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[i])-1 for i in range(n)]

div=[0]*(n+1)
for i in range(1,n+1):
  div[i]+=div[i-1]
  x=i
  while not x&1:
    x>>=1
    div[i]+=1

XOR=0
for i in range(n):
  if div[n-1]<=div[i]+div[n-1-i]:
    XOR^=a[i]
if XOR&1:
  print(1)
  exit(0)


for i in a:
  if i==1:
    print(0)
    exit(0)

XOR=0
for i in range(n):
  if div[n-1]<=div[i]+div[n-1-i]:
    XOR^=a[i]>>1
if XOR&1:
  print(2)
  exit(0)
print(0)