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:
/* 
 * UMANG PANCHAL
 * DAIICT
 */

import java.util.*;
import java.io.*;
import java.math.*;
import java.util.Comparator;
public class Main
{
 
	private static final Comparator<? super Integer> Comparator = null;
	static LinkedList<Integer> adj[];
	static ArrayList<Integer> adj1[];
	static int[] color,visited1;
	static boolean b[],visited[],possible;
	static int level[];
	static Map<Integer,HashSet<Integer>> s;
	static int totalnodes,colored;
	static int count[];
	static long sum[];
	static int nodes;
	static long ans=0;
	static long[] as=new long[10001];
	static long c1=0,c2=0;
	static int[] a,d,k;
	static int max=100000000;
	static long MOD = 1000000007,sm=0,m=Long.MIN_VALUE;
	static boolean[] prime=new boolean[1000005];
	static int[] levl;
    static int[] eat;
    static int price[];
    static int res[],par[],co[];
    static int result=0;
    static int[] root,size,du,dv;
    static long p=Long.MAX_VALUE;
    static int start,end,r=0;
    static boolean[] vis1,vis2;
    static long n;
  
	// --------------------My Code Starts Here----------------------
	
	public static void main(String[] args) throws IOException
	{
		in=new InputReader(System.in);
	    w=new PrintWriter(System.out);
         int n=ni(),k=ni(),m=ni();
         String[] s=ns().split(" ");
         HashMap<String,Long> hm=new HashMap<String,Long>();
         HashMap<String,Integer> hm1=new HashMap<String,Integer>();
         for(int i=0;i<n;i++)
        	 hm.put(s[i],nl());
         long[] a=new long[k];
         Arrays.fill(a,Long.MAX_VALUE);
         for(int i=0;i<k;i++)
         {
        	 int x=ni();
        	 for(int j=0;j<x;j++)
        	 {
        		 int ind=ni()-1;
        		 hm1.put(s[ind],i);
        		 a[i]=Math.min(a[i],hm.get(s[ind]));
        	 }
         }
         long ans=0;
         String[] p=ns().split(" ");
         for(int i=0;i<m;i++)
         {
        	 ans+=a[hm1.get(p[i])];
         }
    	 w.print(ans);
   w.close();
   }

	

	

	// --------------------My Code Ends Here------------------------
     
	
	/*
	 *  PriorityQueue<Integer> pq = new PriorityQueue<Integer>(new Comparator<Integer>()
  			{
  				public int compare(Integer o1, Integer o2)
  				{
  					return Intege
  					r.compare(o2,o1);
  				}
  			});
	 * 
	 * 
	 */
	public static void bfs1(int u)
	{
	    Queue<Integer> q=new LinkedList();
	    q.add(u);
	    visited[u]=true;
	    while(!q.isEmpty())
	    {
	    	//w.print(1);
	    	int p=q.poll();
	      for(int i=0;i<adj[p].size();i++)
	     { 
	    	  if(!visited[adj[p].get(i)])
	    	  {
	    	q.add(adj[p].get(i));
	    	visited[adj[p].get(i)]=true;
	    	  }
	    	  levl[adj[p].get(i)]=levl[p]+1;
	    	  }
	    }
	    
	}
	public static void bfs2(int u)
	{
	    Queue<Integer> q=new LinkedList();
	    q.add(u);
	    vis2[u]=true;
	    while(!q.isEmpty())
	    {
	    	int p=q.poll();
	      for(int i=0;i<adj[p].size();i++)
	     { 
	    	  if(!vis2[adj[p].get(i)])
	    	  {
	    	dv[adj[p].get(i)]=dv[p]+1;
	    	q.add(adj[p].get(i));
	    	  
	    	vis2[adj[p].get(i)]=true;
	    	  }
	    	  }
	    }
	    
	}
	 public static void buildgraph(int n)
	 {
         adj=new LinkedList[n+1];
         visited=new boolean[n];
         level=new int[n];
         par=new int[n];
         for(int i=0;i<=n;i++)
         	{
        	 adj[i]=new LinkedList<Integer>();
         	
         	}
      
	 }
	
	/*public static long kruskal(Pair[] p)
	{
		long ans=0;
		int w=0,x=0,y=0;
		for(int i=0;i<p.length;i++)
		{
			w=p[i].w;
			x=p[i].x;
			y=p[i].y;
			if(root(x)!=root(y))
			{
				ans+=w;
				union(x,y);
			}
		}
		return ans;
	}*/
	
	 static class Pair implements Comparable<Pair>
	 {
		 Integer x,ind;
	        Pair(int x,int ind)
	        {
	            this.x=x;
	            this.ind=ind;
	        }
	        public int compareTo(Pair p)
	        {
	            return Integer.compare(this.x,p.x);
	        }
		
