Question: Who is Máel Snechtai Of Moray's paternal grandmother?

Knowledge 1: Máel Snechtai of Moray
Máel Snechtai of Moray (or Máel Snechtai mac Lulaich) was the ruler of Moray, and, as his name suggests, the son of Lulach, King of Scotland.He is called on his death notice in the Annals of Ulster, "Máel Snechtai m. Lulaigh ri MuirebMáel Snechtai, Lulach's son, King of Moray"), which is a significant terminological development,since previously the titles for the ruler of Moray had either been "King of Scotland" or "Mormaer." The title is repeated for his successor, Óengus (if indeed the latter were his successor).Perhaps then the events of Máel Snechtai's caused some kind of identity disassociation between the Men of Moray and the Men of Scotland.The "Anglo-Saxon Chronicles.a."1078, reports that In this year Máel Coluim seized the mother of Máel Snechtai ...and all his treasures, and his cattle; and he himself escaped [only] with difficulty The  represents a lacuna in the text one line long; but it is clear that Máel Snechtai was defeated by King Máel Coluim III in some kind of conflict.Grant's suggestion that Máel Snechtai subsequently retired to a monastery is based only on textual innuendo, and is made unlikely by the fact that he was called "King of Moray" on his death.Máel Snechtai, as the son of King Lulach, undoubtedly perceived himself as the rightful king of Scotland, and the already noted conflict with Máel Coluim IIIstrongly suggests that he pursued his claim.His death date is based on the year given by the "Annals of Ulster", s.a. 1085. [SEP] Knowledge 2: Lulach
Lulach mac Gille Coemgáin(Modern Gaelic: "Lughlagh mac Gille Chomghain", known in English simply as Lulach, and nicknamed Tairbith, "the Unfortunate" and Fatuus, "the Simple-minded" or "the Foolish"; before 1033 – 17 March 1058) was King of Scots between 15 August 1057 and 17 March 1058.Lulach was the son of Gruoch of Scotland, from her first marriage to Gille Coemgáin, Mormaer of Moray, and thus the stepson of Macbeth (Mac Bethad mac Findlaích).Following the death of Macbeth at the Battle of Lumphanan on 15 August 1057, the king's followers placed Lulach on the throne.He has the distinction of being the first king of Scotland of whom there are coronation details available: he was crowned, probably on 8 September 1057 at Scone.Lulach appears to have been a weak king, as his nicknames suggest, and ruled only for a few months before being assassinated and usurped by Malcolm III.Lulach's son Máel Snechtai was Mormaer of Moray, while Óengus of Moray was the son of Lulach's daughter.He is believed to be buried on Saint Columba's Holy Island of Iona in or around the monastery.The exact position of his grave is unknown.
Knowledge 1: Máel Snechtai of Moray
Máel Snechtai of Moray (or Máel Snechtai mac Lulaich) was the ruler of Moray, and, as his name suggests, the son of Lulach, King of Scotland.He is called on his death notice in the Annals of Ulster, "Máel Snechtai m. Lulaigh ri MuirebMáel Snechtai, Lulach's son, King of Moray"), which is a significant terminological development,since previously the titles for the ruler of Moray had either been "King of Scotland" or "Mormaer." The title is repeated for his successor, Óengus (if indeed the latter were his successor).Perhaps then the events of Máel Snechtai's caused some kind of identity disassociation between the Men of Moray and the Men of Scotland.The "Anglo-Saxon Chronicles.a."1078, reports that In this year Máel Coluim seized the mother of Máel Snechtai ...and all his treasures, and his cattle; and he himself escaped [only] with difficulty The  represents a lacuna in the text one line long; but it is clear that Máel Snechtai was defeated by King Máel Coluim III in some kind of conflict.Grant's suggestion that Máel Snechtai subsequently retired to a monastery is based only on textual innuendo, and is made unlikely by the fact that he was called "King of Moray" on his death.Máel Snechtai, as the son of King Lulach, undoubtedly perceived himself as the rightful king of Scotland, and the already noted conflict with Máel Coluim IIIstrongly suggests that he pursued his claim.His death date is based on the year given by the "Annals of Ulster", s.a. 1085. [SEP] Knowledge 2: Kaoru Hatoyama
After the elections of 2009, she became more widely known as the grandmother of Prime Minister Yukio Hatoyama and his politician brother Kunio Hatoyama.
Knowledge 1: Máel Snechtai of Moray
Máel Snechtai of Moray (or Máel Snechtai mac Lulaich) was the ruler of Moray, and, as his name suggests, the son of Lulach, King of Scotland.He is called on his death notice in the Annals of Ulster, "Máel Snechtai m. Lulaigh ri MuirebMáel Snechtai, Lulach's son, King of Moray"), which is a significant terminological development,since previously the titles for the ruler of Moray had either been "King of Scotland" or "Mormaer." The title is repeated for his successor, Óengus (if indeed the latter were his successor).Perhaps then the events of Máel Snechtai's caused some kind of identity disassociation between the Men of Moray and the Men of Scotland.The "Anglo-Saxon Chronicles.a."1078, reports that In this year Máel Coluim seized the mother of Máel Snechtai ...and all his treasures, and his cattle; and he himself escaped [only] with difficulty The  represents a lacuna in the text one line long; but it is clear that Máel Snechtai was defeated by King Máel Coluim III in some kind of conflict.Grant's suggestion that Máel Snechtai subsequently retired to a monastery is based only on textual innuendo, and is made unlikely by the fact that he was called "King of Moray" on his death.Máel Snechtai, as the son of King Lulach, undoubtedly perceived himself as the rightful king of Scotland, and the already noted conflict with Máel Coluim IIIstrongly suggests that he pursued his claim.His death date is based on the year given by the "Annals of Ulster", s.a. 1085. [SEP] Knowledge 2: Hannah Arnold
Hannah Arnold, also known as Hannah Waterman King, was the grandmother of Benedict Arnolds children.

Answer: Gruoch of Scotland