other peoples of the region, including Heruli, Suebi, Gepids, Thuringii, Bulgars, Sarmatians, the remaining Romans and a few Ostrogoths. But the most important group, other than the Lombards, were the Saxons, of whom 20,000 male warriors with their families participated in the trek. These Saxons were tributaries to the Frankish King Sigebert, and their participation indicates that Alboin had the support of the Franks for his venture. The precise size of the heterogeneous group gathered by Alboin is impossible to know, and many different estimates have been made. Neil Christie considers 150,000 to be a realistic size, a number which would make the Lombards a more numerous force than the Ostrogoths on the eve of their invasion of Italy. Jörg Jarnut proposes 100,000–150,000 as an approximation; Wilfried Menghen in Die Langobarden estimates 150,000 to 200,000; while Stefano Gasparri cautiously judges the peoples united by Alboin to be somewhere between 100,000 and 300,000. As a precautionary move Alboin strengthened his alliance with the Avars, signing what Paul calls a foedus perpetuum ("perpetual treaty") and what is referred to in the 9th-century Historia Langobardorum codicis Gothani as a pactum et foedus amicitiae ("pact and treaty of friendship"), adding that the treaty was put down on paper. By the conditions accepted in the treaty, the Avars were to take possession of Pannonia and the Lombards were promised military support in Italy should the need arise; also, for a period of 200 years the Lombards were to maintain the right to reclaim their former territories if the plan to conquer Italy failed, thus leaving Alboin with an alternative open. The accord also had the advantage of protecting Alboin's rear, as an Avar-occupied Pannonia would make it difficult for the Byzantines to bring forces to Italy by land. The agreement proved immensely successful, and relations with the Avars were almost uninterruptedly friendly during the lifetime of the Lombard Kingdom. A further cause of the Lombard migration into Italy may have been an invitation from Narses. According to a controversial tradition reported by several medieval sources, Narses, out of spite for having been removed by Justinian's successor Justin II, called the Lombards to Italy. Often dismissed as an unreliable tradition, it has been studied with attention by modern scholars, in particular Neil Christie, who see in it a possible record of a formal invitation by the Byzantine state to settle in northern Italy as foederati, to