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: Wrong Answer)

import java.util.*;
import java.util.Map.Entry;
 
class Main {
	 static int mod =  (int) (Math.pow(10,9)+7);
//	 static int mod = 998244353;
	 static List<ArrayList<Integer>> list= new ArrayList<ArrayList<Integer>>();
	 static int[][] c;
	 public static void main(String[] args) {
	        Scanner sc = new Scanner(System.in);
	        int H = sc.nextInt();
	        int W = sc.nextInt();
	        
	        c=new int[10][10];
	        for(long i=0;i<10;i++)list.add(new ArrayList<Integer>());	        
	        for(int i=0;i<10;i++) {
	        	for(int j=0;j<10;j++) {
	        			c[i][j]=sc.nextInt();
	        	}
	        }
	        
	        
	        LinkedList<Integer> queue = new LinkedList<Integer>();
        	int[] weight = new int[10];
	        for(int i=0;i<10;i++) {
	        	boolean[] visited=new boolean[10];
	        	queue.add(i);
	        	queue.add(0);
	        	int min=c[i][1];
	        	while(!queue.isEmpty()){
	        		int now = queue.poll();
	        		int w = queue.poll();
	        		visited[now]=true;
	        		for(int j=0;j<10;j++) {
	        			if(now==j)continue;
	        			if(visited[j])continue;
	        			if(w>min)continue;
	        			if(j==1) {
	        				min=Math.min(min, w+c[now][j]);
	        			} else {
	        				if(w+c[now][j]<min) {
		        				queue.add(j);
		        				queue.add(w+c[now][j]);	        					
	        				}
	        			}
	        		}
	        	}
	        	weight[i]=min;
	        }
	        
	        int ans=0;
	        for(int i=0;i<H;i++) {
	        	for(int j=0;j<W;j++) {
	        		int tmp=sc.nextInt();
	        		if(tmp!=-1) {
	        			ans=ans+weight[tmp];
	        		}
	        	}
	        }
	        
	        
	        
	        System.out.println(ans);
	        
	 }
	 

}