If you can see this check that
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| A. | OUTPUT |
| B. | INPUT |
| C. | FORWARD |
| D. | MANGLE |
| E. | ONWARD |
Only packets created by the localhost go through OUTPUT.
Only packets destined for the localhost go through INPUT.
Input devices routed to output device goes through the FORWARD chain.
The packet probably does go through MANGLE at some point, but there is a better more obvious table in one of the other answers.
I made this name up.