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.*;

public class Main {
    private static IO io = new IO();
    
    public static void main(String[] args) {
        int h = io.nextInt();
        int w = io.nextInt();
        int c[][] = new int[10][10];
		for (int i = 0; i < 10; i++) {
			for (int j = 0; j < 10; j++) {
				c[i][j] = io.nextInt();
			}
		}
		int hin[] = new int[10];
		for (int j = 0; j < h; j++) {
			for (int i = 0; i < w; i++) {
				int a = io.nextInt();
				if (a!=-1) hin[a]++;
			}
		}

		for (int k = 0; k < 10; k++) {
			for (int i = 0; i < 10; i++) {
				for (int j = 0; j < 10; j++) {
					c[i][j] = Math.min(c[i][j], c[i][k] + c[k][j]);
				}
			}
		}
		long ans = 0;
		for (int i = 0; i < 10; i++) {
			if (i==1) continue;
			ans += hin[i]*c[i][1];
		}
		System.out.println(ans);

	}

    private static class IO extends PrintWriter {
		private final InputStream in;
		private final byte[] buffer = new byte[1024];
		private int ptr = 0;
		private int buflen = 0;
		IO() {
			this(System.in);
		}
		IO(InputStream source) {
			super(System.out);
			this.in = source;
		}
		boolean hasNextByte() {
			if (ptr < buflen) {
				return true;
			} else {
				ptr = 0;
				try {
					buflen = in.read(buffer);
				} catch (IOException e) {
					e.printStackTrace();
				}
				if (buflen <= 0) {
					return false;
				}
			}
			return true;
		}
		int readByte() {
			if (hasNextByte()) return buffer[ptr++];
			else return -1;
		}
		boolean isPrintableChar(int c) {
			return 33 <= c && c <= 126;
		}
		boolean isNewLine(int c) {
			return c == '\n' || c == '\r';
		}
		void skipUnprintable() {
			while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
		}
		void skipNewLine() {
			while (hasNextByte() && isNewLine(buffer[ptr])) ptr++;
		}
		boolean hasNext() {
			skipUnprintable();
			return hasNextByte();
		}
		boolean hasNextLine() {
			skipNewLine();
			return hasNextByte();
		}
		String next() {
			if (!hasNext()) {
				throw new NoSuchElementException();
			}
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (isPrintableChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
		char[] nextCharArray(int len) {
			if (!hasNext()) {
				throw new NoSuchElementException();
			}
			char[] s = new char[len];
			int i = 0;
			int b = readByte();
			while (isPrintableChar(b)) {
				if (i == len) {
					throw new InputMismatchException();
				}
				s[i++] = (char) b;
				b = readByte();
			}
			return s;
		}
		String nextLine() {
			if (!hasNextLine()) {
				throw new NoSuchElementException();
			}
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (!isNewLine(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
		long nextLong() {
			if (!hasNext()) {
				throw new NoSuchElementException();
			}
			long n = 0;
			boolean minus = false;
			int b = readByte();
			if (b == '-') {
				minus = true;
				b = readByte();
			}
			if (b < '0' || '9' < b) {
				throw new NumberFormatException();
			}
			while (true) {
				if ('0' <= b && b <= '9') {
					n *= 10;
					n += b - '0';
				} else if (b == -1 || !isPrintableChar(b)) {
					return minus ? -n : n;
				} else {
					throw new NumberFormatException();
				}
				b = readByte();
			}
		}
		int nextInt() {
			long nl = nextLong();
			if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) {
				throw new NumberFormatException();
			}
			return (int) nl;
		}
		char nextChar() {
			if (!hasNext()) {
				throw new NoSuchElementException();
			}
			return (char) readByte();
		}
		double nextDouble() {
			return Double.parseDouble(next());
		}
		int[] arrayInt(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++) a[i] = nextInt();
			return a;
		}
		long[] arrayLong(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++) a[i] = nextLong();
			return a;
		}
		double[] arrayDouble(int n) {
			double[] a = new double[n];
			for (int i = 0; i < n; i++) a[i] = nextDouble();
			return a;
		}
		void arrayInt(int[]... a) {
			for (int i = 0; i < a[0].length; i++) for (int j = 0; j < a.length; j++) a[j][i] = nextInt();
		}
		int[][] matrixInt(int n, int m) {
			int[][] a = new int[n][];
			for (int i = 0; i < n; i++) a[i] = arrayInt(m);
			return a;
		}
		char[][] charMap(int n, int m) {
			char[][] a = new char[n][];
			for (int i = 0; i < n; i++) a[i] = nextCharArray(m);
			return a;
		}
		public void close() {
			super.close();
			try {
				in.close();
			} catch (IOException ignored) {
			}
		}
	}
}