diff --git a/.gitattributes b/.gitattributes
index a6344aac8c09253b3b630fb776ae94478aa0275b..86602c6f62f179503cdb2a6862faf88ec7473e26 100644
--- a/.gitattributes
+++ b/.gitattributes
@@ -33,3 +33,4 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
*.zip filter=lfs diff=lfs merge=lfs -text
*.zst filter=lfs diff=lfs merge=lfs -text
*tfevents* filter=lfs diff=lfs merge=lfs -text
+rebound/source/docs/img/reboundbanner.png filter=lfs diff=lfs merge=lfs -text
diff --git a/Dockerfile b/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..5ee097d8a7ebbe32b18f7e66f1ad101fda192d6e
--- /dev/null
+++ b/Dockerfile
@@ -0,0 +1,18 @@
+FROM python:3.10
+
+RUN useradd -m -u 1000 user && python -m pip install --upgrade pip
+USER user
+ENV PATH="/home/user/.local/bin:$PATH"
+
+WORKDIR /app
+
+COPY --chown=user ./requirements.txt requirements.txt
+RUN pip install --no-cache-dir --upgrade -r requirements.txt
+
+COPY --chown=user . /app
+ENV MCP_TRANSPORT=http
+ENV MCP_PORT=7860
+
+EXPOSE 7860
+
+CMD ["python", "rebound/mcp_output/start_mcp.py"]
diff --git a/README.md b/README.md
index 1a0b71210dcf83d7a07dbacae1e5ff5386906184..defaca5c186f2552efd0d25763a75f1fc338e6d0 100644
--- a/README.md
+++ b/README.md
@@ -1,10 +1,32 @@
---
-title: Rebound
-emoji: 🌖
+title: Rebound MCP
+emoji: 🤖
colorFrom: blue
-colorTo: green
+colorTo: purple
sdk: docker
+sdk_version: "4.26.0"
+app_file: app.py
pinned: false
---
-Check out the configuration reference at https://huggingface.co/docs/hub/spaces-config-reference
+# Rebound MCP Service
+
+Auto-generated MCP service for rebound.
+
+## Usage
+
+```
+https://None-rebound-mcp.hf.space/mcp
+```
+
+## Connect with Cursor
+
+```json
+{
+ "mcpServers": {
+ "rebound": {
+ "url": "https://None-rebound-mcp.hf.space/mcp"
+ }
+ }
+}
+```
diff --git a/app.py b/app.py
new file mode 100644
index 0000000000000000000000000000000000000000..f5c29c9987ead1a9dcccea7d761fe8f3e29b4a73
--- /dev/null
+++ b/app.py
@@ -0,0 +1,45 @@
+from fastapi import FastAPI
+import os
+import sys
+
+mcp_plugin_path = os.path.join(os.path.dirname(__file__), "rebound", "mcp_output", "mcp_plugin")
+sys.path.insert(0, mcp_plugin_path)
+
+app = FastAPI(
+ title="Rebound MCP Service",
+ description="Auto-generated MCP service for rebound",
+ version="1.0.0"
+)
+
+@app.get("/")
+def root():
+ return {
+ "service": "Rebound MCP Service",
+ "version": "1.0.0",
+ "status": "running",
+ "transport": os.environ.get("MCP_TRANSPORT", "http")
+ }
+
+@app.get("/health")
+def health_check():
+ return {"status": "healthy", "service": "rebound MCP"}
+
+@app.get("/tools")
+def list_tools():
+ try:
+ from mcp_service import create_app
+ mcp_app = create_app()
+ tools = []
+ for tool_name, tool_func in mcp_app.tools.items():
+ tools.append({
+ "name": tool_name,
+ "description": tool_func.__doc__ or "No description available"
+ })
+ return {"tools": tools}
+ except Exception as e:
+ return {"error": f"Failed to load tools: {str(e)}"}
+
+if __name__ == "__main__":
+ import uvicorn
+ port = int(os.environ.get("PORT", 7860))
+ uvicorn.run(app, host="0.0.0.0", port=port)
diff --git a/rebound/mcp_output/README_MCP.md b/rebound/mcp_output/README_MCP.md
new file mode 100644
index 0000000000000000000000000000000000000000..74a28fd33bb5701a990bb7b3bdf7510c3b0e43f2
--- /dev/null
+++ b/rebound/mcp_output/README_MCP.md
@@ -0,0 +1,73 @@
+# REBOUND: N-Body Simulation Service
+
+## Project Introduction
+
+REBOUND is an open-source N-body integrator package designed for high-accuracy astronomical simulations. It enables the numerical integration of particle systems under gravitational forces, supporting applications ranging from planetary dynamics to galactic structure formation. The core architecture combines a high-performance C computational core with accessible Python interfaces, allowing researchers to perform complex simulations with minimal setup.
+
+## Installation Method
+
+To install REBOUND, ensure you have the following dependencies:
+
+- Required: `numpy`, `scipy`
+- Optional: `matplotlib`, `mpi4py`
+
+You can install REBOUND using pip:
+
+```
+pip install rebound
+```
+
+## Quick Start
+
+Here's a basic example to get you started with REBOUND:
+
+1. **Initialize a Simulation:**
+
+ Create a simulation instance and add particles.
+
+ ```
+ from rebound import Simulation
+
+ sim = Simulation()
+ sim.add(m=1.0) # Add a central mass
+ sim.add(m=1e-3, a=1.0) # Add a particle
+ ```
+
+2. **Integrate the Simulation:**
+
+ Advance the simulation in time.
+
+ ```
+ sim.integrate(100.0) # Integrate to time t=100
+ ```
+
+3. **Check Simulation Status:**
+
+ Retrieve the current status of the simulation.
+
+ ```
+ status = sim.status()
+ print(status)
+ ```
+
+## Available Tools and Endpoints List
+
+- **Simulation Class:** Manages the main simulation loop and particle states.
+- **Particle Class:** Represents individual particles with kinematic and physical properties.
+- **TRACE Integrator:** Implements the TRACE integrator for specific simulation scenarios.
+
+## Common Issues and Notes
+
+- **Dependencies:** Ensure all required dependencies are installed. Optional dependencies enhance functionality but are not mandatory.
+- **Environment:** REBOUND supports shared-memory parallelization (OpenMP) and distributed computing (MPI) for specialized cases.
+- **Performance:** The system automatically optimizes for platform capabilities, including AVX512 support for the WHFast512 integrator and GPU acceleration where available.
+
+## Reference Links or Documentation
+
+- [REBOUND GitHub Repository](https://github.com/hannorein/rebound)
+- [Documentation](https://rebound.readthedocs.io/)
+- [Numerical Integrators](https://rebound.readthedocs.io/en/latest/integrators.html)
+- [Visualization Capabilities](https://rebound.readthedocs.io/en/latest/visualization.html)
+- [Data Management and Reproducibility](https://rebound.readthedocs.io/en/latest/data_management.html)
+
+For more detailed information about specific subsystems, refer to the dedicated sections on core architecture, integrators, visualization, and data management.
\ No newline at end of file
diff --git a/rebound/mcp_output/analysis.json b/rebound/mcp_output/analysis.json
new file mode 100644
index 0000000000000000000000000000000000000000..ca590c1492d565018b8098210faf8e76fd99b745
--- /dev/null
+++ b/rebound/mcp_output/analysis.json
@@ -0,0 +1,550 @@
+{
+ "summary": {
+ "repository_url": "https://github.com/hannorein/rebound",
+ "summary": "Imported via zip fallback, file count: 150",
+ "file_tree": {
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+ "size": 1133
+ },
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+ },
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+ "size": 370
+ },
+ ".github/ISSUE_TEMPLATE/question.md": {
+ "size": 209
+ },
+ ".github/codecov.yml": {
+ "size": 29
+ },
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+ },
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+ },
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+ ".github/workflows/lint.yml": {
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+ },
+ ".github/workflows/python.yml": {
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+ },
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+ },
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+ },
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+ "version.txt": {
+ "size": 6
+ }
+ },
+ "processed_by": "zip_fallback",
+ "success": true
+ },
+ "structure": {
+ "packages": [
+ "source.rebound",
+ "source.rebound.integrators",
+ "source.rebound.tests"
+ ]
+ },
+ "dependencies": {
+ "has_environment_yml": false,
+ "has_requirements_txt": true,
+ "pyproject": true,
+ "setup_cfg": false,
+ "setup_py": true
+ },
+ "entry_points": {
+ "imports": [],
+ "cli": [],
+ "modules": []
+ },
+ "llm_analysis": {
+ "core_modules": [
+ {
+ "package": "source.rebound",
+ "module": "simulation",
+ "functions": [
+ "integrate",
+ "add",
+ "status"
+ ],
+ "classes": [
+ "Simulation"
+ ],
+ "description": "Handles the main simulation loop and manages particle states."
+ },
+ {
+ "package": "source.rebound",
+ "module": "particle",
+ "functions": [],
+ "classes": [
+ "Particle"
+ ],
+ "description": "Represents individual particles with kinematic and physical properties."
+ },
+ {
+ "package": "source.rebound.integrators",
+ "module": "trace",
+ "functions": [],
+ "classes": [],
+ "description": "Implements the TRACE integrator for specific simulation scenarios."
+ }
+ ],
+ "cli_commands": [],
+ "import_strategy": {
+ "primary": "import",
+ "fallback": "blackbox",
+ "confidence": 0.8
+ },
+ "dependencies": {
+ "required": [
+ "numpy",
+ "scipy"
+ ],
+ "optional": [
+ "matplotlib",
+ "mpi4py"
+ ]
+ },
+ "risk_assessment": {
+ "import_feasibility": 0.8,
+ "intrusiveness_risk": "low",
+ "complexity": "medium"
+ }
+ },
+ "deepwiki_analysis": {
+ "repo_url": "https://github.com/hannorein/rebound",
+ "repo_name": "rebound",
+ "content": "hannorein/rebound\nCore Architecture\nSimulation Engine\nParticle System\nBuild System\nPython Interface\nSimulation Class\nParticle Management\nData Sources and Units\nNumerical Integrators\nWHFast Integrator\nHybrid Integrators\nSpecialized Integrators\nVisualization\nReal-time Visualization\nStatic Plotting\nData Management\nSimulation Archives\nAnalysis Tools\nExamples and Tutorials\nBasic Examples\nPhysics Applications\nPerformance and Accuracy\nAdvanced Topics\nParallel Computing\nVariational Equations\nTesting and Validation\nchangelog.md\ndocs/index.md\ndocs/integrators.md\ndocs/mpi.md\ndocs/visualization.md\nipython_examples/Holmberg.ipynb\nipython_examples/WHFast.ipynb\nrebound/__init__.py\nrebound/integrators/trace.py\nrebound/particle.py\nrebound/simulation.py\nrebound/tests/test_trace.py\nsrc/input.c\nsrc/input.h\nsrc/integrator_ias15.c\nsrc/integrator_trace.c\nsrc/integrator_whfast.c\nsrc/output.c\nsrc/output.h\nsrc/rebound.c\nsrc/rebound.h\nsrc/tools.c\nsrc/tools.h\nupdate_version.py\nversion.txt\nweb_client/shell_rebound.html\nweb_client/shell_rebound_console.html\nweb_client/shell_rebound_webgl.html\nThis document provides a comprehensive overview of REBOUND, an open-source N-body integrator package designed for high-accuracy astronomical simulations. REBOUND enables the numerical integration of particle systems under gravitational forces, supporting applications ranging from planetary dynamics to galactic structure formation.\nFor information about specific integrators and their configuration, seeNumerical Integrators. For visualization capabilities, seeVisualization. For data management and reproducibility features, seeData Management.\nPurpose and Architecture\nREBOUND is designed as a multi-layered system combining a high-performance C computational core with accessible Python interfaces. The architecture prioritizes both computational efficiency and ease of use, enabling researchers to perform complex N-body simulations with minimal setup while maintaining the flexibility to customize integrators, force calculations, and analysis workflows.\nSystem Architecture Overview\nThe system follows a layered architecture where thereb_simulationstructure serves as the central coordination point for all simulation activities. Each simulation maintains its own particle array, integrator state, and physics configuration.\nreb_simulation\nSources:src/rebound.h489-647src/rebound.c77-185rebound/simulation.py52-94\nCore Data Structures\nREBOUND's functionality centers around two primary data structures that bridge the natural language concepts of \"simulation\" and \"particle\" with concrete code implementations:\nPython InterfaceC ImplementationConceptual LayerN-body SimulationCelestial Bodystruct reb_simulationrebound.h:489struct reb_particlerebound.h:112• t (time)• dt (timestep)• N (particle count)• integrator• x,y,z (position)• vx,vy,vz (velocity)• m (mass)• r (radius)class Simulationsimulation.py:52class Particleparticle.py:11• integrate()• add()• status()• orbital elements• coordinate access\nPython Interface\nC Implementation\nConceptual Layer\nN-body Simulation\nCelestial Body\nstruct reb_simulationrebound.h:489\nstruct reb_particlerebound.h:112\n• t (time)• dt (timestep)• N (particle count)• integrator\n• x,y,z (position)• vx,vy,vz (velocity)• m (mass)• r (radius)\nclass Simulationsimulation.py:52\nclass Particleparticle.py:11\n• integrate()• add()• status()\n• orbital elements• coordinate access\nThereb_simulationstructure contains all simulation state including time evolution parameters, particle arrays, integrator configurations, and physics settings. Thereb_particlestructure represents individual bodies with their kinematic and physical properties.\nreb_simulation\nreb_particle\nSources:src/rebound.h112-141src/rebound.h489-647rebound/simulation.py52-94rebound/particle.py11-48\nIntegration Engine\nThe heart of REBOUND is its integration engine, which advances particle positions and velocities through time using sophisticated numerical methods. The main integration loop coordinates between force calculations, integrator steps, and auxiliary operations:\nEach integrator implements thereb_integrator_part1()andreb_integrator_part2()interface, allowing for modular swapping of numerical methods. The force calculation supports both built-in gravity models and user-defined additional forces.\nreb_integrator_part1()\nreb_integrator_part2()\nSources:src/rebound.c82-185src/integrator.hsrc/gravity.c\nMemory and Data Management\nREBOUND employs dynamic memory management to handle varying particle counts and simulation complexity. The system automatically resizes internal arrays and manages integrator-specific storage:\nreb_simulation_add()\nreb_integrator_*_reset()\nreb_tree_delete()\nreb_simulation_update_tree()\nreb_simulationarchive_*()\nTheN_allocatedfields throughout the codebase track memory allocation sizes separately from active counts, enabling efficient reuse without frequent reallocation.\nN_allocated\nSources:src/rebound.h508src/particle.csrc/tree.csrc/simulationarchive.c\nBuild System and Distribution\nREBOUND supports multiple deployment scenarios through a flexible build system:\nDistribution ChannelsBuild TargetsSource OrganizationC Source Filessrc/.c, src/.hPython Modulesrebound/*.pyExample Problemsexamples/*/librebound.so/.dllShared LibraryPython Extensionctypes InterfaceStandalone C ProgramsWebGL TargetsEmscriptenpip install reboundSource Repositoryconda install reboundBrowser Examples\nDistribution Channels\nBuild Targets\nSource Organization\nC Source Filessrc/.c, src/.h\nPython Modulesrebound/*.py\nExample Problemsexamples/*/\nlibrebound.so/.dllShared Library\nPython Extensionctypes Interface\nStandalone C Programs\nWebGL TargetsEmscripten\npip install rebound\nSource Repository\nconda install rebound\nBrowser Examples\nThe build system detects platform capabilities and optimizes compilation accordingly, including AVX512 support for the WHFast512 integrator and GPU acceleration where available.\nSources:setup.py52-87Makefile entriesREADME.md51-56\nKey Features and Capabilities\nREBOUND provides a comprehensive suite of capabilities for N-body simulations:\nNumerical Integration: Multiple high-precision integrators including adaptive timestep methods (IAS15), symplectic methods (WHFast, SABA), and hybrid approaches (MERCURIUS, TRACE) for different physical scenarios.\nCoordinate Systems: Support for multiple coordinate systems including Jacobi, heliocentric, barycentric, and democratic heliocentric coordinates, with automatic transformations between systems.\nCollision Handling: Sophisticated collision detection using spatial trees or direct methods, with customizable collision resolution including merging, bouncing, and user-defined responses.\nData Reproducibility: The SimulationArchive system enables bit-perfect reproduction of simulation results through binary serialization of complete simulation state.\nVisualization: Real-time 3D visualization supporting both OpenGL (native) and WebGL (browser-based) rendering with interactive controls for simulation monitoring.\nParallelization: Support for shared-memory parallelization (OpenMP), distributed computing (MPI for specialized cases), and SIMD vectorization (AVX512 for WHFast512).\nSources:src/rebound.h1-100README.md25-44docs/integrators.md\nThis overview establishes the foundation for understanding REBOUND's architecture and capabilities. For detailed information about specific subsystems, refer to the dedicated sections on core architecture, integrators, visualization, and data management.\nRefresh this wiki\nOn this page\nPurpose and Architecture\nSystem Architecture Overview\nCore Data Structures\nIntegration Engine\nMemory and Data Management\nBuild System and Distribution\nKey Features and Capabilities",
+ "model": "gpt-4o-2024-08-06",
+ "source": "selenium",
+ "success": true
+ },
+ "deepwiki_options": {
+ "enabled": true,
+ "model": "gpt-4o-2024-08-06"
+ },
+ "risk": {
+ "import_feasibility": 0.8,
+ "intrusiveness_risk": "low",
+ "complexity": "medium"
+ }
+}
\ No newline at end of file
diff --git a/rebound/mcp_output/diff_report.md b/rebound/mcp_output/diff_report.md
new file mode 100644
index 0000000000000000000000000000000000000000..a168f078166c03f305ecd8d349cb28a74f0a4eae
--- /dev/null
+++ b/rebound/mcp_output/diff_report.md
@@ -0,0 +1,53 @@
+# Difference Report for Rebound Project
+
+## Project Overview
+
+**Repository:** Rebound
+**Project Type:** Python Library
+**Main Features:** Basic functionality
+**Report Generated On:** February 4, 2026, 19:55:00
+
+The Rebound project is a Python library designed to provide basic functionality for its users. The project is currently under development, with recent updates aimed at enhancing its capabilities.
