Suppose you have perfect knowledge and are able to buy and sell the stock multiple times. Write an algorithm that outputs the maximum profit that can be made by exactly n sales.

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
Each buy must be made on another date after the previous sale

Input

A blank-separated array of numbers.
The first number is the number of sales allowed.
All following numbers are stock-prices.

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

Output

The maximum profit that can be made within that period by n sales.

Constraints

2 <= n <= 10
2 * n <= days with stock-prices <= 50
1 <= stock-price <= 2,147,483,647

Example

Input: 3 12 11 13 9 12 8 14 13 15
where n is 3

Output: 12