Average Permutation

You are given an integer $N$. Find a permutation $P = [P_1, P_2, \ldots, P_N]$ of the integers $\{1, 2, \ldots, N\}$ such that sum of averages of all consecutive triplets is minimized, i.e. $$ \sum_{i=1}^{N-2} \frac{P_i + P_{i+1} + P_{i+2}}{3} $$ is minimized. If multiple permutations are possible, print any of them. ### Input - The first line of input will contain a single integer $T$, deno