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)

int main(){
  int N; cin >> N;
  string S; cin >> S;
  vector<int> a(N); rep(i, N) a[i] = S[i] - '0';
  vector<int> x(N - 1); rep(i, N - 1) x[i] = abs(a[i + 1] - a[i]);
  N--;
  bool check = true;
  rep(i, N) if (x[i] == 1) check = false;
  if (check) rep(i, N) x[i] /= 2;
  else rep(i, N) x[i] %= 2;
  int ans = 0;
  rep(i, N) {
    if (((N - 1) & i) == i) ans ^= x[i];
  }
  if (check) ans *= 2;
  cout << ans << endl;
}