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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Text.RegularExpressions;

public class ABC
{
    //          long[] sp = Console.ReadLine().Split().Select(long .Parse).ToArray();
    //          int[] sp = Console.ReadLine().Split().Select(int.Parse).ToArray();
    //          int N =  int.Parse(Console.ReadLine());
    //CompLib.Collections.PriorityQueue<?>
    public static int juuokunana = (int)Math.Pow(10, 9) + 7;

    public static void Main()
    {
        int H, W;
        new readint(out H, out W);
        int[,] A = new int[H, W];
        int[,] B = new int[H, W];

        for (int i = 0; i < H; i++)
        {
            int[] sp = Console.ReadLine().Split().Select(int.Parse).ToArray();
            for (int j = 0; j < W; j++)
            {
                A[i, j] = sp[j];
            }

        }
        for (int i = 0; i < H; i++)
        {
            int[] sp = Console.ReadLine().Split().Select(int.Parse).ToArray();
            for (int j = 0; j < W; j++)
            {
                B[i, j] = sp[j];
            }

        }

        bool[,,] DP = new bool[H, W, (H+W)*80];

        DP[0, 0, Math.Abs(B[0, 0] - A[0, 0])] = true;
        for (int left = 1; left < H; left++)
        {
            for (int able = 0; able < (H+W)*80; able++)
            {
                if (DP[left - 1, 0, able])
                {
                    int abs = Math.Abs(B[left, 0] - A[left, 0]);

                    DP[left, 0, able + abs] = true;

                        DP[left, 0, Math.Abs(able - abs)] = true;

                }
            }
        }
        for (int right = 1; right < W; right++)
        {
            for (int able = 0; able < (H+W)*80; able++)
            {
                if (DP[0,right-1, able])
                {
                    int abs = Math.Abs(B[0,right] - A[0,right]);

                    DP[0,right, able + abs] = true;

                        DP[0,right, Math.Abs(able - abs)] = true;

                }
            }

        }
        for (int i = 1; i < H; i++)
        {
            for (int j = 1; j < W; j++)
            {
                int abs = Math.Abs(B[i, j] - A[i, j]);
                for (int able = 0; able < (H+W)*80; able++)
                {
                    if (DP[i - 1, j, able])
                    {
                        DP[i, j,able + abs] = true;
                        DP[i, j, Math.Abs(able - abs)] = true;
                    }
                    if (DP[i, j - 1, able])
                    {
                        DP[i, j, able + abs] = true;
                        DP[i, j, Math.Abs(able - abs)] = true;
                    }

                }



            }
        }

        for (int able = 0; able < (H+W)*80; able++)
        {
            if (DP[H - 1, W - 1, able])
            {
                Console.WriteLine(able);
                return;
            }
        }

    }
}


class readint
{



    public readint(out int i)
    {
        i = int.Parse(Console.ReadLine());

    }
    public readint(out int a, out int b)
    {
        int[] sp = Console.ReadLine().Split().Select(int.Parse).ToArray();
        a = sp[0];
        b = sp[1];

    }
    public readint(out int a, out int b, out int c)
    {
        int[] sp = Console.ReadLine().Split().Select(int.Parse).ToArray();
        a = sp[0];
        b = sp[1];
        c = sp[2];
    }
    public readint(out int a, out int b, out int c, out int d)
    {
        int[] sp = Console.ReadLine().Split().Select(int.Parse).ToArray();
        a = sp[0];
        b = sp[1];
        c = sp[2];
        d = sp[3];

    }

}

class readlong
{


    public readlong(out long i)
    {
        i = long.Parse(Console.ReadLine());

    }
    public readlong(out long a, out long b)
    {
        long[] sp = Console.ReadLine().Split().Select(long.Parse).ToArray();
        a = sp[0];
        b = sp[1];

    }
    public readlong(out long a, out long b, out long c)
    {
        long[] sp = Console.ReadLine().Split().Select(long.Parse).ToArray();
        a = sp[0];
        b = sp[1];
        c = sp[2];
    }
    public readlong(out long a, out long b, out long c, out long d)
    {
        long[] sp = Console.ReadLine().Split().Select(long.Parse).ToArray();
        a = sp[0];
        b = sp[1];
        c = sp[2];
        d = sp[3];

