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()))
if N == 2:
    print(abs(a[0]-a[1]))
    exit()
a1 = [abs(a[i]-a[i+1]) for i in range(N-1)]
if 1 in a1:
    s = 0
    for i in range(len(a1)):
        if ((len(a1)-1) | i) == (len(a1)-1):
            s += a1[i] % 2
    print(s % 2)
else:
    s = 0
    for i in range(len(a1)):
        if ((len(a1)-1) | i) == (len(a1)-1):
            s += a1[i] // 2
    print((s % 2) * 2)