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.BufferedReader;
import java.io.Closeable;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.ListIterator;
import java.util.Map.Entry;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

import javax.swing.text.Segment;

public class Main {
	
	public static final long INF = Long.MAX_VALUE / 2 - 1;
	
	public static void main(String[] args) throws IOException {
		try(Scanner sc = new Scanner(System.in)){
			final int N = sc.nextInt();
			final int M = sc.nextInt();
			final int R = sc.nextInt();
			
			int[] rs = sc.nextIntArray(R);
			
			int[][] adj = new int[N][N];
			for(int i = 0; i < N; i++){
				for(int j = 0; j < N; j++){
					adj[i][j] = i == j ? 0 : Integer.MAX_VALUE / 2 - 1;
				}
			}
			
			for(int i = 0; i < M; i++){
				final int a = sc.nextInt() - 1;
				final int b = sc.nextInt() - 1;
				final int c = sc.nextInt();
				
				adj[a][b] = adj[b][a] = c;
			}
			
			for(int k = 0; k < N; k++){
				for(int i = 0; i < N; i++){
					for(int j = 0; j < N; j++){
						adj[i][j] = Math.min(adj[i][j], adj[i][k] + adj[k][j]);
					}
				}
			}
			
			long[][] DP = new long[1 << R][R];
			for(final long[] arr : DP){ Arrays.fill(arr, INF); }
			for(int i = 0; i < R; i++){
				DP[1 << i][i] = 0;
			}
			
			for(int bit = 1; bit < (1 << R); bit++){
				for(int curr = 0; curr < R; curr++){
					if((bit & (1 << curr)) == 0){ continue; }
					if(DP[bit][curr] >= INF){ continue; }
					
					for(int next = 0; next < R; next++){
						if((bit & (1 << next)) != 0){ continue; }
						
						final int next_bit = bit | (1 << next);
						final long next_cost = DP[bit][curr] + adj[rs[curr] - 1][rs[next] - 1];
						
						DP[next_bit][next] = Math.min(DP[next_bit][next], next_cost);
					}
				}
			}
			
			long answer = INF;
			for(int i = 0; i < R; i++){
				answer = Math.min(answer, DP[(1 << R) - 1][i]);
			}
			System.out.println(answer);
		}
	}
	
	public static class Scanner implements Closeable {
		private BufferedReader br;
		private StringTokenizer tok;
 
		public Scanner(InputStream is) throws IOException {
			br = new BufferedReader(new InputStreamReader(is));
		}
 
		private void getLine() throws IOException {
			while (!hasNext()) {
				tok = new StringTokenizer(br.readLine());
			}
		}
 
		private boolean hasNext() {
			return tok != null && tok.hasMoreTokens();
		}
 
		public String next() throws IOException {
			getLine();
			return tok.nextToken();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
		
		public int[] nextIntArray(int n) throws IOException {
			final int[] ret = new int[n];
			for(int i = 0; i < n; i++){
				ret[i] = this.nextInt();
			}
			return ret;
		}
		
		public long[] nextLongArray(int n) throws IOException {
			final long[] ret = new long[n];
			for(int i = 0; i < n; i++){
				ret[i] = this.nextLong();
			}
			return ret;
		}
 
		public void close() throws IOException {
			br.close();
		}
	}
}