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 pascal_parity(N):
    if N & -N == N:
        return [1] * N
    else:
        n = N - (1<<(N.bit_length()-1))
        p = pascal_parity(n)
        return p + [0]*(N-2*n) + p

N = int(input())
A = list(map(lambda x: int(x)-1, input()))
P = pascal_parity(N)
if 1 in A:
    if sum(a*p for a,p in zip(A, P)) % 2 == 1:
        print(1)
    else:
        print(0)
else:
    pa = 0
    for p, a in zip(P, A):
        if p==1 and a==2:
            pa += 1
    if pa % 2 == 1:
        print(2)
    else:
        print(0)