did i deserve to be punished with 4 hr 30 minute saturday detention ?

I go to a good but VERY strict school in england our school detention policy says that anty student getting 3 detentions in a term will automatically go into a 4 hour 30 min satuday detention. well last tuesday i kept messing about in my maths class my teacher told me several times to behave or she would give me a detention, i ignored her and threw a paper plane across the classroom , she then shouted RIGHT THATS IT DETENTION 1 AND A HALF HOURS FRIDAY EVENING it was only at the end of the lesson that i remembered this would be my 3rd detention this term which means satuday detention, i went up to my teacher and said how sorry i was and begged her to let me off , she said NO as i had been warned several times to behave but ignored the warnings, so therefore deserved the satuday detention. last satuday i served my saturday detention it was MISREABLE , he is the timetable
8:45 am REGISTRATION AND SCHOOL UNIFORM INSPECTION , we had to be smartly dressed our white school shirts had to be ironed our collars done up ties neat and tidy shoes polished and school blazer done up,
9am--11am PUNISHMENT ESSAYS we had to sit at our desks in TOTAL silence and write an essay on why we were being punished, i had to write an essay on why its unacceptable to get 3 detentions in a term
11am --11:15 am 15 mute break
11:15am--13 :15 PUNISHMENT ESSAYS back to our desks and write an essay on what we had learned from satuday detention.
13:15 am TIDY CLASSROOM BEFORE GOING HOME we had to pick up any litter before we could go home.
saturday detention was a misreable experiance my parents said i deserved it what do you think ?