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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.Deque;
import java.util.HashSet;
import java.util.Set;
import java.util.regex.Pattern;

public class Main {
    public void solve(Stdin stdin, PrintWriter stdout) throws NumberFormatException, IOException {
        int h = stdin.nextInt();
        int w = stdin.nextInt();
        int[][] a = new int[h][w];
        int[][] b = new int[h][w];
        for (int i = 0; i < h; i++) {
            for (int j = 0; j < w; j++) {
                a[i][j] = stdin.nextInt();
            }
        }
        for (int i = 0; i < h; i++) {
            for (int j = 0; j < w; j++) {
                b[i][j] = stdin.nextInt();
            }
        }

        Set<Tuple> visited = new HashSet<>();
        Deque<Tuple> stack = new ArrayDeque<>();
        stack.addLast(new Tuple(0, 0, Math.abs(a[0][0] - b[0][0])));
        while (!stack.isEmpty()) {
            Tuple current = stack.removeLast();
            int x = current.x;
            int y = current.y;
            int z = current.z;

            if (x == h - 1 && y == w) stdout.println(z);
            if (x == h && y == w - 1) stdout.println(z);

            if (visited.contains(current)) {
                continue;
            }
            visited.add(current);

            if (x + 1 < h) {
                int d = Math.abs(a[x + 1][y] - b[x + 1][y]);
                stack.addLast(new Tuple(x + 1, y, Math.abs(z + d)));
                stack.addLast(new Tuple(x + 1, y, Math.abs(z - d)));
            }
            if (y + 1 < w) {
                int d = Math.abs(a[x][y + 1] - b[x][y + 1]);
                stack.addLast(new Tuple(x, y + 1, Math.abs(z + d)));
                stack.addLast(new Tuple(x, y + 1, Math.abs(z - d)));
            }
        }
        stdout.println(visited.stream().filter(t -> t.x == h - 1 && t.y == w - 1).mapToInt(t -> t.z).min().getAsInt());
    }

    public static void main(String[] args) throws NumberFormatException, IOException {
        Stdin stdin = new Stdin();
        PrintWriter stdout = new PrintWriter(System.out, false);
        new Main().solve(stdin, stdout);
        stdout.flush();
    }

    public static class Stdin {
        private Deque<String> queue;
        private BufferedReader stdin;
        private Pattern delimiter;

        public Stdin() {
            queue = new ArrayDeque<>();
            stdin = new BufferedReader(new InputStreamReader(System.in));
            delimiter = Pattern.compile(" ");
        }

        public String next() throws IOException {
            if (queue.isEmpty()) {
                delimiter.splitAsStream(stdin.readLine()).forEach(queue::addLast);
            }
            return queue.removeFirst();
        }

        public int nextInt() throws NumberFormatException, IOException {
            return Integer.parseInt(next());
        }
    }

    public static class Tuple {
        private int x;
        private int y;
        private int z;
        public Tuple(int x, int y, int z) {
            this.x = x;
            this.y = y;
            this.z = z;
        }
        @Override
        public int hashCode() {
            final int prime = 31;
            int result = 1;
            result = prime * result + x;
            result = prime * result + y;
            result = prime * result + z;
            return result;
        }
        @Override
        public boolean equals(Object obj) {
            if (this == obj)
                return true;
            if (obj == null)
                return false;
            if (getClass() != obj.getClass())
                return false;
            Tuple other = (Tuple) obj;
            if (x != other.x)
                return false;
            if (y != other.y)
                return false;
            if (z != other.z)
                return false;
            return true;
        }
        @Override
        public String toString() {
            return "Tuple [x=" + x + ", y=" + y + ", z=" + z + "]";
        }
    }
}