CF884C Bertown Subway

The construction of subway in Bertown is almost finished! The President of Berland will visit this city soon to look at the new subway himself. There are $ n $ stations in the subway. It was built according to the Bertown Transport Law: 1. For each station $ i $ there exists exactly one train that goes from this station. Its destination station is $ p_{i} $ , possibly $ p_{i}=i $ ; 2. For each station $ i $ there exists exactly one station $ j $ such that $ p_{j}=i $ . The President will consider the convenience of subway after visiting it. The convenience is the number of ordered pairs $ (x,y) $ such that person can start at station $ x $ and, after taking some subway trains (possibly zero), arrive at station $ y $ ( $ 1

The first line contains one integer number $ n $ ( $ 1

Print one number — the maximum possible value of convenience.

In the first example the mayor can change $ p_{2} $ to $ 3 $ and $ p_{3} $ to $ 1 $ , so there will be $ 9 $ pairs: $ (1,1) $ , $ (1,2) $ , $ (1,3) $ , $ (2,1) $ , $ (2,2) $ , $ (2,3) $ , $ (3,1) $ , $ (3,2) $ , $ (3,3) $ . In the second example the mayor can change $ p_{2} $ to $ 4 $ and $ p_{3} $ to $ 5 $ .