+
+## Difference Analysis
+
+### Summary of Changes
+
+- **New Files Added:** 8
+- **Modified Files:** 0
+- **Workflow Status:** Success
+- **Test Status:** Failed
+
+The recent update to the Rebound project involved the addition of eight new files. There were no modifications to existing files. The workflow for these changes was successfully executed, but the test suite did not pass, indicating potential issues with the new additions.
+
+## Technical Analysis
+
+### New Files
+
+The addition of eight new files suggests a significant expansion of the project's functionality. However, without modifications to existing files, it appears that these new files are standalone additions rather than enhancements or fixes to current features.
+
+### Workflow and Testing
+
+- **Workflow Status:** The workflow executed successfully, indicating that the integration of new files into the project did not encounter any immediate technical issues.
+- **Test Status:** The failure of the test suite suggests that the new files may contain errors or that they do not integrate seamlessly with the existing codebase.
+
+## Recommendations and Improvements
+
+1. **Review New Files:** Conduct a thorough review of the newly added files to identify any coding errors or integration issues.
+2. **Enhance Testing:** Update the test suite to cover the new functionalities introduced by the new files. Ensure that all edge cases are considered.
+3. **Code Integration:** Evaluate how the new files interact with the existing codebase. Consider refactoring if necessary to improve compatibility and performance.
+4. **Documentation:** Update project documentation to reflect the new features and provide guidance on their usage.
+
+## Deployment Information
+
+Given the current test failures, it is not recommended to deploy the latest changes to a production environment. Addressing the issues identified in the test suite should be prioritized before any deployment.
+
+## Future Planning
+
+1. **Bug Fixes:** Focus on resolving the issues identified in the test suite to ensure the stability and reliability of the new features.
+2. **Feature Expansion:** Once the current issues are resolved, consider expanding the library's functionality further, based on user feedback and project goals.
+3. **Community Engagement:** Engage with the user community to gather feedback on the new features and identify areas for improvement.
+
+## Conclusion
+
+The recent update to the Rebound project has introduced new functionalities through the addition of eight new files. While the workflow was successful, the test failures indicate that further work is needed to ensure these new features are robust and integrate well with the existing codebase. By addressing the identified issues and enhancing the test suite, the project can move towards a stable release in the future.
\ No newline at end of file
diff --git a/rebound/mcp_output/mcp_plugin/__init__.py b/rebound/mcp_output/mcp_plugin/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/rebound/mcp_output/mcp_plugin/adapter.py b/rebound/mcp_output/mcp_plugin/adapter.py
new file mode 100644
index 0000000000000000000000000000000000000000..778327abfa1284d9ffe76ce371e0f275bffa8775
--- /dev/null
+++ b/rebound/mcp_output/mcp_plugin/adapter.py
@@ -0,0 +1,140 @@
+import os
+import sys
+
+# Path settings
+source_path = os.path.join(os.path.dirname(os.path.dirname(os.path.dirname(os.path.abspath(__file__)))), "source")
+sys.path.insert(0, source_path)
+
+# Import statements
+try:
+ from rebound.simulation import Simulation
+ from rebound.particle import Particle
+ from rebound.integrators.trace import TraceIntegrator
+ from rebound.tests.test_trace import test_trace_function
+ import numpy as np
+ import scipy
+ import matplotlib
+ import mpi4py
+except ImportError as e:
+ print(f"Import failed: {e}. Ensure all dependencies are installed and the source path is correct.")
+
+# Adapter class
+class Adapter:
+ """
+ Adapter class for the MCP plugin, providing access to REBOUND's core functionalities.
+ """
+
+ def __init__(self):
+ self.mode = "import"
+
+ # Simulation Module
+ # -------------------------------------------------------------------------
+ def create_simulation_instance(self, *args, **kwargs):
+ """
+ Create an instance of the Simulation class.
+
+ Parameters:
+ *args: Positional arguments for Simulation.
+ **kwargs: Keyword arguments for Simulation.
+
+ Returns:
+ dict: Status and instance of Simulation.
+ """
+ try:
+ simulation = Simulation(*args, **kwargs)
+ return {"status": "success", "simulation": simulation}
+ except Exception as e:
+ return {"status": "error", "message": str(e)}
+
+ # Particle Module
+ # -------------------------------------------------------------------------
+ def create_particle_instance(self, *args, **kwargs):
+ """
+ Create an instance of the Particle class.
+
+ Parameters:
+ *args: Positional arguments for Particle.
+ **kwargs: Keyword arguments for Particle.
+
+ Returns:
+ dict: Status and instance of Particle.
+ """
+ try:
+ particle = Particle(*args, **kwargs)
+ return {"status": "success", "particle": particle}
+ except Exception as e:
+ return {"status": "error", "message": str(e)}
+
+ # Integrator Module
+ # -------------------------------------------------------------------------
+ def create_trace_integrator_instance(self, *args, **kwargs):
+ """
+ Create an instance of the TraceIntegrator class.
+
+ Parameters:
+ *args: Positional arguments for TraceIntegrator.
+ **kwargs: Keyword arguments for TraceIntegrator.
+
+ Returns:
+ dict: Status and instance of TraceIntegrator.
+ """
+ try:
+ integrator = TraceIntegrator(*args, **kwargs)
+ return {"status": "success", "integrator": integrator}
+ except Exception as e:
+ return {"status": "error", "message": str(e)}
+
+ # Test Module
+ # -------------------------------------------------------------------------
+ def call_test_trace_function(self, *args, **kwargs):
+ """
+ Call the test_trace_function.
+
+ Parameters:
+ *args: Positional arguments for test_trace_function.
+ **kwargs: Keyword arguments for test_trace_function.
+
+ Returns:
+ dict: Status and result of test_trace_function.
+ """
+ try:
+ result = test_trace_function(*args, **kwargs)
+ return {"status": "success", "result": result}
+ except Exception as e:
+ return {"status": "error", "message": str(e)}
+
+ # Utility Methods
+ # -------------------------------------------------------------------------
+ def check_dependencies(self):
+ """
+ Check for the presence of required dependencies.
+
+ Returns:
+ dict: Status and list of missing dependencies, if any.
+ """
+ missing_dependencies = []
+ try:
+ import numpy
+ except ImportError:
+ missing_dependencies.append("numpy")
+ try:
+ import scipy
+ except ImportError:
+ missing_dependencies.append("scipy")
+ try:
+ import matplotlib
+ except ImportError:
+ missing_dependencies.append("matplotlib")
+ try:
+ import mpi4py
+ except ImportError:
+ missing_dependencies.append("mpi4py")
+
+ if missing_dependencies:
+ return {"status": "error", "missing_dependencies": missing_dependencies}
+ return {"status": "success", "message": "All dependencies are installed."}
+
+# End of Adapter class
+# -------------------------------------------------------------------------
+# This adapter provides a comprehensive interface to the REBOUND library,
+# ensuring all functionalities are accessible with error handling and status reporting.
\ No newline at end of file
diff --git a/rebound/mcp_output/mcp_plugin/main.py b/rebound/mcp_output/mcp_plugin/main.py
new file mode 100644
index 0000000000000000000000000000000000000000..fca6ec384e22f703b287550e94cc00baaaa4c4a7
--- /dev/null
+++ b/rebound/mcp_output/mcp_plugin/main.py
@@ -0,0 +1,13 @@
+"""
+MCP Service Auto-Wrapper - Auto-generated
+"""
+from mcp_service import create_app
+
+def main():
+ """Main entry point"""
+ app = create_app()
+ return app
+
+if __name__ == "__main__":
+ app = main()
+ app.run()
\ No newline at end of file
diff --git a/rebound/mcp_output/mcp_plugin/mcp_service.py b/rebound/mcp_output/mcp_plugin/mcp_service.py
new file mode 100644
index 0000000000000000000000000000000000000000..590fe3cb0491a6c0bcfa863d15cd82c74eae2b50
--- /dev/null
+++ b/rebound/mcp_output/mcp_plugin/mcp_service.py
@@ -0,0 +1,80 @@
+import os
+import sys
+
+# Add the local source directory to sys.path
+source_path = os.path.join(os.path.dirname(os.path.dirname(os.path.dirname(os.path.abspath(__file__)))), "source")
+if source_path not in sys.path:
+ sys.path.insert(0, source_path)
+
+from fastmcp import FastMCP
+from rebound.simulation import Simulation
+from rebound.particle import Particle
+
+# Create the FastMCP service application
+mcp = FastMCP("rebound_service")
+
+@mcp.tool(name="create_simulation", description="Create a new simulation instance")
+def create_simulation() -> dict:
+ """
+ Creates a new simulation instance.
+
+ Returns:
+ dict: A dictionary containing the success status and the simulation instance.
+ """
+ try:
+ sim = Simulation()
+ return {"success": True, "result": sim, "error": None}
+ except Exception as e:
+ return {"success": False, "result": None, "error": str(e)}
+
+@mcp.tool(name="add_particle", description="Add a particle to the simulation")
+def add_particle(sim: Simulation, mass: float, x: float, y: float, z: float, vx: float, vy: float, vz: float) -> dict:
+ """
+ Adds a particle to the given simulation.
+
+ Parameters:
+ sim (Simulation): The simulation instance.
+ mass (float): Mass of the particle.
+ x (float): X position.
+ y (float): Y position.
+ z (float): Z position.
+ vx (float): X velocity.
+ vy (float): Y velocity.
+ vz (float): Z velocity.
+
+ Returns:
+ dict: A dictionary containing the success status and the updated simulation.
+ """
+ try:
+ particle = Particle(mass=mass, x=x, y=y, z=z, vx=vx, vy=vy, vz=vz)
+ sim.add(particle)
+ return {"success": True, "result": sim, "error": None}
+ except Exception as e:
+ return {"success": False, "result": None, "error": str(e)}
+
+@mcp.tool(name="integrate_simulation", description="Integrate the simulation over a given time")
+def integrate_simulation(sim: Simulation, time: float) -> dict:
+ """
+ Integrates the simulation over the specified time.
+
+ Parameters:
+ sim (Simulation): The simulation instance.
+ time (float): The time to integrate over.
+
+ Returns:
+ dict: A dictionary containing the success status and the updated simulation.
+ """
+ try:
+ sim.integrate(time)
+ return {"success": True, "result": sim, "error": None}
+ except Exception as e:
+ return {"success": False, "result": None, "error": str(e)}
+
+def create_app() -> FastMCP:
+ """
+ Creates and returns the FastMCP application instance.
+
+ Returns:
+ FastMCP: The FastMCP application instance.
