Democracy
N individuals gather around a circular table to play a game called Democracy. This game consists of multiple rounds. Each round starts with an Election process: every player places a card with their name into a pile. The cards are then thoroughly shuffled, and one card is randomly drawn from the pile, while the rest are discarded. The person whose name is on the drawn card becomes the President for that round. As President, they can issue humorous decrees, send other players into exile until the round ends, and generally do as they please. Once their term as President concludes, the round ends, and a new round begins. If, during any round, the President is someone who has already served as President in any previous round of the current game, the Election is deemed rigged, and the game of Democracy ends.
Naturally, each participant aspires to become President, but there's a challenge: it isn't always feasible for everyone to achieve this in a single game. Thus, an important question arises: on average, how many games will it take for each participant to have served as President at least once?
Input
The input consists of a single line containing a natural number N (1 ≤ N ≤ 100), representing the number of participants.
Output
Output the average number of games required in Democracy, ensuring a precision of at least 10^(-8).