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Let's assume
1. The distance between two poles is 1 unit.
2. The tallest pole is 10unit height.
3. The shortest one is 1 unit, clear from the problem.

Now,
If two tallest pole are neighbor (10 10), then you need only 1 unit of wire to connect.
But if one pole is 10 and another pole is 1, now you need a diagonal distance (sqrt(10*10+1))

Happy case: All the pole is same height
Worst case: One pole is max height, 10 and the next one is 1. It will look like a triangular wave.

Just need to sum up all the non horizontal(diagonal) line of the wave.

We can apply pythagoras theoram to solve the problem.

1: lets assume that the distance between each pole is the same or contant.
2: lets assume that the minimum length of the wire required to join the two poles is the constant distance of the pole between each other.
3: less compare the two poles if the height are the same then we know that we need just the constant distance of the pole as the required length of wire to connect the poles. If the height of the two poles are not the same then we substract the poles among them between the highest and the small pole after substracting, we add the constant distance between two poles and the substracted value, so thats going to be our required wire length to join the two not poles with wire.
Thinking this approach will work.

Here as the question mentions the height of all these poles are constantly changing and hence they can vary for anything between 1-> maxheight, So hence what I think is it is just a max(max_hi[i]-1, max_hi[i+1]-1) and this would be the required length to connect 2 poles no matter what the situation is.