Gray Code: Cyclic Shift and XOR

C++ Hard loops

Task «Gray Code: Cyclic Shift and XOR»

Given an integer N (1 ≤ N ≤ 20). Generate a sequence of 2^N numbers representing the Gray code for numbers from 0 to 2^N-1. Then, for each number in this sequence, perform a cyclic shift of its binary representation to the right by 1 bit and apply the XOR operation with the original number. Output the resulting values in ascending order of the original numbers. Use only loops and bitwise operations, avoiding recursion.

Input Format

One integer N (1 ≤ N ≤ 20).

Output Format

2^N integers separated by spaces, each on a new line.

Examples

Example 1

INPUT

OUTPUT

15

Example 2

INPUT

1 5

OUTPUT

1 2 4 8 16

Example 3

INPUT

5
1 2 3 4 5
2 3

OUTPUT

12

Example 4

INPUT

3

OUTPUT

main.cpp