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
2020-06-22 13:26:46
how is 24 =>27?
2020-06-19 15:03:11
More Testcases:
24 --> 27
25 --> 27
50 --> 57
100 --> 120
150 --> 185
250 --> 253

2020-06-15 12:47:34
input:
1000000000
output:
4243218150
is this true ?
2020-06-01 23:03:30
@banihali for n =24 answer -> 27
2020-06-01 23:02:02
care about long input. so to handle this time of input or avoid TLE , use STL map and recursion.

Last edit: 2020-06-01 23:02:11
2020-05-31 06:14:10
what is answer for n=24?
2020-05-30 05:17:33
@plak4 you don't need long long ints. This can be done using long ints.
2020-05-27 13:47:17
do take care of integer overflow.
2020-05-14 21:38:35
yes @divyansh_09, but then you need infinite amount of computing power :)
2020-05-12 21:20:55
Solved it 0.01s C++ on first try :p
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