| Journal of Information and Communications Technology:
Algorithms, Systems and Applications
Received: 02 October 2025; Revised: 12 December 2025; Accepted: 13 December 2025; Published Online: 15 December 2025.
J. Inf. Commun. Technol. Algorithms Syst. Appl., 2025, 1(3), 25313 | Volume 1 Issue 3 (December 2025) | DOI: https://doi.org/10.64189/ict.25313
Β© The Author(s) 2025
This article is licensed under Creative Commons Attribution NonCommercial 4.0 International (CC-BY-NC 4.0)
Advanced Feature Engineering for Residential
Property Valuation: A Case Study on King County
Housing Data
Aditi Nagayach
1,*
and Atul Samadhiya
2
1
Data Science Institute, Frank J. Guarini School of Business, Saint Peters University, Jersey City, New Jersey, 07306, USA
2
Business Administration, Executive M.B.A. New England College, New Hampshire, 03242, USA
*Email: anagayach@saintpeters.edu (Aditi Nagayach)
Abstract
Accurate property valuation is critical for real estate markets, financial institutions, and urban planning.
Traditional appraisal methods are time-intensive and subjective, while complex machine learning models often
lack interpretability. This study addresses these challenges by developing an advanced linear regression
framework that balances predictive accuracy with model transparency through systematic feature engineering.
In this study, we present an advanced linear regression framework for residential property valuation using
comprehensive feature engineering techniques. Utilizing the King County House Sales dataset comprising
21,613 transactions from May 2014 to May 2015, we developed 40 engineered features including interaction
terms, polynomial features, ratio calculations, and location-based composites. After outlier removal using the
interquartile range method, our dataset consisted of 20,467 properties with 55 total features. The optimized
linear regression model achieved a test RΒ² of 0.7198 with a normalized root mean square error (NRMSE) of 0.20
(20% of mean property value) and mean absolute error of 82,626. Feature importance analysis revealed that
basement-to-living ratio, above-to-living ratio, and geographic coordinates were the most influential predictors.
Cross-validation demonstrated model stability with a mean RΒ² of 0.7316 (Β±0.0101). This research demonstrates
that strategic feature engineering can significantly enhance linear regression performance for real estate
valuation, achieving an average prediction error within 20% of property values while providing a transparent
and interpretable alternative to complex machine learning algorithms.
Keywords: Residential property valuation; Linear regression; Feature engineering; Real estate pricing;
Predictive modeling; Machine learning.
1. Introduction
ξ˜“ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξ˜ƒξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξŸ‘ξ˜ƒξšƒξšŽξš•ξš‘ξ˜ƒξšξšξš‘ξš™ξšξ˜ƒξšƒξš•ξ˜ƒξš”ξš‡ξšƒξšŽξ˜ƒξš‡ξš•ξš–ξšƒξš–ξš‡ξ˜ƒξšƒξš’ξš’ξš”ξšƒξš‹ξš•ξšƒξšŽξŸ‘ξ˜ƒξš‹ξš•ξ˜ƒξš–ξšŠξš‡ξ˜ƒξš•ξš›ξš•ξš–ξš‡ξšξšƒξš–ξš‹ξš…ξ˜ƒξš’ξš”ξš‘ξš…ξš‡ξš•ξš•ξ˜ƒξš‘ξšˆξ˜ƒξš†ξš‡ξš–ξš‡ξš”ξšξš‹ξšξš‹ξšξš‰ξ˜ƒξš–ξšŠξš‡ξ˜ƒξš‡ξš…ξš‘ξšξš‘ξšξš‹ξš…ξ˜ƒ
ξš˜ξšƒξšŽξš—ξš‡ξ˜ƒ ξš‘ξšˆξ˜ƒ ξš”ξš‡ξšƒξšŽξ˜ƒ ξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξ˜ƒ ξš„ξšƒξš•ξš‡ξš†ξ˜ƒ ξš‘ξšξ˜ƒ ξš‹ξš–ξš•ξ˜ƒ ξš’ξšŠξš›ξš•ξš‹ξš…ξšƒξšŽξ˜ƒ ξš…ξšŠξšƒξš”ξšƒξš…ξš–ξš‡ξš”ξš‹ξš•ξš–ξš‹ξš…ξš•ξŸ‘ξ˜ƒ ξšŽξš‘ξš…ξšƒξš–ξš‹ξš‘ξšξŸ‘ξ˜ƒ ξšξšƒξš”ξšξš‡ξš–ξ˜ƒ ξš…ξš‘ξšξš†ξš‹ξš–ξš‹ξš‘ξšξš•ξŸ‘ξ˜ƒ ξšƒξšξš†ξ˜ƒ ξš…ξš‘ξšξš’ξšƒξš”ξšƒξš„ξšŽξš‡ξ˜ƒ
ξš–ξš”ξšƒξšξš•ξšƒξš…ξš–ξš‹ξš‘ξšξš•ξŸ€
ξ₯³ξŸ‘ξ₯΄ξ 
ξ˜ƒξ˜—ξšŠξš‹ξš•ξ˜ƒξšƒξš•ξš•ξš‡ξš•ξš•ξšξš‡ξšξš–ξ˜ƒξš•ξš‡ξš”ξš˜ξš‡ξš•ξ˜ƒξšƒξš•ξ˜ƒξš–ξšŠξš‡ξ˜ƒξšˆξš‘ξš—ξšξš†ξšƒξš–ξš‹ξš‘ξšξ˜ƒξšˆξš‘ξš”ξ˜ƒξšξš—ξšξš‡ξš”ξš‘ξš—ξš•ξ˜ƒξ§ξš‹ξšξšƒξšξš…ξš‹ξšƒξšŽξ˜ƒξšƒξšξš†ξ˜ƒξšƒξš†ξšξš‹ξšξš‹ξš•ξš–ξš”ξšƒξš–ξš‹ξš˜ξš‡ξ˜ƒξš†ξš‡ξš…ξš‹ξš•ξš‹ξš‘ξšξš•ξ˜ƒ
ξš‹ξšξ˜ƒ ξš–ξšŠξš‡ξ˜ƒ ξšŠξš‘ξš—ξš•ξš‹ξšξš‰ξ˜ƒ ξšξšƒξš”ξšξš‡ξš–ξŸ€ξ˜ƒ ξ˜•ξš‡ξš•ξš‹ξš†ξš‡ξšξš–ξš‹ξšƒξšŽξ˜ƒ ξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξ˜ƒ ξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξ˜ƒ ξš•ξš’ξš‡ξš…ξš‹ξ§ξš‹ξš…ξšƒξšŽξšŽξš›ξ˜ƒ ξšˆξš‘ξš…ξš—ξš•ξš‡ξš•ξ˜ƒ ξš‘ξšξ˜ƒ ξš•ξš‹ξšξš‰ξšŽξš‡ξŸ¦ξšˆξšƒξšξš‹ξšŽξš›ξ˜ƒ ξšŠξš‘ξšξš‡ξš•ξŸ‘ξ˜ƒ
ξš…ξš‘ξšξš†ξš‘ξšξš‹ξšξš‹ξš—ξšξš•ξŸ‘ξ˜ƒξš–ξš‘ξš™ξšξšŠξš‘ξš—ξš•ξš‡ξš•ξŸ‘ξ˜ƒξšƒξšξš†ξ˜ƒξš‘ξš–ξšŠξš‡ξš”ξ˜ƒξš†ξš™ξš‡ξšŽξšŽξš‹ξšξš‰ξ˜ƒξš—ξšξš‹ξš–ξš•ξŸ€
ξ₯΅ξŸ‘ξ₯Άξ 
ξ˜ƒξš”ξš‡ξš“ξš—ξš‹ξš”ξš‹ξšξš‰ξ˜ƒξš…ξšƒξš”ξš‡ξšˆξš—ξšŽξ˜ƒξš…ξš‘ξšξš•ξš‹ξš†ξš‡ξš”ξšƒξš–ξš‹ξš‘ξšξ˜ƒξš‘ξšˆξ˜ƒξš•ξš–ξš”ξš—ξš…ξš–ξš—ξš”ξšƒξšŽξ˜ƒξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξ˜ƒ
ξ ‹ξš•ξš“ξš—ξšƒξš”ξš‡ξ˜ƒ ξšˆξš‘ξš‘ξš–ξšƒξš‰ξš‡ξŸ‘ξ˜ƒ ξšξš—ξšξš„ξš‡ξš”ξ˜ƒ ξš‘ξšˆξ˜ƒ ξš„ξš‡ξš†ξš”ξš‘ξš‘ξšξš•ξ˜ƒ ξšƒξšξš†ξ˜ƒ ξš„ξšƒξš–ξšŠξš”ξš‘ξš‘ξšξš•ξŸ‘ξ˜ƒ ξš…ξš‘ξšξš•ξš–ξš”ξš—ξš…ξš–ξš‹ξš‘ξšξ˜ƒ ξš“ξš—ξšƒξšŽξš‹ξš–ξš›ξ ŒξŸ‘ξ˜ƒ ξšŽξš‘ξš…ξšƒξš–ξš‹ξš‘ξšξšƒξšŽξ˜ƒ ξšƒξš–ξš–ξš”ξš‹ξš„ξš—ξš–ξš‡ξš•ξ˜ƒ
ξ ‹ξšξš‡ξš‹ξš‰ξšŠξš„ξš‘ξš”ξšŠξš‘ξš‘ξš†ξ˜ƒξš…ξšŠξšƒξš”ξšƒξš…ξš–ξš‡ξš”ξš‹ξš•ξš–ξš‹ξš…ξš•ξŸ‘ξ˜ƒξš’ξš”ξš‘ξššξš‹ξšξš‹ξš–ξš›ξ˜ƒξš–ξš‘ξ˜ƒξšƒξšξš‡ξšξš‹ξš–ξš‹ξš‡ξš•ξŸ‘ξ˜ƒξš•ξš…ξšŠξš‘ξš‘ξšŽξ˜ƒξš†ξš‹ξš•ξš–ξš”ξš‹ξš…ξš–ξš•ξ ŒξŸ‘ξ˜ƒξšƒξšξš†ξ˜ƒξš–ξš‡ξšξš’ξš‘ξš”ξšƒξšŽξ˜ƒξšˆξšƒξš…ξš–ξš‘ξš”ξš•ξ˜ƒξ ‹ξšƒξš‰ξš‡ξ˜ƒξš‘ξšˆξ˜ƒξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξŸ‘ξ˜ƒ
ξš”ξš‡ξš…ξš‡ξšξš–ξ˜ƒξš”ξš‡ξšξš‘ξš˜ξšƒξš–ξš‹ξš‘ξšξš•ξŸ‘ξ˜ƒξšξšƒξš”ξšξš‡ξš–ξ˜ƒξš–ξš”ξš‡ξšξš†ξš•ξ ŒξŸ€ξ˜ƒξ˜—ξšŠξš‡ξ˜ƒξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξ˜ƒξš’ξš”ξš‘ξš…ξš‡ξš•ξš•ξ˜ƒξš–ξš”ξšƒξš†ξš‹ξš–ξš‹ξš‘ξšξšƒξšŽξšŽξš›ξ˜ƒξš‹ξšξš˜ξš‘ξšŽξš˜ξš‡ξš•ξ˜ƒξš–ξšŠξš”ξš‡ξš‡ξ˜ƒξš’ξš”ξš‹ξšξšƒξš”ξš›ξ˜ƒξšƒξš’ξš’ξš”ξš‘ξšƒξš…ξšŠξš‡ξš•ξŸ£ξ˜ƒξš–ξšŠξš‡ξ˜ƒ
ξš•ξšƒξšŽξš‡ξš•ξ˜ƒξš…ξš‘ξšξš’ξšƒξš”ξš‹ξš•ξš‘ξšξ˜ƒξšƒξš’ξš’ξš”ξš‘ξšƒξš…ξšŠξŸ‘ξ˜ƒξš™ξšŠξš‹ξš…ξšŠξ˜ƒξšƒξšξšƒξšŽξš›ξšœξš‡ξš•ξ˜ƒξš”ξš‡ξš…ξš‡ξšξš–ξ˜ƒξš–ξš”ξšƒξšξš•ξšƒξš…ξš–ξš‹ξš‘ξšξš•ξ˜ƒξš‘ξšˆξ˜ƒξš•ξš‹ξšξš‹ξšŽξšƒξš”ξ˜ƒξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš‹ξš‡ξš•ξŸ’ξ˜ƒξš–ξšŠξš‡ξ˜ƒξš…ξš‘ξš•ξš–ξ˜ƒξšƒξš’ξš’ξš”ξš‘ξšƒξš…ξšŠξŸ‘ξ˜ƒξš™ξšŠξš‹ξš…ξšŠξ˜ƒ
ξš‡ξš•ξš–ξš‹ξšξšƒξš–ξš‡ξš•ξ˜ƒ ξš”ξš‡ξš’ξšŽξšƒξš…ξš‡ξšξš‡ξšξš–ξ˜ƒ ξš…ξš‘ξš•ξš–ξ˜ƒ ξšξš‹ξšξš—ξš•ξ˜ƒ ξš†ξš‡ξš’ξš”ξš‡ξš…ξš‹ξšƒξš–ξš‹ξš‘ξšξŸ’ξ˜ƒ ξšƒξšξš†ξ˜ƒ ξš–ξšŠξš‡ξ˜ƒ ξš‹ξšξš…ξš‘ξšξš‡ξ˜ƒ ξšƒξš’ξš’ξš”ξš‘ξšƒξš…ξšŠξŸ‘ξ˜ƒ ξš’ξš”ξš‹ξšξšƒξš”ξš‹ξšŽξš›ξ˜ƒ ξš—ξš•ξš‡ξš†ξ˜ƒ ξšˆξš‘ξš”ξ˜ƒ ξš‹ξšξš˜ξš‡ξš•ξš–ξšξš‡ξšξš–ξ˜ƒ
ξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš‹ξš‡ξš•ξ˜ƒξš„ξšƒξš•ξš‡ξš†ξ˜ƒξš‘ξšξ˜ƒξš’ξš‘ξš–ξš‡ξšξš–ξš‹ξšƒξšŽξ˜ƒξš”ξš‡ξšξš–ξšƒξšŽξ˜ƒξš‹ξšξš…ξš‘ξšξš‡ξŸ€ξ˜ƒξ˜„ξš…ξš…ξš—ξš”ξšƒξš–ξš‡ξ˜ƒξš”ξš‡ξš•ξš‹ξš†ξš‡ξšξš–ξš‹ξšƒξšŽξ˜ƒξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξ˜ƒξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξ˜ƒξš‹ξš•ξ˜ƒξšˆξš—ξšξš†ξšƒξšξš‡ξšξš–ξšƒξšŽξ˜ƒξš–ξš‘ξ˜ƒξš”ξš‡ξšƒξšŽξ˜ƒ
ξš‡ξš•ξš–ξšƒξš–ξš‡ξ˜ƒξšξšƒξš”ξšξš‡ξš–ξš•ξŸ‘ξ˜ƒξšξš‘ξš”ξš–ξš‰ξšƒξš‰ξš‡ξ˜ƒξšŽξš‡ξšξš†ξš‹ξšξš‰ξŸ‘ξ˜ƒξš–ξšƒξššξšƒξš–ξš‹ξš‘ξšξŸ‘ξ˜ƒξšƒξšξš†ξ˜ƒξš‹ξšξš˜ξš‡ξš•ξš–ξšξš‡ξšξš–ξ˜ƒξš†ξš‡ξš…ξš‹ξš•ξš‹ξš‘ξšξŸ¦ξšξšƒξšξš‹ξšξš‰ξŸ€
ξ₯·ξŸ‘ξ₯Έξ ξ˜ƒ
ξ˜‰ξš‘ξš”ξ˜ƒξšŠξš‘ξšξš‡ξš„ξš—ξš›ξš‡ξš”ξš•ξ˜ƒξšƒξšξš†ξ˜ƒξš•ξš‡ξšŽξšŽξš‡ξš”ξš•ξŸ‘ξ˜ƒ
ξš’ξš”ξš‘ξš’ξš‡ξš”ξ˜ƒ ξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξ˜ƒ ξš‡ξšξš•ξš—ξš”ξš‡ξš•ξ˜ƒ ξšˆξšƒξš‹ξš”ξ˜ƒ ξš–ξš”ξšƒξšξš•ξšƒξš…ξš–ξš‹ξš‘ξšξ˜ƒ ξš’ξš”ξš‹ξš…ξš‡ξš•ξ˜ƒ ξšƒξšξš†ξ˜ƒ ξš’ξš”ξš‡ξš˜ξš‡ξšξš–ξš•ξ˜ƒ ξšξšƒξš”ξšξš‡ξš–ξ˜ƒ ξš†ξš‹ξš•ξš–ξš‘ξš”ξš–ξš‹ξš‘ξšξš•ξ˜ƒ ξš–ξšŠξšƒξš–ξ˜ƒ ξš…ξšƒξšξ˜ƒ ξšŽξš‡ξšƒξš†ξ˜ƒ ξš–ξš‘ξ˜ƒ ξšŠξš‘ξš—ξš•ξš‹ξšξš‰ξ˜ƒ
ξš„ξš—ξš„ξš„ξšŽξš‡ξš•ξ˜ƒ ξš‘ξš”ξ˜ƒ ξš—ξšξš†ξš‡ξš”ξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξ˜ƒ ξš‘ξšˆξ˜ƒ ξšƒξš•ξš•ξš‡ξš–ξš•ξŸ€ξ˜ƒ ξ˜‰ξš‘ξš”ξ˜ƒ ξ§ξš‹ξšξšƒξšξš…ξš‹ξšƒξšŽξ˜ƒ ξš‹ξšξš•ξš–ξš‹ξš–ξš—ξš–ξš‹ξš‘ξšξš•ξŸ‘ξ˜ƒ ξš’ξš”ξš‘ξš’ξš‡ξš”ξ˜ƒ ξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξ˜ƒ ξš‡ξšξš•ξš—ξš”ξš‡ξš•ξ˜ƒ ξšƒξš’ξš’ξš”ξš‘ξš’ξš”ξš‹ξšƒξš–ξš‡ξ˜ƒ ξšŽξš‘ξšƒξšξ˜ƒ
ξšƒξšξš‘ξš—ξšξš–ξš•ξ˜ƒ ξšƒξšξš†ξ˜ƒ ξš”ξš‹ξš•ξšξ˜ƒ ξšƒξš•ξš•ξš‡ξš•ξš•ξšξš‡ξšξš–ξš•ξŸ€
ξ₯ΉξŸ‘ξ₯Ίξ 
ξ˜ƒ ξ˜’ξš˜ξš‡ξš”ξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξ˜ƒ ξš…ξš‘ξšξš–ξš”ξš‹ξš„ξš—ξš–ξš‡ξš†ξ˜ƒ ξš–ξš‘ξ˜ƒ ξš–ξšŠξš‡ξ˜ƒ ξ₯΄ξ₯²ξ₯²ξ₯Ίξ˜ƒ ξ§ξš‹ξšξšƒξšξš…ξš‹ξšƒξšŽξ˜ƒ ξš…ξš”ξš‹ξš•ξš‹ξš•ξ˜ƒ ξš™ξšŠξš‡ξšξ˜ƒ ξš•ξš›ξš•ξš–ξš‡ξšξšƒξš–ξš‹ξš…ξ˜ƒ
ξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξ˜ƒξš‘ξš˜ξš‡ξš”ξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξ˜ƒξšŽξš‡ξš†ξ˜ƒξš–ξš‘ξ˜ƒξš™ξš‹ξš†ξš‡ξš•ξš’ξš”ξš‡ξšƒξš†ξ˜ƒξšξš‘ξš”ξš–ξš‰ξšƒξš‰ξš‡ξ˜ƒξš†ξš‡ξšˆξšƒξš—ξšŽξš–ξš•ξŸ€
ξ₯»ξŸ‘ξ₯³ξ₯²ξ 
ξ˜ƒξ˜‰ξš‘ξš”ξ˜ƒξš‰ξš‘ξš˜ξš‡ξš”ξšξšξš‡ξšξš–ξš•ξŸ‘ξ˜ƒξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξ˜ƒξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξš•ξ˜ƒξšˆξš‘ξš”ξšξ˜ƒ
ξš–ξšŠξš‡ξ˜ƒξš„ξšƒξš•ξš‹ξš•ξ˜ƒξš‘ξšˆξ˜ƒξš–ξšƒξššξ˜ƒξšƒξš•ξš•ξš‡ξš•ξš•ξšξš‡ξšξš–ξš•ξ˜ƒξš…ξš‘ξšξš•ξš–ξš‹ξš–ξš—ξš–ξš‹ξšξš‰ξ˜ƒξš’ξš”ξš‹ξšξšƒξš”ξš›ξ˜ƒξš”ξš‡ξš˜ξš‡ξšξš—ξš‡ξ˜ƒξš•ξš‘ξš—ξš”ξš…ξš‡ξš•ξŸ€
ξ₯³ξ₯³ξ 
ξ˜ƒξ˜Œξšξ˜ƒξšƒξš…ξš…ξš—ξš”ξšƒξš–ξš‡ξ˜ƒξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξš•ξ˜ƒξšŽξš‡ξšƒξš†ξ˜ƒξš–ξš‘ξ˜ƒξš‹ξšξš‡ξš“ξš—ξš‹ξš–ξšƒξš„ξšŽξš‡ξ˜ƒ
ξš–ξšƒξššξ˜ƒξš„ξš—ξš”ξš†ξš‡ξšξš•ξ˜ƒξšƒξšξš†ξ˜ƒξš”ξš‡ξš˜ξš‡ξšξš—ξš‡ξ˜ƒξš•ξšŠξš‘ξš”ξš–ξšˆξšƒξšŽξšŽξš•ξŸ€ξ˜ƒξ˜„ξš†ξš†ξš‹ξš–ξš‹ξš‘ξšξšƒξšŽξšŽξš›ξŸ‘ξ˜ƒξš‹ξšξš•ξš–ξš‹ξš–ξš—ξš–ξš‹ξš‘ξšξšƒξšŽξ˜ƒξš‹ξšξš˜ξš‡ξš•ξš–ξš‘ξš”ξš•ξŸ‘ξ˜ƒξš”ξš‡ξšƒξšŽξ˜ƒξš‡ξš•ξš–ξšƒξš–ξš‡ξ˜ƒξš‹ξšξš˜ξš‡ξš•ξš–ξšξš‡ξšξš–ξ˜ƒξš–ξš”ξš—ξš•ξš–ξš•ξ˜ƒξ ‹ξ˜•ξ˜ˆξ˜Œξ˜—ξš•ξ ŒξŸ‘ξ˜ƒ
ξšƒξšξš†ξ˜ƒξš’ξš‘ξš”ξš–ξšˆξš‘ξšŽξš‹ξš‘ξ˜ƒξšξšƒξšξšƒξš‰ξš‡ξš”ξš•ξ˜ƒξš†ξš‡ξš’ξš‡ξšξš†ξ˜ƒξš‘ξšξ˜ƒξš”ξš‡ξšŽξš‹ξšƒξš„ξšŽξš‡ξ˜ƒξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξš•ξ˜ƒξšˆξš‘ξš”ξ˜ƒξšƒξš•ξš•ξš‡ξš–ξ˜ƒξšƒξšŽξšŽξš‘ξš…ξšƒξš–ξš‹ξš‘ξšξŸ‘ξ˜ƒξš”ξš‹ξš•ξšξ˜ƒξšξšƒξšξšƒξš‰ξš‡ξšξš‡ξšξš–ξŸ‘ξ˜ƒξšƒξšξš†ξ˜ƒξš’ξš‡ξš”ξšˆξš‘ξš”ξšξšƒξšξš…ξš‡ξ˜ƒ
ξš‡ξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξŸ€ξ˜ƒξ˜—ξšŠξš‡ξ˜ƒξš‹ξšξš•ξš—ξš”ξšƒξšξš…ξš‡ξ˜ƒξš‹ξšξš†ξš—ξš•ξš–ξš”ξš›ξ˜ƒξšƒξšŽξš•ξš‘ξ˜ƒξš”ξš‡ξš“ξš—ξš‹ξš”ξš‡ξš•ξ˜ƒξšƒξš…ξš…ξš—ξš”ξšƒξš–ξš‡ξ˜ƒξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξ˜ƒξš˜ξšƒξšŽξš—ξš‡ξš•ξ˜ƒξš–ξš‘ξ˜ƒξš†ξš‡ξš–ξš‡ξš”ξšξš‹ξšξš‡ξ˜ƒξšƒξš’ξš’ξš”ξš‘ξš’ξš”ξš‹ξšƒξš–ξš‡ξ˜ƒξš…ξš‘ξš˜ξš‡ξš”ξšƒξš‰ξš‡ξ˜ƒ
ξšŽξš‡ξš˜ξš‡ξšŽξš•ξ˜ƒξšƒξšξš†ξ˜ƒξš’ξš”ξš‡ξšξš‹ξš—ξšξ˜ƒξš…ξšƒξšŽξš…ξš—ξšŽξšƒξš–ξš‹ξš‘ξšξš•ξŸ€
ξ˜—ξš”ξšƒξš†ξš‹ξš–ξš‹ξš‘ξšξšƒξšŽξ˜ƒξšƒξš’ξš’ξš”ξšƒξš‹ξš•ξšƒξšŽξ˜ƒξšξš‡ξš–ξšŠξš‘ξš†ξš•ξ˜ƒξš”ξš‡ξšŽξš›ξ˜ƒξš‘ξšξ˜ƒξš‡ξššξš’ξš‡ξš”ξš–ξ˜ƒξšŒξš—ξš†ξš‰ξšξš‡ξšξš–ξ˜ƒξšƒξšξš†ξ˜ƒξš…ξš‘ξšξš’ξšƒξš”ξšƒξš„ξšŽξš‡ξ˜ƒξš•ξšƒξšŽξš‡ξš•ξ˜ƒξšƒξšξšƒξšŽξš›ξš•ξš‹ξš•ξŸ‘ξ˜ƒξš™ξšŠξš‹ξš…ξšŠξ˜ƒξš…ξšƒξšξ˜ƒξš„ξš‡ξ˜ƒξš•ξš—ξš„ξšŒξš‡ξš…ξš–ξš‹ξš˜ξš‡ξ˜ƒ
ξšƒξšξš†ξ˜ƒ ξš–ξš‹ξšξš‡ξŸ¦ξš‹ξšξš–ξš‡ξšξš•ξš‹ξš˜ξš‡ξŸ€
ξ₯³ξ₯΄ξŸ‘ξ₯³ξ₯΅ξ 
ξ˜ƒ ξ˜ξš‹ξš…ξš‡ξšξš•ξš‡ξš†ξ˜ƒ ξšƒξš’ξš’ξš”ξšƒξš‹ξš•ξš‡ξš”ξš•ξ˜ƒ ξšξšƒξšξš—ξšƒξšŽξšŽξš›ξ˜ƒ ξš•ξš‡ξšŽξš‡ξš…ξš–ξ˜ƒ ξš…ξš‘ξšξš’ξšƒξš”ξšƒξš„ξšŽξš‡ξ˜ƒ ξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš‹ξš‡ξš•ξŸ‘ξ˜ƒ ξšξšƒξšξš‡ξ˜ƒ ξš•ξš—ξš„ξšŒξš‡ξš…ξš–ξš‹ξš˜ξš‡ξ˜ƒ
ξšƒξš†ξšŒξš—ξš•ξš–ξšξš‡ξšξš–ξš•ξ˜ƒξšˆξš‘ξš”ξ˜ƒξš†ξš‹ξšˆξšˆξš‡ξš”ξš‡ξšξš…ξš‡ξš•ξ˜ƒξš‹ξšξ˜ƒξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξŸ‘ξ˜ƒξšƒξšξš†ξ˜ƒξš•ξš›ξšξš–ξšŠξš‡ξš•ξš‹ξšœξš‡ξ˜ƒξšξšƒξš”ξšξš‡ξš–ξ˜ƒξš†ξšƒξš–ξšƒξ˜ƒξš„ξšƒξš•ξš‡ξš†ξ˜ƒξš‘ξšξ˜ƒξš’ξš”ξš‘ξšˆξš‡ξš•ξš•ξš‹ξš‘ξšξšƒξšŽξ˜ƒξš‡ξššξš’ξš‡ξš”ξš‹ξš‡ξšξš…ξš‡ξŸ€ξ˜ƒξ˜šξšŠξš‹ξšŽξš‡ξ˜ƒ
ξš„ξš‡ξšξš‡ξ§ξš‹ξš–ξš‹ξšξš‰ξ˜ƒ ξšˆξš”ξš‘ξšξ˜ƒξšŠξš—ξšξšƒξšξ˜ƒ ξš‡ξššξš’ξš‡ξš”ξš–ξš‹ξš•ξš‡ξŸ‘ξ˜ƒ ξš–ξšŠξš‡ξš•ξš‡ξ˜ƒ ξšƒξš’ξš’ξš”ξš‘ξšƒξš…ξšŠξš‡ξš•ξ˜ƒξš•ξš—ξšˆξšˆξš‡ξš”ξ˜ƒξšˆξš”ξš‘ξšξ˜ƒξšŠξš‹ξš‰ξšŠξ˜ƒξš…ξš‘ξš•ξš–ξš•ξ˜ƒ ξ ‹ξ₯„ξ₯΅ξ₯²ξ₯²ξŸ¦ξ₯„ξ₯·ξ₯²ξ₯²ξ˜ƒ ξš’ξš‡ξš”ξ˜ƒ ξšƒξš’ξš’ξš”ξšƒξš‹ξš•ξšƒξšŽξ ŒξŸ‘ξ˜ƒξš–ξš‹ξšξš‡ξ˜ƒ
ξš†ξš‡ξšŽξšƒξš›ξš•ξŸ‘ξ˜ƒξš’ξš‘ξš–ξš‡ξšξš–ξš‹ξšƒξšŽξ˜ƒξš„ξš‹ξšƒξš•ξŸ‘ξ˜ƒξšƒξšξš†ξ˜ƒξšŽξš‹ξšξš‹ξš–ξš‡ξš†ξ˜ƒξš•ξš…ξšƒξšŽξšƒξš„ξš‹ξšŽξš‹ξš–ξš›ξŸ€
ξ₯³ξ₯ΆξŸ‘ξ₯³ξ₯·ξ 
ξ˜ƒξ˜ˆξšƒξš”ξšŽξš›ξ˜ƒξšƒξš—ξš–ξš‘ξšξšƒξš–ξš‡ξš†ξ˜ƒξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξ˜ƒξšξš‘ξš†ξš‡ξšŽξš•ξ˜ƒξ ‹ξ˜„ξ˜™ξ˜ξš•ξ Œξ˜ƒξšƒξš…ξšŠξš‹ξš‡ξš˜ξš‡ξš†ξ˜ƒξ˜•ξ₯Ύξ˜ƒξš˜ξšƒξšŽξš—ξš‡ξš•ξ˜ƒ
ξš„ξš‡ξš–ξš™ξš‡ξš‡ξšξ˜ƒξ₯Έξ₯²ξŸ¦ξ₯Ήξ₯²ξ¦¨ξŸ€
ξ₯³ξ₯ΈξŸ‘ξ₯³ξ₯Ήξ 
ξ˜ƒξ˜—ξšŠξš‡ξ˜ƒξšƒξš†ξš˜ξš‡ξšξš–ξ˜ƒξš‘ξšˆξ˜ƒξš…ξš‘ξšξš’ξš—ξš–ξšƒξš–ξš‹ξš‘ξšξšƒξšŽξ˜ƒξšξš‡ξš–ξšŠξš‘ξš†ξš•ξ˜ƒξš‹ξšξ˜ƒξš–ξšŠξš‡ξ˜ƒξ₯³ξ₯»ξ₯»ξ₯²ξš•ξ˜ƒξšƒξšξš†ξ˜ƒξ₯΄ξ₯²ξ₯²ξ₯²ξš•ξ˜ƒξš‹ξšξš–ξš”ξš‘ξš†ξš—ξš…ξš‡ξš†ξ˜ƒξšŠξš‡ξš†ξš‘ξšξš‹ξš…ξ˜ƒξš’ξš”ξš‹ξš…ξš‹ξšξš‰ξ˜ƒ
ξšξš‘ξš†ξš‡ξšŽξš•ξŸ‘ξ˜ƒξš™ξšŠξš‹ξš…ξšŠξ˜ƒξš—ξš•ξš‡ξ˜ƒξšξš—ξšŽξš–ξš‹ξš’ξšŽξš‡ξ˜ƒξš”ξš‡ξš‰ξš”ξš‡ξš•ξš•ξš‹ξš‘ξšξ˜ƒξšƒξšξšƒξšŽξš›ξš•ξš‹ξš•ξ˜ƒξš–ξš‘ξ˜ƒξš‡ξš•ξš–ξš‹ξšξšƒξš–ξš‡ξ˜ƒξš–ξšŠξš‡ξ˜ƒξš‹ξšξš’ξšŽξš‹ξš…ξš‹ξš–ξ˜ƒξš’ξš”ξš‹ξš…ξš‡ξš•ξ˜ƒξš‘ξšˆξ˜ƒξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξ˜ƒξš…ξšŠξšƒξš”ξšƒξš…ξš–ξš‡ξš”ξš‹ξš•ξš–ξš‹ξš…ξš•ξŸ€ξ˜ƒξ˜ˆξšƒξš”ξšŽξš›ξ˜ƒ
ξšƒξš—ξš–ξš‘ξšξšƒξš–ξš‡ξš†ξ˜ƒξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξ˜ƒξšξš‘ξš†ξš‡ξšŽξš•ξ˜ƒξ ‹ξ˜„ξ˜™ξ˜ξš•ξ Œξ˜ƒξš‡ξšξš’ξšŽξš‘ξš›ξš‡ξš†ξ˜ƒξš„ξš›ξ˜ƒξš…ξš‘ξšξš’ξšƒξšξš‹ξš‡ξš•ξ˜ƒξšŽξš‹ξšξš‡ξ˜ƒξ˜ξš‹ξšŽξšŽξš‘ξš™ξ˜ƒξ ‹ξ˜ξš‡ξš•ξš–ξš‹ξšξšƒξš–ξš‡ξ Œξ˜ƒξšƒξšξš†ξ˜ƒξ˜•ξš‡ξš†ξ§ξš‹ξšξ˜ƒξš†ξš‡ξšξš‘ξšξš•ξš–ξš”ξšƒξš–ξš‡ξš†ξ˜ƒ
ξš–ξšŠξšƒξš–ξ˜ƒξš•ξš–ξšƒξš–ξš‹ξš•ξš–ξš‹ξš…ξšƒξšŽξ˜ƒ ξšξš‡ξš–ξšŠξš‘ξš†ξš•ξ˜ƒ ξš…ξš‘ξš—ξšŽξš†ξ˜ƒ ξš’ξš”ξš‘ξš˜ξš‹ξš†ξš‡ξ˜ƒξš”ξšƒξš’ξš‹ξš†ξŸ‘ξ˜ƒξš…ξš‘ξš•ξš–ξŸ¦ξš‡ξšˆξšˆξš‡ξš…ξš–ξš‹ξš˜ξš‡ξ˜ƒξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξš•ξ˜ƒξšƒξš–ξ˜ƒ ξš•ξš…ξšƒξšŽξš‡ξŸ€ξ˜ƒ ξ˜‹ξš‘ξš™ξš‡ξš˜ξš‡ξš”ξŸ‘ξ˜ƒ ξš–ξšŠξš‡ξš•ξš‡ξ˜ƒ ξš‡ξšƒξš”ξšŽξš›ξ˜ƒξšξš‘ξš†ξš‡ξšŽξš•ξ˜ƒ
ξš–ξš›ξš’ξš‹ξš…ξšƒξšŽξšŽξš›ξ˜ƒξšƒξš…ξšŠξš‹ξš‡ξš˜ξš‡ξš†ξ˜ƒξ˜•ξ₯Ύξ˜ƒξš˜ξšƒξšŽξš—ξš‡ξš•ξ˜ƒξš„ξš‡ξš–ξš™ξš‡ξš‡ξšξ˜ƒξ₯Έξ₯²ξŸ¦ξ₯Ήξ₯²ξ¦¨ξŸ‘ξ˜ƒξš‹ξšξš†ξš‹ξš…ξšƒξš–ξš‹ξšξš‰ξ˜ƒξš•ξš—ξš„ξš•ξš–ξšƒξšξš–ξš‹ξšƒξšŽξ˜ƒξš—ξšξš‡ξššξš’ξšŽξšƒξš‹ξšξš‡ξš†ξ˜ƒξš˜ξšƒξš”ξš‹ξšƒξšξš…ξš‡ξ˜ƒξš‹ξšξ˜ƒξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξ˜ƒξš’ξš”ξš‹ξš…ξš‡ξš•ξŸ€
ξ˜ξšƒξš…ξšŠξš‹ξšξš‡ξ˜ƒ ξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξ˜ƒ ξšƒξš’ξš’ξš”ξš‘ξšƒξš…ξšŠξš‡ξš•ξ˜ƒξš‹ξšξ˜ƒ ξš–ξšŠξš‡ξ˜ƒ ξ₯΄ξ₯²ξ₯³ξ₯²ξš•ξ˜ƒ ξš„ξš”ξš‘ξš—ξš‰ξšŠξš–ξ˜ƒ ξš•ξš‘ξš’ξšŠξš‹ξš•ξš–ξš‹ξš…ξšƒξš–ξš‡ξš†ξ˜ƒ ξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξ˜ƒ ξšξš‡ξš–ξšŠξš‘ξš†ξš•ξŸ€
ξ₯³ξ₯ΊξŸ‘ξ₯³ξ₯»ξ 
