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
thunderboltz_:
20200619 15:03:11
More Testcases:


dalimnassar:
20200615 12:47:34
input:


mubasshir00:
20200601 23:03:30
@banihali for n =24 answer > 27 

mubasshir00:
20200601 23:02:02
care about long input. so to handle this time of input or avoid TLE , use STL map and recursion. Last edit: 20200601 23:02:11 

banihali:
20200531 06:14:10
what is answer for n=24? 

devesh_rs:
20200530 05:17:33
@plak4 you don't need long long ints. This can be done using long ints. 

kuldeepkarhana:
20200527 13:47:17
do take care of integer overflow. 

manuver:
20200514 21:38:35
yes @divyansh_09, but then you need infinite amount of computing power :) 

kartikeysm2001:
20200512 21:20:55
Solved it 0.01s C++ on first try :p 

divyansh_09:
20200512 02:14:26
Can it be done without dynamic programming? 
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 