    }

}







class Util
{




    /// <summary>
    /// 2引数の最大公約数を返します。longです。
    /// </summary>
    /// <param name="a">long 引数1</param>
    /// <param name="b">long 引数2</param>
    /// <returns></returns>
    public static long GCD(long a, long b)
    {
        if (a < b)
            swap(ref a, ref b);
        if (a % b == 0) return b;
        return GCD(b, a % b);

    }
    /// <summary>
    /// 2引数の最大公約数を返します。intです。
    /// </summary>
    /// <param name="a">int 引数1</param>
    /// <param name="b">int 引数2</param>
    /// <returns></returns>
    public static int GCD(int a, int b)
    {
        if (a < b)
            swap(ref a, ref b);
        if (a % b == 0) return b;
        return GCD(b, a % b);
    }

    /// <summary>
    /// 2つの変数の中身を交換する。型はなんでもいい
    /// </summary>
    /// <typeparam name="T"></typeparam>
    /// <param name="a"></param>
    /// <param name="b"></param>
    public static void swap<T>(ref T a, ref T b)
    {
        T temp = b;
        b = a;
        a = temp;

    }

    /// <summary>
    /// 2引数の最大公約数を返します。
    /// </summary>
    /// <param name="a"></param>
    /// <param name="b"></param>
    /// <returns></returns>
    public static long LCM(long a, long b)
    {
        return a * b / GCD(a, b);
    }
    /// <summary>
    /// 2引数の最大公約数を返します。
    /// </summary>
    /// <param name="a"></param>
    /// <param name="b"></param>
    /// <returns></returns>
    public static long LCM(int a, int b)
    {
        return Math.BigMul(a, b) / GCD(a, b);
    }


    public static int M = (int)(Math.Pow(10, 9)) + 7;
    private static int[] factorial_modM;

    /// <summary>
    /// 2引数の積 mod Mを求める。Mは10億7。
    /// 変えられるよ。
    /// </summary>
    /// <param name="a"></param>
    /// <param name="b"></param>
    /// <returns></returns>
    public static int Multiple_modM(int a, int b)
    {
        return (int)(Math.BigMul(a, b) % M);
    }
    /// <summary>
    /// n! modMを求めるための準備を行う。引数は最大値。
    /// </summary>
    /// <param name="n"></param>
    public static void factorial_modM_Prepare(int n)
    {
        factorial_modM = new int[n + 1];
        factorial_modM[0] = 1;
        for (int i = 1; i <= n; ++i)
        {
            factorial_modM[i] = Multiple_modM(factorial_modM[i - 1], i);
        }
    }

    /// <summary>
    /// n! mod M を返す。やる前にfactorial_modM_Prepare(n)を実行しといてね。
    /// </summary>
    /// <param name="n"></param>
    /// <returns></returns>
    public static int Factorial(int n)
    {
        return factorial_modM[n];
    }


    public static int Pow(int a, int m)
    {
        switch (m)
        {
            case 0:
                return 1;
            case 1:
                return a;
            default:
                int p1 = Pow(a, m / 2);
                int p2 = Multiple_modM(p1, p1);
                return ((m % 2) == 0) ? p2 : Multiple_modM(p2, a);
        }
    }
    /// <summary>
    /// a / m Mod M を求める。
    /// </summary>
    /// <param name="a"></param>
    /// <param name="b"></param>
    /// <returns></returns>
    public static int Div(int a, int b)
    {
        return Multiple_modM(a, Pow(b, M - 2));
    }
    /// <summary>
    /// nCr mod M を求める。やる前にfactorial_modM_Prepare(n)を実行しといてね。
    /// </summary>
    /// <param name="n"></param>
    /// <param name="r"></param>
    /// <returns></returns>
    public static int nCr_modM(int n, int r)
    {
        if (r < 0) return 0;

        if (n < r) { return 0; }
        if (n == r) { return 1; }
        int res = Factorial(n);
        res = Div(res, Factorial(r));
        res = Div(res, Factorial(n - r));
        return res;
    }

}
/// <summary>
/// Union-Find木を定義する。コンストラクタの指定は、頂点の番号。
/// おすすめとしては、UnionFind<T>[] で宣言してしまう。
/// </summary>
/// <typeparam name="T">int固定でいいよね。</typeparam>
class UnionFind<T>
{
    public int tree_height;
    public UnionFind<T> parent;
    public T item
    {
        get;
        private set;
    }

    public UnionFind(T item)
    {
        tree_height = 0;
        parent = this;

