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.HashMap;
import java.util.InputMismatchException;


public class Main {

    public static void main(String[] args) throws IOException {
        InputReader in = new InputReader(System.in);
        OutputWriter out = new OutputWriter(System.out);
        final int N = in.readInt();
        final int K = in.readInt();
        final int M = in.readInt();
        String[] words = IOUtils.readStringArray(in, N, 1);
        HashMap<String, Integer> wordPosMap = new HashMap<>(N);
        for (int i = 1; i <= words.length - 1; ++i) {
            wordPosMap.put(words[i], i);
        }
        int[] costs = IOUtils.readIntArray(in, N, 1);
        int x, j;
        int[] wordGroupMap = new int[N + 1];
        int[] group;
        int[] groupMinCosts = new int[K + 1];
        int groupMinCost = 0;
        for (int k = 1; k <= K; ++k) {
            x = in.readInt();
            group = IOUtils.readIntArray(in, x, 1);
            groupMinCost = Integer.MAX_VALUE;
            for (j = 1; j <= group.length - 1; ++j) {
                wordGroupMap[group[j]] = k;
                groupMinCost = Math.min(costs[group[j]], groupMinCost);
            }
            groupMinCosts[k] = groupMinCost;
        }
        String msg = in.readLine();
        String[] msgWords = msg.trim().split("\\s+");
        long res = 0;
        for (j = 0; j <= msgWords.length - 1; ++j) {
            if (wordGroupMap[wordPosMap.get(msgWords[j])] == 0) {
                res = res + costs[wordPosMap.get(msgWords[j])];
                continue;
            }
            res = res + groupMinCosts[wordGroupMap[wordPosMap.get(msgWords[j])]];
        }
        out.print(res);
        closeStreams(out, in);
    }

    private static void closeStreams(OutputWriter out, InputReader in) throws IOException {
        out.flush();
        out.close();
        in.close();
    }

    static class InputReader {

        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

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

        public 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++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public double readDouble() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E') {
                    return res * Math.pow(10, readInt());
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E') {
                        return res * Math.pow(10, readInt());
                    }
                    if (c < '0' || c > '9') {
                        throw new InputMismatchException();
                    }
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public long readLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

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

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

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public boolean isEndOfLine(int c) {
            if (filter != null) {
                return filter.isEndOfLine(c);
            }
            return c == '\n' || c == '\r' || c == -1;
        }

        public String next() {
            return readString();
        }

        public void close() throws IOException {
            this.stream.close();
        }

        public interface SpaceCharFilter {
            boolean isSpaceChar(int ch);

            boolean isEndOfLine(int ch);
        }

    }

    static class IOUtils {

        public static int[] readIntArray(InputReader in, int elementCount) {
            return readIntArray(in, elementCount, 0);
        }

        public static int[] readIntArray(InputReader in, int elementCount, int startOffset) {
            int[] array = new int[elementCount + startOffset];
            for (int i = 0; i < elementCount; i++)
                array[i + startOffset] = in.readInt();
            return array;
        }

        public static long[] readLongArray(InputReader in, int elementCount) {
            return readLongArray(in, elementCount, 0);
        }

        public static long[] readLongArray(InputReader in, int elementCount, int startOffset) {
            long[] array = new long[elementCount + startOffset];
            for (int i = 0; i < elementCount; i++)
                array[i + startOffset] = in.readLong();
            return array;
        }

        public static String[] readStringArray(InputReader in, int elementCount) {
            return readStringArray(in, elementCount, 0);
        }

        public static String[] readStringArray(InputReader in, int elementCount, int startOffset) {
            String[] array = new String[elementCount + startOffset];
            for (int i = 0; i < elementCount; i++)
                array[i + startOffset] = in.readString();
            return array;
        }

    }

    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();
        }

    }
}