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 C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Linq;
using System.Numerics;
using System.Collections.Generic;
using System.IO;
using System.Text;
using N = System.Int32;

public class Solver
{
    public void Solve()
    {
        N h = ri, w = ri;
        N[,] a = new N[h, w];
        N[,] b = new N[h, w];
        N[,] d = new N[h, w];
        for (int i = 0; i < h; i++)
        {
            for (int j = 0; j < w; j++)
            {
                a[i, j] = ri;
            }
        }
        for (int i = 0; i < h; i++)
        {
            for (int j = 0; j < w; j++)
            {
                b[i, j] = ri;
            }
        }
        for (int i = 0; i < h; i++)
        {
            for (int j = 0; j < w; j++)
            {
                d[i, j] = a[i, j] - b[i, j];
            }
        }
        bool[,,] dp = new bool[h + 1, w + 1, (h + w) * 80];
        dp[0, 1, 0] = true;
        dp[1, 0, 0] = true;
        for (int i = 1; i <= h; i++)
        {
            for (int j = 1; j <= w; j++)
            {
                for (int k = 0; k <= (i + j - 1) * 80; k++)
                {
                    dp[i, j, k] = dp[i - 1, j, Math.Abs(k + d[i - 1, j - 1])]
                        || dp[i - 1, j, Math.Abs(k - d[i - 1, j - 1])] 
                        || dp[i, j - 1, Math.Abs(k + d[i - 1, j - 1])] 
                        || dp[i, j - 1, Math.Abs(k - d[i - 1, j - 1])];
                }
            }
        }
        N p = 0;
        while (!dp[h, w, p]) p++;
        Write(p);
    }


    int ri { get { return sc.Integer(); } }
    long rl { get { return sc.Long(); } }
    double rd { get { return sc.Double(); } }
    string rs { get { return sc.Scan(); } }
    public StreamScanner sc = new StreamScanner(Console.OpenStandardInput());
    public Algorithm alg = new Algorithm();

    
    private const N mod = 1000000007;
    N Reverse(N n) { return Pow(n, mod - 2); }
    N Mul(params N[] n) { N p = n[0]; for (N i = 1; i < n.Length; i++) { p = (p * n[i]) % mod; } return p; }
    N Pow(N n, N p) { N t = n, q = 1; while (p > 0) { if (p % 2 == 1) { q = (q * t) % mod; } t = (t * t) % mod; p >>= 1; } return q; }
    N PowUpper(N n, N b) { N p = 1; while (p <= n) { p *= b; } return p; }
    N Sign(N n) { return n == 0 ? 0 : n > 0 ? 1 : -1; }
    N Abs(N n) { return (n > 0) ? n : -n; }
    N Gcd(params N[] n) { N p = n[0]; for (N i = 1; i < n.Length; i++) { p = Gcd(p, n[i]); } return p; }
    N Gcd(N a, N b) { return (a == 0) ? b : Gcd(b % a, a); }
    N Lcm(params N[] n) { N p = n[0]; for (N i = 1; i < n.Length; i++) { p = Lcm(p, n[i]); } return p; }
    N Lcm(N a, N b) { return (a / Gcd(a, b) * b) % mod; }
    void Write<T>(T t) { Console.WriteLine(t.ToString()); }
    void YN(bool t) { Console.WriteLine(t ? "YES" : "NO"); }
    void Yn(bool t) { Console.WriteLine(t ? "Yes" : "No"); }
    void yn(bool t) { Console.WriteLine(t ? "yes" : "no"); }
}

static class Program
{
    static public void Main(string[] args)
    {
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        var solver = new Solver();
        solver.Solve();
        Console.Out.Flush();
    }
}

public class Algorithm
{
    public int[] ZAlgorithm(string s)
    {
        int[] p = new int[s.Length];
        p[0] = s.Length;
        int i = 1, j = 0;
        while (i < s.Length)
        {
            while (i + j < s.Length && s[j] == s[i + j]) ++j;
            p[i] = j;
            if (j == 0) { ++i; continue; }
            int k = 1;
            while (i + k < s.Length && k + p[k] < j)
            {
                p[i + k] = p[k];
                ++k;
            }
            i += k; j -= k;
        }
        return p;
    }

    public List<int> SieveOfEratosthenes(int n)
    {
        List<int> l = new List<int>();
        if (n >= 2) { l.Add(2); }
        bool[] t = new bool[(n - 1) / 2];
        for (int p = 3; p <= n; p += 2) { if (!t[(p - 3) / 2]) { l.Add(p); for (int q = p * p; q <= n; q += p) { t[(q - 3) / 2] = true; } } }
        return l;
    }

