De Bruijn Sequence

Your task is to construct a minimum-length bit string that contains all possible substrings of length n. For example, when n=2, the string 00110 is a valid solution, because its substrings of length 2 are 00, 01, 10 and 11.

Input

The only input line has an integer n.

Output

Print a minimum-length bit string that contains all substrings of length n. You can print any valid solution.

Constraints

$1 \le n \le 15$

Example

Input

2

Output

00110