Time limit per test: 0.25
Memory limit: 262144
Football judge is a very important profession. To make stern but fair decisions during the match all judges must be in good shape. For this purpose they regularly have special judge trainings. One of the most popular trainings is a game called "Highlander". The rules of this game are quite simple. Initially, each judge receives one red card with the name of some other judge (no judge gets the card with his own name, and all the cards are different). Then, the game starts. Judges can run anywhere on the football field. The purpose is to catch the judge whose name is written on the card and show the card to him. When judge A catches judge B, judge B loses and doesn't play anymore, and A gets all his cards. Then the game continues. The game ends when the distribution of the cards reaches such a state that it is impossible to catch anybody because no judge has the card with the name of another judge who is still playing. The winner is the judge who gets the most number of cards. If several players get the same maximal amount of cards, they are all considered to be winners.
It is clear that after the distribution of cards some judges have no chance to win. Your task is to determine the expected number of judges that have a theoretical chance to win. All transpositions of cards where no judge gets the card with his name are considered equiprobable.
Input file contains exactly one integer number n
— the number of judges in the game (2 ≤ n
Output should contain one real number with relative or absolute error 10-9
— the answer to the problem.