Rebase order

Find the cheapest order in which to merge a set of feature branches.

A team has n feature branches, numbered 0 to n - 1, and must merge every one of them into the main line, one at a time, in some order of their choosing. When a branch is merged, it has to be rebased against every branch that was merged before it, and each of those earlier branches adds its own conflict-resolution effort. Specifically, merging branch i when the set S of branches is already merged costs the sum of clash[i][j] over all j in S. Merging into an empty main line costs 0.

Note that clash is not necessarily symmetric: clash[i][j] is the effort branch i pays for coming after branch j, and clash[j][i] is what j pays for coming after i. The diagonal entries are 0.

Input: clash, an n x n list of lists of non-negative integers.

Output: an integer, the smallest possible total effort over all n! merge orders.

With n up to 14 there are far too many orders to try one by one.