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 twos_in_factorial(n):
    return n - bin(n).count('1')


def parity_of_nCr(n, i):
    """ if odd, return False. """
    f = twos_in_factorial
    return f(n) - f(n-i) - f(i) > 0


if __name__ == "__main__":
    n = int(input())
    nums = list(map(lambda x: int(x) - 1, input().strip()))
    no_one = False
    if 1 not in nums:
        nums = [num // 2 for num in nums]
        no_one = True

    is_odd = False
    for i, num in enumerate(nums):
        if not parity_of_nCr(n-1, i) and num & 1:
            is_odd ^= 1

    if not is_odd:
        print(0)
    else:
        print(1 << no_one)