I'm confused on the editorial for 1666J - Job Lookup. View the editorial here

In the editorial for 1666J - Job Lookup, when transitioning from $$$a_{i,k - 1}$$$ and $$$a_{k + 1, j}$$$ to $$$a_{i,j},$$$ $$$c_{u, v}$$$ seems to be only added once (the number of messages going from $$$u$$$ to $$$v$$$, for all $$$u,v$$$ such that $$$i \le u \le k - 1$$$ and $$$k < v \le j$$$) even though the total cost should be $$$c_{u,v} \cdot d_{u,v}$$$. What is going on here?

Thank you for the help!