Binary Subsequences

Your task is to find a minimum length bit string that has exactly n distinct subsequences. For example, a correct solution for n=6 is 101 whose distinct subsequences are 0, 1, 01, 10, 11 and 101.

Input

The only input line has an integer n.

Output

Print one bit string: a solution to the task. You can print any valid solution.

Constraints

$1 \le n \le 10^6$

Example

Input

6

Output

101