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:
import sys
input = sys.stdin.readline

N = int(input())
A = list(map(int, list(input().rstrip())))


def contains(n):
    t = n&-n
    return t.bit_length()


def solve1(A, D):
    is1 = False
    cmb_e = 0
    for i, a in enumerate(A):
        if a and cmb_e == 0:
            is1 = not is1
        cmb_e += contains(D-1-i) - contains(i+1)
    return is1

B = [abs(A[i]-A[i+1]) for i in range(N-1)]
if 1 in set(B):
    C = [b%2 for b in B]
    is1 = solve1(C, N-1)
    print(1 if is1 else 0)
else:
    C = [b//2 for b in B]
    is2 = solve1(C, N-1)
    print(2 if is2 else 0)