    }

    /// <summary>
    /// 一番上の親を探す。
    /// 探しながら繋がり方を最適化している。
    /// UnionFindの頂点そのものを返すので、==での比較が可能。
    /// </summary>
    /// <returns></returns>
    public UnionFind<T> FindAdam()
    {
        if (parent == this) return this;
        else
        {
            UnionFind<T> ParentOfParent = parent.FindAdam();
            parent = ParentOfParent;//縦長な構成をつなぎ直している
            return ParentOfParent;
        }
    }
    /// <summary>
    /// unionfind2つを一つにつなぐ。
    /// </summary>
    /// <param name="a"></param>
    /// <param name="b"></param>
    public static void Unite(UnionFind<T> a, UnionFind<T> b)
    {
        UnionFind<T> ParentOfA = a.FindAdam();
        UnionFind<T> ParentOfB = b.FindAdam();
        if (ParentOfA.tree_height < ParentOfB.tree_height)
        {
            ParentOfA.parent = ParentOfB;
            ParentOfB.tree_height = Math.Max(ParentOfA.tree_height + 1, ParentOfB.tree_height);
        }
        else
        {
            ParentOfB.parent = ParentOfA;
            ParentOfA.tree_height = Math.Max(ParentOfB.tree_height + 1, ParentOfA.tree_height);
        }

    }

}

//Treap 平衡二分木
class Treap<T> where T : IComparable
{
    private class Node
    {
        private static Random g_rand = new Random();
        private readonly int m_rank = g_rand.Next();
        private readonly T m_value;
        private Node m_lch;
        private Node m_rch;
        private int m_count;

        public Node(T value)
        {
            m_value = value;
            m_count = 1;
        }

        private static int Count(Node node)
        {
            return (node != null) ? node.m_count : 0;
        }

        private Node Update()
        {
            m_count = Count(m_lch) + Count(m_rch) + 1;
            return this;
        }

        public static Node Merge(Node a, Node b)
        {
            if (a == null) { return b; }
            if (b == null) { return a; }

            if (a.m_rank < b.m_rank)
            {
                a.m_rch = Merge(a.m_rch, b);
                return a.Update();
            }
            else
            {
                b.m_lch = Merge(a, b.m_lch);
                return b.Update();
            }
        }

        public static Tuple<Node, Node> Split(Node t, int k)
        {
            if (t == null) { return new Tuple<Node, Node>(null, null); }

            if (k <= Count(t.m_lch))
            {
                var pair = Split(t.m_lch, k);
                t.m_lch = pair.Item2;
                return new Tuple<Node, Node>(pair.Item1, t.Update());
            }
            else
            {
                var pair = Split(t.m_rch, k - Count(t.m_lch) - 1);
                t.m_rch = pair.Item1;
                return new Tuple<Node, Node>(t.Update(), pair.Item2);
            }
        }

        public int FindIndex(T value)
        {
            int L = Count(m_lch);
            if (value.CompareTo(m_value) < 0)
            {
                return (m_lch != null) ? m_lch.FindIndex(value) : 0;
            }
            else if (value.CompareTo(m_value) > 0)
            {
                return (m_rch != null) ? m_rch.FindIndex(value) + L + 1 : L + 1;
            }
            else
            {
                return L;
            }
        }

        public T this[int i]
        {
            get
            {
                int L = Count(m_lch);
                if (i < L)
                {
                    return m_lch[i];
                }
                else if (i > L)
                {
                    return m_rch[i - L - 1];
                }
                else
                {
                    return m_value;
                }
            }
        }
    }

    private Node node;

    public void Insert(T value)
    {
        if (node != null)
        {
            int k = node.FindIndex(value);
            var pair = Node.Split(node, k);
            node = Node.Merge(Node.Merge(pair.Item1, new Node(value)), pair.Item2);
        }
        else
        {
            node = new Node(value);
        }
    }

    public int FindIndex(T value)
    {
        return node.FindIndex(value);
    }

    public T this[int i]
    {
        get
        {
            return node[i];
        }
    }
}

