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
rajat7:
20160905 11:20:51
AC in one go 

karan_batra:
20160829 14:42:00
Easy one. AC in one go. :D 

rishabh_nitw:
20160825 16:49:46
My 1st DP :) 

manish_hacked:
20160824 21:58:42
AC in first go


suraj_:
20160819 20:56:57
finally ac


monish007:
20160819 19:47:12
Highly recommended for Beginners like me ;) 

ravi shankar:
20160807 11:13:51
boom boom :) must try for every beginners


tushar091:
20160727 21:26:27
how to take input in python as number of testcases is not defined .... gives NZEC error


sharath_111:
20160722 13:23:51
good dp problem :) use long long and recursion for numbers greater than 1000000 

chawla_1209:
20160720 11:52:35
Must do for beginners. 
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 