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;

bool nCr_mod2(int n, int r) {
    return n == (r | (n - r));
}

signed main() {

    cin >> N >> S;

    bool has_1 = false;
    for (auto&& c: S) { --c; has_1 |= c == '1'; }

    if (has_1) for (auto&& c: S) c = c == '2' ? '0' : c;
    else       for (auto&& c: S) c = c == '2' ? '1' : c;

    int res = 0;
    for (int i = 0; i < N; ++i) {
        res += nCr_mod2(N - 1, i) * (S[i] - '0');
    }
    res &= 1;

    if (not has_1) res <<= 1;
    cout << res << endl;

}