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
Ameya:
20160622 23:58:11
I used memoization by hashmap. I'm getting TLC.


mkfeuhrer:
20160622 22:17:23
must for dp beginners :) stl map & AC! 

shovo:
20160621 22:21:32
i think 999 will generate the result 1370.by the way solved :D 

xinnix:
20160617 08:21:56
TLE TLE TLE..... I dont see any other way to make it faster... help!


sayedathar11:
20160616 07:50:12
very nice problem teaches you dp and map datastructures and also a new way of input ac in one go :)


code1monkey1:
20160612 10:14:41
map is the saviour


macbox:
20160608 06:50:45
Easy Logic but need to use some tricks 

top_gun007:
20160605 13:08:00
learned something new..worth it 

get_right_jr:
20160602 19:34:19
AC!!!!


blueranger:
20160602 18:23:21
Time: 0.00, Memory: 3.3M, C++

Added by:  Tomek Czajka 
Date:  20050503 
Time limit:  9s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL 6 VB.net 
Resource:  Purdue Programming Contest Training 