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
Philipp Heeg: 2012-12-22 01:11:31

Test Cases:
Input:
42
123
555555
1000000000

Output:
46
144
1298380
4243218150

Ranker: 2012-12-16 14:47:10

To detect the end of input use the EOF condn i.e while(scanf("%lld",&x) != EOF).

A simple memoization problem........and take care of data type.........int is not enough!

Aayush: 2012-12-15 12:29:38

how do we detect end of input?

xyb: 2012-11-26 01:22:49

use unsigned int not int, if you want to get AC.

Cesar Bretana Glez: 2012-11-06 14:39:08

Mark, in Cpp, the end of file is while the input != EOF

Mark: 2012-10-17 12:45:57

How can I detect end of input?

Ayush Garg: 2012-10-11 13:53:58

getting WA can any1 post some test cases i might be missing out pls..

Shagun Sodhani: 2012-09-25 02:15:06

Where are you storing the intermediate results for the inputs like 1,2 etc .I mean array of what type?

Abhimanyu: 2012-09-15 09:07:50

tle through recursion ... any suggestions ???? help please ....

#vaidy_MIT#: 2012-09-10 16:26:52

HELOW sheldon :)


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