Hywel ap Ieuaf
Hywel ap Ieuaf (died 985) was a King of Gwynedd in north-west Wales from 979 to 985.
Hywel was the son of Ieuaf ap Idwal who had ruled Gwynedd jointly with his brother Iago ab Idwal until 969.
In that year the sons of Idwal quarrelled and Iago took Ieuaf prisoner.
Hywel is first recorded as accompanying Iago to Chester to meet King Edgar of England in 973, when together with a number of other kings including the kings of Scotland and of Strathclyde he pledged that he would be the king's henchmen on sea and land.
Later chroniclers made the kings into eight, all plying the oars of Edgar's state barge on the River Dee.
In 974 Hywel raised an army and drove his uncle from Gwynedd temporarily.
Iago was able to return, but was forced to share power with his nephew.
In 978 Hywel made another attempt to take the kingdom from his uncle, raiding the monastery at Clynnog Fawr.
In this raid Hywel was assisted by English troops, possibly provided by Aelfhere, Earl of Mercia.
Hywel defeated Iago in battle in 979, and the same year Iago was captured by a force of Vikings, possibly in Hywel's pay, and vanished from the scene.
Hywel was left as sole ruler of Gwynedd, but apparently did not set his father free, since according to J.E. Lloyd, Ieuaf remained in captivity until 988.
In 980 Hywel faced a challenge from Iago's son, Custennin ab Iago, who attacked Anglesey in alliance with Gofraid mac Arailt, a Viking chief from the Isle of Man.
Hywel defeated them in battle, killing Custennin and putting Gofraid and his men to flight.
Now securely in possession of Gwynedd, Hywel aimed to expand his kingdom to the south.
He again made an alliance with Aelfhere of Mercia and attacked Brycheiniog and Morgannwg with some success, although he was not able to annex these kingdoms.
However, in 985 his English allies turned on him and killed him, possibly alarmed by his growing power.
He was succeeded by his brother Cadwallon ap Ieuaf, who had not been on the throne long when Gwynedd was annexed by Maredudd ap Owain of Deheubarth.
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Ieuaf
Idwal ab Idwal (died 988), usually known as Ieuaf  to distinguish him from his father Idwal Foel, was joint king of Gwynedd in northern Wales from 950 to 969.
He possibly also ruled Powys for some time.
Ieuaf was a son of King Idwal the Bald.
Upon his father's death in battle against the Anglo-Saxons in 942, he and his brother Iago were driven from their kingdom by their uncle Hywel Dda of Deheubarth, who took the crown for himself.
On Hywel's death in 950, Ieuaf and Iago were able to drive out Hywel's sons, their cousins, at the Battle of Carno and reclaim the kingdom.
However, fighting continued, with the brothers raiding as far south as Dyfed in 952 and their cousins raiding as far north as the Conwy valley in 954.
The southern princes were finally defeated at the Battle of Llanrwst and chased back to Ceredigion.
Having won, the brothers then began to quarrel among themselves.
Iago took Ieuaf prisoner in 969, and Ieuaf played no further role in Gwynedd.
Iago ruled another decade before Ieuaf's son Hywel usurped him in 979; according to historian John Edward Lloyd, Ieuaf remained in captivity until his death in 988.
Rhodri ap Hywel
Rhodri ap Hywel( died 953) was a King of Deheubarth in South Wales, and son of Hywel Dda.
On Hywel's death in 950 Deheubarth was shared between Rhodri and his two brothers, Edwin and Owain.
The sons of Hywel were not able to keep hold of Gwynedd, which was reclaimed for the traditional dynasty of Aberffraw by Iago ap Idwal and Ieuaf ap Idwal, the sons of Idwal Foel.
In 952 Iago and Ieuaf invaded the south, penetrating as far as Dyfed.
The sons of Hywel retaliated by invading the north in 954, reaching as far north as the Conwy valley before being defeated in a battle at Llanrwst and being obliged to retreat to Ceredigion.
Cynan ap Hywel
Cynan ap Hywel( ruled 999–1005) was a Prince of Gwynedd, one of the kingdoms or principalities of medieval Wales.
He was the son of Hywel ap Ieuaf, a previous king from the line of Idwal Foel( his grandfather).
On Hywel's death, the realm was ruled by his brother, but almost immediately was seized by Maredudd ab Owain.
After the death in 999 of Maredudd, the rule of Gwynedd returned to the original dynasty in the form of Cynan ap Hywel.
Cynan reigned until 1005 but very little has been recorded about his reign, and nothing is known about the circumstances in which he was supplanted by Aeddan ap Blegywryd, who was apparently out of the direct line of succession.
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Question: Who is Hywel Ap Ieuaf's paternal grandfather?
Answer: Idwal Foel