Reinforcement learning portfolio python. Since its release, Gym's API has become the field standard for doing this. To associate your repository with the portfolio-management topic, visit your repo's landing page and select "manage topics. Note that this library is several versions ahead of the article. To solve the above limitations and provide a better solution for the portfolio management to the inventors, we then Mar 30, 2023 · Reinforcement learning, a subfield of machine learning, is particularly well-suited for optimizing trading strategies due to its ability to learn from experience and adapt to changing market Sep 12, 2019 · Reinforcement Learning for Portfolio Management. 3 0. Table of contents. This is a framework based on deep reinforcement learning for stock market trading. Q-Learning; Policy Gradient method (on-policy) Actor Critic method; PPO (Proximal Policy Optimization) (on-policy) DDPG (Deep Deterministic Policy Gradient) (off-policy) SAC (Soft Actor-Critic) (off-policy) All these examples are written in Python from scratch without any RL (reinforcement learning) libraries - such as, RLlib, Stable Baselines Add this topic to your repo. To address these issues, we present an open-source Python package (gym-flp) that utilises the OpenAI Gym toolkit Sep 25, 2023 · Deep Reinforcement Learning (DRL) is the crucial fusion of two powerful artificial intelligence fields: deep neural networks and reinforcement learning. This repository represents work in progress for the Worldquant University Capstone Project titled: Asset Portfolio Management using Deep Reinforcement Learning (DRL). Its goal is to facilitate research of networks that perform weight allocation in one forward pass. By combining the benefits of data-driven neural networks and intelligent decision-making, it has sparked an evolutionary change that crosses traditional boundaries. Apply now. Portfolio management is the decision-making process of allocating an amount of fund into different financial investment products. With Python’s computational prowess and Aug 23, 2021 · Source “Continuous Control With Deep Reinforcement Learning” (Lillicrap et al, 2015) 2- Gestion de portfolio. 6 0. 4-Miscellaneous. In this thesis, we develop a comprehensive account of the expressive power, modelling efficiency, and performance advantages of so-called trading agents (i. So every day we just need to rebalance the portfolio weights of the stocks. Define basic functions for formatting the values, sigmoid function, reading the data file, etc. We then feed the input portfolio to our neural network to This is the implementation of our paper, A Deep Reinforcement Learning Framework for the Financial Portfolio Management Problem (arXiv:1706. The name “Q-learning” comes from the Q (s, a) function, that based DQN-Trading. Importing Libraries. Oct 31, 2023 · Python is a popular programming language for data science and machine learning, as it provides an extensive selection of libraries and tools for developing and deploying RL trading strategies. 1%. , Deep Soft Recurrent Q-Network (DSRQN) and Mixture of Score Machines (MSM)), based on both traditional system identification (model-based Author: Brendan Martin Founder of LearnDataSci. In this project, we explored three state-of-art reinforcement learning algorithms, including policy gradient (PG), deep deterministic policy gradient (DDPG) and proximal policy optimization Dec 13, 2021 · [1] C. 2020-05-10 00:25:56 Dec 9, 2021 · However the model would be useless if it wasn’t a close substitute of the prevailing strategies. Dec 20, 2018 · Reinforcement learning is a discipline that tries to develop and understand algorithms to model and train agents that can interact with its environment to maximize a specific goal. This ensemble strategy is based on the Sharpe ratio to automatically select the best agent for trading among SAC, DDPG, and TD3, so that the appropriate agent can be selected at different stages. INTRODUCTION Jan 12, 2022 · Approach 2: Reinforcement Learning Brief Overview. Traditional and generic portfolio strategies require to forecast the future stocks prices as the model inputs, which is not a trivial task in the real-world applications. " GitHub is where people build software. Emma Brunskill. In this project: Implement three state-of-art continous deep reinforcement learning algorithms, Deep Deterministic Policy Gradient (DDPG),Proximal Policy Optimization(PPO) and Policy Gradient (PG) in portfolio management. However, they are still underutilised in facility layout problems (FLPs). More than 100 million people use GitHub to discover, fork, and contribute to over 420 million projects. Chai, and S. 3. Evaluate the agent performance. At the heart of this integration is our robust framework that not only merges advanced DRL algorithms with modern computational techniques but also emphasizes stringent statistical analysis Jun 7, 2019 · In this article, we are going to demonstrate how