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.util.*;

public class Main {

    Scanner sc = new Scanner(System.in);
    int h = sc.nextInt();
    int w = sc.nextInt();
    int[][] score = new int[10][10];
    int[][] input = new int[h][w];
    public static void main(String[] args) {
        new Main().run();
    }

    void run() {

        for (int i=0; i<10; i++) {
            for (int j=0; j<10; j++) {
                score[i][j] = sc.nextInt();
            }
        }

        floyd();

        Map<Integer, Integer> map = new HashMap<>();

        long ans = 0;

        for (int i=0; i<h; i++) {
            for (int j=0; j<w; j++) {
                int tmp = sc.nextInt();
//                if (tmp>=0) ans += score[tmp][1];
                if (map.containsKey(tmp)) {
                    int val = map.get(tmp);
                    map.put(tmp, val+1);
                } else {
                    map.put(tmp, 1);
                }
            }
        }

//        System.out.println(map);

        for (Integer k: map.keySet()) {
            if (k==-1) continue;
            int val = map.get(k);
            ans += score[k][1] * val;
        }


//        for (int i=0; i<10; i++) {
//            for (int j=0; j<9; j++) {
//                System.out.print(score[i][j]+" ");
//            }
//            System.out.println(score[i][9]);
//        }

        System.out.println(ans);

    }

    void floyd() {
        for (int k=0; k<10; k++) {
            start:
            for (int i=0; i<10; i++) {
                if (score[i][k]==0) continue start;
                end:
                for (int j=0; j<10; j++) {
                    if (score[k][j]==0) continue end;
                    if (i==8 && k==4 && j==9) {
//                        System.out.println(score[i][j]);
//                        System.out.println(score[i][k]);
//                        System.out.println(score[k][j]);
                    }

                    score[i][j] = Math.min(score[i][j], score[i][k] + score[k][j]);
                }
            }
        }
    }

}