### Exchange gold coins

In a monetary system each coin has an integer number written on it. A coin '

**n**' can be exchanged in a bank into three coins:**n/2**,**n/3**and**n/4**. But these numbers are all rounded down. You can also sell coins for dollars and their exchange rate is 1:1. You have one gold coin. What is the maximum amount of dollars you can get for it? eg: for a coin with value 120 you can get 144 dollars.Suggest an algorithm to solve the problem.