Wales was never one state, except for very short periods. Normally it was divided into three states, Gwynedd or North Wales, Powys or Mid-Wales, and Deheubarth, all almost incessantly at war with each other.[829] Other subdivisions asserted themselves as opportunity offered, so that the above rough division into provinces must not be regarded as always accurate. A Wales thus divided, and perpetually rent by internal conflicts, invited the aggression of the Saxons, and it is probable that the complete subjugation of Britain would have been accomplished by the descendants of Alfred, if it had not been for the Danish invasions. The position of the Welsh kings after the time of Athelstan seems to have been that of tributaries, who threw off their allegiance whenever it was possible to do so. But still the Anglo-Saxon frontier continued to advance. Professor Lloyd has shown, from a careful examination of Domesday Book, that even before the Norman Conquest the English held the greater part of what is now Flintshire and East Denbighshire, and were advancing into the vale of Montgomery and the Radnor district.[830] The victories of Griffith ap Llywelyn, an able prince who succeeded in bringing all Wales under his sway, devastated these English colonies; but his defeat by Earl Harold in 1063 restored the English ascendancy over these regions. The unimpeachable evidence of Domesday Book shows that a considerable district in North Wales and a portion of Radnor were held respectively by Earl Edwin and Earl Harold before the Norman Conquest. Moreover, the fact mentioned by the _Anglo-Saxon Chronicle_ in 1065, that Harold was building a hunting-seat for King Edward at Portskewet, _after he had subdued it_, suggests that the land between Wye and Usk, which Domesday Book reckons under Gloucestershire, was a conquest of Harold's.[831]