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
2012-09-10 16:26:52 #vaidy_MIT#
HELOW sheldon :)
2012-08-08 07:09:46 Ankit Chaudhary
What is the output for 1,000,000,000?
My code is giving 4,243,218,150 .
get wrong ans.


Last edit: 2012-08-08 07:11:14
2012-08-08 02:27:05 kunal
will it b done through recursion...?
2012-08-08 01:36:24 kunal
how the output for
1000000000
is
4243218150
2012-07-31 09:59:04 Naresh
@shreyas use memoization
2012-07-30 00:24:12 Mayundo Mwenze
For n=1,000,000,000, surely output is 1,083,333,333. How are you guys getting 4,243,218,150?
2012-07-20 20:57:29 Vaibhav Sinha
got TLE in C
AC in C++, strange..

Last edit: 2012-07-20 20:58:09
2012-06-18 08:56:17 nik
About "stopping condition" in python:

while True:
try:
input()
except:
break

Is there other solution?

Last edit: 2012-06-18 08:56:46
2012-06-16 18:31:43 bug detected
tle for using recursion ....... any suggestions?????
2012-06-05 17:54:44 Anuj Arora
@Sandhya,
Read till end of file.
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