Problem:
Score : 700 points

Problem Statement

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}.

Sample Input 1

4
1231

Sample Output 1

1

x_{1,1},x_{1,2},x_{1,3},x_{1,4} are respectively 1,2,3,1.

x_{2,1},x_{2,2},x_{2,3} are respectively |1-2| = 1,|2-3| = 1,|3-1| = 2.

x_{3,1},x_{3,2} are respectively |1-1| = 0,|1-2| = 1.

Finally, x_{4,1} = |0-1| = 1, so the answer is 1.

Sample Input 2

10
2311312312

Sample Output 2

0

Solution in Python (3.4.3) (judge verdict: Time Limit Exceeded)

N = int(input())
A = input()

S = [int(A[i])-1 for i in range(N)]

oddness = 0
for i in range(N):
  m, n = N-1, i
  if S[i] % 2 != 0:
    parity = 1
    while m != 0:
      if m % 2 == 0 and n % 2 == 1:
        parity = 0
        break
      m //= 2
      n //= 2
    oddness += parity
    oddness %= 2

if oddness == 1:
  print(1)
else:
  if 1 in S:
    print(0)
  else:
    S = [S[i]//2 for i in range(N)]
    oddness = 0
    for i in range(N):
      m, n = N-1, i
      if S[i] % 2 != 0:
        parity = 1
        while m != 0:
          if m % 2 == 0 and n % 2 == 1:
            parity = 0
            break
          m //= 2
          n //= 2
        oddness += parity
        oddness %= 2
    if oddness == 1:
      print(2)
    else:
      print(0)