# You are given an array prices where prices[i] is the price of a given stock on
#  the ith day. 
# 
#  Find the maximum profit you can achieve. You may complete at most two transac
# tions. 
# 
#  Note: You may not engage in multiple transactions simultaneously (i.e., you m
# ust sell the stock before you buy again). 
# 
#  
#  Example 1: 
# 
#  
# Input: prices = [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: prices = [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, buy on day 2 and sell them later, as you ar
# e engaging multiple transactions at the same time. You must sell before buying a
# gain.
#  
# 
#  Example 3: 
# 
#  
# Input: prices = [7,6,4,3,1]
# Output: 0
# Explanation: In this case, no transaction is done, i.e. max profit = 0.
#  
# 
#  Example 4: 
# 
#  
# Input: prices = [1]
# Output: 0
#  
# 
#  
#  Constraints: 
# 
#  
#  1 <= prices.length <= 105 
#  0 <= prices[i] <= 105 
#  
#  Related Topics 数组 动态规划 
#  👍 804 👎 0


# leetcode submit region begin(Prohibit modification and deletion)
class Solution:
    def maxProfit(self, prices: List[int]) -> int:
# leetcode submit region end(Prohibit modification and deletion)
