Problem:
Score : 500 points

Problem Statement

We have a grid with H horizontal rows and W vertical columns. Let (i,j) denote the square at the i-th row from the top and the j-th column from the left.

The square (i, j) has two numbers A_{ij} and B_{ij} written on it.

First, for each square, Takahashi paints one of the written numbers red and the other blue.

Then, he travels from the square (1, 1) to the square (H, W). In one move, he can move from a square (i, j) to the square (i+1, j) or the square (i, j+1). He must not leave the grid.

Let the unbalancedness be the absolute difference of the sum of red numbers and the sum of blue numbers written on the squares along Takahashi's path, including the squares (1, 1) and (H, W).

Takahashi wants to make the unbalancedness as small as possible by appropriately painting the grid and traveling on it.

Find the minimum unbalancedness possible.

Constraints

2 \leq H \leq 80

2 \leq W \leq 80

0 \leq A_{ij} \leq 80

0 \leq B_{ij} \leq 80

All values in input are integers.

Input

Input is given from Standard Input in the following format:

H W
A_{11} A_{12} \ldots A_{1W}
:
A_{H1} A_{H2} \ldots A_{HW}
B_{11} B_{12} \ldots B_{1W}
:
B_{H1} B_{H2} \ldots B_{HW}

Output

Print the minimum unbalancedness possible.

Sample Input 1

2 2
1 2
3 4
3 4
2 1

Sample Output 1

0

By painting the grid and traveling on it as shown in the figure below, the sum of red numbers and the sum of blue numbers are 3+3+1=7 and 1+2+4=7, respectively, for the unbalancedness of 0.

Sample Input 2

2 3
1 10 80
80 10 1
1 2 3
4 5 6

Sample Output 2

2

Solution in Fortran (gfortran v4.8.4) (judge verdict: Runtime Error)

program balanced_path
    implicit none
    integer(4):: h,w
    integer(4),allocatable:: a(:,:),b(:,:), mass_abs(:,:), dp(:,:), old_dp(:,:)
    integer(4):: i,j,k, no_
    integer(4),parameter:: inf=100100
    logical,allocatable:: is_exist(:,:,:)
    logical:: is_update

    read*, h,w
    allocate(a(w,h), b(w,h))
    do i=1,h
        read*, a(:,i)
    end do
    do i=1,h
        read*, b(:,i)
    end do
    
    allocate(mass_abs(w,h))
    do i=1,h
        do j=1,w
            mass_abs(j,i) = abs(a(j,i)-b(j,i))
        end do
    end do
    deallocate(a)
    deallocate(b)
    allocate(is_exist(0:maxval(mass_abs(:,:))*(h+w), w+1, h+1))


    is_exist(:,:,:) = .false.
    is_exist(mass_abs(1,1),1,1) = .true.
    is_update = .true.
    block
        integer(4):: max_bias
        max_bias = maxval(mass_abs(:,:))*(h+w)


        do no_ = 1, w+h
            is_update = .false.
            do i=1, h
                do j=1,w
                    do k=0,max_bias
                        if (.not.is_exist(k,j,i)) cycle
                        is_exist(abs(k+mass_abs(j+1,i)),j+1,i) = .true.
                        is_exist(abs(k-mass_abs(j+1,i)),j+1,i) = .true.
                        is_exist(abs(k+mass_abs(j,i+1)),j,i+1) = .true.
                        is_exist(abs(k-mass_abs(j,i+1)),j,i+1) = .true.
                    end do
                end do
            end do
        end do

        do i=0, max_bias
            if(is_exist(i,w,h))then
                print*, i
                stop
            end if
        end do
    end block

end program balanced_path