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
2015-02-14 07:24:46 VĂ­tor Antonioli
A "long int" variable division by 3 works correctly.

A "long long int" variable division by 3 is wrong!

Why?
2015-02-12 09:14:06 Raj Kumar Chauhan
for input 2 how output is 2?
2015-02-04 08:49:08 infinity123
I'm not able to create very large array for memoization in C. How to solve it?

Last edit: 2015-02-04 08:49:28
2015-01-31 07:28:20 Praveen Kulkarni
Feeling happy after solving it...Herd the technique called DP before..but never experienced the feeling of solving one...Nice problem for a beginner...Got introduced to concept called Memoization and also how to implement it..Thanks @Davit for [Link Removed]

re(vamsi): please don't post links to solution(s) here

Last edit: 2015-01-31 13:23:02
2015-01-12 15:22:18 HITESH GARG
cool problem...learnt a lot..

MEMOIZATION+STL+RECURSION (Y)(Y)

my 50th ^_^
2015-01-10 22:28:06 Murat TOPAK
memoization is necessary for this one.
consider the case when n is zero as well.
2015-01-01 19:52:03 shuks
My first STL and memoization ;)
2014-12-25 10:26:13 Sudarshan K
Memoization :)
2014-12-22 19:28:25 Vishesh Raimugia
My first time properly solving a DP!! AC at one go #buzzing very easy sum though :P
2014-12-20 07:18:56 Ankur Singh
don't forget to define for n=0 case..
© Spoj.com. All Rights Reserved. Spoj uses Sphere Engine™ © by Sphere Research Labs.