to implement a basic Reinforcement Learning algorithm which is called the Q-Learning technique. Step 5: Update Q-table values using the equation. Reinforcement learning techniques have raised attention from financial industry, especially by employing reinforcement learning in portfolio managements. Nov 11, 2021 · The agent will be trained on past market behavior by means of Deep Reinforcement Learning. For this Proof-Of-Concept (POC) project we will make things as simple as possible. This book covers: Reinforcement learning Deep Q-learning Python implementations of these algorithms Add this topic to your repo. Reinforcement Learning is definitely one of the most active and stimulating areas of research in AI. Train the agent. The trading agent chooses the next set of weights with a convolutional neural network (CNN) policy. This library provides components for calculating portfolio asset weights in continuous trading process which can make leverage trading, that fills the theoretical gap in the calculation of portfolio weights when shorting. FinRL is the first open source framework for financial reinforcement learning. Usage of policy gradient reinforcement learning to solve portfolio optimization problems (Tactical Asset Allocation). Portfolio Theory, Batched/O ine Reinforcement Learning. 2 Deep Reinforcement Learning The Reinforcement Learning architecture target is to directly generate portfolio trading action end to end according to the market environment. Oct 10, 2022 · We devise a hierarchical decision-making architecture for portfolio optimization on multiple markets. On top of that, we will apply various Jan 12, 2023 · The CS234 Reinforcement Learning course from Stanford is a comprehensive study of reinforcement learning, taught by Prof. 19 0. For the low-level agents, we use a set of Hierarchical Risk Parity (HRP) and Hierarchical Equal Risk Contribution (HERC) models with different Mar 26, 2021 · Portfolio management involves position sizing and resource allocation. nlp/reinforcement learning/supervised & unsupervised learning it covers wider topics including robo-advisors/fraud detection/loan default/derivative pricing/yield curve construction. Mar 29, 2021 · accompanying materials for book Machine Learning and Data Science Blueprints for Finance on top of basic machine learning models i. In recent years, DRL algorithms have been widely applied by scholars for portfolio optimization in consecutive trading periods, since the DRL agent can dynamically adapt to market changes and does not rely on the specification of the joint Feb 15, 2024 · Portfolio Optimization with Modern Portfolio Theory (MPT) in Python offers a transformative journey in investment strategy refinement. In practice, at the end of one episode, the robot has memorized all its states and resulting rewards. The basic logic is as follows. In this paper, we will formulate the problem such that we can apply Reinforcement Learning for the task properly. Please follow the instructions below to run the code: Sep 28, 2019 · The idea of Q-learning applied to portfolio management is the following: we can describe the market with some state s_t and with doing some action on this market and going to the state s_{t+1} we Compared with solely using deep learning or reinforcement learning in portfolio management, deep reinforcement learning mainly has three strengths. 54 0. e. It identified Deep Reinforcement Learning (DRL) as a promising area of research. The paper is available . Google Scholar Cross Ref; Xiao-Yang Liu, Hongyang Yang, Jiechao Gao, and Christina Dan Wang. These projects will be explained with the techniques, datasets and codebase that can be applied. The portfolio will consist of the 30 investment products in the Dow-Jones (DJIA). Report 1 began this journey with a broad review of machine learning and its applications. It facilitates beginners to expose themselves to quantitative finance and to develop stock trading strategies using deep reinforcement learning. At the highest level a Deep Reinforcement Learning (DRL) agent selects among a number of discrete actions, representing low-level agents. FinRL: Deep reinforcement learning framework to automate trading in quantitative finance. The precise formula of the loss is: Nov 17, 2023 · Portfolio management (PM) is a fundamental financial trading task, which explores the optimal periodical reallocation of capitals into different stocks to pursue long-term profits. Dec 25, 2023 · pyqlearning is Python library to implement Reinforcement Learning and Deep Reinforcement Learning, especially for Q-Learning, Deep Q-Network, and Multi-agent Deep Q-Network which can be optimized by Annealing models such as Simulated Annealing, Adaptive Simulated Annealing, and Quantum Monte Carlo Method. 