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.util.*;

public class q2 {
    public static MyScanner in = new MyScanner();
    public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out), true);
    public static MyViewer view = new MyViewer();
    public static BufferedWriter log = new BufferedWriter(new OutputStreamWriter(System.out));
    public static Random rand = new Random(System.currentTimeMillis());

    public static class Pair<A, B> {
        private final A first;
        private final B second;

        public Pair(A first, B second) {
            super();
            this.first = first;
            this.second = second;
        }

        public int hashCode() {
            int hashFirst = first != null ? first.hashCode() : 0;
            int hashSecond = second != null ? second.hashCode() : 0;

            return (hashFirst + hashSecond) * hashSecond + hashFirst;
        }

        public boolean equals(Object other) {
            if (other instanceof Pair) {
                Pair otherPair = (Pair) other;
                return
                        ((this.first == otherPair.first ||
                                (this.first != null && otherPair.first != null &&
                                        this.first.equals(otherPair.first))) &&
                                (this.second == otherPair.second ||
                                        (this.second != null && otherPair.second != null &&
                                                this.second.equals(otherPair.second))));
            }

            return false;
        }

        public String toString() {
            return "(" + first + ", " + second + ")";
        }

        public A getFirst() {
            return first;
        }

        public B getSecond() {
            return second;
        }
    }

    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;
        private boolean randomInput = false;
        private Random rand;

        void randomInput(boolean r) {
            randomInput = r;
            rand = new Random(System.currentTimeMillis());
            //rand = new Random(42);
        }

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

        public MyScanner(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
        }

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

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

        public int nextInt(int val) {
            return randomInput ? val : Integer.parseInt(next());
        }

        public int nextInt(int low, int high) {
            if (randomInput) {
                return rand.nextInt(high - low + 1) + low;
            } else {
                return Integer.parseInt(next());
            }
        }

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

        long nextLong(long val) {
            return randomInput ? val : Long.parseLong(next());
        }

        long nextLong(long low, long high) {
            if (randomInput) {
                return low + ((long) (rand.nextDouble() * (high - low + 1)));
            } else {
                return Long.parseLong(next());
            }
        }

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

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

        int[] arrayInt(int n, int low, int high) {
            int[] a = new int[n];
            if (randomInput) {
                for (int i = 0; i < n; i++) {
                    a[i] = rand.nextInt(high - low + 1) + low;
                }
            } else {
                for (int i = 0; i < n; i++) {
                    a[i] = nextInt();
                }
            }
            return a;
        }

        ArrayList<Integer> list(int n) {
            ArrayList<Integer> a = new ArrayList<Integer>(n);
            for (int i = 0; i < n; i++) {
                a.add(nextInt());
            }
            return a;
        }

        ArrayList<Integer> list(int n, int low, int high) {
            ArrayList<Integer> a = new ArrayList<Integer>(n);
            if (randomInput) {
                for (int i = 0; i < n; i++) {
                    a.add(rand.nextInt(high - low + 1) + low);
                }
            } else {
                for (int i = 0; i < n; i++) {
                    a.add(nextInt());
                }
            }
            return a;
        }

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

        long[] arrayLong(int n, long low, long high) {
            long[] a = new long[n];
            if (randomInput) {
                for (int i = 0; i < n; i++) {
                    double r = rand.nextDouble();
                    a[i] = (long) (r * (double) (high - low + 1)) + low;
                    if (a[i] == 0) {
                        out.println("Ouch : " + r);
                    }
                }
            } else {
                for (int i = 0; i < n; i++) {
                    a[i] = nextLong();
                }
            }
            return a;
        }

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

        void close() {
            try {
                br.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }

        ArrayList<ArrayList<Integer>> randomTree(int n) {
            ArrayList<ArrayList<Integer>> edges = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                edges.add(new ArrayList<>());
            }

            for (int i = 1; i < n; i++) {
                int par = rand.nextInt(i);
                edges.get(par).add(i);
            }
            return edges;
        }
    }

    static class MyViewer {
        private static boolean print = true;

        public void on() {
            print = true;
        }

        public void off() {
            print = false;
        }

        public <T extends List> void list(T a) {
            if (!print) return;
            if (a == null) {
                out.println("List: NULL");
                return;
            }
            if (a.size() == 0) {
                out.println("List: []");
                return;
            }
            out.print("List: [" + a.get(0));
            for (int i = 1; i < a.size(); i++) {
                out.print(", " + a.get(i));
            }
            out.println("] Len: " + a.size());
        }

        public <T> void array(T[] a) {
            if (!print) return;
            if (a == null) {
                out.println("Array: NULL");
                return;
            }
            if (a.length == 0) {
                out.println("Array: []");
                return;
            }
            out.print("Array: [" + a[0]);
            for (int i = 1; i < a.length; i++) {
                out.print(", " + a[i]);
            }
            out.println("] Len: " + a.length);
        }

