Implement `minimum_matrix_chain_cost(dimensions)`. There are `n = len(dimensions) - 1` matrices. Matrix `A_i` has shape `dimensions[i-1] x dimensions[i]` for one-based `i`. Choose a parenthesization that minimizes the number of scalar multiplications and return that minimum cost. Matrix order cannot be changed. ### Constraints - `2 <= len(dimensions) <= 501` - `1 <= dimensions[i] <= 10000` - Return a 64-bit integer. ### Examples - `[10, 30, 5, 60]` returns `4500`, using `(A1 A2) A3`. - `[40, 20, 30, 10, 30]` returns `26000`. - Two dimensions describe one matrix and return cost `0`. ```hint The final multiplication splits an interval For matrices `i..j`, try each final split `k`; the subchains are independent once the split is fixed. ``` ```hint Fill by increasing chain length Every transition depends only on shorter intervals. ```