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 = input()
a = [int(s)-1 for s in S]


from collections import defaultdict

r = 1
d = defaultdict(int)
while 2**r  <= N:
  for i in range(1,N):
    if i*(2**r) <= N:
      d[i*(2**r)] += 1
    else:
      break
  r+=1

def calc(list_of_int):
  # 1と0で構成されているとする
  length = len(list_of_int)
  res = list_of_int[0]
  
  keisu = 0
  for i,r in zip(list_of_int[1:], range(N-1)):
    keisu += d[N-r-1]-d[r+1]
    res = (res + ((2 if keisu>0 else 1)*i) )% 2
  return res

if 1 in a:
  print(calc(a))
else:
  print(calc(list(map(lambda x:x//2,a)))*2)