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
Rishabh: 2014-12-18 22:36:11

Can anyone tell me why simple recurrence won't solve this problem ?

Rahul Jain: 2014-12-18 09:14:42

can anyone tell me how should I use DP, because I thought of taking an array of size 10^9, but I can't take memory > 10^6

Sarthak Taneja: 2014-12-17 13:14:31

What is dp?

slim shadyy: 2014-12-13 04:16:31

my first dp!!..AC in 1 go..:)

ALISHA: 2014-12-12 00:07:28

i used while(scanf("%d",&a)) and got TLE
and with while(cin>>a) it is AC.!!

Swapnil Borse: 2014-12-11 12:12:03

The moment I hit send it turns green "accepted"!!! :D
Nice dp problem ;)

And yeah don't worry about the number of test cases, simply use while(scanf("%lld",&xyz)!=EOF)
This will do the trick :)

Last edit: 2014-12-11 12:13:37
itsdennian: 2014-12-08 16:58:42

Not defining for N=0(result=0) can cost you 1 WA.

Last edit: 2014-12-09 11:18:26
Basant kumar bhala: 2014-12-02 14:17:38

what is the indication for end of test cases?

Manu Agrawal: 2014-11-01 12:14:23

TIME LIMIT EXCEEDING using recursion and scanf(...)!=EOF.....how do i get this solved?

Vaishal Shah: 2014-09-02 18:42:48

Used recursion first..It took 4.5 sec just for one case(10^9)..used dp..it took 0.04 sec for same case :)


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