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;
string s;
vector<int> v, tmp;

int solve();

int main() {
  cin >> n >> s;
  for(int i = 0; i < n; ++i) v.push_back(s[i] - '0');
  cout << solve() << endl;
  return 0;
}

int solve() {
  bool ch = 0;
  for(int i = 0; i < n; ++i)
    if(--v[i] == 1) ch = 1;
  if(ch) {
    ch = 0;
    for(int i = 0; i < n; ++i)
      if(v[i] == 1) ch ^= ((n - 1) & i) == i;
    return ch;
  }
  ch = 0;
  for(int i = 0; i < n; ++i)
    if(v[i] == 2) ch ^= ((n - 1) & i) == i;
  return ch * 2;
}