Given a rod of length `n`

inches and an array of prices that contains prices of all pieces of size smaller than `n`

. Determine the maximum value obtainable by cutting up the rod and selling the pieces. For example, if length of the rod is `8`

and the values of different pieces are given as following, then the maximum obtainable value is `22`

(by cutting in two pieces of lengths `2`

and `6`

)