Improving User Profiles for E-Commerce by Genetic Algorithms Yoda maintains numerous recommendation lists obt ained from human ex perts, clusters of user evaluations, and web navigation patterns analy zed by lustering and content analysis techniques. During the online process, the onfidence values of an active user to the experts are estimated and kept in the user profile. By utilizing the user profile and experts'recommenda tions, Yoda finally generates customized recommendations for the user. As a result, we reduce the time complexity through model based and clustering ap- proaches, alleviate the synonymy problem with content analysis, and address he sparsity problem by implicit identification of the users interests 5, 6 Since Yoda relies on user profiles to recommend products, the accuracy of recommendation results will decline if the user profiles are inaccurate. In practice, obtaining user profiles by explicit acquisitions has been challenging. We utilized the users'relevance feedback and improved the profiles automat ically using GA [4]. To the best of our knowledge, only a few studies [3, 2] rate ga fo the user profiles. In the directly involved in the evolution processes. Because users have to enter data for each product inquiry, they are often frustrated with this method. On the contrary . in design, users are not required to offer additional dat to improve the confidence values. These confidence values are corrected by the gA-based learning mechanisms using users' future navigation behaviors That is, Yoda assumes positive feedback from a user when the user actually navigates through Yoda's recommended items. Our experimental results in dicate a to the integration of the proposed learning mechanism The remainder of this paper is organized as follows. Section 2 describes the concept of genetic algorithms. In Section 3, we provide an overview the functionality of Yoda. In Section 4, we discuss the detailed design of Yoda and the learning mechanism. The results of our evaluations as well as he details of the sy stem implementation and our benchmarking method are described in Section 5. Section 6 concludes the paper 2 Genetic algorithms Genetic algorithms(GAs), which were introduced by Holland [4, are itera- tive search techniques based on the spirit of natural evolution. By emulating biological selection and reproduction, GAs can efficiently search through the solution space of complex problems. Basically, a Ga operates on a popu- lation of candidate solutions called chromosomes. A chromosome which composed of numerous genes, represents an encoding of the problem and as sociates it with a fitness value evaluated by the fitness function