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
2014-04-24 17:01:27 Petar Bosnjak
recursion + memoization+STL
2014-04-19 06:03:17 SHIVAM DIXIT
use dp...also use while(scanf("%d",&n)!=EOF) for scanning inputs in c/cpp

Last edit: 2014-04-19 06:03:37
2014-04-02 11:54:06 Rohit pal
how would program will know how many tesst case are there
2014-02-21 18:38:23 prudhvi _krishna
First DP...AC in one go!!
2014-02-15 20:16:49 RAJAT SINGH
good application of the dynamic problem...........without it will be TLE which i got in first attempt
2014-02-09 07:45:18 Justin Roberts
Good goodness, I know the DP solution is O(logn), but wow, even my pathetic Python solution is scary fast. ideone runs it with 10^200 in less than 1 second.
2014-01-30 04:12:54 Patryk £apiezo
I guess this problem was supposed to be solved with DP, but still you can pass if you limit your recursion for numbers (n/48 >0) :) And for someone who already did this with DP: is the actual solution about (4^i *12) ? It's my guess.
2014-01-29 14:26:54 jiglipufff
my first dp :)
2014-01-18 07:53:51 Anubhav Balodhi
Ac after few tries, 0.00 sec ^_^
Dynamic programming is cool...
2014-01-12 17:28:14 785227
My first DP :)
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