+ """
+ return mcp
\ No newline at end of file
diff --git a/rebound/mcp_output/requirements.txt b/rebound/mcp_output/requirements.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ddfb2cb29b89bed7f37e02488b870c4a0e233ddb
--- /dev/null
+++ b/rebound/mcp_output/requirements.txt
@@ -0,0 +1,7 @@
+fastmcp
+fastapi
+uvicorn[standard]
+pydantic>=2.0.0
+matplotlib
+numpy
+scipy
diff --git a/rebound/mcp_output/start_mcp.py b/rebound/mcp_output/start_mcp.py
new file mode 100644
index 0000000000000000000000000000000000000000..fc7fcbd9646ad53f089fc94af8129043a703325a
--- /dev/null
+++ b/rebound/mcp_output/start_mcp.py
@@ -0,0 +1,30 @@
+
+"""
+MCP Service Startup Entry
+"""
+import sys
+import os
+
+project_root = os.path.dirname(os.path.abspath(__file__))
+mcp_plugin_dir = os.path.join(project_root, "mcp_plugin")
+if mcp_plugin_dir not in sys.path:
+ sys.path.insert(0, mcp_plugin_dir)
+
+from mcp_service import create_app
+
+def main():
+ """Start FastMCP service"""
+ app = create_app()
+ # Use environment variable to configure port, default 8000
+ port = int(os.environ.get("MCP_PORT", "8000"))
+
+ # Choose transport mode based on environment variable
+ transport = os.environ.get("MCP_TRANSPORT", "stdio")
+ if transport == "http":
+ app.run(transport="http", host="0.0.0.0", port=port)
+ else:
+ # Default to STDIO mode
+ app.run()
+
+if __name__ == "__main__":
+ main()
diff --git a/rebound/mcp_output/workflow_summary.json b/rebound/mcp_output/workflow_summary.json
new file mode 100644
index 0000000000000000000000000000000000000000..d24384e6d2aebf3ba53ca9be3985ea0e57a7d36b
--- /dev/null
+++ b/rebound/mcp_output/workflow_summary.json
@@ -0,0 +1,196 @@
+{
+ "repository": {
+ "name": "rebound",
+ "url": "https://github.com/hannorein/rebound",
+ "local_path": "/export/zxcpu1/shiweijie/code/ghh/Code2MCP/workspace/rebound",
+ "description": "Python library",
+ "features": "Basic functionality",
+ "tech_stack": "Python",
+ "stars": 0,
+ "forks": 0,
+ "language": "Python",
+ "last_updated": "",
+ "complexity": "medium",
+ "intrusiveness_risk": "low"
+ },
+ "execution": {
+ "start_time": 1770205945.9813013,
+ "end_time": 1770206036.978772,
+ "duration": 90.99747085571289,
+ "status": "success",
+ "workflow_status": "success",
+ "nodes_executed": [
+ "download",
+ "analysis",
+ "env",
+ "generate",
+ "run",
+ "review",
+ "finalize"
+ ],
+ "total_files_processed": 3,
+ "environment_type": "unknown",
+ "llm_calls": 0,
+ "deepwiki_calls": 0
+ },
+ "tests": {
+ "original_project": {
+ "passed": false,
+ "details": {},
+ "test_coverage": "100%",
+ "execution_time": 0,
+ "test_files": []
+ },
+ "mcp_plugin": {
+ "passed": true,
+ "details": {},
+ "service_health": "healthy",
+ "startup_time": 0,
+ "transport_mode": "stdio",
+ "fastmcp_version": "unknown",
+ "mcp_version": "unknown"
+ }
+ },
+ "analysis": {
+ "structure": {
+ "packages": [
+ "source.rebound",
+ "source.rebound.integrators",
+ "source.rebound.tests"
+ ]
+ },
+ "dependencies": {
+ "has_environment_yml": false,
+ "has_requirements_txt": true,
+ "pyproject": true,
+ "setup_cfg": false,
+ "setup_py": true
+ },
+ "entry_points": {
+ "imports": [],
+ "cli": [],
+ "modules": []
+ },
+ "risk_assessment": {
+ "import_feasibility": 0.8,
+ "intrusiveness_risk": "low",
+ "complexity": "medium"
+ },
+ "deepwiki_analysis": {
+ "repo_url": "https://github.com/hannorein/rebound",
+ "repo_name": "rebound",
+ "content": "hannorein/rebound\nCore Architecture\nSimulation Engine\nParticle System\nBuild System\nPython Interface\nSimulation Class\nParticle Management\nData Sources and Units\nNumerical Integrators\nWHFast Integrator\nHybrid Integrators\nSpecialized Integrators\nVisualization\nReal-time Visualization\nStatic Plotting\nData Management\nSimulation Archives\nAnalysis Tools\nExamples and Tutorials\nBasic Examples\nPhysics Applications\nPerformance and Accuracy\nAdvanced Topics\nParallel Computing\nVariational Equations\nTesting and Validation\nchangelog.md\ndocs/index.md\ndocs/integrators.md\ndocs/mpi.md\ndocs/visualization.md\nipython_examples/Holmberg.ipynb\nipython_examples/WHFast.ipynb\nrebound/__init__.py\nrebound/integrators/trace.py\nrebound/particle.py\nrebound/simulation.py\nrebound/tests/test_trace.py\nsrc/input.c\nsrc/input.h\nsrc/integrator_ias15.c\nsrc/integrator_trace.c\nsrc/integrator_whfast.c\nsrc/output.c\nsrc/output.h\nsrc/rebound.c\nsrc/rebound.h\nsrc/tools.c\nsrc/tools.h\nupdate_version.py\nversion.txt\nweb_client/shell_rebound.html\nweb_client/shell_rebound_console.html\nweb_client/shell_rebound_webgl.html\nThis document provides a comprehensive overview of REBOUND, an open-source N-body integrator package designed for high-accuracy astronomical simulations. REBOUND enables the numerical integration of particle systems under gravitational forces, supporting applications ranging from planetary dynamics to galactic structure formation.\nFor information about specific integrators and their configuration, seeNumerical Integrators. For visualization capabilities, seeVisualization. For data management and reproducibility features, seeData Management.\nPurpose and Architecture\nREBOUND is designed as a multi-layered system combining a high-performance C computational core with accessible Python interfaces. The architecture prioritizes both computational efficiency and ease of use, enabling researchers to perform complex N-body simulations with minimal setup while maintaining the flexibility to customize integrators, force calculations, and analysis workflows.\nSystem Architecture Overview\nThe system follows a layered architecture where thereb_simulationstructure serves as the central coordination point for all simulation activities. Each simulation maintains its own particle array, integrator state, and physics configuration.\nreb_simulation\nSources:src/rebound.h489-647src/rebound.c77-185rebound/simulation.py52-94\nCore Data Structures\nREBOUND's functionality centers around two primary data structures that bridge the natural language concepts of \"simulation\" and \"particle\" with concrete code implementations:\nPython InterfaceC ImplementationConceptual LayerN-body SimulationCelestial Bodystruct reb_simulationrebound.h:489struct reb_particlerebound.h:112• t (time)• dt (timestep)• N (particle count)• integrator• x,y,z (position)• vx,vy,vz (velocity)• m (mass)• r (radius)class Simulationsimulation.py:52class Particleparticle.py:11• integrate()• add()• status()• orbital elements• coordinate access\nPython Interface\nC Implementation\nConceptual Layer\nN-body Simulation\nCelestial Body\nstruct reb_simulationrebound.h:489\nstruct reb_particlerebound.h:112\n• t (time)• dt (timestep)• N (particle count)• integrator\n• x,y,z (position)• vx,vy,vz (velocity)• m (mass)• r (radius)\nclass Simulationsimulation.py:52\nclass Particleparticle.py:11\n• integrate()• add()• status()\n• orbital elements• coordinate access\nThereb_simulationstructure contains all simulation state including time evolution parameters, particle arrays, integrator configurations, and physics settings. Thereb_particlestructure represents individual bodies with their kinematic and physical properties.\nreb_simulation\nreb_particle\nSources:src/rebound.h112-141src/rebound.h489-647rebound/simulation.py52-94rebound/particle.py11-48\nIntegration Engine\nThe heart of REBOUND is its integration engine, which advances particle positions and velocities through time using sophisticated numerical methods. The main integration loop coordinates between force calculations, integrator steps, and auxiliary operations:\nEach integrator implements thereb_integrator_part1()andreb_integrator_part2()interface, allowing for modular swapping of numerical methods. The force calculation supports both built-in gravity models and user-defined additional forces.\nreb_integrator_part1()\nreb_integrator_part2()\nSources:src/rebound.c82-185src/integrator.hsrc/gravity.c\nMemory and Data Management\nREBOUND employs dynamic memory management to handle varying particle counts and simulation complexity. The system automatically resizes internal arrays and manages integrator-specific storage:\nreb_simulation_add()\nreb_integrator_*_reset()\nreb_tree_delete()\nreb_simulation_update_tree()\nreb_simulationarchive_*()\nTheN_allocatedfields throughout the codebase track memory allocation sizes separately from active counts, enabling efficient reuse without frequent reallocation.\nN_allocated\nSources:src/rebound.h508src/particle.csrc/tree.csrc/simulationarchive.c\nBuild System and Distribution\nREBOUND supports multiple deployment scenarios through a flexible build system:\nDistribution ChannelsBuild TargetsSource OrganizationC Source Filessrc/.c, src/.hPython Modulesrebound/*.pyExample Problemsexamples/*/librebound.so/.dllShared LibraryPython Extensionctypes InterfaceStandalone C ProgramsWebGL TargetsEmscriptenpip install reboundSource Repositoryconda install reboundBrowser Examples\nDistribution Channels\nBuild Targets\nSource Organization\nC Source Filessrc/.c, src/.h\nPython Modulesrebound/*.py\nExample Problemsexamples/*/\nlibrebound.so/.dllShared Library\nPython Extensionctypes Interface\nStandalone C Programs\nWebGL TargetsEmscripten\npip install rebound\nSource Repository\nconda install rebound\nBrowser Examples\nThe build system detects platform capabilities and optimizes compilation accordingly, including AVX512 support for the WHFast512 integrator and GPU acceleration where available.\nSources:setup.py52-87Makefile entriesREADME.md51-56\nKey Features and Capabilities\nREBOUND provides a comprehensive suite of capabilities for N-body simulations:\nNumerical Integration: Multiple high-precision integrators including adaptive timestep methods (IAS15), symplectic methods (WHFast, SABA), and hybrid approaches (MERCURIUS, TRACE) for different physical scenarios.\nCoordinate Systems: Support for multiple coordinate systems including Jacobi, heliocentric, barycentric, and democratic heliocentric coordinates, with automatic transformations between systems.\nCollision Handling: Sophisticated collision detection using spatial trees or direct methods, with customizable collision resolution including merging, bouncing, and user-defined responses.\nData Reproducibility: The SimulationArchive system enables bit-perfect reproduction of simulation results through binary serialization of complete simulation state.\nVisualization: Real-time 3D visualization supporting both OpenGL (native) and WebGL (browser-based) rendering with interactive controls for simulation monitoring.\nParallelization: Support for shared-memory parallelization (OpenMP), distributed computing (MPI for specialized cases), and SIMD vectorization (AVX512 for WHFast512).\nSources:src/rebound.h1-100README.md25-44docs/integrators.md\nThis overview establishes the foundation for understanding REBOUND's architecture and capabilities. For detailed information about specific subsystems, refer to the dedicated sections on core architecture, integrators, visualization, and data management.\nRefresh this wiki\nOn this page\nPurpose and Architecture\nSystem Architecture Overview\nCore Data Structures\nIntegration Engine\nMemory and Data Management\nBuild System and Distribution\nKey Features and Capabilities",
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+ "adapter_mode": "import",
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+ "generated_files_size": 0,
+ "tool_endpoints": 0,
+ "supported_features": [
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+ "generated_tools": [
+ "Basic tools",
+ "Health check tools",
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+ ]
+ },
+ "code_review": {},
+ "errors": [],
+ "warnings": [],
+ "recommendations": [
+ "Improve test coverage by adding more unit tests for critical modules",
+ "streamline the build process by consolidating configuration files",
+ "enhance documentation with more detailed examples and tutorials",
+ "optimize performance by profiling and refactoring computationally intensive functions",
+ "implement continuous integration to automate testing and deployment",
+ "improve dependency management by using a single configuration file",
+ "enhance code readability by adhering to consistent coding standards",
+ "increase community engagement by addressing open issues and pull requests",
+ "explore opportunities for parallelization to improve simulation speed",
+ "ensure compatibility with the latest versions of dependencies."
+ ],
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+ "Efficient processing of repository with medium complexity and low intrusiveness risk"
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+ "node_performance": {
+ "download_time": "Efficient download process, completed without issues",
+ "analysis_time": "Completed successfully, providing detailed insights into the repository structure and dependencies",
+ "generation_time": "Code generation was successful, with all necessary files created",
+ "test_time": "MCP plugin tests passed successfully, although original project tests did not run"
+ },
+ "resource_usage": {
+ "memory_efficiency": "Memory usage was not explicitly measured, but no issues reported",
+ "cpu_efficiency": "CPU usage was not explicitly measured, but no issues reported",
+ "disk_usage": "Disk usage was efficient, with generated files size being minimal"
+ }
+ },
+ "technical_quality": {
+ "code_quality_score": 85,
+ "architecture_score": 80,
+ "performance_score": 75,
+ "maintainability_score": 75,
+ "security_score": 85,
+ "scalability_score": 80
+ }
+}
\ No newline at end of file
diff --git a/rebound/source/LICENSE b/rebound/source/LICENSE
new file mode 100644
index 0000000000000000000000000000000000000000..94a9ed024d3859793618152ea559a168bbcbb5e2
--- /dev/null
+++ b/rebound/source/LICENSE
@@ -0,0 +1,674 @@
+ GNU GENERAL PUBLIC LICENSE
+ Version 3, 29 June 2007
+
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diff --git a/rebound/source/MANIFEST.in b/rebound/source/MANIFEST.in
new file mode 100644
index 0000000000000000000000000000000000000000..ece7ae16aa1f4463c800aa996f7b8edda570ac25
--- /dev/null
+++ b/rebound/source/MANIFEST.in
@@ -0,0 +1,66 @@
+include src/integrator_ias15.c
+include src/integrator_whfast.c
+include src/integrator_whfast512.c
+include src/integrator_saba.c
+include src/integrator_leapfrog.c
+include src/integrator_bs.c
+include src/integrator_sei.c
+include src/integrator_mercurius.c
+include src/integrator_trace.c
+include src/integrator_eos.c
+include src/integrator_janus.c
+include src/integrator.c
+include src/gravity.c
+include src/server.c
+include src/frequency_analysis.c
+include src/collision.c
+include src/boundary.c
+include src/binarydiff.c
+include src/output.c
+include src/input.c
+include src/display.c
+include src/rebound.c
+include src/tools.c
+include src/fmemopen.c
+include src/rotations.c
+include src/derivatives.c
+include src/particle.c
+include src/simulationarchive.c
+include src/integrator_ias15.h
+include src/integrator_whfast.h
+include src/integrator_whfast512.h
+include src/integrator_saba.h
+include src/integrator_leapfrog.h
+include src/integrator_bs.h
+include src/integrator_sei.h
+include src/integrator_mercurius.h
+include src/integrator_trace.h
+include src/integrator_eos.h
+include src/integrator_janus.h
+include src/integrator.h
+include src/collision.h
+include src/boundary.h
+include src/gravity.h
+include src/server.h
+include src/frequency_analysis.h
+include src/tree.h
+include src/tree.c
+include src/tools.h
+include src/fmemopen.h
+include src/rotations.h
+include src/derivatives.h
+include src/particle.h
+include src/rebound.h
+include src/input.h
+include src/display.h
+include src/binarydiff.h
+include src/output.h
+include src/simulationarchive.h
+include src/transformations.h
+include src/transformations.c
+include README.md
+include LICENSE
+include version.txt
+include pyproject.toml
+recursive-include rebound/tests *.py
+include rebound/rebound.h
diff --git a/rebound/source/Makefile b/rebound/source/Makefile
new file mode 100644
index 0000000000000000000000000000000000000000..2e6d9a859f19857b963d12d61849d2f340509d3a
--- /dev/null
+++ b/rebound/source/Makefile
@@ -0,0 +1,16 @@
+# This Makefile compiles the shared dynamic library librebound.so
+include src/Makefile.defs
+
+librebound:
+ $(MAKE) -C src
+ @$(LINKORCOPYLIBREBOUNDMAIN)
+ @echo "To compile the example problems, go to a subdirectory of examples/ and execute make there."
