Once upon a time Professor Idioticideasinventor was travelling by train. Watching cheerless landscape outside the window, he decided to invent the theme of his new scientific work. All of a sudden a brilliant idea struck him: to develop an effective algorithm finding an integer number, which is x times less than the sum of all its integer positive predecessors, where number x is given. As far as he has no computer in the train, you have to solve this difficult problem.

Input

  The first line of the input file contains an integer number x (1 ≤ x ≤ 10⁹).

Output

 Output an integer number — the answer to the problem.