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.ArrayList;
import java.util.Scanner;

public class Main {
    public static int[] mincost = new int[10];
    public static void main(String args[]){
        Scanner scanner = new Scanner(System.in);
        for (int i = 0;i < 10;++i){
            mincost[i] = Integer.MAX_VALUE;
        }
        int h = scanner.nextInt();
        int w = scanner.nextInt();
        int cost[][] = new int[10][10];
        int wall[][] = new int[w][h];
        for (int i = 0;i < 100;++i){
            cost[i / 10][i % 10] = scanner.nextInt();
        }
        for (int i = 0;i < h * w;++i){
            wall[i % w][i / w] = scanner.nextInt();
        }
        int costsnumarray[] = new int[10];
        for (int y = 0;y < h;++y){
            for (int x = 0;x < w;++x){
                if(wall[x][y] == -1){
                    continue;
                }
                ++costsnumarray[wall[x][y]];
            }
        }
        for (int i = 0;i < 10;++i){
            ArrayList<Integer> arrayList = new ArrayList<>();
            arrayList.add(i);
            search(cost, arrayList, 0);
        }
        int lastcost = 0;
        for (int i = 0;i < 10;++i){
            if(i == 1){
                continue;
            }
            lastcost += mincost[i] * costsnumarray[i];
        }
        System.out.println(lastcost);
    }

    public static void search(int costarray[][],ArrayList<Integer> root,int cost){
        for (int i = 0;i < 10;++i){
            boolean flag = false;
            for (int k:root){
                if(k == i){
                    flag = true;
                    break;
                }
            }
            if(flag){
                continue;
            }
            int last = root.get(root.size() - 1);
            if(i == 1){
                int start = root.get(0);
                int newcost = cost + costarray[last][i];
                if(newcost < mincost[start]){
                    mincost[start] = newcost;
                }
            }
            else{
                ArrayList<Integer> newarray = new ArrayList<>();
                for (int c = 0;c < root.size();++c){
                    newarray.add(root.get(c));
                }
                newarray.add(i);
                int newcost = cost + costarray[last][i];
                search(costarray, newarray, newcost);
            }
        }
    }


}