LogiQuest

222. Gray Code

MediumBitsRecursion

Print the standard n-bit reflected Gray code sequence as decimal numbers (consecutive values differ in one bit, starting at 0).

Input format

A single integer n.

Output format

2ⁿ numbers.

Example 1

Input

2

Output

0 1 3 2

Example 2

Input

1

Output

0 1

Constraints

1 ≤ n ≤ 12

Read input from standard input and print the answer to standard output. Your code is judged against 4 test cases, most of them hidden.

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