Signing booth pairing

Staff every session of a conference with a sign-language interpreter so that the interpreters spend as little time preparing as possible.

There are n sessions and n interpreters, and every session needs exactly one interpreter, who covers only that session. prep[i][j] is the number of minutes interpreter j must prepare to cover session i (technical vocabulary, speaker slides, and so on), or -1 if interpreter j cannot cover session i at all (not certified in that language, or double-booked). Note that 0 is a valid preparation time.

Choose an interpreter for every session, using each interpreter once and never an unavailable pairing, so that the total preparation time is as small as possible. Many assignments can tie for the minimum; among those, return the one that is lexicographically smallest as a list: compare the interpreter for session 0 first, then for session 1, and so on.

Input: prep, an n x n list of lists of integers.

Output: a list a of length n where a[i] is the 0-based index of the interpreter covering session i. Return [] if no complete assignment exists (and also when n is 0).