Hello everyone, I found this problem a while ago and I'm still stuck on it (there's no OJ to submit it as far as I know):

You are given a permutation of the integers from 1 to *N*. In this case, *moving* an element from *i* to *j* is defined as removing the element from position *i*, and inserting it at position *j*. For example, in this array: `[4,5,2,1,3]`

, moving the element from 2 to 5 gives us the array `[4,2,1,3,5]`

. The cost of moving an element from *i* to *j* is defined as *i* + *j* (1-indexed).

What is the minimum total cost needed to sort the permutation?

Example:`[1,3,4,5,2]`

→ `[1,2,3,4,5]`

with total cost 5 + 2 = 7.

1 ≤ *N* ≤ 1000, however solutions with any reasonable complexity are welcome.