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.*;
			        		    import java.util.*;
		import java.util.regex.Pattern;
		
		import javafx.scene.shape.Line;
			    	     
			        		    public class Main{
			        		  	private static InputStream stream;
			        		    	private static byte[] buf = new byte[1024];
			        		    	private static int curChar;
			        		    	private static int numChars;
			        		    	private static SpaceCharFilter filter;
			        		    	private static PrintWriter pw;
			        		    	private static long count = 0,mod=(long)1e9+7;
			        		    //	private static TreeSet<Integer> ts=new TreeSet[200000];
			public final static int INF = (int) 1E9;
			
			public static void main(String args[]) {
		    	
				InputReader(System.in);
				pw = new PrintWriter(System.out); 
			    new Thread(null ,new Runnable(){
			       public void run(){
			           try{
			        		
			               test();
		
			               pw.close();
			           } catch(Exception e){
			               e.printStackTrace();
			           }
			       }
			   },"1",1<<26).start();
			   	   }
			    static StringBuilder sb;
			    public static void test() throws IOException{
			    	 sb=new StringBuilder();
			    	
			    	 int t=1;
			    	 
			    	 while(t-->0){
			    		
			    		solve();
			    		//pw.println();
			    		//sb.append("\n");
			    	}
			    	//pw.println(sb);
			    }
			    
			    public static long pow(long n, long p,long mod) {
					if(p==0)
						return 1;
					if(p==1)
						return n%mod;
					if(p%2==0){
						long temp=pow(n, p/2,mod);
					return (temp*temp)%mod;
					}else{
						 	long temp=pow(n,p/2,mod);
						 	temp=(temp*temp)%mod;
						 	return(temp*n)%mod;
						 	
					}
				}
			    public static long pow(long n, long p) {
					if(p==0)
						return 1;
					if(p==1)
						return n;
					if(p%2==0){
						long temp=pow(n, p/2);
					return (temp*temp);
					}else{
						 	long temp=pow(n,p/2);
						 	temp=(temp*temp);
						 	return(temp*n);
						 	
					}
				}
			    public static void Merge(long a[],int p,int r){
			        if(p<r){
			            int q = (p+r)/2;
			            Merge(a,p,q);
			            Merge(a,q+1,r);
			            Merge_Array(a,p,q,r);
			        }
			    }
			    public static void Merge_Array(long a[],int p,int q,int r){
			       long b[] = new long[q-p+1];
			        long c[] = new long[r-q];
			        for(int i=0;i<b.length;i++)
			            b[i] = a[p+i];
			        for(int i=0;i<c.length;i++)
			            c[i] = a[q+i+1];
			        int i = 0,j = 0;
			        for(int k=p;k<=r;k++){
			            if(i==b.length){
			                a[k] = c[j];
			                j++;
			            }
			            else if(j==c.length){
			                a[k] = b[i];
			                i++;
			            }
			            else if(b[i]<c[j]){
			                a[k] = b[i];
			                i++;
			            }
			            else{
			                a[k] = c[j];
			                j++;
			            }
			        }
			    }
			    
			  
				public static long gcd(long x, long y) {
					if (x == 0)
						return y;
					else
						return gcd( y % x,x);
				}	
				
				public static boolean isPrime(int n) {
					if (n <= 1)
						return false;
					if (n <= 3)
						return true;
			 
					if (n % 2 == 0 || n % 3 == 0)
						return false;
			 
					for (int i = 5; i * i <= n; i = i + 6)
						if (n % i == 0 || n % (i + 2) == 0)
							return false;
			 
					return true;
				}
				
			        static LinkedList<Integer> adj[],adj2[];
			        static boolean Visited[];
			        static HashSet<Integer> exc;
			        static long oddsum[]=new long[1000001];
			        static long co=0;
			        static int indeg[],outdeg[];
	  		      
			    
			    	private static void buildgraph(int n){
			    		adj=new LinkedList[n+1];
			    		adj2=new LinkedList[n+1];
			    		Visited=new boolean[n+1];
			    		levl=new int[n+1];
			    		indeg=new int[n+1];
			    		outdeg=new int[n+1];
			    		for(int i=0;i<=n;i++){
			    			adj[i]=new LinkedList<Integer>();
			    			adj2[i]=new LinkedList<Integer>();
			    		}
			
