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 <cstdio>
#include <cctype>
#include <cstring>
#include <algorithm>
using namespace std;
const int N = 1e6+5;
int n, ans, flg; char a[N];
int main()
{
    scanf("%d%s", &n, a); for(int i = 0; i < n; ++i) if((a[i] -= '1') == 1) flg = 1;
    if(!flg) for(int i = 0; i < n; ++i) a[i] >>= 1;
    for(int i = 0; i < n; ++i) if(((n-1)&i) == i) ans ^= a[i]&1;
    printf("%d\n", ans<<!flg);
    return 0;
}