YouKn0wWho has an integer n. He wants to find an integer sequence a of size exactly 2n such that 0≤ai<2n for each valid i and for each integer k from 0 to 2n−1, there exists at least one non-empty subsequence of a such that the bitwise AND of the elements of that subsequence is k.
Help YouKn0wWho find such a sequence. If there are multiple such sequences, output any. It can be shown that such a sequence always exists under the given constraints.
A sequence b is a subsequence of a sequence c if b can be obtained from c by deletion of several (possibly, zero or all) elements.
Input
The first and only line of the input will contain single integer n(1≤n≤18).
Output
Output 2n integers a1,a2,…a2n(0≤ai<2n) such that it satisfies the conditions mentioned in the statement. If there are multiple such sequences, output any.
Samples
Input
Output
1
1 0
Input
Output
2
3 1 0 2
Input
Output
3
4 3 5 6 7 1
In the third test case, you can achieve each integer from 0 to 23−1=7 as bitwise AND of the elements of some non-empty subsequence of a: