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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using static System.Math;
using static Extentions;
using static MathExtensions;

public static class Program
{
    public static void Solve()
    {
        var h = I;
        var w = I;

        var gr = new AdjacencyMatrix<int>(10,
            new Monoid<int>(0, (x, y) => x + y),
            new Monoid<int>(int.MaxValue, Min));

        var c = Repeat(10, i => Repeat(10, j => gr[i, j] = I).ToArray()).ToArray();
        var a = Repeat(h, () => Repeat(w, () => I).ToArray()).ToArray();

        var wf = new WarshallFloyd<int>(gr);
        wf.Calculate();

        var ans = 0;

        for (var i = 0; i < h; i++)
            for (var j = 0; j < w; j++) ans += a[i][j] != -1 ? wf.GetMinCost(a[i][j], 1) : 0;

        Console.WriteLine(ans);
    }

    #region Scanners
    static Scanner _scanner;
    static char C => _scanner.NextChar();
    static string S => _scanner.NextString();
    static int I => _scanner.NextInt();
    static long L => _scanner.NextLong();
    static BigInteger B => _scanner.NextBigInteger();
    static double D => _scanner.NextDouble();
    static decimal M => _scanner.NextDecimal();
    #endregion

    public static void Main()
    {
        var sw = new StreamWriter(Console.OpenStandardOutput());
        sw.NewLine = "\n";
#if DEBUG
        sw.AutoFlush = true;
        Console.SetError(sw);
#else
        sw.AutoFlush = false;
#endif
        Console.SetOut(sw);
        _scanner = new Scanner(Console.OpenStandardInput());
        Solve();
        Console.Out.Flush();
    }
}

public static partial class Extentions
{
}

#region OldLibrary
#pragma warning disable
public class Monoid<T>
{
    public T Unit { get; private set; }
    Func<T, T, T> append;
    public T Append(T left, T right) => append(left, right);

    public Monoid(T unit, Func<T, T, T> append)
    {
        this.Unit = unit;
        this.append = append;
    }
}

public abstract class Graph<T> where T : IEquatable<T>
{
    public abstract T this[int source, int target] { get; set; }

    public int V { get; protected set; }
    public Monoid<T> Monoid { get; protected set; }
    public Monoid<T> Comparer { get; protected set; }

    public event Action GraphChanged;
    protected void OnGraphChanged() => GraphChanged?.Invoke();

    public bool HasEdge(int source, int target)
        => !this[source, target].Equals(this.Comparer.Unit);
}

public class AdjacencyMatrix<T> : Graph<T> where T : IEquatable<T>
{
    protected readonly T[,] graph;

    public override T this[int source, int target]
    {
        // O(1)
        get { return graph[source, target]; }

        // O(1)
        set
        {
            var a = this.Comparer.Append(graph[source, target], value);
            if (a.Equals(graph[source, target])) return;
            graph[source, target] = a;
            OnGraphChanged();
        }
    }

    // O(V^2)
    public AdjacencyMatrix(int v, Monoid<T> monoid, Monoid<T> comparer)
    {
        this.V = v;
        this.Monoid = monoid;
        this.Comparer = comparer;
        graph = new T[v, v];
        for (var i = 0; i < v; i++)
            for (var j = 0; j < v; j++)
                graph[i, j] = i == j ? monoid.Unit : comparer.Unit;
    }
}

public class WarshallFloyd<T> where T : IEquatable<T>
{
    AdjacencyMatrix<T> graph;
    T[,] d;
    bool calculated = false;

    // O(1)
    public WarshallFloyd(AdjacencyMatrix<T> graph)
    {
        this.graph = graph;
        d = new T[graph.V, graph.V];
        graph.GraphChanged += () => calculated = false;
    }

    // O(V^3)
    public void Calculate()
    {
        if (calculated) return;

        for (var i = 0; i < graph.V; i++)
            for (var j = 0; j < graph.V; j++) d[i, j] = graph[i, j];

        for (var k = 0; k < graph.V; k++)
            for (var i = 0; i < graph.V; i++)
                for (var j = 0; j < graph.V; j++)
                    d[i, j] = graph.Comparer.Append(d[i, j],
                        d[i, k].Equals(graph.Comparer.Unit)
                        || d[k, j].Equals(graph.Comparer.Unit)
                        ? graph.Comparer.Unit
                        : graph.Monoid.Append(d[i, k], d[k, j]));

        calculated = true;
    }

    // O(1)
    public T GetMinCost(int source, int target)
    {
        if (!calculated) throw new InvalidOperationException();
        return d[source, target];
    }
}
#pragma warning restore
#endregion