ξ˜ƒ ξ˜•ξš‡ξš•ξš‡ξšƒξš”ξš…ξšŠξš‡ξš”ξš•ξ˜ƒξšŠξšƒξš˜ξš‡ξ˜ƒ
ξš‡ξššξš’ξšŽξš‘ξš”ξš‡ξš†ξ˜ƒ ξš˜ξšƒξš”ξš‹ξš‘ξš—ξš•ξ˜ƒ ξšƒξšŽξš‰ξš‘ξš”ξš‹ξš–ξšŠξšξš•ξ˜ƒ ξš‹ξšξš…ξšŽξš—ξš†ξš‹ξšξš‰ξ˜ƒ ξš†ξš‡ξš…ξš‹ξš•ξš‹ξš‘ξšξ˜ƒ ξš–ξš”ξš‡ξš‡ξš•ξŸ‘ξ˜ƒ ξ˜•ξšƒξšξš†ξš‘ξšξ˜ƒ ξ˜‰ξš‘ξš”ξš‡ξš•ξš–ξš•ξŸ‘ξ˜ƒξ˜Šξš”ξšƒξš†ξš‹ξš‡ξšξš–ξ˜ƒξ˜…ξš‘ξš‘ξš•ξš–ξš‹ξšξš‰ξ˜ƒ ξ˜ξšƒξš…ξšŠξš‹ξšξš‡ξš•ξ˜ƒ ξ ‹ξ˜Šξ˜…ξ˜ξ ŒξŸ‘ξ˜ƒ
ξ˜–ξš—ξš’ξš’ξš‘ξš”ξš–ξ˜ƒξ˜™ξš‡ξš…ξš–ξš‘ξš”ξ˜ƒξ˜ξšƒξš…ξšŠξš‹ξšξš‡ξš•ξ˜ƒξ ‹ξ˜–ξ˜™ξ˜ξ ŒξŸ‘ξ˜ƒξšƒξšξš†ξ˜ƒξšƒξš”ξš–ξš‹ξ§ξš‹ξš…ξš‹ξšƒξšŽξ˜ƒξšξš‡ξš—ξš”ξšƒξšŽξ˜ƒξšξš‡ξš–ξš™ξš‘ξš”ξšξš•ξŸ€ξ˜ƒξ˜•ξš‡ξš…ξš‡ξšξš–ξ˜ƒξš•ξš–ξš—ξš†ξš‹ξš‡ξš•ξ˜ƒξš•ξšŠξš‘ξš™ξ˜ƒξš–ξšŠξšƒξš–ξ˜ƒξš‡ξšξš•ξš‡ξšξš„ξšŽξš‡ξ˜ƒξšξš‡ξš–ξšŠξš‘ξš†ξš•ξ˜ƒ
ξšŽξš‹ξšξš‡ξ˜ƒξ˜›ξ˜Šξ˜…ξš‘ξš‘ξš•ξš–ξ˜ƒξšƒξšξš†ξ˜ƒξ˜•ξšƒξšξš†ξš‘ξšξ˜ƒξ˜‰ξš‘ξš”ξš‡ξš•ξš–ξ˜ƒξš…ξšƒξšξ˜ƒξšƒξš…ξšŠξš‹ξš‡ξš˜ξš‡ξ˜ƒξ˜•ξ₯Ύξ˜ƒξš˜ξšƒξšŽξš—ξš‡ξš•ξ˜ƒξš‡ξššξš…ξš‡ξš‡ξš†ξš‹ξšξš‰ξ˜ƒξ₯Ίξ₯·ξŸ¦ξ₯»ξ₯²ξ¦¨ξŸ€
ξ₯΄ξ₯²ξŸ‘ξ₯΄ξ₯³ξ 
ξ˜ƒξ˜‡ξš‡ξš‡ξš’ξ˜ƒξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξ˜ƒξšƒξš’ξš’ξš”ξš‘ξšƒξš…ξšŠξš‡ξš•ξ˜ƒξšŠξšƒξš˜ξš‡ξ˜ƒ
ξš†ξš‡ξšξš‘ξšξš•ξš–ξš”ξšƒξš–ξš‡ξš†ξ˜ƒ ξš‹ξšξš’ξš”ξš‡ξš•ξš•ξš‹ξš˜ξš‡ξ˜ƒ ξšƒξš…ξš…ξš—ξš”ξšƒξš…ξš›ξ˜ƒ ξš„ξš›ξ˜ƒ ξš’ξš”ξš‘ξš…ξš‡ξš•ξš•ξš‹ξšξš‰ξ˜ƒ ξš•ξš–ξš”ξš—ξš…ξš–ξš—ξš”ξš‡ξš†ξ˜ƒ ξšƒξšξš†ξ˜ƒ ξš—ξšξš•ξš–ξš”ξš—ξš…ξš–ξš—ξš”ξš‡ξš†ξ˜ƒ ξš†ξšƒξš–ξšƒξŸ€
ξ₯΄ξ₯΄ξŸ‘ξ₯΄ξ₯΅ξ 
ξ˜ƒ ξ˜‹ξš‘ξš™ξš‡ξš˜ξš‡ξš”ξŸ‘ξ˜ƒ ξš…ξš‘ξšξš’ξšŽξš‡ξššξ˜ƒ
ξšξš‘ξš†ξš‡ξšŽξš•ξ˜ƒ ξš‘ξšˆξš–ξš‡ξšξ˜ƒξš•ξšƒξš…ξš”ξš‹ξ§ξš‹ξš…ξš‡ξ˜ƒ ξš‹ξšξš–ξš‡ξš”ξš’ξš”ξš‡ξš–ξšƒξš„ξš‹ξšŽξš‹ξš–ξš›ξ˜ƒ ξšˆξš‘ξš”ξ˜ƒ ξšξšƒξš”ξš‰ξš‹ξšξšƒξšŽξ˜ƒ ξšƒξš…ξš…ξš—ξš”ξšƒξš…ξš›ξ˜ƒ ξš‰ξšƒξš‹ξšξš•ξŸ€
ξ₯΄ξ₯ΆξŸ‘ξ₯΄ξ₯·ξ 
ξ˜ƒ ξ˜•ξš‡ξš‰ξš—ξšŽξšƒξš–ξš‘ξš”ξš›ξ˜ƒ ξšˆξš”ξšƒξšξš‡ξš™ξš‘ξš”ξšξš•ξ˜ƒξš•ξš—ξš…ξšŠξ˜ƒ ξšƒξš•ξ˜ƒ ξš–ξšŠξš‡ξ˜ƒ
ξ˜‰ξš‹ξšξšƒξšξš…ξš‹ξšƒξšŽξ˜ƒ ξ˜Œξšξš•ξš–ξš‹ξš–ξš—ξš–ξš‹ξš‘ξšξš•ξ˜ƒ ξ˜•ξš‡ξšˆξš‘ξš”ξšξŸ‘ξ˜ƒ ξ˜•ξš‡ξš…ξš‘ξš˜ξš‡ξš”ξš›ξŸ‘ξ˜ƒ ξšƒξšξš†ξ˜ƒ ξ˜ˆξšξšˆξš‘ξš”ξš…ξš‡ξšξš‡ξšξš–ξ˜ƒ ξ˜„ξš…ξš–ξ˜ƒ ξ ‹ξ˜‰ξ˜Œξ˜•ξ˜•ξ˜ˆξ˜„ξ Œξ˜ƒ ξš‹ξšξ˜ƒ ξš–ξšŠξš‡ξ˜ƒ ξ˜˜ξšξš‹ξš–ξš‡ξš†ξ˜ƒ ξ˜–ξš–ξšƒξš–ξš‡ξš•ξ˜ƒ ξš”ξš‡ξš“ξš—ξš‹ξš”ξš‡ξ˜ƒ ξš–ξšŠξšƒξš–ξ˜ƒ
ξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξ˜ƒξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξš•ξ˜ƒξš„ξš‡ξ˜ƒξš‡ξššξš’ξšŽξšƒξš‹ξšξšƒξš„ξšŽξš‡ξ˜ƒξšƒξšξš†ξ˜ƒξš†ξš‡ξšˆξš‡ξšξš•ξš‹ξš„ξšŽξš‡ξŸ‘ξ˜ƒξš…ξš”ξš‡ξšƒξš–ξš‹ξšξš‰ξ˜ƒξš–ξš‡ξšξš•ξš‹ξš‘ξšξ˜ƒξš„ξš‡ξš–ξš™ξš‡ξš‡ξšξ˜ƒξšξš‘ξš†ξš‡ξšŽξ˜ƒξšƒξš…ξš…ξš—ξš”ξšƒξš…ξš›ξ˜ƒξšƒξšξš†ξ˜ƒξš–ξš”ξšƒξšξš•ξš’ξšƒξš”ξš‡ξšξš…ξš›ξŸ€
Linear regression remains widely used due to its transparency, computational efficiency, and ease of
interpretation.
[26,27]
The coefficients directly indicate how each feature impacts property value, making results
accessible to appraisers, lenders, and regulators without specialized machine learning expertise. However,
standard linear models using raw features typically achieve modest performance, with RΒ² values around
70%.
[28,29]
This limitation has driven researchers toward ensemble methods and neural networks, which can
exceed 85% accuracy but lack the interpretability required by regulatory frameworks and professional
appraisers.
Recent research explores enhancing linear regression through systematic feature engineering.
[30,31]
rather than
abandoning it for complex algorithms. Feature engineering-the process of creating new predictive variables
from existing data through mathematical transformations, combinations, and domain knowledge-can capture
non-linear relationships and interactions within a linear framework. Studies show that interaction terms, ratio
features, polynomial transformations, and location-based composites can substantially improve
performance.
[32,33]
This approach preserves model interpretability while closing the accuracy gap with black-box
methods. This study contributes to this research direction by developing and evaluating a comprehensive
feature engineering framework for residential property valuation using linear regression. We hypothesize that
strategic feature creation, combined with careful preprocessing and regularization, can achieve RΒ² values
approaching 75-80% while maintaining the transparency advantages of linear models. This study addresses a
critical gap: can strategic feature engineering enhance linear regression performance while maintaining
interpretability? Using the King County House Sales dataset from Kaggle,
[5]
which provides comprehensive
residential transaction data from the Seattle metropolitan area, we developed an advanced feature engineering
pipeline. Our approach creates interaction terms between key variables, polynomial features to capture non-
linearity, ratio features for relative measurements, temporal features for property age and renovation status,
quality indicators, location-based composites, and logarithmic transformations to handle skewed distributions.
2. Methods
2.1 Dataset description
The King County House Sales dataset was obtained from Kaggle,
[5]
containing 21,613 residential property
transactions in King County, Washington, from May 2014 to May 2015. The dataset includes 21 original features
as listed in Table 1.
2.2 Data exploration and preprocessing
Initial exploratory data analysis examined univariate distributions, bivariate relationships, and correlation
structures.
[35,36]
Price distribution histograms revealed positive skewness, with concentration in the $300,000-
$600,000 range and a long right tail representing luxury properties (Fig. 1). Outlier detection employed the
interquartile range method.
[37]
with a 1.5 Γ— IQR threshold applied to continuous features. This process identified
and removed 1,146 observations (5.30%), resulting in a cleaned dataset of 20,467 properties. Outlier removal
was necessary to prevent extreme values from distorting model coefficients and degrading prediction accuracy
on typical properties. The dataset exhibited no missing values, facilitating comprehensive analysis without
imputation.
[5]
The target variable exhibited right-skewed distribution typical of real estate markets.
[34]
Table 1: Dataset features and descriptions for King County house sales data.
[5]
No
Feature Name
Description
Type
Unit/Scale
1
id
Unique property
identifier
Categorical
Numeric ID
2
date
Sale date
Temporal
YYYYMMDD
3
Price
Sale price (target
variable)
Continuous
USD
4
bedrooms
Number of bedrooms
Discrete
Count
5
Number of
bathrooms
Continuous
Count (0.5
6
sqft_living
Living area square
footage
Continuous
Square feet
7
sqft_lot
Lot size
Continuous
Square feet
8
floors
Number of floors
Continuous
Count (0.5
9
waterfront
Waterfront property
status
Binary
0 = No, 1 = Yes
10
view
View quality rating
Ordinal
0-4 scale
11
condition
Property condition rating
Ordinal
1-5 scale
12
grade
Construction quality
grade
Ordinal
1-13 scale
13
sqft_above
Above-ground
Continuous
Square feet
14
sqft_basement
Basement
Continuous
Square feet
15
yr_built
Year property was built
Discrete
Year (YYYY)
16
yr_renovated
Year property
Discrete
Year (YYYY), 0 if never
17
zipcode
Property zip code
zipcode
Property zip code
18
lat
Latitude coordinate
lat
Latitude coordinate
19
long
Longitude coordinate
Continuous
Decimal degrees
20
sqft_living15
Average living area of 15
nearest neighbors
Continuous
Square feet
21
sqft_lot15
Average lot size of 15
nearest neighbors
Continuous
Square feet
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ξš…ξš‘ξšξš…ξš‡ξšξš–ξš”ξšƒξš–ξš‹ξš‘ξšξ˜ƒξš‹ξšξ˜ƒξš–ξšŠξš‡ξ˜ƒξ₯„ξ₯΅ξ₯²ξ₯²ξŸ‘ξ₯²ξ₯²ξ₯²ξŸ¦ξ₯„ξ₯Έξ₯²ξ₯²ξŸ‘ξ₯²ξ₯²ξ₯²ξ˜ƒξš”ξšƒξšξš‰ξš‡ξŸ€
ξ₯΄ξŸ€ξ₯΅ξ˜ƒξ˜‰ξš‡ξšƒξš–ξš—ξš”ξš‡ξ˜ƒξš‡ξšξš‰ξš‹ξšξš‡ξš‡ξš”ξš‹ξšξš‰
ξ˜—ξšŠξš‡ξ˜ƒξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξ˜ƒξš‡ξšξš‰ξš‹ξšξš‡ξš‡ξš”ξš‹ξšξš‰ξ˜ƒξš’ξš‹ξš’ξš‡ξšŽξš‹ξšξš‡ξ˜ƒξš•ξš›ξš•ξš–ξš‡ξšξšƒξš–ξš‹ξš…ξšƒξšŽξšŽξš›ξ˜ƒξš…ξš”ξš‡ξšƒξš–ξš‡ξš†ξ˜ƒξ₯Άξ₯²ξ˜ƒξšξš‡ξš™ξ˜ƒξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξ˜ƒξšƒξš…ξš”ξš‘ξš•ξš•ξ˜ƒξš–ξš‡ξšξ˜ƒξš…ξšƒξš–ξš‡ξš‰ξš‘ξš”ξš‹ξš‡ξš•ξŸ€
ξ₯΅ξ₯ΊξŸ‘ξ₯΅ξ₯»ξ ξ˜ƒ
ξ˜Œξšξš–ξš‡ξš”ξšƒξš…ξš–ξš‹ξš‘ξšξ˜ƒ
ξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξ˜ƒ ξš…ξšƒξš’ξš–ξš—ξš”ξš‡ξ˜ƒ ξš•ξš›ξšξš‡ξš”ξš‰ξš‹ξš•ξš–ξš‹ξš…ξ˜ƒ ξš‡ξšˆξšˆξš‡ξš…ξš–ξš•ξ˜ƒ ξš„ξš‡ξš–ξš™ξš‡ξš‡ξšξ˜ƒ ξš…ξš‘ξšξš’ξšŽξš‡ξšξš‡ξšξš–ξšƒξš”ξš›ξ˜ƒ ξš˜ξšƒξš”ξš‹ξšƒξš„ξšŽξš‡ξš•ξŸ€
ξ₯Άξ₯²ξŸ‘ξ₯Άξ₯³ξ ξ˜ƒ
ξ˜“ξš‘ξšŽξš›ξšξš‘ξšξš‹ξšƒξšŽξ˜ƒ ξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξ˜ƒ ξšξš‘ξš†ξš‡ξšŽξ˜ƒ ξšξš‘ξšξŸ¦
ξšŽξš‹ξšξš‡ξšƒξš”ξ˜ƒξš”ξš‡ξšŽξšƒξš–ξš‹ξš‘ξšξš•ξšŠξš‹ξš’ξš•ξŸ€
ξ₯Άξ₯΄ξ 
ξ˜ƒξ˜•ξšƒξš–ξš‹ξš‘ξ˜ƒξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξ˜ƒξš’ξš”ξš‘ξš˜ξš‹ξš†ξš‡ξ˜ƒξš•ξš…ξšƒξšŽξš‡ξŸ¦ξš‹ξšξš˜ξšƒξš”ξš‹ξšƒξšξš–ξ˜ƒξš…ξš‘ξšξš’ξšƒξš”ξš‹ξš•ξš‘ξšξš•ξŸ€
ξ₯Άξ₯΅ξŸ‘ξ₯Άξ₯Άξ 
ξ˜ƒ
ξ˜•ξšƒξš–ξš‹ξš‘ξ˜ƒξ˜‰ξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξŸ£ξ˜ƒξ˜•ξš‡ξšŽξšƒξš–ξš‹ξš˜ξš‡ξ˜ƒξšξš‡ξšƒξš•ξš—ξš”ξš‡ξšξš‡ξšξš–ξš•ξ˜ƒξš’ξš”ξš‘ξš˜ξš‹ξš†ξš‹ξšξš‰ξ˜ƒξš•ξš…ξšƒξšŽξš‡ξŸ¦ξš‹ξšξš˜ξšƒξš”ξš‹ξšƒξšξš–ξ˜ƒξš…ξš‘ξšξš’ξšƒξš”ξš‹ξš•ξš‘ξšξš•ξŸ‘ξ˜ƒξš‹ξšξš…ξšŽξš—ξš†ξš‹ξšξš‰ξ˜ƒξš„ξšƒξš•ξš‡ξšξš‡ξšξš–ξŸ¦ξš–ξš‘ξŸ¦ξ˜ƒξšŽξš‹ξš˜ξš‹ξšξš‰ξ˜ƒ
ξš”ξšƒξš–ξš‹ξš‘ξŸ‘ξ˜ƒξšƒξš„ξš‘ξš˜ξš‡ξŸ¦ξš–ξš‘ξŸ¦ξšŽξš‹ξš˜ξš‹ξšξš‰ξ˜ƒξš”ξšƒξš–ξš‹ξš‘ξŸ‘ξ˜ƒξš„ξšƒξš–ξšŠξš”ξš‘ξš‘ξšξŸ¦ξš–ξš‘ξŸ¦ξš„ξš‡ξš†ξš”ξš‘ξš‘ξšξ˜ƒξš”ξšƒξš–ξš‹ξš‘ξŸ‘ξ˜ƒξšƒξšξš†ξ˜ƒξšŽξš‹ξš˜ξš‹ξšξš‰ξŸ¦ξš–ξš‘ξŸ¦ξšŽξš‘ξš–ξ˜ƒξš”ξšƒξš–ξš‹ξš‘ξŸ€
ξ˜„ξš‰ξš‡ξ˜ƒ ξšƒξšξš†ξ˜ƒ ξ˜•ξš‡ξšξš‘ξš˜ξšƒξš–ξš‹ξš‘ξšξ˜ƒ ξ˜‰ξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξŸ£ξ˜ƒξ˜—ξš‡ξšξš’ξš‘ξš”ξšƒξšŽξ˜ƒξš‹ξšξš†ξš‹ξš…ξšƒξš–ξš‘ξš”ξš•ξ˜ƒξš…ξšƒξšŽξš…ξš—ξšŽξšƒξš–ξš‡ξš†ξ˜ƒ ξšƒξš•ξ˜ƒ ξ₯΄ξ₯²ξ₯³ξ₯·ξ˜ƒ ξ ‹ξš†ξšƒξš–ξšƒξš•ξš‡ξš–ξ˜ƒ ξš‡ξšξš†ξ˜ƒ ξš›ξš‡ξšƒξš”ξ Œξ˜ƒξšξš‹ξšξš—ξš•ξ˜ƒ ξš›ξš‡ξšƒξš”ξ˜ƒξš„ξš—ξš‹ξšŽξš–ξŸ‘ξ˜ƒ
ξš…ξš”ξš‡ξšƒξš–ξš‹ξšξš‰ξ˜ƒξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξ˜ƒξšƒξš‰ξš‡ξŸ€ξ˜ƒξ˜…ξš‹ξšξšƒξš”ξš›ξ˜ƒξš”ξš‡ξšξš‘ξš˜ξšƒξš–ξš‹ξš‘ξšξ˜ƒξš•ξš–ξšƒξš–ξš—ξš•ξ˜ƒξšƒξšξš†ξ˜ƒξš›ξš‡ξšƒξš”ξš•ξŸ¦ξš•ξš‹ξšξš…ξš‡ξŸ¦ξš”ξš‡ξšξš‘ξš˜ξšƒξš–ξš‹ξš‘ξšξ˜ƒξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξ˜ƒξš…ξšƒξš’ξš–ξš—ξš”ξš‡ξš†ξ˜ƒξšξš‘ξš†ξš‡ξš”ξšξš‹ξšœξšƒξš–ξš‹ξš‘ξšξ˜ƒ
ξš‡ξšˆξšˆξš‡ξš…ξš–ξš•ξŸ€
ξ˜”ξš—ξšƒξšŽξš‹ξš–ξš›ξ˜ƒ ξ˜Œξšξš†ξš‹ξš…ξšƒξš–ξš‘ξš”ξš•ξŸ£ξ˜ƒ ξ˜†ξš‘ξšξš’ξš‘ξš•ξš‹ξš–ξš‡ξ˜ƒ ξšξš‡ξš–ξš”ξš‹ξš…ξš•ξ˜ƒ ξš…ξš‘ξšξš„ξš‹ξšξš‹ξšξš‰ξ˜ƒ ξšξš—ξšŽξš–ξš‹ξš’ξšŽξš‡ξ˜ƒ ξš“ξš—ξšƒξšŽξš‹ξš–ξš›ξ˜ƒ ξš†ξš‹ξšξš‡ξšξš•ξš‹ξš‘ξšξš•ξŸ‘ξ˜ƒ ξš‹ξšξš…ξšŽξš—ξš†ξš‹ξšξš‰ξ˜ƒ ξš‰ξš”ξšƒξš†ξš‡ξ˜ƒ ξ¦­ξ˜ƒ ξš…ξš‘ξšξš†ξš‹ξš–ξš‹ξš‘ξšξ˜ƒ
ξš‹ξšξš–ξš‡ξš”ξšƒξš…ξš–ξš‹ξš‘ξšξ˜ƒξšƒξšξš†ξ˜ƒξšŠξš‹ξš‰ξšŠξŸ¦ξš‰ξš”ξšƒξš†ξš‡ξ˜ƒξš„ξš‹ξšξšƒξš”ξš›ξ˜ƒξš‹ξšξš†ξš‹ξš…ξšƒξš–ξš‘ξš”ξš•ξ˜ƒξ ‹ξš‰ξš”ξšƒξš†ξš‡ξ˜ƒξ¦·ξ˜ƒξ₯³ξ₯²ξ ŒξŸ€
ξ˜ξš‘ξš…ξšƒξš–ξš‹ξš‘ξšξŸ¦ξ˜…ξšƒξš•ξš‡ξš†ξ˜ƒξ˜‰ξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξŸ£ξ˜ƒξ˜Šξš‡ξš‘ξš‰ξš”ξšƒξš’ξšŠξš‹ξš…ξ˜ƒξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξ˜ƒξš‡ξšξš‰ξš‹ξšξš‡ξš‡ξš”ξš‹ξšξš‰ξ˜ƒξš‹ξšξš…ξšŽξš—ξš†ξš‹ξšξš‰ξ˜ƒξšŽξšƒξš–ξš‹ξš–ξš—ξš†ξš‡ξ˜ƒξ¦­ξ˜ƒξšŽξš‘ξšξš‰ξš‹ξš–ξš—ξš†ξš‡ξ˜ƒξš‹ξšξš–ξš‡ξš”ξšƒξš…ξš–ξš‹ξš‘ξšξ˜ƒξš–ξš‘ξ˜ƒξš…ξšƒξš’ξš–ξš—ξš”ξš‡ξ˜ƒ
ξšξš‡ξš‹ξš‰ξšŠξš„ξš‘ξš”ξšŠξš‘ξš‘ξš†ξ˜ƒξš’ξš”ξš‡ξšξš‹ξš—ξšξ˜ƒξš‡ξšˆξšˆξš‡ξš…ξš–ξš•ξ˜ƒξšƒξšξš†ξ˜ƒξš†ξš‹ξš•ξš–ξšƒξšξš…ξš‡ξ˜ƒξš…ξšƒξšŽξš…ξš—ξšŽξšƒξš–ξš‹ξš‘ξšξš•ξ˜ƒξšˆξš”ξš‘ξšξ˜ƒξš—ξš”ξš„ξšƒξšξ˜ƒξš…ξš‡ξšξš–ξš‡ξš”ξš•ξŸ€
ξ˜–ξš‹ξšœξš‡ξ˜ƒξ˜†ξšƒξš–ξš‡ξš‰ξš‘ξš”ξš‹ξšœξšƒξš–ξš‹ξš‘ξšξŸ£ξ˜ƒξ˜‡ξš‹ξš•ξš…ξš”ξš‡ξš–ξš‡ξ˜ƒξš„ξš‹ξšξš•ξ˜ƒξšˆξš‘ξš”ξ˜ƒξšŽξš‹ξš˜ξš‹ξšξš‰ξ˜ƒξšƒξš”ξš‡ξšƒξ˜ƒξ ‹ξš•ξšξšƒξšŽξšŽξŸ£ξ˜ƒξ¦΄ξ₯³ξŸ‘ξ₯·ξ₯²ξ₯²ξ˜ƒξš•ξš“ξ˜ƒξšˆξš–ξŸ’ξ˜ƒξšξš‡ξš†ξš‹ξš—ξšξŸ£ξ˜ƒξ₯³ξŸ‘ξ₯·ξ₯²ξ₯²ξŸ¦ξ₯΄ξŸ‘ξ₯·ξ₯²ξ₯²ξ˜ƒξš•ξš“ξ˜ƒξšˆξš–ξŸ’ξ˜ƒξšŽξšƒξš”ξš‰ξš‡ξŸ£ξ˜ƒξ¦΅ξ₯΄ξŸ‘ξ₯·ξ₯²ξ₯²ξ˜ƒ
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ξ˜ξš‘ξš‰ξŸ¦ξ˜—ξš”ξšƒξšξš•ξšˆξš‘ξš”ξšξš‡ξš†ξ˜ƒξ˜‰ξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξŸ£ξ˜ƒξ˜‘ξšƒξš–ξš—ξš”ξšƒξšŽξ˜ƒξšŽξš‘ξš‰ξšƒξš”ξš‹ξš–ξšŠξšξš•ξ˜ƒξš‘ξšˆξ˜ƒξš•ξšξš‡ξš™ξš‡ξš†ξ˜ƒξš…ξš‘ξšξš–ξš‹ξšξš—ξš‘ξš—ξš•ξ˜ƒξš˜ξšƒξš”ξš‹ξšƒξš„ξšŽξš‡ξš•ξ˜ƒξ ‹ξšŽξš‹ξš˜ξš‹ξšξš‰ξ˜ƒξšƒξš”ξš‡ξšƒξŸ‘ξ˜ƒξšŽξš‘ξš–ξ˜ƒξš•ξš‹ξšœξš‡ξŸ‘ξ˜ƒξš’ξš”ξš‹ξš…ξš‡ξ Œξ˜ƒξš–ξš‘ξ˜ƒ
ξšξš‘ξš”ξšξšƒξšŽξš‹ξšœξš‡ξ˜ƒξš†ξš‹ξš•ξš–ξš”ξš‹ξš„ξš—ξš–ξš‹ξš‘ξšξš•ξ˜ƒξšƒξšξš†ξ˜ƒξšŽξš‹ξšξš‡ξšƒξš”ξš‹ξšœξš‡ξ˜ƒξš”ξš‡ξšŽξšƒξš–ξš‹ξš‘ξšξš•ξšŠξš‹ξš’ξš•ξŸ€
ξ˜‘ξš‡ξš‹ξš‰ξšŠξš„ξš‘ξš”ξšŠξš‘ξš‘ξš†ξ˜ƒ ξ˜†ξš‘ξšξš’ξšƒξš”ξš‹ξš•ξš‘ξšξ˜ƒ ξ˜‰ξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξŸ£ξ˜ƒ ξ˜•ξšƒξš–ξš‹ξš‘ξš•ξ˜ƒ ξš…ξš‘ξšξš’ξšƒξš”ξš‹ξšξš‰ξ˜ƒ ξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξ˜ƒ ξšƒξš–ξš–ξš”ξš‹ξš„ξš—ξš–ξš‡ξš•ξ˜ƒ ξš–ξš‘ξ˜ƒ ξšξš‡ξš‹ξš‰ξšŠξš„ξš‘ξš”ξšŠξš‘ξš‘ξš†ξ˜ƒ ξšƒξš˜ξš‡ξš”ξšƒξš‰ξš‡ξš•ξŸ‘ξ˜ƒ
ξš‹ξšξš…ξšŽξš—ξš†ξš‹ξšξš‰ξ˜ƒξšŽξš‹ξš˜ξš‹ξšξš‰ξŸ¦ξš–ξš‘ξŸ¦ξšξš‡ξš‹ξš‰ξšŠξš„ξš‘ξš”ξšŠξš‘ξš‘ξš†ξ˜ƒξš”ξšƒξš–ξš‹ξš‘ξ˜ƒξšƒξšξš†ξ˜ƒξšŽξš‘ξš–ξŸ¦ξš–ξš‘ξŸ¦ξšξš‡ξš‹ξš‰ξšŠξš„ξš‘ξš”ξšŠξš‘ξš‘ξš†ξ˜ƒξš”ξšƒξš–ξš‹ξš‘ξŸ€
ξ˜†ξš‘ξšξš’ξš‘ξš•ξš‹ξš–ξš‡ξ˜ƒξ˜”ξš—ξšƒξšŽξš‹ξš–ξš›ξ˜ƒξ˜–ξš…ξš‘ξš”ξš‡ξš•ξŸ£ξ˜ƒξ˜šξš‡ξš‹ξš‰ξšŠξš–ξš‡ξš†ξ˜ƒξš…ξš‘ξšξš„ξš‹ξšξšƒξš–ξš‹ξš‘ξšξš•ξ˜ƒξš‘ξšˆξ˜ƒξš‰ξš”ξšƒξš†ξš‡ξŸ‘ξ˜ƒξš…ξš‘ξšξš†ξš‹ξš–ξš‹ξš‘ξšξŸ‘ξ˜ƒξšƒξšξš†ξ˜ƒξš˜ξš‹ξš‡ξš™ξ˜ƒξš”ξšƒξš–ξš‹ξšξš‰ξš•ξ˜ƒξš–ξš‘ξ˜ƒξš…ξš”ξš‡ξšƒξš–ξš‡ξ˜ƒξšŠξš‘ξšŽξš‹ξš•ξš–ξš‹ξš…ξ˜ƒξš“ξš—ξšƒξšŽξš‹ξš–ξš›ξ˜ƒ
ξšξš‡ξš–ξš”ξš‹ξš…ξš•ξŸ€ξ˜ƒ ξ˜—ξšŠξš‹ξš•ξ˜ƒ ξš’ξš”ξš‘ξš…ξš‡ξš•ξš•ξ˜ƒ ξš‡ξššξš’ξšƒξšξš†ξš‡ξš†ξ˜ƒ ξš–ξšŠξš‡ξ˜ƒ ξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξ˜ƒ ξš•ξš’ξšƒξš…ξš‡ξ˜ƒ ξšˆξš”ξš‘ξšξ˜ƒ ξ₯΄ξ₯³ξ˜ƒ ξš–ξš‘ξ˜ƒ ξ₯Έξ₯³ξ˜ƒ ξš˜ξšƒξš”ξš‹ξšƒξš„ξšŽξš‡ξš•ξŸ€ξ˜ƒ ξ˜‰ξš‡ξšƒξš–ξš—ξš”ξš‡ξ˜ƒ ξš•ξš‡ξšŽξš‡ξš…ξš–ξš‹ξš‘ξšξ˜ƒ ξš”ξš‡ξš†ξš—ξš…ξš‡ξš†ξ˜ƒ
ξš†ξš‹ξšξš‡ξšξš•ξš‹ξš‘ξšξšƒξšŽξš‹ξš–ξš›ξ˜ƒ ξš–ξš‘ξ˜ƒ ξ₯·ξ₯·ξ˜ƒ ξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξ˜ƒξš„ξš›ξ˜ƒξš”ξš‡ξšξš‘ξš˜ξš‹ξšξš‰ξ˜ƒ ξšŠξš‹ξš‰ξšŠξšŽξš›ξ˜ƒξš…ξš‘ξšŽξšŽξš‹ξšξš‡ξšƒξš”ξ˜ƒ ξš˜ξšƒξš”ξš‹ξšƒξš„ξšŽξš‡ξš•ξ˜ƒξ ‹ξš…ξš‘ξš”ξš”ξš‡ξšŽξšƒξš–ξš‹ξš‘ξšξ˜ƒ ξ¦΅ξ˜ƒ ξ₯²ξŸ€ξ₯»ξ₯·ξ Œξ˜ƒ ξšƒξšξš†ξ˜ƒ ξšŽξš‘ξš™ξŸ¦ξš˜ξšƒξš”ξš‹ξšƒξšξš…ξš‡ξ˜ƒ
ξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξŸ€
2.4 Data standardization
All features were standardized using StandardScaler,
[45,46]
which transforms each feature to have zero mean and
unit variance. This normalization ensures equal contribution and facilitates convergence.
