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())
S = ''.join([str(int(d) - 1) for d in input()])

def solve01(s):
    "solve the problem when 's' consists of 0 or 1"
    ans = 0
    for k, d in enumerate(s):
        if k & (N - 1) == k:
            ans ^= int(d)
    return ans      

if '1' in S: # 0 or 1
    print(solve01(S.replace('2', '0')))
else: # 0 or 2
    print(solve01(S.replace('2', '1')) * 2)