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.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.util.*;
import java.util.Map.Entry;

public class Main
{
	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;
	private PrintWriter pw;
	private long mod = 1000000000
			+ 7;

	private StringBuilder ans_sb;
	private long sum = 0;
	private int cnt;

	private void soln()
	{
		int n = nextInt();
		int k = nextInt();
		int m = nextInt();
		String[] arr = nextLine()
				.split(" ");
		int[] c = nextIntArray(
				n);
		for (int i = 0; i < k; i++)
		{
			int x = nextInt();
			int cc = Integer.MAX_VALUE;
			ArrayList<Integer> l = new ArrayList<>();
			for (int j = 0; j < x; j++)
			{
				int xx = nextInt()
						- 1;
				l.add(xx);
				cc = Math
						.min(cc, c[xx]);
			}
			for (int xx : l)
			{
				c[xx] = cc;
			}
		}
		HashMap<String, Integer> map = new HashMap<>();
		for (int i = 0; i < n; i++)
		{
			map.put(arr[i],
					c[i]);
		}
		String[] nn = nextLine()
				.split(" ");
		long ccc = 0;
		for (int i = 0; i < m; i++)
		{
			ccc += (long) map
					.get(nn[i]);
		}
		pw.println(
				ccc);
	}

	private long[][] ans(
			long pow,
			HashSet<Integer> set,
			long[][] ans1,
			long[][] tmp)
	{
		if (pow == 1)
			return ans1;
		ans1 = ans(
				pow / 2,
				set,
				ans1,
				tmp);
		ans1 = multiply(
				ans1,
				ans1);
		if ((pow & 1) != 0)
			ans1 = multiply(
					ans1,
					tmp);
		return ans1;
	}

	private long[][] multiply(
			long[][] a,
			long[][] b)
	{
		int m = a.length;
		long[][] ret = new long[m][m];
		for (int i = 0; i < m; i++)
		{
			for (int j = 0; j < m; j++)
			{
				for (int k = 0; k < m; k++)
				{
					ret[i][j] = (ret[i][j]
							+ ((a[i][k]
									* b[k][j])
									% mod))
							% mod;
				}
			}
		}
		return ret;
	}

	class BitsetLong
	{

		static final int LOG = 6;
		static final int SIZE = 1 << LOG;
		static final int MASK = SIZE
				- 1;

		private long[] data;

		public BitsetLong(
				int n)
		{
			data = new long[(n >> LOG)
					+ 2];
		}

		void set(
				int i)
		{
			data[i >> LOG] |= 1L << (i
					& MASK);
		}

		void unset(
				int i)
		{
			data[i >> LOG] &= ~(1L << (i
					& MASK));
		}

		void flip(
				int i)
		{
			data[i >> LOG] ^= 1L << (i
					& MASK);
		}

		int get(int i)
		{
			return (int) ((data[i >> LOG] >>> (i
					& MASK))
					& 1);
		}

		void print()
		{
			for (int i = 0; i < data.length; i++)
			{
				System.out
						.print(Long
								.toString(
										data[i],
										2));
			}
			System.out
					.println();
		}

		long getWord(
				int i)
		{
			if (i <= -SIZE
					|| (i >> LOG)
							+ 1 >= data.length)
			{
				return 0;
			}
			int rem = i
					& MASK;
			int idx = i >> LOG;

			if (rem == 0)
			{
				return data[idx];
			}

			long head = idx < 0
					? 0
					: (data[idx] >>> rem);
			long tail = data[idx
					+ 1] << (SIZE
							- rem);

			return head
					| tail;
		}
	}

	int count(
			long[] bs,
			int len)
	{
		int ret = 0;
		for (int i = 0; i << 6 < len; i++)
		{
			if (((i + 1) << 6) <= len)
			{
				ret += Long
						.bitCount(
								bs[i]);
			} else
			{
				int rem = len
						& 63;
				ret += Long
						.bitCount(
								bs[i] << (64
										- rem));
			}
		}
		return ret;
	}

	private class Pair
			implements
			Comparable<Pair>
	{
		int v, i,
				j;

		public Pair(
				int a,
				int b,
				int c)
		{
			v = a;
			i = b;
			j = c;
		}

