Question: Who is Muirchertach Nár Mac Guairi's paternal grandfather?

Knowledge 1: Muirchertach Nár mac Guairi
Muirchertach Nár mac Guairi (died 668) was a possible King of Connacht from the Ui Fiachrach Aidhne branch of the Connachta.He was the son of Guaire Aidne mac Colmáin (died 663), famous in Irish sagas.The Irish king lists such ascontained in "The Book of Leinster" do not list Muirchertach as king but have instead Cenn Fáelad mac Colgan (died 682) as the successor to Guaire.Only the "Chronicum Scotorum" of the Irish annals mentions him as king of Connacht in his death obit.A number of annals record the death of his brother Cellach in 666 however during the plague years.The "Annals of Innisfallen" records an event under the year 665 in which the Connachta fought a battle with the Munstermen at Loch Fén(Loughfane, Limerick,Co.)but there is no mention of who won or whether it was fought by the Connachta or just the Ui Fiachrach Aidhne. [SEP] Knowledge 2: Guaire Aidne mac Colmáin
Guaire Aidne mac Colmáin (died 663) was a king of Connacht.A member of the Ui Fiachrach Aidhne and son of king Colmán mac Cobthaig (died 622).Guaire ruled at the height of Ui Fiachrach Aidne power in south Connacht.
Knowledge 1: Muirchertach Nár mac Guairi
Muirchertach Nár mac Guairi (died 668) was a possible King of Connacht from the Ui Fiachrach Aidhne branch of the Connachta.He was the son of Guaire Aidne mac Colmáin (died 663), famous in Irish sagas.The Irish king lists such ascontained in "The Book of Leinster" do not list Muirchertach as king but have instead Cenn Fáelad mac Colgan (died 682) as the successor to Guaire.Only the "Chronicum Scotorum" of the Irish annals mentions him as king of Connacht in his death obit.A number of annals record the death of his brother Cellach in 666 however during the plague years.The "Annals of Innisfallen" records an event under the year 665 in which the Connachta fought a battle with the Munstermen at Loch Fén(Loughfane, Limerick,Co.)but there is no mention of who won or whether it was fought by the Connachta or just the Ui Fiachrach Aidhne. [SEP] Knowledge 2: Cenn Fáelad mac Colgan
Cenn Fáelad mac Colgan (died 682) was a King of Connacht from the Uí Briúin branch of the Connachta.He was of the branch which developed into the Uí Briúin Seóla, who were centred on Tuam in modern County Galway.He is the first member of this branch mentioned in the annals.The first mention of Cenn Fáelad in the annals is in the year 653 when the ally of the Ui Fiachrach Aidhne, Marcán mac Tomaini, the king of the Ui Maine was slain in battle in Iarthair Seola by Cenn Fáelad and Máenach mac Báethíne of the Uí Briúin.In the "Annals of the Four Masters" it is Maenach who is referred to as chief of the Uí Briúin.The next mention of Cenn Fáelad is in 663 when the "Annals of Tigernach" mention that he became king of Connacht in succession to Guaire Aidne mac Colmáin (died 663).The king lists such as that in the "Book of Leinster" also place his reign after Guaire.However, the "Chronicum Scotorum" mentions the death of Muirchertach Nár mac Guairi (died 668) as king of Connacht in 668.The annals also mention a certain Dub-Indracht mac Dúnchada as king of the Uí Briúin of Mag nAi in 666.The last mention of Cenn Fáelad in the annals is in 682 when he was killed by Ulcha Dearg ua Caillidhe of the Conmhaícne Cúile, a subject tribe of the Seóla region.Francis Byrne believed this killing was in response to the Uí Briúin policy of subjugation and annexation of subject tribal territories.Cenn Fáelad's descendants included the Muintir Murchadha and their chief, the O'Flaherty, through his son Amhalgadh, sometimes titled kings of Iarthair Connacht in the annals; and the Clann Cosgraigh, headed by McHugh, through Cenn Fáelad's son Dungalaigh.
Knowledge 1: Guaire Aidne mac Colmáin
Guaire Aidne mac Colmáin (died 663) was a king of Connacht.A member of the Ui Fiachrach Aidhne and son of king Colmán mac Cobthaig (died 622).Guaire ruled at the height of Ui Fiachrach Aidne power in south Connacht. [SEP] Knowledge 2: Cenn Fáelad mac Colgan
Cenn Fáelad mac Colgan (died 682) was a King of Connacht from the Uí Briúin branch of the Connachta.He was of the branch which developed into the Uí Briúin Seóla, who were centred on Tuam in modern County Galway.He is the first member of this branch mentioned in the annals.The first mention of Cenn Fáelad in the annals is in the year 653 when the ally of the Ui Fiachrach Aidhne, Marcán mac Tomaini, the king of the Ui Maine was slain in battle in Iarthair Seola by Cenn Fáelad and Máenach mac Báethíne of the Uí Briúin.In the "Annals of the Four Masters" it is Maenach who is referred to as chief of the Uí Briúin.The next mention of Cenn Fáelad is in 663 when the "Annals of Tigernach" mention that he became king of Connacht in succession to Guaire Aidne mac Colmáin (died 663).The king lists such as that in the "Book of Leinster" also place his reign after Guaire.However, the "Chronicum Scotorum" mentions the death of Muirchertach Nár mac Guairi (died 668) as king of Connacht in 668.The annals also mention a certain Dub-Indracht mac Dúnchada as king of the Uí Briúin of Mag nAi in 666.The last mention of Cenn Fáelad in the annals is in 682 when he was killed by Ulcha Dearg ua Caillidhe of the Conmhaícne Cúile, a subject tribe of the Seóla region.Francis Byrne believed this killing was in response to the Uí Briúin policy of subjugation and annexation of subject tribal territories.Cenn Fáelad's descendants included the Muintir Murchadha and their chief, the O'Flaherty, through his son Amhalgadh, sometimes titled kings of Iarthair Connacht in the annals; and the Clann Cosgraigh, headed by McHugh, through Cenn Fáelad's son Dungalaigh.

Answer: Colmán mac Cobthaig