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 is_odd_binomial(n, m):
    return ((~n) & m) == 0


N = int(input())
a = list(map(lambda x: int(x) - 1, input()))

parity = sum(a[i] for i in range(N) if is_odd_binomial(N - 1, i))
if parity % 2 == 1:
    ans = 1
elif 1 in a:
    ans = 0
elif parity % 4 == 2:
    ans = 2
else:
    ans = 0

print(ans)