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Buy and Sell Twice

Goal

Given is the price-development of an arbitrary stock.

stock-price over time

Suppose you have perfect knowledge and are able to buy and sell the stock twice. Write an algorithm that outputs the maximum profit that can be made.

  • The price-development is given for an arbitrary number of days.
  • A stock can only be sold on the next day.
  • Stock-prices are given as integers
  • The second buy must be made on another date after the first sale

Input

A blank-separated array of stock-prices.

Each position symbolises the stock-price of a given day.

Output

The maximum profit that can be made within that day.

Constraints

  • 4 <= days with stock-prices <= 50
  • 1 <= stock-price <= 2,147,483,647

Example

Input: 12 11 13 9 12 8 14 13 15

Output: 10