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:
import math

N = int(input())
A = list(map(int,input()))
B = []

for i in range(N):
  if N-1 == (i|N-1-i):
    B.append(1)
  else:
    B.append(0)
    
b = 0
for i in range(N):
  b += B[i]*A[i]
if b % 2 == 1:
  print(1)
else:
  for i in range(N):
    if A[i] == 2:
      print(0)
      break
  else:
    c = 0
    for i in range(N):
      A[i] = (A[i]-1)//2
      c += B[i]*A[i]
    if c % 2 == 1:
      print(2)
    else:
      print(0)