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;

using ll = long long;

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    int N;
    cin >> N;
    string s;
    cin >> s;
    bool has_1 = false;
    valarray<int> vals(N);
    for (int i = 0; i < N; i++) {
        vals[i] = s[i] - '1';
        has_1 |= vals[i] == 1;
    }
    if (has_1)
        vals %= 2;
    else
        vals /= 2;
    bool parity = 0;
    for (int i = 0; i < N; i++) {
        parity ^= vals[i] && ((N - 1) | i) == N - 1;
    }
    cout << (parity ? (has_1 ? 1 : 2) : 0) << endl;
}