Problem: Mahmoud wants to send a message to his friend Ehab. Their language consists of n words numbered from 1 to n. Some words have the same meaning so there are k groups of words such that all the words in some group have the same meaning.

Mahmoud knows that the i-th word can be sent with cost ai. For each word in his message, Mahmoud can either replace it with another word of the same meaning or leave it as it is. Can you help Mahmoud determine the minimum cost of sending the message?

The cost of sending the message is the sum of the costs of sending every word in it.

Input

The first line of input contains integers n, k and m (1 ≤ k ≤ n ≤ 105, 1 ≤ m ≤ 105) — the number of words in their language, the number of groups of words, and the number of words in Mahmoud's message respectively.

The second line contains n strings consisting of lowercase English letters of length not exceeding 20 which represent the words. It's guaranteed that the words are distinct.

The third line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) where ai is the cost of sending the i-th word.

The next k lines describe the groups of words of same meaning. The next k lines each start with an integer x (1 ≤ x ≤ n) which means that there are x words in this group, followed by x integers which represent the indices of words in this group. It's guaranteed that each word appears in exactly one group.

The next line contains m space-separated words which represent Mahmoud's message. Each of these words appears in the list of language's words.

Output

The only line should contain the minimum cost to send the message after replacing some words (maybe none) with some words of the same meaning.

Examples

Input

5 4 4
i loser am the second
100 1 1 5 10
1 1
1 3
2 2 5
1 4
i am the second


Output

107

Input

5 4 4
i loser am the second
100 20 1 5 10
1 1
1 3
2 2 5
1 4
i am the second


Output

116

Note

In the first sample, Mahmoud should replace the word "second" with the word "loser" because it has less cost so the cost will be 100+1+5+1=107.

In the second sample, Mahmoud shouldn't do any replacement so the cost will be 100+1+5+10=116.

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.*;
import java.util.*;

public class test {

	public static void main(String[] args) {
//		int t = fs.nextInt();
		int test = 1;
		for (int t = 0; t < test; t++) {
			int n = fs.nextInt();
			int k = fs.nextInt();
			int m = fs.nextInt();
			HashMap<String, Integer> hm = new HashMap<String, Integer>();
			String ar[] = new String[n];
			for (int i = 0; i < n; i++) {
				ar[i] = fs.next();
			}
			for (int i = 0; i < n; i++) {
				hm.put(ar[i], fs.nextInt());
			}
			
			for (int i = 0; i < k; i++) {
				int size = fs.nextInt();
				int all[] = new int[size];
				for (int l = 0; l < size; l++) {
					all[l] = fs.nextInt()-1;
				}
				int mincost = Integer.MAX_VALUE;
				for (int l = 0; l < size; l++) {
					int ind = all[l];
					String z = ar[ind];
					int cost = hm.get(z);
					if (cost < mincost) {
						mincost = cost;
					}
				}
				for (int l = 0; l < size; l++) {
					int ind = all[l];
					String z = ar[ind];
					hm.put(z, mincost);
				}
			}
			long totalcost = 0;
			for (int i = 0; i < m; i++) {
				String s = fs.next();
				long z = hm.get(s);
				totalcost += z;
			}
			System.out.println(totalcost);
		}
	}

	/*
	 * array list
	 * 
	 * ArrayList<Integer> al=new ArrayList<>(); creating BigIntegers
	 * 
	 * BigInteger a=new BigInteger(); BigInteger b=new BigInteger();
	 * 
	 * hash map
	 * 
	 * HashMap<Integer,Integer> hm=new HashMap<Integer,Integer>(); for(int
	 * i=0;i<ar.length;i++) { Integer c=hm.get(ar[i]); if(hm.get(ar[i])==null) {
	 * hm.put(ar[i],1); } else { hm.put(ar[i],++c); } }
	 * 
	 * while loop
	 * 
	 * int t=sc.nextInt(); while(t>0) { t--; }
	 * 
	 * array input
	 * 
	 * int n = sc.nextInt(); int ar[] = new int[n]; for (int i = 0; i < ar.length;
	 * i++) { ar[i] = sc.nextInt(); }
	 */

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

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

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

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

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}

	static class Pair {
		int first, second;

		public Pair(int first, int second) {
			this.first = first;
			this.second = second;
		}

