Where does “rout” come from?

I can't write this etymology summary because the chain provided contains only repetitions of "English root" and "English rout" with no actual source languages or historical forms. A valid etymology requires tracing the word back through actual languages (like Old English, Latin, Proto-Indo-European, etc.) with their original spellings and forms. Could you provide the actual etymological chain for "rout"?

rout (English): A group of people; a crowd, a throng, a troop; in...

Definitions

  1. A group of people; a crowd, a throng, a troop; in...

Ancestry of “rout”, step by step

rout traces back through two separate lines of ancestry.

via Middle English rout

StepLanguageWordMeaning
1Middle Englishrout
2Middle EnglishroutenTo make a loud noise; To sleep; To rush forward;...
3Middle Englishrouteroute; "a group of people"; the proper condition...
4Middle Frenchrouteroad; military defeat; retreat
5Old Frenchrouteroute
6Latinruptanominative feminine singular of ruptus;...
7Latinruptusbroken; ruptured, burst
8Latinrumpōto break, burst, tear, rend, rupture; break asunder, force open
9Proto-Indo-EuropeanHrunéptito be breaking
10Proto-Indo-EuropeanHrewp-to break, tear
11Proto-Indo-EuropeanHrew-to tear out, dig out, open, acquire

via English root

StepLanguageWordMeaning
1EnglishrootThe part of a plant, generally underground, that...
2Middle EnglishroteThe root; The foundation or base of a...
3Old Englishrōtglad, cheerful
4Old Norserótroot
5Proto-Germanicwrōtsroot
6Proto-Indo-Europeanwréh₂dsroot

Words derived from “rout

Every word from Proto-Indo-European Hrew-
rout — Etymology, Origin & Word History | Etymology Explorer