Best Time to Buy and Sell Stocks III

Say you have an array for which the ith 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 (ie, you must sell the stock before you buy again).

Example :

Input : [1 2 1 2]
Output : 2

Explanation : 
  Day 1 : Buy 
  Day 2 : Sell
  Day 3 : Buy
  Day 4 : Sell

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details.