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.
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priyanshuofcl:
20170723 15:52:12
i have solved this problem with simple recursions with a little modifications, i am now learning dp, can anyone share code for that in c++ 

r15habhgup11:
20170722 08:46:24
solved in one go use simply recursion


i_insist:
20170720 12:30:59
bottom up approach using map gives TLE, big time, can't figure out why???


ash_maurya:
20170718 16:47:41
Very straightforward DP problem. The only thing you have to keep in your mind is that you cannot use DP with memoization for N as big as 10^9 . You can settle for some number in order of 10^5 and then do recursion for N bigger than that. That's AC in 0.00 . 

larunrahul:
20170711 13:49:29
For Java people, to read input, create a BufferedReader object and do the following to read the input


pratique007:
20170710 00:20:46
my first DP on spoj, learned to use map in c++ 

ogamiq:
20170705 22:18:28
My solution on ideone and during my testing is working fine. But I get time limit exceeded. How to cope with that kind of input, where number of test cases isn't provided first (C#)? Does the program need to close after time limit or is it enough to provide right output in this time? Last edit: 20170705 22:19:03 

gboduljak:
20170625 18:12:13
awesome introduction to DP, must do for beginners 

bsiddhartha:
20170624 10:33:24
while(scanf("%lld",&n)!=EOF) use this @mayank_tyagi :) 

mayank_tyagi:
20170623 21:54:23
can some one clear the input format, do i have to scan no. of test cases

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 