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
2016-12-06 13:17:18
my first dp ...!!!!!!! for concept see this video https://www.youtube.com/watch?v=dZ0OS4YUs2A
2016-12-01 17:25:48
#15
2016-11-28 13:34:47
Must use long long . Costed me a WA.
2016-11-14 11:58:01
too easy....


Last edit: 2016-11-25 20:59:53
2016-11-10 23:37:33
TLE with the approach of recursion
some1....plss help...
thanxx in advance :)
2016-11-10 07:03:58
use map and unsigned long int
AC in 1 GO
2016-11-09 16:29:03
Got TLE in first attempt but second time I precomputed some data upto 5000 and hardcoded in array. AC in 0.08!!!!

Last edit: 2016-11-09 16:29:24
2016-11-07 19:28:35
i am getting wrong answer. It is working fine on ideone. What might be wrong?
2016-11-05 18:24:55
Folks, for n = 1000000000, output = 4243218150.
2016-10-30 14:06:29
Good problem to understand how to take boundless input and DP. Costed me 1 WA due to " int " return type of recursive method XD
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