Midrasch zu Jirmejahu 33:1

(Bamidbar 29:35) "On the eighth day, a withholding ("atzereth") shall there be for you": Scripture "withheld" him from leaving. If one brought his offerings from Beth Paggai (outside of Jerusalem) to Jerusalem, I might think that he could eat them in Jerusalem and sleep in Beth Paggai. It is, therefore, written "On the eighth day, an atzereth shall there be for you" — Scripture withheld him from leaving (until the morning of the next day [viz. Devarim 16:7]). "atzirah" connotes confinement, as in (Jeremiah 36:5) "I am atzur; I cannot go to the Temple of the L-rd" and (Ibid. 33:1) "Then the word of the L-rd came to Jeremiah a second time while he was still atzur in the prison yard." This tells me only of the last day of the festival that he is forbidden to leave. Whence do I derive (the same for) the first day? It follows inductively, viz. Since both are called "a calling of holiness," just as it is forbidden to leave the first day, so it is forbidden to leave the last day.