Max Profit with At Most Two Transactions

amazon Given an integer array where the i-th element represents the stock price on day i, design an algorithm to find the maximum profit. 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: [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: [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, then sell on day 2 and buy again later. Constraints: Length of array is at most 10^5. Prices are in the range [0, 10^4]. Example Input [3,3,5,0,0,3,1,4]