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