YouKn0wWho has an integer . He wants to find an integer sequence of size exactly such that for each valid and for each integer from to , there exists at least one non-empty subsequence of such that the bitwise AND of the elements of that subsequence is .
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 is a subsequence of a sequence if can be obtained from by deletion of several (possibly, zero or all) elements.
The first and only line of the input will contain single integer .
Output integers such that it satisfies the conditions mentioned in the statement. If there are multiple such sequences, output any.
3 1 0 2
4 3 5 6 7 1
In the third test case, you can achieve each integer from to as bitwise AND of the elements of some non-empty subsequence of :
Here, is the bitwise AND operator.