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.


Added by:Tomek Czajka
Date:2005-05-03
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

hide comments
2013-06-10 11:39:49 aar
Do take 10 inputs on your own, as they have not mentioned to input no. of test cases..
2013-05-31 10:25:54 Radnus Mayhs
awesome problem. took a while to figure it out. recursion with memoization. wonderful! kudos to the problem setter. more of the same please.
2013-05-28 18:58:27 Erti-Chris Eelmaa
Sweet problem. Simple, but yet takes some skill to solve. Fixed integer overflow & wrapped everything into try/catch and there I went! Just read line by line until you encounter line that isn't digit.
2013-05-28 05:46:58 Aman Kr Shrivastava
Nice prb.
learned something new
2013-05-28 05:26:51 xxx
Nice memoization problem :) !!
2013-04-25 19:37:08 Eduardo Nunes
indeed, nice memorization one... though ive got 4 SIGSEGVs, 3 TLEs and 2 WAs :-(
finally AC! 110th :-)

Last edit: 2013-04-25 21:59:17
2013-04-09 11:35:50 ওয়াসী (Wasi)
Accepted!
after some silly mistake submissions :P
nice problem
2013-03-25 07:48:45 Sridharan Ramachandran
can anyone explain how for this input this output is coming

Input:
42
123

Output:
46
144
2013-02-26 05:21:15 shashank
How to terminate this program in java??
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