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())-1
a=input()
l=[None]*N
for i in range(N):
    l[i]=abs(int(a[i+1])-int(a[i]))
for i in range(19,0,-1):
    if N>2**i:
        t=2**i
        N-=t
        lb=[None]*N
        for i in range(N):
            if l[i+t//2]==1 and l[i]+l[i+t]==2:
                lb[i]=0
            else:
                lb[i]=abs(l[i]-l[i+t])
        l=lb
if len(l)==1:
    print(l[0])
else:
    print(abs(l[0]-l[1]))