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