Buy and Sell Twice

Goal

Given is the price-development of an arbitrary stock.

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