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.Linq;

class Procon {
  public Procon () { }
  static void Main (string[] agrs) {
    new Procon ().Do ();
  }

  Scanner cin;

  public void Do () {
    cin = new Scanner ();
    int H = cin.nextInt ();
    int W = cin.nextInt ();
    int[, ] c = new int[10, 10];

    for (int i = 0; i < 10; i++) {
      for (int j = 0; j < 10; j++) {
        c[i, j] = cin.nextInt ();
      }
    }

    int[, ] A = new int[H, W];
    for (int i = 0; i < H; i++) {
      for (int j = 0; j < W; j++) {
        A[i, j] = cin.nextInt ();
      }
    }

    int[] DP = new int[10];
    for (int i = 0; i < 10; i++) {
      DP[i] = c[i, 1];
    }

    for (int j = 0; j < 10; j++) {
      for (int i = 0; i < 10; i++) {
        for (int k = 0; k < 10; k++) {
          int tmp = c[i, k] + DP[k];
          if (tmp < DP[i]) {
            DP[i] = tmp;
          }
        }
      }
    }

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

class Scanner {
  string[] s;
  int i;
  int max_i;

  public Scanner () {
    s = new string[0];
    max_i = 0;
    i = 0;
  }

  public string nextString () {
    if (i >= s.Length) {
      s = Console.ReadLine ().Split (' ');
      max_i = s.Length;
      i = 0;
      if (max_i == 0) {
        return "";
      }
      return s[i++];
    } else {
      return s[i++];
    }
  }

  public int nextInt () {
    return int.Parse (nextString ());
  }

  public long nextLong () {
    return long.Parse (nextString ());
  }

  public double nextDouble () {
    return double.Parse (nextString ());
  }

  public string[] arrayString () {
    return Console.ReadLine ().Split (' ');
  }

  public int[] arrayInt () {
    string[] str = Console.ReadLine ().Split (' ');
    int[] array = new int[str.Length];
    for (int i = 0; i < str.Length; i++) {
      array[i] = int.Parse (str[i]);
    }
    return array;
  }

  public long[] arrayLong () {
    string[] str = Console.ReadLine ().Split (' ');
    long[] array = new long[str.Length];
    for (int i = 0; i < str.Length; i++) {
      array[i] = long.Parse (str[i]);
    }
    return array;
  }

  public double[] arrayDouble () {
    string[] str = Console.ReadLine ().Split (' ');
    double[] array = new double[str.Length];
    for (int i = 0; i < str.Length; i++) {
      array[i] = double.Parse (str[i]);
    }
    return array;
  }
}