Decompose rate matrix

A freight desk publishes a rate card as a rectangular table of whole cents, where rates[o][d] is the quoted price to move one pallet from origin depot o to destination depot d. The desk claims every quote is nothing more than an origin handling fee plus a destination handling fee, and an auditor wants that claim checked. Return a flat list holding the origin fees in order followed by the destination fees in order, pinning the split with the convention that destination 0 carries a fee of exactly 0 cents. Fees may come out negative, since a depot can be quoted at a discount. If no pair of fee lists reproduces the whole table, return an empty list. An empty table returns an empty list. Every row has the same length, and a table with at least one row has at least one column.