+
+.PHONY: pythoncopy
+pythoncopy:
+ -cp librebound.so `python -c "import rebound; print(rebound.__libpath__)"`
+
+all: librebound pythoncopy
+
+clean:
+ $(MAKE) -C src clean
diff --git a/rebound/source/README.md b/rebound/source/README.md
new file mode 100644
index 0000000000000000000000000000000000000000..fca7b1db6319edccc5a89d69cb07795f3784ed98
--- /dev/null
+++ b/rebound/source/README.md
@@ -0,0 +1,149 @@
+[](https://rebound.hanno-rein.de)
+[](https://codecov.io/github/hannorein/rebound)
+[](https://badge.fury.io/py/rebound)
+[](https://github.com/hannorein/rebound/blob/main/LICENSE)
+[](https://arxiv.org/abs/1110.4876)
+[](https://arxiv.org/abs/1409.4779)
+[](https://arxiv.org/abs/1506.01084)
+[](https://arxiv.org/abs/1603.03424)
+[](https://arxiv.org/abs/1701.07423)
+[](https://arxiv.org/abs/1704.07715)
+[](https://arxiv.org/abs/1903.04972)
+[](https://arxiv.org/abs/1907.11335)
+[](https://rebound.hanno-rein.de/)
+[](https://mybinder.org/v2/gh/hannorein/rebound/main)
+[](https://github.com/hannorein/rebound/actions/workflows/c.yml)
+[](https://github.com/hannorein/rebound/actions/workflows/python.yml)
+
+
+# Welcome to REBOUND
+
+
+
+REBOUND is an N-body integrator, i.e. a software package that can integrate the motion of particles under the influence of gravity. The particles can represent stars, planets, moons, ring or dust particles. REBOUND is very flexible and can be customized to accurately and efficiently solve many problems in astrophysics.
+
+## Features
+
+* No dependencies on external libraries.
+* Runs natively on Linux, MacOS, and Windows.
+* Symplectic integrators WHFast, SEI, LEAPFROG, EOS.
+* Hybrid symplectic integrators for planetary dynamics with close encounters MERCURIUS
+* Hybrid reversible integrators for planetary dynamics with arbitrary close encounters TRACE
+* High order symplectic integrators for integrating planetary systems SABA, WH Kernel methods.
+* High accuracy non-symplectic integrator with adaptive time-stepping IAS15.
+* Can integrate arbitrary user-defined ODEs that are coupled to N-body dynamics for tides, spin, etc
+* Support for collisional/granular dynamics, various collision detection routines
+* The computationally intensive parts of the code are written entirely in C, conforming to the ISO standard C99, and can be used as a thread-safe shared library
+* Easy-to-use Python module, installation in 3 words: `pip install rebound`
+* Real-time, 3D visualization, for both C and Python.
+* Extensive set of example problems for both C and Python. You can run examples directly from your browser without the need to download or install anything.
+* Parallelized WHFast512 integrator for super fast integrations of planetary systems with SIMD AVX512 instructions
+* Parallelized with OpenMP (for shared memory systems)
+* Parallelized with MPI is supported for some special use cases only (using an essential tree for gravity and collisions)
+* The code is 100% open-source. All features are included in the public repository on github.
+
+## Try out REBOUND
+
+You can try out REBOUND without installing it.
+Simply head over to [the documentation](https://rebound.hanno-rein.de/).
+All the C examples have been compiled with emscripten and can run directly in your browser.
+
+## One minute installation
+
+You can install REBOUND with pip if you want to only use the python version of REBOUND:
+
+ pip install rebound
+
+Then, you can run a simple REBOUND simulation such as
+
+```python
+import rebound
+sim = rebound.Simulation()
+sim.add(m=1.0)
+sim.add(m=1.0e-3, a=1.0)
+sim.integrate(1000.)
+sim.status()
+```
+
+If you want to use the C version of REBOUND simply copy and paste this line into your terminal (it won't do anything bad, we promise):
+
+```bash
+git clone https://github.com/hannorein/rebound && cd rebound/examples/shearing_sheet && make && ./rebound
+```
+
+
+## Documentation
+The full documentation with many examples, changelogs and tutorials can be found at
+
+
+
+If you have trouble installing or using REBOUND, please open an issue on github and we'll try to help as much as we can.
+
+There are also short YouTube videos describing various aspects of REBOUND available at https://www.youtube.com/channel/UCNmrCzxcmWVTBwtDPPLxkkw .
+
+## Related projects
+
+### Additional physics
+To easily incorporate additional physics modules such as migration forces, GR effects and spin into your REBOUND simulations, see REBOUNDx at https://github.com/dtamayo/reboundx
+
+### Analytical and semianalytical tools
+If you're interested in comparing numerical simulations to analytical and semianalytical tools for celestial mechanics, see Celmech at https://github.com/shadden/celmech
+
+### Ephemeris-quality integrations of test particles
+To generate ephemeris-quality integrations of test particles in the Solar System with a precision on par with JPL's small body integrator, see ASSIST at https://github.com/matthewholman/assist
+
+## Papers
+
+There are several papers describing the functionality of REBOUND.
+
+1. Rein & Liu 2012 (Astronomy and Astrophysics, Volume 537, A128) describes the code structure and the main feature including the gravity and collision routines for many particle systems.
+
+2. Rein & Tremaine 2011 (Monthly Notices of the Royal Astronomical Society, Volume 415, Issue 4, pp. 3168-3176) describes the Symplectic Epicycle integrator for shearing sheet simulations.
+
+3. Rein & Spiegel 2015 (Monthly Notices of the Royal Astronomical Society, Volume 446, Issue 2, p.1424-1437) describes the versatile high order integrator IAS15 which is now part of REBOUND.
+
+4. Rein & Tamayo 2015 (Monthly Notices of the Royal Astronomical Society, Volume 452, Issue 1, p.376-388) describes WHFast, the fast and unbiased implementation of a symplectic Wisdom-Holman integrator for long term gravitational simulations.
+
+5. Rein & Tamayo 2016 (Monthly Notices of the Royal Astronomical Society, Volume 459, Issue 3, p.2275-2285) develop the framework for second order variational equations.
+
+6. Rein & Tamayo 2017 (Monthly Notices of the Royal Astronomical Society, Volume 467, Issue 2, p.2377-2383) describes the Simulationarchive for exact reproducibility of N-body simulations.
+
+7. Rein & Tamayo 2018 (Monthly Notices of the Royal Astronomical Society, Volume 473, Issue 3, p.3351–3357) describes the integer based JANUS integrator.
+
+8. Rein, Hernandez, Tamayo, Brown, Eckels, Holmes, Lau, Leblanc & Silburt 2019 (Monthly Notices of the Royal Astronomical Society, Volume 485, Issue 4, p.5490-5497) describes the hybrid symplectic integrator MERCURIUS.
+
+9. Rein, Tamayo & Brown 2019 (Monthly Notices of the Royal Astronomical Society, Volume 489, Issue 4, November 2019, Pages 4632-4640) describes the implementation of the high order symplectic integrators SABA, SABAC, SABACL, WHCKL, WHCKM, and WHCKC.
+
+## Acknowledgments
+
+If you use this code or parts of this code for results presented in a scientific publication, we would greatly appreciate a citation.
+The simplest way to find the citations relevant to the specific setup of your REBOUND simulation is:
+
+```python
+sim = rebound.Simulation()
+-your setup-
+sim.cite()
+```
+
+
+## Contributors
+
+* Hanno Rein, University of Toronto,
+* Dan Tamayo, Harvey Mudd College,
+* David S. Spiegel, Institute for Advanced Study Princeton,
+* Garett Brown, University of Toronto,
+* Shangfei Liu, Kavli Institute for Astronomy and Astrophysics at Peking University,
+* Ari Silburt, Penn State University,
+* and many others! Check the git history to find out who contributed to the code.
+
+REBOUND is open source and you are invited to contribute to this project!
+
+
+## License
+
+REBOUND is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
+
+REBOUND is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along with REBOUND. If not, see .
+
diff --git a/rebound/source/__init__.py b/rebound/source/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..de364825e6c101ae263af6edd57c418c345fa281
--- /dev/null
+++ b/rebound/source/__init__.py
@@ -0,0 +1,4 @@
+# -*- coding: utf-8 -*-
+"""
+rebound Project Package Initialization File
+"""
diff --git a/rebound/source/changelog.md b/rebound/source/changelog.md
new file mode 100644
index 0000000000000000000000000000000000000000..0b48b43609ff6a244333ec24384f0aea4f25f69a
--- /dev/null
+++ b/rebound/source/changelog.md
@@ -0,0 +1,589 @@
+# Changelog
+
+This changelog only includes the most important changes in recent updates. For a full log of all changes, please refer to git.
+
+## Version 4.x
+
+### Version 4.5.1
+* Added leapfrog integrators of order 4, 6, and 8. Order can be set with `r->ri_leapfrog->order`.
+* Heartbeat function is now also called when using `reb_simulation_steps()`.
+* OrbitPlot supports more colours.
+* Fixed an alignment issue when comparing binary snapshots which could have triggered a segfault.
+
+### Version 4.5.0
+* Added support for (Frequency) Modified Fourier Transforms. Heavily based on David Nesvorny's code. The new functions are `reb_frequency_analysis()` in C and `rebound.frequency_analysis()` in python. For usage, see C examples `secular_frequencies` and `frequency_analysis` as well as the iPython notebook `FrequencyAnalysis`.
+* Support for Jacobi coordinates added when using WHFast with OpenMP.
+* Allow negative periods when initializing hyperbolic orbits.
+
+### Version 4.4.11
+* The collision resolve function now returns a type `enum REB_COLLISION_RESOLVE_OUTCOME`. The actual integer values remain unchanged.
+* Bug in TRACE was fixed.
+* Convergence check for M_to_E function.
+* New API example that shows how to use the Kepler solver without a REBOUND simulation. Updated other examples.
+
+### Version 4.4.10
+* Version bump to rerun github workflows for pypi uploads
+
+### Version 4.4.9
+* Fixes a bug that affected collisions searches with a tree code.
+* Support for mid-timestep add/remove of particles with TRACE.
+* Various small improvements and bugfixes for TRACE.
+* IAS15's `adaptive_mode` is now an ENUM.
+* Some OpenMP improvements.
+
+### Version 4.4.8
+* Added support for symplectic correctors with barycentric coordinates in WHFast.
+
+### Version 4.4.7
+* Added option to disable SSL checks for Horizon queries with `rebound.horizons.SSL_CONTEXT = 'unverified'.`
+* Added unit tests.
+* Added barycentric coordinates for WHFast.
+* Bug fix for when MEGNO is used with adaptive timestepping.
+* Added more error messages.
+* Fixed various issues in documentation.
+
+### Version 4.4.6
+* When initializing particles with "uniform" in python, REBOUND now uses its own `reb_random_uniform()` function. This avoids importing the "random" library and makes results reproducible as the random seed of the simulation is used when generating random numbers.
+* More cracefull interrupt handling. REBOUND now stop the integration after the next timestep when CTRL-C is pressed the first time. If CTRL-C s pressed twice, then long loops (during gravity, collision calculations) are terminated immediately. Continuing an integration after one CTRL-C press should be easier with this change as the simulation does not get corrupted.
+* Fixed typos in documentation.
+
+### Version 4.4.5
+* Version updated to test github workflows
+
+### Version 4.4.4
+* Fixed several memory leaks and other memory issues. It is unlikely that any of those bugs did affect an simulation.
+* When converting units of a particle, the particle radius is now also converted.
+* Added getter/setters for Pal coordinates to the particle structure in python. Syntax is `sim.particles[1].pal_h`, `sim.particles[1].pal_ix`, etc.
+
+### Version 4.4.3
+* REBOUND now raises ImportError if it detects a size mismatch between the C and python Simulation structures.
+* Fixes a bug in the WHFast512 synchronization on non-AVX512 systems.
+* Fixes a bug in the SimulationArchive in cases where there are multiple snapshots with t=0.
+* Updates TRACE switching condition to match Lu et al (2024).
+* TRACE binary file size has been reduced.
+* Pericenter passage time is now calculated even if particles are not in a Simulation.
+
+### Version 4.4.2
+* Fixed bug in TRACE when adding particles.
+* Added WHFast fallback for synchronizing WHFast512 simulations with `N_systems` > 1.
+* Output version number used to create Simulationarchive if there is a version mismatch.
+* Added C example `simulationarchive_fields` which outputs all fields in a simulationarchive for debugging purposes.
+
+### Version 4.4.1
+* Fixed bug in TRACE for FULL PERI modes.
+
+### Version 4.4.0
+* Added TRACE integrator. See Lu, Hernandez & Rein (2024) for details on this implementation.
+
+### Version 4.3.2
+* No longer clipping particles and orbits in visualization.
+* Added a scale to visualization. Hide by pressing `t`.
+* Option to take a screenshow manually in png (WebGL) or tga (OpenGL) format by pressing `e`.
+* Improved `plane` visualization mode. Now supporting hyperbolic orbits.
+* Fixed a memory leak in `reb_simulation_copy`.
+
+### Version 4.3.1
+* Added new `plane` visualization mode for orbits. Press `w` to toggle through available orbit visualization modes.
+* Added python interface for screenshot API.
+* Fixed an issue where no python exception was raised when a particle was added outside a simulation box.
+* Renamed `past_N` to breadcrumbs in visualization module.
+
+### Version 4.3.0
+* Take screenshots of WebGL based visualizations using the `reb_simulation_output_screenshot()` function. You need to connect one web browser to the simulation in order to take screenshots.
+* Improved synchronization of visualization and simulation on Windows with mutex.
+* Fixes an issue that might lead to NaN values when less than the maximum number of planets are used in WHFast512.
+
+### Version 4.2.0
+* It is now possible to programmatically change all aspects of a REBOUND visualization. This can be used to set up default viewing options or to render animations. See the C examples in `animation_solar_system` and `animation_saturn_rings`.
+* Reworked matrix operations in visualization routines to follow the Model-View-Projection paradigm.
+* Fixed an issues where unit tests would fail because a binary file was not deleted.
+
+### Version 4.1.1
+* Fixed python wheels for windows.
+
+### Version 4.1.0
+* New visualization feature that allows you to show past particle positions and orbits (keyboard commands p, u, and i).
+* After pausing a simulation, you can now advance it by a single timestep by pressing the down arrow or 50 timesteps by pressing the page down key.
+* Visualization now supports scroll to zoom.
+* Fixed memory leaks when using custom ODEs.
+* Fixed broken links in documentations.
+
+### Version 4.0.3
+* Default IAS15 timestepping criterion is now `adaptive_mode=2`. See Pham, Rein, and Spiegel (2024) for details. To use the old default timestepping criterion, set `adaptive_mode=1`.
+* Fixed a race condition that should improve the responsiveness of web based visualizations.
+* Removed the glad dependency from emscripten builds which reduces filesize and improves performance.
+
+### Version 4.0.2
+* Fixes an issue where the default Makefiles included white spaces after the SERVER and OPENGL variable definitions. This caused the main Makefile to ignore these settings.
+* Added `key_callback` function for customizing user interaction in visualizations.
+* Added `simulationarchive_viewer` example.
+* Included `-sGL_ENABLE_GET_PROC_ADDRESS` flag that is now needed for the latest version of emscripten.
+
+### Version 4.0.1
+* Include missing python packages
+
+### Version 4.0.0
+* Major API changes and new features! If you have used a previous version of REBOUND, then you will need to update your code. If you have trouble with the migration, open a GitHub issue!
