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