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
singhar:
20200822 13:07:14
no use of dp here just use recursion only,your answer will be accepted.Yes of course you can use dp to reduce the time complexity. 

Ritesh:
20200805 07:56:59
Check out Screencast Tutorial for this problem: https://youtu.be/KW6eI4ODRs Last edit: 20200805 07:57:43 

deerawat:
20200803 20:22:43
AC in second go!!


rehank478:
20200725 16:01:38
AC in one go!


lovro_nidogon1:
20200707 20:13:27
!Spoiler!


saurabh_shinde:
20200707 16:40:23
how to take input ??


Rohit Rawat:
20200706 19:48:01
24 => 27


Rohit Rawat:
20200706 19:45:28
Test cases with answers from accepted solution:


lordsaurabh_19:
20200701 13:19:16
Most basic DP problem 

bearded_bong_:
20200622 13:26:46
how is 24 =>27?

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 