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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)



import java.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {
    static int[][] minpath(int[][] c){
        int[][] path = c.clone();
        /*
        for(int i=0; i<c.length; i++){
            for(int j=0; j<c[0].length; j++){
                path[i][j] = Integer.MAX_VALUE;
            }
        }
        */

        for(int k=0; k<c.length; k++){
            for(int i=0; i<c.length; i++){
                for(int j=0; j<c.length; j++){
                    path[i][j] = Math.min(path[i][j], path[i][k]+path[k][j]);
                }
            }
        }
        return path;
    }

    static int minMF(int[][] c, int[][] A){
        int result = 0;
        int[][] minpath = minpath(c);
        for(int i=0; i<A.length; i++){
            for(int j=0; j<A[0].length; j++){
                if(A[i][j] == -1) continue;
                else result += minpath[A[i][j]][1];
            }
        }
        return result;
    }

    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] inputstr = br.readLine().trim().split(" ");
        int[][] A = new int[Integer.parseInt(inputstr[0])][Integer.parseInt(inputstr[1])];
        int[][] c = new int[10][10];
        for(int i=0; i<c.length; i++){
            inputstr = br.readLine().trim().split(" ");
            for(int j=0; j<c[0].length; j++){
                c[i][j] = Integer.parseInt(inputstr[j]);
            }
        }
        for(int i=0; i<A.length; i++){
            inputstr = br.readLine().trim().split(" ");
            for(int j=0; j<A[0].length; j++){
                A[i][j] = Integer.parseInt(inputstr[j]);
            }
        }
        System.out.println(minMF(c, A));

    }
}