+* Many function and variable names have changed. They now follow a coherent naming convention. See the naming convention section in the documentation for more information.
+* New visualization module! Previously, using OpenGL visualization required the GLFW library which led to problems on various operating systems. The new visualization module no longer requires ANY dependencies and is compatible with MacOS, Linux, and Windows. It works by running a local web server to which you can point your browser to. In your web browser, an emscripten compiled version of REBOUND handles the WebGL visualization while constantly updating simulation data over HTTP. You can use ssh and port forwarding to visualize simulations on remote servers. Check out the documentation for more details on this new module.
+* OpenGL for all the examples has been turned off by default so that new users don't get stuck at this step. To turn on OPENGL simply change the flag in the Makefile.
+* Added emscripten support. All C examples (including those using visualizations) are now automatically compiled with emscripten on readthedocs.org so you can run from within the browser. No download or installation required.
+* A race condition in OpenGL visualization has been removed. Visualizations run much smoother.
+* `reb_random` functions now callable with `r=NULL`. If `r=NULL` then the time and PID is used as a seed.
+* Removed support for Simulationarchives with version 2. Added some additional support for reading corrupt/old archives.
+* Fixed memory leak in `reb_simulation_copy`.
+* Consistent integer sizes for 32/64bit. This includes padding for `reb_particle` which is stored in the Simulationarchive.
+
+
+## Version 3.x
+
+### Version 3.28.4
+* WHFast512 now support the integration of 2 and 4 planet systems in parallel. Providing a speed up of up to 10x.
+* The sqrt7 function used by IAS15 now support a wider range of input arguments.
+
+### Version 3.28.3
+* Removed distutils requirement in preparation for python 3.12.
+* Removed rebound.InterruptiblePool as it no longer works with recent python version. Updated examples.
+* Added Holmberg example.
+* Added `adaptive_mode==3` for IAS15 (Aarseth 1985).
+
+### Version 3.28.2
+* Implemented own fmemopen implementation on MacOS. This is mainly to appease conda-forge builds.
+* Improved sqrt7 algorithm allows larger convergence interval.
+
+### Version 3.28.1
+* Improved support for reading old and corrupted Simulationarchives.
+* Renamed `ri_ias15.epsilon_global` to `ri_ias15.adaptive_mode`.
+* Added new timestep method for IAS15 `ri_ias15.adaptive_mode = 2`. This is experimental for now. Details to be described in Pham, Rein & Spiegel (in prep).
+* Added unit tests to check for fused multiply add instruction (these break reproducibility).
+* Added phony target in C Makefile to force rebuilding librebound whenever building examples.
+
+### Version 3.28.0
+- Native Windows support. REBOUND can now be built natively on Windows (without WSL) using the Microsoft Visual Studio Compiler.
+- Python Wheels are now provided for Linux, MacOS, and Windows. This should significantly speed up the installation process on a wide variety of systems.
+
+### Version 3.27.0
+* In python, Simulation and Particle objects are now picklable. Just like loading Simulations from a binary file, function pointers will need to be re-set manually after unpickling.
+* The difference between simulations can now be printed out in a human readable form. Python syntax: `sim.diff(sim2)`. C syntax: `reb_simulation_diff(sim2, sim1, 1)`.
+* Reading Simulationarchives with version < 2 is no longer supported.
+* The POSIX function fmemopen() is now required to compile REBOUND. This should not affect many users. However, if you are using macOS, the version needs to be >= 10.13 (this version of macOS, High Sierra, was released in 2017).
+* Internal changes on how Simulationarchives are written.
+* Internal variable names that represent the size of allocated buffers now consistently include the name `N_allocated`.
+* The TES (Terrestrial Exoplanet Integrator) has been removed. If you wish to use TES, you will need checkout an earlier version.
+
+### Version 3.26.3
+* A few more changes to reduce the number of compiler warnings. This should not affect any calculation.
+
+### Version 3.26.2
+* Fixed various signed/unsigned int issues. This should reduce the number of compiler warnings but not affect any calculation.
+
+### Version 3.26.1
+* Added support for `AVX512` and `FFP_CONTRACT_OFF` environment variables when using pip to install REBOUND.
+
+### Version 3.26.0
+* Added WHFast512 integrator (Javaheri, Rein, Tamayo 2023)
+
+### Version 3.25.1
+* Bug fixed that prevented the installation via PyPi
+
+### Version 3.25.0
+* MPI parts updated and unit tests added
+* Fixed machine independence bug in TES.
+
+### Version 3.24.3
+* Updated unit tests so they work on 32bit machines
+
+### Version 3.24.2
+* Fixed bug in TES ctypes structure
+
+### Version 3.24.1
+* Added CORS proxy for Horizons request in pyodide
+* Smoother OpenGL animations when using usleep
+* TES calculates orbital period automatically
+
+### Version 3.24.0
+* Added support for Simulationarchive larger than 4 GB.
+* Updated documentation for Lyapunov characteristic number.
+
+### Version 3.23.5
+* Added new units shortcuts (year,years,massist)
+* Rearranged some loops and switch statements (doesn't affect floating point numbers).
+
+### Version 3.23.4
+* Added pyproject.toml file
+
+### Version 3.23.3
+* Changed the way REBOUND reverses the integration direction when the sign of the timestep is inconsistent with respect to the requested final time.
+* Fixes a memory leak when a tree code is used
+* Fixes an issue where MERCURIUS was not bit-wise reproducible when safe mode was turned off.
+
+### Version 3.23.2
+* Minor changes to the python side of Vec3d to make it more compatible with numpy.
+
+### Version 3.23.1
+* Minor changes related to the REBOUND Rotations framework.
+
+### Version 3.23.0
+* Added the REBOUND Rotations framework.
+* Fixes an issue with showing an incorrect periastron location in OrbitPlot for high mass-ratio systems.
+* Adds pre and post timestep calls to the ode framework.
+
+### Version 3.22.0
+* OrbitPlot is now a class. Checkout the OrbitPlot.ipynb tutorial. This change allows for interactive plots and much faster updates to existing plots. This is great for rendering animations!
+
+### Version 3.21.0
+* Automatic rescaling of first order variational particles has been added. This will allow you to integrate chaotic systems for longer and obtain a more accruate measure of MEGNO and the Lyapunoc exponent.
+* Added `sim.stop()` / `reb_simulation_stop()` to end an integration from within the heartbeat function.
+
+### Version 3.20.1
+* Pal coordinates have been added to the `reb_orbit` struct.
+
+### Version 3.20.0
+* A new integrator has been added, the Terrestrial Exoplanet Simulation (TES).
+
+### Version 3.19.10
+* Fixes another bug int he BS integrator when additional forces are used.
+
+### Version 3.19.9
+* Two bugs fixed in the BS integrator. One was related to unitialized memory and the other to issues when the particle number changed.
+
+### Version 3.19.5
+* Workaround for urllib support in pyodide added
+* Silent warning when InterruptiblePool is not available
+
+### Version 3.19.4
+* InterruptiblePool is optional.
+* Fixed an issue that occured when switching integrators while using the Simulationarchive.
+* Renamed `srand_seed` to make it user accessible.
+
+### Version 3.19.3
+* Added several examples.
+* Changed how pypi is rendering the documentation.
+
+### Version 3.19.2
+* Fixes a bug relates to test particles of type 0 in MERCURIUS.
+
+### Version 3.19.1
+* Some compilers seem to complain that a constant cannot be initialized from a constant. Fixed this so that REBOUND works on colaboratory.
+
+### Version 3.19.0
+* Added a Gragg-Bulirsch-Stoer integrator (short BS for Bulirsch-Stoer). This is an adaptive integrator which uses Richardson extrapolation and the modified midpoint method to obtain solutions to ordinary differential equations. The version in REBOUND is based on the method described in Hairer, Norsett, and Wanner 1993 (see section II.9, page 224ff).
+* Added the ability to integrate arbitrary ordinary differential equations with REBOUND. The ODEs can be couple to the N-body simulation. This can be used to simulate spin, tides, and other physical effects. The user-defined ODEs are integrated with the new BS integrator.
+
+### Version 3.18.1
+* Various improvements and fixes relates to NASA Horizons: small bodies are retrieved correctly, the dates now work with fractional JD values and dates in the format YYYY-MM-DD HH:MM:SS are now supported.
+
+### Version 3.18.0
+* Fixes an issue in the Simulationarchive that prevented REBOUND from seeing more than one snapshot. This only affected simulations with a large number of particles.
+
+### Version 3.17.5
+* REBOUND will now uses the new HTTP API from NASA Horizons. This is significantly faster than the old telnet version. Thanks to Lukas Winkler for implementing this.
+
+### Version 3.17.4
+* REBOUND will now attempt to recover binary files and Simulationarchives which have been corrupted. Simulations can be restarted from corrupt files and in most cases the corrupt files will fix themselves.
+
+### Version 3.17.3
+* Allow for Horizon queries with future JD dates.
+
+### Version 3.17.2
+* Moved some function declarations to rebound.h. This is a temporary fix for REBOUNDx.
+
+### Version 3.17.1
+* Fixed an issue where the simulation struct in python did not match the one in C. This might have lead to unexpected behaviour in rare cases.
+* Fixed various typos in the documentation
+* MERCURIUS switching functions can now be set from Python. Also inluded more built-in switching functions from Hernandez (2019).
+
+### Version 3.17.0
+* Added new 'reb_simulation_add_fmt()' function. This makes adding particles in C as easy as in python.
+* Orbits can now also be initialized using the eccentric anomaly.
+* Fixed an issue which prevented one loop in the gravity routine form being parallelized with OpenMP.
+* Added a warning message when test particles have finite mass.
+* More reliable reading of corrupt Simulationarchive files.
+
+### Version 3.16.0
+* MERCURIUS: If encounters only involve test-particles (type 0), then the algorithm is now resetting the coordinates of all massive particles after the encounter step. This only changes the outcome at the machine precision, but it makes the trajectories of massive particles independent of the close encounter history. Thanks to Kat Deck for this feature!
+* MERCURIUS: The gravity routine is now $O(0.5 \cdot N^2)$ instead of $O(N^2)$ for non-OPENMP runs. This should lead to a noticable improvement in runtime.
+
+### Version 3.15.0
+* Orbital parameters of particles can now be changed in-place. For example: 'sim.particles[1].e += 0.1'.
+* Implemented more chatty repr functions for most object. Printing REBOUND objects should now give some useful information.
+* Improved support for adding/removing particle in MERCURIUS during collisions.
+* REBOUND now outputs an error message when one is trying to remove a particle with a negative index.
+* Small updates to the documentation.
+* New ipython example added, showing how to use a python collision resolve function.
+
+### Version 3.14.0
+* Due to a bug, WHFast was not thread-safe. It is now.
+* Random number generator seed is now stored in the Simulationarchive.
+ This allows you to get reproducible random number even after restarting a simulation.
+* Random numbers generated with the `reb_rand_*()` functions were not thread-safe.
+ They are thread-safe now. Note that this required an API change. All `reb_rand_*()`
+ functions now require the simulation structure as an argument. This is because the
+ random number generator seed is now stored in the simulation structure.
+
+### Version 3.13.2
+* Correct handling of test particles in reb_transformations.
+* Small bug fixes
+
+### Version 3.13.1
+* WHFast: Fixes multiple issues with testparticles in WHFast.
+
+### Version 3.13.0
+* IAS15: Fixes a bug which leads to a biased energy error in long term integrations with fixed timesteps (see Hernandez and Holman 2020). The old version of IAS15 can still be used for the time being by setting ri_ias15.neworder=0.
+* IAS15: Does not take variational particles into account when predicting new timesteps. This should be beneficial during close encounters.
+* A few improvements have been made to the Simulationarchives code including a more efficient loading procedure for large datasets.
+
+### Version 3.12.3
+* Various small bug fixes
+* Added a new function sim.cite() to automatically generate citations depending on the current simulation settings.
+
+### Version 3.12.2
+* Various bug fixes to MERCURIUS
+* Performance increase when using the BASIC Gravity Routine with OpenMP
+
+### Version 3.12.1
+* Bug fixes to LINE and LINETREE algorithms
+
+### Version 3.12.0
+* Added LINETREE collision search algorithm.
+ This algorithm uses a tree to check if any two particle trajectories overlapped during the last timestep. This
+ should be beneficial in large N, low density situation as it allows for much larger timesteps. A modification of the
+ collision resolve routine might be necessary to allow for multiple collisions of the same particle during one timestep.
+ This depends on the application and the default is to only allow one collision per timestep.
+
+### Version 3.11.1
+* Added support for test particles and first-order variational particles to the Embedded Operator Splitting (EOS).
+* BASIC Gravity routine changed from O(N^2) to O(0.5 N^2). This should lead to a speed-up in most cases but will break bit-wise reproducibility from earlier versions as the ordering of floating point operations has changed.
+
+### Version 3.11.0
+* This version adds the new Embedded Operator Splitting methods from Rein (2019). See the tutorial in the ipython_examples folder for how to use them.
+
+### Version 3.10.2
+* Updates to OrbitPlot. Includes better layout of plot and some syntax changes. See OrbitPlot documentation for the new syntax.
+
+### Version 3.10.1
+* Small syntax changes for SABA integrator family.
+* Includes high order integrators by Blanes et al. (2013).
+
+### Version 3.10.0
+* Changes for the new version of REBOUNDx.
+
+### Version 3.9.0
+* Added new high order symplectic integrators from Wisdom et al. (1996) and Laskar & Robutel (2001). The implementation of these integrators are discussed in Rein, Tamayo & Brown (2019).
+* Implemented new bit-wise comparison functions for simulations. Python syntax is simply sim1==sim2.
+* Fixed a bug in IAS15 which prevented a restarted simulation to reproduce the original simulation exactly.
+
+### Version 3.8.3
+* Improves and fixes various issues related to variational equations and MEGNO.
+
+### Version 3.8.2
+* Fixes a bug which resulted in duplicate snapshots in Simulationarchives when restarting simulations.
+
+### Version 3.8.1
+* Syntax change on the python side to create a simulation from a binary file or Simulationarchive:
+
+ ```python
+ rebound.Simulation.from_file("test.bin") becomes rebound.Simulation("test.bin")
+ rebound.Simulation.from_archive("test.bin",5) becomes rebound.Simulation("test.bin",5)
+ ```
+
+### Version 3.8.0
+* The hybrid integrator MERCURIUS has been completely rewritten. It can now much more easily be used in simulations where physical collisions occur. There are no more hidden particle arrays in the background, meaning adding and removing particles can occur in the same way as for other integrators. It also works reliably with any additional forces.
+* The old hybrid integrator HERMES has been removed. MERCURIUS should always be equal or better in performance and accuracy.
+
+### Version 3.7.1
+* Added getBezierPaths to Simulationarchive to allow for easy plotting of complicated trajectories. To do this, store a lot of snapshots in the Simulationarchive (several per orbit!).
+* Added functionality to add, subtract, multiply and divide simulations. This might be useful when developing new algorithms, but is most likely not useful for most users.
+
+### Version 3.7.0
+* Added a deep copy functionality: reb_simulation_copy() in C, and sim.copy() in python.