		@Override
		public int compareTo(
				Pair arg0)
		{
			return this.v
					- arg0.v;
		}
	}

	private String solveEqn(
			long a,
			long b)
	{
		long x = 0,
				y = 1,
				lastx = 1,
				lasty = 0,
				temp;
		while (b != 0)
		{
			long q = a
					/ b;
			long r = a
					% b;
			a = b;
			b = r;
			temp = x;
			x = lastx
					- q * x;
			lastx = temp;
			temp = y;
			y = lasty
					- q * y;
			lasty = temp;
		}
		return lastx
				+ " "
				+ lasty;
	}

	private void debug(
			Object... o)
	{
		System.out
				.println(
						Arrays.deepToString(
								o));
	}

	private long pow(
			long a,
			long b,
			long c)
	{
		if (b == 0)
			return 1;
		long p = pow(
				a,
				b / 2,
				c);
		p = (p * p)
				% c;
		return (b
				% 2 == 0)
						? p
						: (a * p)
								% c;
	}

	private long gcd(
			long n,
			long l)
	{
		if (l == 0)
			return n;
		return gcd(
				l,
				n % l);
	}

	public static void main(
			String[] args)
			throws Exception
	{
		new Thread(
				null,
				new Runnable()
				{
					@Override
					public void run()
					{
						new Main()
								.solve();
					}
				},
				"1",
				1 << 26).start();
		// new Main().solve();
	}

	public StringBuilder solve()
	{
		InputReader(
				System.in);
		/*
		 * try { InputReader(new FileInputStream("C:\\Users\\hardik\\Desktop\\in.txt"));
		 * } catch(FileNotFoundException e) {}
		 */
		pw = new PrintWriter(
				System.out);
		// ans_sb = new StringBuilder();
		soln();

		pw.close();
		// System.out.println(ans_sb);
		return ans_sb;
	}

	public void InputReader(
			InputStream stream1)
	{
		stream = stream1;
	}

	private boolean isWhitespace(
			int c)
	{
		return c == ' '
				|| c == '\n'
				|| c == '\r'
				|| c == '\t'
				|| c == -1;
	}

	private boolean isEndOfLine(
			int c)
	{
		return c == '\n'
				|| c == '\r'
				|| c == -1;
	}

	private 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 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 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 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 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 int[] nextIntArray(
			int n)
	{
		int[] arr = new int[n];
		for (int i = 0; i < n; i++)
		{
			arr[i] = nextInt();
		}
		return arr;
	}

	private long[] nextLongArray(
			int n)
	{
		long[] arr = new long[n];
		for (int i = 0; i < n; i++)
		{
			arr[i] = nextLong();
		}
		return arr;
	}

	private void pArray(
			int[] arr)
	{
		for (int i = 0; i < arr.length; i++)
		{
			System.out
					.print(arr[i]
							+ " ");
		}
		System.out
				.println();
		return;
	}

	private void pArray(
			long[] arr)
	{
		for (int i = 0; i < arr.length; i++)
		{
			System.out
					.print(arr[i]
							+ " ");
		}
		System.out
				.println();
		return;
	}

	private boolean isSpaceChar(
			int c)
	{
		if (filter != null)
			return filter
					.isSpaceChar(
							c);
		return isWhitespace(
				c);
	}

	private char nextChar()
	{
		int c = read();
		while (isSpaceChar(
				c))
			c = read();
		char c1 = (char) c;
		while (!isSpaceChar(
				c))
			c = read();
		return c1;
	}

	private interface SpaceCharFilter
	{
		public boolean isSpaceChar(
				int ch);
	}
}