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 sys
input = sys.stdin.readline
def pr2(x):
  ret = 0
  while x%2 == 0:
    ret += 1
    x //= 2
  return ret
n = int(input())
s = input()
x = []
flg = 0
if s.count("2") >= 1:
  for i in range(n-1):
    t = abs(int(s[i+1])-int(s[i]))
    x.append(t%2)
else:
  flg = 1
  for i in range(n-1):
    t = abs(int(s[i+1])-int(s[i]))
    x.append(t//2)
n -= 1
num2 = 0
ans = 0
for i in range(n):
  if i == 0:
    ans += x[i]
    continue
  num2 += pr2(n-i)-pr2(i)
  if num2>0:
    continue
  else:
    ans += x[i]
if ans%2:
  print(flg+1)
else:
  print(0)