TUTOR

문제

You need to compute a sequence of actions in order to maximize cash earned in a tutor simulation game. The actions involve earning cash from tuition (TEACH), studying in college to increase your knowledge (TRAIN), and buying books (BUY). The TRAIN action allows you to increase tuition income. The BUY action allows you to reduce time units consumed for each TRAIN action. Each of these actions consumes time units and there are only maxTimeUnits available for work.

Like all games, the puzzle difficulty depends on the game variables and certain rules. For this task, there are 4 game variables and 5 game rules. Value ranges are provided where appropriate.

Game Variables

1. maxTimeUnits (10 - 1000): The maximum number of time units in the simulation game.
2. learningRate (1, 2, 4, or 8): Scales down the time units consumed by a TRAIN action, based on the number of book in your possession.
3. paybackRate (5, 10, or 20): Scales up the tuition income earned from a TEACH action, based on the knowledge level.
4. bookCost: An array of 4 integers in non decreasing order where the i-th integer is the cost of the i-th book. (The cost of each book is in the range of \5 - \500).

Game Rules

1. Before the start of the simulation, you have maxTimeUnits left; your cash is 0; your knowledge is 0; and you have 0 book.
2. The simulation game lasts for maxTimeUnits. Your aim is to obtain as much cash as possible.
3. Every TEACH action spends 2 time units. The formula below gives the tuition income per TEACH action. That is, the more knowledge that you have, the higher your income will be.
   income = 10 + min(20, knowledge) * paybackRate
4. Every TRAIN action costs 20 dollars and it will increase the knowledge level by 1 unit. The formula below gives the trainingTime per TRAIN action. That is, the more book or the higher learningRate that you have, the lower your trainingTime will be.
   trainingTime = max(1, (int)(8 / max(1, book * learningRate)))
5. There are 4 books in this game. The i-th BUY action will buy the i-th book. It takes i time units to buy the i-th book (0-based indexing, i.e. the first book can be bought with 0 time unit) and the cost of the i-th book is stated in bookCost[i]. As there are at most 4 books, you can perform at most 4 BUY actions.

Write a program that reads in the game variable values (see sample input), and determines the best possible sequence of actions. You need to implement a planner so that your cash is maximum at a certain time unit t where t ∈ [0 .. maxTimeUnits]. However, you should not violate the following important constraints:

1. You cannot overshoot the maxTimeUnits, when choosing an action.
2. You cannot incur negative cash at any point; i.e. you must be able to pay for any TRAIN or BUY action.

For example, suppose maxTimeUnits, learningRate, and paybackRate are 13, 8, and 20, respectively. Assume the cost of the 4 books are \5, \50, \100, and \200.

Since you have 13 time units, a simple solution is to perform TEACH 6 times. You can already get 6∗(10+min(20, 0)∗20) = 6∗10 = \60. However, this is not the best answer (you will not get any marks by giving this answer). The optimal answer for this test case has <code>cash</code> = \95 and shown below:

t	cash	knowledge	book	remarks
0	0	0	0	start of simulation
2	10	0	0	TEACH (income = 10)
2	5	0	1	BUY (the 0-th book, 5\$, no change in t)
4	15	0	1	TEACH (income = 10)
6	25	0	1	TEACH (income = 10)
7	5	1	1	TRAIN (we have 1 book, trainingTime = 1)
9	35	1	1	TEACH (income = 30)
11	65	1	1	TEACH (income = 30)
13	95	1	1	TEACH (income = 30)

입력

The input (from standard input) consists of two lines. The first line contains 3 integers, which are the maxTimeUnits, learningRate, and paybackRate. The second input line contains 4 integers where the i-th integer is the cost of the i-th book.

출력

The required output (to standard output), consists of a single number, specifying the maximum cash that you can gain.

13 8 20
5 50 100 200

95