#region Library
public class Scanner
{
    private readonly Stream _stream;
    private const int _bufferSize = 1024;
    private readonly byte[] _buf = new byte[_bufferSize];
    private int _len, _ptr;

    public Scanner(Stream stream)
    {
        _stream = stream;
    }

    public byte ReadByte()
    {
        if (_ptr >= _len) { _len = _stream.Read(_buf, 0, 1024); _ptr = 0; }
        return _buf[_ptr++];
    }

    public char ReadChar() => (char)ReadByte();

    public string ReadLine()
    {
        var r = new StringBuilder();
        if (_ptr == 0) r.Append(ReadChar());
        for (; _ptr < _len; _ptr++) r.Append((char)_buf[_ptr]);
        return r.ToString();
    }

    public char NextChar() => char.Parse(NextString());

    public string NextString()
    {
        var r = new StringBuilder();
        var b = ReadChar();
        while (b != ' ' && b != '\n') { r.Append(b); b = ReadChar(); }
        return r.ToString();
    }

    public int NextInt() => (int)NextLong();

    public long NextLong()
    {
        var r = 0L;
        var b = ReadByte();
        var n = b == '-';
        if (n) b = ReadByte();
        while (b != ' ' && b != '\n') { r = r * 10 + b - '0'; b = ReadByte(); }
        return n ? -r : r;
    }

    public BigInteger NextBigInteger()
    {
        var r = new BigInteger();
        var b = ReadByte();
        var n = b == '-';
        if (n) b = ReadByte();
        while (b != ' ' && b != '\n') { r = r * 10 + b - '0'; b = ReadByte(); }
        return n ? -r : r;
    }

    public double NextDouble()
    {
        var i = 0L;
        var b = ReadByte();
        var n = b == '-';
        if (n) b = ReadByte();
        while (b != '.' && b != ' ' && b != '\n') { i = i * 10 + b - '0'; b = ReadByte(); }
        if (b != '.') return n ? -i : i;
        b = ReadByte();
        var f = 0L;
        var p = 0;
        while (b != ' ' && b != '\n') { f = f * 10 + b - '0'; b = ReadByte(); p++; }
        var r = i + (double)f / Pow(10, p);
        return n ? -r : r;
    }

    public decimal NextDecimal() => decimal.Parse(NextString());

    public T Next<T>(Func<string, T> parser) => parser(NextString());
}

[DebuggerStepThrough]
public static partial class Extentions
{
    public static void Assert(bool condition)
    {
        if (!condition) throw new Exception("Assertion failed");
    }

    public static string AsString(this IEnumerable<char> source) => new string(source.ToArray());

    public static void ForEach<T>(this IEnumerable<T> source, Action<T> action)
    {
        foreach (var item in source) action(item);
    }

    public static void ForEach<T, _>(this IEnumerable<T> source, Func<T, _> func)
    {
        foreach (var item in source) func(item);
    }

    public static void ForEach<T>(this IEnumerable<T> source, Action<T, int> action)
    {
        var i = 0;
        foreach (var item in source) action(item, i++);
    }

    public static void ForEach<T, _>(this IEnumerable<T> source, Func<T, int, _> func)
    {
        var i = 0;
        foreach (var item in source) func(item, i++);
    }

    public static T Iterate<T>(int count, T seed, Func<T, T> func)
    {
        var r = seed;
        Repeat(count, () => { r = func(r); });
        return r;
    }

    public static void Repeat(int count, Action action)
    {
        for (var i = 0; i < count; i++) action();
    }

    public static void Repeat(int count, Action<int> action)
    {
        for (var i = 0; i < count; i++) action(i);
    }

    public static IEnumerable<T> Repeat<T>(Func<T> func)
    {
        for (var i = 0; ; i++) yield return func();
    }

    public static IEnumerable<T> Repeat<T>(int count, Func<T> func)
    {
        for (var i = 0; i < count; i++) yield return func();
    }

    public static IEnumerable<T> Repeat<T>(Func<int, T> func)
    {
        for (var i = 0; ; i++) yield return func(i);
    }

    public static IEnumerable<T> Repeat<T>(int count, Func<int, T> func)
    {
        for (var i = 0; i < count; i++) yield return func(i);
    }

    public static void Swap<T>(ref T x, ref T y)
    {
        var tmp = x; x = y; y = tmp;
    }
}

[DebuggerStepThrough]
public static class MathExtensions
{
    public static int Gcd(int left, int right)
    {
        int r;
        while ((r = left % right) != 0) { left = right; right = r; }
        return right;
    }

    public static long Gcd(long left, long right)
    {
        long r;
        while ((r = left % right) != 0L) { left = right; right = r; }
        return right;
    }

    public static BigInteger Gcd(BigInteger left, BigInteger right)
        => BigInteger.GreatestCommonDivisor(left, right);

    public static int HighestOneBit(int x)
    {
        x |= x >> 01;
        x |= x >> 02;
        x |= x >> 04;
        x |= x >> 08;
        x |= x >> 16;
        return x - (x >> 1);
    }

    public static long HighestOneBit(long x)
    {
        x |= x >> 01;
        x |= x >> 02;
        x |= x >> 04;
        x |= x >> 08;
        x |= x >> 16;
        x |= x >> 32;
        return x - (x >> 1);
    }

    public static int Lcm(int left, int right) => left / Gcd(left, right) * right;

    public static long Lcm(long left, long right) => left / Gcd(left, right) * right;

    public static BigInteger Lcm(BigInteger left, BigInteger right)
        => left / Gcd(left, right) * right;

    public static int Pow(int value, int exponent)
    {
        var r = 1;
        while (exponent > 0)
        {
            if ((exponent & 1) == 1) r *= value;
            value *= value;
            exponent >>= 1;
        }
        return r;
    }

    public static long Pow(long value, int exponent)
    {
        var r = 1L;
        while (exponent > 0)
        {
            if ((exponent & 1) == 1) r *= value;
            value *= value;
            exponent >>= 1;
        }
        return r;
    }

    public static long Fact(int value)
    {
        var r = 1L;
        for (var i = 2; i <= value; i++) r *= i;
        return r;
    }
}
#endregion