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.*;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {
    static final int offset = 12800, UNCALC = -1, INF = (int) 1e9;
    static int n, m;
    static int memo[][][];
    static int[][] a, b;

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        n = sc.nextInt();
        m = sc.nextInt();
        a = new int[n][m];
        b = new int[n][m];
        for (int i = 0; i < n; i++)
            a[i] = sc.nextIntArray(m);
        for (int i = 0; i < n; i++)
            b[i] = sc.nextIntArray(m);
        memo = new int[n][m][2 * offset + 1];
        for (int[][] a : memo)
            for (int[] b : a)
                Arrays.fill(b, UNCALC);
        out.println(Math.min(dp(0, 0, offset + a[0][0] - b[0][0]), dp(0, 0, offset - a[0][0] + b[0][0])));
        out.flush();
        out.close();
    }

    static int dp(int i, int j, int sum) {
        if (i == n - 1 && j == m - 1) return Math.abs(sum - offset);
        if (memo[i][j][sum] != UNCALC) return memo[i][j][sum];
        int best = INF;
        if (i != n - 1)
            best = Math.min(dp(i + 1, j, sum + a[i + 1][j] - b[i + 1][j]), dp(i + 1, j, sum - a[i + 1][j] + b[i + 1][j]));
        if (j != m - 1)
            best = Math.min(best, Math.min(dp(i, j + 1, sum + a[i][j + 1] - b[i][j + 1]), dp(i, j + 1, sum - a[i][j + 1] + b[i][j + 1])));
        return memo[i][j][sum] = best;
    }

    static class Scanner {

        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream system) {
            br = new BufferedReader(new InputStreamReader(system));
        }


        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

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

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        public char nextChar() throws IOException {
            return next().charAt(0);
        }

        public Long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public int[] nextIntArray(int n) throws IOException {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public long[] nextLongArray(int n) throws IOException {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }


        public Integer[] nextIntegerArray(int n) throws IOException {
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public double[] nextDoubleArray(int n) throws IOException {
            double[] ans = new double[n];
            for (int i = 0; i < n; i++)
                ans[i] = nextDouble();
            return ans;
        }

        public short nextShort() throws IOException {
            return Short.parseShort(next());
        }

    }

}