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:
# coding: utf-8


def solve(*args: str) -> str:
    n = int(args[0])
    A = [ord(a)-48 for a in args[1]]

    A = [abs(A[i]-A[i+1]) for i in range(n-1)]
    r = 2 if A.count(1) == 0 else 1

    ret = 0
    for i in range(n-1):
        ret += (A[i]//r)*(n-2 == (i | (n-2-i)))

    return str((ret % 2)*r)


if __name__ == "__main__":
    print(solve(*(open(0).read().splitlines())))