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
alche_mist02:
20200124 08:03:06
How to get continuous inputs in c++... I didnt get it 

ankitkawatia:
20200122 13:08:08
I am getting NZEC runtime error. Though the code runs in my computer. I am using Java language. Can anyone help? 

mishra_tara_7:
20200115 15:56:34
Can we do it using bottomup approach?If yes then what would be max value for the size? 

sangmai:
20200114 09:20:53
@dvjpy786 while(cin >> n) {} would do it. 

aryan__0406:
20200113 20:36:32
what will be the answer of 1000000000.Though my solution is accepted but i have doubt bcz my answer of this expression is 1000000000.


sameer_19:
20200107 18:03:19
Apply recursion with memoization . Just get values of 0<=n<1000000 stored in array and then get those values for n>1000000 using recursion. 

noob_again:
20191229 12:37:16
AC in one go. ^_^ Solved in JAVA using Hashmap for memorization and one recursive function. 

zenitsu:
20191221 18:27:53
mriow is recursion with memoization different from DP . I don't think so !


dvjpy786:
20191128 19:10:56
how to take input in this?


kaizukizio:
20191121 11:58:05
How can you do recursion with memoization when the n is really big? creating array[1000000000] will give you error.. 
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 