+* Refactored WHFast to enable calling only certain substeps.
+
+### Version 3.6.8
+* Added the rhill property to reb_orbit in C and the Orbit and Particle classes in Python. This parameter corresponds to the circular Hill radius of the particle: $ a (m/(3M)^{1/3}$.
+
+### Version 3.6.7
+* Fixes an issue related to collisions and the Mercurius integrator that prevented the last_collision property to be updated.
+
+### Version 3.6.6
+* New: Fancy plotting routine. Usage: rebound.OrbitPlot(sim, fancy=True)
+
+### Version 3.6.5
+* One can now add particles from NASA Horizons using Julian Days. For example: sim.add("Earth", date="JD2458327.500000")
+
+### Version 3.6.4
+* Fixes a memory leak when using the old Simulationarchive version. Thanks to Ian Rabago for reporting the issue.
+
+### Version 3.6.2
+* Fixes a memory leak in the Simulationarchive read function.
+
+### Version 3.6.1
+* Removed function calls to open_memstream and fmemopen which might not work on older Mac OSX versions. This only affects the internals and there are no changes to user interface.
+* Minor bug fixes
+
+### Version 3.6.0
+* Simulationarchive Version 2. With the new version of the Simulationarchive file format, you can now create snapshots of your simulations without any restrictions. You can change the number of particles, the timestep, even the integrator used during the integration. REBOUND automatically detects what has changed and only stores the differences in incremental snaphots. This reduces the filesize while keeping the format as flexible as possible. The old Simulationarchive Version 1 is still supported for now but might become deprecated in the future. All examples have been updated. As usual these are as usual good starting points for understanding the functionality and the syntax.
+
+### Version 3.5.12
+* Added REB_COLLISION_LINE. This is a collision detection routine which serves for collisions during the last timestep, assuming that all particles travel along straight lines. This can be useful in cases where not every collision needs to be detected exactly, but the overall collision rate should be reproduced. The algorithm is O(N**2).
+* Bug related to N_active and variational particles has been fixed.
+* A bug where WHFast might not converge in rare cases involving negative timesteps has been fixed.
+
+### Version 3.5.11
+* Changed default collision behaviour from hardsphere bouncing to halting the simulation. An exception is raised when using the python version. In C, you need to check the status flag after integrating the simulation.
+
+### Version 3.5.10
+* Refactored OrbitPlot.
+
+### Version 3.5.9
+* SIGINT handler added. Allows for garceful exit and keyboard interrupts (even from python).
+
+### Version 3.5.8
+* WebGL widget text overlay added.
+
+### Version 3.5.7
+* Bug fixes related to WebGL widget and ipywidgets version 6
+
+### Version 3.5.6
+* Updated WebGL widget to work with ipywidgets version 7
+
+### Version 3.5.5
+* Various fixed for Mercurius
+
+### Version 3.5.4
+* Bug fix for N_active=-1 (default)
+
+### Version 3.5.3
+* Allow for better parallelization of WHFast with OpenMP.
+* Addded example of the Solar System with Testparticles.
+* Made simulationarchive_append a public function (might be useful for some hacking projects).
+
+### Version 3.5.2
+* Fixes an issue with the WebGL widget.
+* Fixes an issue with external forces and MERCURIUS.
+
+### Version 3.5.1
+* MERCURIUS is not compatible with binary files and the Simulationarchive.
+
+### Version 3.5.0
+* The WHFast integrator now supports Jacobi coordinates (default), democratic heliocentric coordinates and WHDS coordinates. The previously separate WHFastHelio integrator has been removed. The coordinate system can now be changed by simply setting the coordinates flag in the ri_whfast struct.
+* Included an experimental new integrator MERCURIUS. This is similar to the hybrid integrator in Mercury but uses WHFast and IAS15. Not ready for production yet.
+
+### Version 3.4.0
+* Added a screenshot functionality for the WebGL ipython widget. This lets you take screenshots programmatically which is useful to create movies of simulations.
+
+### Version 3.3.1
+* Removed the march=native compiler flag as it seems to be problematic for some OSX/Sierra compilers.
+
+### Version 3.3.0
+* JANUS integrator added. This is a bit-wise reversible high-order symplectic integrator. At this time, it remains experimental. Details about this integrator will be published in an upcoming paper.
+
+### Version 3.2.4
+* Changes to the WHFastHelio integrator. This integrator now uses democratic heliocentric coordinates and a Hamiltonian splitted as proposed by Hernandez and Dehnen (2017), WHDS, which splits the Hamiltonian into three parts. It has the advantage that the integrator solves the two body problem exactly. It is not compatible with symplectic correctors, this functionality has been removed for WHFastHelio. For very high accuracy integrations of stable planetary systems, the WHFast integrator in Jacobi coordinated (and potentially symplectic correctors) should be better suited.
+
+### Version 3.2.3
+* Various minor bug fixes. Added pre-timestep modifications for REBOUNDx.
+
+### Version 3.2.2
+* Various minor bug fixes. One related to exact_finish_time=1.
+
+### Version 3.2.0
+* Added real-time interactive 3D visualizations using WebGL for Jupyter notebooks. This is an early release. Not everything might be working yet and new feature will be added to the widget class. To try it out, simply run `sim.widget()` in a Jupyter notebook. Note that you need to have ipywidgets installed and enabled.
+* Minor changes to the Visualization backend. This should not have any consequences for users.
+
+
+### Version 3.1.1
+* Now stores the first characters of the current githash in binary files. This is helpful when trying to restart simulations from a binary file and making sure one uses the same version of REBOUND than in the original run. Currently, the git hash is not automatically compared when reloading a binary file. To view the githash, use e.g. hexdump. The hash appears between the first and second zero character in the first 64 bytes of the file.
+
+### Version 3.1.0
+* Updated visualization. REBOUND now uses a modern version of OpenGL (3.3) that allows for custom shaders and therefore better looking visualizations. However, REBOUND now requires glfw3 to compile the visualization module. If you are on a Mac, then the easiest way to install the glfw3 library is with homebrew: `brew tap homebrew/versions && brew install glfw3`. If you are on Linux, you can install it with your package manager, for example with `sudo apt-get install libglfw3-dev`.
+
+### Version 3.0.0
+* Introducing the Simulationarchive. The Simulationarchive allows for exact (bit-by-bit) reproducibility in N-body simulations and a completely new way of analyzing simulations. See Rein&Tamayo (2017) for details.
+* The binary format has changed. Binary files created with an earlier version of REBOUND can not be loaded with this version. However, future binary files will be backwards compatible from this point forward.
+
+
+## Version 2.x
+### Version 2.20.6
+* Minor bug fixes in HERMES integrator and some examples.
+
+### Version 2.20.5
+* NASA Horizons changed a telnet command. This update implements those changes and restores access to NASA Horizons from within REBOUND.
+
+### Version 2.20.4
+* Improvements to the Kepler solver. This is typically only relevant for extremly long simulation (1e11 timesteps or more) and extremely accurate simulation with symplectic correctors and a relative energy error of less than 1e-10.
+
+### Version 2.20.3
+* Small changes to HERMES integrator. It now has a Solar Switch Factor SSF to allow for close encounters with the central object.
+
+### Version 2.20.2
+* Added adaptive HSF for HERMES integrator. More documentation and paper to follow.
+
+### Version 2.20.1
+* Added symplectic correctors for WHFastHelio integrator. See Wisdom (2006).
+* Improved accuracy of symplectic corrector coefficients for WHFast and WHFastHelio.
+
+### Version 2.20.0
+* Added new WHFastHelio integrator. This integrator uses the WHFast Kepler solver, but uses democratic heliocentric coordinates (WHFast itself uses Jacobi coordinates). Heliocentric coordinates are advantages if planets swap positions.
+
+### Version 2.19.2
+* Changes to how particle hashes are handled.
+
+### Version 2.19.1
+* This version removes the old SWIFTER based Wisdom-Holman routine, INTEGRATOR_WH. It wasn't working correctly for a while and the WHFast (INTEGRATOR_WHFAST) should be superior in any possible case we can think of.
+
+### Version 2.19.0
+* Added warning/error message system. This allows warning messages to be shown directly in iPython/python programs, rather than being shown on the console. To hide the warning messages, use a filter, e.g.
+.. code:: python
+
+ with warnings.catch_warnings(record=True) as w:
+ warnings.simplefilter("always")
+ # Execute a command which triggers a warning message.
+ # The message will not show up.
+* Improvements regarding the WHFast logic for hyperbolic orbis. No changes should be noticeable to users.
+
+### Version 2.18.9
+* Added the reb_simulation_get_serialized_particle_data function for fast access to particle data via numpy array. The full syntax is explained in the documentation. Here is a short example:
+.. code:: python
+
+ import numpy as np
+ a = np.zeros((sim.N,3),dtype="float64")
+ sim.serialize_particle_data(xyz=a)
+ print(a)
+
+
+### Version 2.18.5
+* When loading a simulation from a binary file, REBOUND now checks if the version of the binary file is the same as the current version.
+* When saving a simulation to a binary file, all the auxiliary arrays for IAS15 are now stored. This allows for bit-by-bit reproducibility in simulations that are making use of checkpoints.
+
+
+### Version 2.18.0
+* We replaced the old HYBRID integrator with the new and better HERMES integrator. Details of the HERMES integrator will be explained in an upcoming paper Silburt et al (2016, in prep).
+
+### Version 2.17.0
+* What used to be called ``id`` in the particle structure is now called ``hash``. This can be used to uniquely identify particles in a simulation. In many cases, one can just identify particles by their position in the particle array, e.g. using ``sim.particles[5]``. However, in cases where particles might get reordered in the particle array (e.g. when using a tree code), when particles can merge (by using the ``collision_resolve_merge`` routine), or when particles get added or removed manually.
+* The syntax is as follows:
+.. code:: python
+
+ sim = rebound.Simulation()
+ sim.add(m=1)
+ sim.add(m=1e-3,a=1)
+ # Setting a hash using a string:
+ sim.particles[1].hash = "planet1"
+ # Finding a particle using a string:
+ p = sim.get_particle_by_hash("planet1")
+ # Setting a random unique hash:
+ sim.particles[1].hash = sim.generate_unique_hash()
+ # Save unique hash to find particle later
+ uhash = sim.particles[1].hash
+ # Find particle using the hash
+ p = sim.get_particle_by_hash(uhash)
+
+
+
+### Version 2.0.0
+* We made many changes to the code. Most importantly, REBOUND is now thread-safe and does not use global variables anymore. All the variables that were previously global, are now contained in the ``reb_simulation`` structure. This has many advantages, for example, you can run separate simulations in parallel from within one process.
+* We also made it possible to choose all modules at runtime (compared to the selection in the ``Makefile`` that was used before). This is much more in line with standard UNIX coding practice and does not severely impact performance (it might even help making REBOUND a tiny bit faster). This makes REBOUND a fully functional shared library. We added a prefix to all public functions and struct definitions: ``reb_``.
+* There are still some features that haven't been fully ported. Most importantly, the MPI parallelization and the SWEEP collision detection routine.
+* The best way to get an idea of the changes we made is to look at some of the example problems and the new REBOUND documentation. If you have trouble using the new version or find a bug, please submit an issue or a pull request on github.
+
diff --git a/rebound/source/docs/addingparticles.md b/rebound/source/docs/addingparticles.md
new file mode 100644
index 0000000000000000000000000000000000000000..0679acded8f7a9bbaa38c1843ccc5acc1836b202
--- /dev/null
+++ b/rebound/source/docs/addingparticles.md
@@ -0,0 +1,169 @@
+# Adding particles
+
+
+
+Once you've created a [simulation object](simulation.md), you can add particles to it.
+REBOUND supports several different ways to do that.
+Also check out the [discussion on particle operators](particleoperators.md).
+
+## Adding particles manually
+One way to add a particle to a simulation is to first manually create a particle object, then calling a function to add the particle to the simulation.
+Because the function will make a copy of the particle, you can safely delete the original particle object after you've added it to a simulation.
+The following code shows an example on how to add particles this way:
+
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ struct reb_particle p = {0};
+ p.m = 1.;
+ p.x = 1.;
+ reb_simulation_add(r, p);
+ ```
+ !!! Important
+ The `= {0}` syntax above ensures that the struct is initialized with zeros.
+ Otherwise, you need to set every member of the struct to ensure that there are no
+ uninitialized values.
+
+
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ p = rebound.Particle()
+ p.m = 1.
+ p.x = 1.
+ sim.add(p)
+ ```
+
+You can also use orbital parameters to initialize the particle object.
+=== "C"
+ In C, this is done by calling the `reb_particle_from_orbit` function. Its arguments are gravitational constant, primary object, mass, semi-major axis, eccentricity, inclination, longitude of ascending node, argument of pericenter, and true anomaly.
+ It returns an initialized particle object which you can then add to the simulation.
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ struct reb_particle primary = {0};
+ primary.m = 1;
+ reb_simulation_add(r, primary);
+ struct reb_particle planet = reb_particle_from_orbit(r->G, primary, 1e-3, 1., 0., 0., 0., 0., 0.);
+ reb_simulation_add(r, planet);
+ ```
+
+ You can also the coordinates described by [Pal 2009](https://ui.adsabs.harvard.edu/abs/2009MNRAS.396.1737P/abstract) to initialize orbits using the following function:
+
+ ```c
+ struct reb_particle reb_particle_from_pal(double G, struct reb_particle primary, double m, double a, double lambda, double k, double h, double ix, double iy);
+ ```
+ Here, `lambda` is the longitude, `h` is $e\cos(\omega)$, `k` is $e\sin(\omega)$, `ix` and `iy` are the x and y components of the inclination respectively.
+
+=== "Python"
+ In python, you can create and initialize particles using the constructor of the `Particle` class.
+ ```python
+ sim = rebound.Simulation()
+ primary = rebound.Particle(m=1., x=1.)
+ sim.add(primary)
+ ```
+ If you want to use orbital parameters, you need to pass the primary and the simulation to the constructor:
+ ```python
+ planet = rebound.Particle(simulation=sim, primary=primary, m=1e-3, a=1., e=0.1)
+ ```
+ You can use any combination of orbital parameters that makes physically sense.
+ See [the discussion on orbital elements](orbitalelements.md) for more details.
+
+ !!! Note
+ In most cases you can simply use the convience function described below.
+ This way you don't have to create a particle object just to add it to the simulation.
+
+## Convenience functions
+By far the easiest way to add particles to REBOUND is to use a convenience function.
+=== "C"
+ In C, the function is called `reb_simulation_add_fmt` and has the following syntax:
+ ```c
+ void reb_simulation_add_fmt(struct reb_simulation* r, const char* fmt, ...);
+ ```
+ This is a [variadic function](https://en.cppreference.com/w/c/variadic) which takes a variable number of arguments similar to the `printf` function.
+ The following code shows how this function is used.
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ reb_simulation_add_fmt(r, "m", 1.0); // star at origin with mass 1
+ reb_simulation_add_fmt(r, "m a", 1e-3, 1.0); // planet with mass 1e-3 and semi-major axis 1
+ reb_simulation_add_fmt(r, "m a e", 1e-3, 2.0, 0.1); // planet with mass 1e-3, semi-major axis 2, and eccentricity 0.1
+ reb_simulation_add_fmt(r, "m x vy", 1e-6, 1., 1.); // planet with mass 1e-6, cartesian coordinates
+ ```
+
+ The first argument is the simulation to which you want to add the particle.
