Time limit per test: 0.5 second(s) Memory limit: 65536 kilobytes

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.

Example(s)

sample input #1

    1

sample output #1

    3

sample input #2

    2

sample output #2

    5