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()
b = []
att = 1
for i in range(n):
  b.append(int(a[i])-1)
#print(b)
for i in range(n):
  if b[i] % 2 == 1:
    break
else:
  att = 2
  for i in range(n):
    b[i] //= 2
for i in range(n):
  if b[i] == 2:
    b[i] = 0
#print(b)
pre = [0 for _ in range(10**6)]
now = 2
while now < 10**6 + 5:
  for k in range(10**6):
    try:
      pre[k*now] += 1
    except:
      now *= 2
      break
#print(pre)
nm = [0]
for i in range(1,n):
  nm.append(nm[-1]-pre[i]+pre[n-i])
for i in range(n):
  if nm[i]:
    nm[i] = 0
  else:
    nm[i] = 1
#print(nm)
ans = 0
for i in range(n):
  ans ^= b[i]*nm[i]
print(ans*att)