[47]
The transformation
is defined as:
z = (x -  / ξ‘ξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒ (1)
where x represents the original feature value,  is the feature mean,  is the standard deviation, and z is the
standardized value.
2.5 Model development and training
The standardized dataset was partitioned into training (80%, n=16,373) and testing (20%, n=4,094) sets using
stratified random sampling to preserve price distribution characteristics across both subsets.
[48]
Six models were trained and evaluated:
1. Linear Regression (Ordinary Least Squares): The baseline model without regularization
2. Ridge Regression ξ₯³ξ ŒξŸ£ L2 regularization with minimal penalty
3. Ridge Regression ξ₯·ξ ŒξŸ£ Moderate L2 regularization
4. Ridge Regression ξ₯³ξ₯²ξ ŒξŸ£ Moderate-high L2 regularization
5. Ridge Regression ξ₯·ξ₯²ξ ŒξŸ£ High L2 regularization
6. Ridge Regression ξ₯³ξ₯²ξ₯²ξ ŒξŸ£ Very high L2 regularization
Ridge regression introduces a penalty term to the loss function to prevent overfitting by constraining coefficient
magnitudes.
[49]
The Ridge objective function is:
minimize: ||y - ξ˜›ξ Ύξ ξ ξ₯Ύ + ξ₯Ύξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ˜ƒξ ‹ξ₯΄ξ Œ
ξš™ξšŠξš‡ξš”ξš‡ξ˜ƒ ξš›ξ˜ƒ ξš‹ξš•ξ˜ƒ ξš–ξšŠξš‡ξ˜ƒ ξš–ξšƒξš”ξš‰ξš‡ξš–ξ˜ƒ ξš˜ξš‡ξš…ξš–ξš‘ξš”ξŸ‘ξ˜ƒ ξ˜›ξ˜ƒ ξš‹ξš•ξ˜ƒ ξš–ξšŠξš‡ξ˜ƒ ξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξ˜ƒ ξšξšƒξš–ξš”ξš‹ξššξŸ‘ξ˜ƒ ξ Ύξ˜ƒ ξš”ξš‡ξš’ξš”ξš‡ξš•ξš‡ξšξš–ξš•ξ˜ƒ ξš…ξš‘ξš‡ξšˆξšˆξš‹ξš…ξš‹ξš‡ξšξš–ξš•ξŸ‘ξ˜ƒ ξšƒξšξš†ξ˜ƒ ξ ½ξ˜ƒ ξš‹ξš•ξ˜ƒ ξš–ξšŠξš‡ξ˜ƒ ξš”ξš‡ξš‰ξš—ξšŽξšƒξš”ξš‹ξšœξšƒξš–ξš‹ξš‘ξšξ˜ƒ
strength.
[50]
2.6 Model evaluation
Model performance was assessed using multiple metrics.
[51,52]
: RΒ² Score, RMSE, MAE, and five-fold cross-
validation
[53]
.
RΒ² Score (Coefficient of Determination): Proportion of variance in property prices explained by the model,
calculated as RΒ² = 1 - (SS_res / SS_tot), where SS_res is the residual sum of squares and SS_tot is the total sum of
squares.
Root Mean Square Error (RMSE): Square root of the average squared prediction error, providing error
magnitude in original price units (dollars).
Mean Absolute Error (MAE): Average absolute difference between predicted and actual prices, less sensitive to
outliers than RMSE.
Cross-Validation: Five-fold cross-validation on the training set to assess model stability and generalization
capability, reporting mean RΒ² and standard deviation across folds.
ξ₯΄ξŸ€ξ₯Ήξ˜ƒξ˜‰ξš‡ξšƒξš–ξš—ξš”ξš‡ξ˜ƒξš‹ξšξš’ξš‘ξš”ξš–ξšƒξšξš…ξš‡ξ˜ƒξšƒξšξšƒξšŽξš›ξš•ξš‹ξš•
ξ˜‰ξš‡ξšƒξš–ξš—ξš”ξš‡ξ˜ƒξš‹ξšξš’ξš‘ξš”ξš–ξšƒξšξš…ξš‡ξ˜ƒξš™ξšƒξš•ξ˜ƒξš“ξš—ξšƒξšξš–ξš‹ξ§ξš‹ξš‡ξš†ξ˜ƒξš—ξš•ξš‹ξšξš‰ξ˜ƒξš–ξšŠξš‡ξ˜ƒξšƒξš„ξš•ξš‘ξšŽξš—ξš–ξš‡ξ˜ƒξš˜ξšƒξšŽξš—ξš‡ξš•ξ˜ƒξš‘ξšˆξ˜ƒξš•ξš–ξšƒξšξš†ξšƒξš”ξš†ξš‹ξšœξš‡ξš†ξ˜ƒξš”ξš‡ξš‰ξš”ξš‡ξš•ξš•ξš‹ξš‘ξšξ˜ƒξš…ξš‘ξš‡ξšˆξ§ξš‹ξš…ξš‹ξš‡ξšξš–ξš•ξŸ€ξ˜ƒξ˜–ξš‹ξšξš…ξš‡ξ˜ƒξšƒξšŽξšŽξ˜ƒ
ξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξ˜ƒξš™ξš‡ξš”ξš‡ξ˜ƒξš•ξš–ξšƒξšξš†ξšƒξš”ξš†ξš‹ξšœξš‡ξš†ξŸ‘ξ˜ƒξš…ξš‘ξš‡ξšˆξ§ξš‹ξš…ξš‹ξš‡ξšξš–ξ˜ƒξšξšƒξš‰ξšξš‹ξš–ξš—ξš†ξš‡ξš•ξ˜ƒξš†ξš‹ξš”ξš‡ξš…ξš–ξšŽξš›ξ˜ƒξš‹ξšξš†ξš‹ξš…ξšƒξš–ξš‡ξ˜ƒξš”ξš‡ξšŽξšƒξš–ξš‹ξš˜ξš‡ξ˜ƒξš‹ξšξš’ξš‘ξš”ξš–ξšƒξšξš…ξš‡ξ˜ƒξš‹ξšξ˜ƒξš’ξš”ξš‡ξš†ξš‹ξš…ξš–ξš‹ξšξš‰ξ˜ƒξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξ˜ƒ
ξš’ξš”ξš‹ξš…ξš‡ξš•ξŸ€ξ˜ƒξ˜—ξšŠξš‡ξ˜ƒξš–ξš‘ξš’ξ˜ƒξš–ξš‡ξšξ˜ƒξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξ˜ƒξš„ξš›ξ˜ƒξšƒξš„ξš•ξš‘ξšŽξš—ξš–ξš‡ξ˜ƒξš…ξš‘ξš‡ξšˆξ§ξš‹ξš…ξš‹ξš‡ξšξš–ξ˜ƒξš˜ξšƒξšŽξš—ξš‡ξ˜ƒξš™ξš‡ξš”ξš‡ξ˜ƒξš‹ξš†ξš‡ξšξš–ξš‹ξ§ξš‹ξš‡ξš†ξ˜ƒξšƒξšξš†ξ˜ƒξš˜ξš‹ξš•ξš—ξšƒξšŽξš‹ξšœξš‡ξš†ξ˜ƒξš–ξš‘ξ˜ƒξš’ξš”ξš‘ξš˜ξš‹ξš†ξš‡ξ˜ƒξš‹ξšξš–ξš‡ξš”ξš’ξš”ξš‡ξš–ξšƒξš„ξšŽξš‡ξ˜ƒ
ξš‹ξšξš•ξš‹ξš‰ξšŠξš–ξš•ξ˜ƒξš‹ξšξš–ξš‘ξ˜ƒξš˜ξšƒξšŽξš—ξš‡ξ˜ƒξš†ξš”ξš‹ξš˜ξš‡ξš”ξš•ξŸ€
ξ₯΅ξŸ€ξ˜ƒξ˜•ξš‡ξš•ξš—ξšŽξš–ξš•
ξ₯΅ξŸ€ξ₯³ξ˜ƒξ˜ξš‘ξš†ξš‡ξšŽξ˜ƒξš’ξš‡ξš”ξšˆξš‘ξš”ξšξšƒξšξš…ξš‡ξ˜ƒξš…ξš‘ξšξš’ξšƒξš”ξš‹ξš•ξš‘ξš
Table 2 summarizes the performance of all six trained models across training and testing datasets. And Table 3
summarizes of key performance metrics for the optimal linear regression model. The baseline linear regression
model achieved the highest test RΒ² of 0.7198, explaining 71.98% of variance in property prices (Table 4). Ridge
regression with varying regularization strengths produced marginally lower test RΒ² values (0.7182-0.7187),
indicating that the engineered features did not introduce substantial overfitting requiring regularization (Fig.
2). The minimal difference between training RΒ² (0.7356) and test RΒ² (0.7198) demonstrates good generalization
with limited overfitting. Cross-validation results showed consistent performance across folds (mean RΒ² =
0.7316, SD = 0.0101), confirming model stability. Root mean square error of $108,014 indicates that the model's
typical prediction error is approximately 20% of the mean property price ($540,088). Mean absolute error of
$82,626 suggests that half of predictions fall within Β±$82,626 of actual sale prices.
ξ˜—ξšƒξš„ξšŽξš‡ ξ₯΄ξŸ£ ξ˜ξš‘ξš†ξš‡ξšŽ ξš’ξš‡ξš”ξšˆξš‘ξš”ξšξšƒξšξš…ξš‡ metrics.
Model
Test RMSE ($)
Test MAE ($)
CV RΒ² Mean (Β±SD)
Linear Regression
108,014.08
82,626.44
0.7316 (Β±0.0101)
Ridge ξ₯³ξ Œ
108,241.06
-
0.7308 (Β±0.0108)
Ridge ξ₯·ξ Œ
108,236.82
-
0.7309 (Β±0.0108)
Ridge ξ₯³ξ₯²ξ Œ
108,238.23
-
0.7309 (Β±0.0109)
Ridge ξ₯·ξ₯²ξ Œ
108,281.88
-
0.7309 (Β±0.0108)
Ridge ξ₯³ξ₯²ξ₯²ξ Œ
108,328.16
-
0.7307 (Β±0.0107)
ξ˜—ξšƒξš„ξšŽξš‡ξ˜ƒξ₯΅ξŸ£ ξ˜–ξš—ξšξšξšƒξš”ξš›ξ˜ƒξš‘ξšˆξ˜ƒξšξš‡ξš›ξ˜ƒξš’ξš‡ξš”ξšˆξš‘ξš”ξšξšƒξšξš…ξš‡ξ˜ƒξšξš‡ξš–ξš”ξš‹ξš…ξš•ξ˜ƒξšˆξš‘ξš”ξ˜ƒξš–ξšŠξš‡ξ˜ƒξš‘ξš’ξš–ξš‹ξšξšƒξšŽξ˜ƒξšŽξš‹ξšξš‡ξšƒξš”ξ˜ƒξš”ξš‡ξš‰ξš”ξš‡ξš•ξš•ξš‹ξš‘ξšξ˜ƒξšξš‘ξš†ξš‡ξšŽξŸ€ξ˜ƒ
Metric
Value
Meaning
Test RΒ²
71.98%
Explains ~72 % of price variance
Test RMSE
108,014
ξ˜„ξš˜ξš‡ξš”ξšƒξš‰ξš‡ξ˜ƒξš’ξš”ξš‡ξš†ξš‹ξš…ξš–ξš‹ξš‘ξšξ˜ƒξš‡ξš”ξš”ξš‘ξš”ξ˜ƒξ¦³ξ˜ƒξ₯΄ξ₯²ξ¦¨ξ˜ƒξš‘ξšˆξ˜ƒξšξš‡ξšƒξšξ˜ƒξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξ˜ƒξš’ξš”ξš‹ξš…ξš‡ξ˜ƒξ ‹ξ₯·ξ₯Άξ₯²ξŸ‘ξ₯²ξ₯Ίξ₯Ίξ˜ƒξ˜˜ξ˜–ξ˜‡ξ Œ
Test MAE
82,626
Typical absolute deviation between predicted and actual prices
CV RΒ²
0.7316 Β± 0.0101
Stable across folds
ξ˜‰ξš‹ξš‰ξŸ€ξ˜ƒξ₯΄ξŸ£ξ˜ƒξ˜†ξš‘ξšξš’ξšƒξš”ξš‹ξš•ξš‘ξšξ˜ƒξš‘ξšˆξ˜ƒξšξš‘ξš†ξš‡ξšŽξ˜ƒξš’ξš‡ξš”ξšˆξš‘ξš”ξšξšƒξšξš…ξš‡ξ˜ƒξšƒξš…ξš”ξš‘ξš•ξš•ξ˜ƒξš†ξš‹ξšˆξšˆξš‡ξš”ξš‡ξšξš–ξ˜ƒξš”ξš‡ξš‰ξš—ξšŽξšƒξš”ξš‹ξšœξšƒξš–ξš‹ξš‘ξšξ˜ƒξš•ξš–ξš”ξš‡ξšξš‰ξš–ξšŠξš•ξŸ‘ξ˜ƒξš•ξšŠξš‘ξš™ξš‹ξšξš‰ξ˜ƒξšξš‹ξšξš‹ξšξšƒξšŽξ˜ƒξš˜ξšƒξš”ξš‹ξšƒξš–ξš‹ξš‘ξšξ˜ƒξš‹ξšξ˜ƒξš–ξš‡ξš•ξš–ξ˜ƒ
ξ˜•ξ₯Ύξ˜ƒξš˜ξšƒξšŽξš—ξš‡ξš•ξŸ€
ξ˜—ξšƒξš„ξšŽξš‡ξ˜ƒξ₯ΆξŸ£ ξ˜“ξš‡ξš”ξšˆξš‘ξš”ξšξšƒξšξš…ξš‡ξ˜ƒξš…ξš‘ξšξš’ξšƒξš”ξš‹ξš•ξš‘ξšξ˜ƒξš™ξš‹ξš–ξšŠξ˜ƒξš’ξš”ξš‹ξš‘ξš”ξ˜ƒξšƒξš’ξš’ξš”ξš‘ξšƒξš…ξšŠξš‡ξš•ξŸ€ξ˜ƒ
Approach
RΒ² Score
Improvement
Prior Work (raw features)
70%
Baseline
Proposed Model (with engineered
features)
71.98%
1.98%
3.2 Feature importance analysis
Analysis of standardized regression coefficients revealed the relative importance of engineered features in
predicting property values. Table 5 presents the top ten most influential features. Fig. 3 shows top ten most
important features by absolute coefficient value, showing dominance of ratio and geographic features.
Table 5: Top ten most important features.
Rank
Feature
Coefficient Impact
Direction
1
basement_to_living_ratio
25,806,316.70
Negative
2
above_to_living_ratio
25,776,914.47
Negative
3
lat_x_long
6,585,722.01
Negative
4
lat (latitude)
5,819,289.11
Negative
5
long (longitude)
2,358,865.06
Positive
6
sqft_living_squared
152,662.94
Positive
7
sqft_living
136,562.81
Negative
8
sqft_above
118,362.83
Negative
9
log_sqft_living
110,380.89
Positive
10
sqft_living_x_grade
90,846.45
Positive
ξ˜‰ξš‹ξš‰ξŸ€ξ˜ƒξ₯΅ξŸ£ξ˜ƒξ˜—ξš‘ξš’ξ˜ƒξš–ξš‡ξšξ˜ƒξšξš‘ξš•ξš–ξ˜ƒξš‹ξšξš’ξš‘ξš”ξš–ξšƒξšξš–ξ˜ƒξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξ˜ƒξš„ξš›ξ˜ƒξšƒξš„ξš•ξš‘ξšŽξš—ξš–ξš‡ξ˜ƒξš…ξš‘ξš‡ξšˆξ§ξš‹ξš…ξš‹ξš‡ξšξš–ξ˜ƒξš˜ξšƒξšŽξš—ξš‡ξŸ‘ξ˜ƒξš•ξšŠξš‘ξš™ξš‹ξšξš‰ξ˜ƒξš†ξš‘ξšξš‹ξšξšƒξšξš…ξš‡ξ˜ƒξš‘ξšˆξ˜ƒξš”ξšƒξš–ξš‹ξš‘ξ˜ƒξšƒξšξš†ξ˜ƒξš‰ξš‡ξš‘ξš‰ξš”ξšƒξš’ξšŠξš‹ξš…ξ˜ƒ
ξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξŸ€
ξ˜—ξšŠξš‡ξ˜ƒξš–ξš™ξš‘ξ˜ƒξšξš‘ξš•ξš–ξ˜ƒξš‹ξšξ§ξšŽξš—ξš‡ξšξš–ξš‹ξšƒξšŽξ˜ƒξš’ξš”ξš‡ξš†ξš‹ξš…ξš–ξš‘ξš”ξš•ξ˜ƒξš™ξš‡ξš”ξš‡ξ˜ƒξš”ξšƒξš–ξš‹ξš‘ξ˜ƒξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξŸ£ξ˜ƒξš„ξšƒξš•ξš‡ξšξš‡ξšξš–ξŸ¦ξš–ξš‘ξŸ¦ξšŽξš‹ξš˜ξš‹ξšξš‰ξ˜ƒξš”ξšƒξš–ξš‹ξš‘ξ˜ƒξšƒξšξš†ξ˜ƒξšƒξš„ξš‘ξš˜ξš‡ξŸ¦ξš–ξš‘ξŸ¦ξšŽξš‹ξš˜ξš‹ξšξš‰ξ˜ƒξš”ξšƒξš–ξš‹ξš‘ξŸ€ξ˜ƒξ˜—ξšŠξš‡ξ˜ƒ
ξšŽξšƒξš”ξš‰ξš‡ξ˜ƒξšξš‡ξš‰ξšƒξš–ξš‹ξš˜ξš‡ξ˜ƒξš…ξš‘ξš‡ξšˆξ§ξš‹ξš…ξš‹ξš‡ξšξš–ξš•ξ˜ƒξš‹ξšξš†ξš‹ξš…ξšƒξš–ξš‡ξ˜ƒξš–ξšŠξšƒξš–ξ˜ƒξšƒξš•ξ˜ƒξš–ξšŠξš‡ξš•ξš‡ξ˜ƒξš”ξšƒξš–ξš‹ξš‘ξš•ξ˜ƒξš‹ξšξš…ξš”ξš‡ξšƒξš•ξš‡ξ˜ƒξ ‹ξšξš‡ξšƒξšξš‹ξšξš‰ξ˜ƒξšŽξšƒξš”ξš‰ξš‡ξš”ξ˜ƒξš’ξš”ξš‘ξš’ξš‘ξš”ξš–ξš‹ξš‘ξšξš•ξ˜ƒξš‘ξšˆξ˜ƒξš„ξšƒξš•ξš‡ξšξš‡ξšξš–ξ˜ƒξš‘ξš”ξ˜ƒ
ξšƒξš„ξš‘ξš˜ξš‡ξŸ¦ξš‰ξš”ξš‘ξš—ξšξš†ξ˜ƒξš•ξš’ξšƒξš…ξš‡ξ˜ƒξš”ξš‡ξšŽξšƒξš–ξš‹ξš˜ξš‡ξ˜ƒξš–ξš‘ξ˜ƒξš–ξš‘ξš–ξšƒξšŽξ˜ƒξšŽξš‹ξš˜ξš‹ξšξš‰ξ˜ƒξšƒξš”ξš‡ξšƒξ ŒξŸ‘ξ˜ƒξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξ˜ƒξš˜ξšƒξšŽξš—ξš‡ξš•ξ˜ƒξš–ξš‡ξšξš†ξ˜ƒξš–ξš‘ξ˜ƒξš†ξš‡ξš…ξš”ξš‡ξšƒξš•ξš‡ξ˜ƒξš™ξšŠξš‡ξšξ˜ƒξš…ξš‘ξšξš–ξš”ξš‘ξšŽξšŽξš‹ξšξš‰ξ˜ƒξšˆξš‘ξš”ξ˜ƒξš‘ξš–ξšŠξš‡ξš”ξ˜ƒ
ξšˆξšƒξš…ξš–ξš‘ξš”ξš•ξŸ€ξ˜ƒ ξ˜—ξšŠξš‹ξš•ξ˜ƒ ξš…ξš‘ξš—ξšξš–ξš‡ξš”ξš‹ξšξš–ξš—ξš‹ξš–ξš‹ξš˜ξš‡ξ˜ƒ ξ§ξš‹ξšξš†ξš‹ξšξš‰ξ˜ƒ ξšŽξš‹ξšξš‡ξšŽξš›ξ˜ƒ ξš”ξš‡ξ§ξšŽξš‡ξš…ξš–ξš•ξ˜ƒ ξšξš—ξšŽξš–ξš‹ξš…ξš‘ξšŽξšŽξš‹ξšξš‡ξšƒξš”ξš‹ξš–ξš›ξ˜ƒ ξš‡ξšˆξšˆξš‡ξš…ξš–ξš•ξŸ‘ξ˜ƒ ξš™ξšŠξš‡ξš”ξš‡ξ˜ƒ ξš–ξšŠξš‡ξš•ξš‡ξ˜ƒ ξš”ξšƒξš–ξš‹ξš‘ξš•ξ˜ƒ ξš‹ξšξš˜ξš‡ξš”ξš•ξš‡ξšŽξš›ξ˜ƒ
ξš…ξš‘ξš”ξš”ξš‡ξšŽξšƒξš–ξš‡ξ˜ƒξš™ξš‹ξš–ξšŠξ˜ƒ ξš‘ξš–ξšŠξš‡ξš”ξ˜ƒ ξš’ξš‘ξš•ξš‹ξš–ξš‹ξš˜ξš‡ξ˜ƒξš˜ξšƒξšŽξš—ξš‡ξ˜ƒξš†ξš”ξš‹ξš˜ξš‡ξš”ξš•ξŸ€ξ˜ƒξ˜Šξš‡ξš‘ξš‰ξš”ξšƒξš’ξšŠξš‹ξš…ξ˜ƒξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξ˜ƒξš†ξš‡ξšξš‘ξšξš•ξš–ξš”ξšƒξš–ξš‡ξš†ξ˜ƒξš•ξš—ξš„ξš•ξš–ξšƒξšξš–ξš‹ξšƒξšŽξ˜ƒ ξš‹ξšξš’ξš‘ξš”ξš–ξšƒξšξš…ξš‡ξŸ‘ξ˜ƒ ξš™ξš‹ξš–ξšŠξ˜ƒ
ξšŽξšƒξš–ξš‹ξš–ξš—ξš†ξš‡ξ˜ƒξ¦­ξ˜ƒξšŽξš‘ξšξš‰ξš‹ξš–ξš—ξš†ξš‡ξ˜ƒξš‹ξšξš–ξš‡ξš”ξšƒξš…ξš–ξš‹ξš‘ξšξŸ‘ξ˜ƒξšŽξšƒξš–ξš‹ξš–ξš—ξš†ξš‡ξŸ‘ξ˜ƒξšƒξšξš†ξ˜ƒξšŽξš‘ξšξš‰ξš‹ξš–ξš—ξš†ξš‡ξ˜ƒξš‘ξš…ξš…ξš—ξš’ξš›ξš‹ξšξš‰ξ˜ƒξš–ξšŠξš”ξš‡ξš‡ξ˜ƒξš‘ξšˆξ˜ƒξš–ξšŠξš‡ξ˜ƒξš–ξš‘ξš’ξ˜ƒξ§ξš‹ξš˜ξš‡ξ˜ƒξš’ξš‘ξš•ξš‹ξš–ξš‹ξš‘ξšξš•ξŸ€ξ˜ƒξ˜—ξšŠξš‡ξ˜ƒξšξš‡ξš‰ξšƒξš–ξš‹ξš˜ξš‡ξ˜ƒ
ξšŽξšƒξš–ξš‹ξš–ξš—ξš†ξš‡ξ˜ƒξš…ξš‘ξš‡ξšˆξ§ξš‹ξš…ξš‹ξš‡ξšξš–ξ˜ƒξš•ξš—ξš‰ξš‰ξš‡ξš•ξš–ξš•ξ˜ƒξš–ξšŠξšƒξš–ξ˜ƒξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš‹ξš‡ξš•ξ˜ƒξšˆξšƒξš”ξš–ξšŠξš‡ξš”ξ˜ƒξšξš‘ξš”ξš–ξšŠξ˜ƒξš™ξš‹ξš–ξšŠξš‹ξšξ˜ƒξ˜Žξš‹ξšξš‰ξ˜ƒξ˜†ξš‘ξš—ξšξš–ξš›ξ˜ƒξ ‹ξšŠξš‹ξš‰ξšŠξš‡ξš”ξ˜ƒξšŽξšƒξš–ξš‹ξš–ξš—ξš†ξš‡ξ˜ƒξš˜ξšƒξšŽξš—ξš‡ξš•ξ Œξ˜ƒξš…ξš‘ξšξšξšƒξšξš†ξ˜ƒ
ξšŽξš‘ξš™ξš‡ξš”ξ˜ƒξš’ξš”ξš‹ξš…ξš‡ξš•ξŸ‘ξ˜ƒξš™ξšŠξš‹ξšŽξš‡ξ˜ƒξš–ξšŠξš‡ξ˜ƒξš’ξš‘ξš•ξš‹ξš–ξš‹ξš˜ξš‡ξ˜ƒξšŽξš‘ξšξš‰ξš‹ξš–ξš—ξš†ξš‡ξ˜ƒξš…ξš‘ξš‡ξšˆξ§ξš‹ξš…ξš‹ξš‡ξšξš–ξ˜ƒξš‹ξšξš†ξš‹ξš…ξšƒξš–ξš‡ξš•ξ˜ƒξš–ξšŠξšƒξš–ξ˜ƒξš‡ξšƒξš•ξš–ξš™ξšƒξš”ξš†ξ˜ƒξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš‹ξš‡ξš•ξ˜ƒξ ‹ξšŽξš‡ξš•ξš•ξ˜ƒξšξš‡ξš‰ξšƒξš–ξš‹ξš˜ξš‡ξ˜ƒξšŽξš‘ξšξš‰ξš‹ξš–ξš—ξš†ξš‡ξŸ‘ξ˜ƒ
ξšˆξšƒξš”ξš–ξšŠξš‡ξš”ξ˜ƒξšˆξš”ξš‘ξšξ˜ƒξ˜“ξš—ξš‰ξš‡ξš–ξ˜ƒξ˜–ξš‘ξš—ξšξš†ξ Œξ˜ƒξšŠξšƒξš˜ξš‡ξ˜ƒξšŠξš‹ξš‰ξšŠξš‡ξš”ξ˜ƒξš˜ξšƒξšŽξš—ξš‡ξš•ξŸ‘ξ˜ƒξš’ξš‘ξš–ξš‡ξšξš–ξš‹ξšƒξšŽξšŽξš›ξ˜ƒξš”ξš‡ξ§ξšŽξš‡ξš…ξš–ξš‹ξšξš‰ξ˜ƒξš‹ξšξšŽξšƒξšξš†ξ˜ƒξš•ξš—ξš„ξš—ξš”ξš„ξšƒξšξ˜ƒξš’ξš”ξš‡ξšˆξš‡ξš”ξš‡ξšξš…ξš‡ξš•ξŸ€ξ˜ƒξ˜ξš‹ξš˜ξš‹ξšξš‰ξ˜ƒξšƒξš”ξš‡ξšƒξ˜ƒ
ξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξ˜ƒ ξšƒξš’ξš’ξš‡ξšƒξš”ξš‡ξš†ξ˜ƒ ξš‹ξšξ˜ƒ ξšξš—ξšŽξš–ξš‹ξš’ξšŽξš‡ξ˜ƒ ξšˆξš‘ξš”ξšξš•ξŸ£ξ˜ƒ ξš”ξšƒξš™ξ˜ƒ ξš•ξš“ξš—ξšƒξš”ξš‡ξ˜ƒ ξšˆξš‘ξš‘ξš–ξšƒξš‰ξš‡ξ˜ƒ ξ ‹ξš”ξšƒξšξšξ˜ƒ ξ₯Ήξ ŒξŸ‘ξ˜ƒ ξš•ξš“ξš—ξšƒξš”ξš‡ξš†ξ˜ƒ ξš–ξš‡ξš”ξšξ˜ƒ ξ ‹ξš”ξšƒξšξšξ˜ƒ ξ₯Έξ ŒξŸ‘ξ˜ƒ ξšŽξš‘ξš‰ξšƒξš”ξš‹ξš–ξšŠξšξš‹ξš…ξ˜ƒ
ξš–ξš”ξšƒξšξš•ξšˆξš‘ξš”ξšξšƒξš–ξš‹ξš‘ξšξ˜ƒ ξ ‹ξš”ξšƒξšξšξ˜ƒ ξ₯»ξ ŒξŸ‘ξ˜ƒ ξšƒξšξš†ξ˜ƒ ξš‹ξšξš–ξš‡ξš”ξšƒξš…ξš–ξš‹ξš‘ξšξ˜ƒ ξš™ξš‹ξš–ξšŠξ˜ƒ ξš‰ξš”ξšƒξš†ξš‡ξ˜ƒ ξ ‹ξš”ξšƒξšξšξ˜ƒ ξ₯³ξ₯²ξ ŒξŸ€ξ˜ƒ ξ˜—ξšŠξš‹ξš•ξ˜ƒ ξš”ξš‡ξš†ξš—ξšξš†ξšƒξšξš…ξš›ξ˜ƒ ξšƒξš…ξš”ξš‘ξš•ξš•ξ˜ƒ ξš–ξš”ξšƒξšξš•ξšˆξš‘ξš”ξšξšƒξš–ξš‹ξš‘ξšξš•ξ˜ƒ
ξš‹ξšξš†ξš‹ξš…ξšƒξš–ξš‡ξš•ξ˜ƒξš–ξšŠξšƒξš–ξ˜ƒξšŽξš‹ξš˜ξš‹ξšξš‰ξ˜ƒξšƒξš”ξš‡ξšƒξ˜ƒξš‹ξš•ξ˜ƒξšƒξ˜ƒξšˆξš—ξšξš†ξšƒξšξš‡ξšξš–ξšƒξšŽξ˜ƒξš˜ξšƒξšŽξš—ξš‡ξ˜ƒξš†ξš”ξš‹ξš˜ξš‡ξš”ξŸ‘ξ˜ƒξš„ξš—ξš–ξ˜ƒξš‹ξš–ξš•ξ˜ƒξš”ξš‡ξšŽξšƒξš–ξš‹ξš‘ξšξš•ξšŠξš‹ξš’ξ˜ƒξš™ξš‹ξš–ξšŠξ˜ƒξš’ξš”ξš‹ξš…ξš‡ξ˜ƒξš‡ξššξšŠξš‹ξš„ξš‹ξš–ξš•ξ˜ƒξšξš‘ξšξŸ¦ξšŽξš‹ξšξš‡ξšƒξš”ξš‹ξš–ξš›ξ˜ƒ
ξš…ξšƒξš’ξš–ξš—ξš”ξš‡ξš†ξ˜ƒξš„ξš›ξ˜ƒξš’ξš‘ξšŽξš›ξšξš‘ξšξš‹ξšƒξšŽξ˜ƒξšƒξšξš†ξ˜ƒξšŽξš‘ξš‰ξšƒξš”ξš‹ξš–ξšŠξšξš‹ξš…ξ˜ƒξš–ξš‡ξš”ξšξš•ξŸ€
3.3 Prediction analysis
Scatter plots of predicted versus actual prices for the test set revealed strong linear correspondence along the
identity line, with some heteroscedasticity (Fig. 4). Prediction errors increased for luxury properties above
$1,500,000, where the model tended to underpredict values. This pattern reflects the limited representation of
high-end properties in the training data (only 5.3% of properties exceeded $1,000,000) despite luxury
indicators and size interactions driving major model decisions (Table 6). Residual analysis showed
approximately normal distribution centered at zero, with slightly heavier tails than a Gaussian distribution.
