123 - Best Time to Buy and Sell Stock III\.

Hard

You are given an array prices where prices[i] is the price of a given stock on the <code>i^th</code> day.

Find the maximum profit you can achieve. You may complete at most two transactions.

Note: You may not engage in multiple transactions simultaneously (i.e., you must sell the stock before you buy again).

Example 1:

Input: prices = 3,3,5,0,0,3,1,4

Output: 6

Explanation: Buy on day 4 (price = 0) and sell on day 6 (price = 3), profit = 3-0 = 3. Then buy on day 7 (price = 1) and sell on day 8 (price = 4), profit = 4-1 = 3.

Example 2:

Input: prices = 1,2,3,4,5

Output: 4

Explanation: Buy on day 1 (price = 1) and sell on day 5 (price = 5), profit = 5-1 = 4. Note that you cannot buy on day 1, buy on day 2 and sell them later, as you are engaging multiple transactions at the same time. You must sell before buying again.

Example 3:

Input: prices = 7,6,4,3,1

Output: 0

Explanation: In this case, no transaction is done, i.e. max profit = 0.

Constraints:

• <code>1 <= prices.length <= 10⁵</code>

• <code>0 <= pricesi<= 10⁵</code>