Problem D
Finishing Monopoly

credits: cottonbro, The looong game

Asmus, David and Helle were playing Monopoly until one of them went bankrupt and the player’s property was auctioned off to the two others. The remaining players have now arranged for a quick ending to the game, as the computer they are on will not let them restart the game before it is over. Player 2 has agreed to let the Player 1 win, but wants to know how fast they can reach this outcome if they work together by using their telepathic powers to control the six sided die. Help them end the game as quickly as possible by calculating the minimum amount of rounds they need for Player 2 to go bankrupt.

The players do not want the game to take too long, so they cut some of the rules from the original game and decide to only use one die. Therefore the rules are as follows:

• The players take turns throwing the die and moving their token on the board.

• A player must roll the die when it becomes their turn and move the amount of fields corresponding to the upward-facing dots on the die. Remember that the players are able to control the die with their telepathic powers.

• If a player lands on a parking spot he must pay a fee to the owner of that property.

• A player do not pay parking fees if he owns the property.

• If a player at any point has no money he goes bankrupt and has lost.

• A round always starts with Player 1, then Player 2 and then they alternate.

• A round is over when the players have moved on the board, and payed what they owe.

There are two possible cases for this problem:

1. Player 2 only has properties for which parking is free.

2. Player 2 has at least one property for which parking is not free.

Player 1 always has at least one property where parking is not free.

Input

The input consist only of integers.

The first number $n$ is the amount of properties on the board, $1 \leq n \leq 1,000$.

The second line contains integers $o_{0}, ..., o_{n-1} $ where $o_{i}$ is the id of the player who owns the property of index $i$, $o_{i} \in \{ 1, 2\} $.

The third line contains integers $p_{0}, ..., p_{n-1} $ where $p_{i}$ is the parking fee for the property of index $i$, $ {0} \leq {p_{i}} \leq {3}$.

The fourth line contains two numbers $x_{1}$, $x_{2}$ indicating the current position of Player 1 and Player 2 respectively, $0 \leq x_{1}$, $x_{2} < n$.

The fifth line contains numbers $c_{1}$, $c_{2}$ indicating the current capital of Player 1 and Player 2 respectively, ${0} < {c_{1}}$, ${c_{2}} < {50,000}$.

Output

One number, the minimum amount of rounds required for Player 2 to go bankrupt.

Examples

The sample output is 2 for sample input 1, because of the following optimal sequence:

1. Player 2 rolls a 2 to land on position 2 and pays 3 to Player 1.

2. Player 2 rolls a 3 to land on position 2 and pays 3 to Player 1.

3. Player 2 goes bankrupt due to having lost 6 while only having 5.

Another possible sequence which leads to this output is as follows:

1. Player 2 rolls a 1 to land on position 1 and pays 2 to Player 1.

2. Player 2 rolls a 1 to land on position 2 and pays 3 to Player 1.

3. Player 2 goes bankrupt due to having lost 5 while only having 5.

In these cases Player 1 can do any sequence of throws as they do not have to pay any fees to Player 2 when landing on their properties.

The sample output is 3 for sample input 2, because of the following optimal sequence:

1. Player 1 rolls a 1 to land on position 1 and does not pay because it is Player 1’s house.

2. Player 2 rolls a 1 to land on position 1 and pays 2 to Player 1.

3. Player 1 rolls a 1 to land on position 2 and does not pay because it is Player 1’s house.

4. Player 2 rolls a 1 to land on position 2 and pays 1 to Player 1.

5. Player 1 rolls a 2 to land on position 4 and does not pay because it is Player 1’s house.

6. Player 2 rolls a 6 to land on position 8 and pays 3 to Player 1.

7. Player 2 goes bankrupt due to having lost 6 while only having 5.

Another possible sequence which leads to this output is as follows:

1. Player 1 rolls a 1 to land on position 1 and does not pay because it is Player 1’s house.

2. Player 2 rolls a 1 to land on position 1 and pays 2 to Player 1.

3. Player 1 rolls a 1 to land on position 2 and does not pay because it is Player 1’s house.

4. Player 2 rolls a 2 to land on position 3 and does not pay because it is Player 2’s house.

5. Player 1 rolls a 2 to land on position 4 and does not pay because it is Player 1’s house.

6. Player 2 rolls a 5 to land on position 8 and pays 3 to Player 1.

7. Player 2 goes bankrupt due to having lost 5 while only having 5.

3
1 1 1
1 2 3
0 0
5 5

2

9
1 1 1 2 1 2 1 2 1
1 2 1 1 1 0 1 3 3
0 0
5 5

3