Residual variance increased modestly with predicted price, indicating mild heteroscedasticity but not severe
enough to invalidate model assumptions.
ξ˜‰ξš‹ξš‰ξŸ€ξ˜ƒ ξ₯ΆξŸ£ξ˜ƒ ξ˜–ξš…ξšƒξš–ξš–ξš‡ξš”ξ˜ƒ ξš’ξšŽξš‘ξš–ξ˜ƒ ξš‘ξšˆξ˜ƒ ξš’ξš”ξš‡ξš†ξš‹ξš…ξš–ξš‡ξš†ξ˜ƒ ξš˜ξš‡ξš”ξš•ξš—ξš•ξ˜ƒ ξšƒξš…ξš–ξš—ξšƒξšŽξ˜ƒ ξš’ξš”ξš‹ξš…ξš‡ξš•ξ˜ƒ ξš•ξšŠξš‘ξš™ξš‹ξšξš‰ξ˜ƒ ξš•ξš–ξš”ξš‘ξšξš‰ξ˜ƒ ξšŽξš‹ξšξš‡ξšƒξš”ξ˜ƒ ξš…ξš‘ξš”ξš”ξš‡ξš•ξš’ξš‘ξšξš†ξš‡ξšξš…ξš‡ξ˜ƒ ξš™ξš‹ξš–ξšŠξ˜ƒ ξš•ξš‘ξšξš‡ξ˜ƒ
ξšŠξš‡ξš–ξš‡ξš”ξš‘ξš•ξš…ξš‡ξš†ξšƒξš•ξš–ξš‹ξš…ξš‹ξš–ξš›ξ˜ƒξšƒξš–ξ˜ƒξšŠξš‹ξš‰ξšŠξš‡ξš”ξ˜ƒξš’ξš”ξš‹ξš…ξš‡ξ˜ƒξš”ξšƒξšξš‰ξš‡ξš•ξŸ€
ξ˜—ξšƒξš„ξšŽξš‡ξ˜ƒξ₯ΈξŸ£ ξ˜—ξš‘ξš’ξ˜ƒξš–ξš‡ξšξ˜ƒξšξš‘ξš•ξš–ξ˜ƒξš‹ξšξš’ξš‘ξš”ξš–ξšƒξšξš–ξ˜ƒξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξ˜ƒξš”ξšƒξšξšξš‡ξš†ξ˜ƒξš„ξš›ξ˜ƒξšƒξš„ξš•ξš‘ξšŽξš—ξš–ξš‡ξ˜ƒξš•ξš–ξšƒξšξš†ξšƒξš”ξš†ξš‹ξšœξš‡ξš†ξ˜ƒξš”ξš‡ξš‰ξš”ξš‡ξš•ξš•ξš‹ξš‘ξšξ˜ƒξš…ξš‘ξš‡ξšˆξ§ξš‹ξš…ξš‹ξš‡ξšξš–ξ˜ƒξš˜ξšƒξšŽξš—ξš‡ξš•ξŸ€ξ˜ƒ
Rank
Feature
Type
Impact
1
sqft_living Γ— grade
Interaction
Strongest
2
sqft_livingΒ²
Polynomial
Very Strong
3
gradeΒ²
Polynomial
Strong
4
waterfront
Original
Strong
5
dist_from_downtown
Domain
Negative
6
quality_score
Composite
Moderate
7
sqft_living Γ— condition
Interaction
Moderate
8
is_luxury
Composite
Moderate
9
log_sqft_living
Transformed
Moderate
10
renovation_impact
Domain
Moderate
3.4 Correlation structure
Correlation heatmaps of the top features revealed several strong pairwise relationships (Fig. 5). Living area
correlated highly with above-ground area (r=0.88), number of bathrooms (r=0.76), and grade (r=0.72).
Geographic coordinates showed negative correlation (r=-0.67), reflecting the northwest-to-southeast
orientation of King County. Engineered ratio features exhibited intentionally lower correlations with raw
features, successfully introducing orthogonal information. For example, basement-to-living ratio correlated only
moderately with living area (r=0.34), indicating that this ratio captures distinct variation in property
configuration beyond simple size effects.
4. Discussion
4.1 Performance achievement and comparison
This study achieved a test RΒ² of 0.7198 using linear regression with engineered features, representing a 2.8
percentage point improvement over the typical 70% baseline for raw features. While falling short of the 80%
target, this performance demonstrates that domain-informed feature engineering can substantially enhance
interpretable linear models. Compared to recent literature, our results are competitive for linear approaches.
Previous studies report RΒ² values of 0.65-0.72 for basic linear regression,
[28,29,54]
while tree-based ensembles
achieve 0.80-0.88.
[20,21,55]
Recent work on prototype-based learning achieved similar interpretability goals.
[56]
Studies using BIM and AI integration show promising directions for future enhancement.
[57]
The minimal benefit
from Ridge regularization suggests that the engineered feature set, despite its expansion to 55 variables, did not
introduce substantial multicollinearity problems requiring penalization. This finding validates the feature
selection process, which removed highly correlated variables before modeling.
ξ˜‰ξš‹ξš‰ξŸ€ξ˜ƒξ₯·ξŸ£ξ˜ƒξ˜†ξš‘ξš”ξš”ξš‡ξšŽξšƒξš–ξš‹ξš‘ξšξ˜ƒξšŠξš‡ξšƒξš–ξšξšƒξš’ξ˜ƒξš‘ξšˆξ˜ƒξš–ξš‘ξš’ξ˜ƒξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξ˜ƒξš•ξšŠξš‘ξš™ξš‹ξšξš‰ξ˜ƒξš”ξš‡ξšŽξšƒξš–ξš‹ξš‘ξšξš•ξšŠξš‹ξš’ξš•ξ˜ƒξš„ξš‡ξš–ξš™ξš‡ξš‡ξšξ˜ƒξš‡ξšξš‰ξš‹ξšξš‡ξš‡ξš”ξš‡ξš†ξ˜ƒξšƒξšξš†ξ˜ƒξš‘ξš”ξš‹ξš‰ξš‹ξšξšƒξšŽξ˜ƒξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξš•ξŸ€
4.2 Feature engineering insights
The dominance of ratio features aligns with hedonic pricing theory.
[58,59]
Absolute square footage matters, but
its relationship to property value depends on configuration. A 2,000 sq ft home with 500 sq ft basement differs
substantially from one with 1,500 sq ft above ground, even with identical total living area. Geographic features'
prominence underscores location primacy in real estate valuation.
[60,61]
The latitude Γ— longitude interaction term
captures neighborhood premium effects beyond simple coordinate values, suggesting that specific geographic
clusters command disproportionate value. This finding aligns with hedonic pricing theory, where location
serves as a proxy for school quality, amenities, safety, and prestige. Multiple appearances of living area across
transformations reveal non-linearity successfully captured within the linear framework.
[62,63]
Properties exhibit
increasing marginal value per square foot up to approximately 2,500 sq ft, after which marginal returns
diminish. Polynomial and logarithmic terms successfully capture this curvature within the linear framework.
Surprisingly, waterfront status and view ratings did not rank among the top ten features despite their expected
importance. This may reflect their low prevalence in the dataset (only 0.75% of properties had waterfront
access), limiting their statistical impact despite large per-property effects.
4.3 Practical applications
The developed model offers several practical advantages for real estate professionals. First, coefficient
interpretability enables appraisers to explain valuation logic to clients and regulatory bodies, unlike black- box
models. Second, computational efficiency allows real-time valuations on standard hardware, facilitating high-
volume automated appraisals. Third, the feature engineering framework is transferable to other geographic
markets with appropriate local calibration. For property sellers and buyers, the feature importance rankings
provide actionable insights supported by recent market analysis.
[64,65]
Location remains the dominant factor,
suggesting that buyers prioritizing value should focus on less fashionable neighborhoods with growth potential
rather than marginal property improvements in premium locations. Mortgage lenders can utilize the model for
initial loan-to-value assessments as demonstrated in recent applications.
[66,67]
The 108,014 RMSE provides a
quantifiable uncertainty bound for risk modeling in mortgage portfolios.
4.4 Limitations and future directions
Several limitations constrain this study's findings as:
1. The dataset's temporal scope (2014-2015) predates recent market dynamics,
[68]
including the COVID-19
pandemic's effects on housing preferences. Model retraining with current data incorporating geospatial analysis
would improve relevance.
[69,70]
Incorporating additional variables through feature augmentation could approach
higher targets.[71,72].
2. The 71.98% RΒ² indicates that 28% of price variation remains unexplained. Factors not captured in the dataset
likely include interior condition details (finishes, appliances, layout efficiency), school district quality, crime
rates, walkability scores, and proximity to employment centers. Incorporating these variables through feature
augmentation could approach the 80% target.
3. The model assumes linear relationships after feature transformation. While polynomial and logarithmic
terms introduce non-linearity, more complex interactions might require generalized additive models or spline-
based approaches.
4. Geographic information is represented only by latitude and longitude coordinates. Spatial econometric
techniques like kriging or geographically weighted regression could better capture localized market dynamics
and spatial autocorrelation in residuals.
Future research should explore automated feature engineering
[73,74]
ensemble methods,
[75]
and spatial
econometric techniques.
[76,77]
Automated feature engineering using genetic algorithms or neural architecture
search could systematically discover optimal transformations beyond human domain knowledge. Finally, model
deployment requires ongoing monitoring for temporal drift, as housing market dynamics evolve with economic
conditions, interest rates, and demographic shifts.
[78]
5. Conclusions
This research demonstrates that systematic feature engineering can substantially enhance linear regression
performance for residential property valuation. By creating 40 engineered features capturing interaction
effects, non-linearities, ratios, temporal dynamics, and geographic patterns, we achieved a test RΒ² of 0.7198 and
RMSE of $108,014 on the King County housing dataset. Feature importance analysis revealed that configuration
ratios (basement-to-living, above-to-living), geographic coordinates, and living area transformations are the
most influential predictors of property value.
The minimal benefit from regularization indicates that the
engineered feature set achieves complexity without problematic multicollinearity. While falling short of the
80% RΒ² target, our interpretable linear model achieves 85-90% of the accuracy of complex machine learning
algorithms while maintaining complete transparency in predictions. This balance makes the approach
particularly suitable for regulatory environments and professional practice where model interpretability is
essential. The feature engineering framework is generalizable to other markets.
Future research incorporating
additional contextual variables may close the remaining performance gap while preserving interpretability.
Acknowledgments
The authors acknowledge Kaggle for providing the King County House Sales dataset and the open-source Python
data science community for developing the analytical tools used in this research.
Funding Declaration
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit
sectors.
Data Availability Statement
The datasets generated and/or analyzed during the current study that support the findings are available from the
corresponding author upon reasonable request.
ξ˜†ξš‘ξšξ§ξšŽξš‹ξš…ξš–ξ˜ƒξš‘ξšˆξ˜ƒξ˜Œξšξš–ξš‡ξš”ξš‡ξš•ξš–
ξ˜—ξšŠξš‡ξš”ξš‡ξ˜ƒξš‹ξš•ξ˜ƒξšξš‘ξ˜ƒξš…ξš‘ξšξ§ξšŽξš‹ξš…ξš–ξ˜ƒξš‘ξšˆξ˜ƒξš‹ξšξš–ξš‡ξš”ξš‡ξš•ξš–ξŸ€
ξ˜„ξš”ξš–ξš‹ξ§ξš‹ξš…ξš‹ξšƒξšŽξ˜ƒξ˜Œξšξš–ξš‡ξšŽξšŽξš‹ξš‰ξš‡ξšξš…ξš‡ξ˜ƒξ ‹ξ˜„ξ˜Œξ Œξ˜ƒξ˜˜ξš•ξš‡ξ˜ƒξ˜‡ξš‹ξš•ξš…ξšŽξš‘ξš•ξš—ξš”ξš‡
ξ˜—ξšŠξš‡ξ˜ƒ ξšƒξš—ξš–ξšŠξš‘ξš”ξš•ξ˜ƒ ξš†ξš‡ξš…ξšŽξšƒξš”ξš‡ξ˜ƒ ξš–ξšŠξšƒξš–ξ˜ƒ ξšƒξš”ξš–ξš‹ξ§ξš‹ξš…ξš‹ξšƒξšŽξ˜ƒ ξš‹ξšξš–ξš‡ξšŽξšŽξš‹ξš‰ξš‡ξšξš…ξš‡ξ˜ƒ ξ ‹ξ˜„ξ˜Œξ ŒξŸ¦ξšƒξš•ξš•ξš‹ξš•ξš–ξš‡ξš†ξ˜ƒ ξš–ξš‘ξš‘ξšŽξš•ξ˜ƒ ξš™ξš‡ξš”ξš‡ξ˜ƒ ξš—ξš•ξš‡ξš†ξ˜ƒ ξš‘ξšξšŽξš›ξ˜ƒ ξšˆξš‘ξš”ξ˜ƒ ξšŽξšƒξšξš‰ξš—ξšƒξš‰ξš‡ξ˜ƒ ξš”ξš‡ξ§ξš‹ξšξš‡ξšξš‡ξšξš–ξŸ‘ξ˜ƒ
ξš‰ξš”ξšƒξšξšξšƒξš”ξ˜ƒξš‹ξšξš’ξš”ξš‘ξš˜ξš‡ξšξš‡ξšξš–ξŸ‘ξ˜ƒξšƒξšξš†ξ˜ƒξšξšƒξšξš—ξš•ξš…ξš”ξš‹ξš’ξš–ξ˜ƒξš•ξš–ξš”ξš—ξš…ξš–ξš—ξš”ξš‹ξšξš‰ξ˜ƒξš’ξš—ξš”ξš’ξš‘ξš•ξš‡ξš•ξ˜ƒξš†ξš—ξš”ξš‹ξšξš‰ξ˜ƒξš–ξšŠξš‡ξ˜ƒξš’ξš”ξš‡ξš’ξšƒξš”ξšƒξš–ξš‹ξš‘ξšξ˜ƒξš‘ξšˆξ˜ƒξš–ξšŠξš‹ξš•ξ˜ƒξš™ξš‘ξš”ξšξŸ€ξ˜ƒξ˜„ξšŽξšŽξ˜ƒξš–ξš‡ξš…ξšŠξšξš‹ξš…ξšƒξšŽξ˜ƒ
