Permutation Construction

You are given an integer $N$. Find a permutation$^\dagger$ $P$ of the integers $1$ to $N$ such that $$ P_i \geq \left( P_{i+1} - P_{i-1} \right)^2 $$ holds for *every* index $i$ from $2$ to $N-1$. It can be proved that at least one solution exists. If multiple solutions exist, print any of them. $^\dagger$ A permutation of the integers $1$ to $N$ is an array of length $N$ that contains eve