This task is adapted from following video with Neil Sloane (founder of the On-Line Encyclopedia of Integer Sequences). There are a few interesting sequences are shown in the video (so I recommend you to watch it all), but this particular mission is dedicated to the very first one - toothpicks sequence.

So, you have an infinite number of toothpicks of equal length and put them down on the table according to the rule. On the first step you just put one toothpick. It has two free ends, on which on the second step you respectively put two toothpicks perpendicularly. Now you have four free ends and put the next four toothpicks on the step three. If two toothpicks ends touch each other, the are not free, so after step three you again have four free end and so on.

The playground of this and other patterns may be seen on the page. It will be easier to solve the task and it's just a beautiful hypnotic view!)

So, your function must return the number of toothpicks, placed on the table, after step steps.

Input: Number of steps as integer.

Output: Number of toothpicks as integer.


assert toothpicks(1) == 1
assert toothpicks(2) == 3
assert toothpicks(3) == 7
assert toothpicks(4) == 11
Invalid hot key. Each hot key should be unique and valid
Hot keys:
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