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 i64 = long long;

int main() {
    int n;
    std::string s;
    std::cin >> n >> s;
    std::vector<int> a;
    for (int i = 1; i < n; i++) a.push_back(abs(s[i] - s[i - 1]));

    bool f = std::find(a.begin(), a.end(), 1) != a.end();
    if (f) for (auto &e : a) e &= 1;
    else for (auto &e : a) e >>= 1;

    bool g = false;
    for (int i = 0; i < n - 1; i++) {
        if (a[i] && n - 2 == (i | (n - 2 - i))) g = !g;
    }

    std::cout << (f ? 1 : 2) * (g ? 1 : 0) << std::endl;

    return 0;
}