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Gray Code

1. The gray code is a binary numeral system where two successive numbers differ in only one bit. 2. Given a non-negative integer n representing the total number of bits in the code, print the sequence of gray code. A gray code sequence must begin with 0. Example: Input: 2 Output: [0,1,3,2] Explanation: 00 - 0 01 - 1 11 - 3 10 - 2 [0,2,3,1] is also a valid gray code sequence. 00 - 0 10 - 2 11 - 3 01 - 1

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Gray Code

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1. The gray code is a binary numeral system where two successive numbers differ in only one bit. 2. Given a non-negative integer n representing the total number of bits in the code, print the sequence of gray code. A gray code sequence must begin with 0. Example: Input: 2 Output: [0,1,3,2] Explanation: 00 - 0 01 - 1 11 - 3 10 - 2 [0,2,3,1] is also a valid gray code sequence. 00 - 0 10 - 2 11 - 3 01 - 1

Constraints

0<=n<=20

Format

Input

First line contains n(number of digits).

Output

Return the list of numbers in any valid order.

Example

Sample Input

2

Sample Output

[0, 1, 2, 3]

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