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Given an integer n
, find a sequence that satisfies all of the following:
1
occurs once in the sequence.2
and n
occurs twice in the sequence.i
between 2
and n
, the distance between the two occurrences of i
is exactly i
.The distance between two numbers on the sequence, a[i]
and a[j]
, is the absolute difference of their indices, |j - i|
.
Return the lexicographically largest sequence. It is guaranteed that under the given constraints, there is always a solution.
A sequence a
is lexicographically larger than a sequence b
(of the same length) if in the first position where a
and b
differ, sequence a
has a number greater than the corresponding number in b
. For example, [0,1,9,0]
is lexicographically larger than [0,1,5,6]
because the first position they differ is at the third number, and 9
is greater than 5
.
Example 1:
Input: n = 3 Output: [3,1,2,3,2] Explanation: [2,3,2,1,3] is also a valid sequence, but [3,1,2,3,2] is the lexicographically largest valid sequence.
Example 2:
Input: n = 5 Output: [5,3,1,4,3,5,2,4,2]
Constraints:
1 <= n <= 20
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