N (2<=N<=10^18) players take part in tennis championship. In every match loser is out. Two players can play a game if in that moment the difference of played games of that two players is not more than 1. They are interested, how many matches will be in the champioship (maximal possible number) and what's the maximal possible number of games in which can take part the champion in that case.

Input

Single number N.

Output

Two numbers - answers to the questions.

Example

Input:
4

Output:
2 3