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
2014-09-01 22:02:18 KnockturnAlley
my c++ code is working fine :) but the one I wrote in c is not :( can someone please tell me the error in <snip>

Last edit: 2022-08-09 22:49:14
2014-08-27 00:36:08 Rajat (1307086)
Good one! Learned a new technique and named that 'partial memoization'.
2014-08-17 22:05:54 RAJESH KUMAR SINHA
really a intuitive question
2014-08-17 08:22:55 /* Nitin Jaiman */
Awesome learning.A Must do problem.
2014-08-11 17:54:46 Piyush Nirmal
my first dp..easy but nice
2014-08-09 15:47:23 Srikar Vedantam
Maximum amount can get huge. Look out for integer overflows.
2014-08-09 07:41:26 Richa Jain
using array gave SIGKILL but then changed it to map and got AC!
2014-07-31 19:25:02 sHaShAnK sHeKhAr
Cakewalk...AC in 1 go
Simple memorization B|

Last edit: 2014-08-11 20:31:38
2014-07-30 17:57:41 kaviraj
Why we need to use long long, Well, the limit is between 1 billion right? Please clarify.
2014-07-11 19:58:31 Dhruv Gupta
Learnt so much solving this problem. Memoization ftw!
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