To clarify this p_w_picpath, consider this. If we get a packet into the first routing decision that is not destined for the local machine itself, it will be routed through the FORWARD chain. If the packet is, on the other hand, destined for an IP address that the local machine is listening to, we would send the packet through the INPUT chain and to the local machine.
Also worth a note, is the fact that packets may be destined for the local machine, but the destination address may be changed within the PREROUTING chain by doing NAT. Since this takes place before the first routing decision, the packet will be looked upon after this change. Because of this, the routing may be changed before the routing decision is done. Do note, that all packets will be going through one or the other path in this p_w_picpath. If you DNAT a packet back to the same network that it came from, it will still travel through the rest of the chains until it is back out on the network.
