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.


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karthik_spoj1: 2021-01-26 13:28:44

be careful while taking inputs
while(cin>>n){} -- works
and
arrays + recursion - exceeds memory
using map
the not 1000 000 000 memory is created
it depends on the testcases>
so map works - but is not the optimal way all the time.

aashish0909: 2021-01-21 14:13:38

@deep_97
Your array is exceeding the memory limit

deep_97: 2021-01-19 18:09:31

Why is map working to store the data and not arrays? When I am using arrays to store the data, it is giving SIGKILL but for map it's running smoothly?

princemishra: 2021-01-09 14:29:13

just use recursion + map in cpp

dhruv_sh: 2021-01-07 07:03:11

AC on the second attempt.
Be careful while taking input.
while(cin>>n){.....} <- this helped

saikumarpatel: 2021-01-05 11:47:44

<snip>
help me where is my mistake?

[NG]: Read the footer.

Last edit: 2021-01-05 22:20:33
tejasreddyk: 2021-01-05 11:46:51

It was little confusing 1 gold coin = 1 $, I considered any gold coin to be worth 1$.... apparently it was a 2$ if it was labeled 2 on it

nitish_verma26: 2020-12-11 17:56:02

Use long long.
I found it interesting that for numbers less than 12, max value will be that number itself.
Recursion + Map to memoize seems like the way to go.

monkeyboy9996: 2020-12-07 18:22:20

Can be done via recursion too!!!

selectaman: 2020-12-01 09:21:17

When to stop taking test cases? Here number of test cases is not taken as input.


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