This fitness value determines the goodness and the survival ability of the chromosome Generally, Ga starts by initializing the population and evaluating its cor- responding fitness values. Before it terminates, Ga produces newer genera- tions iteratively At each generation, a portion of the chromosomes is selected❙❯❢❣❧❛❩❇❥✣s✦❵❚♥❨✡r✐❞q❳P❩ ☎❩❇❥✍➦❉③ ❳✽❞✟✉④❥✍❩✸❽❁❸❡❤✕❥❦❢❣❢❣❳P❩❇♦✽❳✸➝❲❝✮➺✐❳✽❚♥❳P❱❇❵ ♦✖⑦❍③❨❦❥✍❩❇❵❱❇✇♥❢❣❞ ✝ ❂✼➱⑧❑❊❏á✃①❏✦❃❋♥❒✽❏✦❃❋▲◗✮❋❉❖❊✃✵■✍◆P➱❛❖▲◗✧◆P■❦➮✣➱❛✃✵✃✵■✍❋▲❑❊❏❲❒P❃➱❛❋➯Ï ❃④◗❇❒✽◗✮➱❛❘⑧❒✽❏✦❃❋❊■❦❑ ❮➊◆P➱❛✃ ❈❉❖❊✃①❏✦❋➯■✣é❉❅ ß➩■✍◆❭❒✽◗✍❐➩➮✣Ï❖▲◗❇❒P■✍◆✽◗✸➱✦❮✟❖▲◗❭■✍◆✖■✍Ò❲❏✦Ï❖▲❏❲❒P❃➱❛❋▲◗✍❐❊❏✦❋▲❑✝ç✐■✍❘✝❋▲❏tÒ❉❃Ð♥❏❲❒P❃➱❛❋☞ß▲❏❲❒❭❒P■✍◆P❋▲◗✖❏✦❋▲❏✦Ï▼❉❰✍■❦❑➧❘❉▼ ➮✣Ï❖▲◗❇❒P■✍◆P❃❋❊Ðà❏✦❋▲❑⑩➮✣➱❛❋♥❒P■✍❋♥❒➢❏✦❋▲❏✦Ï▼⑧◗❭❃④◗✧❒P■❦➮✽❈❊❋❊❃④Ñ♥❖❊■❦◗✍ä✎✹✡❖❊◆P❃❋❊Ðá❒P❈❊■✿➱❛❋❊Ï ❃❋❊■✿ß❊◆P➱⑧➮✣■❦◗P◗✍❐②❒P❈❊■ ➮✣➱❛❋❆￾➩❑⑧■✍❋▲➮✣■✝Ò❲❏✦Ï❖❊■❦◗✵➱✦❮❣❏✦❋⑩❏❛➮❫❒P❃Ò❛■✝❖▲◗❭■✍◆✮❒P➱ ❒P❈❊■✿■✣é⑧ß➩■✍◆❭❒✽◗①❏✦◆P■☞■❦◗❇❒P❃✃①❏❲❒P■❦❑⑩❏✦❋▲❑➯Ó❛■✍ß⑧❒ ❃❋ ❒P❈❊■➧❖▲◗❭■✍◆✮ß❊◆P➱✥￾▲Ï■❛ä■✘✐▼ ❖⑧❒P❃ Ï ❃❰✍❃❋❊Ðå❒P❈❊■☞❖▲◗❭■✍◆✮ß❊◆P➱✥￾▲Ï■➧❏✦❋▲❑à■✣é⑧ß➩■✍◆❭❒✽◗✍ü✕◆P■❦➮✣➱❛✃✵✃✵■✍❋▲❑❊❏❲❅ ❒P❃➱❛❋▲◗✍❐♥❂✼➱⑧❑❊❏ ￾▲❋▲❏✦Ï Ï▼✵Ð❛■✍❋❊■✍◆✽❏❲❒P■❦◗✐➮✣❖▲◗❇❒P➱❛✃✵❃❰✍■❦❑➢◆P■❦➮✣➱❛✃✵✃✵■✍❋▲❑❊❏❲❒P❃➱❛❋▲◗✟❮➊➱❛◆✐❒P❈❊■❄❖▲◗❭■✍◆❦ä Þ◗✸❏ ◆P■❦◗❭❖❊Ï❒❦❐❦ç✐■✐◆P■❦❑⑧❖▲➮✣■✼❒P❈❊■❍❒P❃✃✵■✸➮✣➱❛✃✵ß❊Ï■✣é⑧❃❒❇▼❄❒P❈❊◆P➱❛❖❊Ð❛❈❣✃✵➱⑧❑⑧■✍Ï❉❘▲❏❛◗❭■❦❑✛❏✦❋▲❑✧➮✣Ï❖▲◗❇❒P■✍◆P❃❋❊Ð❄❏✦ß⑧❅ ß❊◆P➱♥❏❛➮✽❈❊■❦◗✍❐✦❏✦Ï Ï■✍Ò❉❃④❏❲❒P■✸❒P❈❊■✡◗❭▼❉❋❊➱❛❋❉▼❉✃✧▼✛ß❊◆P➱❛❘❊Ï■✍✃➫ç✱❃❒P❈➢➮✣➱❛❋♥❒P■✍❋♥❒❍❏✦❋▲❏✦Ï▼⑧◗❭❃④◗✍❐❛❏✦❋▲❑✵❏❛❑❊❑⑧◆P■❦◗P◗ ❒P❈❊■✛◗❭ß▲❏✦◆✽◗❭❃❒❇▼①ß❊◆P➱❛❘❊Ï■✍✃ ❘❉▼➧❃✃✵ß❊Ï ❃④➮✣❃❒✖❃④❑⑧■✍❋♥❒P❃￾➩➮✍❏❲❒P❃➱❛❋☞➱✦❮✕❒P❈❊■❣❖▲◗❭■✍◆✽◗✸❃❋♥❒P■✍◆P■❦◗❇❒✽◗✰✯ ✁ ❐ ✵✞✸❡ä ❆❉❃❋▲➮✣■✮❂✼➱⑧❑❊❏☞◆P■✍Ï ❃■❦◗➽➱❛❋✢❖▲◗❭■✍◆❣ß❊◆P➱✥￾▲Ï■❦◗✡❒P➱✝◆P■❦➮✣➱❛✃✵✃✵■✍❋▲❑✢ß❊◆P➱⑧❑⑧❖▲➮❫❒✽◗✍❐➤❒P❈❊■➢❏❛➮✍➮✣❖❊◆✽❏❛➮✣▼ ➱✦❮✼◆P■❦➮✣➱❛✃✵✃✵■✍❋▲❑❊❏❲❒P❃➱❛❋✝◆P■❦◗❭❖❊Ï❒✽◗✖ç✱❃ Ï Ï②❑⑧■❦➮✣Ï ❃❋❊■✧❃❮✟❒P❈❊■✮❖▲◗❭■✍◆✡ß❊◆P➱✥￾▲Ï■❦◗✖❏✦◆P■✛❃❋▲❏❛➮✍➮✣❖❊◆✽❏❲❒P■❛ä▲èq❋ ß❊◆✽❏❛➮❫❒P❃④➮✣■❛❐✦➱❛❘⑧❒✽❏✦❃❋❊❃❋❊Ð❣❖▲◗❭■✍◆✼ß❊◆P➱✥￾▲Ï■❦◗✟❘❉▼✮■✣é⑧ß❊Ï ❃④➮✣❃❒✐❏❛➮✍Ñ♥❖❊❃④◗❭❃❒P❃➱❛❋▲◗✟❈▲❏❛◗✟❘➩■✍■✍❋➢➮✽❈▲❏✦Ï Ï■✍❋❊Ð❛❃❋❊Ð▲ä ûá■✡❖⑧❒P❃ Ï ❃❰✍■❦❑✵❒P❈❊■✡❖▲◗❭■✍◆✽◗✍ü✦◆P■✍Ï■✍Ò❲❏✦❋▲➮✣■✱❮➊■✍■❦❑⑧❘▲❏❛➮✽Ó✵❏✦❋▲❑✵❃✃✵ß❊◆P➱❲Ò❛■❦❑✧❒P❈❊■✡ß❊◆P➱✥￾▲Ï■❦◗❍❏✦❖⑧❒P➱❛✃①❏❲❒❭❅ ❃④➮✍❏✦Ï Ï▼á❖▲◗❭❃❋❊ÐP✮Þ ✯✲✥✸❡ä✕æ✈➱✿❒P❈❊■➧❘➩■❦◗❇❒✮➱✦❮✱➱❛❖❊◆✛Ó❉❋❊➱❲ç✱Ï■❦❑⑧Ð❛■❛❐✂➱❛❋❊Ï▼ ❏✝❮➊■✍ç ◗❇❒P❖▲❑⑧❃■❦◗✚✯❚❊❐ ✷✤✸ ❃❋▲➮✣➱❛◆Pß➩➱❛◆✽❏❲❒P■✚✮Þ ❮➊➱❛◆✮❃✃✵ß❊◆P➱❲Ò❉❃❋❊Ð✿❒P❈❊■➧❖▲◗❭■✍◆✮ß❊◆P➱✥￾▲Ï■❦◗✍ä✈èq❋à❒P❈❊■❦◗❭■☞◗❇❒P❖▲❑⑧❃■❦◗✍❐②❖▲◗❭■✍◆✽◗✧❏✦◆P■ ❑⑧❃ ◆P■❦➮❫❒PÏ▼✮❃❋❉Ò❛➱❛ÏÒ❛■❦❑✮❃❋①❒P❈❊■✖■✍Ò❛➱❛Ï❖⑧❒P❃➱❛❋①ß❊◆P➱⑧➮✣■❦◗P◗❭■❦◗✍ä❉✘✐■❦➮✍❏✦❖▲◗❭■✱❖▲◗❭■✍◆✽◗✟❈▲❏tÒ❛■✸❒P➱✧■✍❋♥❒P■✍◆❍❑❊❏❲❒✽❏ ❮➊➱❛◆➧■❦❏❛➮✽❈⑩ß❊◆P➱⑧❑⑧❖▲➮❫❒➧❃❋▲Ñ♥❖❊❃ ◆P▼❛❐✼❒P❈❊■✍▼✫❏✦◆P■✿➱✦❮➀❒P■✍❋⑩❮➊◆P❖▲◗❇❒P◆✽❏❲❒P■❦❑⑩ç✱❃❒P❈✫❒P❈❊❃④◗➢✃✵■✣❒P❈❊➱⑧❑❁ä ✺❋ ❒P❈❊■☞➮✣➱❛❋♥❒P◆✽❏✦◆P▼❛❐✂❃❋ ➱❛❖❊◆✵❑⑧■❦◗❭❃Ð❛❋✂❐✈❖▲◗❭■✍◆✽◗✧❏✦◆P■➢❋❊➱✦❒✮◆P■❦Ñ♥❖❊❃ ◆P■❦❑á❒P➱✢➱✦â➤■✍◆✮❏❛❑❊❑⑧❃❒P❃➱❛❋▲❏✦Ï✐❑❊❏❲❒✽❏ ❒P➱✿❃✃✵ß❊◆P➱❲Ò❛■✮❒P❈❊■➧➮✣➱❛❋❆￾➩❑⑧■✍❋▲➮✣■✵Ò❲❏✦Ï❖❊■❦◗✍ä✈æ✸❈❊■❦◗❭■➢➮✣➱❛❋❆￾➩❑⑧■✍❋▲➮✣■①Ò❲❏✦Ï❖❊■❦◗✛❏✦◆P■①➮✣➱❛◆P◆P■❦➮❫❒P■❦❑✢❘❉▼ ❒P❈❊■✰✮Þ❅❡❘▲❏❛◗❭■❦❑➢Ï■❦❏✦◆P❋❊❃❋❊Ð✧✃✵■❦➮✽❈▲❏✦❋❊❃④◗❭✃①◗❍❖▲◗❭❃❋❊Ð✮❖▲◗❭■✍◆✽◗✍ü❛❮➊❖⑧❒P❖❊◆P■❄❋▲❏tÒ❉❃Ð♥❏❲❒P❃➱❛❋①❘➩■✍❈▲❏tÒ❉❃➱❛◆✽◗✍ä æ✸❈▲❏❲❒✖❃④◗✍❐⑧❂✼➱⑧❑❊❏①❏❛◗P◗❭❖❊✃✵■❦◗✸ß➩➱♥◗❭❃❒P❃Ò❛■❄❮➊■✍■❦❑⑧❘▲❏❛➮✽Ó①❮➊◆P➱❛✃✥❏✵❖▲◗❭■✍◆✱ç✱❈❊■✍❋☞❒P❈❊■❣❖▲◗❭■✍◆✡❏❛➮❫❒P❖▲❏✦Ï Ï▼ ❋▲❏tÒ❉❃Ð♥❏❲❒P■❦◗✸❒P❈❊◆P➱❛❖❊Ð❛❈✝❂✼➱⑧❑❊❏❊ü ◗✖◆P■❦➮✣➱❛✃✵✃✵■✍❋▲❑⑧■❦❑✝❃❒P■✍✃①◗✍ä ✺❖❊◆✡■✣é⑧ß➩■✍◆P❃✃✵■✍❋♥❒✽❏✦Ï✈◆P■❦◗❭❖❊Ï❒✽◗✖❃❋⑧❅ ❑⑧❃④➮✍❏❲❒P■①❏☞◗❭❃Ð❛❋❊❃￾➩➮✍❏✦❋♥❒➽❃❋▲➮✣◆P■❦❏❛◗❭■✮❃❋✢❒P❈❊■①❏❛➮✍➮✣❖❊◆✽❏❛➮✣▼✝➱✦❮✐◆P■❦➮✣➱❛✃✵✃✵■✍❋▲❑❊❏❲❒P❃➱❛❋å◆P■❦◗❭❖❊Ï❒✽◗❣❑⑧❖❊■ ❒P➱✵❒P❈❊■➽❃❋♥❒P■✍Ð❛◆✽❏❲❒P❃➱❛❋☞➱✦❮✈❒P❈❊■❣ß❊◆P➱❛ß➩➱♥◗❭■❦❑➧Ï■❦❏✦◆P❋❊❃❋❊Ð✮✃✵■❦➮✽❈▲❏✦❋❊❃④◗❭✃✝ä æ✸❈❊■✮◆P■✍✃①❏✦❃❋▲❑⑧■✍◆➽➱✦❮❍❒P❈❊❃④◗➽ß▲❏✦ß➩■✍◆➽❃④◗➽➱❛◆PÐ♥❏✦❋❊❃❰✍■❦❑å❏❛◗✡❮➊➱❛Ï Ï➱❲ç✖◗✍ä❁❆❉■❦➮❫❒P❃➱❛❋ ✷➧❑⑧■❦◗P➮✣◆P❃❘➩■❦◗ ❒P❈❊■➢➮✣➱❛❋▲➮✣■✍ß⑧❒❣➱✦❮✐Ð❛■✍❋❊■✣❒P❃④➮①❏✦ÏÐ❛➱❛◆P❃❒P❈❊✃①◗✍ä➤èq❋à❆❉■❦➮❫❒P❃➱❛❋❵❚❊❐✂ç✐■✵ß❊◆P➱❲Ò❉❃④❑⑧■✵❏✦❋á➱❲Ò❛■✍◆PÒ❉❃■✍ç ➱❛❋ ❒P❈❊■✿❮➊❖❊❋▲➮❫❒P❃➱❛❋▲❏✦Ï ❃❒❇▼⑩➱✦❮➽❂✼➱⑧❑❊❏❊ä❍èq❋ ❆❉■❦➮❫❒P❃➱❛❋ ✲▲❐❍ç✐■å❑⑧❃④◗P➮✣❖▲◗P◗①❒P❈❊■✢❑⑧■✣❒✽❏✦❃ Ï■❦❑✫❑⑧■❦◗❭❃Ð❛❋✫➱✦❮ ❂✼➱⑧❑❊❏➢❏✦❋▲❑✝❒P❈❊■✧Ï■❦❏✦◆P❋❊❃❋❊Ð①✃✵■❦➮✽❈▲❏✦❋❊❃④◗❭✃✝ä➩æ✸❈❊■✧◆P■❦◗❭❖❊Ï❒✽◗✖➱✦❮✟➱❛❖❊◆✡■✍Ò❲❏✦Ï❖▲❏❲❒P❃➱❛❋▲◗✖❏❛◗✖ç✐■✍Ï Ï②❏❛◗ ❒P❈❊■❣❑⑧■✣❒✽❏✦❃ Ï④◗✸➱✦❮✈❒P❈❊■❣◗❭▼⑧◗❇❒P■✍✃ ❃✃✵ß❊Ï■✍✃✵■✍❋♥❒✽❏❲❒P❃➱❛❋✝❏✦❋▲❑➧➱❛❖❊◆✸❘➩■✍❋▲➮✽❈❊✃①❏✦◆PÓ❉❃❋❊Ð✮✃✵■✣❒P❈❊➱⑧❑☞❏✦◆P■ ❑⑧■❦◗P➮✣◆P❃❘➩■❦❑➧❃❋å❆❉■❦➮❫❒P❃➱❛❋ ✁ ä▲❆❉■❦➮❫❒P❃➱❛❋ ✵✵➮✣➱❛❋▲➮✣Ï❖▲❑⑧■❦◗✐❒P❈❊■❣ß▲❏✦ß➩■✍◆❦ä ✂ ✄✆☎✈Ö✝☎❁×❊Ý❭Ü✟✞✆✠☛✡✼Ù✼Ø▲Ýq×✌☞✎✍✑✏ ✮❄■✍❋❊■✣❒P❃④➮✮❏✦ÏÐ❛➱❛◆P❃❒P❈❊✃①◗★✜✡✮Þ◗☞✣❫❐❁ç✱❈❊❃④➮✽❈åç✐■✍◆P■✧❃❋♥❒P◆P➱⑧❑⑧❖▲➮✣■❦❑✿❘❉▼✕✦✖➱❛Ï Ï④❏✦❋▲❑✁✯✲✥✸❡❐➤❏✦◆P■✧❃❒P■✍◆✽❏❲❅ ❒P❃Ò❛■➽◗❭■❦❏✦◆✽➮✽❈✵❒P■❦➮✽❈❊❋❊❃④Ñ♥❖❊■❦◗✐❘▲❏❛◗❭■❦❑①➱❛❋➢❒P❈❊■➽◗❭ß❊❃ ◆P❃❒✸➱✦❮✈❋▲❏❲❒P❖❊◆✽❏✦Ï➩■✍Ò❛➱❛Ï❖⑧❒P❃➱❛❋✂ä✙✘✐▼✵■✍✃✧❖❊Ï④❏❲❒P❃❋❊Ð ❘❊❃➱❛Ï➱❛Ð❛❃④➮✍❏✦Ï➤◗❭■✍Ï■❦➮❫❒P❃➱❛❋➧❏✦❋▲❑➢◆P■✍ß❊◆P➱⑧❑⑧❖▲➮❫❒P❃➱❛❋✂❐❆✮Þ◗✱➮✍❏✦❋➢■✣ã➢➮✣❃■✍❋♥❒PÏ▼➧◗❭■❦❏✦◆✽➮✽❈✵❒P❈❊◆P➱❛❖❊Ð❛❈➢❒P❈❊■ ◗❭➱❛Ï❖⑧❒P❃➱❛❋⑩◗❭ß▲❏❛➮✣■✝➱✦❮❣➮✣➱❛✃✵ß❊Ï■✣é➯ß❊◆P➱❛❘❊Ï■✍✃①◗✍ä✑✘✸❏❛◗❭❃④➮✍❏✦Ï Ï▼❛❐✼❏ ✮Þ ➱❛ß➩■✍◆✽❏❲❒P■❦◗✵➱❛❋✫❏áß➩➱❛ß❊❖⑧❅ Ï④❏❲❒P❃➱❛❋à➱✦❮✡➮✍❏✦❋▲❑⑧❃④❑❊❏❲❒P■➧◗❭➱❛Ï❖⑧❒P❃➱❛❋▲◗✧➮✍❏✦Ï Ï■❦❑✫☎✽ô❉òPï❲ð①ïtí✍ï❲ð①ñ❫í❫ä Þ ➮✽❈❊◆P➱❛✃✵➱♥◗❭➱❛✃✵■❛❐✂ç✱❈❊❃④➮✽❈à❃④◗ ➮✣➱❛✃✵ß➩➱♥◗❭■❦❑➢➱✦❮✈❋❉❖❊✃✵■✍◆P➱❛❖▲◗✐Ð❛■✍❋❊■❦◗✍❐❉◆P■✍ß❊◆P■❦◗❭■✍❋♥❒✽◗✐❏✦❋➧■✍❋▲➮✣➱⑧❑⑧❃❋❊Ð✮➱✦❮✈❒P❈❊■➽ß❊◆P➱❛❘❊Ï■✍✃ ❏✦❋▲❑➧❏❛◗❇❅ ◗❭➱⑧➮✣❃④❏❲❒P■❦◗✐❃❒✖ç✱❃❒P❈✿❏★￾❊❒P❋❊■❦◗P◗✸Ò❲❏✦Ï❖❊■➽■✍Ò❲❏✦Ï❖▲❏❲❒P■❦❑☞❘❉▼①❒P❈❊■❩￾❊❒P❋❊■❦◗P◗✸❮➊❖❊❋▲➮❫❒P❃➱❛❋✂ä▲æ✸❈❊❃④◗❄￾❊❒P❋❊■❦◗P◗ Ò❲❏✦Ï❖❊■✛❑⑧■✣❒P■✍◆P✃✵❃❋❊■❦◗✐❒P❈❊■❣Ð❛➱❉➱⑧❑⑧❋❊■❦◗P◗✸❏✦❋▲❑➧❒P❈❊■✛◗❭❖❊◆PÒ❉❃Ò❲❏✦Ï✂❏✦❘❊❃ Ï ❃❒❇▼➢➱✦❮✈❒P❈❊■✛➮✽❈❊◆P➱❛✃✵➱♥◗❭➱❛✃✵■❛ä ✮❄■✍❋❊■✍◆✽❏✦Ï Ï▼❛❐❉✮Þ ◗❇❒✽❏✦◆❭❒✽◗✟❘❉▼✧❃❋❊❃❒P❃④❏✦Ï ❃❰✍❃❋❊Ð➽❒P❈❊■✖ß➩➱❛ß❊❖❊Ï④❏❲❒P❃➱❛❋①❏✦❋▲❑✵■✍Ò❲❏✦Ï❖▲❏❲❒P❃❋❊Ð❣❃❒✽◗✼➮✣➱❛◆❭❅ ◆P■❦◗❭ß➩➱❛❋▲❑⑧❃❋❊Ð ￾❊❒P❋❊■❦◗P◗❄Ò❲❏✦Ï❖❊■❦◗✍ä❀✘✐■✣❮➊➱❛◆P■✮❃❒❄❒P■✍◆P✃✵❃❋▲❏❲❒P■❦◗✍❐◆✮Þ ß❊◆P➱⑧❑⑧❖▲➮✣■❦◗❄❋❊■✍ç✐■✍◆➽Ð❛■✍❋❊■✍◆✽❏❲❅ ❒P❃➱❛❋▲◗②❃❒P■✍◆✽❏❲❒P❃Ò❛■✍Ï▼❛ä Þ❒✟■❦❏❛➮✽❈✮Ð❛■✍❋❊■✍◆✽❏❲❒P❃➱❛❋✂❐❲❏❄ß➩➱❛◆❭❒P❃➱❛❋✮➱✦❮▲❒P❈❊■✖➮✽❈❊◆P➱❛✃✵➱♥◗❭➱❛✃✵■❦◗✈❃④◗✟◗❭■✍Ï■❦➮❫❒P■❦❑