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.util.*;
import java.io.*;

public class Codeforces {
    
    InputStream is;
    PrintWriter out;
    String INPUT = "";

//----------------------------------------------------------------------------------------------------//
    void solve() {
        int n=ni();
        int k=ni();
        int m=ni();
        Map<String, Integer> map = new HashMap<String, Integer>();
        for (int i = 0; i < n; i++) {
            map.put(ns(), i);
        }
        int c[]=na(n);
        int g[]=new int[n];
        long lc[]=new long[k];
        for (int i = 0; i < k; i++) {
            int x=ni();
            int s=Integer.MAX_VALUE;
            for (int j = 0; j < x; j++) {
                int y=ni()-1;
                g[y]=i;
                if(c[y]<=s)s=c[y];
            }
            lc[i]=s;
        }
        long ans=0;
        for (int i = 0; i < m; i++) {
            ans+=lc[g[map.get(ns())]];
        }
        out.println(ans);
    }

//----------------------------------------------------------------------------------------------------//
    boolean isPrime(int n) {
        if (n <= 1) {
            return false;
        }
        for (int i = 2; i <= (int) Math.sqrt(n); i++) {
            if (n % i == 0) {
                return false;
            }
        }
        return true;
    }
    
    Vector<Integer> sieveOfEratosthenes(int n) {
        boolean[] prime = new boolean[n + 1];
        for (int i = 0; i < n; i++) {
            prime[i] = true;
        }
        for (int p = 2; p * p <= n; p++) {
            if (prime[p] == true) {
                for (int j = p * p; j <= n; j += p) {
                    prime[j] = false;
                }
            }
        }
        Vector<Integer> v = new Vector<>();
        for (int i = 2; i <= n; i++) {
            if (prime[i]) {
                v.add(i);
            }
        }
        return v;
    }
    
    void swap(int a[], int l, int r) {
        int temp = a[l];
        a[l] = a[r];
        a[r] = temp;
    }
    
    long nCr(int n, int k) {
        long C[] = new long[k + 1];
        // nC0 is 1 
        C[0] = 1;
        for (int i = 1; i <= n; i++) {
            for (int j = Math.min(i, k); j > 0; j--) {
                C[j] = C[j] + C[j - 1];
            }
        }
        return C[k];
    }
    
    public int gcd(int s, int l) {
        if (s == 0) {
            return l;
        }
        
        return gcd(l % s, s);
    }
    
    public HashMap<Integer, Integer> sortByValue(HashMap<Integer, Integer> hm) {
        // Create a list from elements of HashMap 
        List<Map.Entry<Integer, Integer>> list
                = new LinkedList<>(hm.entrySet());

        //->change o1,o2 for reverseorder
        Collections.sort(list, (Map.Entry<Integer, Integer> o1, Map.Entry<Integer, Integer> o2) -> (o1.getValue()).compareTo(o2.getValue()));

        // put data from sorted list to hashmap  
        HashMap<Integer, Integer> temp = new LinkedHashMap<>();
        list.forEach((aa) -> {
            temp.put(aa.getKey(), aa.getValue());
        });
        return temp;
    }
    
    void run() throws Exception {
        is = System.in;//oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        
        long s = System.currentTimeMillis();
        solve();
        out.flush();
        tr(System.currentTimeMillis() - s + "ms");
    }
    
    public static void main(String[] args) throws Exception {
        new Codeforces().run();
    }
    
    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;
    
    private int readByte() {
        if (lenbuf == -1) {
            throw new InputMismatchException();
        }
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = is.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0) {
                return -1;
            }
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }
    
    private int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b));
        return b;
    }
    
    private double nd() {
        return Double.parseDouble(ns());
    }
    
    private char nc() {
        return (char) skip();
    }
    
    private String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for (int i = 0; i < n; i++) {
            map[i] = ns(m);
        }
        return map;
    }
    
    private int[] na(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = ni();
        }
        return a;
    }
    
    private int ni() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
    
    private void tr(Object... o) {
        if (!oj) {
            System.out.println(Arrays.deepToString(o));
            
        }
    }
    
    class Pair {

        /*SORTING PAIRS BY COMPARING Y OF PAIR.
    Pair[] p=new Pair[n];
    p[i]=new Pair(i,ni());
    Arrays.sort(p,( p1, p2) -> {return p1.y-p2.y;});
         */
        int x;
        int y;
        
        Pair(int u, int v) {
            x = u;
            y = v;
        }
        
        @Override
        public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (!(o instanceof Pair)) {
                return false;
            }
            Pair key = (Pair) o;
            return x == key.x && y == key.y;
        }
        
        @Override
        public int hashCode() {
            int result = x;
            result = 31 * result + y;
            return result;
        }
        
    }

    class Dsu {

        int par[];
        int size[];

        Dsu(int n) {
            par = new int[n];
            size = new int[n];
            for (int i = 0; i < n; i++) {
                par[i] = i;
                size[i] = 1;
            }
        }

        int root(int i) {
            if (i == par[i]) {
                return i;
            }
            return par[i] = root(par[i]);
        }

        boolean find(int p, int q) {
            return root(p) == root(q);
        }

        void union(int p, int q) {
            int a = root(p);
            int b = root(q);
            if (a == b) {
                return;
            }
            if (size[a] > size[b]) {
                par[b] = a;
                size[a] += size[b];
            } else {
                par[a] = b;
                size[b] += size[a];
            }
        }
        
    }
}
//isPrime(int)
//Vector<Integer> sieveOfEratosthenes(int n){PRIME NO <=n}
//swap(arr,i,j)
//HashMap sortByValue(map);
//long comb=nCr(5,2);
//int gcd(s,l);
//Pair p=new Pair(x,y);
// Dsu dsu=new Dsu(n);