#967. Gray code
You get n. Print the n-bit Gray code (code i = i XOR (i >> 1)) for i from 0 to 2ⁿ-1, each as a binary string of length n, one per line.
### Input
One integer n (1 ≤ n ≤ 5).
### Output
2ⁿ lines.
Examples
Input
2
Output
00 01 11 10
Input
4
Output
0000 0001 0011 0010 0110 0111 0101 0100 1100 1101 1111 1110 1010 1011 1001 1000
💡 You can solve it with Python, JavaScript or blocks. Read the input line by line with input(). Don't print a question (like input("Number: ")). Print exactly what the output asks for, nothing more.