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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Deque;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.List;
import java.util.Map;

public class Main {
    FastScanner in = new FastScanner(System.in);
    PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) {
        new Main().calc();
    }
    
    int N,M,R;
    int[] r,A,B,C;
    boolean[] done;
    int[][] dist;
    int ans;
    
    public void calc() {
        N = in.nextInt();
        M = in.nextInt();
        R = in.nextInt();
        r = new int[R];
        A = new int[M];
        B = new int[M];
        C = new int[M];

        for (int i = 0; i < R; i++) {
            r[i] = in.nextInt() - 1;
        }

        for (int i = 0; i < M; i++) {
            A[i] = in.nextInt() - 1;
            B[i] = in.nextInt() - 1;
            C[i] = in.nextInt();
        }
        
        dist = new int[N][N];
        
        for (int i = 0; i < N; i++) {
            for (int j = 0; j < N; j++) {
                dist[i][j] = 99999999;
            }
            dist[i][i] = 0;  
        }
        
        for (int i = 0; i < M; i++) {
            dist[A[i]][B[i]] = Math.min(C[i], dist[A[i]][B[i]]);
            dist[B[i]][A[i]] = dist[A[i]][B[i]];
        }      
        
        for (int k = 0; k < N; k++) {
            for (int i = 0; i < N; i++) {
                for (int j = 0; j < N; j++) {
                    dist[i][j] = Math.min(dist[i][j], dist[i][k] + dist[k][j]);
                }
            }
        }

        done = new boolean[R];
        ans = Integer.MAX_VALUE;
        
        dfs(0, -1, 0);
        
        out.println(ans);
        out.close();
    }
    
    /**
     * 
     * @param curNum 現在訪れた町の数
     * @param curTown 今訪れている町
     * @param d 今まで歩いてきた距離
     */
    private void dfs(int curNum, int curTown, int d) {
        // out.println("curNum: " + curNum + " curTown: " + curTown + " d: " + d);
        // 最後の町にたどり着いたら
        if (curNum == R) {
            // 答えを更新
            if (ans > d) {
                ans = d;
            }
            return;
        }
        
        // まだ訪れていない町を訪問
        for (int i = 0; i < R; i++) {
            // 訪れていなければ
            if (!done[i]) {
                // 訪れたことにする
                done[i] = true;
                
                // これが訪れた最初の町なら，距離dは0で次に進む
                if (curTown == -1) {                    
                    dfs(curNum+1, i, 0);
                }
                // 最初の町でなければ，今までの距離dと，次の町への距離を加える
                // 次の町への距離は，現在の町r[curTown]から，次の町r[i]への最短距離distになる
                else {
                    dfs(curNum+1, i, d+dist[r[curTown]][r[i]]);                
                }
                
                done[i] = false;
            }
        }   
    }
    
    class FastScanner {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public FastScanner(InputStream stream) {
            this.stream = stream;
        }

        int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        boolean isEndline(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] nextIntArray(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; i++)
                array[i] = nextInt();

            return array;
        }

        int[][] nextIntMap(int n, int m) {
            int[][] map = new int[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = in.nextIntArray(m);
            }
            return map;
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        long[] nextLongArray(int n) {
            long[] array = new long[n];
            for (int i = 0; i < n; i++)
                array[i] = nextLong();

            return array;
        }

        long[][] nextLongMap(int n, int m) {
            long[][] map = new long[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = in.nextLongArray(m);
            }
            return map;
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        double[] nextDoubleArray(int n) {
            double[] array = new double[n];
            for (int i = 0; i < n; i++)
                array[i] = nextDouble();

            return array;
        }

        double[][] nextDoubleMap(int n, int m) {
            double[][] map = new double[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = in.nextDoubleArray(m);
            }
            return map;
        }

        String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        String[] nextStringArray(int n) {
            String[] array = new String[n];
            for (int i = 0; i < n; i++)
                array[i] = next();

            return array;
        }

        String nextLine() {
            int c = read();
            while (isEndline(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndline(c));
            return res.toString();
        }
    }
}