The inheritance of Japanese morning glory (日本牵牛花）flower color is controlled by two independtly genes and their interaction type is addive effect. The flowers with A_B_ are bule, flowers with aabb are red, flowers with A_bb and aaB_ are purple. When the F1 generated from two purple homozygous plant cross AAbb ×aaBB backcoss with one of the parant, what are the phentoype and their proportians of the progeny?