	}

	static class OutputWriter {
		private final PrintWriter writer;

		public OutputWriter(OutputStream outputStream) {
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}

		public OutputWriter(Writer writer) {
			this.writer = new PrintWriter(writer);
		}

		public void print(Object... objects) {
			for (int i = 0; i < objects.length; i++) {
				if (i != 0)
					writer.print(' ');
				writer.print(objects[i]);
			}
		}

		public void printLine(Object... objects) {
			print(objects);
			writer.println();
		}

		public void close() {
			writer.close();
		}

		public void flush() {
			writer.flush();
		}

	}

	private static final Scanner sc = new Scanner(System.in);
	private static final FastReader fs = new FastReader();
	private static final OutputWriter op = new OutputWriter(System.out);

	static int[] getintarray(int n) {
		int ar[] = new int[n];
		for (int i = 0; i < n; i++) {
			ar[i] = fs.nextInt();
		}
		return ar;
	}

	static long[] getlongarray(int n) {
		long ar[] = new long[n];
		for (int i = 0; i < n; i++) {
			ar[i] = fs.nextLong();
		}
		return ar;
	}

	static int[][] get2darray(int n, int m) {
		int ar[][] = new int[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				ar[i][j] = fs.nextInt();
			}
		}
		return ar;
	}

	static Pair[] getpairarray(int n) {
		Pair ar[] = new Pair[n];
		for (int i = 0; i < n; i++) {
			ar[i] = new Pair(fs.nextInt(), fs.nextInt());
		}
		return ar;
	}

	static void printarray(int ar[]) {
		for (int i : ar) {
			op.print(i + " ");
		}
		op.flush();
	}

	static int fact(int n) {
		int fact = 1;
		for (int i = 2; i <= n; i++) {
			fact *= i;
		}
		return fact;
	}

//	static int getans(int[] a, int[] b) {
//		int a1 = a[0];
//		int a2 = b[0];
//		int b1 = a[1];
//		int b2 = b[1];
//		int c1 = a[2];
//		int c2 = b[2];
//
//		if (((a1 == a2) && (b1 == b2) && (c1 == c2)))
//			return 0;
//		else if ((a2 - a1) == (b2 - b1) && (b2 - b1) == (c2 - c1))
//			return 1;
//		else if ((a2 / a1 == b2 / b1) && (b2 / b1 == c2 / c1) && (a2 / a1 == c2 / c1)
//				&& (a2 % a1 == 0 && b2 % b1 == 0 && c2 % c1 == 0))
//			return 1;
//		else if (((a1 == a2) && (b1 == b2)) || ((a1 == a2) && (c1 == c2)) || ((c1 == c2) && (b1 == b2))) {
//			return 1;
//		} else if (a1 == a2) {
//			if ((b2 - b1) == (c2 - c1) || ((b2 / b1 == c2 / c1) && (b2 % b1 == 0 && c2 % c1 == 0)))
//				return 1;
//		} else if (b1 == b2) {
//			if ((a2 - a1) == (c2 - c1) || ((a2 / a1 == c2 / c1) && (a2 % a1 == 0 && c2 % c1 == 0)))
//				return 1;
//		} else if (c1 == c2) {
//			if ((b2 - b1) == (a2 - a1) || ((b2 / b1 == a2 / a1) && (b2 % b1 == 0 && a2 % a1 == 0)))
//				return 1;
//		} else if ((((a2 - a1) != (b2 - b1) && (b2 - b1) != (c2 - c1) && (a2 - a1) != (c2 - c1))
//				&& ((a2 / a1 != b2 / b1) && (b2 / b1 != c2 / c1) && (a2 / a1 != c2 / c1)))) {
//			return 3;
//		} else if ((((a2 - a1) != (b2 - b1) && (b2 - b1) != (c2 - c1) && (a2 - a1) != (c2 - c1)))) {
//			if ((a2 / a1 == b2 / b1 && a2 % a1 != 0 && b2 % b1 != 0)
//					|| (a2 / a1 == c2 / c1 && a2 % a1 != 0 && c2 % c1 != 0)
//					|| (c2 / c1 == b2 / b1 && c2 % c1 != 0 && b2 % b1 != 0))
//				return 3;
//
//		}
//		return 2;
//
//	}

	// function to find largest prime factor

}/*
	 * 1 5 -2 -3 -1 -4 -6till here
	 */

//		while (t > 0) {
//			int a[] = getintarray(3);
//			int b[] = getintarray(3);
//			int ans = getans(a, b);
//			System.out.println(ans);
//		}