Question #38633

You have a block of platinum that can be exchanged in your bank either for cash

or for smaller blocks of platinum. If you exchange a block of m grams, you get

three blocks of weight m/2, m/3 and m/4 grams each. You don't get any fractional

part, as the division process rounds down the value. If you exchange the block of

platinum for cash, you get m units of currency. You can do any number of

exchanges for smaller blocks or currency.

Given the value of a block in grams as input, write a program that would print the

largest possible currency value that you can receive as the output. Assume that

the maximum value of a block that can be given as an input is 1,000,000,000

grams and the minimum value is 2 grams.

Sample input 1

12

Sample output 1

13

Explanation: You can change 12 into blocks of 12/2 = 6, 12/3 = 4 and 12/4 = 3,

and then exchange these for 6 + 4 + 3 = 13 units of currency

13

Sample input 2 2

Sample output 2 2

Explanation: If you exchange 2 grams into smaller blocks, it gives 2/2 =

or for smaller blocks of platinum. If you exchange a block of m grams, you get

three blocks of weight m/2, m/3 and m/4 grams each. You don't get any fractional

part, as the division process rounds down the value. If you exchange the block of

platinum for cash, you get m units of currency. You can do any number of

exchanges for smaller blocks or currency.

Given the value of a block in grams as input, write a program that would print the

largest possible currency value that you can receive as the output. Assume that

the maximum value of a block that can be given as an input is 1,000,000,000

grams and the minimum value is 2 grams.

Sample input 1

12

Sample output 1

13

Explanation: You can change 12 into blocks of 12/2 = 6, 12/3 = 4 and 12/4 = 3,

and then exchange these for 6 + 4 + 3 = 13 units of currency

13

Sample input 2 2

Sample output 2 2

Explanation: If you exchange 2 grams into smaller blocks, it gives 2/2 =

Expert's answer

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