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>
#include <string>
#include <algorithm>
#include <cstring>
#include <cstdlib>
#include <cmath>
using namespace std;
using ll = long long;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);

    int n;
    cin >> n;

    string s;
    cin >> s;

    int b = 2;
    for (int i = 0; i < n; i++) {
        s[i] -= '1';
        if (s[i] == 1) b = 1;
    }

    int r = 0;
    for (int i = 0; i < n; i++) {
        r ^= (s[i] == b && (i & ~(n - 1)) == 0);
    }

    cout << r * b << endl;

    return 0;
}