			
			    	}
			      
			       
			        static int[] levl;
			        static int[] eat;
			        static int n,m;
			        static int price[];
			        //ind frog crab
			    
			        
			        static long d,x,y;
					static long modInverse(long A, long M)
					{
					extendedEuclid(A,M);
					return (x%M+M)%M;    //x may be negative
					}
					static void extendedEuclid(long A, long B) {
					if(B == 0) {
					d = A;
					x = 1;
					y = 0;
					}
					else {
					extendedEuclid(B, A%B);
					long temp = x;
					x = y;
					y = temp - (A/B)*y;
					}
					}
			        static double distance(int x1,int y1,int x2,int y2){
			        	return Math.sqrt((x1-x2)*(x1-x2) + (y1-y2)*(y1-y2));
			        }
			        static double area(int x1, int y1, int x2, int y2, int x3, int y3)
			        {
			           return Math.abs((x1*(y2-y3) + x2*(y3-y1)+ x3*(y1-y2))/2.0);
			        }
			        static boolean isInside(int x1, int y1, int x2, int y2, int x3, int y3, int x, int y)
			        {   
			           double A = area (x1, y1, x2, y2, x3, y3);
			         
			           double A1 = area (x, y, x2, y2, x3, y3);
			         
			           double A2 = area (x1, y1, x, y, x3, y3);
			         
			           double A3 = area (x1, y1, x2, y2, x, y);
			           
			          return (A == A1 + A2 + A3);
			        }
			      
					static int col[];
			    public static boolean isVowel(char c){
			    	if(c=='a' || c=='e'||c=='i' || c=='o' || c=='u')
			    		return true;
			    	return false;
			    }
			static long arr[], lazy[],ans[];
			static int c[],nodes[];
			static int dp[][];
			static long a[][];
			
			private static boolean isPrim(long n,int p){
				for (long i = 2; i * i <= n; i++) {
			        if (n % i == 0 && i <= p) return false;
			    }
			    return true;
			}
			//price - starting index of string with given hash
			//rating-count of number of time of a hash
			static ArrayList<String> all_perm;
			static boolean[][] visited1;
			static  boolean won;
			static boolean containsCycle;
			static ArrayList<Integer> anss;
			private static int size = 0;
		public static void solve() throws IOException{
			HashSet<Integer> prime = new HashSet<Integer>();
			for(int i=2;i<=1;i++){
				if(isPrime(i))
					prime.add(i);
			}
			int n=nextInt();
			int k=nextInt();
			int m=nextInt();
			String s=nextLine();
			HashMap<String,Integer> hm=new HashMap<String,Integer>();
			String sp[]=s.split(" ");
			for(int i=0;i<sp.length;i++){
				hm.put(sp[i], i+1);
			}
			long cost[]=nextLongArray(n);
			long arr[]=new long[n+1];
			for(int i=0;i<k;i++){
				int x=nextInt();
				int in[]=nextIntArray(x);
				long min=Long.MAX_VALUE;
				for(int j=0;j<x;j++){
					min = Math.min(min, cost[in[j]-1]);
				}
				for(int j=0;j<x;j++){
					arr[in[j]] = min;
				}
			}
			String msg[]=nextLine().split(" ");
			long tot=0;
			for(int i=0;i<msg.length;i++){
				tot += arr[hm.get(msg[i])];
			}
			pw.println(tot);
			
			
		}
			private static int mySoln(int n,int a,int b){
				int tempa=Math.min(a, b);
				int tempb=Math.max(a, b);
				ArrayList<Integer> list = new ArrayList<Integer>();
				for(int i=1;i<=n;i++){
					list.add(i);
				}
				
				int round=1;
				while(true){
					ArrayList<Integer> temp = new ArrayList<Integer>();
					
					for(int i=0;i<list.size();i+=2){
						if(list.get(i)==tempa && list.get(i+1)==tempb){
							
							return round;
						}
						if(list.get(i)==tempa ||  list.get(i)==tempb){
							temp.add(list.get(i));
						}else if(list.get(i+1)==tempa || list.get(i+1)==tempb){
							temp.add(list.get(i+1));
						}else{
							temp.add(list.get(i));
						}
					}
					
					list.clear();
					for(int i:temp){
						list.add(i);
					}
				
					round++;
				
