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.
\n\nA 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.
\n
Example 1:
\n\n\nInput: n = 3\nOutput: [3,1,2,3,2]\nExplanation: [2,3,2,1,3] is also a valid sequence, but [3,1,2,3,2] is the lexicographically largest valid sequence.\n\n\n
Example 2:
\n\n\nInput: n = 5\nOutput: [5,3,1,4,3,5,2,4,2]\n\n\n
\n
Constraints:
\n\n1 <= n <= 20Compiled with clang 11 using the latest C++ 20 standard.
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