Указать время под каждой цифрой. (Past.simple,Past.cont ,Pas.perfect Pas.per.con) The Search for the Lost City

When Professor Mallory, the famous archaeologist,(1)invited me to take part in his expedition to find the Lost City of the Himalayas, 1(2)did not hesitate to accept
his invitation. Mallory (3)had discovered an ancient map showing the position of the city, although no European (4)had ever gone to the area before. In fact, most of Mallory's colleagues either (5)believed that the city(6)had never existed or (7)felt that it(8)vanished long ago and (9)became simply a legend. According to the Professor, the builders of the city(10)had hidden) it among the mountains in order to protect its immense riches. He(11)believed that the descendants of these ancient people(12)were still keeping themselves apart from the rest of mankind for the very same reasons. So when we (13)set off on a cool May morning towards the distant mountains, each of us (14)was looking forward to exciting discoveries. For a week or more we (15)were climbing higher and higher, following the map, which Mallory(16)studied from time to time. Then one afternoon, while we(17)were resting
(rest) at the top of a valley, we (18)noticed that a rider on a horse(19)was waving at us from the other side of the valley. A rider whose clothes(20)were shining like gold