Best Time to Buy and Sell Stock III

Problem

Say you have an array for which the i-th element is the price of a given stock 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 at the same time (i.e., you must sell the stock before you buy again).

Example

Given an example [4, 4, 6, 1, 1, 4, 2, 5], return 6.