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 main() {
    int n;
    string s;
    cin >> n >> s;
    vector<int> a(n);
    for (int i = 0; i < n; i++) a[i] = s[i] - '1';

    int ans = 0;
    if (s.find("2") != string::npos) {  
        for (int i = 0; i < n; i++) {
            int val = (a[i] & 1);
            if (((n - 1) & i) == i) ans ^= val;
        }
    } else {
        for (int i = 0; i < n; i++) {
            int val = min(a[i], 1);
           if (((n - 1) & i) == i) ans ^= val;
        }
        ans *= 2;
    }

    cout << ans << '\n';

    return 0;
}