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; cin >> N;
    string s; cin >> s;
    bool f = true;
    vector<int> a(N); for (int i = 0; i < N; i++) {
        a[i] = s[i]-'0' - 1;
        if (a[i] == 1) f = false;
    }
    if (f) for (int i = 0; i < N; i++) a[i] /= 2;

    int ans = 0;
    for (int i = 0; i < N; i++) {
        ans = (ans + (N-1 == (i | (N - 1 - i))) * a[i] ) % 2;
    }
    if (ans == 1) {
        if (f) {
            cout << 2 << endl;
        } else {
            cout << 1 << endl;
        }
    } else {
        cout << 0 << endl;
    }
}