Frank is a portfolio manager of a closed-end fund for Advanced Commercial Markets (ACM ). Fund collects money (cash) from individual investors for a certain period of time and invests cash into various securities in accordance with fund's investment strategy. At the end of the period all assets are sold out and cash is distributed among individual investors of the fund proportionally to their share of original investment.
Frank manages equity fund that invests money into stock market. His strategy is explained below.
Frank's fund has collected c
When price of the stock changes to p'i
Each stock has its own volatility and risks, so to minimize the overall risk of the fund, for each stock there is the maximum number of lots ki
Any trade to buy or sell one lot of stock completely occupies Frank's day, and thus he can perform at most one such trade per day. Frank is not allowed to buy partial lots if there is not enough cash in the fund for a whole lot at the time of purchase.
Now, when fund's period has ended, Frank wants to know what is the maximum profit he could have made with this strategy having known the prices of each stock in advance. Your task is to write a program to find it out.
It is assumed that there is a single price for each stock for each day that Frank could have bought or sold shares of the stock at. Any overheads such as fees and commissions are ignored, and thus cash spent to buy or gained on a sell of one lot of stock is exactly equal to its price on this day multiplied by the number of shares in a lot.
The first line of the input file contains four numbers -- c
The following 2n
The first line for each stock contains the stock name followed by two integer numbers si
The second line for each stock contains m
Cash and prices in the input file are formatted as a string of decimal digits, optionally followed by a dot with one or two digits after a dot.
Write to the output file m + 1
On the first line write a single decimal number -- the precise value for the maximal amount of cash that can be collected in the fund by the end of its period. The answer will not exceed 1 000 000 000.00. Cash must be formatted as a string of decimal digits, optionally followed by a dot with one or two digits after a dot.
On the following m
Input
c
100000000.00)
m
100)
n
8)
k
8)
si
1000000)
ki
k)
Output
Sample Input
144624.00 9 5 3
IBM 500 3
97.27 98.31 97.42 98.9 100.07 98.89 98.65 99.34 100.82
GOOG 100 1
467.59 483.26 487.19 483.58 485.5 489.46 499.72 505 504.28
JAVA 1000 2
5.54 5.69 5.6 5.65 5.73 6 6.14 6.06 6.06
MSFT 250 1
29.86 29.81 29.64 29.93 29.96 29.66 30.7 31.21 31.16
ORCL 300 3
17.51 17.68 17.64 17.86 17.82 17.77 17.39 17.5 17.3
Sample Output
151205.00
BUY GOOG
BUY IBM
BUY IBM
HOLD
SELL IBM
BUY MSFT
SELL MSFT
SELL GOOG
SELL IBM