An array nums of length n is considered beautiful if it is a permutation of the integers from $1$ to n, and for every pair of indices i and j with $0 \leq$ i $<$ j $<$ n, there does not exist any index k with i $<$ k $<$ j such that:

$2 imes$ nums[k] $=$ nums[i] $+$ nums[j]

Given an integer n, return any beautiful array nums of length n. It is guaranteed that at least one valid answer exists for the given n.

Constraints:

• $1 \leq$ n $\leq 1000$

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