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.BigInteger;
import java.text.DecimalFormat;
import java.util.*;

public class Solution
{
    public static void main(String[] args)
    {
        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));

        //--------Solution-------------------------------------------------------//
        int n=sc.nextInt();
        int k=sc.nextInt();
        int m=sc.nextInt();

        String[] s=new String[n+1];

        for(int i=1;i<=n;i++){
            s[i]=sc.next();
        }

        HashMap<String,Integer> si=new HashMap<>();
        for(int i=1;i<=n;i++){si.put(s[i],i);}

        HashMap<String,Integer> h=new HashMap<>();
        for(int i=1;i<=n;i++){
            int a=sc.nextInt();
            h.put(s[i],a);
        }

        int[] cost=new int[n+1];

        for(int i=0;i<k;i++){
            int x=sc.nextInt();
            int[] in=new int[x];
            int min=Integer.MAX_VALUE;

            for(int j=0;j<x;j++){
                in[j]=sc.nextInt();
                min=Math.min(min,h.get(s[in[j]]));
            }

            for(int j=0;j<x;j++){cost[in[j]]=min;}
        }

        long ans=0;
        for(int i=0;i<m;i++){
            int ix=si.get(sc.next());
            ans += cost[ix];
        }

        out.println(ans);
        //-----------------------------------------------------------------------//

        out.close();
    }

    //-----------Helper Functions------------------------------------------------//
    static int[] readIntArray(MyScanner sc,int n){
        int[] a = new int[n];
        for(int i=0;i<n;i++) a[i]= sc.nextInt();
        return a;
    }

    static long[] readLongArray(MyScanner sc,int n){
        long[] a = new long[n];
        for(int i=0;i<n;i++) a[i]=sc.nextLong();
        return a;
    }

    static int[] toIntArray(String s){
        int[] a = new int[s.length()];
        for(int i=0;i<s.length();i++) a[i]=s.charAt(i)-'0';
        return a;
    }

    static long mod(long a){
        long M=(long)1e9+7;
        return (a%M + M) % M;
    }

    static int gcd(int a,int b){
        while(b!=0){
            int r=a%b;
            a=b;
            b=r;
        }
        return a;
    }

    static boolean isPrime(long n) {
        if(n==2||n==3) return true;
        if(n%2==0 || n%3==0) return false;

        long i=5,w=2;

        while(i*i<=n){
            if(n%i==0) return false;

            i += w;
            w = 6 - w;
        }

        return true;
    }

    static long exp(long base,int exp){
        long M=(long)1e9+7;
        long res=1L;

        while(exp>0){
            if(exp%2==1) res = (res*base)%M;
            base = (base*base)%M;
            exp /= 2;
        }

        return res;
    }

    static int floor(int[] a,int i){
        int lo=0,hi=a.length-1;
        int ans=-1;

        while(lo<=hi){
            int mid = lo + (hi-lo)/2;
            if(a[mid]==i){ans=mid; break;}
            else if(a[mid]<i){ans=mid; lo=mid+1;}
            else{hi=mid-1;}
        }

        return ans;
    }

    static boolean nextPermutation(int[] a){
        int i = a.length - 1;
        while(i>0 && a[i-1]>=a[i]) i--;

        if(i==0) return false;

        int j = a.length - 1;
        while(a[j]<=a[i-1]) j--;

        int temp = a[i-1];
        a[i-1]=a[j];
        a[j]=temp;

        j = a.length - 1;
        while(i<j){
            temp = a[i];
            a[i] = a[j];
            a[j] = temp;
            i++; j--;
        }
        return true;
    }

    static boolean nextPermutation(char[] a){
        int i = a.length - 1;
        while(i>0 && a[i-1]>=a[i]) i--;

        if(i==0) return false;

        int j = a.length - 1;
        while(a[j]<=a[i-1]) j--;

        char temp = a[i-1];
        a[i-1]=a[j];
        a[j]=temp;

        j = a.length - 1;
        while(i<j){
            temp = a[i];
            a[i] = a[j];
            a[j] = temp;
            i++; j--;
        }
        return true;
    }

    static long max_subarray(long[] a){
        long lmax = a[0], gmax=a[0];

        for(int i=1; i<a.length; i++){
            lmax = Math.max(a[i],lmax+a[i]);
            gmax = Math.max(lmax,gmax);
        }
        return gmax;
    }

    //-----------PrintWriter for faster output-----------------------------------//
    public static PrintWriter out;

    //-----------MyScanner class for faster input--------------------------------//
    public static class MyScanner
    {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner(){
            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;
        }

    }
}


//-----------------------Helper Classes------------------------------------------//
class Pair<A extends Comparable<A>,B> implements Comparable<Pair<A,B>>
{
    A first;
    B second;

    Pair(A f,B s){
        first=f;
        second=s;
    }

    public int compareTo(Pair<A,B> p){
        return this.first.compareTo(p.first);
    }
}

class DifferenceComparator implements Comparator<Pair<Integer,Integer>>{
    @Override
    public int compare(Pair<Integer,Integer> a, Pair<Integer,Integer> b){
        Integer a1=a.first-a.second;
        Integer b1=b.first-b.second;
        return Integer.compare(a1,b1);
    }
}