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
2019-06-18 15:01:07
AC in one go
First DP problem
2019-06-10 19:38:12
finally solved a dp problem!!!!
(had a problem in taking the input use while(cin>>a)
2019-06-07 23:56:52
My first DP problem
2019-06-07 16:42:11
Why is this a dp problem
2019-06-04 05:28:40
Dont forget to use long long int
2019-05-27 17:24:42
Using stl map for memorization
2019-05-15 16:40:42
People solving this using Java must make sure to use long as the data type and also not to use long as the index of the array (typecast to int).
2019-05-13 10:44:05
Just use a recursion and a simple condition
2019-04-12 16:40:34
i get it that we have to use while(cin>>n) for input, but i didn't understand it properly... can someone provide more details about this operation?
2019-04-11 17:04:17
if number of test cases is not provided then while(cin>>n){ do the work }
will work perfectly fine : )

Last edit: 2019-04-11 17:04:36
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