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
2017-04-04 15:42:14
Hi @mohit_97. I have a solution. Its giving answers. I just don't know if they are correct! :-) Also, whenever I submit to this website, a working Pascal program fails. I don't know why. Finally, I don't know what dp is. Thanks!
2017-04-03 22:36:00
store the values in map and use recurssion.Easy dp ,first step towards dp.
2017-04-03 18:58:34
Hi. Is there a list of answers, for some set of input 1..N? Thanks!
2017-03-30 08:13:55
Used map with recursion and remember
AC in one go 0.00 sec !!
2017-03-29 13:39:54
wtf!!!!! why !cin.eof() is giving WAs...
2017-03-08 09:33:04 lotus_guy
Think a bit different :D
2017-03-07 07:51:07
Use dictionary in python
2017-02-26 20:01:12
Nice one. Recommended for beginners looking for practicing DP problems.
2017-02-24 22:52:30
Why does array give runtime error but map does not?
2017-02-04 16:26:06
I was getting SIGSEGV. As it turns out I was using simple arrays (to check if the value had already been calculated) in C++ (not std ones) but I failed to initialize them so when I tried to compare to a -1 or 0 or whatever, it failed. Then it was just a matter of initializing the array and AC.
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