Report chain headcount

Roll up headcounts for a company org chart and flag the people whose reporting chain is broken.

reports is a list of [employee, manager] lines exported from an HR system. A manager of "" (empty) means the employee is at the top of the company. If an employee appears on several lines, only the last line counts (people get reassigned).

Follow an employee's manager, then that manager's manager, and so on. The chain is intact if it ends at someone whose manager is "". It is broken if it reaches a manager who has no line of their own, or if it runs into a loop (including someone who is their own manager). Everybody whose chain passes through a broken person is broken too.

For every intact employee, the headcount is the number of intact employees anywhere below them (direct reports, their reports' reports, and so on), not counting themselves.

Input: reports, a list of [employee, manager] pairs of strings.

Output: a list of two lists. The first holds one string "name headcount" for every intact employee, ordered by headcount descending, then by name ascending (plain character order, so "Zed" comes before "amy"). The second holds the names of all broken employees in ascending order. If the input is empty, return [[], []].