Editing 2016 Jan Platinum Problem 2 Mowing the Field (section)

== Problem ==

Farmer John has a field of N (1 <= N <= 100,000) cells that he wishes to mow. Each cell is labeled with a distinct positive integer value between 1 and N. The cells are arranged in a sequence, and each cell can be reached from its neighbor in the sequence in unit time.

Farmer John starts with his mower at the cell labeled 1, and every time step, he can either wait in his current cell or move to the next cell in the sequence. The time required to mow a cell depends on the amount of grass in the cell. Initially, each cell contains grass of height one unit. The grass in a cell grows by one unit for each time step that Farmer John is not in the cell.

The problem is to determine the minimum amount of time required for Farmer John to mow all the cells. Farmer John must mow each cell exactly once, and he can only mow the cell he is currently in.