Question: The Second Intermediate Period marks a period when Ancient Egypt fell into disarray for a second time, between the end of the Middle Kingdom and the start of which period in ancient Egyptian history between the 16th century BC and the 11th century BC, covering the Eighteenth, Nineteenth, and Twentieth Dynasties of Egypt?

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Valley of the Kings: The Valley of the Kings (Arabic: وادي الملوك‎ ‎ "Wādī al Mulūk" ), the "Valley of the Gates of the Kings" (Arabic: وادي ابواب الملوك‎ ‎ "Wādī Abwāb al Mulūk" ), is a valley in Egypt where, for a period of nearly 500 years from the 16th to 11th century BC, rock cut tombs were excavated for the Pharaohs and powerful nobles of the New Kingdom (the Eighteenth to the Twentieth Dynasties of Ancient Egypt).

New Kingdom of Egypt: The New Kingdom of Egypt, also referred to as the Egyptian Empire, is the period in ancient Egyptian history between the 16th century BC and the 11th century BC, covering the Eighteenth, Nineteenth, and Twentieth Dynasties of Egypt.  Radiocarbon dating places the exact beginning of the New Kingdom between 1570 BC and 1544 BC.

Rifeh: Rifeh or Deir Rifeh (also known as Rifa) is a village in Egypt.  The name refers today most often to a series of Ancient Egyptian cemeteries nearby.  These are the burial grounds of the ancient town Shashotep.  The cemeteries date from the end of the First Intermediate Period to the Roman Period.  Especially important are the burials of the Middle Kingdom.  In this period Shashotep was the capital of the 11th Upper Egyptian province.  Several decorated rock cut tombs were carved into the rocky hills.  They belong to the local governors of the period.  Nakht-Khnum and Nefer-Khnum are the two whose names survived.  In front of these tombs were burials of lower officials that were working for these local governors.  One of them is the Tomb of two Brothers, that was found undisturbed and still contained an array of important artcfacts.  Further away and closer to the Nile were the burials of the more common people.  Typical for many of these burials dating to the Middle Kingdom model clay houses, once placed on top of the burial.  They are called in Egyptology "soul houses".  Further burials belong to the Second Intermediate Period and to the New Kingdom, when Shashotep was no longer the capital of a province.

Aperanat: 'Aper-'Anati (also written Aper-Anat and Aperanat) was a ruler of Lower Egypt during the Second Intermediate Period in the mid-17th century BC.  According to Jürgen von Beckerath he was the second king of the 16th Dynasty and a vassal of the Hyksos kings of the 15th Dynasty.  This opinion was recently rejected by Kim Ryholt.  In his 1997 study of the second intermediate period, Ryholt argues that the kings of the 16th Dynasty ruled an independent Theban realm c. 1650–1580 BC.  Consequently, Ryholt sees 'Aper-'Anati as an early Hyksos king of the 15th Dynasty, perhaps its second ruler.  This analysis has convinced some egyptologists, such as Darrell Baker and Janine Bourriau, but not others including Stephen Quirke.

Nuya: Nuya was a ruler of some part of Lower Egypt during the Second Intermediate Period, possibly during the 17th century BC.  Nuya is attested by a single scarab seal of unknown provenance.  Based on a seriation of the seals of the Second Intermediate Period, the Danish Egyptologist Kim Ryholt has proposed that Nuya was a king of the 14th Dynasty, reigning after Nehesy and before Yaqub-Har.  As such, he would have ruled in the 17th century BC from Avaris over the eastern Nile Delta and possibly over the Western Delta as well.

Thirteenth Dynasty of Egypt: The Thirteenth Dynasty of ancient Egypt (notated Dynasty XIII) is often combined with Dynasties XI, XII and XIV under the group title "Middle Kingdom".  Some writers separate it from these dynasties and join it to Dynasties XIV through XVII as part of the "Second Intermediate Period".  Dynasty XIII lasted from approximately 1803 BC until approximately 1649 BC, i.e. for 154 years.

Semqen: Semqen (also Šamuqēnu) was an Hyksos ruler of Lower Egypt during the Second Intermediate Period in the mid 17th century BC.  According to Jürgen von Beckerath he was the third king of the 16th Dynasty and a vassal of the Hyksos kings of the 15th Dynasty.  This opinion was shared by William C. Hayes and Wolfgang Helck but recently rejected by Kim Ryholt.  In his 1997 study of the second intermediate period, Ryholt argues that the kings of the 16th Dynasty ruled an independent Theban realm c. 1650–1580 BC.  Consequently, Ryholt sees Semqen as an early Hyksos king of the 15th Dynasty, perhaps its first ruler.  This analysis has convinced some egyptologists, such as Darrell Baker and Janine Bourriau, but not others including Stephen Quirke.

First Intermediate Period of Egypt: The First Intermediate Period, often described as a "dark period" in ancient Egyptian history, spanned approximately one hundred and twenty-five years, from c. 2181–2055 BC, after the end of the Old Kingdom.  It comprises the seventh (although it is mostly considered spurious by Egyptologists), eighth, ninth, tenth, and part of the eleventh dynasties.  Very little monumental evidence survives from this period, especially towards the beginning of the era.  The First Intermediate Period was a dynamic time in history where rule of Egypt was roughly divided between two competing power bases.  One of those bases resided at Heracleopolis in Lower Egypt, a city just south of the Faiyum region.  The other resided at Thebes in Upper Egypt.  It is believed that during this time, the temples were pillaged and violated, their existing artwork was vandalized, and the statues of kings were broken or destroyed as a result of this alleged political chaos.  These two kingdoms would eventually come into conflict, with the Theban kings conquering the north, resulting in reunification of Egypt under a single ruler during the second part of the eleventh dynasty.

Second Intermediate Period of Egypt: The Second Intermediate Period marks a period when Ancient Egypt fell into disarray for a second time, between the end of the Middle Kingdom and the start of the New Kingdom.

Sheshi: Maaibre Sheshi (also Sheshy) was a ruler of areas of Egypt during the Second Intermediate Period.  The dynasty, chronological position, duration and extent of his reign are uncertain and subject to ongoing debate.  The difficulty of identification is mirrored by problems in determining events from the end of the Middle Kingdom to the arrival of the Hyksos in Egypt.  Nonetheless, Sheshi is, in terms of the number of artefacts attributed to him, the best attested king of the period spanning the end of the Middle Kingdom and the Second Intermediate period; roughly from c. 1800 BC until 1550 BC.  Hundreds of scaraboid seals bearing his name have been found throughout Canaan, Egypt, Nubia and as far away as Carthage where some were still in use 1500 years after his death.

Supporting paragraphs: Second Intermediate Period of Egypt New Kingdom of Egypt
Answer: New Kingdom of Egypt