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 Fortran (GNU Fortran 9.2.1) (judge verdict: Time Limit Exceeded)

program one_two_three_triangle
  implicit none
  integer :: n, a(1000000) = 0, i, j
  character(1000000) :: s
  read(*,*) n
  read(*,*) s
  do i = 1, n
    a(i) = ichar(s(i:i)) - 49
  end do
  if (mod(n, 2) == 0) then
    do i = 1, n - 1
      a(i) = abs(a(i) - a(i + 1))
    end do
    n = n - 1
  end if
  do i = n - 2, 1, -2
    do j = 1, i
      a(j) = abs(abs(a(j) - a(j + 1)) - abs(a(j + 1) - a(j + 2)))
    end do
  end do
  write(*,'(i0)') a(1)
end program one_two_three_triangle