ξš…ξš‘ξšξš–ξš‡ξšξš–ξŸ‘ξ˜ƒξš‡ξššξš’ξš‡ξš”ξš‹ξšξš‡ξšξš–ξšƒξšŽξ˜ƒξš‹ξšξš’ξšŽξš‡ξšξš‡ξšξš–ξšƒξš–ξš‹ξš‘ξšξŸ‘ξ˜ƒξš”ξš‡ξš•ξš—ξšŽξš–ξš•ξŸ‘ξ˜ƒξšƒξšξš†ξ˜ƒξš‹ξšξš–ξš‡ξš”ξš’ξš”ξš‡ξš–ξšƒξš–ξš‹ξš‘ξšξš•ξ˜ƒξš™ξš‡ξš”ξš‡ξ˜ƒξš‹ξšξš†ξš‡ξš’ξš‡ξšξš†ξš‡ξšξš–ξšŽξš›ξ˜ƒξš†ξš‡ξš˜ξš‡ξšŽξš‘ξš’ξš‡ξš†ξ˜ƒξšƒξšξš†ξ˜ƒξš˜ξš‡ξš”ξš‹ξ§ξš‹ξš‡ξš†ξ˜ƒ
ξš„ξš›ξ˜ƒξš–ξšŠξš‡ξ˜ƒξšƒξš—ξš–ξšŠξš‘ξš”ξš•ξŸ€
ξ˜–ξš—ξš’ξš’ξš‘ξš”ξš–ξš‹ξšξš‰ξ˜ƒξ˜Œξšξšˆξš‘ξš”ξšξšƒξš–ξš‹ξš‘ξš
ξ˜‘ξš‘ξš–ξ˜ƒξšƒξš’ξš’ξšŽξš‹ξš…ξšƒξš„ξšŽξš‡ξŸ€
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ξ˜ξŸ€ξ˜ƒξ˜–ξšξš‹ξš–ξšŠξŸ‘ξ˜ƒξ˜„ξŸ€ξ˜ƒξ˜ξš‘ξšŠξšξš•ξš‘ξšξŸ‘ξ˜ƒξ˜•ξš‡ξšƒξšŽξ˜ƒξš‡ξš•ξš–ξšƒξš–ξš‡ξ˜ƒξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξ˜ƒξš—ξš•ξš‹ξšξš‰ξ˜ƒξšξšƒξš…ξšŠξš‹ξšξš‡ξ˜ƒξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξŸ£ξ˜ƒξ˜„ξ˜ƒξš…ξš‘ξšξš’ξš”ξš‡ξšŠξš‡ξšξš•ξš‹ξš˜ξš‡ξ˜ƒξš”ξš‡ξš˜ξš‹ξš‡ξš™ξŸ‘ξ˜ƒξ˜ξš‘ξš—ξš”ξšξšƒξšŽξ˜ƒξš‘ξšˆξ˜ƒ
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ξ₯΄ξ 
ξ˜•ξš‘ξš†ξš”ξš‹ξš‰ξš—ξš‡ξšœξŸ¦ξ˜–ξš‡ξš”ξš”ξšƒξšξš‘ξŸ‘ξ˜ƒξ˜ξŸ€ξ˜„ξŸ€ξŸ‘ξ˜ƒξ˜“ξš”ξš‘ξš–ξš‘ξš–ξš›ξš’ξš‡ξŸ¦ξš„ξšƒξš•ξš‡ξš†ξ˜ƒξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξ˜ƒξšˆξš‘ξš”ξ˜ƒξš”ξš‡ξšƒξšŽξ˜ƒξš‡ξš•ξš–ξšƒξš–ξš‡ξ˜ƒξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξŸ£ξ˜ƒξšƒξ˜ƒξšξšƒξš…ξšŠξš‹ξšξš‡ξ˜ƒξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξ˜ƒξšξš‘ξš†ξš‡ξšŽξ˜ƒ
ξš–ξšŠξšƒξš–ξ˜ƒξš‡ξššξš’ξšŽξšƒξš‹ξšξš•ξ˜ƒξš’ξš”ξš‹ξš…ξš‡ξš•ξŸ‘ξ˜ƒ ξ˜„ξšξšξšƒξšŽξš•ξ˜ƒξš‘ξšˆξ˜ƒξ˜’ξš’ξš‡ξš”ξšƒξš–ξš‹ξš‘ξšξš•ξ˜ƒξ˜•ξš‡ξš•ξš‡ξšƒξš”ξš…ξšŠξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯ΆξŸ‘ξ˜ƒ ξ₯΅ξ₯Άξ₯ΆξŸ‘ξ˜ƒξ₯΄ξ₯Ίξ₯ΉξŸ¦ξ₯΅ξ₯³ξ₯³ξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯²ξ₯²ξ₯Ήξ €ξš•ξ₯³ξ₯²ξ₯Άξ₯Ήξ₯»ξŸ¦ξ₯²ξ₯΄ξ₯ΆξŸ¦
ξ₯²ξ₯Έξ₯΄ξ₯Ήξ₯΅ξŸ¦ξ₯³ξŸ€
ξ₯΅ξ 
ξ˜ξŸ€ξ˜ƒ ξ˜ξšŠξšƒξšξš‰ξŸ‘ξ˜ƒ ξ˜‹ξŸ€ξ˜ƒ ξ˜ξš‹ξš—ξŸ‘ξ˜ƒ ξ˜‰ξš‡ξšƒξš–ξš—ξš”ξš‡ξ˜ƒ ξš‡ξšξš‰ξš‹ξšξš‡ξš‡ξš”ξš‹ξšξš‰ξ˜ƒ ξšˆξš‘ξš”ξ˜ƒ ξšŠξš‘ξš—ξš•ξš‹ξšξš‰ξ˜ƒ ξš’ξš”ξš‹ξš…ξš‡ξ˜ƒ ξš’ξš”ξš‡ξš†ξš‹ξš…ξš–ξš‹ξš‘ξšξŸ£ξ˜ƒ ξ˜„ξšξ˜ƒ ξš‡ξšξš’ξš‹ξš”ξš‹ξš…ξšƒξšŽξ˜ƒ ξš•ξš–ξš—ξš†ξš›ξŸ‘ξ˜ƒ ξ˜•ξš‡ξšƒξšŽξ˜ƒ ξ˜ˆξš•ξš–ξšƒξš–ξš‡ξ˜ƒ
ξ˜ˆξš…ξš‘ξšξš‘ξšξš‹ξš…ξš•ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯΄ξŸ‘ξ˜ƒξ₯·ξ₯²ξŸ‘ξ˜ƒξ₯Ίξ₯»ξ₯³ξŸ¦ξ₯»ξ₯³ξ₯·ξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯³ξ₯³ξ₯³ξ €ξ₯³ξ₯·ξ₯Άξ₯²ξŸ¦ξ₯Έξ₯΄ξ₯΄ξ₯»ξŸ€ξ₯³ξ₯΄ξ₯΅ξ₯Άξ₯·ξŸ€
ξ₯Άξ 
ξ˜ξŸ€ξ˜ƒξ˜„ξšξš†ξš‡ξš”ξš•ξš‘ξšξŸ‘ξ˜ƒξ˜•ξŸ€ξ˜ƒξ˜šξš‹ξšŽξšŽξš‹ξšƒξšξš•ξŸ‘ξ˜ƒξ˜ξš‹ξšξš‡ξšƒξš”ξ˜ƒξš”ξš‡ξš‰ξš”ξš‡ξš•ξš•ξš‹ξš‘ξšξ˜ƒξš‹ξšξ˜ƒξš”ξš‡ξšƒξšŽξ˜ƒξš‡ξš•ξš–ξšƒξš–ξš‡ξ˜ƒξšƒξš’ξš’ξš”ξšƒξš‹ξš•ξšƒξšŽξŸ£ξ˜ƒξ˜ξš‡ξš–ξšŠξš‘ξš†ξš•ξ˜ƒξšƒξšξš†ξ˜ƒξšƒξš’ξš’ξšŽξš‹ξš…ξšƒξš–ξš‹ξš‘ξšξš•ξŸ‘ξ˜ƒξ˜ξš‘ξš—ξš”ξšξšƒξšŽξ˜ƒ
ξš‘ξšˆξ˜ƒξ˜•ξš‡ξšƒξšŽξ˜ƒξ˜ˆξš•ξš–ξšƒξš–ξš‡ξ˜ƒξ˜‰ξš‹ξšξšƒξšξš…ξš‡ξ˜ƒξšƒξšξš†ξ˜ƒξ˜ˆξš…ξš‘ξšξš‘ξšξš‹ξš…ξš•ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯³ξŸ‘ξ˜ƒξ₯Έξ₯΅ξŸ‘ξ˜ƒξ₯Άξ₯³ξ₯΄ξŸ¦ξ₯Άξ₯΅ξ₯ΊξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯²ξ₯²ξ₯Ήξ €ξš•ξ₯³ξ₯³ξ₯³ξ₯Άξ₯ΈξŸ¦ξ₯²ξ₯΄ξ₯²ξŸ¦ξ₯²ξ₯»ξ₯Ίξ₯Ήξ₯ΈξŸ¦ξ₯·ξŸ€
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ξ˜Žξš‹ξšξš‰ξ˜ƒ ξ˜†ξš‘ξš—ξšξš–ξš›ξ˜ƒ ξ˜„ξš•ξš•ξš‡ξš•ξš•ξš‘ξš”ξŸ‘ξ˜ƒ ξ˜“ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξ˜ƒ ξ˜–ξšƒξšŽξš‡ξš•ξ˜ƒ ξ˜‡ξšƒξš–ξšƒξŸ‘ξ˜ƒ ξ₯΄ξ₯²ξ₯³ξ₯ΆξŸ¦ξ₯΄ξ₯²ξ₯³ξ₯·ξŸ‘ξ˜ƒ ξ˜Žξšƒξš‰ξš‰ξšŽξš‡ξŸ‘ξ˜ƒ
ξšŠξš–ξš–ξš’ξš•ξŸ£ξ €ξ €ξš™ξš™ξš™ξŸ€ξšξšƒξš‰ξš‰ξšŽξš‡ξŸ€ξš…ξš‘ξšξ €ξš†ξšƒξš–ξšƒξš•ξš‡ξš–ξš•ξ €ξšŠξšƒξš”ξšŽξšˆξš‘ξššξš‡ξšξ €ξšŠξš‘ξš—ξš•ξš‡ξš•ξšƒξšŽξš‡ξš•ξš’ξš”ξš‡ξš†ξš‹ξš…ξš–ξš‹ξš‘ξšξŸ‘ξ˜ƒξ˜„ξš…ξš…ξš‡ξš•ξš•ξš‡ξš†ξ˜ƒξ₯³ξ₯·ξ˜ƒξ˜’ξš…ξš–ξš‘ξš„ξš‡ξš”ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯ΆξŸ€
ξ₯Έξ 
ξ˜ξŸ€ξ˜ƒξ˜‘ξš‘ξš”ξš‹ξš‡ξš‰ξšƒξŸ‘ξ˜ƒξ˜ξŸ€ξ˜ƒξ˜Œξš•ξš‹ξšξŸ‘ξ˜ƒξ˜•ξš‡ξšƒξšŽξ˜ƒξš‡ξš•ξš–ξšƒξš–ξš‡ξ˜ƒξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξ˜ƒξš†ξš‡ξš…ξš‹ξš•ξš‹ξš‘ξšξŸ¦ξšξšƒξšξš‹ξšξš‰ξ˜ƒξš•ξš›ξš•ξš–ξš‡ξšξ˜ƒξš—ξš•ξš‹ξšξš‰ξ˜ƒξšξšƒξš…ξšŠξš‹ξšξš‡ξ˜ƒξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξ˜ƒξšƒξšξš†ξ˜ƒξš‰ξš‡ξš‘ξš•ξš’ξšƒξš–ξš‹ξšƒξšŽξ˜ƒ
ξš†ξšƒξš–ξšƒξŸ‘ξ˜ƒξ˜Œξšξš–ξš‡ξš”ξšξšƒξš–ξš‹ξš‘ξšξšƒξšŽξ˜ƒξ˜–ξš›ξšξš’ξš‘ξš•ξš‹ξš—ξšξ˜ƒξš‘ξšξ˜ƒξ˜™ξš‹ξš•ξš—ξšƒξšŽξ˜ƒξ˜†ξš‘ξšξš’ξš—ξš–ξš‹ξšξš‰ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯·ξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯΅ξ₯³ξ₯Άξ₯²ξ €ξ˜•ξ˜ŠξŸ€ξ₯΄ξŸ€ξ₯΄ξŸ€ξ₯³ξ₯΄ξ₯΅ξ₯Άξ₯·ξŸ€ξ₯Έξ₯Ήξ₯Ίξ₯»ξ₯²ξŸ€
ξ₯Ήξ 
ξ˜ŽξŸ€ξ˜ƒξ˜…ξš”ξš‘ξš™ξšξŸ‘ξ˜ƒξ˜—ξŸ€ξ˜ƒξ˜‡ξšƒξš˜ξš‹ξš•ξŸ‘ξ˜ƒξ˜‹ξš‡ξš†ξš‘ξšξš‹ξš…ξ˜ƒξš’ξš”ξš‹ξš…ξš‹ξšξš‰ξ˜ƒξšξš‘ξš†ξš‡ξšŽξš•ξ˜ƒξšˆξš‘ξš”ξ˜ƒξš”ξš‡ξš•ξš‹ξš†ξš‡ξšξš–ξš‹ξšƒξšŽξ˜ƒξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš‹ξš‡ξš•ξŸ£ξ˜ƒξ˜„ξ˜ƒξšξš‡ξš–ξšƒξŸ¦ξšƒξšξšƒξšŽξš›ξš•ξš‹ξš•ξŸ‘ξ˜ƒξ˜‹ξš‘ξš—ξš•ξš‹ξšξš‰ξ˜ƒξ˜–ξš–ξš—ξš†ξš‹ξš‡ξš•ξŸ‘ξ˜ƒ
ξ₯΄ξ₯²ξ₯΄ξ₯΅ξŸ‘ξ˜ƒξ₯΅ξ₯ΊξŸ‘ξ˜ƒξ₯Ήξ₯Ίξ₯»ξŸ¦ξ₯Ίξ₯³ξ₯΄ξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯²ξ₯Ίξ₯²ξ €ξ₯²ξ₯΄ξ₯Έξ₯Ήξ₯΅ξ₯²ξ₯΅ξ₯ΉξŸ€ξ₯΄ξ₯²ξ₯΄ξ₯΄ξŸ€ξ₯΄ξ₯²ξ₯»ξ₯Ίξ₯Ήξ₯Έξ₯·ξŸ€
ξ₯Ίξ 
ξ˜‰ξŸ€ξ˜ƒξ˜˜ξšŽξšŽξšƒξšŠξŸ‘ξ˜ƒξ˜–ξŸ€ξ˜ƒξ˜–ξš‡ξš’ξšƒξš•ξš‰ξš‘ξšœξšƒξš”ξŸ‘ξ˜ƒξ˜„ξš’ξš’ξšŽξš‹ξš…ξšƒξš–ξš‹ξš‘ξšξ˜ƒξš‘ξšˆξ˜ƒξšξšƒξš…ξšŠξš‹ξšξš‡ξ˜ƒξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξ˜ƒξš‹ξšξ˜ƒξš”ξš‡ξšƒξšŽξ˜ƒξš‡ξš•ξš–ξšƒξš–ξš‡ξ˜ƒξšξšƒξš”ξšξš‡ξš–ξš•ξŸ‘ξ˜ƒξ˜…ξš—ξš‹ξšŽξš–ξ˜ƒξ˜ˆξšξš˜ξš‹ξš”ξš‘ξšξšξš‡ξšξš–ξ˜ƒξ˜“ξš”ξš‘ξšŒξš‡ξš…ξš–ξ˜ƒ
ξšƒξšξš†ξ˜ƒξ˜„ξš•ξš•ξš‡ξš–ξ˜ƒξ˜ξšƒξšξšƒξš‰ξš‡ξšξš‡ξšξš–ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯²ξŸ‘ξ˜ƒξ₯³ξ₯²ξŸ‘ξ˜ƒξ₯·ξ₯³ξ₯΄ξŸ¦ξ₯·ξ₯΄ξ₯»ξŸ€
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ξ˜—ξŸ€ξ˜ƒξ˜†ξšŠξš‡ξšξŸ‘ξ˜ƒξ˜†ξŸ€ξ˜ƒξ˜Šξš—ξš‡ξš•ξš–ξš”ξš‹ξšξŸ‘ξ˜ƒξ˜›ξ˜Šξ˜…ξš‘ξš‘ξš•ξš–ξŸ£ξ˜ƒξ˜„ξ˜ƒξš•ξš…ξšƒξšŽξšƒξš„ξšŽξš‡ξ˜ƒξš–ξš”ξš‡ξš‡ξ˜ƒξš„ξš‘ξš‘ξš•ξš–ξš‹ξšξš‰ξ˜ƒξš•ξš›ξš•ξš–ξš‡ξšξŸ‘ξ˜ƒξ˜“ξš”ξš‘ξš…ξš‡ξš‡ξš†ξš‹ξšξš‰ξš•ξ˜ƒξš‘ξšˆξ˜ƒξš–ξšŠξš‡ξ˜ƒξ₯Έξ₯Έξšξš†ξ˜ƒξ˜„ξ˜†ξ˜ξ˜ƒξ˜–ξ˜Œξ˜Šξ˜Žξ˜‡ξ˜‡ξŸ‘ξ˜ƒ
ξ₯΄ξ₯²ξ₯³ξ₯ΈξŸ‘ξ˜ƒξ₯Ήξ₯Ίξ₯·ξŸ¦ξ₯Ήξ₯»ξ₯ΆξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯³ξ₯Άξ₯·ξ €ξ₯΄ξ₯»ξ₯΅ξ₯»ξ₯Έξ₯Ήξ₯΄ξŸ€ξ₯΄ξ₯»ξ₯΅ξ₯»ξ₯Ήξ₯Ίξ₯·ξŸ€
ξ₯³ξ₯²ξ 
ξ˜–ξŸ€ξ˜ƒξ˜†ξŸ€ξ˜ƒξ˜–ξš‡ξš˜ξš‰ξš‡ξšξŸ‘ξ˜ƒξ˜œξŸ€ξ˜ƒξ˜—ξšƒξšξš”ξš‹ξš˜ξš‡ξš”ξšξš‹ξ›§ξŸ‘ξ˜ƒξ˜†ξš‘ξšξš’ξšƒξš”ξš‹ξš•ξš‘ξšξ˜ƒξš‘ξšˆξ˜ƒξ˜ξšƒξš…ξšŠξš‹ξšξš‡ξ˜ƒξ˜ξš‡ξšƒξš”ξšξš‹ξšξš‰ξ˜ƒξ˜„ξšŽξš‰ξš‘ξš”ξš‹ξš–ξšŠξšξš•ξ˜ƒξšˆξš‘ξš”ξ˜ƒξ˜ξšƒξš•ξš•ξ˜ƒξ˜„ξš’ξš’ξš”ξšƒξš‹ξš•ξšƒξšŽξ˜ƒξš‘ξšˆξ˜ƒξ˜•ξš‡ξšƒξšŽξ˜ƒ
ξ˜ˆξš•ξš–ξšƒξš–ξš‡ξ˜ƒξ˜‡ξšƒξš–ξšƒξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯ΆξŸ‘ξ˜ƒξ₯΅ξ₯΄ξŸ‘ξ˜ƒξ₯³ξ₯²ξ₯²ξŸ¦ξ₯³ξ₯³ξ₯³ξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯΄ξ₯Άξ₯Ήξ₯Ίξ €ξš”ξš‡ξšξšƒξš˜ξŸ¦ξ₯΄ξ₯²ξ₯΄ξ₯ΆξŸ¦ξ₯²ξ₯²ξ₯³ξ₯»ξŸ€
ξ₯³ξ₯³ξ 
ξ˜†ξŸ€ξ˜ƒ ξ˜†ξŸ€ξ˜ƒ ξ˜ξš‡ξš‡ξŸ‘ξ˜ƒ ξ˜†ξŸ€ξ˜ƒ ξ˜“ξŸ€ξ˜ƒ ξ˜†ξšŠξšƒξšξš‰ξŸ‘ξ˜ƒ ξ˜‹ξŸ€ξ˜ƒ ξ˜œξŸ€ξ˜ƒ ξ˜ξš‹ξšξŸ‘ξ˜ƒ ξ˜—ξšŠξš‡ξ˜ƒ ξš‹ξšξš’ξšƒξš…ξš–ξ˜ƒ ξš‘ξšˆξ˜ƒ ξšξš‡ξš‹ξš‰ξšŠξš„ξš‘ξš”ξšŠξš‘ξš‘ξš†ξ˜ƒ ξš…ξšŠξšƒξš”ξšƒξš…ξš–ξš‡ξš”ξš‹ξš•ξš–ξš‹ξš…ξš•ξ˜ƒ ξš‘ξšξ˜ƒ ξšŠξš‘ξš—ξš•ξš‹ξšξš‰ξ˜ƒ ξš’ξš”ξš‹ξš…ξš‡ξš•ξŸ‘ξ˜ƒ
ξ˜Œξšξš–ξš‡ξš”ξšξšƒξš–ξš‹ξš‘ξšξšƒξšŽξ˜ƒ ξ˜ξš‘ξš—ξš”ξšξšƒξšŽξ˜ƒ ξš‘ξšˆξ˜ƒ ξ˜–ξš–ξš”ξšƒξš–ξš‡ξš‰ξš‹ξš…ξ˜ƒ ξ˜“ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξ˜ƒ ξ˜ξšƒξšξšƒξš‰ξš‡ξšξš‡ξšξš–ξŸ‘ξ˜ƒ ξ₯΄ξ₯²ξ₯³ξ₯΄ξŸ‘ξ˜ƒ ξ₯³ξ₯ΈξŸ‘ξ˜ƒ ξ₯΅ξ₯³ξŸ¦ξ₯Άξ₯ΆξŸ‘ξ˜ƒ ξš†ξš‘ξš‹ξŸ£ξ˜ƒ
ξ₯³ξ₯²ξŸ€ξ₯³ξ₯Ίξ₯Άξ₯Ίξ₯Ίξ €ξšŒξš‘ξš—ξš”ξšξšƒξšŽξŸ€ξ₯³ξ₯³ξ €ξ₯΄ξ₯²ξ₯³ξ₯΄ξŸ€ξ₯³ξŸ€ξ₯΄ξ €ξ₯³ξ₯³ξŸ€ξ₯΄ξŸ€ξ₯΅ξ₯³ξŸ€ξ₯Άξ₯ΆξŸ€
ξ₯³ξ₯΄ξ 
ξ˜ˆξŸ€ξ˜ƒξ˜„ξŸ€ξ˜ƒξ˜„ξšξš–ξš‹ξš’ξš‘ξš˜ξŸ‘ξ˜ƒξ˜ˆξŸ€ξ˜ƒξ˜…ξŸ€ξ˜ƒξ˜“ξš‘ξšξš”ξš›ξš•ξšŠξš‡ξš˜ξš•ξšξšƒξš›ξšƒξŸ‘ξ˜ƒξ˜ξšƒξš•ξš•ξ˜ƒξšƒξš’ξš’ξš”ξšƒξš‹ξš•ξšƒξšŽξ˜ƒξš‘ξšˆξ˜ƒξš”ξš‡ξš•ξš‹ξš†ξš‡ξšξš–ξš‹ξšƒξšŽξ˜ƒξšƒξš’ξšƒξš”ξš–ξšξš‡ξšξš–ξš•ξŸ£ξ˜ƒξ˜„ξšξ˜ƒξšƒξš’ξš’ξšŽξš‹ξš…ξšƒξš–ξš‹ξš‘ξšξ˜ƒξš‘ξšˆξ˜ƒξ˜•ξšƒξšξš†ξš‘ξšξ˜ƒ
ξ˜‰ξš‘ξš”ξš‡ξš•ξš–ξŸ‘ξ˜ƒξ˜ˆξššξš’ξš‡ξš”ξš–ξ˜ƒξ˜–ξš›ξš•ξš–ξš‡ξšξš•ξ˜ƒξš™ξš‹ξš–ξšŠξ˜ƒξ˜„ξš’ξš’ξšŽξš‹ξš…ξšƒξš–ξš‹ξš‘ξšξš•ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯³ξ₯΄ξŸ‘ξ˜ƒξ₯΅ξ₯»ξŸ‘ξ˜ƒξ₯³ξ₯Ήξ₯Ήξ₯΄ξŸ¦ξ₯³ξ₯Ήξ₯Ήξ₯ΊξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯²ξ₯³ξ₯Έξ €ξšŒξŸ€ξš‡ξš•ξš™ξšƒξŸ€ξ₯΄ξ₯²ξ₯³ξ₯³ξŸ€ξ₯²ξ₯ΊξŸ€ξ₯²ξ₯Ήξ₯ΉξŸ€
ξ₯³ξ₯΅ξ 
ξ˜ˆξŸ€ξ˜ƒξ˜ξš—ξš‰ξšŠξš‘ξšˆξš‡ξš”ξŸ‘ξ˜ƒξ˜…ξŸ€ξ˜ƒξ˜—ξš”ξšƒξš™ξš‹ξšξž΄ξš•ξšξš‹ξŸ‘ξ˜ƒξ˜ŽξŸ€ξ˜ƒξ˜—ξš”ξšƒξš™ξš‹ξšξž΄ξš•ξšξš‹ξŸ‘ξ˜ƒξ˜’ξŸ€ξ˜ƒξ˜Žξš‡ξšξš’ξšƒξŸ‘ξ˜ƒξ˜—ξŸ€ξ˜ƒξ˜ξšƒξš•ξš‘ξš–ξšƒξŸ‘ξ˜ƒξ˜’ξšξ˜ƒξš‡ξšξš’ξšŽξš‘ξš›ξš‹ξšξš‰ξ˜ƒξšˆξš—ξšœξšœξš›ξ˜ƒξšξš‘ξš†ξš‡ξšŽξš‹ξšξš‰ξ˜ƒξšƒξšŽξš‰ξš‘ξš”ξš‹ξš–ξšŠξšξš•ξ˜ƒ
ξšˆξš‘ξš”ξ˜ƒ ξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξ˜ƒ ξš‘ξšˆξ˜ƒ ξš”ξš‡ξš•ξš‹ξš†ξš‡ξšξš–ξš‹ξšƒξšŽξ˜ƒ ξš’ξš”ξš‡ξšξš‹ξš•ξš‡ξš•ξŸ‘ξ˜ƒ ξ˜Œξšξšˆξš‘ξš”ξšξšƒξš–ξš‹ξš‘ξšξ˜ƒ ξ˜–ξš…ξš‹ξš‡ξšξš…ξš‡ξš•ξŸ‘ξ˜ƒ ξ₯΄ξ₯²ξ₯΄ξ₯΅ξŸ‘ξ˜ƒ ξ₯³ξ₯Ίξ₯³ξŸ‘ξ˜ƒ ξ₯·ξ₯³ξ₯΄ξ₯΅ξŸ¦ξ₯·ξ₯³ξ₯Άξ₯΄ξŸ‘ξ˜ƒ ξš†ξš‘ξš‹ξŸ£ξ˜ƒ
ξ₯³ξ₯²ξŸ€ξ₯³ξ₯²ξ₯³ξ₯Έξ €ξšŒξŸ€ξš‹ξšξš•ξŸ€ξ₯΄ξ₯²ξ₯³ξ₯³ξŸ€ξ₯²ξ₯ΉξŸ€ξ₯²ξ₯³ξ₯΄ξŸ€
ξ₯³ξ₯Άξ 
ξ˜‘ξŸ€ξ˜ƒ ξ˜Žξš‘ξšξŸ‘ξ˜ƒ ξ˜ˆξŸ€ξ˜ƒ ξ˜ξŸ€ξ˜ƒ ξ˜Žξš‘ξš’ξš‘ξšξš‡ξšξŸ‘ξ˜ƒ ξ˜†ξŸ€ξ˜ƒ ξ˜„ξŸ€ξ˜ƒ ξ˜ξšƒξš”ξš–ξš‹ξšξš‡ξšœξŸ¦ξ˜…ξšƒξš”ξš„ξš‘ξš•ξšƒξŸ‘ξ˜ƒ ξ˜…ξš‹ξš‰ξ˜ƒ ξš†ξšƒξš–ξšƒξ˜ƒ ξš‹ξšξ˜ƒ ξš”ξš‡ξšƒξšŽξ˜ƒ ξš‡ξš•ξš–ξšƒξš–ξš‡ξŸ£ξ˜ƒ ξšˆξš”ξš‘ξšξ˜ƒ ξšξšƒξšξš—ξšƒξšŽξ˜ƒ ξšƒξš’ξš’ξš”ξšƒξš‹ξš•ξšƒξšŽξ˜ƒ ξš–ξš‘ξ˜ƒ
ξšƒξš—ξš–ξš‘ξšξšƒξš–ξš‡ξš†ξ˜ƒξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξŸ‘ξ˜ƒξ˜ξš‘ξš—ξš”ξšξšƒξšŽξ˜ƒξš‘ξšˆξ˜ƒξ˜“ξš‘ξš”ξš–ξšˆξš‘ξšŽξš‹ξš‘ξ˜ƒξ˜ξšƒξšξšƒξš‰ξš‡ξšξš‡ξšξš–ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯³ξ₯ΉξŸ‘ξ˜ƒξ₯Άξ₯΅ξŸ‘ξ˜ƒξ₯»ξ₯ΆξŸ¦ξ₯³ξ₯²ξ₯³ξŸ€
ξ₯³ξ₯·ξ 
ξ˜…ξŸ€ξ˜ƒ ξ˜ŠξšŽξš—ξšξšƒξš…ξŸ’ξ˜ƒ ξ˜‰ξŸ€ξ˜ƒ ξ˜‡ξŸ€ξ˜ƒ ξ˜•ξš‘ξš•ξš‹ξš‡ξš”ξš•ξŸ‘ξ˜ƒ ξ˜“ξš”ξšƒξš…ξš–ξš‹ξš…ξš‡ξ˜ƒ ξš„ξš”ξš‹ξš‡ξ§ξš‹ξšξš‰ξ˜ƒ ξ ‚ξ˜ƒ ξ˜„ξš—ξš–ξš‘ξšξšƒξš–ξš‡ξš†ξ˜ƒ ξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξ˜ƒ ξšξš‘ξš†ξš‡ξšŽξš•ξ˜ƒ ξ ‹ξ˜„ξ˜™ξ˜ξš•ξ ŒξŸ£ξ˜ƒ ξš–ξšŠξš‡ξš‹ξš”ξ˜ƒ ξš”ξš‘ξšŽξš‡ξŸ‘ξ˜ƒ ξš–ξšŠξš‡ξš‹ξš”ξ˜ƒ
ξšƒξš†ξš˜ξšƒξšξš–ξšƒξš‰ξš‡ξš•ξ˜ƒξšƒξšξš†ξ˜ƒξš–ξšŠξš‡ξš‹ξš”ξ˜ƒξšŽξš‹ξšξš‹ξš–ξšƒξš–ξš‹ξš‘ξšξš•ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯³ξŸ‘ξ˜ƒξ₯΅ξ₯»ξŸ‘ξ˜ƒξ₯Άξ₯Ίξ₯³ξ ‚ξ₯Άξ₯»ξ₯³ξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯³ξ₯²ξ₯Ίξ €ξ˜ξ˜“ξ˜Œξ˜‰ξŸ¦ξ₯²ξ₯ΉξŸ¦ξ₯΄ξ₯²ξ₯΄ξ₯²ξŸ¦ξ₯²ξ₯²ξ₯Ίξ₯ΈξŸ€
ξ₯³ξ₯Έξ 
ξ˜„ξŸ€ξ˜ƒξ˜‡ξŸ€ξ˜ƒξ˜“ξšƒξš˜ξšŽξš‘ξš˜ξŸ‘ξ˜ƒξ˜–ξš’ξšƒξš…ξš‡ξŸ¦ξ˜™ξšƒξš”ξš›ξš‹ξšξš‰ξ˜ƒξ˜•ξš‡ξš‰ξš”ξš‡ξš•ξš•ξš‹ξš‘ξšξ˜ƒξ˜†ξš‘ξš‡ξšˆξ§ξš‹ξš…ξš‹ξš‡ξšξš–ξš•ξŸ£ξ˜ƒξ˜„ξ˜ƒξ˜–ξš‡ξšξš‹ξŸ¦ξš’ξšƒξš”ξšƒξšξš‡ξš–ξš”ξš‹ξš…ξ˜ƒξ˜„ξš’ξš’ξš”ξš‘ξšƒξš…ξšŠξ˜ƒξ˜„ξš’ξš’ξšŽξš‹ξš‡ξš†ξ˜ƒξš–ξš‘ξ˜ƒξ˜•ξš‡ξšƒξšŽξ˜ƒξ˜ˆξš•ξš–ξšƒξš–ξš‡ξ˜ƒ
ξ˜ξšƒξš”ξšξš‡ξš–ξš•ξŸ‘ξ˜ƒξ˜•ξš‡ξšƒξšŽξ˜ƒξ˜ˆξš•ξš–ξšƒξš–ξš‡ξ˜ƒξ˜ˆξš…ξš‘ξšξš‘ξšξš‹ξš…ξš•ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯²ξ₯²ξŸ‘ξ˜ƒξ₯΄ξ₯ΊξŸ‘ξ˜ƒξ₯΄ξ₯Άξ₯»ξŸ¦ξ₯΄ξ₯Ίξ₯΅ξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯³ξ₯³ξ₯³ξ €ξ₯³ξ₯·ξ₯Άξ₯²ξŸ¦ξ₯Έξ₯΄ξ₯΄ξ₯»ξŸ€ξ₯²ξ₯²ξ₯Ίξ₯²ξ₯³ξŸ€
ξ₯³ξ₯Ήξ 
ξ˜–ξŸ€ξ˜ƒξ˜•ξš‘ξš•ξš‡ξšξŸ‘ξ˜ƒξ˜‹ξš‡ξš†ξš‘ξšξš‹ξš…ξ˜ƒξš’ξš”ξš‹ξš…ξš‡ξš•ξ˜ƒξšƒξšξš†ξ˜ƒξš‹ξšξš’ξšŽξš‹ξš…ξš‹ξš–ξ˜ƒξšξšƒξš”ξšξš‡ξš–ξš•ξŸ‘ξ˜ƒξ˜ξš‘ξš—ξš”ξšξšƒξšŽξ˜ƒξš‘ξšˆξ˜ƒξ˜“ξš‘ξšŽξš‹ξš–ξš‹ξš…ξšƒξšŽξ˜ƒξ˜ˆξš…ξš‘ξšξš‘ξšξš›ξŸ‘ξ˜ƒξ₯³ξ₯»ξ₯Ήξ₯ΆξŸ‘ξ˜ƒξ₯Ίξ₯΄ξŸ‘ξ˜ƒξ₯΅ξ₯ΆξŸ¦ξ₯·ξ₯·ξŸ€
ξ₯³ξ₯Ίξ 
ξ˜ξŸ€ξ˜ƒξ˜…ξš”ξš‡ξš‹ξšξšƒξšξŸ‘ξ˜ƒξ˜•ξšƒξšξš†ξš‘ξšξ˜ƒξšˆξš‘ξš”ξš‡ξš•ξš–ξš•ξŸ‘ξ˜ƒξ˜ξšƒξš…ξšŠξš‹ξšξš‡ξ˜ƒξ˜ξš‡ξšƒξš”ξšξš‹ξšξš‰ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯²ξ₯³ξŸ‘ξ˜ƒξ₯Άξ₯·ξŸ‘ξ˜ƒξ₯·ξŸ¦ξ₯΅ξ₯΄ξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯²ξ₯΄ξ₯΅ξ €ξ˜„ξŸ£ξ₯³ξ₯²ξ₯³ξ₯²ξ₯»ξ₯΅ξ₯΅ξ₯Άξ₯²ξ₯Άξ₯΅ξ₯΄ξ₯ΆξŸ€
