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 even_or_odd(a):
    ans = a[0] % 2
    for i in range(1, N):
        ans ^= int((N-1) & i == i) & a[i]
    return ans

N = int(input())
a = [x-1 for x in list(map(int, list(input())))]

if even_or_odd([x % 2 for x in a]) == 1:
    print(1)
elif 1 in a:
    print(0)
elif even_or_odd([x//2 for x in a]) == 1:
    print(2)
else:
    print(0)