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.stream.IntStream;
import java.util.Arrays;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.UncheckedIOException;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author mikit
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        LightScanner in = new LightScanner(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, LightScanner in, PrintWriter out) {
            int n = in.ints(), m = in.ints(), r = in.ints();
            int[] d = in.ints(r);
            AdjacencyMatrix g = new AdjacencyMatrix(n);
            for (int i = 0; i < m; i++) {
                g.addEdge(in.ints() - 1, in.ints() - 1, in.ints());
            }
            g.shorten();

            int[] u = IntStream.range(0, r).toArray();
            int ans = Integer.MAX_VALUE;
            do {
                int t = 0;
                for (int i = 1; i < r; i++) {
                    t += g.getWeightBetween(d[u[i - 1]] - 1, d[u[i]] - 1);
                }
                ans = Math.min(ans, t);
            } while ((u = Permutation.nextPermutation(u)) != null);
            out.println(ans);
        }

    }

    static final class AdjacencyMatrix implements Graph {
        private static final int INF = 0x2fffffff;
        private final int n;
        private final long[][] matrix;

        public AdjacencyMatrix(int n) {
            this.n = n;
            this.matrix = new long[n][n];
            ArrayUtil.fill(matrix, INF);
        }

        public void addDirectedEdge(int from, int to, long weight) {
            matrix[from][to] = weight;
        }

        public long getWeightBetween(int from, int to) {
            return matrix[from][to];
        }

        public void shorten() {
            for (int i = 0; i < matrix.length; i++) {
                for (int j = 0; j < matrix.length; j++) {
                    for (int k = 0; k < matrix.length; k++) {
                        matrix[j][k] = Math.min(matrix[j][k], matrix[j][i] + matrix[i][k]);
                    }
                }
            }
        }

    }

    static final class Permutation {
        private Permutation() {
        }

        public static int[] nextPermutation(int[] a) {
            if (a == null || a.length < 2) {
                return null;
            }
            int p = 0;
            for (int i = a.length - 2; i >= 0; i--) {
                if (a[i] < a[i + 1]) {
                    p = i;
                    break;
                }
            }
            int q = 0;
            for (int i = a.length - 1; i > p; i--) {
                if (a[i] > a[p]) {
                    q = i;
                    break;
                }
            }
            if (p == 0 && q == 0) {
                return null;
            }
            int temp = a[p];
            a[p] = a[q];
            a[q] = temp;
            ArrayUtil.reverse(a, p + 1, a.length - 1);
            return a;
        }

    }

    static interface Graph {
        void addDirectedEdge(int from, int to, long weight);

        default void addEdge(int one, int other, long weight) {
            addDirectedEdge(one, other, weight);
            addDirectedEdge(other, one, weight);
        }

    }

    static class LightScanner {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public LightScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        public String string() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new UncheckedIOException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int ints() {
            return Integer.parseInt(string());
        }

        public int[] ints(int length) {
            return IntStream.range(0, length).map(x -> ints()).toArray();
        }

    }

    static final class ArrayUtil {
        private ArrayUtil() {
        }

        public static void fill(long[] a, long v) {
            Arrays.fill(a, v);
        }

        public static void fill(long[][] a, long v) {
            for (int i = 0; i < a.length; i++) {
                fill(a[i], v);
            }
        }

        public static void reverse(int[] a, int left, int right) {
            while (left < right) {
                int temp = a[left];
                a[left] = a[right];
                a[right] = temp;
                left++;
                right--;
            }
        }

    }
}