D - Minimum Cost

An array of integers $P1,P2,…,Pn$ is called a permutation if it contains each number from $1$ to $n$ exactly once. For example, the following arrays $ [1,2,3],[1],[4,3,2,1]$ are permutations. The following arrays $[2],[1,1],[2,4,1]$ are not permutations. You are standing at position $1$. From position $i$, you can travel to $ j(1<=j<=n)$ with cost $|i-j|*X$ . From position $i$, you can also trave