	}
	 static  class npair implements Comparable<npair>
	 {
	     int a,b;
	     
	
		npair(int a,int b)
		{
			this.a=a;
			this.b=b;
			//this.index=index;
		}


		public int compareTo(npair o) {
			// TODO Auto-generated method stub
			return Integer.compare(this.a,o.a);
		}


	
		
	}
	public static int root(int i)
	{
		while(root[i]!=i)
		{
			root[i]=root[root[i]];
			i=root[i];
		}
		return i;
	}
	
	public static void init(int n)
	{
		root=new int[n+1];
		for(int i=1;i<=n;i++)
			root[i]=i;
	}
	public static void union(int a,int b)
	{
	    int root_a=root(a);	
	    int root_b=root(b);
	    root[root_a]=root_b;
	   // size[root_b]+=size[root_a];
	}


	
	public static boolean isPrime(long n)
	{
	    // Corner cases
	    if (n <= 1)  return false;
	    if (n <= 3)  return true;
	 
	    // This is checked so that we can skip 
	    // middle five numbers in below loop
	    if (n%2 == 0 || n%3 == 0)
	    	return false;
	 
	    for (long i=5; i*i<=n; i=i+6)
	        if (n%i == 0 || n%(i+2) == 0)
	           return false;
	 
	    return true;
	}
	

	
	public static String ns()
	{
		return in.nextLine();
	}
	public static int ni()
	{
		return in.nextInt();
	}
	public static long nl()
	{
		return in.nextLong();
	}
	public static int[] na(int n)
	{
		int[] a=new int[n];
		for(int i=0;i<n;i++)
		a[i]=ni();
		return a;
	}
	public static long[] nla(int n)
	{
		long[] a=new long[n];
		for(int i=0;i<n;i++)
		a[i]=nl();
		return a;
	}
	public static void sieve()
	    {
	       int n=prime.length;
	        for(int i=0;i<n;i++)
	            prime[i] = true;
	         
	        for(int p = 2; p*p <=n; p++)
	        {
	            if(prime[p] == true)
	            {
	                for(int i = p*2; i <n; i += p)
	                    prime[i] = false;
	            }
	        }
	    }

  public static String rev(String s)
	{
		StringBuilder sb=new StringBuilder(s);
		sb.reverse();
		return sb.toString();
	}
	static long lcm(long a, long b)
	{
	    return a * (b / gcd(a, b));
	}
	static long gcd(long a, long b)
	{
	    while (b > 0)
	    {
	        long temp = b;
	        b = a % b; // % is remainder
	        a = temp;
	    }
	    return a;
	}
	static InputReader in;
	static PrintWriter w;
static class InputReader 
{
 
private final InputStream stream;
private final byte[] buf = new byte[8192];
private int curChar, snumChars;
private SpaceCharFilter filter;
 
public InputReader(InputStream stream)
{
  this.stream = stream;
}
 
public int snext()
{
  if (snumChars == -1)
    throw new InputMismatchException();
  if (curChar >= snumChars)
  {
    curChar = 0;
    try 
    {
      snumChars = stream.read(buf);
    }
    catch (IOException e)
    {
      throw new InputMismatchException();
    }
    if (snumChars <= 0)
      return -1;
  }
  return buf[curChar++];
}
 
public int nextInt() 
{
  int c = snext();
  while (isSpaceChar(c)) 
  {
    c = snext();
  }
  int sgn = 1;
  if (c == '-')
  {
    sgn = -1;
    c = snext();
  }
  int res = 0;
  do
  {
    if (c < '0' || c > '9')
      throw new InputMismatchException();
    res *= 10;
    res += c - '0';
    c = snext();
  }
  while (!isSpaceChar(c));
  return res * sgn;
}
 
public long nextLong() 
{
  int c = snext();
  while (isSpaceChar(c)) 
  {
    c = snext();
  }
  int sgn = 1;
  if (c == '-')
  {
    sgn = -1;
    c = snext();
  }
  long res = 0;
  do
  {
    if (c < '0' || c > '9')
      throw new InputMismatchException();
    res *= 10;
    res += c - '0';
    c = snext();
  }
  while (!isSpaceChar(c));
  return res * sgn;
}	    
public String readString() 
{
  int c = snext();
  while (isSpaceChar(c)) 
  {
    c = snext();
  }
  StringBuilder res = new StringBuilder();
  do
  {
    res.appendCodePoint(c);
    c = snext();
  }
  while (!isSpaceChar(c));
  return res.toString();
}
 
public String nextLine() 
{
  int c = snext();
  while (isSpaceChar(c))
    c = snext();
  StringBuilder res = new StringBuilder();
  do
  {
    res.appendCodePoint(c);
    c = snext();
  }
  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;
}
 
private boolean isEndOfLine(int c) 
{
  return c == '\n' || c == '\r' || c == -1;
}
 
public interface SpaceCharFilter
{
  public boolean isSpaceChar(int ch);
}
}
	
}