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;
class Search
{
    public long[,,] GetMin(long[,] a)
    {
        int n = a.Length;
        n = (int)Math.Pow(n, 0.5);
        long[,,] b = new long[n - 1, n, n];
        for (int i = 0; i < n; i++)
            for (int j = 0; j < n; j++)
                b[0, i, j] = a[i, j];
        for (int g = 0; g < n; g++)
        {
            for (int k = 1; k < n - 1; k++)
            {
                for (int l = 0; l < n; l++)
                {
                    long min = long.MaxValue;
                    for (int i = 0; i < n; i++)
                    {
                        if (i != l && a[l, i] != -1 && b[k - 1, i, g] != -1)
                        {
                            min = Math.Min(min, a[l, i] + b[k - 1, i, g]);
                        }
                        if (b[k - 1, l, g] != -1)
                            b[k, l, g] = Math.Min(b[k - 1, l, g], min);
                        else if (min != long.MaxValue)
                            b[k, l, g] = min;
                        else
                            b[k, l, g] = -1;
                    }
                }
            }
        }
        return b; //b[k,l,g]はlから最大k個の点を経由してgまで行く最短距離
    }
}
class Program
{
    public static void Main()
    {
        Search s = new Search();
        string[] str = Console.ReadLine().Split(' ');
        int h = int.Parse(str[0]);
        int w = int.Parse(str[1]);
        long[,] c = new long[10, 10];
        for (int i = 0; i < 10; i++)
        {
            str = Console.ReadLine().Split(' ');
            for (int j = 0; j < 10; j++)
                c[i, j] = long.Parse(str[j]);
        }
        long[,,] b = s.GetMin(c);
        long sum = 0;
        for (int i = 0; i < h; i++)
        {
            str = Console.ReadLine().Split(' ');
            for (int j = 0; j < w; j++)
                if (int.Parse(str[j]) != -1)
                    sum += b[8, int.Parse(str[j]), 1];
        }
        Console.WriteLine(sum);
    }
}