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: Runtime Error)

program example
	implicit none

	integer(16) :: i=1,j=1,N
    integer(16),allocatable :: x(:,:),A(:)
    
    read(*,*) N
     
    allocate(x(N,N),A(N))

	do
		read(*,"(i1)",advance="no",end=100) A(i)
    	x(1,j)=A(i)
        if (mod(j,2000)==0) then
        	deallocate(A)
            allocate(A(N))
        	i=1
            j=j+1
        else
        
        	i=i+1
        	j=j+1
            
        end if
        
    end do

100    do i=2,N
     
    	do j=1,N+1-i
        
        	x(i,j)=abs(x(i-1,j)-x(i-1,j+1))
        
        end do
    
    end do
    
    write(*,*) x(N,1)

end program