Matcom Online Grader
Faculty of Mathematics and Computer Science of University of Havana

The topographic prominence of a peak is a measure of special interest to mountain climbers and can be dened as follows: the prominence of a peak p with altitude h, relative to the sea level, is the greatest d such that any path on the terrain from p 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 h itself. Those peaks with topographic prominence greater than or equal to $150000$ centimeters (precision is of great importance to climbers!) have a special name: they are called "Ultras". You have to write a program that identies all the Ultras that occur in a two dimensional prole 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 $7$, $12$, $14$, $20$ and $23$.

The first line contains an integer $N (3 \leq N \leq 10^5)$ representing the number of points in the prole. The second line contains $N$ integers $H_i$ indicating the altitudes (in centimeters) of the points, in the order in which they appear in the prole $(0 \leq Hi \leq 10^6 \textrm{ for } i = 1, 2,..., N )$. Consecutive points have different altitudes $(H_i \neq H_{i+1} \textrm{ for } i = 1, 2,..., N-1)$, while the first and the last points are at sea level $(H_1 = H_N= 0)$. You may assume that the prole 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 prole.