9%. H. Since most stock portfolios consist of any combination of high-volatility and low-volatility stocks, these two-stock portfo-lios would represent a reduced model of an actual portfolio. The general solution of portfolio management is to score the potential of assets, buy assets with upside potential and increase their weighting, and sell assets that are likely to fall or are Jul 16, 2023 · The idea of Q-learning applied to portfolio management is the following: we can describe the market with some state s_t and with doing some action on this market and going to the state s_ {t+1} we get a reward (changed value of our portfolio based on the weights we applied). 18 0. 2 0 0. To overcome the above limitations and provide a better solution for portfolio management, we developed a Portfolio Apr 15, 2023 · The experiment uses Python development tools on the keras platform, and runs on 64-bit operating system (Linux Ubuntu), with 128G of RAM and Nvidia GTX 2080ti. This project is the implementation code for the two papers: Learning financial asset-specific trading rules via deep reinforcement learning. Dec 9, 2021 · Uta Pigorsch, Sebastian Schäfer. At any given time (episode), an agent abserves it's current state (n-day window stock price representation), selects and performs an action (buy/sell/hold), observes a subsequent state, receives some reward signal (difference in portfolio position) and lastly adjusts it's 65 Portfolio Optimization Using Reinforcement Learning … 725 0. Edit social preview. 46 0. It also knows its current G table. 2–1 Principe. 2 BRK JPM BAC MS 65. 1 Model Definition 1) Action: The action space describes the allowed actions that the agent interacts with the environment. Create the agent who will make all decisions. an imitation learning objective into the reinforcement learning framework. Mr. In reality, common examples are stock selection and the Enhanced Index Fund (EIF). Kanwar, “Deep Reinforcement Learning-based Portfolio Management,” 2019. Feb 23, 2024 · As a model-free algorithm, deep reinforcement learning (DRL) agent learns and makes decisions by interacting with the environment in an unsupervised way. Contribute to filangelos/qtrader development by creating an account on GitHub. 35 0 0 0 0. Oct 14, 2020 · Portfolio management is a critical issue which should be skilled by position sizing and resource allocation. 26 0. Practice: Every chapter is accompanied by high quality implementation based on Python 3, Gym 0. Python 3. In this blog, we will get introduced to reinforcement learning with Python with examples and implementations in Python. A quick start: Stock_NeurIPS2018. Gym is an open source Python library for developing and comparing reinforcement learning algorithms by providing a standard API to communicate between learning algorithms and environments, as well as a standard set of environments compliant with that API. Reinforcement Learning for Portfolio Management. 2. At the same time, RL research relies on standardised benchmarks such as the Arcade Learning Environment. 14 0. In this article, Toptal Machine Learning Expert Adam Stelmaszczyk walks us through implementing deep Q-learning, a fundamental algorithm in the AI/ML world, with modern Feb 27, 2024 · This research paper delves into the application of Deep Reinforcement Learning (DRL) in asset-class agnostic portfolio optimization, integrating industry-grade methodologies with quantitative finance. Key words :Data driven, Artificial intelligence, Deep reinforcement learning, Portfolio management , Investment decision optimization . Brief exposure to object-oriented programming in Python, machine learning, or deep learning will also be a plus point. ca/talks/Objective-Driven-Portfolio Jul 16, 2023 · Machine Learning Capabilities: With the rise of machine learning in finance, Python’s popular machine learning libraries like Scikit-learn and TensorFlow enable investors to apply advanced Dec 5, 2016 · 5 Dec 2016 · Zhengyao Jiang , Jinjun Liang ·. In this demonstration, we attempt to teach a bot to reach its destination using the Q-Learning technique. The main focus of this research paper is to study Deep Reinforcement Learning and replicate trading strategies based on Convolutional Neural Network. - GitHub - SvenBecker/TAA-PG: Usage of policy gradient reinforcement learning to solve portfolio optimization problems (Tactical Asset Allocation). Betancourt and W. This paper will focus on use of existing Reinforcement Learning (RL) algorithms (Q-Learning & Policy Optimization) and extend the RL methods with time-series analytic techniques. This repository presents our work during a project realized in the context of the IEOR 8100 Reinforcement Leanrning at Columbia University. 