static class Permutation<T>
{
    private static void Search(List<T[]> perms, Stack<T> stack, T[] a)
    {
        int N = a.Length;
        if (N == 0)
        {
            perms.Add(stack.Reverse().ToArray());
        }
        else
        {
            var b = new T[N - 1];
            Array.Copy(a, 1, b, 0, N - 1);
            for (int i = 0; i < a.Length; ++i)
            {
                stack.Push(a[i]);
                Search(perms, stack, b);
                if (i < b.Length) { b[i] = a[i]; }
                stack.Pop();
            }
        }
    }
    public static IEnumerable<T[]> All(IEnumerable<T> src)
    {
        var perms = new List<T[]>();
        Search(perms, new Stack<T>(), src.ToArray());
        return perms;
    }
}



namespace CompLib.Collections
{
    #region PriorityQueue
    /// <summary>
    /// 指定した型のインスタンスを最も価値が低い順に取り出すことが可能な可変サイズのコレクションを表します．
    /// </summary>
    /// <typeparam name="T">優先度付きキュー内の要素の型を指定します．</typeparam>
    /// <remarks>内部的にはバイナリヒープによって実装されています．</remarks>
    public class PriorityQueue<T>
    {
        readonly List<T> heap = new List<T>();
        readonly Comparison<T> cmp;

        /// <summary>
        /// デフォルトの比較子を使用してインスタンスを初期化します．
        /// </summary>
        /// <remarks>この操作は O(1) で実行されます．</remarks>
        public PriorityQueue() { cmp = Comparer<T>.Default.Compare; }

        /// <summary>
        /// デリゲートで表されるような比較関数を使用してインスタンスを初期化します．
        /// </summary>
        /// <param name="comparison"></param>
        /// <remarks>この操作は O(1) で実行されます．</remarks>
        public PriorityQueue(Comparison<T> comparison) { cmp = comparison; }

        /// <summary>
        /// 指定された比較子を使用してインスタンスを初期化します．
        /// </summary>
        /// <param name="comparer"></param>
        /// <remarks>この操作は O(1) で実行されます．</remarks>
        public PriorityQueue(IComparer<T> comparer) { cmp = comparer.Compare; }

        /// <summary>
        /// 優先度付きキューに要素を追加します．
        /// </summary>
        /// <param name="item">優先度付きキューに追加される要素</param>
        /// <remarks>最悪計算量 O(log N) で実行されます．</remarks>
        public void Enqueue(T item)
        {
            var pos = heap.Count;
            heap.Add(item);
            while (pos > 0)
            {
                var par = (pos - 1) / 2;
                if (cmp(heap[par], item) <= 0)
                    break;
                heap[pos] = heap[par];
                pos = par;
            }
            heap[pos] = item;

        }

        /// <summary>
        /// 優先度付きキューから最も価値が低い要素を削除し，返します．
        /// </summary>
        /// <returns>優先度付きキューから削除された要素．</returns>
        /// <remarks>最悪計算量 O(log N) で実行されます．</remarks>
        public T Dequeue()
        {
            var ret = heap[0];
            var pos = 0;
            var x = heap[heap.Count - 1];

            while (pos * 2 + 1 < heap.Count - 1)
            {
                var lch = pos * 2 + 1;
                var rch = pos * 2 + 2;
                if (rch < heap.Count - 1 && cmp(heap[rch], heap[lch]) < 0) lch = rch;
                if (cmp(heap[lch], x) >= 0)
                    break;
                heap[pos] = heap[lch];
                pos = lch;
            }
            heap[pos] = x;
            heap.RemoveAt(heap.Count - 1);
            return ret;

        }
        /// <summary>
        ///  優先度付きキューに含まれる最も価値が低い要素を削除せずに返します．
        /// </summary>
        /// <returns>優先度付きキューに含まれる最も価値が低い要素．</returns>
        /// <remarks>この操作は O(1) で実行されます．</remarks>
        public T Peek() { return heap[0]; }

