An array `nums` of length `n` is beautiful if:

- `nums` is a permutation of the integers in the range `[1, n]`.
- For every `0 <= i < j < n`, there is no index `k` with `i < k < j` where `2 * nums[k] == nums[i] + nums[j]`.

Given the integer `n`, return any beautiful array `nums` of length `n`. There will be at least one valid answer for the given `n`.

Example 1:

    Input: n = 4
    Output: [2,1,4,3]

Example 2:

    Input: n = 5
    Output: [3,1,2,5,4]

Constraints:

- `1 <= n <= 1000`