CF821C Okabe and Boxes

Okabe and Super Hacker Daru are stacking and removing boxes. There are $ n $ boxes numbered from $ 1 $ to $ n $ . Initially there are no boxes on the stack. Okabe, being a control freak, gives Daru $ 2n $ commands: $ n $ of which are to add a box to the top of the stack, and $ n $ of which are to remove a box from the top of the stack and throw it in the trash. Okabe wants Daru to throw away the boxes in the order from $ 1 $ to $ n $ . Of course, this means that it might be impossible for Daru to perform some of Okabe's remove commands, because the required box is not on the top of the stack. That's why Daru can decide to wait until Okabe looks away and then reorder the boxes in the stack in any way he wants. He can do it at any point of time between Okabe's commands, but he can't add or remove boxes while he does it. Tell Daru the minimum number of times he needs to reorder the boxes so that he can successfully complete all of Okabe's commands. It is guaranteed that every box is added before it is required to be removed.

The first line of input contains the integer $ n $ ( $ 1

Print the minimum number of times Daru needs to reorder the boxes to successfully complete all of Okabe's commands.

In the first sample, Daru should reorder the boxes after adding box $ 3 $ to the stack. In the second sample, Daru should reorder the boxes after adding box $ 4 $ and box $ 7 $ to the stack.