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:
N = int(input())
A = list(map(int, input()))

num = 0
for i in range(N):
    num += (N - 1 == (i | N - 1 - i)) * ((-1)**i) * A[i]
if num % 2 == 1:
    print(1)
else:
    for i in range(N - 1):
        if abs(A[i]-A[i+1]) == 1:
            print(0)
            break
    else:
        B = []
        for i in range(N-1):
            if A[i] == A[i+1]:
                B.append(0)
            else:
                B.append(1)
        for i in range(N-1):
            num += (N - 2 == (i | N - 2 - i)) * ((-1)**i) * B[i]
        if num % 2 == 1:
            print(2)
        else:
            print(0)