#ABC147E. [ABC147E] Balanced Path

[ABC147E] Balanced Path

Score : 500500 points

Problem Statement

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

The square (i,j)(i, j) has two numbers AijA_{ij} and BijB_{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)(1, 1) to the square (H,W)(H, W). In one move, he can move from a square (i,j)(i, j) to the square (i+1,j)(i+1, j) or the square (i,j+1)(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)(1, 1) and (H,W)(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

  • 2H802 \leq H \leq 80
  • 2W802 \leq W \leq 80
  • 0Aij800 \leq A_{ij} \leq 80
  • 0Bij800 \leq B_{ij} \leq 80
  • All values in input are integers.

Input

Input is given from Standard Input in the following format:

HH WW

A11A_{11} A12A_{12} \ldots A1WA_{1W}

::

AH1A_{H1} AH2A_{H2} \ldots AHWA_{HW}

B11B_{11} B12B_{12} \ldots B1WB_{1W}

::

BH1B_{H1} BH2B_{H2} \ldots BHWB_{HW}

Output

Print the minimum unbalancedness possible.

2 2
1 2
3 4
3 4
2 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=73+3+1=7 and 1+2+4=71+2+4=7, respectively, for the unbalancedness of 00.

Figure

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