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())
arr=list(input())
arr=[int(arr[i]) for i in range(n)]
if n==1:
  print(arr[0])
if n==2:
  print(abs(arr[0]-arr[1]))
else:
  tmp=[]
  for i in range(n-2):
    tmp.append(abs(abs(arr[i]-arr[i+1])-abs(arr[i+1]-arr[i+2])))
  arr=tmp
  while len(arr)>3:
    tmp=[]
    if len(arr)%2==0:
      for i in range(len(arr)//2):
        tmp.append(abs(arr[2*i]-arr[2*i+1]))
    else:
      for i in range(len(arr)-1):
        tmp.append(abs(arr[i]-arr[i+1]))
    arr=tmp
  if len(arr)==1:
    print(arr[0])
  elif len(arr)==2:
    print(abs(arr[0]-arr[1]))
  elif len(arr)==3:
    print(abs(abs(arr[0]-arr[1])-abs(arr[1]-arr[2])))