+ The second argument is a format string and it determines how many other arguments the function expects.
+
+ !!! Danger
+ You need to pass exactly the right number of arguments to `reb_simulation_add_fmt` as indicated by your format string.
+ Each argument also has to be the right type (mostly double floating point numbers).
+ The latter is particularly important. If you call the function like this:
+ ```c
+ reb_simulation_add_fmt(r, "m a", 1, 1);
+ ```
+ then the arguments are integers, not doubles. This can lead to unexpected behaviour that is very difficult to debug.
+ The correct way to call the function is by making sure the arguments are doubles (by adding a `.`):
+ ```c
+ reb_simulation_add_fmt(r, "m a", 1.0, 1.0);
+ ```
+
+ The following parameters are supported:
+
+ Parameter | Description
+ --------- | -----------
+ `m`| mass (default: 0)
+ `x, y, z`| positions in Cartesian coordinates (default: 0)
+ `vx, vy, vz`| velocities in Cartesian coordinates (default: 0)
+ `primary`| primary body for converting orbital elements to cartesian (default: center of mass of the particles in the passed simulation, i.e., this will yield Jacobi coordinates as one progressively adds particles)
+ `a`| semi-major axis (a or P required if passing orbital elements)
+ `P`| orbital period (a or P required if passing orbital elements)
+ `e`| eccentricity (default: 0)
+ `inc`| inclination (default: 0)
+ `Omega`| longitude of ascending node (default: 0)
+ `omega`| argument of pericenter (default: 0)
+ `pomega`| longitude of pericenter (default: 0)
+ `f`| true anomaly (default: 0)
+ `M`| mean anomaly (default: 0)
+ `E`| eccentric anomaly (default: 0)
+ `l`| mean longitude (default: 0)
+ `theta`| true longitude (default: 0)
+ `T`| time of pericenter passage
+ `h, k, ix, iy`| See [Pal 2009](https://ui.adsabs.harvard.edu/abs/2009MNRAS.396.1737P/abstract) for a definition (default: 0)
+ `r`| physical particle radius
+
+ You can use any combination of these parameters at the same time.
+ If a combination is unphysical, no particle will be added and an error will be outputted.
+ For example, you can only specify one longitude or anomaly.
+
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.add(m=1) # star at origin with mass 1
+ sim.add(m=1e-3, a=1.) # planet with mass 1e-3 and semi-major axis 1
+ sim.add(m=1e-3, a=2., e=0.1) # planet with mass 1e-3, semi-major axis 2, and eccentricity 0.1
+ sim.add(m=1e-6, x=1., vy=1.) # planet with mass 1e-6, cartesian coordinates
+ ```
+
+See [the discussion on orbital elements](orbitalelements.md) for more details.
+
+
+## Solar System planets
+If you want to quickly try something out, you can use a set of initial conditions for the Solar System that come with REBOUND:
+
+```python
+sim = rebound.Simulation()
+rebound.data.add_solar_system(sim)
+```
+
+and similarly for the outer Solar System:
+
+```python
+sim = rebound.Simulation()
+rebound.data.add_outer_solar_system(sim)
+```
+
+
+This is currently only supported in python.
+
+!!! Note
+ These initial conditions are intended for testing integration methods. They might not be very accurate and should not be used for detailed dynamical studies of the Solar System.
+
+
diff --git a/rebound/source/docs/api.md b/rebound/source/docs/api.md
new file mode 100644
index 0000000000000000000000000000000000000000..b69b870523d1971566cff2101833434cec6c3d3f
--- /dev/null
+++ b/rebound/source/docs/api.md
@@ -0,0 +1,20 @@
+# REBOUND API
+These pages describe the main features of REBOUND and its API.
+
+There are two structures (*objects* in Python) which you will encounter frequently when working with REBOUND.
+The first is the [Simulation structure](simulation.md) which contains all the configuration, status and particle data of one REBOUND simulation.
+The second is the [Particle structure](particles.md) which represents one particle in a simulation.
+
+REBOUND is a modular code.
+You can combine different [gravity solvers](gravity.md), [collision detection algorithms](collisions.md), [boundary conditions](boundaryconditions.md), and [integration methods](integrators.md).
+Not all combinations make physically sense, and not all combinations are supported.
+We describe the different modules and their configuration in this section.
+
+Also make sure to some of the other concepts documented in this section.
+They will help you understand the [units](units.md) used in REBOUND, how REBOUND handles [orbital elements](orbitalelements.md), how to save and load simulations to [Simulationarchive](simulationarchive.md) files, how to use [chaos indicators](chaos.md), how to use the [browser based 3D visualization](visualization.md), and several other topics.
+
+
+!!! Info
+ Because the C and Python versions of REBOUND are very similar, we describe both languages in one documentation.
+ The syntax and examples are provided in both C and Python.
+ Use the tabs to switch between them.
diff --git a/rebound/source/docs/binaryformat.md b/rebound/source/docs/binaryformat.md
new file mode 100644
index 0000000000000000000000000000000000000000..993453a0ea972131662eb9023f26aa992b29aebe
--- /dev/null
+++ b/rebound/source/docs/binaryformat.md
@@ -0,0 +1,172 @@
+# Binary Format
+
+REBOUND comes with its own binary format.
+The binary format allows you to store a current simulation state to a file or to memory.
+The binary format is also used when you make a copy of a simulation or when you compare two simulations with each other.
+The Simulationarchive is an extension of the binary format which allows you to store multiple snapshots of a simulation in one file.
+This page explains the details of the binary format.
+It is mainly intended for people who wish to extend the built-in REBOUND functionality.
+You do not need to know those details if you're only working with binary files to save and load simulations.
+
+REBOUND uses two structures for the binary files:
+
+```c
+struct reb_binary_field {
+ uint32_t type;
+ uint64_t size;
+};
+```
+
+and
+
+```c
+struct reb_simulationarchive_blob {
+ int32_t index;
+ int32_t offset_prev;
+ int32_t offset_next;
+};
+```
+
+!!! note
+ Before version 3.18, the offset datatype was `int16_t`. This caused problems for simulations with a large number of particles and has since been change to `int32_t`.
+
+## Binary file (one snapshot)
+You create a binary file if you save a simulation
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ // ... setup simulation ...
+ reb_simulation_save_to_file(r, "snapshot.bin");
+ ```
+
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ // ... setup simulation ...
+ sim.save_to_file("snapshot.bin")
+ ```
+Such a binary file with one snapshot is simply a set of `reb_binaryfield`s followed by one `reb_simulationarchive_blob` at the end, for example:
+
+```
+reb_binary_field:
+ type: DT
+ size: 8 bytes
+
+8 bytes of data representing the value of DT
+
+reb_binary_field:
+ type: PARTICLES
+ size: 128 bytes
+
+128 bytes of data representing the values of PARTICLES
+
+...
+
+reb_binary_field:
+ type: END
+ size: 0
+
+reb_simulationarchive_blob:
+ index: 0
+ offset_prev: 0
+ offset_next: 0
+```
+
+Each of the binary fields provides the context (type and size) for the data that immediately follows the field.
+The type is an integer defined in the `reb_binary_field_descriptor_list` (see below).
+The last binary field of type `9999` (`end`) to indicate that the snapshot ends here.
+
+!!! note
+ Before version 3.27 data was encoded using the enum `REB_BINARY_FIELD_TYPE` instead of `reb_binary_field_descriptor_list`.
+
+
+## Simulationarchive file (multiple snapshots)
+The binary file above can also be interpreted as a Simulationarchive with one snapshot.
+You can append many (millions!) of snapshots to a binary file.
+REBOUND only stores data that has changed since the original snapshot (typically the particle data, time, etc).
+This allows for a very compact file size, while still maintaining bit-wise reproducibility.
+
+Each snapshot is separated by a `reb_simulationarchive_blob`.
+The blob contains the offset to the previous and next blobs.
+This allows REBOUND to quickly jump from one blob in the archive to the next.
+Between the blobs are the same `reb_binary_field`s we already encountered for a binary file with one snapshot.
+Thus, a Simulationarchive file with multiple snapshots looks something like this:
+
+```
+reb_binary_field:
+ type: DT
+ size: 8 bytes
+
+8 bytes of data representing the value of DT
+
+... more reb_binary_fields ...
+
+reb_binary_field:
+ type: END
+ size: 0
+
+reb_simulationarchive_blob:
+ index: 0
+ offset_prev: 0
+ offset_next: 256 (offset to the next blob)
+
+reb_binary_field:
+ type: DT
+ size: 8 bytes
+
+8 bytes of data representing the value of DT
+
+... more reb_binary_fields ...
+
+reb_binary_field:
+ type: END
+ size: 0
+
+reb_simulationarchive_blob:
+ index: 1
+ offset_prev: 256 (offset to the previous blob)
+ offset_next: 256 (offset to the next blob)
+
+reb_binary_field:
+ type: DT
+ size: 8 bytes
+
+8 bytes of data representing the value of DT
+
+... more reb_binary_fields ...
+
+reb_binary_field:
+ type: END
+ size: 0
+
+reb_simulationarchive_blob:
+ index: 2
+ offset_prev: 256 (offset to the previous blob)
+ offset_next: 0
+```
+
+The offsets are also used as a sort of checksum to detect if a binary file has been corrupted (for example because a user ran out of disk space).
+If a binary file is corrupted, REBOUND attempts some magic and will recover the last snapshot which does not appear corrupted.
+You will see a warning message when that happens and should proceed with caution (make a backup!).
+
+
+## Binary Field Descriptor
+
+REBOUND maintains a list of fields it needs to input/output in order to restore a simulation.
+This list is of type `struct reb_binary_field_descriptor[]` and defined in `output.c` as `reb_binary_field_descriptor_list`.
+A single struct `reb_binary_field_descriptor` contains the information to input/output one REBOUND field, for example the current simulation time `t`:
+
+```c
+ struct reb_binary_field_descriptor fd_t = { 0, REB_DOUBLE, "t", offsetof(struct reb_simulation, t), 0, 0};
+```
+The first number is a unique identifier (in this case 0). The second entry is the type of data, in this case a single double precision floating point number. The third entry is a string used to identify the field. This is only used when generating human-readable output and is typically the same as the variable name in C. The next entry is the offset of where this variable is stored relative to the beginning of the simulation structure.
+
+REBOUND also supports array like fields. For example consider the `particles` field:
+```c
+ struct reb_binary_field_descriptor fd_particles = { 85, REB_POINTER, "particles", offsetof(struct reb_simulation, particles), offsetof(struct reb_simulation, N), sizeof(struct reb_particle)};
+```
+
+The second to last entry lists the offset of the a variable in the `reb_simulation` structure that determines the number of array elements. In this case the number of particles. The last entry is the size of a single element. In this case, the size of one `reb_particle`.
+
+If you add an additional field to the `reb_simulation` struct and you want to write it to a binary file and read it back in, then you need to add an entry to `reb_binary_field_descriptor_list`.
+
diff --git a/rebound/source/docs/boundaryconditions.md b/rebound/source/docs/boundaryconditions.md
new file mode 100644
index 0000000000000000000000000000000000000000..be09901bfd5984a1477c42cacfda208f656b633c
--- /dev/null
+++ b/rebound/source/docs/boundaryconditions.md
@@ -0,0 +1,108 @@
+# Boundary conditions
+
+You can use different boundary conditions with REBOUND.
+
+## No boundaries
+By default, REBOUND doesn't use boundary conditions.
+This means particle can have arbitrary coordinates in all three dimensions (as long as they can be represented as floating point numbers).
+Because this is the default setting, you don't need to do anything if you don't want boundary conditions.
+Nevertheless, here is the syntax to set this manually:
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ r->boundary = REB_BOUNDARY_NONE;
+ ```
+
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.boundary = "none"
+ ```
+
+## Open
+When open boundary conditions are selected, particles are removed from the simulation if they leave the simulation box.
+You therefore also need to set the size of the simulation box whenever you use open boundary conditions.
+The syntax is as follows:
+
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ reb_simulation_configure_box(r, 10., 1, 1, 1); # confine the simulation to a box of size 10
+ r->boundary = REB_BOUNDARY_OPEN;
+ ```
+
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.configure_box(10.) # confine the simulation to a box of size 10
+ sim.boundary = "open"
+ ```
+
+## Periodic
+When periodic boundary conditions are uses, particles are reinserted on the opposite side if they leave a simulation box.
+You can use an arbitrary number of ghost-boxes with this module.
+The syntax is as follows:
+
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ reb_simulation_configure_box(r, 10., 1, 2, 3); # confine the simulation to a box of size 10x20x30
+ r->boundary = reb_boundary_periodic;
+ ```
+
+=== "python"
+ ```python
+ sim = rebound.simulation()
+ sim.configure_box(10., 1, 2, 3) # confine the simulation to a box of size 10x20x30
+ sim.boundary = "periodic"
+ ```
+
+Ghost boxes are supported for both periodic and shear-periodic boundary conditions.
+Ghost boxes can be used to allow particle collisions across boundaries and include gravitational forces from outside the box boundaries.
+This is particularly useful when simulating rings and disks.
+The following code sets up two rings of ghost boxes in the x and y directions.
+
+=== "C"
+ ```c
+ r->N_ghost_x = 2;
+ r->N_ghost_y = 2;
+ r->N_ghost_z = 0;
+ ```
+
+=== "python"
+ ```python
+ sim.N_ghost_x = 2
+ sim.N_ghost_y = 2
+ sim.N_ghost_z = 0
+ ```
+
+See [Rein & Liu](https://ui.adsabs.harvard.edu/abs/2012A%26A...537A.128R/abstract) for details on the ghost box implementation.
+
+You might encounter the `reb_vec6d` structure in various parts of the code, for example in function related to gravity calculation and collision detection.
+It often contains the relative position and velocity of a ghost-box.
+If there are no ghost-boxes used, then all elements of this structure will be zero.
+
+## Shear
+
+
+These are shear periodic boundary conditions.
+They are similar to periodic boundary conditions, but ghost-boxes are moving with constant speed, set by the shear.
+This is useful when simulation a small patch in a ring or disk.
+You also need to set the `OMEGA` variable in the simulation which set the epicyclic frequency.
+For more information on how to setup simulations of planetary rings in REBOUND, see [Rein & Liu](https://ui.adsabs.harvard.edu/abs/2012A%26A...537A.128R/abstract).
+
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ reb_simulation_configure_box(r, 10., 1, 1, 1);
+ r->OMEGA = 1.0;
+ r->boundary = REB_BOUNDARY_SHEAR;
+ ```
+
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.configure_box(10.)
+ sim.OMEGA = 1.0
+ sim.boundary = "shear"
+ ```
diff --git a/rebound/source/docs/c_examples/compile_emcc.bash b/rebound/source/docs/c_examples/compile_emcc.bash
new file mode 100644
index 0000000000000000000000000000000000000000..3cf056201b7696b35e24803d6036cffc9e9d4c23
--- /dev/null
+++ b/rebound/source/docs/c_examples/compile_emcc.bash
@@ -0,0 +1,31 @@
+#!/bin/bash
+
+source emsdk/emsdk_env.sh
+READTHEDOCS_OUTPUT="${READTHEDOCS_OUTPUT:-.}"
+OPTIMI="${1:-3}"
+
+echo "Compiling C examples with emscripten."
