Go up the Ultras#6587
The topographic prominence of a peak is a measure of special interest to mountain climbers and can be defined as follows: the prominence of a peak with altitude , relative to the sea level, is the greatest such that any path on the terrain from to any strictly higher peak will pass through a point of altitude h-d. If there is no strictly higher peak, then the prominence is itself. Those peaks with topographic prominence greater than or equal to centimeters (precision is of great importance to climbers!) have a special name: they are called "Ultras".
You have to write a program that identifies all the Ultras that occur in a two dimensional profile of a mountain range represented as a sequence of points. Note that the horizontal distance between points is not important; all that you need is the altitude of each point. In the picture below, the Ultras are the points , , , and .
The first line contains an integer (3 \le N \le 10^5) representing the number of points in the profile. The second line contains integers H_i indicating the altitudes (in centimeters) of the points, in the order in which they appear in the profile (0 \le H_i \le 10^6 for i = 1, 2, \ldots, N). Consecutive points have different altitudes (H_i \ne H_{i+1} for i = 1, 2, \ldots, N-1), while the first and the last points are at sea level (H_1 = H_N = 0). You may assume that the profile contains at least one Ultra.
Output a line with the indices of all the Ultras in the mountain range, in the order in which they appear in the profile.
Example 1