					
				}
			}
			private static int othersoln(int n,int a,int b){
			for(int i=16;i>=0;i--){
				if(BB(a,i) ^ BB(b,i)){
					int m=i+1;
					
						return m;
								
			}
			}
			return 0;
			
			}
			private static boolean BB(int n,int i){
				return (n & (1<<i)) >0;
			}
					private static boolean check(int x,int y,int n,int m){
				if(x>=0 && x<n && y>=0 && y<m)
					return true;
				return false;
			}
					
					
					
					private static void dfs(int curr,int par){
				Visited[curr]=true;
				for(int i:adj[curr]){
					if(!Visited[i]){
						dfs(i,curr);
					}
				}
				dp[curr][nodes[curr]]++;
				for(int i=0;i<26;i++){
					dp[par][i]+=dp[curr][i];
				}
			}
		
			
			
			    private static boolean Check(int x,int y,int n){
					if(x>=0 && x<n && y>=0 && y<n)
						return true;
					return false;
				}
			    
			    public static String reverseString(String s) {
					StringBuilder sb = new StringBuilder(s);
					sb.reverse();
					return (sb.toString());
				}
			    
			  /*  
			   private static void BFS(int sou){
			    	Queue<Integer> q=new LinkedList<Integer>();
			    	q.add(sou);
			    	Visited[sou]=true;
			    	levl[sou]=0;
			    	while(!q.isEmpty()){
			    		int top=q.poll();
			    		
			    		for(int i:adj[top]){
			    			//pw.println(i+" "+top);
						if(!Visited[i])
						{
							
							q.add(i);
							levl[i]=levl[top]+1;
						}
						
						Visited[i]=true;
						
						}
					}
				}*/
				
			
			
			
			    		      
			    		   /* private static void kahn(int n){
			    		    	
			    		    	PriorityQueue<Integer> q=new PriorityQueue<Integer>();
			    				for(int i=1;i<=n;i++){
			    					if(indeg[i]==0){
			    						q.add(i);
			    					}
			    				}
			    				while(!q.isEmpty()){
			    					int top=q.poll();
			    					st.push(top);
			    					for(Node i:adj[top]){
			    						indeg[i.to]--;
			    						if(indeg[i.to]==0){
			    							q.add(i.to);
			    						}
			    					}
			    				}
			    		    }
			    		        
			    		        static int state=1;
			    		        static long no_exc=0,no_vert=0;
			    		      static Stack<Integer> st;
			    		      static HashSet<Integer> inset;
			    		     /*   private static void topo(int curr){
			    		        	
			    		        	Visited[curr]=true;
			    		        	inset.add(curr);
			    		        	for(int x:adj[curr]){
			    		        		if(adj[x].contains(curr) || inset.contains(x)){
			    		        			state=0;
			    		        			return;
			    		        		}
			    		        		if(state==0)
			    		        			return;
			    		        		
			    		        	}
			    		        	st.push(curr);
			    		        	
			    		        	inset.remove(curr);
			    		        }*/
			    		        static HashSet<Integer> hs;
			    		       
			    		     
			    		     	static boolean prime[];
								static int spf[];
								public static void sieve(int n){
									prime=new boolean[n+1];
									spf=new int[n+1];
									
									Arrays.fill(spf, 1);
									Arrays.fill(prime, true);
								prime[1]=false;
									spf[2]=2;
									
								for(int i=4;i<=n;i+=2){
									spf[i]=2;
								}
								for(int i=3;i<=n;i+=2){
									if(prime[i]){
										spf[i]=i;
										for(int j=2*i;j<=n;j+=i){
											
											prime[j]=false;
										if(spf[j]==1){
											spf[j]=i;
										}
										}
									}
								}
								
