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 <iostream>
#include <vector>
int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    int n;
    std::cin >> n;
    std::vector<int> a(n);
    bool one = false;
    for (int i = 0; i < n; ++i) {
        char c;
        std::cin >> c;
        a[i] = c - '0' - 1;
        if (a[i] == 1)
            one = true;
    }
    if (one)
        for (int i = 0; i < n; ++i)
            a[i] %= 2;
    int ans = 0;
    for (int i = 0; i < n; ++i)
        if (((n - 1) & i) == i)
            ans ^= a[i];
    std::cout << ans << "\n";
    return 0;
}