Best Time to Trade with Cooldown

You are given stock prices for n consecutive days, and you want to maximize your profit by buying and selling shares. After you sell a share, you have a mandatory cooldown period of one day before you can buy again.

Formally, let \(prices[i]\) be the price on day \(i\) (0-indexed). You may complete as many transactions as you like (i.e. buy one and sell one share of the stock multiple times) with the following restriction: after selling a share, you cannot buy on the next day (i.e. cooldown for 1 day).

Your task is to compute the maximum profit achievable. If no profit can be achieved, output 0.

Example: For prices [1, 2, 3, 0, 2], the maximum profit is 3.

inputFormat

The first line contains an integer \(n\), representing the number of days.

The second line contains \(n\) space-separated integers, where the \(i\)-th integer denotes the stock price on day \(i\).

If \(n = 0\), the second line will be absent.

outputFormat

Output a single integer that denotes the maximum profit achievable under the cooldown constraint.

## sample

5
1 2 3 0 2

3

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