    public Dictionary<int,int> PrimeFactor(int n, List<int> primetable)
    {
        Dictionary<int, int> d = new Dictionary<int, int>();
        int t = 0;
        foreach(int i in primetable)
        {
            if (n % i == 0)
            {
                while (n % 2 == 0) { n /= i; t++; }
                d.Add(i, t);
            }
        }
        if (n > 1) { d.Add(n, 1); }
        return d;
    }
}

public class PriorityQueue<T> where T : IComparable
{
    private IComparer<T> _comparer = null;
    private int _type = 0;

    private T[] _heap;
    private int _sz = 0;

    private int _count = 0;

    /// <summary>
    /// Priority Queue with custom comparer
    /// </summary>
    public PriorityQueue(IComparer<T> comparer)
    {
        _heap = new T[128];
        _comparer = comparer;
    }

    /// <summary>
    /// Priority queue
    /// </summary>
    /// <param name="type">0: asc, 1:desc</param>
    public PriorityQueue(int type = 0)
    {
        _heap = new T[128];
        _type = type;
    }

    private int Compare(T x, T y)
    {
        if (_comparer != null) return _comparer.Compare(x, y);
        return _type == 0 ? x.CompareTo(y) : y.CompareTo(x);
    }

    public void Push(T x)
    {
        _count++;
        if (_count > _heap.Length)
        {
            var newheap = new T[_heap.Length * 2];
            for (int n = 0; n < _heap.Length; n++) newheap[n] = _heap[n];
            _heap = newheap;
        }

        //node number
        var i = _sz++;

        while (i > 0)
        {
            //parent node number
            var p = (i - 1) / 2;

            if (Compare(_heap[p], x) <= 0) break;

            _heap[i] = _heap[p];
            i = p;
        }

        _heap[i] = x;
    }

    public T Pop()
    {
        _count--;

        T ret = _heap[0];
        T x = _heap[--_sz];

        int i = 0;
        while (i * 2 + 1 < _sz)
        {
            //children
            int a = i * 2 + 1;
            int b = i * 2 + 2;

            if (b < _sz && Compare(_heap[b], _heap[a]) < 0) a = b;

            if (Compare(_heap[a], x) >= 0) break;

            _heap[i] = _heap[a];
            i = a;
        }

        _heap[i] = x;

        return ret;
    }

    public int Count()
    {
        return _count;
    }

    public T Peek()
    {
        return _heap[0];
    }

    public bool Contains(T x)
    {
        for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true;
        return false;
    }

    public void Clear()
    {
        while (this.Count() > 0) this.Pop();
    }

    public IEnumerator<T> GetEnumerator()
    {
        var ret = new List<T>();

        while (this.Count() > 0)
        {
            ret.Add(this.Pop());
        }

        foreach (var r in ret)
        {
            this.Push(r);
            yield return r;
        }
    }

    public T[] ToArray()
    {
        T[] array = new T[_sz];
        int i = 0;

        foreach (var r in this)
        {
            array[i++] = r;
        }

        return array;
    }
}

public class StreamScanner
{
    public StreamScanner(Stream stream) { str = stream; }
    private readonly Stream str;
    private readonly byte[] buf = new byte[1024];
    private int len, ptr;
    public bool isEof = false;
    public bool IsEndOfStream { get { return isEof; } }
    private byte read()
    {
        if (isEof) throw new EndOfStreamException();
        if (ptr >= len)
        {
            ptr = 0;
            if ((len = str.Read(buf, 0, 1024)) <= 0)
            {
                isEof = true;
                return 0;
            }
        }
        return buf[ptr++];
    }
    public char Char()
    {
        byte b = 0;
        do b = read();
        while (b < 33 || 126 < b);
        return (char)b;
    }
    public string Scan()
    {
        var sb = new StringBuilder();
        for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
            sb.Append(b);
        return sb.ToString();
    }
    public long Long()
    {
        long ret = 0; byte b = 0; var ng = false;
        do b = read();
        while (b != '-' && (b < '0' || '9' < b));
        if (b == '-') { ng = true; b = read(); }
        for (; true; b = read())
        {
            if (b < '0' || '9' < b)
                return ng ? -ret : ret;
            else ret = ret * 10 + b - '0';
        }
    }
    public int Integer() { return (int)Long(); }
    public double Double() { return double.Parse(Scan()); }
}