Attack on Krypton
Superman Has Lost his powers,and taking advantage of this Lex Luther has attacked Krypton.Now in order to rule efficiently,he has introduced American Currency over there.The people have no choice left but to exchange Krypton Gold Coins with American Dollars.
Krypton has a very strange monetary system.Each Krypton gold 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 (the banks have to make a profit).You can also sell Krypton coins for American Dollars.The exchange rate is 1:1.But you can not buy Krypton Gold coins.
You have one gold coin. What is the maximum amount of American Dollars you can get for it?
The input will contain several test cases.
Each testcase is a single line with a number n (not more than 50 lines). It is the number written on your coin.
For each test case output a single line, containing the maximum amount of American dollars you can get.
0 <= n <= 1,000,000,000
You can change 12 into 6, 4 and 3, and then change these into $6+$4+$3 = $13.
If you try changing the coin 2 into 3 smaller coins, you will get 1, 0 and 0, and later you can get no more than $1 out of them.
It is better just to change the 2 coin directly into $2.
Problem Setter: Bipul Agarwal