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: Wrong Answer)


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.List;
import java.util.StringTokenizer;

public class Main {

	public static void main(String[] args) throws IOException {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskX solver = new TaskX();
		solver.solve(1, in, out);
		out.close();
	}

	static int INF = 1 << 28;

	static class TaskX {
		public void solve(int testNumber, InputReader in, PrintWriter out) {

			int n = in.nextInt();
			int m = in.nextInt();
			int r = in.nextInt();
			int[] rn = in.nextIntArray(r);
			for (int i = 0; i < r; i++) {
				rn[i]--;
			}

			int[][] d = new int[n][n];
			for (int i = 0; i < n; i++) {
				Arrays.fill(d[i], INF);
			}
			for (int i = 0; i < n; i++) {
				d[i][i] = 0;
			}
			for (int i = 0; i < m; i++) {
				int a = in.nextInt() - 1;
				int b = in.nextInt() - 1;
				int c = in.nextInt();
				d[a][b] = c;
				d[b][a] = c;
			}

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

			int cost = INF;
			while (Permutation.next(rn)) {
				int tmp = 0;
				for (int j = 0; j < r - 1; j++) {
					tmp += d[rn[j]][rn[j + 1]];
				}
				cost = Math.min(cost, tmp);
			}
			out.println(cost);

		}
	}

	static class Permutation {
		public static boolean next(int[] a) {
			int n = a.length;

			int i = n - 1;
			while (i > 0 && a[i - 1] >= a[i])
				i--;
			if (i <= 0)
				return false;

			int j = n - 1;
			while (a[j] <= a[i - 1])
				j--;
			swap(a, i - 1, j);

			int k = n - 1;
			while (i < k)
				swap(a, i++, k--);

			return true;
		}

		private static void swap(int[] a, int i, int j) {
			int tmp = a[i];
			a[i] = a[j];
			a[j] = tmp;
		}

	}

	static void warshallFloyd(int[][] d) {
		int INF = 1 << 28;
		int len = d.length;
		for (int k = 0; k < len; k++) {
			for (int i = 0; i < len; i++) {
				if (d[i][k] == INF)
					continue;
				for (int j = 0; j < len; j++) {
					if (d[k][j] == INF)
						continue;
					d[i][j] = Math.min(d[i][j], d[i][k] + d[k][j]);
				}
			}
		}
	}

	public static List<String> permute(char[] ary, int startIndex,
			int endIndex, List<String> list) {
		if (startIndex == endIndex) {
			list.add(String.valueOf(ary));
		} else {
			for (int i = startIndex; i <= endIndex; i++) {
				swap(ary, startIndex, i);
				permute(ary, startIndex + 1, endIndex, list);
				swap(ary, startIndex, i);
			}
		}
		return list;
	}

	public static void swap(char[] ary, int x, int y) {
		char temp = ary[x];
		ary[x] = ary[y];
		ary[y] = temp;
	}

	static class InputReader {
		BufferedReader in;
		StringTokenizer tok;

		public String nextString() {
			while (!tok.hasMoreTokens()) {
				try {
					tok = new StringTokenizer(in.readLine(), " ");
				} catch (IOException e) {
					throw new InputMismatchException();
				}
			}
			return tok.nextToken();
		}

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

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

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

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

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

		public InputReader(InputStream inputStream) {
			in = new BufferedReader(new InputStreamReader(inputStream));
			tok = new StringTokenizer("");
		}

	}

}