2. The input to our system is a portfolio containing one high-volatility stock and one low-volatility stock. The clipping will put a pessimistic bound on our loss: lower return estimates will be favored compared to higher ones. This field saw huge developments in recent years, because of the increased computational power and increased research in sequential Jun 7, 2019 · For each change in state, select any one among all possible actions for the current state (S). [12] S Explore the first generative pre-trained forecasting model and apply it in a project with Python Feb 27, 2024 · Reinforcement learning represents a promising paradigm for portfolio optimization in finance, fostering adaptive decision-making, dynamic asset allocation, and robust risk management. The idea is quite straightforward: the agent is aware of its own State t , takes an Action A t , which leads him to State t+1 and receives a reward R t . ABSTRACT: The authors propose models for the solution of the fundamental problem of option replication subject to discrete trading, round lotting, and nonlinear transaction costs using state-of-the-art methods in deep reinforcement learning (DRL), including deep Q-learning, deep Q-learning with Pop-Art, and proximal policy optimization (PPO). 2 Ensemble Strategy. Traditional and generic portfolio strategies require forecasting of future stock prices as model inputs, which is not a trivial task since those values are difficult to obtain in the real-world applications. 1-Inputs and datasets. MlFinLab helps portfolio managers and traders who want to leverage the power of machine learning by providing reproducible, interpretable, and easy to use tools. This repository accompanies our arXiv preprint "Deep Deterministic Portfolio Optimization" where we explore deep reinforcement learning methods to solve portfolio optimization problems. Dec 9, 2020 · Stock portfolio optimization is the process of constant re-distribution of money to a pool of various stocks. Most of you have probably heard of AI learning to play computer games on their own, a very popular example being Deepmind. An autonomous agent is any system that can make decisions and act in response to its environment independent of direct instruction by a human user. 3 0 0. Jul 7, 2022 · Our learning formula is G_state = G_state + α(target — G_state) . ipynb. Chen, “Deep reinforcement learning for portfolio management of markets with a dynamic number of assets”, Expert Systems with Applications, vol 164, p. al. 256 samples as a batch-size are randomly selected from the replay buffer to train the policy network each time, the learning rate is set to 0. Normally, action a can have three values: Five Deep Reinforcement Learning (DRL) agents are trained in two different environments to test the agents’ abil- ity to learn the best trading strategies to allocate assets, expecting to generate FinRL has three layers: market environments, agents, and applications. Reinforcement Learning (RL) Algorithms Plenty of Python implementations of models and algorithms Apply these algorithms to 5 Financial/Trading problems: (Dynamic) Asset-Allocation to maximize Utility of Consumption Pricing and Hedging of Derivatives in an Incomplete Market Optimal Exercise/Stopping of Path-dependent American Options May 4, 2022 · FinRL: A deep reinforcement learning library for automated stock trading in quantitative finance. Feb 11, 2021 · Dynamic Portfolio optimization is the process of distribution and rebalancing of a fund into different financial assets such as stocks, cryptocurrencies, etc, in consecutive trading periods to maximize accumulated profits or minimize risks over a time horizon. The interest in this field grew exponentially over the last couple of years, following great (and greatly publicized) advances, such as DeepMind's AlphaGo beating the word champion of GO, and OpenAI AI models beating professional Mar 29, 2021 · This project seeks to address the Tactical Asset Allocation problem by employing Deep Reinforcement Learning (DRL) Algorithms in a Machine Learning Environment as well as employing Neural Network Autoencoders for selection of portfolio assets. Then, we will perform a given number of optimization steps with random sub-samples of this batch using a clipped version of the REINFORCE loss. 5 Discussion The incorporation of the reinforcement learning in portfolio optimization is inter-esting to be sought after considering the increasing number of 30 Reinforcement Learning Project Ideas [with source code] Deep Learning. Deterministic Policy Gradient and Deep Deterministic Policy Gradient algorithms are selected to update our Reinforcement Learning Portfolio These are the source codes for the published paper titled "Dynamic portfolio rebalancing through reinforcement learning" at Neural Computing and Applications journal - cao-q/Dynamic-portf This session aims to teach you about the methods of Optimal Portfolio Allocation Using Machine Learning. utoronto. In this article, we will provide some ideas on reinforcement learning applications. Cryptocurrencies are electronic and decentralized alternatives to government-issued money, with Bitcoin as the best-known example of a cryptocurrency. A Reinforcement Learning Based Encoder-Decoder Framework for Learning Stock Trading Rules. 