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 PYTHON3):

Solution:
def main():
    n = int(input())
    a = list(map(lambda x: int(x)-1, list(input())))
    b = [i % 2 for i in a]

    def all_a(x):
        ans = 0
        for j, i in enumerate(x):
            ans ^= (n-1 | j == n-1)*i
        return ans

    all_b = all_a(b)
    if all_b == 1:
        print(1)
        return
    if 1 in a:
        print(0)
        return
    b = [i//2 for i in a]
    print(all_a(b)*2)


main()