Problem:
Score : 400 points

Problem Statement

Joisino the magical girl has decided to turn every single digit that exists on this world into 1.

Rewriting a digit i with j (0≤i,j≤9) costs c_{i,j} MP (Magic Points).

She is now standing before a wall. The wall is divided into HW squares in H rows and W columns, and at least one square contains a digit between 0 and 9 (inclusive).

You are given A_{i,j} that describes the square at the i-th row from the top and j-th column from the left, as follows:

If A_{i,j}≠-1, the square contains a digit A_{i,j}.

If A_{i,j}=-1, the square does not contain a digit.

Find the minimum total amount of MP required to turn every digit on this wall into 1 in the end.

Constraints

1≤H,W≤200

1≤c_{i,j}≤10^3 (i≠j)

c_{i,j}=0 (i=j)

-1≤A_{i,j}≤9

All input values are integers.

There is at least one digit on the wall.

Input

Input is given from Standard Input in the following format:

H W
c_{0,0} ... c_{0,9}
:
c_{9,0} ... c_{9,9}
A_{1,1} ... A_{1,W}
:
A_{H,1} ... A_{H,W}

Output

Print the minimum total amount of MP required to turn every digit on the wall into 1 in the end.

Sample Input 1

2 4
0 9 9 9 9 9 9 9 9 9
9 0 9 9 9 9 9 9 9 9
9 9 0 9 9 9 9 9 9 9
9 9 9 0 9 9 9 9 9 9
9 9 9 9 0 9 9 9 9 2
9 9 9 9 9 0 9 9 9 9
9 9 9 9 9 9 0 9 9 9
9 9 9 9 9 9 9 0 9 9
9 9 9 9 2 9 9 9 0 9
9 2 9 9 9 9 9 9 9 0
-1 -1 -1 -1
8 1 1 8

Sample Output 1

12

To turn a single 8 into 1, it is optimal to first turn 8 into 4, then turn 4 into 9, and finally turn 9 into 1, costing 6 MP.

The wall contains two 8s, so the minimum total MP required is 6×2=12.

Sample Input 2

5 5
0 999 999 999 999 999 999 999 999 999
999 0 999 999 999 999 999 999 999 999
999 999 0 999 999 999 999 999 999 999
999 999 999 0 999 999 999 999 999 999
999 999 999 999 0 999 999 999 999 999
999 999 999 999 999 0 999 999 999 999
999 999 999 999 999 999 0 999 999 999
999 999 999 999 999 999 999 0 999 999
999 999 999 999 999 999 999 999 0 999
999 999 999 999 999 999 999 999 999 0
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1

Sample Output 2

0

Note that she may not need to change any digit.

Sample Input 3

3 5
0 4 3 6 2 7 2 5 3 3
4 0 5 3 7 5 3 7 2 7
5 7 0 7 2 9 3 2 9 1
3 6 2 0 2 4 6 4 2 3
3 5 7 4 0 6 9 7 6 7
9 8 5 2 2 0 4 7 6 5
5 4 6 3 2 3 0 5 4 3
3 6 2 3 4 2 4 0 8 9
4 6 5 4 3 5 3 2 0 8
2 1 3 4 5 7 8 6 4 0
3 5 2 6 1
2 5 3 2 1
6 9 2 5 6

Sample Output 3

47

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Convert;
using static System.Math;
//using Debug;
//using static System.Globalization.CultureInfo;
//using Edge = Pair<long, int>;
using System.Text;
class Program
{ 
    static void Main(string[] args)
    {
        Solve();
        //WriteLine(Solve());
    }
    static void Solve()
    {
        var hw = Input.ar;
        var cs = Input.ar2D(10);
        var list = new List<Pair<long, int, int>>();
        for (var i = 0; i < 10; i++)
            for (var j = 0; j < 10; j++)
                list.Add(new Pair<long, int, int>(cs[i][j], i, j));
        var ar = Input.ar2D(hw[0]);
        var dist = ShortestPath.WarshallFloyd(10, list,true);
        var res = 0L;
        for (var i = 0; i < hw[0]; i++)
            for (var j = 0; j < hw[1]; j++)
                if(ar[i][j]!=-1)
                res += dist[ar[i][j]][1];
        WriteLine(res);
    }
}