82 0. Reinforcement Q-Learning from Scratch in Python with OpenAI Gym. It will be a basic code to demonstrate the working of an RL algorithm. Learn how to use algorithms that leverage machine le Gym. PGPortfolio - source code of "A Deep Reinforcement Learning Framework for the Financial Portfolio Management Problem" gym-trading - Environment for reinforcement-learning algorithmic trading models. Sep 26, 2023 · Reinforcement learning (RL) is a general framework where agents learn to perform actions in an environment so as to maximize a reward. crypto-rl/ agent/ reinforcement learning algorithm implementations data_recorder/ tools to connect, download, and retrieve limit order book data gym_trading/ extended openai. The deep reinforcement learning framework is the core part of the library. . Using this formula, the robot will update each row in the G table according to this simple formula. This course covers a wide range of topics in RL, including foundational concepts such as MDPs and Monte Carlo methods, as well as more advanced techniques like temporal difference learning and deep The Deep Q-learning algorithm and extensions. Thesis - Reinforcement Learning for Automated Trading Jul 6, 2018 · A Deep Dive Into Reinforcement Learning. By harnessing the power of MPT principles, diversification can be achieved, as advocated by Harry Markowitz, thus mitigating risk while striving for higher returns. Robots and self-driving cars are examples of autonomous agents. Through imitating different expert demonstrations, MetaTrader acquires a set of trading policies with great diversity. Cho, “Deep learning in finance and banking: A literature review and classification,” Frontiers of Business Research Speaker: Jithin Pradeep & Tina Ruiwen Wang, The Vanguard GroupDate: February 16, 2023Abstract: http://www. fields. Teach a Taxi to pick up and drop off passengers at the right locations with Reinforcement Learning. To maintain a realistic assumption about the market, we will incorporate transaction cost and risk factor into the state as well. Aug 9, 2023 · 3. Huang, J. Xinyi Li, Yinchuan Li, Yuanchen Zhan, Xiao-Yang Liu, "Optimistic Bull or Pessimistic Bear: Adaptive Deep Reinforcement Learning for Stock Portfolio Allocation," International Conference on Machine Learning (ICML) Workshop on AI in Finance, May 2019. [2] J. First, with market’s information as its input and allocating vector as its output, deep reinforcement learning is an totally artificial intelligent methods in trading, which avoids the hand- Theory: Starting from a uniform mathematical framework, this book derives the theory and algorithms of reinforcement learning, including all major algorithms such as eligibility traces and soft actor-critic algorithms. deepdow (read as "wow") is a Python package connecting portfolio optimization and deep learning. Reinforcement learning (RL) has recently shown its potential to train profitable agents for PM through interacting with financial markets. bulbea - Deep Learning based Python Library for Stock Market Prediction and Modelling. 3-Model evaluation. Mar 5, 2024 · Reinforcement learning (RL) algorithms have proven to be useful tools for combinatorial optimisation. 2017). We provide the original implementation for "Cost-Sensitive Portfolio Selection via Deep Reinforcement Learning (IEEE TKDE 2020)". The two main components are the environment, which represents the problem to be solved, and the agent, which represents the learning algorithm. The policy optimization method we described in the paper is designed specifically for portfolio management problem. 45 0. 2-Code and implementation. Dec 12, 2020 · We hire a smart portfolio manager- Mr. For a trading task (on the top), an agent (in the middle) interacts with a market environment (at the bottom), making sequential decisions. Jan 24, 2021 · [11] N. Reinforcement Learning is an area in machine learning where we train an agent to perceive and interpret its environment, take actions and learn Dec 29, 2022 · This is the original implementation of our paper, A Deep Reinforcement Learning Framework for the Financial Portfolio Management Problem (arXiv:1706. 10059), together with a toolkit of portfolio management research. 18 1 0. 2017 [1]. Well as it turns out the trained model was able to beat Dragon portfolio over the test period of A Deep Reinforcement Learning Framework for the Financial Portfolio Management Problem; Continuous control with deep reinforcement learning; The code is inspired by CSCI 599 deep learning and its applications final project; The environment is inspired by wassname/rl-portfolio-management Dec 23, 2020 · Steps for designing a reinforcement learning model is –. 2 0. Motivated by "A Deep Reinforcement Learning Framework for the Financial Portfolio Management Problem" by Jiang et. 8 1 1. All of them are widely-used in game playing and robot control. gym environment to observe limit order book data indicators/ technical indicators implemented to be O(1) time complexity design-patterns/ visual diagrams module architecture venv/ virtual environment for This work uses a Model-free Reinforcement Learning technique called Deep Q-Learning (neural variant of Q-Learning). 