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
2015-07-19 10:20:57 monkz
i have used an array of 10^9 size with memoization and it still gives me tle with 155M of memory . please help.
2015-07-15 19:23:40
plzz reply why you guys are doing
if(n<1000001)
{if(r[n]!=0) cout<<r[n];
else
return r[n]=max(n,((n/2)+(n/3)+(n/4)));
}
why only 1000001? when given n is <=1000000000.
2015-07-11 19:04:29 Rohit
great problem for understanding dp. Learnt Map also.
2015-07-10 04:04:17 QuickGun93
while(cin >> n) would do too!
2015-07-09 23:35:48 jarvis
First dp!!! :D the Eof point costed 4 WA.@poojan use while(scanf("%lld",&n)!=EOF)
2015-07-09 05:54:15 poojan
how to eof in c? for this problem! thanks
2015-07-05 17:28:30
'long' values are only 32 bit( same as 'int'), i had to use 'unsigned long' instead. This cost me 2 WA :(
2015-06-25 17:19:02
learnt a lot from this problem. you can find the solution at
<snip>

Last edit: 2022-08-09 22:49:03
2015-06-24 09:39:38 Meghraj
solved in 0.00 and 2.6M Good question
2015-06-21 14:58:40 Kripa Shankar
Thankyou Everyone who comented!
You were right , we learn a lot from it
My Map get started from this problem.....have fun
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