public class Input
{
    public static string read => ReadLine().Trim();
    public static int[] ar => read.Split(' ').Select(int.Parse).ToArray();
    public  static int num => ToInt32(read);
    public static long[] arL => read.Split(' ').Select(long.Parse).ToArray();
    public  static long numL => ToInt64(read);
    public static char[][] gred(int h) 
        => Enumerable.Repeat(0, h).Select(_ => read.ToCharArray()).ToArray();
    public static int[] ar1D(int n)
        => Enumerable.Repeat(0, n).Select(_ => num).ToArray();
    public static long[] arL1D(int n)
        => Enumerable.Repeat(0, n).Select(_ => numL).ToArray();
    public static string[] strs(int n)
        => Enumerable.Repeat(0, n).Select(_ => read).ToArray();
    public static int[][] ar2D(int n)
        => Enumerable.Repeat(0, n).Select(_ => ar).ToArray();
    public static long[][] arL2D(int n)
        => Enumerable.Repeat(0, n).Select(_ => arL).ToArray();
    public static T getValue<T>(string g)
    {
        var t = typeof(T);
        if (t == typeof(int))
            return (T)(object)int.Parse(g);
        if (t == typeof(long))
            return (T)(object)long.Parse(g);
        if (t == typeof(string))
            return (T)(object)g;
        if (t == typeof(char))
            return (T)(object)char.Parse(g);
        if (t == typeof(double))
            return (T)(object)double.Parse(g);
        if (t == typeof(bool))
            return (T)(object)bool.Parse(g);
        return default(T);
    }
    public const long Inf = (long)1e18;
    public const double eps = 1e-6;
    public  const string Alfa = "abcdefghijklmnopqrstuvwxyz";
    public  const int MOD = 1000000007;
}
public class PriorityQueue<T> where T : IComparable<T>
{
    public List<T> _item;
    public int Count { get { return _item.Count; } }
    public bool IsMaxHeap { get; set; }
    public T Peek { get { return _item[0]; } }
    public PriorityQueue(bool IsMaxHeap = true) { _item = new List<T>(); this.IsMaxHeap = IsMaxHeap; }
    private int Compare(int i, int j) => (IsMaxHeap ? 1 : -1) * _item[i].CompareTo(_item[j]);
    private int Parent(int i)
        => (i - 1) >> 1;
    private int Left(int i)
        => (i << 1) + 1;
    public T Enqueue(T val)
    {
        int i = _item.Count;
        _item.Add(val);
        while (i > 0)
        {
            int p = Parent(i);
            if (Compare(i, p) > 0)
            {
                var tmp = _item[i];
                _item[i] = _item[p];
                _item[p] = tmp;
            }
            i = p;
        }
        return val;
    }
    public T Dequeue()
    {
        T val = _item[0];
        _item[0] = _item[_item.Count-1];
        _item.RemoveAt(_item.Count - 1);
        for (int i = 0, j; (j = Left(i)) < _item.Count; i = j)
        {
            if (j != _item.Count - 1 && Compare(j, j + 1) < 0) j++;
            if (Compare(i, j) < 0)
            {
                var tmp = _item[i];
                _item[i] = _item[j];
                _item[j] = tmp;
            }
        }
        return val;
    }
}

public class Pair<T1, T2> : IComparable<Pair<T1, T2>>
{
    public T1 v1 { get; set; }
    public T2 v2 { get; set; }
    public Pair() : this(default(T1), default(T2)) { }
    public Pair(T1 v1, T2 v2)
    { this.v1 = v1;this.v2 = v2; }

    public int CompareTo(Pair<T1, T2> p)
    {
        var c = Comparer<T1>.Default.Compare(v1, p.v1);
        if (c == 0)
            c = Comparer<T2>.Default.Compare(v2, p.v2);
        return c;
    }
    public static Pair<T1, T2> MakePair()
    {
        var r = ReadLine().Split(' ');
        return new Pair<T1, T2>(Input.getValue<T1>(r[0]), Input.getValue<T2>(r[1]));
    }
    public override string ToString()
        => $"{v1.ToString()} {v2.ToString()}";
}

public class Pair<T1, T2, T3> : Pair<T1, T2>, IComparable<Pair<T1, T2, T3>>
{
    public T3 v3 { get; set; }
    public Pair() : base() { v3 = default(T3); }
    public Pair(T1 v1, T2 v2, T3 v3) : base(v1,v2)
    { this.v3 = v3; }
    
    public int CompareTo(Pair<T1, T2, T3> p)
    {
        var c = base.CompareTo(p);
        if (c == 0)
            c = Comparer<T3>.Default.Compare(v3, p.v3);
        return c;
    }
    public new static Pair<T1, T2, T3> MakePair()
    {
        var r = ReadLine().Split(' ');
        return new Pair<T1, T2, T3>(Input.getValue<T1>(r[0]), Input.getValue<T2>(r[1]), Input.getValue<T3>(r[2]));
    }
    public override string ToString()
        => $"{base.ToString()} {v3.ToString()}";
}

public class ShortestPath
{
    public static long[] Dijkstra(IList<IEnumerable<Pair<long,int>>> edges,int st)
    {
        var dist = Enumerable.Repeat(long.MaxValue, edges.Count).ToArray();
        var pq = new PriorityQueue<Pair<long, int>>(false);
        pq.Enqueue(new Pair<long, int>(0, st));
        dist[st] = 0;
        while (pq.Count != 0)
        {
            var p = pq.Dequeue();
            if (dist[p.v2] < p.v1) continue;
            foreach (var e in edges[p.v2])
                if (dist[e.v2] > e.v1 + dist[p.v2])
                {
                    dist[e.v2] = e.v1 + dist[p.v2];
                    pq.Enqueue(new Pair<long, int>(dist[e.v2], e.v2));
                }
        }
        return dist;
    }

    public static long[][] WarshallFloyd(int num, IEnumerable<Pair<long, int, int>> edges, bool directed = false)
    {
        var dist = Enumerable.Repeat(0, num).Select(_ => Enumerable.Repeat(long.MaxValue / 2, num).ToArray()).ToArray();
        foreach (var e in edges)
        {
            dist[e.v2][e.v3] = e.v1;
            if (!directed)
                dist[e.v3][e.v2] = e.v1;
        }
        for (var k = 0; k < num; k++)
            for (var i = 0; i < num; i++)
                for (var j = 0; j < num; j++)
                    dist[i][j] = Min(dist[i][j], dist[i][k] + dist[k][j]);
        return dist;
    }
}