        public void array(boolean[] a) {
            if (!print) return;
            if (a == null) {
                out.println("boolean[]: NULL");
                return;
            }
            if (a.length == 0) {
                out.println("boolean[]: Len: 0");
                return;
            }
            out.print("boolean[] Len: " + a.length + " [");
            for (boolean x : a) {
                out.print(x + ", ");
            }
            out.println("\b\b]");
        }

        public void array(int[] a) {
            if (!print) return;

            if (a == null) {
                out.println("Array: NULL");
                return;
            }
            if (a.length == 0) {
                out.println("Array: []");
                return;
            }
            out.print("int[] Len: " + a.length + " [");
            for (int x : a) {
                out.print(x + ", ");
            }
            out.println("\b\b]");
        }

        public void array(long[] a) {
            if (!print) return;
            if (a == null) {
                out.println("Array: NULL");
                return;
            }
            if (a.length == 0) {
                out.println("Array: []");
                return;
            }
            out.print("long Array: [");
            for (long x : a) {
                out.print(x + ", ");
            }
            out.println("\b\b] Len: " + a.length);
        }

        public void matrix(int[][] a, int cutoff) {
            if (cutoff == 0)
                cutoff = Integer.MAX_VALUE;
            if (a == null) {
                out.println("Matrix: NULL");
                return;
            }
            for (int i = 0; i < a.length; i++) {
                if (i < cutoff) {
                    printMatrixRow(a[i], cutoff);
                } else {
                    out.println("     ...");
                    printMatrixRow(a[a.length - 1], cutoff);
                    break;
                }
            }
        }

        public void matrix(long[][] a, long cutoff) {
            if (cutoff == 0)
                cutoff = Long.MAX_VALUE;
            if (a == null) {
                out.println("Matrix: NULL");
                return;
            }
            for (int i = 0; i < a.length; i++) {
                if (i < cutoff) {
                    printMatrixRow(a[i], cutoff);
                } else {
                    out.println("     ...");
                    printMatrixRow(a[a.length - 1], cutoff);
                    break;
                }
            }
        }

        public void matrix(boolean[][] a, int cutoff) {
            if (cutoff == 0)
                cutoff = Integer.MAX_VALUE;
            if (a == null) {
                out.println("Matrix: NULL");
                return;
            }
            for (int i = 0; i < a.length; i++) {
                if (i < cutoff) {
                    printMatrixRow(a[i], cutoff);
                } else {
                    out.println("     ...");
                    printMatrixRow(a[a.length - 1], cutoff);
                    break;
                }
            }
        }

        private void printMatrixRow(int[] a, int cutoff) {
            for (int j = 0; j < a.length; j++) {
                if (j < cutoff) {
                    out.printf("%6d  ", a[j]);
                } else {
                    out.printf(" ... %6d", a[a.length - 1]);
                    break;
                }
            }
            out.println();
        }

        private void printMatrixRow(long[] a, long cutoff) {
            for (int j = 0; j < a.length; j++) {
                if (j < cutoff) {
                    out.printf("%6d  ", a[j]);
                } else {
                    out.printf(" ... %6d", a[a.length - 1]);
                    break;
                }
            }
            out.println();
        }

        private void printMatrixRow(boolean[] a, int cutoff) {
            for (int j = 0; j < a.length; j++) {
                if (j < cutoff) {
                    out.print(a[j] ? "T " : "F ");
                } else {
                    out.print(" ... " + (a[a.length - 1] ? "T" : "F"));
                    break;
                }
            }
            out.println();
        }

    }

    public static void main(String[] args) throws IOException {


        int n = in.nextInt();
        int k = in.nextInt();
        int m = in.nextInt();

        String s = in.nextLine();

        String[] words = new String[n];
        words = s.split(" ");

        HashMap<String, Integer> whm = new HashMap<>();
        for(int i = 0 ;i <n; i ++) {
            whm.put(words[i], i);
        }

        int[] a = in.arrayInt(n);

        ArrayList<ArrayList<Integer>> gr = new ArrayList<>();

        int[] w2g = new int[n];

        for (int i = 0; i < k; i++) {
            ArrayList<Integer> row = new ArrayList<>();
            int x = in.nextInt();
            for (int j = 0; j < x; j++) {
                int y = in.nextInt() - 1;
                w2g[y] = i;
                row.add(y);
            }
            Collections.sort(row, (r1, r2) -> {
                if (a[r1] < a[r2])
                    return -1;
                if (a[r1] > a[r2])
                    return 1;
                return 0;
            });
            gr.add(row);
        }

        String sent = in.nextLine();
        String[] p = sent.split(" ");

        long cost = 0;

        for( String w : p) {
            int idx = whm.get(w);
            cost += a[gr.get(w2g[idx]).get(0)];
        }

        out.println(cost);

        log.flush();
        in.close();
    }
}