EllysSki

Elly hates the cold, but for some weird reason she likes skiing. Now she has started organizing a new ski adventure on a mountain ridge she hasn't visited before.

Elly has a map of the mountain ridge: the int[] height. The mountain (when viewed from a side) has the shape of a polyline that goes through the points (0, height[0]), (1, height[1]), (2, height[2]), and so on. For example, suppose height = {3, 4, 11, 6, 2, 2, 2, 5, 7, 7, 10, 8, 5, 8, 1, 4}. If you walk along this mountain from the left to the right, you start at altitude 3, go up to altitude 4, then up some more to altitude 11. From there it goes down the hill to altitudes 6, 2, and so on.

Elly can hire a helicopter to bring her up to any point on the mountain. She can then pick a direction (either left or right) and start skiing. There are only two restrictions:

• She cannot ski uphill.
• While skiing, she cannot change direction. (If she started skiing left, she cannot turn around and ski right, or vice versa.)

For example, suppose Elly starts at index 2 (altitude 11) and chooses to go right. In this case the longest possible ski run consists of five points: {11, 6, 2, 2, 2}. She cannot continue farther because the next segment of the mountain goes uphill. Should she start at the same place and go left instead, she would only visit three points (altitudes 11, 4, and 3, in this order).

Find the longest section of the mountain Elly can ski in a single run, and return the number of points that form the section.