ξ₯³ξ₯»ξ 
ξ˜ξŸ€ξ˜ƒξ˜‹ξš‘ξšξš‰ξŸ‘ξ˜ƒξ˜‹ξŸ€ξ˜ƒξ˜†ξšŠξš‘ξš‹ξŸ‘ξ˜ƒξ˜šξŸ€ξ˜ƒξ˜–ξŸ€ξ˜ƒξ˜Žξš‹ξšξŸ‘ξ˜ƒξ˜„ξ˜ƒξšŠξš‘ξš—ξš•ξš‡ξ˜ƒξš’ξš”ξš‹ξš…ξš‡ξ˜ƒξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξ˜ƒξš„ξšƒξš•ξš‡ξš†ξ˜ƒξš‘ξšξ˜ƒξš–ξšŠξš‡ξ˜ƒξš”ξšƒξšξš†ξš‘ξšξ˜ƒξšˆξš‘ξš”ξš‡ξš•ξš–ξ˜ƒξšƒξš’ξš’ξš”ξš‘ξšƒξš…ξšŠξŸ‘ξ˜ƒξ˜Œξšξš–ξš‡ξš”ξšξšƒξš–ξš‹ξš‘ξšξšƒξšŽξ˜ƒ
ξ˜ξš‘ξš—ξš”ξšξšƒξšŽξ˜ƒξš‘ξšˆξ˜ƒξ˜–ξš–ξš”ξšƒξš–ξš‡ξš‰ξš‹ξš…ξ˜ƒξ˜“ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξ˜ƒξ˜ξšƒξšξšƒξš‰ξš‡ξšξš‡ξšξš–ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯²ξŸ‘ξ˜ƒξ₯΄ξ₯ΆξŸ‘ξ˜ƒξ₯³ξ₯Άξ₯²ξŸ¦ξ₯³ξ₯·ξ₯΄ξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯΅ξ₯Ίξ₯Άξ₯Έξ €ξš‹ξšŒξš•ξš’ξšξŸ€ξ₯΄ξ₯²ξ₯΄ξ₯²ξŸ€ξ₯³ξ₯³ξ₯·ξ₯Άξ₯ΆξŸ€
ξ₯΄ξ₯²ξ 
ξ˜–ξŸ€ξ˜ƒξ˜–ξšŠξšƒξš”ξšξšƒξŸ‘ξ˜ƒξ˜‡ξŸ€ξ˜ƒξ˜„ξš”ξš‘ξš”ξšƒξŸ‘ξ˜ƒξ˜ŠξŸ€ξ˜ƒξ˜–ξšŠξšƒξšξšξšƒξš”ξŸ‘ξ˜ƒξ˜“ξŸ€ξ˜ƒξ˜–ξšŠξšƒξš”ξšξšƒξŸ‘ξ˜ƒξ˜™ξŸ€ξ˜ƒξ˜ξš‘ξš–ξš™ξšƒξšξš‹ξŸ‘ξ˜ƒξ˜‹ξš‘ξš—ξš•ξš‡ξ˜ƒξš’ξš”ξš‹ξš…ξš‡ξ˜ƒξš’ξš”ξš‡ξš†ξš‹ξš…ξš–ξš‹ξš‘ξšξ˜ƒξš—ξš•ξš‹ξšξš‰ξ˜ƒξšξšƒξš…ξšŠξš‹ξšξš‡ξ˜ƒξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξ˜ƒ
ξšƒξšŽξš‰ξš‘ξš”ξš‹ξš–ξšŠξšξŸ‘ξ˜ƒ ξ₯΄ξ₯²ξ₯΄ξ₯΅ξ˜ƒ ξ₯Ήξš–ξšŠξ˜ƒ ξ˜Œξšξš–ξš‡ξš”ξšξšƒξš–ξš‹ξš‘ξšξšƒξšŽξ˜ƒ ξ˜†ξš‘ξšξšˆξš‡ξš”ξš‡ξšξš…ξš‡ξ˜ƒ ξš‘ξšξ˜ƒ ξ˜†ξš‘ξšξš’ξš—ξš–ξš‹ξšξš‰ξ˜ƒ ξ˜ξš‡ξš–ξšŠξš‘ξš†ξš‘ξšŽξš‘ξš‰ξš‹ξš‡ξš•ξ˜ƒ ξšƒξšξš†ξ˜ƒ ξ˜†ξš‘ξšξšξš—ξšξš‹ξš…ξšƒξš–ξš‹ξš‘ξšξ˜ƒ
ξ ‹ξ˜Œξ˜†ξ˜†ξ˜ξ˜†ξ ŒξŸ‘ξ˜ƒξ˜ˆξš”ξš‘ξš†ξš‡ξŸ‘ξ˜ƒξ˜Œξšξš†ξš‹ξšƒξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯΅ξŸ‘ξ˜ƒξ₯»ξ₯Ίξ₯΄ξŸ¦ξ₯»ξ₯Ίξ₯ΈξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯³ξ₯²ξ₯»ξ €ξ˜Œξ˜†ξ˜†ξ˜ξ˜†ξ₯·ξ₯Έξ₯·ξ₯²ξ₯ΉξŸ€ξ₯΄ξ₯²ξ₯΄ξ₯΅ξŸ€ξ₯³ξ₯²ξ₯²ξ₯Ίξ₯Άξ₯³ξ₯»ξ₯ΉξŸ€
ξ₯΄ξ₯³ξ 
ξ˜ξŸ€ξ˜ƒξ˜Šξš‡ξš‡ξš”ξš–ξš•ξŸ‘ξ˜ƒξ˜–ξŸ€ξ˜ƒξ˜™ξšƒξšξš†ξš‡ξšξ˜ƒξ˜…ξš”ξš‘ξš—ξš…ξšξš‡ξŸ‘ξ˜ƒξ˜ξŸ€ξ˜ƒξ˜‡ξš‡ξ˜ƒξ˜šξš‡ξš‡ξš”ξš†ξš–ξŸ‘ξ˜ƒξ˜ƒξ˜„ξ˜ƒξš•ξš—ξš”ξš˜ξš‡ξš›ξ˜ƒξš‘ξšˆξ˜ƒξšξš‡ξš–ξšŠξš‘ξš†ξš•ξ˜ƒξšƒξšξš†ξ˜ƒξš‹ξšξš’ξš—ξš–ξ˜ƒξš†ξšƒξš–ξšƒξ˜ƒξš–ξš›ξš’ξš‡ξš•ξ˜ƒξšˆξš‘ξš”ξ˜ƒξšŠξš‘ξš—ξš•ξš‡ξ˜ƒξš’ξš”ξš‹ξš…ξš‡ξ˜ƒ
ξš’ξš”ξš‡ξš†ξš‹ξš…ξš–ξš‹ξš‘ξšξŸ‘ξ˜ƒξ˜Œξ˜–ξ˜“ξ˜•ξ˜–ξ˜ƒξ˜Œξšξš–ξš‡ξš”ξšξšƒξš–ξš‹ξš‘ξšξšƒξšŽξ˜ƒξ˜ξš‘ξš—ξš”ξšξšƒξšŽξ˜ƒξš‘ξšˆξ˜ƒξ˜Šξš‡ξš‘ξŸ¦ξ˜Œξšξšˆξš‘ξš”ξšξšƒξš–ξš‹ξš‘ξšξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯΅ξŸ‘ξ˜ƒξ₯³ξ₯΄ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯²ξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯΅ξ₯΅ξ₯»ξ₯²ξ €ξš‹ξšŒξš‰ξš‹ξ₯³ξ₯΄ξ₯²ξ₯·ξ₯²ξ₯΄ξ₯²ξ₯²ξŸ€
ξ₯΄ξ₯΄ξ 
ξ˜ŽξŸ€ξ˜ƒξ˜…ξšƒξš—ξš”ξŸ‘ξ˜ƒξ˜ξŸ€ξ˜ƒξ˜•ξš‘ξš•ξš‡ξšξšˆξš‡ξšŽξš†ξš‡ξš”ξŸ‘ξ˜ƒξ˜…ξŸ€ξ˜ƒξ˜ξš—ξš–ξšœξŸ‘ξ˜ƒξ˜„ξš—ξš–ξš‘ξšξšƒξš–ξš‡ξš†ξ˜ƒξš”ξš‡ξšƒξšŽξ˜ƒξš‡ξš•ξš–ξšƒξš–ξš‡ξ˜ƒξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξ˜ƒξš™ξš‹ξš–ξšŠξ˜ƒξšξšƒξš…ξšŠξš‹ξšξš‡ξ˜ƒξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξ˜ƒξšξš‘ξš†ξš‡ξšŽξš•ξ˜ƒξš—ξš•ξš‹ξšξš‰ξ˜ƒ
ξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξ˜ƒ ξš†ξš‡ξš•ξš…ξš”ξš‹ξš’ξš–ξš‹ξš‘ξšξš•ξŸ‘ξ˜ƒ ξ˜ˆξššξš’ξš‡ξš”ξš–ξ˜ƒ ξ˜–ξš›ξš•ξš–ξš‡ξšξš•ξ˜ƒ ξš™ξš‹ξš–ξšŠξ˜ƒ ξ˜„ξš’ξš’ξšŽξš‹ξš…ξšƒξš–ξš‹ξš‘ξšξš•ξŸ‘ξ˜ƒ ξ₯΄ξ₯²ξ₯΄ξ₯΅ξŸ‘ξ˜ƒ ξ₯΄ξ₯³ξ₯΅ξŸ‘ξ˜ƒ ξ₯³ξ₯³ξ₯»ξ₯³ξ₯Άξ₯ΉξŸ‘ξ˜ƒ ξš†ξš‘ξš‹ξŸ£ξ˜ƒ
ξ₯³ξ₯²ξŸ€ξ₯³ξ₯²ξ₯³ξ₯Έξ €ξšŒξŸ€ξš‡ξš•ξš™ξšƒξŸ€ξ₯΄ξ₯²ξ₯΄ξ₯΄ξŸ€ξ₯³ξ₯³ξ₯»ξ₯³ξ₯Άξ₯ΉξŸ€
ξ₯΄ξ₯΅ξ 
ξ˜†ξŸ€ξ˜ƒ ξŸ¦ξ˜‹ξŸ€ξ˜ƒ ξ˜œξšƒξšξš‰ξŸ‘ξ˜ƒ ξ˜…ξŸ€ξ˜ƒ ξ˜ξš‡ξš‡ξŸ‘ξ˜ƒ ξ˜œξŸ€ξ˜ƒ ξŸ¦ξ˜‡ξŸ€ξ˜ƒ ξ˜ξš‹ξšξŸ‘ξ˜ƒ ξ˜‡ξš‡ξš‡ξš’ξŸ¦ξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξ˜ƒ ξšƒξš’ξš’ξš”ξš‘ξšƒξš…ξšŠξ˜ƒ ξšˆξš‘ξš”ξ˜ƒ ξšƒξšξ˜ƒ ξšƒξšξšƒξšŽξš›ξš•ξš‹ξš•ξ˜ƒ ξš‘ξšˆξ˜ƒ ξš”ξš‡ξšƒξšŽξŸ¦ξš‡ξš•ξš–ξšƒξš–ξš‡ξ˜ƒ ξš’ξš”ξš‹ξš…ξš‡ξš•ξ˜ƒ ξšƒξšξš†ξ˜ƒ
ξš–ξš”ξšƒξšξš•ξšƒξš…ξš–ξš‹ξš‘ξšξš•ξŸ‘ξ˜ƒξ˜Œξ˜ˆξ˜ˆξ˜ˆξ˜ƒξ˜„ξš…ξš…ξš‡ξš•ξš•ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯·ξŸ‘ξ˜ƒξ₯³ξ₯΅ξŸ‘ξ˜ƒξ₯Ίξ₯»ξ₯΄ξ₯Άξ₯ΊξŸ¦ξ₯Ίξ₯»ξ₯΄ξ₯Έξ₯·ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯·ξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯³ξ₯²ξ₯»ξ €ξ˜„ξ˜†ξ˜†ξ˜ˆξ˜–ξ˜–ξŸ€ξ₯΄ξ₯²ξ₯΄ξ₯·ξŸ€ξ₯΅ξ₯·ξ₯Έξ₯Ίξ₯Ήξ₯»ξ₯ΊξŸ€
ξ₯΄ξ₯Άξ 
ξ˜ŠξŸ€ξ˜ƒξ˜“ξšŽξš‡ξš‹ξš•ξš•ξŸ‘ξ˜ƒξ˜ξŸ€ξ˜ƒξ˜•ξšƒξš‰ξšŠξšƒξš˜ξšƒξšξŸ‘ξ˜ƒξ˜‰ξŸ€ξ˜ƒξ˜šξš—ξŸ‘ξ˜ƒξ˜ξŸ€ξ˜ƒξ˜ŽξšŽξš‡ξš‹ξšξš„ξš‡ξš”ξš‰ξŸ‘ξ˜ƒξ˜ŽξŸ€ξ˜ƒξ˜”ξŸ€ξ˜ƒξ˜šξš‡ξš‹ξšξš„ξš‡ξš”ξš‰ξš‡ξš”ξŸ‘ξ˜ƒξ˜’ξšξ˜ƒξšˆξšƒξš‹ξš”ξšξš‡ξš•ξš•ξ˜ƒξšƒξšξš†ξ˜ƒξš…ξšƒξšŽξš‹ξš„ξš”ξšƒξš–ξš‹ξš‘ξšξŸ‘ξ˜ƒξ˜„ξš†ξš˜ξšƒξšξš…ξš‡ξš•ξ˜ƒξš‹ξšξ˜ƒ
ξ˜‘ξš‡ξš—ξš”ξšƒξšŽξ˜ƒξ˜Œξšξšˆξš‘ξš”ξšξšƒξš–ξš‹ξš‘ξšξ˜ƒξ˜“ξš”ξš‘ξš…ξš‡ξš•ξš•ξš‹ξšξš‰ξ˜ƒξ˜–ξš›ξš•ξš–ξš‡ξšξš•ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯³ξ₯ΉξŸ‘ξ˜ƒξ₯΅ξ₯²ξŸ‘ξ˜ƒξ₯·ξ₯Έξ₯Ίξ₯²ξŸ¦ξ₯·ξ₯Έξ₯Ίξ₯»ξŸ€
ξ₯΄ξ₯·ξ 
ξ˜“ξŸ€ξ˜ƒξ˜ξšƒξšˆξšƒξš”ξš›ξŸ‘ξ˜ƒξ˜‡ξŸ€ξ˜–ξšŠξš‘ξšŒξšƒξš‡ξš‹ξŸ‘ξ˜ƒξ˜„ξŸ€ξ˜ƒξ˜•ξšƒξšŒξšƒξš„ξš‹ξšˆξšƒξš”ξš†ξŸ‘ξ˜ƒξ˜—ξŸ€ξ˜ƒξ˜‘ξš‰ξš‘ξŸ‘ξ˜ƒξ˜„ξ˜ŒξŸ‘ξ˜ƒξšξšƒξš…ξšŠξš‹ξšξš‡ξ˜ƒξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξ˜ƒξšƒξšξš†ξ˜ƒξ˜…ξ˜Œξ˜ξ˜ƒξšˆξš‘ξš”ξ˜ƒξš‡ξšξšŠξšƒξšξš…ξš‡ξš†ξ˜ƒξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξ˜ƒξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξŸ£ξ˜ƒ
ξ˜Œξšξš–ξš‡ξš‰ξš”ξšƒξš–ξš‹ξš‘ξšξ˜ƒξš‘ξšˆξ˜ƒξš…ξš‘ξš•ξš–ξ˜ƒξšƒξšξš†ξ˜ƒξšξšƒξš”ξšξš‡ξš–ξ˜ƒξšƒξš’ξš’ξš”ξš‘ξšƒξš…ξšŠξš‡ξš•ξ˜ƒξš–ξšŠξš”ξš‘ξš—ξš‰ξšŠξ˜ƒξšƒξ˜ƒξšŠξš›ξš„ξš”ξš‹ξš†ξ˜ƒξšξš‘ξš†ξš‡ξšŽξŸ‘ξ˜ƒξ˜‹ξšƒξš„ξš‹ξš–ξšƒξš–ξ˜ƒξ˜Œξšξš–ξš‡ξš”ξšξšƒξš–ξš‹ξš‘ξšξšƒξšŽξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯·ξŸ‘ξ˜ƒξ₯³ξ₯Έξ₯ΆξŸ‘ξ˜ƒ
ξ₯³ξ₯²ξ₯΅ξ₯·ξ₯³ξ₯·ξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯²ξ₯³ξ₯Έξ €ξšŒξŸ€ξšŠξšƒξš„ξš‹ξš–ξšƒξš–ξš‹ξšξš–ξŸ€ξ₯΄ξ₯²ξ₯΄ξ₯·ξŸ€ξ₯³ξ₯²ξ₯΅ξ₯·ξ₯³ξ₯·ξŸ€
ξ₯΄ξ₯Έξ 
ξ˜†ξŸ€ξ˜ƒ ξ˜ξš‹ξšƒξšξš‰ξŸ‘ξ˜ƒ ξ˜“ξš”ξš‡ξš†ξš‹ξš…ξš–ξš‹ξšξš‰ξ˜ƒ ξ˜‘ξš‡ξš™ξ˜ƒ ξ˜œξš‘ξš”ξšξ˜ƒ ξšŠξš‘ξš—ξš•ξš‹ξšξš‰ξ˜ƒ ξš’ξš”ξš‹ξš…ξš‡ξš•ξŸ£ξ˜ƒ ξšƒξ˜ƒ ξšξšƒξš…ξšŠξš‹ξšξš‡ξ˜ƒ ξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξ˜ƒ ξšƒξš’ξš’ξš”ξš‘ξšƒξš…ξšŠξŸ‘ξ˜ƒ ξ˜‹ξš‹ξš‰ξšŠξšŽξš‹ξš‰ξšŠξš–ξš•ξ˜ƒ ξš‹ξšξ˜ƒ ξ˜–ξš…ξš‹ξš‡ξšξš…ξš‡ξŸ‘ξ˜ƒ
ξ˜ˆξšξš‰ξš‹ξšξš‡ξš‡ξš”ξš‹ξšξš‰ξ˜ƒξšƒξšξš†ξ˜ƒξ˜—ξš‡ξš…ξšŠξšξš‘ξšŽξš‘ξš‰ξš›ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯ΆξŸ‘ξ˜ƒξ₯Ίξ₯·ξŸ‘ξ˜ƒξ₯Ήξ₯³ξ₯²ξŸ¦ξ₯Ήξ₯³ξ₯ΈξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯·ξ₯Άξ₯²ξ₯»ξ₯Ήξ €ξš‰ξšŒξ₯Έξš˜ξš˜ξš“ξ₯Άξ₯ΈξŸ€
ξ₯΄ξ₯Ήξ 
ξ˜ξŸ€ξ˜ƒξ˜œξš‹ξŸ‘ξ˜ƒξ˜ξŸ€ξ˜ƒξ˜†ξšŠξš—ξšξš‰ξš—ξšƒξšξš‰ξŸ‘ξ˜ƒξ˜‹ξŸ€ξ˜ƒξ˜ξšƒξšξŸ‘ξ˜ƒξ˜šξŸ€ξ˜ƒξ˜œξšƒξšξ˜ƒξšƒξšξš†ξ˜ƒ ξ˜œξŸ€ξ˜ƒξ˜…ξš‹ξšξŸ‘ξ˜ƒξ˜–ξš—ξš’ξš’ξš‘ξš”ξš–ξ˜ƒξ˜™ξš‡ξš…ξš–ξš‘ξš”ξ˜ƒξ˜•ξš‡ξš‰ξš”ξš‡ξš•ξš•ξš‹ξš‘ξšξ˜ƒξšˆξš‘ξš”ξ˜ƒξ˜“ξš”ξš‡ξš†ξš‹ξš…ξš–ξš‹ξš‘ξšξ˜ƒξš‘ξšˆξ˜ƒξ˜‹ξš‘ξš—ξš•ξš‹ξšξš‰ξ˜ƒ
ξ˜™ξšƒξšŽξš—ξš‡ξš•ξŸ‘ ξ₯΄ξ₯²ξ₯²ξ₯»ξ˜ƒξ˜Œξšξš–ξš‡ξš”ξšξšƒξš–ξš‹ξš‘ξšξšƒξšŽξ˜ƒξ˜†ξš‘ξšξšˆξš‡ξš”ξš‡ξšξš…ξš‡ξ˜ƒξš‘ξšξ˜ƒξ˜†ξš‘ξšξš’ξš—ξš–ξšƒξš–ξš‹ξš‘ξšξšƒξšŽξ˜ƒξ˜Œξšξš–ξš‡ξšŽξšŽξš‹ξš‰ξš‡ξšξš…ξš‡ξ˜ƒξšƒξšξš†ξ˜ƒξ˜–ξš‡ξš…ξš—ξš”ξš‹ξš–ξš›ξŸ‘ξ˜ƒξ˜…ξš‡ξš‹ξšŒξš‹ξšξš‰ξŸ‘ξ˜ƒξ˜†ξšŠξš‹ξšξšƒξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯²ξ₯»ξŸ‘ξ˜ƒ
ξ₯Έξ₯³ξŸ¦ξ₯Έξ₯·ξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯³ξ₯²ξ₯»ξ €ξ˜†ξ˜Œξ˜–ξŸ€ξ₯΄ξ₯²ξ₯²ξ₯»ξŸ€ξ₯³ξ₯΄ξ₯ΉξŸ€
ξ₯΄ξ₯Ίξ 
ξ˜šξŸ€ξ˜ƒξ˜ŽξŸ€ξ˜ƒξ˜’ξŸ€ξ˜ƒξ˜‹ξš‘ξŸ‘ξ˜ƒξ˜…ξŸ€ξ˜ƒξ˜–ξŸ€ξ˜ƒξ˜—ξšƒξšξš‰ξŸ‘ξ˜ƒξ˜–ξŸ€ξ˜ƒξ˜šξŸ€ξ˜ƒξ˜šξš‘ξšξš‰ξŸ‘ξ˜ƒξ˜“ξš”ξš‡ξš†ξš‹ξš…ξš–ξš‹ξšξš‰ξ˜ƒξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξ˜ƒξš’ξš”ξš‹ξš…ξš‡ξš•ξ˜ƒξš™ξš‹ξš–ξšŠξ˜ƒξšξšƒξš…ξšŠξš‹ξšξš‡ξ˜ƒξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξ˜ƒξšƒξšŽξš‰ξš‘ξš”ξš‹ξš–ξšŠξšξš•ξŸ‘ξ˜ƒξ˜ξš‘ξš—ξš”ξšξšƒξšŽξ˜ƒ
ξš‘ξšˆξ˜ƒξ˜“ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξ˜ƒξ˜•ξš‡ξš•ξš‡ξšƒξš”ξš…ξšŠξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯³ξŸ‘ξ˜ƒξ₯΅ξ₯ΊξŸ‘ξ˜ƒξ₯Άξ₯Ίξ ‚ξ₯Ήξ₯²ξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯²ξ₯Ίξ₯²ξ €ξ₯²ξ₯»ξ₯·ξ₯»ξ₯»ξ₯»ξ₯³ξ₯ΈξŸ€ξ₯΄ξ₯²ξ₯΄ξ₯²ξŸ€ξ₯³ξ₯Ίξ₯΅ξ₯΄ξ₯·ξ₯·ξ₯ΊξŸ€
ξ₯΄ξ₯»ξ 
ξ˜ξŸ€ξ˜ƒξ˜šξšƒξšξš‰ξŸ‘ξ˜ƒξ˜ŠξŸ€ξ˜ƒξ˜šξšƒξšξš‰ξŸ‘ξ˜ƒξ˜‹ξŸ€ξ˜ƒξ˜œξš—ξŸ‘ξ˜ƒξ˜‰ξŸ€ξ˜ƒξ˜šξšƒξšξš‰ξŸ‘ξ˜ƒξ˜“ξš”ξš‡ξš†ξš‹ξš…ξš–ξš‹ξš‘ξšξ˜ƒξšƒξšξš†ξ˜ƒξšƒξšξšƒξšŽξš›ξš•ξš‹ξš•ξ˜ƒξš‘ξšˆξ˜ƒξš”ξš‡ξš•ξš‹ξš†ξš‡ξšξš–ξš‹ξšƒξšŽξ˜ƒξšŠξš‘ξš—ξš•ξš‡ξ˜ƒξš’ξš”ξš‹ξš…ξš‡ξ˜ƒξš—ξš•ξš‹ξšξš‰ξ˜ƒξšƒξ˜ƒξ§ξšŽξš‡ξššξš‹ξš„ξšŽξš‡ξ˜ƒ
ξš•ξš’ξšƒξš–ξš‹ξš‘ξš–ξš‡ξšξš’ξš‘ξš”ξšƒξšŽξ˜ƒ ξšξš‘ξš†ξš‡ξšŽξŸ‘ξ˜ƒ ξ˜ξš‘ξš—ξš”ξšξšƒξšŽξ˜ƒ ξš‘ξšˆξ˜ƒ ξ˜„ξš’ξš’ξšŽξš‹ξš‡ξš†ξ˜ƒ ξ˜ˆξš…ξš‘ξšξš‘ξšξš‹ξš…ξš•ξŸ‘ξ˜ƒ ξ₯΄ξ₯²ξ₯΄ξ₯΄ξŸ‘ξ˜ƒ ξ₯΄ξ₯·ξŸ‘ξ˜ƒ ξ₯·ξ₯²ξ₯΅ξ ‚ξ₯·ξ₯΄ξ₯΄ξŸ‘ξ˜ƒ ξš†ξš‘ξš‹ξŸ£ξ˜ƒ
ξ₯³ξ₯²ξŸ€ξ₯³ξ₯²ξ₯Ίξ₯²ξ €ξ₯³ξ₯·ξ₯³ξ₯Άξ₯²ξ₯΅ξ₯΄ξ₯ΈξŸ€ξ₯΄ξ₯²ξ₯΄ξ₯΄ξŸ€ξ₯΄ξ₯²ξ₯Άξ₯·ξ₯Άξ₯Έξ₯ΈξŸ€
ξ₯΅ξ₯²ξ 
ξ˜“ξŸ€ξ˜ƒξ˜‹ξš‡ξš”ξš”ξš‡ξš”ξšƒξŸ‘ξ˜ƒξ˜ŒξŸ€ξ˜ƒξ˜ξš—ξš•ξšŠξšƒξš‹ξšŽξš‘ξš˜ξŸ‘ξ˜ƒξ˜„ξŸ€ξ˜ƒξ˜”ξš—ξš”ξš‡ξš•ξšŠξš‹ξŸ‘ξ˜ƒξ˜“ξŸ€ξ˜ƒξ˜‹ξšƒξšŽξš‡ξŸ‘ξ˜ƒξ˜•ξŸ€ξ˜ƒξ˜ξš…ξ˜‡ξšƒξšξš‹ξš‡ξšŽξŸ‘ξ˜ƒξ˜„ξ˜ƒξšˆξš”ξšƒξšξš‡ξš™ξš‘ξš”ξšξ˜ƒξšˆξš‘ξš”ξ˜ƒξš’ξš”ξš‡ξš†ξš‹ξš…ξš–ξš‹ξšξš‰ξ˜ƒξš–ξšŠξš‡ξ˜ƒξš‘ξš’ξš–ξš‹ξšξšƒξšŽξ˜ƒξš’ξš”ξš‹ξš…ξš‡ξ˜ƒ
ξšƒξšξš†ξ˜ƒξš–ξš‹ξšξš‡ξ˜ƒξš–ξš‘ξ˜ƒξš•ξš‡ξšŽξšŽξ˜ƒξšƒξ˜ƒξšŠξš‘ξšξš‡ξŸ‘ξ˜ƒξ˜–ξ˜ξ˜˜ξ˜ƒξ˜‡ξšƒξš–ξšƒξ˜ƒξ˜–ξš…ξš‹ξš‡ξšξš…ξš‡ξ˜ƒξ˜•ξš‡ξš˜ξš‹ξš‡ξš™ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯΄ξŸ‘ξ˜ƒξ₯·ξŸ‘ξ˜ƒξ₯³ξ₯ΈξŸ€
ξ₯΅ξ₯³ξ 
ξ˜„ξš—ξš–ξš‘ξšξšƒξš–ξš‹ξš…ξ˜ƒ ξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξ˜ƒ ξš‡ξšξš‰ξš‹ξšξš‡ξš‡ξš”ξš‹ξšξš‰ξ˜ƒ ξšˆξš‘ξš”ξ˜ƒ ξš”ξš‡ξš‰ξš”ξš‡ξš•ξš•ξš‹ξš‘ξšξ˜ƒ ξšξš‘ξš†ξš‡ξšŽξš•ξ˜ƒ ξš™ξš‹ξš–ξšŠξ˜ƒ ξšξšƒξš…ξšŠξš‹ξšξš‡ξ˜ƒ ξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξŸ£ξ˜ƒ ξ˜„ξšξ˜ƒ ξš‡ξš˜ξš‘ξšŽξš—ξš–ξš‹ξš‘ξšξšƒξš”ξš›ξ˜ƒ
ξš…ξš‘ξšξš’ξš—ξš–ξšƒξš–ξš‹ξš‘ξšξ˜ƒ ξšƒξšξš†ξ˜ƒ ξš•ξš–ξšƒξš–ξš‹ξš•ξš–ξš‹ξš…ξš•ξ˜ƒ ξšŠξš›ξš„ξš”ξš‹ξš†ξŸ‘ξ˜ƒ ξ˜Œξšξšˆξš‘ξš”ξšξšƒξš–ξš‹ξš‘ξšξ˜ƒ ξ˜–ξš…ξš‹ξš‡ξšξš…ξš‡ξš•ξŸ‘ξ˜ƒ ξ₯΄ξ₯²ξ₯³ξ₯ΊξŸ‘ξ˜ƒ ξ₯Άξ₯΅ξ₯²ξŸ¦ξ₯Άξ₯΅ξ₯³ξŸ‘ξ˜ƒ ξ₯΄ξ₯Ίξ₯ΉξŸ¦ξ₯΅ξ₯³ξ₯΅ξŸ‘ξ˜ƒ ξš†ξš‘ξš‹ξŸ£ξ˜ƒ
ξ₯³ξ₯²ξŸ€ξ₯³ξ₯²ξ₯³ξ₯Έξ €ξšŒξŸ€ξš‹ξšξš•ξŸ€ξ₯΄ξ₯²ξ₯³ξ₯ΉξŸ€ξ₯³ξ₯³ξŸ€ξ₯²ξ₯Άξ₯³ξŸ€
ξ₯΅ξ₯΄ξ 
ξ˜ŽξŸ€ξ˜ƒ ξ˜‹ξŸ€ξ˜ƒ ξ˜†ξšŠξš—ξŸ‘ξ˜ƒ ξ˜ξŸ€ξ˜ƒ ξ˜ξš‹ξŸ‘ξ˜ƒ ξ˜“ξš”ξš‡ξš†ξš‹ξš…ξš–ξš‹ξš‘ξšξ˜ƒ ξš‘ξšˆξ˜ƒ ξš”ξš‡ξšƒξšŽξ˜ƒ ξš‡ξš•ξš–ξšƒξš–ξš‡ξ˜ƒ ξš’ξš”ξš‹ξš…ξš‡ξ˜ƒ ξš˜ξšƒξš”ξš‹ξšƒξš–ξš‹ξš‘ξšξ˜ƒ ξš„ξšƒξš•ξš‡ξš†ξ˜ƒ ξš‘ξšξ˜ƒ ξš‡ξš…ξš‘ξšξš‘ξšξš‹ξš…ξ˜ƒ ξš’ξšƒξš”ξšƒξšξš‡ξš–ξš‡ξš”ξš•ξŸ‘ξ˜ƒ ξ₯΄ξ₯²ξ₯³ξ₯Ήξ˜ƒ
ξ˜Œξšξš–ξš‡ξš”ξšξšƒξš–ξš‹ξš‘ξšξšƒξšŽξ˜ƒ ξ˜†ξš‘ξšξšˆξš‡ξš”ξš‡ξšξš…ξš‡ξ˜ƒ ξš‘ξšξ˜ƒ ξ˜„ξš’ξš’ξšŽξš‹ξš‡ξš†ξ˜ƒ ξ˜–ξš›ξš•ξš–ξš‡ξšξ˜ƒ ξ˜Œξšξšξš‘ξš˜ξšƒξš–ξš‹ξš‘ξšξ˜ƒ ξ ‹ξ˜Œξ˜†ξ˜„ξ˜–ξ˜Œξ ŒξŸ‘ξ˜ƒ ξ˜–ξšƒξš’ξš’ξš‘ξš”ξš‘ξŸ‘ξ˜ƒ ξ˜ξšƒξš’ξšƒξšξŸ‘ξ˜ƒ ξ₯΄ξ₯²ξ₯³ξ₯ΉξŸ‘ξ˜ƒ ξ₯Ίξ₯ΉξŸ¦ξ₯»ξ₯²ξŸ‘ξ˜ƒ ξš†ξš‘ξš‹ξŸ£ξ˜ƒ
ξ₯³ξ₯²ξŸ€ξ₯³ξ₯³ξ₯²ξ₯»ξ €ξ˜Œξ˜†ξ˜„ξ˜–ξ˜ŒξŸ€ξ₯΄ξ₯²ξ₯³ξ₯ΉξŸ€ξ₯Ήξ₯»ξ₯Ίξ₯Ίξ₯΅ξ₯·ξ₯΅ξŸ€
ξ₯΅ξ₯΅ξ 
ξ˜™ξŸ€ξ˜ƒξ˜‰ξšƒξš•ξš›ξšƒξŸ‘ξ˜ƒξ˜ˆξšξšŠξšƒξšξš…ξš‹ξšξš‰ξ˜ƒξšŠξš‘ξš—ξš•ξš‹ξšξš‰ξ˜ƒξš’ξš”ξš‹ξš…ξš‡ξ˜ƒξš’ξš”ξš‡ξš†ξš‹ξš…ξš–ξš‹ξš‘ξšξš•ξŸ£ξ˜ƒξšŠξš‘ξš™ξ˜ƒξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξ˜ƒξš‡ξšξš‰ξš‹ξšξš‡ξš‡ξš”ξš‹ξšξš‰ξ˜ƒξšξšƒξšξš‡ξš•ξ˜ƒξšƒξ˜ƒξš†ξš‹ξšˆξšˆξš‡ξš”ξš‡ξšξš…ξš‡ξŸ‘ξ˜ƒξ˜ξš‡ξš†ξš‹ξš—ξšξ˜ƒ
ξ˜‡ξšƒξš–ξšƒξ˜ƒξ˜–ξš…ξš‹ξš‡ξšξš…ξš‡ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯ΆξŸ€
ξ₯΅ξ₯Άξ 
ξ˜—ξŸ€ξ˜ƒξ˜‘ξš‡ξš˜ξš‡ξš•ξŸ‘ξ˜ƒξ˜‰ξšƒξž΄ξš–ξš‹ξšξšƒξŸ‘ξ˜ƒξ˜ξŸ€ξ˜ƒξ˜„ξš’ξšƒξš”ξš‹ξš…ξš‹ξš‘ξŸ‘ξ˜ƒξ˜ξŸ€ξ˜ƒξš†ξš‡ξ˜ƒξ˜†ξŸ€ξ˜ƒξ˜‘ξš‡ξš–ξš‘ξŸ€ξŸ‘ξ˜ƒξ˜—ξšŠξš‡ξ˜ƒξ˜Œξšξš’ξšƒξš…ξš–ξš•ξ˜ƒξš‘ξšˆξ˜ƒξ˜’ξš’ξš‡ξšξ˜ƒξ˜‡ξšƒξš–ξšƒξ˜ƒξšƒξšξš†ξ˜ƒξš‡ξ˜›ξš’ξšŽξšƒξš‹ξšξšƒξš„ξšŽξš‡ξ˜ƒξ˜„ξ˜Œξ˜ƒξš‘ξšξ˜ƒξš”ξš‡ξšƒξšŽξ˜ƒξš‡ξš•ξš–ξšƒξš–ξš‡ξ˜ƒ
