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.IOException;
import java.io.InputStream;
import java.io.PrintStream;
import java.util.Arrays;
import java.util.NoSuchElementException;
import java.util.Scanner;

public class Main {
	InputStream in = System.in;
	PrintStream out = System.out;

	public void _main(String[] args) {
		FastScanner sc = new FastScanner(in);

		int H = sc.nextInt();
		int W = sc.nextInt();
		
		int[][] c = new int[10][10];
		for(int i=0;i<10;i++) {
			for(int j=0;j<10;j++) {
				c[i][j] = sc.nextInt();
			}
		}

		for(int k=0;k<10;k++) {
			for(int s=0;s<10;s++) {
				for(int e=0;e<10;e++) {
					c[s][e] = Math.min(c[s][e], c[s][k]+c[k][e]);
				}
			}
		}
		
		
		long ans = 0;
		
		for(int i=0;i<H;i++) {
			for(int j=0;j<W;j++) {
				int a = sc.nextInt();
				if(a != -1)
					ans += c[a][1];
			}
		}
		
		out.println(ans);
		
		
	}

	public static void main(String[] args) {
		new Main()._main(args);
	}

	@SuppressWarnings("unused")
	private String join(String delimiter, int[] a) {
		StringBuilder sb = new StringBuilder();

		for (int i = 0; i < a.length; i++) {
			sb.append(a[i]);
			sb.append(delimiter);
		}
		return sb.substring(0, Math.max(sb.length() - delimiter.length(), 0));
	}

	@SuppressWarnings("unused")
	private String join(String delimiter, long[] a) {
		StringBuilder sb = new StringBuilder();

		for (int i = 0; i < a.length; i++) {
			sb.append(a[i]);
			sb.append(delimiter);
		}
		return sb.substring(0, Math.max(sb.length() - delimiter.length(), 0));
	}

	@SuppressWarnings("unused")
	private int max(int[] arr) {
		if(arr == null || arr.length == 0) {
			throw new IllegalArgumentException(Arrays.toString(arr));
		}

		int candidate = arr[0];
		for(int i=1;i<arr.length;i++) {
			candidate = candidate > arr[i] ? candidate : arr[i];
		}
		return candidate;
	}

	@SuppressWarnings("unused")
	private long max(long[] arr) {
		if(arr == null || arr.length == 0) {
			throw new IllegalArgumentException(Arrays.toString(arr));
		}

		long candidate = arr[0];
		for(int i=1;i<arr.length;i++) {
			candidate = candidate > arr[i] ? candidate : arr[i];
		}
		return candidate;
	}

	@SuppressWarnings("unused")
	private int min(int[] arr) {
		if(arr == null || arr.length == 0) {
			throw new IllegalArgumentException(Arrays.toString(arr));
		}

		int candidate = arr[0];
		for(int i=1;i<arr.length;i++) {
			candidate = candidate < arr[i] ? candidate : arr[i];
		}
		return candidate;
	}

	@SuppressWarnings("unused")
	private long min(long[] arr) {
		if(arr == null || arr.length == 0) {
			throw new IllegalArgumentException(Arrays.toString(arr));
		}

		long candidate = arr[0];
		for(int i=1;i<arr.length;i++) {
			candidate = candidate < arr[i] ? candidate : arr[i];
		}
		return candidate;
	}

	@SuppressWarnings("unused")
	private int[] nextIntArray(Scanner sc, int n) {
		int[] result = new int[n];
		for (int i = 0; i < n; i++) {
			result[i] = sc.nextInt();
		}
		return result;
	}

	@SuppressWarnings("unused")
	private long[] nextLongArray(Scanner sc, int n) {
		long[] result = new long[n];
		for (int i = 0; i < n; i++) {
			result[i] = sc.nextLong();
		}
		return result;
	}

	@SuppressWarnings("unused")
	private int[] nextIntArray1origin(Scanner sc, int n) {
		int[] result = new int[n + 1];
		for (int i = 1; i <= n; i++) {
			result[i] = sc.nextInt();
		}
		return result;
	}
}
class FastScanner {
	private InputStream in;

	public FastScanner(InputStream source) {
		this.in = source;
	}
	public void close(){
	}
	
	private final int BUF_SIZE = 1024 * 4;
	byte[] buf = new byte[BUF_SIZE];
	int bufPtr = 0;
	int bufLen = 0;

	private int nextByte() {
		if (bufLen == -1) {
			throw new NoSuchElementException();
		}

		if (bufPtr >= bufLen) {
			try {
				bufLen = in.read(buf);
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
			bufPtr = 0;

			if (bufLen <= 0) {
				return -1;
			}
		}
		return buf[bufPtr++];
	}

	private static boolean isPrintableCharacter(int c) {
		return c >= 0x21 && c <= 0x7e;
	}

	public int nextInt() {
		long l = nextLong();
		if(l > Integer.MAX_VALUE || l < Integer.MIN_VALUE) {
			throw new NumberFormatException();
		}
		return (int)l;
	}

	public long nextLong() {
		long result = 0;
		int sign = 1;
		
		int c;
		while (!isPrintableCharacter(c = nextByte()))
			;
		
		if( c == '-' ) {
			sign = -1;
			c = nextByte();
		}else if(c== '+') {
			c = nextByte();
		}
		result = c - '0';
		
		while((isPrintableCharacter(c = nextByte()))) {
			result *= 10;
			result += c-'0';
		}
		
		return sign * result;
	}

	public double nextDouble() {
		return Double.parseDouble(next());
	}

	public String next() {
		StringBuilder sb = new StringBuilder();
		int b;

		while (!isPrintableCharacter(b = nextByte()))
			;
		do {
			sb.appendCodePoint(b);
		} while (isPrintableCharacter(b = nextByte()));

		return sb.toString();
	}

	public int[] nextIntArray(int n) {
		int[] result = new int[n];
		for (int i = 0; i < n; i++) {
			result[i] = nextInt();
		}
		return result;
	}

	public int[] nextIntArray1origin(int n) {
		int[] result = new int[n + 1];
		for (int i = 0; i < n; i++) {
			result[i + 1] = nextInt();
		}
		return result;
	}

	public long[] nextLongArray(int n) {
		long[] result = new long[n];
		for (int i = 0; i < n; i++) {
			result[i] = nextLong();
		}
		return result;
	}

	public long[] nextLongArray1origin(int n) {
		long[] result = new long[n + 1];
		for (int i = 0; i < n; i++) {
			result[i + 1] = nextLong();
		}
		return result;
	}

	public char[] nextCharArray(int n) {
		char[] result = new char[n];
		for (int i = 0; i < n; i++) {
			result[i] = (char) nextByte();
		}
		return result;
	}

	public char[][] nextChar2DArray(int n, int m) {
		char[][] result = new char[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				result[i][j] = (char) nextByte();
			}
		}
		return result;
	}

	public char[][] nextChar2DArray1origin(int n, int m) {
		char[][] result = new char[n + 1][m + 1];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				result[i + 1][j + 1] = (char) nextByte();
			}
		}
		return result;
	}

}