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 (gfortran v4.8.4) (judge verdict: Time Limit Exceeded)

program main
    implicit none
    integer n
    integer, allocatable, dimension(:) :: x
    integer i, j, d
    character s*1000000

    read(*,*) n
    read(*,*) s
    allocate(x(n))
    
    do i = 1,n
        read(s(i:i),*) x(i)
    end do

    do j = 2, n
        do i = 1, n+1-j
            d = x(i) - x(i+1)
            x(i) = xor(d,rshift(d,31))-rshift(d,31)
        end do
    end do

    write(*,*) x(1)

    deallocate(x)

end program