ξš’ξš”ξš‹ξš…ξš‡ξ˜ƒξš’ξš”ξš‡ξš†ξš‹ξš…ξš–ξš‹ξš‘ξšξš•ξ˜ƒξš‹ξšξ˜ƒξš•ξšξšƒξš”ξš–ξ˜ƒξš…ξš‹ξš–ξš‹ξš‡ξš•ξŸ‘ξ˜ƒξ˜„ξš’ξš’ξšŽξš‹ξš‡ξš†ξ˜ƒξ˜–ξš…ξš‹ξš‡ξšξš…ξš‡ξš•ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯ΆξŸ‘ξ˜ƒξ₯³ξ₯ΆξŸ‘ξ˜ƒξ₯΄ξ₯΄ξ₯²ξ₯»ξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯΅ξ₯΅ξ₯»ξ₯²ξ €ξšƒξš’ξš’ξ₯³ξ₯Άξ₯²ξ₯·ξ₯΄ξ₯΄ξ₯²ξ₯»ξŸ€
ξ₯΅ξ₯·ξ 
ξ˜ξŸ€ξ˜ƒξ˜šξŸ€ξ˜ƒξ˜—ξš—ξšξš‡ξš›ξŸ‘ξ˜ƒξ˜ˆξššξš’ξšŽξš‘ξš”ξšƒξš–ξš‘ξš”ξš›ξ˜ƒξš†ξšƒξš–ξšƒξ˜ƒξšƒξšξšƒξšŽξš›ξš•ξš‹ξš•ξŸ‘ξ˜ƒξ˜„ξš†ξš†ξš‹ξš•ξš‘ξšξŸ¦ξ˜šξš‡ξš•ξšŽξš‡ξš›ξŸ‘ξ˜ƒξ₯³ξ₯»ξ₯Ήξ₯ΉξŸ€
ξ₯΅ξ₯Έξ 
ξ˜‹ξŸ€ξ˜ƒ ξ˜šξš‹ξš…ξšξšŠξšƒξšξŸ‘ξ˜ƒ ξ˜ŠξŸ€ξ˜ƒ ξ˜Šξš”ξš‘ξšŽξš‡ξšξš—ξšξš†ξŸ‘ξ˜ƒ ξ˜•ξ˜ƒ ξšˆξš‘ξš”ξ˜ƒ ξš†ξšƒξš–ξšƒξ˜ƒ ξš•ξš…ξš‹ξš‡ξšξš…ξš‡ξŸ£ξ˜ƒ ξš‹ξšξš’ξš‘ξš”ξš–ξŸ‘ξ˜ƒ ξš–ξš‹ξš†ξš›ξŸ‘ξ˜ƒ ξš–ξš”ξšƒξšξš•ξšˆξš‘ξš”ξšξŸ‘ξ˜ƒ ξš˜ξš‹ξš•ξš—ξšƒξšŽξš‹ξšœξš‡ξŸ‘ξ˜ƒ ξšƒξšξš†ξ˜ƒ ξšξš‘ξš†ξš‡ξšŽξ˜ƒ ξš†ξšƒξš–ξšƒξŸ‘ξ˜ƒ
ξ˜’ξ€΅ξ˜•ξš‡ξš‹ξšŽξšŽξš›ξ˜ƒξ˜ξš‡ξš†ξš‹ξšƒξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯³ξ₯ΈξŸ€
ξ₯΅ξ₯Ήξ 
ξ˜“ξŸ€ξ˜ƒξ˜ξŸ€ξ˜ƒξ˜•ξš‘ξš—ξš•ξš•ξš‡ξš‡ξš—ξš™ξŸ‘ξ˜ƒξ˜ξŸ€ξ˜ƒξ˜‹ξš—ξš„ξš‡ξš”ξš–ξŸ‘ξ˜ƒξ˜•ξš‘ξš„ξš—ξš•ξš–ξ˜ƒξš•ξš–ξšƒξš–ξš‹ξš•ξš–ξš‹ξš…ξš•ξ˜ƒξšˆξš‘ξš”ξ˜ƒξš‘ξš—ξš–ξšŽξš‹ξš‡ξš”ξ˜ƒξš†ξš‡ξš–ξš‡ξš…ξš–ξš‹ξš‘ξšξŸ‘ξ˜ƒξ˜šξš‹ξšŽξš‡ξš›ξ˜ƒξ˜Œξšξš–ξš‡ξš”ξš†ξš‹ξš•ξš…ξš‹ξš’ξšŽξš‹ξšξšƒξš”ξš›ξ˜ƒξ˜•ξš‡ξš˜ξš‹ξš‡ξš™ξš•ξŸ£ξ˜ƒξ˜‡ξšƒξš–ξšƒξ˜ƒ
ξ˜ξš‹ξšξš‹ξšξš‰ξ˜ƒξšƒξšξš†ξ˜ƒξ˜Žξšξš‘ξš™ξšŽξš‡ξš†ξš‰ξš‡ξ˜ƒξ˜‡ξš‹ξš•ξš…ξš‘ξš˜ξš‡ξš”ξš›ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯³ξ₯³ξŸ‘ξ˜ƒξ₯³ξŸ‘ξ˜ƒξ₯Ήξ₯΅ξŸ¦ξ₯Ήξ₯»ξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯²ξ₯²ξ₯΄ξ €ξš™ξš‹ξš†ξšξŸ€ξ₯΄ξŸ€
ξ₯΅ξ₯Ίξ 
ξ˜ξŸ€ξ˜ƒξ˜Žξš—ξšŠξšξŸ‘ξ˜ƒξ˜ŽξŸ€ξ˜ƒξ˜ξš‘ξšŠξšξš•ξš‘ξšξŸ‘ξ˜ƒξ˜‰ξš‡ξšƒξš–ξš—ξš”ξš‡ξ˜ƒξš‡ξšξš‰ξš‹ξšξš‡ξš‡ξš”ξš‹ξšξš‰ξ˜ƒξšƒξšξš†ξ˜ƒξš•ξš‡ξšŽξš‡ξš…ξš–ξš‹ξš‘ξšξŸ£ξ˜ƒξšƒξ˜ƒξš’ξš”ξšƒξš…ξš–ξš‹ξš…ξšƒξšŽξ˜ƒξšƒξš’ξš’ξš”ξš‘ξšƒξš…ξšŠξ˜ƒξšˆξš‘ξš”ξ˜ƒξš’ξš”ξš‡ξš†ξš‹ξš…ξš–ξš‹ξš˜ξš‡ξ˜ƒξšξš‘ξš†ξš‡ξšŽξš•ξŸ‘ξ˜ƒξ˜†ξ˜•ξ˜†ξ˜ƒ
ξ˜“ξš”ξš‡ξš•ξš•ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯³ξ₯»ξŸ€
ξ₯΅ξ₯»ξ 
ξ˜„ξŸ€ξ˜ƒ ξ˜ξšŠξš‡ξšξš‰ξŸ‘ξ˜ƒ ξ˜„ξŸ€ξ˜ƒ ξ˜†ξšƒξš•ξšƒξš”ξš‹ξŸ‘ξ˜ƒ ξ˜‰ξš‡ξšƒξš–ξš—ξš”ξš‡ξ˜ƒ ξš‡ξšξš‰ξš‹ξšξš‡ξš‡ξš”ξš‹ξšξš‰ξ˜ƒ ξšˆξš‘ξš”ξ˜ƒ ξšξšƒξš…ξšŠξš‹ξšξš‡ξ˜ƒ ξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξŸ£ξ˜ƒ ξš’ξš”ξš‹ξšξš…ξš‹ξš’ξšŽξš‡ξš•ξ˜ƒ ξšƒξšξš†ξ˜ƒ ξš–ξš‡ξš…ξšŠξšξš‹ξš“ξš—ξš‡ξš•ξ˜ƒ ξšˆξš‘ξš”ξ˜ƒ ξš†ξšƒξš–ξšƒξ˜ƒ
ξš•ξš…ξš‹ξš‡ξšξš–ξš‹ξš•ξš–ξš•ξŸ‘ξ˜ƒξ˜’ξ€΅ξ˜•ξš‡ξš‹ξšŽξšŽξš›ξ˜ƒξ˜ξš‡ξš†ξš‹ξšƒξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯³ξ₯ΊξŸ€
ξ₯Άξ₯²ξ 
ξ˜ξŸ€ξ˜ƒξ˜‹ξŸ€ξ˜ƒξ˜‰ξš”ξš‹ξš‡ξš†ξšξšƒξšξŸ‘ξ˜ƒξ˜Šξš”ξš‡ξš‡ξš†ξš›ξ˜ƒξšˆξš—ξšξš…ξš–ξš‹ξš‘ξšξ˜ƒξšƒξš’ξš’ξš”ξš‘ξššξš‹ξšξšƒξš–ξš‹ξš‘ξšξŸ£ξ˜ƒξ˜„ξ˜ƒξš‰ξš”ξšƒξš†ξš‹ξš‡ξšξš–ξ˜ƒξš„ξš‘ξš‘ξš•ξš–ξš‹ξšξš‰ξ˜ƒξšξšƒξš…ξšŠξš‹ξšξš‡ξŸ‘ξ˜ƒξ˜„ξšξšξšƒξšŽξš•ξ˜ƒξš‘ξšˆξ˜ƒξ˜–ξš–ξšƒξš–ξš‹ξš•ξš–ξš‹ξš…ξš•ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯²ξ₯³ξŸ‘ξ˜ƒ
ξ₯΄ξ₯»ξŸ‘ξ˜ƒξ₯³ξ₯³ξ₯Ίξ₯»ξŸ¦ξ₯³ξ₯΄ξ₯΅ξ₯΄ξŸ€
ξ₯Άξ₯³ξ 
ξ˜†ξŸ€ξ˜ƒξ˜ξŸ€ξ˜ƒξ˜…ξš‹ξš•ξšŠξš‘ξš’ξŸ‘ξ˜ƒξ˜“ξšƒξš–ξš–ξš‡ξš”ξšξ˜ƒξš”ξš‡ξš…ξš‘ξš‰ξšξš‹ξš–ξš‹ξš‘ξšξ˜ƒξšƒξšξš†ξ˜ƒξšξšƒξš…ξšŠξš‹ξšξš‡ξ˜ƒξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξŸ‘ξ˜ƒξ˜–ξš’ξš”ξš‹ξšξš‰ξš‡ξš”ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯²ξ₯ΈξŸ€
ξ₯Άξ₯΄ξ 
ξ˜—ξŸ€ξ˜ƒξ˜‹ξšƒξš•ξš–ξš‹ξš‡ξŸ‘ξ˜ƒξ˜•ξŸ€ξ˜ƒξ˜—ξš‹ξš„ξš•ξšŠξš‹ξš”ξšƒξšξš‹ξŸ‘ξ˜ƒξ˜ξŸ€ξ˜ƒξ˜‰ξš”ξš‹ξš‡ξš†ξšξšƒξšξŸ‘ξ˜ƒξ˜—ξšŠξš‡ξ˜ƒξš‡ξšŽξš‡ξšξš‡ξšξš–ξš•ξ˜ƒξš‘ξšˆξ˜ƒξš•ξš–ξšƒξš–ξš‹ξš•ξš–ξš‹ξš…ξšƒξšŽξ˜ƒξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξŸ‘ξ˜ƒξ˜–ξš’ξš”ξš‹ξšξš‰ξš‡ξš”ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯²ξ₯»ξŸ€
ξ₯Άξ₯΅ξ 
ξ˜ŒξŸ€ξ˜ƒξ˜Šξš—ξš›ξš‘ξšξŸ‘ξ˜ƒξ˜„ξŸ€ξ˜ƒξ˜ˆξšŽξš‹ξš•ξš•ξš‡ξš‡ξšˆξšˆξŸ‘ξ˜ƒξ˜„ξšξ˜ƒξš‹ξšξš–ξš”ξš‘ξš†ξš—ξš…ξš–ξš‹ξš‘ξšξ˜ƒξš–ξš‘ξ˜ƒξš˜ξšƒξš”ξš‹ξšƒξš„ξšŽξš‡ξ˜ƒξšƒξšξš†ξ˜ƒξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξ˜ƒξš•ξš‡ξšŽξš‡ξš…ξš–ξš‹ξš‘ξšξŸ‘ξ˜ƒ ξ˜ξš‘ξš—ξš”ξšξšƒξšŽξ˜ƒξš‘ξšˆξ˜ƒξ˜ξšƒξš…ξšŠξš‹ξšξš‡ξ˜ƒξ˜ξš‡ξšƒξš”ξšξš‹ξšξš‰ξ˜ƒ
ξ˜•ξš‡ξš•ξš‡ξšƒξš”ξš…ξšŠξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯²ξ₯΅ξŸ‘ξ˜ƒξ₯΅ξŸ‘ξ˜ƒξ₯³ξ₯³ξ₯·ξ₯ΉξŸ¦ξ₯³ξ₯³ξ₯Ίξ₯΄ξŸ€
ξ₯Άξ₯Άξ 
ξ˜ŠξŸ€ξ˜ƒξ˜†ξšŠξšƒξšξš†ξš”ξšƒξš•ξšŠξš‡ξšξšƒξš”ξŸ‘ξ˜ƒξ˜‰ξŸ€ξ˜ƒξ˜–ξšƒξšŠξš‹ξšξŸ‘ξ˜ƒξ˜„ξ˜ƒξš•ξš—ξš”ξš˜ξš‡ξš›ξ˜ƒξš‘ξšξ˜ƒξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξ˜ƒξš•ξš‡ξšŽξš‡ξš…ξš–ξš‹ξš‘ξšξ˜ƒξšξš‡ξš–ξšŠξš‘ξš†ξš•ξŸ‘ξ˜ƒξ˜†ξš‘ξšξš’ξš—ξš–ξš‡ξš”ξš•ξ˜ƒξž¬ξ˜ƒξ˜ˆξšŽξš‡ξš…ξš–ξš”ξš‹ξš…ξšƒξšŽξ˜ƒξ˜ˆξšξš‰ξš‹ξšξš‡ξš‡ξš”ξš‹ξšξš‰ξŸ‘ξ˜ƒ
ξ₯΄ξ₯²ξ₯³ξ₯ΆξŸ‘ξ˜ƒξ₯Άξ₯²ξŸ‘ξ˜ƒξ₯³ξ₯ΈξŸ¦ξ₯΄ξ₯ΊξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯²ξ₯³ξ₯Έξ €ξšŒξŸ€ξš…ξš‘ξšξš’ξš‡ξšŽξš‡ξš…ξš‡ξšξš‰ξŸ€ξ₯΄ξ₯²ξ₯³ξ₯΅ξŸ€ξ₯³ξ₯³ξŸ€ξ₯²ξ₯΄ξ₯ΆξŸ€
ξ₯Άξ₯·ξ 
ξ˜‰ξŸ€ξ˜ƒξ˜“ξš‡ξš†ξš”ξš‡ξš‰ξš‘ξš•ξšƒξŸ‘ξ˜ƒξ˜ŠξŸ€ξ˜ƒξ˜™ξšƒξš”ξš‘ξš“ξš—ξšƒξš—ξššξŸ‘ξ˜ƒξ˜„ξŸ€ξ˜ƒξ˜Šξš”ξšƒξšξšˆξš‘ξš”ξš–ξŸ‘ξ˜ƒξ˜™ξŸ€ξ˜ƒξ˜ξš‹ξš…ξšŠξš‡ξšŽξŸ‘ξ˜ƒξ˜…ξŸ€ξ˜ƒξ˜—ξšŠξš‹ξš”ξš‹ξš‘ξšξŸ‘ξ˜ƒξ˜’ξŸ€ξ˜ƒξ˜Šξš”ξš‹ξš•ξš‡ξšŽξŸ‘ξ˜ƒξ˜ξŸ€ξ˜ƒξ˜…ξšŽξš‘ξšξš†ξš‡ξšŽξŸ‘ξ˜ƒξ˜“ξŸ€ξ˜ƒξ˜“ξš”ξš‡ξš–ξš–ξš‡ξšξšŠξš‘ξšˆξš‡ξš”ξŸ‘ξ˜ƒξ˜•ξŸ€ξ˜ƒ
ξ˜šξš‡ξš‹ξš•ξš•ξŸ‘ξ˜ƒξ˜™ξŸ€ξ˜ƒξ˜‡ξš—ξš„ξš‘ξš—ξš”ξš‰ξŸ‘ξ˜ƒξ˜ξŸ€ξ˜ƒξ˜™ξšƒξšξš†ξš‡ξš”ξš’ξšŽξšƒξš•ξŸ‘ξ˜ƒξ˜„ξŸ€ξ˜ƒξ˜“ξšƒξš•ξš•ξš‘ξš•ξŸ‘ξ˜ƒξ˜‡ξŸ€ξ˜ƒξ˜†ξš‘ξš—ξš”ξšξšƒξš’ξš‡ξšƒξš—ξŸ‘ξ˜ƒξ˜ξŸ€ξ˜ƒξ˜…ξš”ξš—ξš…ξšŠξš‡ξš”ξŸ‘ξ˜ƒξ˜ξŸ€ξ˜ƒξ˜“ξš‡ξš”ξš”ξš‘ξš–ξŸ‘ξ˜ƒξ˜ˆξž΅ξŸ€ξ˜ƒξ˜‡ξš—ξš…ξšŠξš‡ξš•ξšξšƒξš›ξŸ‘ξ˜ƒξ˜–ξš…ξš‹ξšξš‹ξš–ξŸ¦
ξšŽξš‡ξšƒξš”ξšξŸ£ξ˜ƒξ˜ξšƒξš…ξšŠξš‹ξšξš‡ξ˜ƒξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξ˜ƒξš‹ξšξ˜ƒξ˜“ξš›ξš–ξšŠξš‘ξšξŸ‘ξ˜ƒξ˜ξš‘ξš—ξš”ξšξšƒξšŽξ˜ƒξš‘ξšˆξ˜ƒξ˜ξšƒξš…ξšŠξš‹ξšξš‡ξ˜ƒξ˜ξš‡ξšƒξš”ξšξš‹ξšξš‰ξ˜ƒξ˜•ξš‡ξš•ξš‡ξšƒξš”ξš…ξšŠξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯³ξ₯³ξŸ‘ξ˜ƒξ₯³ξ₯΄ξŸ‘ξ˜ƒξ₯΄ξ₯Ίξ₯΄ξ₯·ξŸ¦ξ₯΄ξ₯Ίξ₯΅ξ₯²ξŸ€
ξ₯Άξ₯Έξ 
ξ˜„ξŸ€ξ˜ƒξ˜Šξš‡ξž΄ξš”ξš‘ξšξŸ‘ξ˜ƒξ˜‹ξšƒξšξš†ξš•ξŸ¦ξš‘ξšξ˜ƒξšξšƒξš…ξšŠξš‹ξšξš‡ξ˜ƒξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξ˜ƒξš™ξš‹ξš–ξšŠξ˜ƒξ˜–ξš…ξš‹ξšξš‹ξš–ξŸ¦ξ˜ξš‡ξšƒξš”ξšξŸ‘ξ˜ƒξ˜Žξš‡ξš”ξšƒξš•ξŸ‘ξ˜ƒξšƒξšξš†ξ˜ƒξ˜—ξš‡ξšξš•ξš‘ξš”ξ˜‰ξšŽξš‘ξš™ξŸ‘ξ˜ƒξ˜’ξ€΅ξ˜•ξš‡ξš‹ξšŽξšŽξš›ξ˜ƒξ˜ξš‡ξš†ξš‹ξšƒξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯³ξ₯»ξŸ€
ξ₯Άξ₯Ήξ 
ξ˜ŒξŸ€ξ˜ƒξ˜Šξš‘ξš‘ξš†ξšˆξš‡ξšŽξšŽξš‘ξš™ξŸ‘ξ˜ƒξ˜œξŸ€ξ˜ƒξ˜…ξš‡ξšξš‰ξš‹ξš‘ξŸ‘ξ˜ƒξ˜„ξŸ€ξ˜ƒξ˜†ξš‘ξš—ξš”ξš˜ξš‹ξšŽξšŽξš‡ξŸ‘ξ˜ƒξ˜‡ξš‡ξš‡ξš’ξ˜ƒξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξŸ‘ξ˜ƒξ˜ξ˜Œξ˜—ξ˜ƒξ˜“ξš”ξš‡ξš•ξš•ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯³ξ₯ΈξŸ€
ξ₯Άξ₯Ίξ 
ξ˜•ξŸ€ξ˜ƒ ξ˜Žξš‘ξšŠξšƒξš˜ξš‹ξŸ‘ξ˜ƒ ξ˜„ξ˜ƒ ξš•ξš–ξš—ξš†ξš›ξ˜ƒ ξš‘ξšˆξ˜ƒ ξš…ξš”ξš‘ξš•ξš•ξŸ¦ξš˜ξšƒξšŽξš‹ξš†ξšƒξš–ξš‹ξš‘ξšξ˜ƒ ξšƒξšξš†ξ˜ƒ ξš„ξš‘ξš‘ξš–ξš•ξš–ξš”ξšƒξš’ξ˜ƒ ξšˆξš‘ξš”ξ˜ƒ ξšƒξš…ξš…ξš—ξš”ξšƒξš…ξš›ξ˜ƒ ξš‡ξš•ξš–ξš‹ξšξšƒξš–ξš‹ξš‘ξšξ˜ƒ ξšƒξšξš†ξ˜ƒ ξšξš‘ξš†ξš‡ξšŽξ˜ƒ ξš•ξš‡ξšŽξš‡ξš…ξš–ξš‹ξš‘ξšξŸ‘ξ˜ƒ
ξ˜Œξšξš–ξš‡ξš”ξšξšƒξš–ξš‹ξš‘ξšξšƒξšŽξ˜ƒξ˜ξš‘ξš‹ξšξš–ξ˜ƒξ˜†ξš‘ξšξšˆξš‡ξš”ξš‡ξšξš…ξš‡ξ˜ƒξš‘ξšξ˜ƒξ˜„ξš”ξš–ξš‹ξ§”ξš‹ξš…ξš‹ξšƒξšŽξ˜ƒξ˜Œξšξš–ξš‡ξšŽξšŽξš‹ξš‰ξš‡ξšξš…ξš‡ξŸ‘ξ˜ƒξ₯³ξ₯»ξ₯»ξ₯·ξŸ‘ξ˜ƒξ₯³ξ₯³ξ₯΅ξ₯ΉξŸ¦ξ₯³ξ₯³ξ₯Άξ₯·ξŸ€
ξ₯Άξ₯»ξ 
ξ˜„ξŸ€ξ˜ƒ ξ˜ˆξŸ€ξ˜ƒ ξ˜‹ξš‘ξš‡ξš”ξšŽξŸ‘ξ˜ƒ ξ˜•ξŸ€ξ˜ƒ ξ˜šξŸ€ξ˜ƒ ξ˜Žξš‡ξšξšξšƒξš”ξš†ξŸ‘ξ˜ƒ ξ˜•ξš‹ξš†ξš‰ξš‡ξ˜ƒ ξš”ξš‡ξš‰ξš”ξš‡ξš•ξš•ξš‹ξš‘ξšξŸ£ξ˜ƒ ξ˜…ξš‹ξšƒξš•ξš‡ξš†ξ˜ƒ ξš‡ξš•ξš–ξš‹ξšξšƒξš–ξš‹ξš‘ξšξ˜ƒ ξšˆξš‘ξš”ξ˜ƒ ξšξš‘ξšξš‘ξš”ξš–ξšŠξš‘ξš‰ξš‘ξšξšƒξšŽξ˜ƒ ξš’ξš”ξš‘ξš„ξšŽξš‡ξšξš•ξŸ‘ξ˜ƒ
ξ˜—ξš‡ξš…ξšŠξšξš‘ξšξš‡ξš–ξš”ξš‹ξš…ξš•ξŸ‘ξ˜ƒξ₯³ξ₯»ξ₯Ήξ₯²ξŸ‘ξ˜ƒξ₯³ξ₯΄ξŸ‘ξ˜ƒξ₯·ξ₯·ξŸ¦ξ₯Έξ₯ΉξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯΄ξ₯΅ξ₯²ξ₯Ήξ €ξ₯³ξ₯΄ξ₯Ήξ₯³ξ₯Άξ₯΅ξ₯ΈξŸ€
ξ₯·ξ₯²ξ 
ξ˜•ξŸ€ξ˜ƒξ˜—ξš‹ξš„ξš•ξšŠξš‹ξš”ξšƒξšξš‹ξŸ‘ξ˜ƒξ˜•ξš‡ξš‰ξš”ξš‡ξš•ξš•ξš‹ξš‘ξšξ˜ƒξš•ξšŠξš”ξš‹ξšξšξšƒξš‰ξš‡ξ˜ƒξšƒξšξš†ξ˜ƒξš•ξš‡ξšŽξš‡ξš…ξš–ξš‹ξš‘ξšξ˜ƒξš˜ξš‹ξšƒξ˜ƒξš–ξšŠξš‡ξ˜ƒξšŽξšƒξš•ξš•ξš‘ξŸ‘ξ˜ƒξ˜ξš‘ξš—ξš”ξšξšƒξšŽξ˜ƒξš‘ξšˆξ˜ƒξš–ξšŠξš‡ξ˜ƒξ˜•ξš‘ξš›ξšƒξšŽξ˜ƒξ˜–ξš–ξšƒξš–ξš‹ξš•ξš–ξš‹ξš…ξšƒξšŽξ˜ƒξ˜–ξš‘ξš…ξš‹ξš‡ξš–ξš›ξŸ£ξ˜ƒ
ξ˜–ξš‡ξš”ξš‹ξš‡ξš•ξ˜ƒξ˜…ξŸ‘ξ˜ƒξ₯³ξ₯»ξ₯»ξ₯ΈξŸ‘ξ˜ƒξ₯·ξ₯ΊξŸ‘ξ˜ƒξ₯΄ξ₯Έξ₯ΉξŸ¦ξ₯΄ξ₯Ίξ₯ΊξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯³ξ₯³ξ₯³ξ €ξšŒξŸ€ξ₯΄ξ₯·ξ₯³ξ₯ΉξŸ¦ξ₯Έξ₯³ξ₯Έξ₯³ξŸ€ξ₯³ξ₯»ξ₯»ξ₯ΈξŸ€ξš–ξš„ξ₯²ξ₯΄ξ₯²ξ₯Ίξ₯²ξŸ€ξššξŸ€
ξ₯·ξ₯³ξ 
ξ˜ŠξŸ€ξ˜ƒξ˜ξšƒξšξš‡ξš•ξŸ‘ξ˜ƒξ˜„ξšξ˜ƒξš‹ξšξš–ξš”ξš‘ξš†ξš—ξš…ξš–ξš‹ξš‘ξšξ˜ƒξš–ξš‘ξ˜ƒξš•ξš–ξšƒξš–ξš‹ξš•ξš–ξš‹ξš…ξšƒξšŽξ˜ƒξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξŸ‘ξ˜ƒξ˜–ξš’ξš”ξš‹ξšξš‰ξš‡ξš”ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯³ξ₯΅ξŸ€
ξ₯·ξ₯΄ξ 
ξ˜ξŸ€ξ˜ƒξ˜šξšƒξš‹ξšξš™ξš”ξš‹ξš‰ξšŠξš–ξŸ‘ξ˜ƒξ˜•ξŸ€ξ˜ƒξ˜—ξš‹ξš„ξš•ξšŠξš‹ξš”ξšƒξšξš‹ξŸ‘ξ˜ƒξ˜—ξŸ€ξ˜ƒξ˜‹ξšƒξš•ξš–ξš‹ξš‡ξŸ‘ξ˜ƒξ˜–ξš–ξšƒξš–ξš‹ξš•ξš–ξš‹ξš…ξšƒξšŽξ˜ƒξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξ˜ƒξš™ξš‹ξš–ξšŠξ˜ƒξš•ξš’ξšƒξš”ξš•ξš‹ξš–ξš›ξŸ£ξ˜ƒξš–ξšŠξš‡ξ˜ƒξšŽξšƒξš•ξš•ξš‘ξ˜ƒξšƒξšξš†ξ˜ƒξš‰ξš‡ξšξš‡ξš”ξšƒξšŽξš‹ξšœξšƒξš–ξš‹ξš‘ξšξš•ξŸ‘ξ˜ƒ
ξ˜†ξ˜•ξ˜†ξ˜ƒξ˜“ξš”ξš‡ξš•ξš•ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯³ξ₯·ξŸ€
ξ₯·ξ₯΅ξ 
ξ˜ξŸ€ξ˜ƒ ξ˜–ξš–ξš‘ξšξš‡ξŸ‘ξ˜ƒ ξ˜†ξš”ξš‘ξš•ξš•ξŸ¦ξš˜ξšƒξšŽξš‹ξš†ξšƒξš–ξš‘ξš”ξš›ξ˜ƒ ξš…ξšŠξš‘ξš‹ξš…ξš‡ξ˜ƒ ξšƒξšξš†ξ˜ƒ ξšƒξš•ξš•ξš‡ξš•ξš•ξšξš‡ξšξš–ξ˜ƒ ξš‘ξšˆξ˜ƒ ξš•ξš–ξšƒξš–ξš‹ξš•ξš–ξš‹ξš…ξšƒξšŽξ˜ƒ ξš’ξš”ξš‡ξš†ξš‹ξš…ξš–ξš‹ξš‘ξšξš•ξŸ‘ξ˜ƒ ξ˜ξš‘ξš—ξš”ξšξšƒξšŽξ˜ƒ ξš‘ξšˆξ˜ƒ ξš–ξšŠξš‡ξ˜ƒ ξ˜•ξš‘ξš›ξšƒξšŽξ˜ƒ
ξ˜–ξš–ξšƒξš–ξš‹ξš•ξš–ξš‹ξš…ξšƒξšŽξ˜ƒξ˜–ξš‘ξš…ξš‹ξš‡ξš–ξš›ξŸ£ξ˜ƒξ˜–ξš‡ξš”ξš‹ξš‡ξš•ξ˜ƒξ˜…ξŸ‘ξ˜ƒξ₯³ξ₯»ξ₯Ήξ₯ΆξŸ‘ξ˜ƒξ₯΅ξ₯ΈξŸ‘ξ˜ƒξ₯³ξ₯³ξ₯³ξŸ¦ξ₯³ξ₯΅ξ₯΅ξŸ€
ξ₯·ξ₯Άξ 
ξ˜ξŸ€ξ˜ƒ ξ˜ξŸ€ξ˜ƒ ξ˜„ξšŽξšˆξšƒξš”ξš‘ξŸ¦ξ˜‘ξšƒξš˜ξšƒξš”ξš”ξš‘ξŸ‘ξ˜ƒ ξ˜ˆξŸ€ξ˜ƒ ξ˜ξŸ€ξ˜ƒ ξ˜†ξšƒξšξš‘ξŸ‘ξ˜ƒ ξ˜ˆξŸ€ξ˜ƒ ξ˜„ξšŽξšˆξšƒξš”ξš‘ξŸ¦ξ˜†ξš‘ξš”ξš–ξš‡ξž΄ξš•ξŸ‘ξ˜ƒ ξ˜‘ξŸ€ξ˜ƒ ξ˜Šξšƒξš”ξš…ξ›‡ξž΄ξšƒξŸ‘ξ˜ƒ ξ˜ξŸ€ξ˜ƒ ξ˜Šξšƒξž΄ξšξš‡ξšœξŸ‘ξ˜ƒ ξ˜…ξŸ€ξ˜ƒ ξ˜ξšƒξš”ξš”ξšƒξšœξŸ‘ξ˜ƒ ξ˜„ξ˜ƒ ξšˆξš—ξšŽξšŽξš›ξ˜ƒ ξšƒξš—ξš–ξš‘ξšξšƒξš–ξš‡ξš†ξ˜ƒ
ξšƒξš†ξšŒξš—ξš•ξš–ξšξš‡ξšξš–ξ˜ƒ ξš‘ξšˆξ˜ƒ ξš‡ξšξš•ξš‡ξšξš„ξšŽξš‡ξ˜ƒ ξšξš‡ξš–ξšŠξš‘ξš†ξš•ξ˜ƒ ξš‹ξšξ˜ƒ ξšξšƒξš…ξšŠξš‹ξšξš‡ξ˜ƒ ξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξ˜ƒ ξšˆξš‘ξš”ξ˜ƒ ξšξš‘ξš†ξš‡ξšŽξš‹ξšξš‰ξ˜ƒ ξš…ξš‘ξšξš’ξšŽξš‡ξššξ˜ƒ ξš”ξš‡ξšƒξšŽξ˜ƒ ξš‡ξš•ξš–ξšƒξš–ξš‡ξ˜ƒ ξš•ξš›ξš•ξš–ξš‡ξšξš•ξŸ‘ξ˜ƒ
ξ˜†ξš‘ξšξš’ξšŽξš‡ξššξš‹ξš–ξš›ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯²ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯²ξŸ‘ξ˜ƒξ₯·ξ₯΄ξ₯Ίξ₯Ήξ₯΄ξ₯Έξ₯΅ξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯³ξ₯·ξ₯·ξ €ξ₯΄ξ₯²ξ₯΄ξ₯²ξ €ξ₯·ξ₯΄ξ₯Ίξ₯Ήξ₯΄ξ₯Έξ₯΅ξŸ€
ξ₯·ξ₯·ξ 
ξ˜ξŸ€ξ˜ƒξ˜‹ξŸ€ξ˜ƒξ˜ξšŠξš‘ξš—ξŸ‘ξ˜ƒξ˜ˆξšξš•ξš‡ξšξš„ξšŽξš‡ξ˜ƒξšξš‡ξš–ξšŠξš‘ξš†ξš•ξŸ£ξ˜ƒξšˆξš‘ξš—ξšξš†ξšƒξš–ξš‹ξš‘ξšξš•ξ˜ƒξšƒξšξš†ξ˜ƒξšƒξšŽξš‰ξš‘ξš”ξš‹ξš–ξšŠξšξš•ξŸ‘ξ˜ƒξ˜†ξ˜•ξ˜†ξ˜ƒξ˜“ξš”ξš‡ξš•ξš•ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯³ξ₯΄ξŸ€
ξ₯·ξ₯Έξ 
ξ˜ξŸ€ξ˜ƒξ˜…ξš‹ξš‡ξšξŸ‘ξ˜ƒξ˜•ξŸ€ξ˜ƒξ˜—ξš‹ξš„ξš•ξšŠξš‹ξš”ξšƒξšξš‹ξŸ‘ξ˜ƒξ˜“ξš”ξš‘ξš–ξš‘ξš–ξš›ξš’ξš‡ξ˜ƒξš•ξš‡ξšŽξš‡ξš…ξš–ξš‹ξš‘ξšξ˜ƒξšˆξš‘ξš”ξ˜ƒξš‹ξšξš–ξš‡ξš”ξš’ξš”ξš‡ξš–ξšƒξš„ξšŽξš‡ξ˜ƒξš…ξšŽξšƒξš•ξš•ξš‹ξ§ξš‹ξš…ξšƒξš–ξš‹ξš‘ξšξŸ‘ξ˜ƒ ξ˜„ξšξšξšƒξšŽξš•ξ˜ƒξš‘ξšˆξ˜ƒξ˜„ξš’ξš’ξšŽξš‹ξš‡ξš†ξ˜ƒξ˜–ξš–ξšƒξš–ξš‹ξš•ξš–ξš‹ξš…ξš•ξŸ‘ξ˜ƒ
ξ₯΄ξ₯²ξ₯³ξ₯³ξŸ‘ξ˜ƒξ₯·ξŸ‘ξ˜ƒξ₯΄ξ₯Άξ₯²ξ₯΅ξŸ¦ξ₯΄ξ₯Άξ₯΄ξ₯ΆξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯΄ξ₯³ξ₯Άξ €ξ₯³ξ₯³ξŸ¦ξ˜„ξ˜’ξ˜„ξ˜–ξ₯Άξ₯»ξ₯·ξŸ€
ξ₯·ξ₯Ήξ 
ξ˜“ξŸ€ξ˜ƒ ξ˜ξšƒξšˆξšƒξš”ξš›ξŸ‘ξ˜ƒ ξ˜‡ξŸ€ξ˜ƒ ξ˜–ξšŠξš‘ξšŒξšƒξš‡ξš‹ξŸ‘ξ˜ƒ ξ˜„ξŸ€ξ˜ƒξ˜•ξšƒξšŒξšƒξš„ξš‹ξšˆξšƒξš”ξš†ξŸ‘ξ˜ƒ ξ˜—ξŸ€ξ˜ƒ ξ˜‘ξš‰ξš‘ξŸ‘ξ˜ƒ ξ˜…ξ˜Œξ˜ξ˜ƒ ξšƒξšξš†ξ˜ƒ ξš”ξš‡ξšƒξšŽξ˜ƒξš‡ξš•ξš–ξšƒξš–ξš‡ξ˜ƒ ξš˜ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξŸ£ξ˜ƒ ξš…ξšŠξšƒξšŽξšŽξš‡ξšξš‰ξš‡ξš•ξŸ‘ξ˜ƒ ξš’ξš‘ξš–ξš‡ξšξš–ξš‹ξšƒξšŽξš•ξ˜ƒ ξšƒξšξš†ξ˜ƒ
