Following the Spanish conquest of the Inca Empire in the 1530s, a few members of the royal family established the small independent Neo-Inca State in Vilcabamba, which was located in the relatively inaccessible Upper Amazon to the northeast of Cusco. The founder of this state was Manco Inca Yupanqui , who had initially allied himself with the Spanish, then led an unsuccessful war against them before establishing himself in Vilcabamba in 1540. After a Spanish attack in 1544 in which Manco Inca Yupanqui was killed, his son Sayri Tupac assumed the title of Sapa Inca , before accepting Spanish authority in 1558, moving to Cuzco, and dying  in 1561.  He was succeeded in Vilcabamba by his brother Titu Cusi, who himself died in 1571. Túpac Amaru, another brother of the two preceding emperors, then succeeded to the title in Vilcabamba.. How many years after  Manco Inca Yupanqui died did his son die?