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.*;
import java.util.*;
import static java.lang.Math.*;

public class Main {
  public static void main(String[] args) {
    new Main().solve();
  }

  private void solve() {
    try(InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out)) {

      int n = in.nextInt();
      int m = in.nextInt();
      int r = in.nextInt();

      int[] t = in.mapInt(r);

      final int INF = 1 << 28;
      Graph G = new Graph(n, r, t);

      for (int a[] : G.graph) Arrays.fill(a, INF);
      for (int i = 0; i < m; i++) {
        int v1 = in.nextInt() - 1;
        int v2 = in.nextInt() - 1;
        int c  = in.nextInt();
        G.graph[v1][v2] = c;
        G.graph[v2][v1] = c;
      }

      // warshall-Froyd
      for (int k = 0; k < n; k++) {
        for (int i = 0; i < n; i++) {
          for (int j = 0; j < n; j++) {
            G.graph[i][j] = min(G.graph[i][j], G.graph[i][k] + G.graph[k][j]);
          }
        }
      }

      final int ans = G.compute();
      out.println(ans);
    }
    catch(IOException e) {
      System.err.println(e);
    }
  }

 class Graph {
    private int enm;
    private int[] pmt;
    private int ret;
    private boolean[] visited;

    public int[][] graph;
    // option
    private int t[];

    public Graph(int n, int enm, int[] t) {
      this.enm = enm;
      this.t = t;
      ret = Integer.MAX_VALUE;
      graph = new int[n][n];
      pmt = new int[enm];
      visited = new boolean[n];
    }

    public int compute() {
      dfs(0);
      return ret;
    }

    private void dfs(int cnt) {
      if(cnt == enm) {
        evalute();
        return;
      }
  
      for (int v: t) {
        if(visited[--v]) continue;

        pmt[cnt] = v;
        visited[v] = true;
        dfs(cnt+1);
        visited[v] = false;
      }
    }
  
    private void evalute() {
      int result = 0;
      for (int i = 1; i < enm; i++) result += graph[pmt[i-1]][pmt[i]];
      ret = min(ret, result);
    }
  }
  static int  atoi(String s) { return Integer.parseInt(s); }
  static long atol(String s) { return Long.parseLong(s); }

  static class InputReader implements AutoCloseable {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
      reader = new BufferedReader(new InputStreamReader(stream), 32768);
      tokenizer = null;
    }
    public String next() {
      if (tokenizer == null || !tokenizer.hasMoreTokens()) {
        try { tokenizer = new StringTokenizer(reader.readLine());
        } catch (IOException e) {
          throw new UncheckedIOException(e);
        }
      }
      return tokenizer.nextToken();
    }
    public int nextInt() { return Integer.parseInt(next()); }
    public long nextLong() { return Long.parseLong(next()); }
    int[] mapInt(int len) {
      int[] ret = new int[len];
      for (int i = 0; i < len; i++) ret[i] = Integer.parseInt(next());
      return ret;
    }
    long[] mapLong(int len) {
      long[] ret = new long[len];
      for (int i = 0; i < len; i++) ret[i] = Long.parseLong(next());
      return ret;
    }
    @Override
    public void close() throws IOException { reader.close(); }
  }
}