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;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;

namespace AtCoder.ABC079.C
{
    class Program
    {
        static void Main ()
        {
            var hw = Console.ReadLine ().Split (' ');
            int H = int.Parse (hw[0]);
            int W = int.Parse (hw[1]);
            var c = new int[10][];
            var A = new int[H][];
            for (int i = 0; i < 10; i++)
            {
                var inputs = Console.ReadLine ().Split (' ')
                    .Select (elem => int.Parse (elem))
                    .ToArray ();
                c[i] = inputs;
            }
            for (int i = 0; i < H; i++)
            {
                var inputs = Console.ReadLine ().Split (' ')
                    .Select (elem => int.Parse (elem))
                    .ToArray ();
                A[i] = inputs;
            }

            var costToOne = new int[10];
            var isFinal = new bool[10];
            for (int i = 0; i < 10; i++)
            {
                costToOne[i] = c[i][1];
            }
            isFinal[1] = true;
            while (isFinal.Contains (false))
            {
                int minval = int.MaxValue;
                int minidx = 0;
                for (int i = 0; i < 10; i++)
                {
                    if (isFinal[i]) continue;
                    if (minval > costToOne[i])
                    {
                        minval = costToOne[i];
                        minidx = i;
                    }
                }
                int j = minidx;
                isFinal[j] = true;
                for (int i = 0; i < 10; i++)
                {
                    if (isFinal[i]) continue;
                    if (costToOne[i] > costToOne[j] + c[i][j])
                    {
                        costToOne[i] = costToOne[j] + c[i][j];
                    }
                }
            }

            int mp = 0;
            for (int i = 0; i < H; i++)
            {
                for (int j = 0; j < W; j++)
                {
                    if (A[i][j] == -1) continue;
                    mp += costToOne[A[i][j]];
                }
            }
            Console.WriteLine (mp);
        }
    }
}