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;

class Program
{
    static string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("2 4");
            WillReturn.Add("0 9 9 9 9 9 9 9 9 9");
            WillReturn.Add("9 0 9 9 9 9 9 9 9 9");
            WillReturn.Add("9 9 0 9 9 9 9 9 9 9");
            WillReturn.Add("9 9 9 0 9 9 9 9 9 9");
            WillReturn.Add("9 9 9 9 0 9 9 9 9 2");
            WillReturn.Add("9 9 9 9 9 0 9 9 9 9");
            WillReturn.Add("9 9 9 9 9 9 0 9 9 9");
            WillReturn.Add("9 9 9 9 9 9 9 0 9 9");
            WillReturn.Add("9 9 9 9 2 9 9 9 0 9");
            WillReturn.Add("9 2 9 9 9 9 9 9 9 0");
            WillReturn.Add("-1 -1 -1 -1");
            WillReturn.Add("8 1 1 8");
            //12
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("5 5");
            WillReturn.Add("0 999 999 999 999 999 999 999 999 999");
            WillReturn.Add("999 0 999 999 999 999 999 999 999 999");
            WillReturn.Add("999 999 0 999 999 999 999 999 999 999");
            WillReturn.Add("999 999 999 0 999 999 999 999 999 999");
            WillReturn.Add("999 999 999 999 0 999 999 999 999 999");
            WillReturn.Add("999 999 999 999 999 0 999 999 999 999");
            WillReturn.Add("999 999 999 999 999 999 0 999 999 999");
            WillReturn.Add("999 999 999 999 999 999 999 0 999 999");
            WillReturn.Add("999 999 999 999 999 999 999 999 0 999");
            WillReturn.Add("999 999 999 999 999 999 999 999 999 0");
            WillReturn.Add("1 1 1 1 1");
            WillReturn.Add("1 1 1 1 1");
            WillReturn.Add("1 1 1 1 1");
            WillReturn.Add("1 1 1 1 1");
            WillReturn.Add("1 1 1 1 1");
            //0
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("3 5");
            WillReturn.Add("0 4 3 6 2 7 2 5 3 3");
            WillReturn.Add("4 0 5 3 7 5 3 7 2 7");
            WillReturn.Add("5 7 0 7 2 9 3 2 9 1");
            WillReturn.Add("3 6 2 0 2 4 6 4 2 3");
            WillReturn.Add("3 5 7 4 0 6 9 7 6 7");
            WillReturn.Add("9 8 5 2 2 0 4 7 6 5");
            WillReturn.Add("5 4 6 3 2 3 0 5 4 3");
            WillReturn.Add("3 6 2 3 4 2 4 0 8 9");
            WillReturn.Add("4 6 5 4 3 5 3 2 0 8");
            WillReturn.Add("2 1 3 4 5 7 8 6 4 0");
            WillReturn.Add("3 5 2 6 1");
            WillReturn.Add("2 5 3 2 1");
            WillReturn.Add("6 9 2 5 6");
            //47
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static void Main()
    {
        List<string> InputList = GetInputList();

        int[] wkArr = { };
        Action<string> SplitAct = pStr =>
            wkArr = pStr.Split(' ').Select(X => int.Parse(X)).ToArray();

        int[,] CostArr = new int[10, 10];
        for (int I = 1; I <= 10; I++) {
            SplitAct(InputList[I]);
            for (int J = 0; J <= 9; J++) {
                CostArr[I - 1, J] = wkArr[J];
            }
        }

        var NumList = new List<int>();
        foreach (string EachStr in InputList.Skip(1 + 10)) {
            SplitAct(EachStr);
            foreach (int EachInt in wkArr) {
                if (EachInt == -1) continue;
                NumList.Add(EachInt);
            }
        }

        //ワーシャルフロイド法でノードの組み合わせごとの最短経路を求める
        for (int K = 0; K <= 9; K++) {
            for (int I = 0; I <= 9; I++) {
                for (int J = 0; J <= 9; J++) {
                    CostArr[I, J] = Math.Min(CostArr[I, J], CostArr[I, K] + CostArr[K, J]);
                }
            }
        }

        long Answer = 0;
        NumList.ForEach(X => Answer += CostArr[X, 1]);
        Console.WriteLine(Answer);
    }
}