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
2018-07-17 19:38:41
Why runtime error on using memoization. It is running on ideone
2018-07-16 22:34:33
My code is running fine on ideone but here it is showing nzec error. don't know why??
2018-07-16 22:32:56
to check next input in java use

Scanner s=new Scanner(System.in);
while(s.hasNext()){
//.... your code
//...
}
2018-07-16 09:49:18
simply use unordered_map instead of using array
2018-07-11 18:57:57
use long to cater overflow
2018-07-02 10:29:17
constraints are too high to be able to use just memoization. so just use memoization till 1000000 then recursion.
2018-06-30 18:12:56
first dp !!
ac in 4 go!!
use recursion
2018-06-24 11:39:38
used while(cin>>s) for knowing test cases
2018-06-15 09:28:09
Do we know the no of test cases?
2018-06-04 07:38:31
how do i take variable inputs in java??? Because the question does not specify the no of test cases?
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