Here you are in the castle. Despite the fact that it’s already about 200 years old, it doesn’t look like an ancient ruin at all. In the great hall (of a very odd geometrical form) you’re seeing the following: - a beautiful spiral staircase leading to the 2nd floor; - an equally attractive staircase that leads into the dungeon; - a lot of doors of a wide variety of different shapes, colors and designs. Having decided to explore the doors on this floor first, you’ve assumed that the most interesting things should be in the very last room. However, finding it won’t be as easy as it seems.

Before going on this trip, you’ve gathered some information about the Lord Escher's quirks. One of them was a very unusual numbering of doors - he numbered them according to how the numbers go in the alphabetical order. For example, if there were five doors positioned from left to right, they were numbered as: five, four, one, three, two (instead of a completely logical numeration - 1, 2, 3, 4, 5). Thus, the very last door was actually the leftmost, not the very right one, as it might be assumed. Your task is to find the very last door.

secret_room(5) == 1, #five, four, one, three, two
secret_room(3) == 2, #one, three, two
secret_room(1000) == 551