Wowo is playing an interesting game. Initially, there are numbers .

For each round, if there is more than one remaining number, Wowo will choose two numbers from them with equal probability. If are coprime, Wowo will get 1 point. Then, will be deleted.

The game continues until there are less than two numbers.

Please calculate the expectation of the points Wowo can get from the game.

The only line contains one integer .

Output one number  -- the expectation of the points Wowo can get from the game.
 should be coprime.

2

1/1

4

5/3