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
2016-07-20 11:52:35
Must do for beginners.
2016-07-19 16:48:57 Saif
Problem can also be done without maps
First use dp for nos upto 10^7 and for larger nos use normal recursion
2016-07-19 03:12:07 Wumbolo
wa and sigfxsxxxz because %I64d modificator instead of %lld
2016-07-17 21:08:41
my 50th and first dp!...A good one!
2016-07-17 10:30:28 liuxueyang
Use Integer as key and BigInteger as value in JAVA HashMap... test with 1000000000, output should be: 4243218150
thanks for @vstepano 's comment.
2016-07-06 12:12:29
1st dp problem
2016-06-22 23:58:11 Ameya
I used memoization by hashmap. I'm getting TLC.

edit: Got it. I didn't make the map global. Was initializing it every time the method was called.

Last edit: 2016-06-23 00:26:08
2016-06-22 22:17:23
must for dp beginners :-) stl map & AC!
2016-06-21 22:21:32
i think 999 will generate the result 1370.by the way solved :D
2016-06-17 08:21:56
TLE TLE TLE..... I dont see any other way to make it faster... help!
Edit: Ok.... I was passing map through function, needed to make it global. Lol

Last edit: 2016-06-17 15:24:33
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