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())
slist=input()

def fact_mod2(n,r):
  if n==(r|(n-r)):
    return 1
  else:
    return 0

alist=[]
for s in slist:
  alist.append(int(s)-1)  
#print(alist)

parity=0
for i in range(N):
  parity+=fact_mod2(N-1,i)*alist[i]
#print(parity)

if parity%2==1:
  print(1)
else:
  if 1 in alist:
    print(0)
  else:
    for i in range(N):
      alist[i]//=2
    
    parity=0
    for i in range(N):
      parity+=fact_mod2(N-1,i)*alist[i]
    if parity%2==1:
      print(2)
    else:
      print(0)