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;
char s[1000010];
int n;
int main() {
    scanf("%d%s", &n, s);
    int tag1 = 0, tag2 = 0, tag3 = 0;
    n--;
    for (int i = 0; i <= n; i++) {
        int now = s[i] - '0';
        if (now == 2) tag2 = 1;
        if ((i & n) == i) tag1 ^= now & 1, tag3 ^= ((now - 1) / 2) & 1;
    }
    return cout << (tag1 ? 1 : tag2 ? 0 : tag3 ? 2 : 0) << endl, 0;
}