A Gray code is a list of all $2^n$ bit strings of length $n$, where any two successive strings differ in exactly one bit (i.e., their Hamming distance is one).

Your task is to create a Gray code for a given length $n$.

Input

The only input line has an integer $n$.

Output

Print $2^n$ lines that describe the Gray code. You can print any valid solution.

Constraints

• $1 \le n \le 16$

Example

Input:

2

Output:

00
01
11
10