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.*;
import java.io.*;
import java.nio.charset.StandardCharsets;

public class Main {
	static class Tuple implements Comparable<Tuple> {
		int src, dst, cost;

		Tuple(int src, int dst, int cost) {
			this.src = src;
			this.dst = dst;
			this.cost = cost;
		}

		@Override
		public int compareTo(Tuple o) {
			return Integer.compare(this.cost, o.cost);
		}
	}

	public static void main(String[] args) throws IOException {
		InputStreamReader reader = new InputStreamReader(System.in, StandardCharsets.UTF_8);
		BufferedReader in = new BufferedReader(reader);
		String[] tokens = in.readLine().split(" ");
		int H = Integer.parseInt(tokens[0]);
		int W = Integer.parseInt(tokens[1]);
		Tuple[][] cost = new Tuple[10][10];
		int[][] distMatrix = new int[10][10];
		for (int i = 0; i < 10; ++i) {
			tokens = in.readLine().split(" ");
			for (int j = 0; j < 10; ++j) {
				cost[i][j] = new Tuple(i, j, Integer.parseInt(tokens[j]));
				distMatrix[i][j] = cost[i][j].cost;
			}
		}

		// 対角成分以外をqueueに入れる
		Queue<Tuple> que = new PriorityQueue<>();
		for (int i = 0; i < 10; ++i) {
			for (int j = 0; j < 10; ++j) {
				if (i == j)
					continue;
				que.add(cost[i][j]);
			}
		}

		// 順に評価する
		while (!que.isEmpty()) {
			Tuple tuple = que.poll();
			int c = tuple.cost;
			for (int med = 0; med < 10; ++med) {
				if (tuple.src == med || tuple.dst == med) {
					continue;
				}
				c = Math.min(c, distMatrix[tuple.src][med] + distMatrix[med][tuple.dst]);
			}
			distMatrix[tuple.src][tuple.dst] = c;
			// 次に経由する部分を評価
			// src->tuple.src->tuple.dst
			for (int src = 0; src < 10; ++src) {
				if (tuple.src == src || tuple.dst == src) {
					continue;
				}
				if (distMatrix[src][tuple.src] + c < distMatrix[src][tuple.dst]) {
					distMatrix[src][tuple.dst] = distMatrix[src][tuple.src] + c;
				}
			}
			// tuple.src->tuple.dst->dst
			for (int dst = 0; dst < 10; ++dst) {
				if (tuple.src == dst || tuple.dst == dst) {
					continue;
				}
				if (c + distMatrix[tuple.dst][dst] < distMatrix[tuple.src][dst]) {
					distMatrix[tuple.src][dst] = c + distMatrix[tuple.dst][dst];
				}
			}
		}

		// これをもとに置き換える
		int[][] A = new int[H][W];
		for (int i = 0; i < H; ++i) {
			tokens = in.readLine().split(" ");
			for (int j = 0; j < W; ++j) {
				A[i][j] = Integer.parseInt(tokens[j]);
			}
		}
		int result = 0;
		for (int i = 0; i < H; ++i) {
			for (int j = 0; j < W; ++j) {
				if (A[i][j] == 1 || A[i][j] == -1) {
					continue;
				}
				result += distMatrix[A[i][j]][1];
			}
		}
		System.out.println(result);
	}

}