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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;
import java.util.ArrayList;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author silviase
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DJoisinosTravel solver = new DJoisinosTravel();
        solver.solve(1, in, out);
        out.close();
    }

    static class DJoisinosTravel {
        public void solve(int testNumber, Scanner in, PrintWriter out) {

            int n = in.nextInt();
            int m = in.nextInt();
            int r = in.nextInt();
            Integer[] per = new Integer[r];
            Graph g = new Graph(n);
            for (int i = 0; i < r; i++)
                per[i] = in.nextInt() - 1;

            Arrays.sort(per);

            for (int i = 0; i < m; i++)
                g.addUnDirectedEdge(new Edge(in.nextInt() - 1, in.nextInt() - 1, in.nextInt()));

            long[][] d = g.warshallFloyd();
            NextPermutation<Integer> np = new NextPermutation<>();

            long min = Long.MAX_VALUE;

            while (true) {
                long cmp = 0;
                for (int i = 0; i < r - 1; i++)
                    cmp += d[per[i]][per[i + 1]];
                min = Math.min(min, cmp);
                if (np.nextPermutation(per) == null) break;
            }

            out.println(min);


        }

    }

    static class Edge {
        public int from;
        public int to;
        public long cost;

        public Edge(int to) {
            this.to = to;
        }

        public Edge(int to, long cost) {
            this.to = to;
            this.cost = cost;
        }

        public Edge(int from, int to, long cost) {
            this.from = from;
            this.to = to;
            this.cost = cost;
        }

        public Edge inv() {
            return new Edge(to, from, cost);
        }

        public String toString() {
            return "Edge{" +
                    "from=" + from +
                    ", to=" + to +
                    ", cost=" + cost +
                    '}';
        }

    }

    static class NextPermutation<T extends Comparable<T>> {
        public T[] nextPermutation(T[] array) {
            int k = -1;
            int i = array.length - 2;
            while (i >= 0) {
                if (array[i].compareTo(array[i + 1]) < 0) {
                    k = i;
                    break;
                }
                i--;
            }

            // 存在しない場合nullを返す
            if (k == -1) return null;
            int l = k + 1;
            i = array.length - 1;
            while (i > k + 1) {
                if (array[k].compareTo(array[i]) < 0) {
                    l = i;
                    break;
                }
                i--;
            }

            T tmp = array[k];
            array[k] = array[l];
            array[l] = tmp;
            int[] res = new int[array.length];
            // k+1 <-> n-1
            for (int j = k + 1; j < array.length + k - j; j++) {
                tmp = array[j];
                array[j] = array[array.length + k - j];
                array[array.length + k - j] = tmp;
            }
            return array;
        }

    }

    static class Graph {
        public int size;
        public ArrayList<Edge>[] adj;
        public int[] inDeg;
        public int[] vertexCost;

        public Graph(int size) {
            this.size = size;
            adj = new ArrayList[size];
            inDeg = new int[size];
            vertexCost = new int[size];
            for (int i = 0; i < size; i++) {
                adj[i] = new ArrayList<>();
            }
        }

        public void addEdge(Edge e) {
            adj[e.from].add(e);
            inDeg[e.to]++;
        }

        public void addUnDirectedEdge(Edge e) {
            addEdge(e);
            addEdge(e.inv());
        }

        public long[][] warshallFloyd() {
            long[][] dist = new long[size][size];
            for (int i = 0; i < size; i++) {
                Arrays.fill(dist[i], Long.MAX_VALUE / 3);
                dist[i][i] = 0;
            }

            for (ArrayList<Edge> ale : adj) {
                for (Edge e : ale) {
                    dist[e.from][e.to] = Math.min(e.cost, dist[e.from][e.to]);
                }
            }

            for (int k = 0; k < size; k++) {
                for (int i = 0; i < size; i++) {
                    for (int j = 0; j < size; j++) {
                        dist[i][j] = Math.min(dist[i][k] + dist[k][j], dist[i][j]);
                    }
                }
            }

            return dist;
        }

    }
}