CF555A Case of Matryoshkas

Andrewid the Android is a galaxy-famous detective. He is now investigating the case of vandalism at the exhibition of contemporary art. The main exhibit is a construction of $ n $ matryoshka dolls that can be nested one into another. The matryoshka dolls are numbered from $ 1 $ to $ n $ . A matryoshka with a smaller number can be nested in a matryoshka with a higher number, two matryoshkas can not be directly nested in the same doll, but there may be chain nestings, for example, $ 1→2→4→5 $ . In one second, you can perform one of the two following operations: - Having a matryoshka $ a $ that isn't nested in any other matryoshka and a matryoshka $ b $ , such that $ b $ doesn't contain any other matryoshka and is not nested in any other matryoshka, you may put $ a $ in $ b $ ; - Having a matryoshka $ a $ directly contained in matryoshka $ b $ , such that $ b $ is not nested in any other matryoshka, you may get $ a $ out of $ b $ . According to the modern aesthetic norms the matryoshka dolls on display were assembled in a specific configuration, i.e. as several separate chains of nested matryoshkas, but the criminal, following the mysterious plan, took out all the dolls and assembled them into a single large chain ( $ 1→2→...→n $ ). In order to continue the investigation Andrewid needs to know in what minimum time it is possible to perform this action.

The first line contains integers $ n $ ( $ 1

In the single line print the minimum number of seconds needed to assemble one large chain from the initial configuration.

In the first sample test there are two chains: $ 1→2 $ and $ 3 $ . In one second you can nest the first chain into the second one and get $ 1→2→3 $ . In the second sample test you need to disassemble all the three chains into individual matryoshkas in 2 + 1 + 1 = 4 seconds and then assemble one big chain in 6 seconds.