In a packet switched network, a source host transmits packets of $800$ bytes each, which travels over one link to a router then from the router over a second link to a destination end system. The propagation speed on both links is $2\backslash$times $108$ m$/$s$.$ The transmission rate of the first link and the second link is $160$Mbps and $130$Mbps respectively. Packet processing on the router consumes $5$ microseconds per kilobyte. The length of the first link is $1400$ km$,$ and the length of the second link is $1100$ km$.$ Assume no other packets exist in the network. Ignore the processing and queueing delay on hosts. If the router buffer size is $24$ megabytes $($MB$),$ which packet is the first one to be lost? Provide the answer as an integer.