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popup15 problemsession 1

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2015-09-25 03:15 AKDT

## popup15 problemsession 1

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2015-09-25 07:45 AKDT
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# Problem EShopaholic

Lindsay is a shopaholic. Whenever there is a discount of the kind where you can buy three items and only pay for two, she goes completely mad and feels a need to buy all items in the store. You have given up on curing her for this disease, but try to limit its effect on her wallet.

You have realized that the stores coming with these offers are quite selective when it comes to which items you get for free; it is always the cheapest ones. As an example, when your friend comes to the counter with seven items, costing $400$, $350$, $300$, $250$, $200$, $150$, and $100$ dollars, she will have to pay $1500$ dollars. In this case she got a discount of $250$ dollars. You realize that if she goes to the counter three times, she might get a bigger discount. E.g. if she goes with the items that costs $400$, $300$ and $250$, she will get a discount of $250$ the first round. The next round she brings the item that costs $150$ giving no extra discount, but the third round she takes the last items that costs $350$, $200$ and $100$ giving a discount of an additional $100$ dollars, adding up to a total discount of $350$.

Your job is to find the maximum discount Lindsay can get.

## Input

The first line of input gives the number of items Lindsay is buying, $1\le n \le 200\, 000$. The next line gives the prices of these items, which are integers $1 \le p_ i \le 200\, 000$.

## Output

Output one line giving the maximum discount Lindsay can get by selectively choosing which items she brings to the counter at the same time.

Sample Input 1 Sample Output 1
6
400 100 200 350 300 250

400