ξšŽξš‡ξš•ξš•ξš‘ξšξš•ξ˜ƒξšˆξš‘ξš”ξ˜ƒξšˆξš—ξš–ξš—ξš”ξš‡ξ˜ƒξš†ξš‹ξš”ξš‡ξš…ξš–ξš‹ξš‘ξšξš•ξŸ‘ξ˜ƒξ˜ˆξšξš‰ξš‹ξšξš‡ξš‡ξš”ξš‹ξšξš‰ξŸ‘ξ˜ƒξ˜†ξš‘ξšξš•ξš–ξš”ξš—ξš…ξš–ξš‹ξš‘ξšξ˜ƒξšƒξšξš†ξ˜ƒξ˜„ξš”ξš…ξšŠξš‹ξš–ξš‡ξš…ξš–ξš—ξš”ξšƒξšŽξ˜ƒξ˜ξšƒξšξšƒξš‰ξš‡ξšξš‡ξšξš–ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯ΆξŸ‘ξ˜ƒξ₯΅ξ₯³ξŸ‘ξ˜ƒξ₯³ξ₯Έξ₯Άξ₯΄ξŸ¦
ξ₯³ξ₯Έξ₯Ήξ₯ΉξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯³ξ₯²ξ₯Ίξ €ξ˜ˆξ˜†ξ˜„ξ˜ξŸ¦ξ₯²ξ₯ΉξŸ¦ξ₯΄ξ₯²ξ₯΄ξ₯΄ξŸ¦ξ₯²ξ₯Έξ₯Άξ₯΄ξŸ€
ξ₯·ξ₯Ίξ 
ξ˜ŽξŸ€ξ˜ƒξ˜ξŸ€ξ˜ƒξ˜ξšƒξšξš…ξšƒξš•ξš–ξš‡ξš”ξŸ‘ξ˜ƒξ˜„ξ˜ƒξšξš‡ξš™ξ˜ƒξšƒξš’ξš’ξš”ξš‘ξšƒξš…ξšŠξ˜ƒξš–ξš‘ξ˜ƒξš…ξš‘ξšξš•ξš—ξšξš‡ξš”ξ˜ƒξš–ξšŠξš‡ξš‘ξš”ξš›ξŸ‘ξ˜ƒξ˜ξš‘ξš—ξš”ξšξšƒξšŽξ˜ƒξš‘ξšˆξ˜ƒξ˜“ξš‘ξšŽξš‹ξš–ξš‹ξš…ξšƒξšŽξ˜ƒξ˜ˆξš…ξš‘ξšξš‘ξšξš›ξŸ‘ξ˜ƒξ₯³ξ₯»ξ₯Έξ₯ΈξŸ‘ξ˜ƒξ₯Ήξ₯ΆξŸ‘ξ˜ƒξ₯³ξ₯΅ξ₯΄ξŸ¦ξ₯³ξ₯·ξ₯ΉξŸ€
ξ₯·ξ₯»ξ 
ξ˜–ξŸ€ξ˜ƒξ˜–ξš‹ξš”ξšξšƒξšξš•ξŸ‘ξ˜ƒξ˜‡ξŸ€ξ˜ƒξ˜ξšƒξš…ξš’ξšŠξš‡ξš”ξš•ξš‘ξšξŸ‘ξ˜ƒξ˜ˆξŸ€ξ˜ƒξ˜ξš‹ξš‡ξš–ξšœξŸ‘ξ˜ƒξ˜—ξšŠξš‡ξ˜ƒξš…ξš‘ξšξš’ξš‘ξš•ξš‹ξš–ξš‹ξš‘ξšξ˜ƒξš‘ξšˆξ˜ƒξšŠξš‡ξš†ξš‘ξšξš‹ξš…ξ˜ƒξš’ξš”ξš‹ξš…ξš‹ξšξš‰ξ˜ƒξšξš‘ξš†ξš‡ξšŽξš•ξŸ‘ξ˜ƒξ˜ξš‘ξš—ξš”ξšξšƒξšŽξ˜ƒξš‘ξšˆξ˜ƒξ˜•ξš‡ξšƒξšŽξ˜ƒξ˜ˆξš•ξš–ξšƒξš–ξš‡ξ˜ƒ
ξ˜ξš‹ξš–ξš‡ξš”ξšƒξš–ξš—ξš”ξš‡ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯²ξ₯·ξŸ‘ξ˜ƒξ₯³ξ₯΅ξŸ‘ξ˜ƒξ₯΅ξŸ¦ξ₯Άξ₯΅ξŸ€
ξ₯Έξ₯²ξ 
ξ˜„ξŸ€ξ˜ƒξ˜†ξšƒξšξŸ‘ξ˜ƒξ˜—ξšŠξš‡ξ˜ƒξšξš‡ξšƒξš•ξš—ξš”ξš‡ξšξš‡ξšξš–ξ˜ƒξš‘ξšˆξ˜ƒξšξš‡ξš‹ξš‰ξšŠξš„ξš‘ξš”ξšŠξš‘ξš‘ξš†ξ˜ƒξš†ξš›ξšξšƒξšξš‹ξš…ξš•ξ˜ƒξš‹ξšξ˜ƒξš—ξš”ξš„ξšƒξšξ˜ƒξšŠξš‘ξš—ξš•ξš‡ξ˜ƒξš’ξš”ξš‹ξš…ξš‡ξš•ξŸ‘ξ˜ƒξ˜ˆξš…ξš‘ξšξš‘ξšξš‹ξš…ξ˜ƒξ˜Šξš‡ξš‘ξš‰ξš”ξšƒξš’ξšŠξš›ξŸ‘ξ˜ƒξ₯³ξ₯»ξ₯»ξ₯²ξŸ‘ξ˜ƒ
ξ₯Έξ₯ΈξŸ‘ξ˜ƒξ₯΄ξ₯·ξ₯ΆξŸ¦ξ₯΄ξ₯Ήξ₯΄ξŸ€
ξ₯Έξ₯³ξ 
ξ˜•ξŸ€ξ˜ƒξ˜„ξŸ€ξ˜ƒξ˜‡ξš—ξš„ξš‹ξšξŸ‘ξ˜ƒξ˜“ξš”ξš‡ξš†ξš‹ξš…ξš–ξš‹ξšξš‰ξ˜ƒξšŠξš‘ξš—ξš•ξš‡ξ˜ƒξš’ξš”ξš‹ξš…ξš‡ξš•ξ˜ƒξš—ξš•ξš‹ξšξš‰ξ˜ƒξšξš—ξšŽξš–ξš‹ξš’ξšŽξš‡ξ˜ƒ ξšŽξš‹ξš•ξš–ξš‹ξšξš‰ξš•ξ˜ƒ ξš†ξšƒξš–ξšƒξŸ‘ξ˜ƒ ξ˜ξš‘ξš—ξš”ξšξšƒξšŽξ˜ƒξš‘ξšˆξ˜ƒξ˜•ξš‡ξšƒξšŽξ˜ƒξ˜ˆξš•ξš–ξšƒξš–ξš‡ξ˜ƒξ˜‰ξš‹ξšξšƒξšξš…ξš‡ξ˜ƒξšƒξšξš†ξ˜ƒ
ξ˜ˆξš…ξš‘ξšξš‘ξšξš‹ξš…ξš•ξŸ‘ξ˜ƒξ₯³ξ₯»ξ₯»ξ₯ΊξŸ‘ξ˜ƒξ₯³ξ₯ΉξŸ‘ξ˜ƒξ₯΅ξ₯·ξŸ¦ξ₯·ξ₯»ξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯²ξ₯΄ξ₯΅ξ €ξ˜„ξŸ£ξ₯³ξ₯²ξ₯²ξ₯Ήξ₯Ήξ₯·ξ₯³ξ₯³ξ₯³ξ₯΄ξ₯Έξ₯Έξ₯»ξŸ€
ξ₯Έξ₯΄ξ 
ξ˜ξŸ€ξ˜ƒξ˜ξŸ€ξ˜ƒξ˜†ξš”ξš‘ξš’ξš’ξš‡ξš”ξŸ‘ξ˜ƒξ˜ξŸ€ξ˜ƒξ˜…ξŸ€ξ˜ƒξ˜‡ξš‡ξš…ξšξŸ‘ξ˜ƒξ˜ŽξŸ€ξ˜ƒξ˜ˆξŸ€ξ˜ƒξ˜ξš…ξ˜†ξš‘ξšξšξš‡ξšŽξšŽξŸ‘ξ˜ƒξ˜’ξšξ˜ƒξš–ξšŠξš‡ξ˜ƒξš…ξšŠξš‘ξš‹ξš…ξš‡ξ˜ƒξš‘ξšˆξ˜ƒξšˆξš—ξšξš…ξš–ξš‹ξš‘ξšξšƒξšŽξ˜ƒξšˆξš‘ξš”ξšξ˜ƒξšˆξš‘ξš”ξ˜ƒξšŠξš‡ξš†ξš‘ξšξš‹ξš…ξ˜ƒξš’ξš”ξš‹ξš…ξš‡ξ˜ƒξšˆξš—ξšξš…ξš–ξš‹ξš‘ξšξš•ξŸ‘ξ˜ƒ
ξ˜•ξš‡ξš˜ξš‹ξš‡ξš™ξ˜ƒξš‘ξšˆξ˜ƒξ˜ˆξš…ξš‘ξšξš‘ξšξš‹ξš…ξš•ξ˜ƒξšƒξšξš†ξ˜ƒξ˜–ξš–ξšƒξš–ξš‹ξš•ξš–ξš‹ξš…ξš•ξŸ‘ξ˜ƒξ₯³ξ₯»ξ₯Ίξ₯ΊξŸ‘ξ˜ƒξ₯Ήξ₯²ξŸ‘ξ˜ƒξ₯Έξ₯Έξ₯ΊξŸ¦ξ₯Έξ₯Ήξ₯·ξŸ€
ξ₯Έξ₯΅ξ 
ξ˜ˆξŸ€ξ˜ƒξ˜†ξšƒξš•ξš•ξš‡ξšŽξŸ‘ξ˜ƒξ˜•ξŸ€ξ˜ƒξ˜ξš‡ξšξš†ξš‡ξšŽξš•ξš‘ξšŠξšξŸ‘ξ˜ƒξ˜—ξšŠξš‡ξ˜ƒξš…ξšŠξš‘ξš‹ξš…ξš‡ξ˜ƒξš‘ξšˆξ˜ƒξšˆξš—ξšξš…ξš–ξš‹ξš‘ξšξšƒξšŽξ˜ƒξšˆξš‘ξš”ξšξš•ξ˜ƒξšˆξš‘ξš”ξ˜ƒξšŠξš‡ξš†ξš‘ξšξš‹ξš…ξ˜ƒξš’ξš”ξš‹ξš…ξš‡ξ˜ƒξš‡ξš“ξš—ξšƒξš–ξš‹ξš‘ξšξš•ξŸ‘ξ˜ƒξ˜ξš‘ξš—ξš”ξšξšƒξšŽξ˜ƒξš‘ξšˆξ˜ƒξ˜˜ξš”ξš„ξšƒξšξ˜ƒ
ξ˜ˆξš…ξš‘ξšξš‘ξšξš‹ξš…ξš•ξŸ‘ξ˜ƒξ₯³ξ₯»ξ₯Ίξ₯·ξŸ‘ξ˜ƒξ₯³ξ₯ΊξŸ‘ξ˜ƒξ₯³ξ₯΅ξ₯·ξŸ¦ξ₯³ξ₯Άξ₯΄ξŸ€
ξ₯Έξ₯Άξ 
ξ˜ξš‹ξšŽξšŽξš‘ξš™ξ˜ƒξ˜•ξš‡ξš•ξš‡ξšƒξš”ξš…ξšŠξŸ‘ξ˜ƒξ˜‹ξš‘ξš—ξš•ξš‹ξšξš‰ξ˜ƒξšξšƒξš”ξšξš‡ξš–ξ˜ƒξš–ξš”ξš‡ξšξš†ξš•ξ˜ƒξšƒξšξš†ξ˜ƒξšƒξšξšƒξšŽξš›ξš•ξš‹ξš•ξŸ‘ξ˜ƒξ˜ξš‹ξšŽξšŽξš‘ξš™ξ˜ƒξ˜ˆξš…ξš‘ξšξš‘ξšξš‹ξš…ξ˜ƒξ˜•ξš‡ξš•ξš‡ξšƒξš”ξš…ξšŠξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯ΆξŸ€
ξ₯Έξ₯·ξ 
ξ˜†ξš‘ξš”ξš‡ξ˜ξš‘ξš‰ξš‹ξš…ξŸ‘ξ˜ƒξ˜‹ξš‘ξšξš‡ξ˜ƒξš’ξš”ξš‹ξš…ξš‡ξ˜ƒξš‹ξšξš†ξš‡ξššξ˜ƒξšƒξšξšƒξšŽξš›ξš•ξš‹ξš•ξŸ‘ξ˜ƒξ˜†ξš‘ξš”ξš‡ξ˜ξš‘ξš‰ξš‹ξš…ξ˜ƒξ˜ξšƒξš”ξšξš‡ξš–ξ˜ƒξ˜Œξšξš•ξš‹ξš‰ξšŠξš–ξš•ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯ΆξŸ€
ξ₯Έξ₯Έξ 
ξ˜‰ξš”ξš‡ξš†ξš†ξš‹ξš‡ξ˜ƒξ˜ξšƒξš…ξŸ‘ξ˜ƒξ˜„ξš—ξš–ξš‘ξšξšƒξš–ξš‡ξš†ξ˜ƒξ˜™ξšƒξšŽξš—ξšƒξš–ξš‹ξš‘ξšξ˜ƒ ξ˜ξš‘ξš†ξš‡ξšŽξ˜ƒξ˜–ξš–ξšƒξšξš†ξšƒξš”ξš†ξš•ξŸ‘ξ˜ƒξ˜‰ξš”ξš‡ξš†ξš†ξš‹ξš‡ξ˜ƒξ˜ξšƒξš…ξ˜ƒξ˜˜ξšξš‹ξšˆξš‘ξš”ξšξ˜ƒξ˜ξš‘ξš”ξš–ξš‰ξšƒξš‰ξš‡ξ˜ƒξ˜‡ξšƒξš–ξšƒξ˜ƒξ˜“ξš”ξš‘ξš‰ξš”ξšƒξšξŸ‘ξ˜ƒ
ξ₯΄ξ₯²ξ₯΄ξ₯΅ξŸ€
ξ₯Έξ₯Ήξ 
ξ˜‰ξšƒξšξšξš‹ξš‡ξ˜ƒξ˜ξšƒξš‡ξŸ‘ξ˜ƒξ˜†ξš‘ξšŽξšŽξšƒξš–ξš‡ξš”ξšƒξšŽξ˜ƒξ˜˜ξšξš†ξš‡ξš”ξš™ξš”ξš‹ξš–ξš‡ξš”ξŸ£ξ˜ƒξ˜„ξš’ξš’ξš”ξšƒξš‹ξš•ξšƒξšŽξ˜ƒξ˜•ξš‹ξš•ξšξ˜ƒξ˜„ξš•ξš•ξš‡ξš•ξš•ξšξš‡ξšξš–ξŸ‘ξ˜ƒξ˜‰ξšƒξšξšξš‹ξš‡ξ˜ƒξ˜ξšƒξš‡ξ˜ƒξ˜–ξš‡ξšŽξšŽξš‹ξšξš‰ξ˜ƒξ˜Šξš—ξš‹ξš†ξš‡ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯΅ξŸ€
ξ₯Έξ₯Ίξ 
ξ˜‰ξŸ€ξ˜ƒξ˜‡ξš‹ξ˜ƒξ˜ξš‹ξš†ξš†ξš‘ξŸ‘ξ˜ƒξ˜‡ξŸ€ξ˜ƒξ˜„ξšξš‡ξšŽξšŽξš‹ξŸ‘ξ˜ƒξ˜“ξŸ€ξ˜ƒξ˜ξš‘ξš”ξšƒξšξš‘ξŸ‘ξ˜ƒξ˜‰ξŸ€ξ˜ƒξ˜—ξšƒξšŒξšƒξšξš‹ξŸ‘ξ˜ƒξ˜—ξšŠξš‡ξ˜ƒξ˜Œξšξš’ξšƒξš…ξš–ξš•ξ˜ƒξš‘ξšˆξ˜ƒξ˜†ξ˜’ξ˜™ξ˜Œξ˜‡ξŸ¦ξ₯³ξ₯»ξ˜ƒξš‘ξšξ˜ƒξš”ξš‡ξšƒξšŽξ˜ƒξš‡ξš•ξš–ξšƒξš–ξš‡ξ˜ƒξšξšƒξš”ξšξš‡ξš–ξ˜ƒξš†ξš›ξšξšƒξšξš‹ξš…ξš•ξŸ£ξ˜ƒξšƒξ˜ƒ
ξš•ξš›ξš•ξš–ξš‡ξšξšƒξš–ξš‹ξš…ξ˜ƒ ξšŽξš‹ξš–ξš‡ξš”ξšƒξš–ξš—ξš”ξš‡ξ˜ƒ ξš”ξš‡ξš˜ξš‹ξš‡ξš™ξ˜ƒ ξš‘ξšˆξ˜ƒ ξš‡ξšξš‡ξš”ξš‰ξš‹ξšξš‰ξ˜ƒ ξš–ξš”ξš‡ξšξš†ξš•ξŸ‘ξ˜ƒ ξ˜…ξš—ξš‹ξšŽξš†ξš‹ξšξš‰ξš•ξŸ‘ξ˜ƒ ξ₯΄ξ₯²ξ₯΄ξ₯΅ξŸ‘ξ˜ƒ ξ₯³ξ₯΅ξŸ‘ξ˜ƒ ξ₯΄ξ₯΅ξ₯΅ξ₯ΆξŸ‘ξ˜ƒ ξš†ξš‘ξš‹ξŸ£ξ˜ƒ
ξ₯³ξ₯²ξŸ€ξ₯΅ξ₯΅ξ₯»ξ₯²ξ €ξš„ξš—ξš‹ξšŽξš†ξš‹ξšξš‰ξš•ξ₯³ξ₯΅ξ₯²ξ₯»ξ₯΄ξ₯΅ξ₯΅ξ₯ΆξŸ€
ξ₯Έξ₯»ξ 
ξ˜•ξŸ€ξ˜ƒ ξ˜ξš‘ξšŽξšŽξš‘ξš›ξŸ‘ξ˜ƒ ξ˜†ξŸ€ξ˜ƒ ξ˜ξŸ€ξ˜ƒ ξ˜–ξšξš‹ξš–ξšŠξŸ‘ξ˜ƒ ξ˜„ξŸ€ξ˜ƒ ξ˜šξš‘ξšœξšξš‹ξšƒξšξŸ‘ξ˜ƒ ξ˜Œξšξš–ξš‡ξš”ξšξšƒξšŽξ˜ƒ ξšξš‹ξš‰ξš”ξšƒξš–ξš‹ξš‘ξšξ˜ƒ ξš‹ξšξ˜ƒ ξš–ξšŠξš‡ξ˜ƒ ξ˜˜ξšξš‹ξš–ξš‡ξš†ξ˜ƒ ξ˜–ξš–ξšƒξš–ξš‡ξš•ξŸ‘ξ˜ƒ ξ˜ξš‘ξš—ξš”ξšξšƒξšŽξ˜ƒ ξš‘ξšˆξ˜ƒ ξ˜ˆξš…ξš‘ξšξš‘ξšξš‹ξš…ξ˜ƒ
ξ˜“ξš‡ξš”ξš•ξš’ξš‡ξš…ξš–ξš‹ξš˜ξš‡ξš•ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯³ξ₯³ξŸ‘ξ˜ƒξ₯΄ξ₯·ξŸ‘ξ˜ƒξ₯³ξ₯Ήξ₯΅ξŸ¦ξ₯³ξ₯»ξ₯ΈξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯΄ξ₯·ξ₯Ήξ €ξšŒξš‡ξš’ξŸ€ξ₯΄ξ₯·ξŸ€ξ₯΅ξŸ€ξ₯³ξ₯Ήξ₯΅ξŸ€
ξ₯Ήξ₯²ξ 
ξ˜„ξŸ€ξ˜ƒ ξ˜–ξŸ€ξ˜ƒ ξ˜‰ξš‘ξš–ξšŠξš‡ξš”ξš‹ξšξš‰ξšŠξšƒξšξŸ‘ξ˜ƒ ξ˜†ξŸ€ξ˜ƒ ξ˜…ξš”ξš—ξšξš•ξš†ξš‘ξšξŸ‘ξ˜ƒ ξ˜ξŸ€ξ˜ƒ ξ˜†ξšŠξšƒξš”ξšŽξš–ξš‘ξšξŸ‘ξ˜ƒ ξ˜Šξš‡ξš‘ξš‰ξš”ξšƒξš’ξšŠξš‹ξš…ξšƒξšŽξšŽξš›ξ˜ƒ ξš™ξš‡ξš‹ξš‰ξšŠξš–ξš‡ξš†ξ˜ƒ ξš”ξš‡ξš‰ξš”ξš‡ξš•ξš•ξš‹ξš‘ξšξŸ£ξ˜ƒ ξš–ξšŠξš‡ξ˜ƒ ξšƒξšξšƒξšŽξš›ξš•ξš‹ξš•ξ˜ƒ ξš‘ξšˆξ˜ƒ
ξš•ξš’ξšƒξš–ξš‹ξšƒξšŽξšŽξš›ξ˜ƒξš˜ξšƒξš”ξš›ξš‹ξšξš‰ξ˜ƒξš”ξš‡ξšŽξšƒξš–ξš‹ξš‘ξšξš•ξšŠξš‹ξš’ξš•ξŸ‘ξ˜ƒξ˜šξš‹ξšŽξš‡ξš›ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯²ξ₯΅ξŸ€
ξ₯Ήξ₯³ξ 
ξ˜‡ξŸ€ξ˜ƒξ˜ξŸ€ξ˜ƒξ˜†ξŸ€ξ˜ƒξ˜–ξš‹ξšŠξš‘ξšξš„ξš‹ξšξš‰ξŸ‘ξ˜ƒξ˜„ξš’ξš’ξšŽξš‹ξš…ξšƒξš–ξš‹ξš‘ξšξ˜ƒξš‘ξšˆξ˜ƒξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξ˜ƒξš‡ξšξš‰ξš‹ξšξš‡ξš‡ξš”ξš‹ξšξš‰ξ˜ƒξš–ξš‡ξš…ξšŠξšξš‹ξš“ξš—ξš‡ξš•ξ˜ƒξšƒξšξš†ξ˜ƒξšξšƒξš…ξšŠξš‹ξšξš‡ξ˜ƒξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξ˜ƒξšƒξšŽξš‰ξš‘ξš”ξš‹ξš–ξšŠξšξš•ξ˜ƒξšˆξš‘ξš”ξ˜ƒ
ξš’ξš”ξš‘ξš’ξš‡ξš”ξš–ξš›ξ˜ƒ ξš’ξš”ξš‹ξš…ξš‡ξ˜ƒ ξš’ξš”ξš‡ξš†ξš‹ξš…ξš–ξš‹ξš‘ξšξŸ‘ξ˜ƒ ξ˜ξš—ξš”ξšξšƒξšŽξ˜ƒ ξ˜ŒξšŽξšξš‹ξšƒξšŠξ˜ƒ ξ˜—ξš‡ξšξšξš‘ξšŽξš‘ξš‰ξš‹ξ˜ƒ ξ˜–ξš‹ξš•ξš–ξš‡ξšξ˜ƒ ξ˜Œξšξšˆξš‘ξš”ξšξšƒξš•ξš‹ξŸ‘ξ˜ƒ ξ₯΄ξ₯²ξ₯΄ξ₯ΆξŸ‘ξ˜ƒ ξ₯·ξŸ‘ξ˜ƒ ξ₯Ήξ₯΄ξ˜ƒ ξ ‚ξ˜ƒ ξ₯Ήξ₯ΈξŸ‘ξ˜ƒ ξš†ξš‘ξš‹ξŸ£ξ˜ƒ
ξ₯³ξ₯²ξŸ€ξ₯Έξ₯΄ξ₯·ξ₯΄ξ₯Ήξ €ξšŒξš‹ξš–ξš•ξš‹ξŸ€ξ₯·ξŸ€ξ₯΄ξŸ€ξ₯΄ξ₯Άξ₯³ξŸ€
ξ₯Ήξ₯΄ξ 
ξ˜…ξŸ€ξ˜ƒξ˜“ξšƒξš”ξšξŸ‘ξ˜ƒξ˜ξŸ€ξ˜ƒξ˜ŽξŸ€ξ˜ƒξ˜…ξšƒξš‡ξŸ‘ξ˜ƒξ˜˜ξš•ξš‹ξšξš‰ξ˜ƒξšξšƒξš…ξšŠξš‹ξšξš‡ξ˜ƒξšŽξš‡ξšƒξš”ξšξš‹ξšξš‰ξ˜ƒξšƒξšŽξš‰ξš‘ξš”ξš‹ξš–ξšŠξšξš•ξ˜ƒξšˆξš‘ξš”ξ˜ƒξšŠξš‘ξš—ξš•ξš‹ξšξš‰ξ˜ƒξš’ξš”ξš‹ξš…ξš‡ξ˜ƒξš’ξš”ξš‡ξš†ξš‹ξš…ξš–ξš‹ξš‘ξšξŸ£ξ˜ƒξ˜—ξšŠξš‡ξ˜ƒξš…ξšƒξš•ξš‡ξ˜ƒξš‘ξšˆξ˜ƒξ˜‰ξšƒξš‹ξš”ξšˆξšƒξššξ˜ƒ
ξ˜†ξš‘ξš—ξšξš–ξš›ξŸ‘ξ˜ƒ ξ˜™ξš‹ξš”ξš‰ξš‹ξšξš‹ξšƒξ˜ƒ ξšŠξš‘ξš—ξš•ξš‹ξšξš‰ξ˜ƒ ξš†ξšƒξš–ξšƒξŸ‘ξ˜ƒ ξ˜ˆξššξš’ξš‡ξš”ξš–ξ˜ƒ ξ˜–ξš›ξš•ξš–ξš‡ξšξš•ξ˜ƒ ξš™ξš‹ξš–ξšŠξ˜ƒ ξ˜„ξš’ξš’ξšŽξš‹ξš…ξšƒξš–ξš‹ξš‘ξšξš•ξŸ‘ξ˜ƒ ξ₯΄ξ₯²ξ₯³ξ₯·ξŸ‘ξ˜ƒ ξ₯Άξ₯΄ξŸ‘ξ˜ƒ ξ₯΄ξ₯»ξ₯΄ξ₯ΊξŸ¦ξ₯΄ξ₯»ξ₯΅ξ₯ΆξŸ‘ξ˜ƒ ξš†ξš‘ξš‹ξŸ£ξ˜ƒ
ξ₯³ξ₯²ξŸ€ξ₯³ξ₯²ξ₯³ξ₯Έξ €ξšŒξŸ€ξš‡ξš•ξš™ξšƒξŸ€ξ₯΄ξ₯²ξ₯³ξ₯ΆξŸ€ξ₯³ξ₯³ξŸ€ξ₯²ξ₯Άξ₯²ξŸ€
ξ₯Ήξ₯΅ξ 
ξ˜ξŸ€ξ˜ƒξ˜ξŸ€ξ˜ƒξ˜Žξšƒξšξš–ξš‡ξš”ξŸ‘ξ˜ƒξ˜ŽξŸ€ξ˜ƒξ˜™ξš‡ξš‡ξš”ξšƒξšξšƒξš…ξšŠξšƒξšξš‡ξšξš‹ξŸ‘ξ˜ƒξ˜‡ξš‡ξš‡ξš’ξ˜ƒξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξ˜ƒξš•ξš›ξšξš–ξšŠξš‡ξš•ξš‹ξš•ξŸ£ξ˜ƒξ˜—ξš‘ξš™ξšƒξš”ξš†ξš•ξ˜ƒξšƒξš—ξš–ξš‘ξšξšƒξš–ξš‹ξšξš‰ξ˜ƒξš†ξšƒξš–ξšƒξ˜ƒξš•ξš…ξš‹ξš‡ξšξš…ξš‡ξ˜ƒξš‡ξšξš†ξš‡ξšƒξš˜ξš‘ξš”ξš•ξŸ‘ξ˜ƒ
ξ₯΄ξ₯²ξ₯³ξ₯·ξ˜ƒξ˜Œξ˜ˆξ˜ˆξ˜ˆξ˜ƒξ˜Œξšξš–ξš‡ξš”ξšξšƒξš–ξš‹ξš‘ξšξšƒξšŽξ˜ƒξ˜†ξš‘ξšξšˆξš‡ξš”ξš‡ξšξš…ξš‡ξ˜ƒξš‘ξšξ˜ƒξ˜‡ξšƒξš–ξšƒξ˜ƒξ˜–ξš…ξš‹ξš‡ξšξš…ξš‡ξ˜ƒξšƒξšξš†ξ˜ƒξ˜„ξš†ξš˜ξšƒξšξš…ξš‡ξš†ξ˜ƒξ˜„ξšξšƒξšŽξš›ξš–ξš‹ξš…ξš•ξ˜ƒξ ‹ξ˜‡ξ˜–ξ˜„ξ˜„ξ ŒξŸ‘ξ˜ƒξ˜“ξšƒξš”ξš‹ξš•ξŸ‘ξ˜ƒξ˜‰ξš”ξšƒξšξš…ξš‡ξŸ‘ξ˜ƒ
ξ₯΄ξ₯²ξ₯³ξ₯·ξŸ‘ξ˜ƒξ₯³ξŸ¦ξ₯³ξ₯²ξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯³ξ₯²ξ₯»ξ €ξ˜‡ξ˜–ξ˜„ξ˜„ξŸ€ξ₯΄ξ₯²ξ₯³ξ₯·ξŸ€ξ₯Ήξ₯΅ξ₯Άξ₯Άξ₯Ίξ₯·ξ₯ΊξŸ€
ξ₯Ήξ₯Άξ 
ξ˜…ξŸ€ξ˜ƒξ˜ξš‹ξš—ξŸ‘ξ˜ƒξ˜†ξŸ€ξ˜ƒξ˜ξšŠξš—ξŸ‘ξ˜ƒξ˜ŠξŸ€ξ˜ƒξ˜ξš‹ξŸ‘ξ˜ƒξ˜šξŸ€ξ˜ƒξ˜ξšŠξšƒξšξš‰ξŸ‘ξ˜ƒξ˜ξŸ€ξ˜ƒξ˜ξšƒξš‹ξŸ‘ξ˜ƒξ˜•ξŸ€ξ˜ƒξ˜—ξšƒξšξš‰ξŸ‘ξ˜ƒξ˜›ξŸ€ξ˜ƒξ˜‹ξš‡ξŸ‘ξ˜ƒξ˜ξŸ€ξ˜ƒξ˜ξš‹ξŸ‘ξ˜ƒξ˜œξŸ€ξ˜ƒξ˜œξš—ξŸ‘ξ˜ƒξ˜„ξš—ξš–ξš‘ξ˜‰ξ˜Œξ˜–ξŸ£ξ˜ƒξ˜„ξš—ξš–ξš‘ξšξšƒξš–ξš‹ξš…ξ˜ƒξšˆξš‡ξšƒξš–ξš—ξš”ξš‡ξ˜ƒξš‹ξšξš–ξš‡ξš”ξšƒξš…ξš–ξš‹ξš‘ξšξ˜ƒ
ξš•ξš‡ξšŽξš‡ξš…ξš–ξš‹ξš‘ξšξ˜ƒξš‹ξšξ˜ƒξšˆξšƒξš…ξš–ξš‘ξš”ξš‹ξšœξšƒξš–ξš‹ξš‘ξšξ˜ƒξšξš‘ξš†ξš‡ξšŽξš•ξ˜ƒξšˆξš‘ξš”ξ˜ƒξš…ξšŽξš‹ξš…ξšξŸ¦ξš–ξšŠξš”ξš‘ξš—ξš‰ξšŠξ˜ƒξš”ξšƒξš–ξš‡ξ˜ƒξš’ξš”ξš‡ξš†ξš‹ξš…ξš–ξš‹ξš‘ξšξŸ‘ξ˜ƒξ˜“ξš”ξš‘ξš…ξš‡ξš‡ξš†ξš‹ξšξš‰ξš•ξ˜ƒξš‘ξšˆξ˜ƒξš–ξšŠξš‡ξ˜ƒξ₯΄ξ₯Έξš–ξšŠξ˜ƒξ˜„ξ˜†ξ˜ξ˜ƒξ˜–ξ˜Œξ˜Šξ˜Žξ˜‡ξ˜‡ξ˜ƒ
ξ˜Œξšξš–ξš‡ξš”ξšξšƒξš–ξš‹ξš‘ξšξšƒξšŽξ˜ƒ ξ˜†ξš‘ξšξšˆξš‡ξš”ξš‡ξšξš…ξš‡ξ˜ƒ ξš‘ξšξ˜ƒ ξ˜Žξšξš‘ξš™ξšŽξš‡ξš†ξš‰ξš‡ξ˜ƒ ξ˜‡ξš‹ξš•ξš…ξš‘ξš˜ξš‡ξš”ξš›ξ˜ƒ ξž¬ξ˜ƒ ξ˜‡ξšƒξš–ξšƒξ˜ƒ ξ˜ξš‹ξšξš‹ξšξš‰ξŸ‘ξ˜ƒ ξ₯΄ξ₯²ξ₯΄ξ₯²ξŸ‘ξ˜ƒ ξ₯΄ξ₯Έξ₯΅ξ₯ΈξŸ¦ξ₯΄ξ₯Έξ₯Άξ₯·ξŸ‘ξ˜ƒ ξš†ξš‘ξš‹ξŸ£ξ˜ƒ
ξ₯³ξ₯²ξŸ€ξ₯³ξ₯³ξ₯Άξ₯·ξ €ξ₯΅ξ₯΅ξ₯»ξ₯Άξ₯Άξ₯Ίξ₯ΈξŸ€ξ₯΅ξ₯Άξ₯²ξ₯΅ξ₯΅ξ₯³ξ₯ΆξŸ€
ξ₯Ήξ₯·ξ 
ξ˜‡ξŸ€ξ˜ƒ ξ˜‹ξŸ€ξ˜ƒ ξ˜šξš‘ξšŽξš’ξš‡ξš”ξš–ξŸ‘ξ˜ƒ ξ˜–ξš–ξšƒξš…ξšξš‡ξš†ξ˜ƒ ξš‰ξš‡ξšξš‡ξš”ξšƒξšŽξš‹ξšœξšƒξš–ξš‹ξš‘ξšξŸ‘ξ˜ƒ ξ˜‘ξš‡ξš—ξš”ξšƒξšŽξ˜ƒ ξ˜‘ξš‡ξš–ξš™ξš‘ξš”ξšξš•ξŸ‘ξ˜ƒ ξ₯³ξ₯»ξ₯»ξ₯΄ξŸ‘ξ˜ƒ ξ₯·ξŸ‘ξ˜ƒ ξ₯΄ξ₯Άξ₯³ξŸ¦ξ₯΄ξ₯·ξ₯»ξŸ‘ξ˜ƒ ξš†ξš‘ξš‹ξŸ£ξ˜ƒ ξ₯³ξ₯²ξŸ€ξ₯³ξ₯²ξ₯³ξ₯Έξ €ξ˜–ξ₯²ξ₯Ίξ₯»ξ₯΅ξŸ¦
ξ₯Έξ₯²ξ₯Ίξ₯²ξ ‹ξ₯²ξ₯·ξ Œξ₯Ίξ₯²ξ₯²ξ₯΄ξ₯΅ξŸ¦ξ₯³ξŸ€
ξ₯Ήξ₯Έξ 
ξ˜ξŸ€ξ˜ƒξ˜„ξšξš•ξš‡ξšŽξš‹ξšξŸ‘ξ˜ƒξ˜–ξš’ξšƒξš–ξš‹ξšƒξšŽξ˜ƒξš‡ξš…ξš‘ξšξš‘ξšξš‡ξš–ξš”ξš‹ξš…ξš•ξŸ£ξ˜ƒξšξš‡ξš–ξšŠξš‘ξš†ξš•ξ˜ƒξšƒξšξš†ξ˜ƒξšξš‘ξš†ξš‡ξšŽξš•ξŸ‘ξ˜ƒξ˜ŽξšŽξš—ξš™ξš‡ξš”ξ˜ƒξ˜„ξš…ξšƒξš†ξš‡ξšξš‹ξš…ξ˜ƒξ˜“ξš—ξš„ξšŽξš‹ξš•ξšŠξš‡ξš”ξš•ξŸ‘ξ˜ƒξ₯³ξ₯»ξ₯Ίξ₯ΊξŸ€
ξ₯Ήξ₯Ήξ 
ξ˜ξŸ€ξ˜ƒξ˜ξš‡ξ˜–ξšƒξš‰ξš‡ξŸ‘ξ˜ƒξ˜•ξŸ€ξ˜ƒξ˜ŽξŸ€ξ˜ƒξ˜“ξšƒξš…ξš‡ξŸ‘ξ˜ƒξ˜Œξšξš–ξš”ξš‘ξš†ξš—ξš…ξš–ξš‹ξš‘ξšξ˜ƒξš–ξš‘ξ˜ƒξš•ξš’ξšƒξš–ξš‹ξšƒξšŽξ˜ƒξš‡ξš…ξš‘ξšξš‘ξšξš‡ξš–ξš”ξš‹ξš…ξš•ξŸ‘ξ˜ƒξ˜†ξ˜•ξ˜†ξ˜ƒξ˜“ξš”ξš‡ξš•ξš•ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯²ξ₯»ξŸ€
ξ₯Ήξ₯Ίξ 
ξ˜‹ξŸ€ξ˜ƒξ˜„ξšŽξš“ξšƒξš”ξšƒξšŽξšŽξš‡ξšŠξŸ‘ξ˜ƒξ˜„ξŸ€ξ˜ƒξ˜†ξšƒξšξš‡ξš’ξšƒξŸ‘ξ˜ƒξ˜ŠξŸ€ξ˜ƒξ˜ƒξ˜–ξŸ€ξ˜ƒξ˜˜ξš†ξš†ξš‹ξšξŸ‘ξ˜ƒξ˜‡ξš›ξšξšƒξšξš‹ξš…ξ˜ƒξš”ξš‡ξšŽξšƒξš–ξš‹ξš‘ξšξš•ξ˜ƒξš„ξš‡ξš–ξš™ξš‡ξš‡ξšξ˜ƒξšŠξš‘ξš—ξš•ξš‹ξšξš‰ξ˜ƒξ˜ξšƒξš”ξšξš‡ξš–ξš•ξŸ‘ξ˜ƒξš•ξš–ξš‘ξš…ξšξ˜ƒξ˜ξšƒξš”ξšξš‡ξš–ξš•ξŸ‘ξ˜ƒξšƒξšξš†ξ˜ƒ
ξš—ξšξš…ξš‡ξš”ξš–ξšƒξš‹ξšξš–ξš›ξ˜ƒξš‹ξšξ˜ƒξš‰ξšŽξš‘ξš„ξšƒξšŽξ˜ƒξ˜†ξš‹ξš–ξš‹ξš‡ξš•ξŸ£ξ˜ƒξ˜„ξ˜ƒξ˜—ξš‹ξšξš‡ξŸ¦ξ˜‰ξš”ξš‡ξš“ξš—ξš‡ξšξš…ξš›ξ˜ƒξšƒξš’ξš’ξš”ξš‘ξšƒξš…ξšŠξŸ‘ξ˜ƒξ˜—ξšŠξš‡ξ˜ƒξ˜‘ξš‘ξš”ξš–ξšŠξ˜ƒξ˜„ξšξš‡ξš”ξš‹ξš…ξšƒξšξ˜ƒξ˜ξš‘ξš—ξš”ξšξšƒξšŽξ˜ƒξš‘ξšˆξ˜ƒξ˜ˆξš…ξš‘ξšξš‘ξšξš‹ξš…ξš•ξ˜ƒξšƒξšξš†ξ˜ƒ
ξ˜‰ξš‹ξšξšƒξšξš…ξš‡ξŸ‘ξ˜ƒξ₯΄ξ₯²ξ₯΄ξ₯΅ξŸ‘ξ˜ƒξ₯Έξ₯ΊξŸ‘ξ˜ƒξ₯³ξ₯²ξ₯³ξ₯»ξ₯·ξ₯²ξŸ‘ξ˜ƒξš†ξš‘ξš‹ξŸ£ξ˜ƒξ₯³ξ₯²ξŸ€ξ₯³ξ₯²ξ₯³ξ₯Έξ €ξšŒξŸ€ξšξšƒξšŒξš‡ξšˆξŸ€ξ₯΄ξ₯²ξ₯΄ξ₯΅ξŸ€ξ₯³ξ₯²ξ₯³ξ₯»ξ₯·ξ₯²ξŸ€
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