Combinatorics Is Fun

Consider a multiset $S$ and a positive integer $X$. Suppose we partition $S$ into $L$ non-empty subsets such that each element of $S$ is present in **exactly one** subset. The cost of such partition is $\sum_{i=1}^L X +$ `max`$_i - $ `min`$_i$, where `max`$_i$ and `min`$_i$ denote the maximum and minimum elements of the $i-$th subset respectively. Let $F(S, X)$ denote the minimum cost required