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
Ameya: 2016-06-22 23:58:11

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
mkfeuhrer: 2016-06-22 22:17:23

must for dp beginners :-) stl map & AC!

shovo: 2016-06-21 22:21:32

i think 999 will generate the result 1370.by the way solved :D

xinnix: 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
sayedathar11: 2016-06-16 07:50:12

very nice problem teaches you dp and map datastructures and also a new way of input ac in one go :)

code1monkey1: 2016-06-12 10:14:41

map is the saviour
1st dp problem , woohoo

macbox: 2016-06-08 06:50:45

Easy Logic but need to use some tricks

top_gun007: 2016-06-05 13:08:00

learned something new..worth it

get_right_jr: 2016-06-02 19:34:19

AC!!!!
1st DP problem :)
It was amazing problem!
Use HashMap ;)

Last edit: 2016-06-02 20:15:05
blueranger: 2016-06-02 18:23:21

Time: 0.00, Memory: 3.3M, C++
AC in one go!!!!!!!!!! :)

Last edit: 2016-06-02 18:52:25

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 PERL 6 VB.net
Resource:Purdue Programming Contest Training