        /// <summary>
        /// 優先度付きキュー内の要素の数を取得します．
        /// </summary>
        /// <returns>優先度付キュー内にある要素の数</returns>
        /// <remarks>最悪計算量 O(1) で実行されます．</remarks>
        public int Count { get { return heap.Count; } }
        /// <summary>
        /// 優先度付きキュー内に要素が存在するかどうかを O(1) で判定します．
        /// </summary>
        /// <returns>優先度付キュー内にある要素が存在するならば true，そうでなければ　false．</returns>
        /// <remarks>この操作は O(1) で実行されます．</remarks>
        public bool Any() { return heap.Count > 0; }

        /// <summary>
        /// 優先度付きキューに含まれる要素を昇順に並べて返します．
        /// </summary>
        /// <remarks>この操作は計算量 O(N log N)で実行されます．</remarks>
        public T[] Items
        {
            get
            {
                var ret = heap.ToArray();
                Array.Sort(ret, cmp);
                return ret;
            }
        }
    }
    #endregion
}

/// <summary>
/// SEGTREEは1-BASE運用でございます
/// よろしくおねがいします
/// </summary>
/// <typeparam name="T"></typeparam>
class Segtree<T>
{
    int n;//高さ
    T[] tree;//本体
    Func<T, T, T> f;//更新関数。a -> b -> ab使ったなにか
    T exnum;//初期値
    int count;
    /// <summary>
    /// !!!WARNING!!! 1-BASEです。
    /// </summary>
    /// <param name="m">最大値。200001とか入れておくとよい</param>
    /// <param name="f">２引数の関数</param>
    /// <param name="ex">葉に書いてある値の初期値。fの関数に影響を与えない数値にしておくべき。バグり散らかす。</param>
    public Segtree(int m, Func<T, T, T> f, T ex)
    {
        this.count = 0;
        this.f = f;
        this.exnum = ex;
        n = 1;
        while (n < m) n <<= 1;

        tree = new T[(n << 1) - 1];
        for (int i = 0; i < tree.Length; i++) tree[i] = ex;
    }
    public Segtree(int m, T ini, Func<T, T, T> f, T ex) : this(m, f, ex)
    {
        this.count = 0;
        for (int i = 0; i < m; ++i) tree[i + n - 1] = ini;
        all_update();
    }

    /// <summary>
    /// j番目の値をxにする。計算し直さないので、
    /// 入れ替えた後はall_update();を使おう
    /// </summary>
    /// <param name="j">番目</param>
    /// <param name="x">更新後の値</param>
    public void assign_without_update(int j, T x)
    {
        tree[j + n - 1] = x;
    }
    /// <summary>
    /// j番目の値をxにする。計算し直すので、ちょっと計算時間がかかる
    /// </summary>
    /// <param name="j">番目</param>
    /// <param name="x">更新後の値</param>
    public void update(int j, T x)//j番目をxにする
    {
        int i = j + n - 1;
        tree[i] = x;
        while (i > 0)
        {
            i = (i - 1) >> 1;
            tree[i] = f(tree[(i << 1) + 1], tree[(i << 1) + 2]);
        }
        this.count++;
    }

    /// <summary>
    /// 木を全部計算し直す。多分NlogN。違うかも知れないから
    /// よかったら教えて
    /// </summary>
    public void all_update()
    {
        for (int i = n - 2; i >= 0; i--)
            tree[i] = f(tree[(i << 1) + 1], tree[(i << 1) + 2]);
    }
    public T look(int i) { return tree[i + n - 1]; }

    /// <summary>
    /// j番目を消す。
    /// </summary>
    /// <param name="j"></param>
    public void delete(int j)
    {
        int i = j + n - 1;
        tree[i] = exnum;
        int moved = 0;

        while (true)
        {
            tree[i + 1] = tree[i];
            T check = tree[i];
            moved++;
            if (moved + j + 2 > count)
            {
                break;
            }

        }
        all_update();
    }


    // [s, t)
    /// <summary>
    /// s番目からt番目までの結果を返す。
    /// これも当然のように1-BASE.
    /// </summary>
    /// <param name="s"></param>
    /// <param name="t"></param>
    /// <returns></returns>
    public T run(int s, int t) { return query(s, t, 0, 0, n); }
    T query(int s, int t, int k, int l, int r)
    {
        if (r <= s || t <= l) return exnum;
        if (s <= l && r <= t) return tree[k];

        return f(query(s, t, (k << 1) + 1, l, (l + r) >> 1), query(s, t, (k + 1) << 1, (l + r) >> 1, r));
    }
}