									
								}
			    		     	
			    		    	// To Get Input
			// Some Buffer Methods
			 
			    		     	public static void sort(long a[]){
			    		     		Merge(a, 0, a.length-1);
			    		     	}
			    		    	public static void InputReader(InputStream stream1) {
			    		    		stream = stream1;
			    		    	}
			 
			    		    	private static boolean isWhitespace(int c) {
			    		    		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
			    		    	}
			 
			    		    	private static boolean isEndOfLine(int c) {
			    		    		return c == '\n' || c == '\r' || c == -1;
			    		    	}
			 
			    		    	private static 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++];
			    		    	}
			 
			    		    	private static int nextInt() {
			    		    		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;
			    		    	}
			 
			    		    	private static long nextLong() {
			    		    		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;
			    		    	}
			 
			    		    	private static String nextToken() {
			    		    		int c = read();
			    		    		while (isSpaceChar(c))
			    		    			c = read();
			    		    		StringBuilder res = new StringBuilder();
			    		    		do {
			    		    			res.appendCodePoint(c);
			    		    			c = read();
			    		    		} while (!isSpaceChar(c));
			    		    		return res.toString();
			    		    	}
			 
			    		    	private static String nextLine() {
			    		    		int c = read();
			    		    		while (isSpaceChar(c))
			    		    			c = read();
			    		    		StringBuilder res = new StringBuilder();
			    		    		do {
			    		    			res.appendCodePoint(c);
			    		    			c = read();
			    		    		} while (!isEndOfLine(c));
			    		    		return res.toString();
			    		    	}
			 
			    		    	private static int[] nextIntArray(int n) {
			    		    		int[] arr = new int[n];
			    		    		for (int i = 0; i < n; i++) {
			    		    			arr[i] = nextInt();
			    		    		}
			    		    		return arr;
			    		    	}
			 
			    		    	private static long[][] next2dArray(int n, int m) {
			    		    		long[][] arr = new long[n][m];
			    		    		for (int i = 0; i < n; i++) {
			    		    			for (int j = 0; j < m; j++) {
			    		    				arr[i][j] = nextLong();
			    		    			}
			    		    		}
			    		    		return arr;
			    		    	}
			    		    	private static char[][] nextCharArray(int n,int m){
			    		    		char [][]c=new char[n][m];
			    		    		for(int i=0;i<n;i++){
			    		    			String s=nextLine();
			    		    			for(int j=0;j<s.length();j++){
			    		    				c[i][j]=s.charAt(j);
			    		    			}
			    		    		}
			    		    		return c;
			    		    	}
			 
			    		    	private static long[] nextLongArray(int n) {
			    		    		long[] arr = new long[n];
			    		    		for (int i = 0; i < n; i++) {
			    		    			arr[i] = nextLong();
			    		    		}
			    		    		return arr;
			    		    	}
			 
			    		    	private static void pArray(int[] arr) {
			    		    		for (int i = 0; i < arr.length; i++) {
			    		    			pw.print(arr[i] + " ");
			    		    		}
			    		    		pw.println();
			    		    		return;
			    		    	}
			 
			    		    	private static void pArray(long[] arr) {
			    		    		for (int i = 0; i < arr.length; i++) {
			    		    			pw.print(arr[i] + " ");
			    		    		}
			    		    		pw.println();
			    		    		return;
			    		    	}
			 
			    		    	private static void pArray(boolean[] arr) {
			    		    		for (int i = 0; i < arr.length; i++) {
			    		    			pw.print(arr[i] + " ");
			    		    		}
			    		    		pw.println();
			    		    		return;
			    		    	}
			 
			    		    	private static boolean isSpaceChar(int c) {
			    		    		if (filter != null)
			    		    			return filter.isSpaceChar(c);
			    		    		return isWhitespace(c);
			    		    	}
			 
			    		    	private interface SpaceCharFilter {
			    		    		public boolean isSpaceChar(int ch);
			    		    	}
			    		    	
			
			}
			    		    
			    		        class Node{
			    		    	int to;
			    		    	long dist;
			    		    	Node(int to,long dist){
			    		    		this.to=to;
			    		    		this.dist=dist;
			    		    	}
			    		    	
