Problem:
Score : 400 points

Problem Statement

There are N towns in the State of Atcoder, connected by M bidirectional roads.

The i-th road connects Town A_i and B_i and has a length of C_i.

Joisino is visiting R towns in the state, r_1,r_2,..,r_R (not necessarily in this order).

She will fly to the first town she visits, and fly back from the last town she visits, but for the rest of the trip she will have to travel by road.

If she visits the towns in the order that minimizes the distance traveled by road, what will that distance be?

Constraints

2≤N≤200

1≤M≤N×(N-1)/2

2≤R≤min(8,N) (min(8,N) is the smaller of 8 and N.)

r_i≠r_j (i≠j)

1≤A_i,B_i≤N, A_i≠B_i

(A_i,B_i)≠(A_j,B_j),(A_i,B_i)≠(B_j,A_j) (i≠j)

1≤C_i≤100000

Every town can be reached from every town by road.

All input values are integers.

Input

Input is given from Standard Input in the following format:

N M R
r_1 ... r_R
A_1 B_1 C_1
:
A_M B_M C_M

Output

Print the distance traveled by road if Joisino visits the towns in the order that minimizes it.

Sample Input 1

3 3 3
1 2 3
1 2 1
2 3 1
3 1 4

Sample Output 1

2

For example, if she visits the towns in the order of 1, 2, 3, the distance traveled will be 2, which is the minimum possible.

Sample Input 2

3 3 2
1 3
2 3 2
1 3 6
1 2 2

Sample Output 2

4

The shortest distance between Towns 1 and 3 is 4. Thus, whether she visits Town 1 or 3 first, the distance traveled will be 4.

Sample Input 3

4 6 3
2 3 4
1 2 4
2 3 3
4 3 1
1 4 1
4 2 2
3 1 6

Sample Output 3

3

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using static System.Math;

namespace NotFounds
{
    public class Program
    {
        public static void Main(string[] args)
        {
            new Program().Solve();
        }

        public void Solve()
        {
            var cin = new MyInputStream();

            var N = cin.ri();
            var M = cin.ri();
            var R = cin.ri();
            var r = new int[R];
          
            for (var i = 0; i < R; ++i)
                r[i] = cin.ri() - 1;
            
            const long INF = (long)1e12;
            var d = new long[N, N];
            for (var i = 0; i < N; ++i)
                for (var j = 0; j < N; ++j)
                    d[i, j] = INF;

            for (var i = 0; i < M; ++i)
            {
                var A = cin.ri() - 1;
                var B = cin.ri() - 1;
                var C = cin.ri();
                d[A, B] = C;
                d[B, A] = C;
            }
          
            // Warshall-Floyd
            for (var i = 0; i < N; ++i)
                for (var j = 0; j < N; ++j)
                    for (var k = 0; k < N; ++k)
                        if (d[i, j] > d[i, k] + d[k, j])
                            d[i, j] = d[i, k] + d[k, j];
          
            var ans = (long)INF;
            foreach (var p in r.Permutations())
            {
                var perm = p.ToList();
                var dist = 0L;
            	for (var i = 0; i < perm.Count - 1; ++i)
                	dist += d[perm[i], perm[i + 1]];
                if (ans > dist)
                  ans = dist;
            }
            WriteLine(ans.ToString());
        }
    }

    public class MyInputStream
    {
        private char separator = ' ';
        private Queue<string> inputStream;
        public MyInputStream(char separator = ' ')
        {
            this.separator = separator;
            inputStream = new Queue<string>();
        }

        public string Read()
        {
            if (inputStream.Count != 0) return inputStream.Dequeue();
            string[] tmp = Console.ReadLine().Trim().Split(separator);
            for (int i = 0; i < tmp.Length; i++)
            {
                inputStream.Enqueue(tmp[i]);
            }
            return inputStream.Dequeue();
        }
        public string ReadLine() => Console.ReadLine();
        public int ReadInt() => int.Parse(Read());
        public long ReadLong() => long.Parse(Read());
        public double ReadDouble() => double.Parse(Read());
        public string r() => Read();
        public int ri() => ReadInt();
        public long rl() => ReadLong();
        public double rd() => ReadDouble();
    }
  
    public static class MyExtentions
    {
        public static IEnumerable<IEnumerable<T>> Permutations<T>(this IEnumerable<T> source)
        {
            if (source.Count() != 0)
            {
                int index = 0;
                foreach (var item in source)
                {
                    var allOtherItems = source.RemoveAt(index++);
                    foreach (var permutation in allOtherItems.Permutations())
                    {
                        yield return new[] { item }.Concat(permutation);
                    }
                }
            }
            else { yield return new T[0]; }
        }

        public static IEnumerable<T> RemoveAt<T>(this IEnumerable<T> source, int indexToRemove)
        {
            int index = 0;
            foreach (T item in source)
                if (index++ != indexToRemove)
                    yield return item;
        }
    }
}