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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.Serializable;
import java.util.Arrays;
import java.util.StringTokenizer;

//System.out.println();
public class Main implements Runnable { //クラス名はJoisinosTravel

	public static void main(String[] args) {
		Thread.setDefaultUncaughtExceptionHandler((t, e) -> System.exit(1));
		new Thread(null, new Main(), "", 16 * 1024 * 1024).start(); //16MBスタックを確保して実行
	}

	public void run() {
		FastScannerJoisinosTravel sc = new FastScannerJoisinosTravel(System.in);

		try {
			int N = sc.nextInt();
			int M = sc.nextInt();
			int R = sc.nextInt();
			int INF = Integer.MAX_VALUE;

			Integer[] travels = new Integer[R];
			for (int i = 0; i < R; i++) {
				travels[i] = sc.nextInt();
			}

			long[][] dp = new long[N][N];

			WarshallFloyd wf = new WarshallFloyd(N);

			for (int i = 0; i < M; i++) {
				int from = sc.nextInt() - 1;
				int to = sc.nextInt() - 1;
				int cost = sc.nextInt();
				wf.set(from, to, cost);
				wf.set(to, from, cost);
			}

			wf.calc();

			dp = wf.getd();

			/*
			for (int i = 0; i < N; i++) {
				System.out.println(Arrays.toString(dp[i]));
			}
			*/

			//System.out.println("-----------------");

			long ans = Long.MAX_VALUE;
			Permutation<Integer> p = new Permutation<>(travels);
			do {
				//System.out.println(Arrays.toString(p.getObjes()));
				Integer[] per = p.getObjes();
				long eachans = 0;
				for (int i = 0; i < per.length; i++) {
					if (i > 0) {
						eachans += wf.distance(per[i - 1] - 1, per[i] - 1);
					}
				}

				if (ans > eachans) {
					ans = eachans;
				}

			} while (p.next());

			System.out.println(ans);

		} catch (Exception e) {
			e.printStackTrace();
		}

	}
}

class Permutation<T extends Serializable> {

	private int baseIndex;
	private int index;
	private T[] objs;

	private Permutation<T> subPermutation;

	public Permutation(T[] objs) {
		this(0, 0, objs.clone());
	}

	private Permutation(int baseIndex, int index, T[] objs) {
		if (objs == null || objs.length == 0) {
			throw new IllegalArgumentException();
		}

		this.baseIndex = baseIndex;
		this.index = index;
		this.objs = objs;

		if (this.index < this.objs.length - 1) {
			this.subPermutation = new Permutation<T>(this.baseIndex + 1, this.index + 1, this.objs);
		}
	}

	public T[] getTarget() {
		return this.objs;
	}

	public boolean next() {
		if (this.subPermutation == null) {
			return false;
		}

		boolean result = this.subPermutation.next();
		if (result == true) {
			return true;
		}

		this.swap(this.baseIndex, this.index);

		++this.index;
		if (this.objs.length <= this.index) {
			this.index = this.baseIndex;
			return false;
		}

		this.swap(this.index, this.baseIndex);
		return true;
	}

	public T[] getObjes() {
		return this.objs;
	}

	private void swap(int index1, int index2) {
		T tmp = this.objs[index1];
		this.objs[index1] = this.objs[index2];
		this.objs[index2] = tmp;
	}
}

/**
 * WarshallFloyd法による全点対最短経路問題の実装.<br>
 * 負の辺があっても動作する
 */
class WarshallFloyd {

	private final long INF = Long.MAX_VALUE / 3;
	private long[][] d;
	private int V;

	/**
	 * 初期化
	 *
	 * @param n 頂点の数
	 */
	public WarshallFloyd(int n) {
		this.d = new long[n][n];
		for (long[] ls : this.d) {
			Arrays.fill(ls, this.INF);
		}
		this.V = n;
	}

	public void set(int from, int to, long cost) {
		this.d[from][to] = cost;
	}

	/**
	 * すべての2頂点間の最短距離を計算する O(|V|^3)
	 */
	public void calc() {
		for (int k = 0; k < this.V; k++) {
			for (int i = 0; i < this.V; i++) {
				for (int j = 0; j < this.V; j++) {
					this.d[i][j] = Math.min(this.d[i][j], this.d[i][k] + this.d[k][j]);
				}
			}
		}
	}

	/**
	 * 全ての配列を返却
	 * @return d
	 */
	public long[][] getd() {
		return this.d;
	}

	/**
	 * fromからtoまでの最短距離を返す O(1).<br>
	 * 経路が存在しない場合はINF(Long.MAX_VALUE / 3)を返す
	 *
	 * @param from
	 * @param to
	 * @return fromからtoまでの最短距離
	 */
	public long distance(int from, int to) {
		return this.d[from][to];
	}

}

//高速なScanner
class FastScannerJoisinosTravel {
	private BufferedReader reader = null;
	private StringTokenizer tokenizer = null;

	public FastScannerJoisinosTravel(InputStream in) {
		reader = new BufferedReader(new InputStreamReader(in));
		tokenizer = null;
	}

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

	public String nextLine() {
		if (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken("\n");
	}

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

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

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

	public int[] nextIntArray(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = nextInt();
		return a;
	}

	public long[] nextLongArray(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nextLong();
		return a;
	}
}