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
2017-07-11 13:49:29
For Java people, to read input, create a BufferedReader object and do the following to read the input
while((str = br.readLine()) != null){
}

Last edit: 2017-07-12 09:19:45
2017-07-10 00:20:46
my first DP on spoj, learned to use map in c++
2017-07-05 22:18:28
My solution on ideone and during my testing is working fine. But I get time limit exceeded. How to cope with that kind of input, where number of test cases isn't provided first (C#)? Does the program need to close after time limit or is it enough to provide right output in this time?

Last edit: 2017-07-05 22:19:03
2017-06-25 18:12:13
awesome introduction to DP, must do for beginners
2017-06-24 10:33:24
while(scanf("%lld",&n)!=EOF) use this @mayank_tyagi :)
2017-06-23 21:54:23
can some one clear the input format, do i have to scan no. of test cases
2017-06-19 19:13:10
beware of long long everywhere.. costed to WAs
2017-06-15 11:20:57
my 50th on spoj
2017-06-13 19:30:31
take care that spoj accepts long long and shows WA on long int.
2017-06-07 09:01:19
@p3arl_03..yes! we can exchange!they had not given! But i understood by its tag "dp".. Done using DP for num < 10^5 and Recursion for num>10^5! AC in 0.00! Hurray!!

Last edit: 2017-06-07 09:02:52
© Spoj.com. All Rights Reserved. Spoj uses Sphere Engine™ © by Sphere Research Labs.