Problem: Kostya is a progamer specializing in the discipline of Dota 2. Valve Corporation, the developer of this game, has recently released a new patch which turned the balance of the game upside down. Kostya, as the captain of the team, realizes that the greatest responsibility lies on him, so he wants to resort to the analysis of innovations patch from the mathematical point of view to choose the best heroes for his team in every game.

A Dota 2 match involves two teams, each of them must choose some heroes that the players of the team are going to play for, and it is forbidden to choose the same hero several times, even in different teams. In large electronic sports competitions where Kostya's team is going to participate, the matches are held in the Captains Mode. In this mode the captains select the heroes by making one of two possible actions in a certain, predetermined order: pick or ban.

  * To pick a hero for the team. After the captain picks, the picked hero goes to his team (later one of a team members will play it) and can no longer be selected by any of the teams. 
  * To ban a hero. After the ban the hero is not sent to any of the teams, but it still can no longer be selected by any of the teams. 



The team captain may miss a pick or a ban. If he misses a pick, a random hero is added to his team from those that were available at that moment, and if he misses a ban, no hero is banned, as if there was no ban.

Kostya has already identified the strength of all the heroes based on the new patch fixes. Of course, Kostya knows the order of picks and bans. The strength of a team is the sum of the strengths of the team's heroes and both teams that participate in the match seek to maximize the difference in strengths in their favor. Help Kostya determine what team, the first one or the second one, has advantage in the match, and how large the advantage is.

Input

The first line contains a single integer n (2 ≤ n ≤ 100) — the number of heroes in Dota 2.

The second line contains n integers s1, s2, ..., sn (1 ≤ si ≤ 106) — the strengths of all the heroes.

The third line contains a single integer m (2 ≤ m ≤ min(n, 20)) — the number of actions the captains of the team must perform.

Next m lines look like "action team", where action is the needed action: a pick (represented as a "p") or a ban (represented as a "b"), and team is the number of the team that needs to perform the action (number 1 or 2).

It is guaranteed that each team makes at least one pick. Besides, each team has the same number of picks and the same number of bans.

Output

Print a single integer — the difference between the strength of the first team and the strength of the second team if the captains of both teams will act optimally well.

Examples

Input

2
2 1
2
p 1
p 2


Output

1


Input

6
6 4 5 4 5 5
4
b 2
p 1
b 1
p 2


Output

0


Input

4
1 2 3 4
4
p 2
b 2
p 1
b 1


Output

-2

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;

public class Main
{
	public static FastInputStream in;
	
	public static void main(String[] args) throws IOException
	{
		in = new FastInputStream(System.in);
		
		System.out.println(solve());
		
		in.close();
	}
	
	public static int solve() throws IOException
	{
		int[] strength = new int[in.nextInt()];
		
		for (int i = 0; i < strength.length; i++)
			strength[i] = -in.nextInt();
		
		Arrays.sort(strength);
		
		int picks = in.nextInt();
		
		strength = truncate(strength, picks);
		
		for (int i = 0; i < strength.length; i++)
			strength[i] = -strength[i];
		
		boolean[] type = new boolean[picks];
		boolean[] team = new boolean[picks];
		
		for (int i = 0; i < picks; i++)
		{
			type[i] = in.nextChar() == 'p';
			team[i] = in.nextInt() == 1;
		}
		
		Integer[] state = new Integer[1 << picks];
		state[state.length - 1] = 0;
		
		for (int i = picks - 1; i >= 0; i--)
		{
			int comb = (2 << i) - 1;
			
			while (comb < (1 << picks))
			{
				int firstBits = comb;
				
				while (firstBits != 0)
				{
					int firstBit = firstBits & (-firstBits);
					int firstBitPos = getFirstOne(firstBit);
					firstBits ^= firstBit;
					
					if (state[comb - firstBit] == null)
						state[comb - firstBit] = team[i] ? Integer.MIN_VALUE : Integer.MAX_VALUE;
					
					if (type[i])
					{
						if (team[i])
							state[comb - firstBit] = Math.max(state[comb - firstBit], state[comb] + strength[firstBitPos]);
						else
							state[comb - firstBit] = Math.min(state[comb - firstBit], state[comb] - strength[firstBitPos]);
					} else
					{
						if (team[i])
							state[comb - firstBit] = Math.max(state[comb - firstBit], state[comb]);
						else
							state[comb - firstBit] = Math.min(state[comb - firstBit], state[comb]);
					}
				}
				
				comb = nextCombination(comb);
			}
		}
		
		return state[0];
	}
	
	public static int[] truncate(int[] data, int len)
	{
		int[] data2 = data;
		data = new int[len];
		System.arraycopy(data2, 0, data, 0, len);
		data2 = null;
		return data;
	}
	
	public static int nextCombination(int x)
	{
		int smallest = x & -x;
		int ripple = x + smallest;
		int ones = ((x ^ ripple) >> 2) / smallest;
		return ripple | ones;
	}
	
	public static int getFirstOne(int bitmask)
	{
		if (bitmask == 0)
			return -1;
		
		int first = 0;
		while ((bitmask & 1) != 1)
		{
			first++;
			bitmask = bitmask >> 1;
		}
		
		return first;
	}
	
	static class FastInputStream extends InputStream
	{
		private InputStream in;
		
		private byte[] buffer = new byte[512];
		private int loaded = 0;
		private int pointer = 0;
		
		public FastInputStream(InputStream in)
		{
			this.in = in;
		}

		@Override
		public int read() throws IOException
		{
			if (hasNext())
				return buffer[pointer++];
			else
				return -1;
		}

		public void skipWhitespace() throws IOException
		{
			while (hasNext())
			{
				char c = (char) buffer[pointer];

				if (c == ' ' || c == '\t' || c == '\n' || c == '\r') pointer++;
				else return;
			}
		}
		
		public Character nextChar() throws IOException
		{
			skipWhitespace();
			
			if (!hasNext()) return null;
			
			return (char) buffer[pointer++];
		}

		public Integer nextInt() throws IOException
		{
			skipWhitespace();

			if (!hasNext()) return null;

			byte multiplier = 1;
			int number = 0;

			if (buffer[pointer] == '-')
			{
				multiplier = -1;
				pointer++;
			}

			while (hasNext())
			{
				char c = (char) buffer[pointer];

				if (c >= '0' && c <= '9')
				{
					number = (number << 3) + (number << 1) + c - '0';
					pointer++;
				} else break;
			}

			return number * multiplier;
		}
		
		public void close() throws IOException
		{
			in.close();
		}
		
		public boolean hasNext() throws IOException
		{
			while (pointer == loaded)
			{
				loaded = in.read(buffer);
				pointer = 0;
				
				if (loaded == -1) return false;
			}
			return loaded != -1;
		}
	}
}