			    		    }
			    		        class Qu{
			    		    		long a0,a1,a2,a3;
			    		    		public Qu(long a0,long a1,long a2,long a3) {
			    		    			this.a0=a0;
			    		    			this.a1=a1;
			    		    			this.a2=a2;
			    		    			this.a3=a3;
			    		    		}
			    		    }
			    		
			class Dsu{
			private int rank[], parent[] ,n;
			long str[],si[],larg[];
			long max=0;
			int cnt=0;
			private static int[] parent1;
			Dsu(int size){
				this.n=size+1;
				rank=new int[n];
				cnt=n-1;
				//parent=new int[n];
			    		    		    		parent=new int[n];
			    		    		    		str=new long[n];
			    		    		    		si=new long[n];
			    		    		
			    		    		    		larg=new long[n];
			    		    		    		makeSet();
			    		    		
			    		    		    	}
			    		    		    	
			    		    		    	void makeSet(){
			    		    		    		for(int i=0;i<n;i++){
			    		    		    			parent[i]=i;
			    		    		    			si[i]=1;
			    		    		    		}
			    		    		    	}
			    		    		    	
			    		    		    	int find(int x){
			    		    		    		if(parent[x]!=x){
			    		    		    			
			    		    		    			parent[x]=find(parent[x]);
			    		    		    		}
			    		    		    		return parent[x];
			    		    		    	}
			    		    		    	
			    		    		    	void join(int ind,long val){
			    		    		    		if(str[ind]==0){
			    		    		    			str[ind]=val;
			    		    		    			larg[ind]=val;
			    		    		    			max=Math.max(max, str[ind]);
			    		    		    		}
			    		    		    		int prev_ind=(ind-1);
			    		    		    		int next_ind=(ind+1);
			    		    		    		if(prev_ind>0 && larg[prev_ind]!=0){
			    		    		    			union(prev_ind,ind);
			    		    		    		}
			    		    		    		if(next_ind<n && larg[next_ind]!=0){
			    		    		    			union(next_ind,ind);
			    		    		    		}
			    		    		    		
			    		    		    	}
			    		    		    
			    		    		    	
			    		    		    	boolean union(int x,int y){
			    		    		    		int xRoot=find(x);
			    		    		    		int yRoot=find(y);
			    		    		    
			    		    		    	
			    		    		    		if(xRoot==yRoot)
			    		    		    			return false;
			    		    		    		if(rank[xRoot]<rank[yRoot]){
			    		    		    		parent[xRoot]=yRoot;
			    		    		    		
			    		    		    		larg[yRoot]=Math.max(larg[xRoot], larg[yRoot]);
			    		    		    		
			    		    		    		si[yRoot]+=si[xRoot];
			    		    		    		str[yRoot]=larg[yRoot]*si[yRoot];
			    		    		    			max=Math.max(str[yRoot], max);
			    		    		    		}else if(rank[yRoot]<rank[xRoot]){
			    		    		    			parent[yRoot]=xRoot;
			     
			    		    		    			larg[xRoot]=Math.max(larg[xRoot], larg[yRoot]);
			        		    		    		
			        		    		    		si[xRoot]+=si[yRoot];
			        		    		    		str[xRoot]=larg[xRoot]*si[xRoot];
			    			    		    		max=Math.max(str[xRoot], max);
			    		    		    		}else{
			    		    		    			parent[yRoot]=xRoot;
			    		    		    			rank[xRoot]++;
			     
			    		    		    			larg[xRoot]=Math.max(larg[xRoot], larg[yRoot]);
			        		    		    		
			        		    		    		si[xRoot]+=si[yRoot];
			        		    		    		str[xRoot]=larg[xRoot]*si[xRoot];
			    			    		    		max=Math.max(str[xRoot], max);
			    		    		    		
			    		    		    		}
			    		    		    		cnt--;
			    		    		    		return true;
			    		    		    	}
			    	
			    		    		     
			    		    		    }
		class Pair1 implements Comparable<Pair1>{
				long price,rating;
				Pair1(long a,long b){
					this.price=a;
					this.rating=b;
				}
				@Override
				public int compareTo(Pair1 arg0) {
					
						return (int)(price-arg0.price);
					
				}
			
			
			}