5-Common issues/bugs. In this paper, we implement three state-of-art continuous reinforcement learning algorithms, Deep Deterministic Policy Gradient (DDPG), Proximal Policy Optimization (PPO) and Policy Gradient (PG)in portfolio management. Jul 23, 2023 · This article will provide a comprehensive introduction to reinforcement learning concepts and practical examples implemented in Python. 00025, the optimization method is ADAM, and Deep Reinforcement Learning for Portfolio Management. More precisely, we consider three tractable cost models for which the optimal or approximately optimal solutions are well known in the literature. 114002, 2021. python finance machine-learning research trading investing portfolio-optimization quantitative-finance algorithmic-trading portfolio-management financial-machine-learning 2. Mar 25, 2024 · Reinforcement learning (RL) is a type of machine learning process that focuses on decision making by autonomous agents. 4. Deep Q learning estimates the value of the available actions for a given state using a deep neural network. The main difference is the decision making module, where we develop a new leverage operation that contributes a lot. Understanding the Basics of Reinforcement Learning Portfolio management is the task of obtaining higher excess returns through the flexible allocation of asset weights. We are grateful to Agostino Capponi (discussant), Bing Han, Andrew Karolyi, Serhiy Kozak, Andreas Neuhierl (discussant), and Mao Ye for detailed feedback and to Si Cheng for kindly sharing the data on market illiquidity. 16 0. The agent and environment continuously interact with each other. DRL will give us daily advice includes the portfolio weights or the proportions of money to invest in these 30 stocks. . automated portfolio and investment advisor tools, and the goal of this paper is to leverage the success of the AI/ML stock portfolio trade management research to date. The state of the FX market is represented via 512 features in X_train and X_test. Open-Source Internship opportunity by OpenGenus for programmers. Step 2: Defining and visualising the graph. However, existing work mostly focuses on fixed stock pools, which is Feb 21, 2024 · Introduction. Step 1: Importing the required libraries. The intent of this project was to gain a better understanding of how machine learning could be used to perform portfolio optimization. 4 0. 26, and TensorFlow 2 / PyTorch 1&2. Machine learning and artificial intelligence are popular topics, vast domains with multiple paradigms to solve any given challenge. The actions are portfolio weights. Step 3: Travel to the next state (S’) as a result of that action (a). NeurIPS Workshop on Deep Reinforcement Learning (2020). ML practitioners, financial traders, portfolio managers, strategists, and analysts will focus on the implementation of these algorithms in the form of self-contained Python code and the application to important financial problems. La gestion de portefeuille implique la sélection, la construction Aug 15, 2023 · Introduction. For FX Reinforcement Learning Playground This repository contains an open challenge for a Portfolio Balancing AI in Forex. The work presented explores the use of Deep Reinforcement Learning in dynamically allocating assets in a portfolio in order to solve the Tactical Asset Allocation (TAA) problem. The framework of the proposed ensemble strategy is showed in Fig. 42 0. This paper proposes a Deep Reinforcement Learning algorithm for financial portfolio trading based on Deep Q-learning. Jupyter Notebook 96. It was introduced by Deep Mind’s Playing Atari with Deep Reinforcement Learning (2013), where RL agents learned to play games solely from pixel input. The cumulative reward is the final value of the portfolio at the end of the test period. Deep Reinforcement Learning. Step 4: For all possible actions from the state (S’) select the one with the highest Q-value. 1. In reinforcement learning terminology, the goal of the agent is to maximize the cumulative reward based on market actions. In the second stage, MetaTrader learns a meta-policy to recognize the market conditions and decide on the most proper learned policy to follow. Videos FinRL at AI4Finance Youtube Channel. 2021. This Deep Policy Network Reinforcement Learning project is our implementation and further research of the original paper A Deep Reinforcement Learning Framework for the Financial Portfolio Management Problem (Jiang et al. The algorithm is capable of trading high-dimensional portfolios from cross-sectional datasets of any size which may include data gaps and non-unique history lengths in the assets. Aug 29, 2018 · Adversarial Deep Reinforcement Learning in Portfolio Management. od sy fz vn qi ly xe ak ua hh
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