Was Egypt under indirect rule or under direct rule?

This question gets into nebulous territory because there is no timeframe set. It's further nebulous because Egypt has had three types of regimes. The first are regimes ruled by people of Egyptian ethnicity from a capital in Egypt (what most people term direct rule) and will be indicated by "EE" (Egyptians in Egypt) below. The second type are regimes ruled by people of a non-Egyptian ethnicity from a capital outside of Egypt (what most people term indirect rule) and will be indicated by "FF" (Foreigners in Foreign Lands) below. The third type are regimes ruled by people of a non-Egyptian ethnicity from a capital within Egypt and will be indicated below by "FE" (Foreigners in Egypt).

Early Dynastic Period of Egypt: 31st to 27th Centuries BCE - EE

Old Kingdom of Egypt: 27th to 22nd Centuries BCE - EE

First Intermediate Period: 22nd to 21st Centuries BCE - EE

Middle Kingdom of Egypt: 21st to 17th Centuries BCE - EE

Second Intermediate Period: ca 1640 to 1750 BCE - FE (Hyksos)

New Kingdom of Egypt: 1570 to 1070 BCE - EE

Achaemenid Egypt: 525 to 402 BCE - FF (Persians)

Alexander the great: 343 to 332 BCE -FF (Macedons)

Ptolemaic Egypt: 332 to 30 BCE -FE (Greeks)

Roman Egypt: 30 BCE to 395 CE -FF (Romans)

Rightly-Guided and Umayyad Caliphates: 639 to 750 CE -FF (Arabs)

Fatimid and Other Egyptian Caliphates: 750 to 1250 CE -EE

Mamluk Egypt: 1250 to 1517 CE -FE (Arabs)

Ottoman Egypt: 1517 to 1805 CE -FF (Turks)

Khedivites: 1805 to 1882 CE -FE (Turks)

Colonial Egypt: 1882 to 1922 CE -FF (Britain)

Kingdom of Egypt: 1922 to 1953 CE -EE

Republic of Egypt: 1953 to Present -EE