Best Time to Buy and Sell Stocks III

Say you have an array, A, 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 2 transactions.

Return the maximum possible profit.

Note: You may not engage in multiple transactions at the same time (ie, you must sell the stock before you buy again).

Input Format:

The first and the only argument is an integer array, A.

Output Format:

Return an integer, representing the maximum possible profit.

Constraints:

1 <= length(A) <= 7e5
1 <= A[i] <= 1e7

Examples:

Input 1:
    A = [1, 2, 1, 2]

Output 1:
    2

Explanation 1: 
    Day 0 : Buy 
    Day 1 : Sell
    Day 2 : Buy
    Day 3 : Sell

Input 2:
    A = [7, 2, 4, 8, 7]

Output 2:
    6

Explanation 2:
    Day 1 : Buy
    Day 3 : 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.