Little Sub lives in a country with n cities A[0..n − 1]. He loves traveling very much.
It is Feb.14th, the Valentine Day. Little Sub decides to travel around the country with his girl friend.
Little Sub lives in A and he wants to visit each city exactly once and go back to A eventually. However, Little Sub has made a rule for his journey: Suppose he is in city A[i], the next city he is about to visit must be either A[(i ∗ 2)%n] or A[(i ∗ 2 + 1)%n].
Please help him find a possible route. If there are multiple answers, please give the one with the maximum alphabet order.
We say route A is larger than route B in the alphabet order when there exists i that A[i] > B[i]&A[1..i − 1] = B[1..i − 1] meets.
The first line contains a positive integers n(2 ≤ n ≤ 10000).
If there exists a legal route, please output n+1 integer separated by spaces in a single line, indicating the route.
If there is no possible route, please output −1 instead.