COINS  Bytelandian gold coins
In Byteland they have a very strange monetary system.
Each Bytelandian 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 Bytelandian coins for American dollars. The exchange rate is 1:1. But you can not buy Bytelandian coins.
You have one gold coin. What is the maximum amount of American dollars you can get for it?
Input
The input will contain several test cases (not more than 10). Each testcase is a single line with a number n, 0 <= n <= 1 000 000 000. It is the number written on your coin.
Output
For each test case output a single line, containing the maximum amount of American dollars you can make.
Example
Input: 12 2 Output: 13 2
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.
hide comments
selectaman:
20201201 09:21:17
When to stop taking test cases? Here number of test cases is not taken as input. 

scrapperdb:
20201120 17:39:57
@ashish_sinha5


tomatoispotato:
20201030 13:59:24
Hint: Recursion + dictionary 

stevebobs:
20201021 00:04:12
got AC from 2nd attempt. Use long instead of int for end result. Cheers! Last edit: 20201021 00:10:13 

coder582:
20201006 07:40:00
n is BIG 

wille_25:
20201001 21:40:30
finally got AC in 3 attempt, recursive + dp that's it ...be careful while taking input cost me WA ..in cpp take i/p like this


abhishen99:
20200921 18:24:36
dont getting problem  see this ''can be exchanged '', and you will get the choices to choose from. 

ashish_sinha5:
20200913 21:02:27
How to take input for python


lakshya1st:
20200901 18:53:49
AC in one go!! 

aditigedam:
20200827 12:45:12
don't forget that n is very very big. 
Added by:  Tomek Czajka 
Date:  20050503 
Time limit:  9s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 VB.NET 
Resource:  Purdue Programming Contest Training 