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 = input()

S = [int(A[i])-1 for i in range(N)]
Lucas = [0 for i in range(N)]
D = {0: 1}
base, m = 1, N - 1
while m != 0:
  if m % 2 == 1:
    L = [i for i in D]
    for i in L:
      D[i+base] = 1
  m //= 2
  base *= 2
for i in D:
  Lucas[i] = 1
oddness = 0
for i in range(N):
  if S[i] % 2 != 0:
    oddness += Lucas[i]
    oddness %= 2

if oddness == 1:
  print(1)
else:
  if 1 in S:
    print(0)
  else:
    S = [S[i]//2 for i in range(N)]
    oddness = 0
    for i in range(N):
      if S[i] % 2 != 0:
        oddness += Lucas[i]
        oddness %= 2
    if oddness == 1:
      print(2)
    else:
      print(0)