Router Switching Problem

[marmoor]

Hello, I'm wondering if anyone could help rest my case regarding this question:
Consider the switch shown below. Suppose that all datagrams have the same fixed length, that the switch operates in a slotted, synchronous manner, and that in one time slot a datagram can be transferred from an input port to an output port. The switch fabric is a crossbar so that at most one datagram can
be transferred to a given output port in a time slot, but different output ports can receive datagrams from different input ports in a single time slot. What is the minimal number of time slots needed to transfer the packets shown from input ports to their output ports, assuming any input queue scheduling order you want (i.e., it need not have HOL blocking)?

My TA said it requires a minimum of 3 time slots, along with other forums online:
Slot  1: send X  in top input queue, send  Y in middle input queue.     
Slot  2:  send X in middle  input  queue, send  Y in bottom input queue
Slot  3: send Z  in bottom  input queue.


But because it clearly stated that HOL blocking can be eliminated, I don't understand why can't it be as follows:
Slot  1: send X  in top input queue, send  Y in middle input queue, send Z in bottom input queue [applicable since HOL is not enforced].     
Slot  2: send X in middle input queue, send  Y in bottom input queue.

Therefore requiring only 2 time slots as minimum.

Thank you in advance.

[deanwebb]

Question: did all the datagrams arrive simultaneously, or are the bottom two input queues showing datagrams arriving at different times?