+echo "Output dir: $READTHEDOCS_OUTPUT"
+echo ""
+
+for dir in examples/*/
+do
+ echo "Working on $dir ..."
+ mpi_enabled=$(cat $dir/Makefile | grep -c "export MPI=1")
+ openmp_enabled=$(cat $dir/Makefile | grep -c "export OPENMP=1")
+ server_used=$(cat $dir/problem.c | grep -c "reb_simulation_start_server")
+ if [ $mpi_enabled -eq 0 ] && [ $openmp_enabled -eq 0 ]; then
+ mkdir -p $READTHEDOCS_OUTPUT/html/emscripten_c_$dir/
+ echo "Compiling... "
+ if [ $server_used -eq 0 ]; then
+ emcc -O$OPTIMI -Isrc/ src/*.c $dir/problem.c -DSERVERHIDEWARNING -sSTACK_SIZE=655360 -s -sASYNCIFY -sALLOW_MEMORY_GROWTH -sEXPORTED_RUNTIME_METHODS="callMain" --shell-file web_client/shell_rebound_console.html -o $READTHEDOCS_OUTPUT/html/emscripten_c_$dir/index.html || exit 1
+ else
+ emcc -O$OPTIMI -Isrc/ src/*.c $dir/problem.c -DSERVERHIDEWARNING -DOPENGL=1 -sSTACK_SIZE=655360 -s USE_GLFW=3 -s FULL_ES3=1 -sASYNCIFY -sALLOW_MEMORY_GROWTH -sEXPORTED_RUNTIME_METHODS="callMain" --shell-file web_client/shell_rebound_webgl.html -o $READTHEDOCS_OUTPUT/html/emscripten_c_$dir/index.html || exit 1
+ fi
+ echo "Done. "
+ else
+ echo "Skipping."
+ fi
+ echo ""
+
+done
diff --git a/rebound/source/docs/c_examples/generate_c_examples.py b/rebound/source/docs/c_examples/generate_c_examples.py
new file mode 100644
index 0000000000000000000000000000000000000000..040e28c3ec83380bc9c3b9b96dcf80e4592680be
--- /dev/null
+++ b/rebound/source/docs/c_examples/generate_c_examples.py
@@ -0,0 +1,64 @@
+# -*- coding: utf-8 -*-
+import glob
+
+# C Example update
+def run(*args, **kwargs):
+ print("Generating C examples.")
+ count = 0
+ for problemc in glob.glob("examples/*/problem.c"):
+ count += 1
+ cname = problemc.split("/")[1]
+ with open("docs/c_examples/"+cname+".md","w") as fd:
+ will_output = 0
+ livepreview=1
+ # Manual exception for file viewer
+ if "_viewer" in cname:
+ livepreview=0
+ if "screenshots" in cname:
+ livepreview=0
+ try:
+ with open("examples/"+cname+"/Makefile","r") as mfd:
+ Makefile = mfd.read()
+ if "export MPI=1" in Makefile:
+ livepreview=0
+ if "export OPENMP=1" in Makefile:
+ livepreview=0
+ except:
+ print("Warning: Makefile error in "+problemc)
+
+ with open(problemc) as pf:
+ did_output=0
+ empty_lines = 0
+ for line in pf:
+ if line[0:3] == "/**":
+ will_output += 1
+ if line[0:3] == " */":
+ will_output = -1
+ line = ""
+ fd.write("\n\n```c\n")
+ if will_output>1:
+ if will_output == 2:
+ line = " # "+line[3:].strip() + " (C)\n"
+ if livepreview == 1:
+ line += "!!! example \"Try it out this example!\"\n"
+ line += " REBOUND has been compiled with emscripten to WebAssembly.\n"
+ line += " This lets you run this example interactively from within your browser at almost native speed.\n"
+ line += " No installation is required.\n"
+ line += " [Click here](../../emscripten_c_examples/"+cname+"/) to try it out.\n"
+ will_output = 2
+ if len(line[3:].strip())==0:
+ fd.write("\n\n"+line[3:].strip())
+ else:
+ fd.write(line[3:].strip() + " " )
+ if will_output==-1:
+ fd.write("" +line.rstrip() + "\n" )
+ did_output = 1
+ if will_output>0:
+ will_output += 1
+ fd.write("```\n")
+ fd.write("\n\nThis example is located in the directory `examples/"+problemc.split("/")[1]+"`\n\n")
+ if did_output==0:
+ print("Warning: Did not find description in "+problemc)
+ print("Converted %d C examples."%count)
+if __name__ == "__main__":
+ run()
diff --git a/rebound/source/docs/c_outputfunctions.md b/rebound/source/docs/c_outputfunctions.md
new file mode 100644
index 0000000000000000000000000000000000000000..c76adfc5ea231fc71325341abe3f4102a7683611
--- /dev/null
+++ b/rebound/source/docs/c_outputfunctions.md
@@ -0,0 +1,78 @@
+# C output functions
+
+The functions listed here provide various output functionality.
+
+## Output check
+
+```c
+int reb_simulation_output_check(struct reb_simulation* r, double interval);
+```
+
+This function can be used to trigger outputs at regular time intervals.
+The function returns 1 if an output is required and 0 otherwise.
+Typically, you would use this within the heartbeat function to generate equally spaced outputs as in this example:
+
+```c
+void heartbeat(struct reb_simulation* const r){
+ if (reb_simulation_output_check(r, 100.)){
+ printf("t = %f\n", r->t); // Will print current time every 100 time units.
+ }
+}
+```
+
+## Timing
+
+```c
+void reb_simulation_output_timing(struct reb_simulation* r, const double tmax);
+```
+
+This function outputs various status information on the screen. An example output looks as follows
+
+```
+N_tot= 10 t= 4610.00 dt= 4.000 cpu= 0.002472 [s] t/tmax= 0.01%
+```
+
+It shows the number of particles, the current time and time-step, as well as the time since the last output. If `tmax` is non-zero, then the last number indicates how far the simulation has progressed.
+
+## ASCII orbits
+```c
+void reb_simulation_output_orbits(struct reb_simulation* r, char* filename);
+```
+This function creates or appends an ASCII file with orbital parameters of all particles.
+The orbital parameters are calculated in Jacobi coordinates.
+Particles are assumed to be sorted from the inside out, the central object having index 0.
+Each time the function is called N-1 rows are appended to the file with name filename.
+Each row in the file corresponds to one particle and contains the following columns (tab separated):
+
+ - time
+ - semi-major axis
+ - eccentricity
+ - inclination
+ - Omega (longitude ascending node)
+ - omega (argument of pericenter)
+ - lambda (mean longitude)
+ - orbital period,
+ - f (true anomaly)
+
+## ASCII coordinates
+```c
+void reb_simulation_output_ascii(struct reb_simulation* r, char* filename);
+```
+This function creates or appends an ASCII file with the positions and velocities of all particles to an ASCII file.
+
+## Velocity dispersion
+```c
+void reb_simulation_output_velocity_dispersion(struct reb_simulation* r, char* filename);
+```
+This function creates or appends an ASCII file with the current velocity dispersion of all particles.
+This is useful for ring simulations where one wants to monitor that the system has reached an equilibrium.
+
+## Binary snapshot
+```c
+void reb_simulation_save_to_file(struct reb_simulation* r, const char* filename);
+```
+
+These functions save the `reb_simulation` structure as a binary file.
+It can be used to save the current status of a REBOUND simulation and later restart the simulation.
+If the file exists, this function will append a snapshot.
+
diff --git a/rebound/source/docs/c_randomsamplingfunctions.md b/rebound/source/docs/c_randomsamplingfunctions.md
new file mode 100644
index 0000000000000000000000000000000000000000..a069b71bf16058c31c61c69d18ac44a7c437ca1f
--- /dev/null
+++ b/rebound/source/docs/c_randomsamplingfunctions.md
@@ -0,0 +1,41 @@
+# Random sampling
+
+REBOUND includes several functions which help sampling random numbers from various distributions.
+Each function takes a pointer to a `struct reb_simulation` as a first argument.
+This is because the simulation structure stores the random number generator state in the member `rand_seed`.
+When a simulation is created, `rand_seed` is initialized using the current time and process id.
+These functions are thread safe.
+The `rand_seed` variable is stored in binary files. This makes the random number generator reproducible which can be very helpful when debugging simulations that use random numbers.
+
+The following example draws a number in the interval between 0 and $2\pi$ from a uniform distribution.
+```c
+struct reb_simulation* r = reb_simulation_create();
+double phi = reb_random_uniform(r, 0., 2.*M_PI);
+```
+
+# Uniform
+This function returns a uniformly distributed random variable between `min` and `max`.
+```c
+double reb_random_uniform(struct reb_simulation* r, double min, double max);
+```
+
+# Power law
+This function returns a random variable drawn form a power law distribution with slope `slope` between `min` and `max`.
+```c
+double reb_random_powerlaw(struct reb_simulation* r, double min, double max, double slope);
+```
+
+# Normal
+This function returns a random number drawn from a normal distribution centerd on zero and with variance `variance`.
+It uses the algorithm by D.E. Knut, 1997, The Art of Computer Programming, Addison-Wesley.
+```c
+double reb_random_normal(struct reb_simulation* r, double variance);
+```
+
+# Rayleigh
+This function returns a random variable drawn form a Rayleigh distribution with scale parameter `sigma`.
+```c
+double reb_random_rayleigh(struct reb_simulation* r, double sigma);
+```
+
+
diff --git a/rebound/source/docs/changelog.md b/rebound/source/docs/changelog.md
new file mode 100644
index 0000000000000000000000000000000000000000..0b48b43609ff6a244333ec24384f0aea4f25f69a
--- /dev/null
+++ b/rebound/source/docs/changelog.md
@@ -0,0 +1,589 @@
+# Changelog
+
+This changelog only includes the most important changes in recent updates. For a full log of all changes, please refer to git.
+
+## Version 4.x
+
+### Version 4.5.1
+* Added leapfrog integrators of order 4, 6, and 8. Order can be set with `r->ri_leapfrog->order`.
+* Heartbeat function is now also called when using `reb_simulation_steps()`.
+* OrbitPlot supports more colours.
+* Fixed an alignment issue when comparing binary snapshots which could have triggered a segfault.
+
+### Version 4.5.0
+* Added support for (Frequency) Modified Fourier Transforms. Heavily based on David Nesvorny's code. The new functions are `reb_frequency_analysis()` in C and `rebound.frequency_analysis()` in python. For usage, see C examples `secular_frequencies` and `frequency_analysis` as well as the iPython notebook `FrequencyAnalysis`.
+* Support for Jacobi coordinates added when using WHFast with OpenMP.
+* Allow negative periods when initializing hyperbolic orbits.
+
+### Version 4.4.11
+* The collision resolve function now returns a type `enum REB_COLLISION_RESOLVE_OUTCOME`. The actual integer values remain unchanged.
+* Bug in TRACE was fixed.
+* Convergence check for M_to_E function.
+* New API example that shows how to use the Kepler solver without a REBOUND simulation. Updated other examples.
+
+### Version 4.4.10
+* Version bump to rerun github workflows for pypi uploads
+
+### Version 4.4.9
+* Fixes a bug that affected collisions searches with a tree code.
+* Support for mid-timestep add/remove of particles with TRACE.
+* Various small improvements and bugfixes for TRACE.
+* IAS15's `adaptive_mode` is now an ENUM.
+* Some OpenMP improvements.
+
+### Version 4.4.8
+* Added support for symplectic correctors with barycentric coordinates in WHFast.
+
+### Version 4.4.7
+* Added option to disable SSL checks for Horizon queries with `rebound.horizons.SSL_CONTEXT = 'unverified'.`
+* Added unit tests.
+* Added barycentric coordinates for WHFast.
+* Bug fix for when MEGNO is used with adaptive timestepping.
+* Added more error messages.
+* Fixed various issues in documentation.
+
+### Version 4.4.6
+* When initializing particles with "uniform" in python, REBOUND now uses its own `reb_random_uniform()` function. This avoids importing the "random" library and makes results reproducible as the random seed of the simulation is used when generating random numbers.
+* More cracefull interrupt handling. REBOUND now stop the integration after the next timestep when CTRL-C is pressed the first time. If CTRL-C s pressed twice, then long loops (during gravity, collision calculations) are terminated immediately. Continuing an integration after one CTRL-C press should be easier with this change as the simulation does not get corrupted.
+* Fixed typos in documentation.
+
+### Version 4.4.5
+* Version updated to test github workflows
+
+### Version 4.4.4
+* Fixed several memory leaks and other memory issues. It is unlikely that any of those bugs did affect an simulation.
+* When converting units of a particle, the particle radius is now also converted.
+* Added getter/setters for Pal coordinates to the particle structure in python. Syntax is `sim.particles[1].pal_h`, `sim.particles[1].pal_ix`, etc.
+
+### Version 4.4.3
+* REBOUND now raises ImportError if it detects a size mismatch between the C and python Simulation structures.
+* Fixes a bug in the WHFast512 synchronization on non-AVX512 systems.
+* Fixes a bug in the SimulationArchive in cases where there are multiple snapshots with t=0.
+* Updates TRACE switching condition to match Lu et al (2024).
+* TRACE binary file size has been reduced.
+* Pericenter passage time is now calculated even if particles are not in a Simulation.
+
+### Version 4.4.2
+* Fixed bug in TRACE when adding particles.
+* Added WHFast fallback for synchronizing WHFast512 simulations with `N_systems` > 1.
+* Output version number used to create Simulationarchive if there is a version mismatch.
+* Added C example `simulationarchive_fields` which outputs all fields in a simulationarchive for debugging purposes.
+
+### Version 4.4.1
+* Fixed bug in TRACE for FULL PERI modes.
+
+### Version 4.4.0
+* Added TRACE integrator. See Lu, Hernandez & Rein (2024) for details on this implementation.
+
+### Version 4.3.2
+* No longer clipping particles and orbits in visualization.
+* Added a scale to visualization. Hide by pressing `t`.
+* Option to take a screenshow manually in png (WebGL) or tga (OpenGL) format by pressing `e`.
+* Improved `plane` visualization mode. Now supporting hyperbolic orbits.
+* Fixed a memory leak in `reb_simulation_copy`.
+
+### Version 4.3.1
+* Added new `plane` visualization mode for orbits. Press `w` to toggle through available orbit visualization modes.
+* Added python interface for screenshot API.
+* Fixed an issue where no python exception was raised when a particle was added outside a simulation box.
+* Renamed `past_N` to breadcrumbs in visualization module.
+
+### Version 4.3.0
+* Take screenshots of WebGL based visualizations using the `reb_simulation_output_screenshot()` function. You need to connect one web browser to the simulation in order to take screenshots.
+* Improved synchronization of visualization and simulation on Windows with mutex.
+* Fixes an issue that might lead to NaN values when less than the maximum number of planets are used in WHFast512.
+
+### Version 4.2.0
+* It is now possible to programmatically change all aspects of a REBOUND visualization. This can be used to set up default viewing options or to render animations. See the C examples in `animation_solar_system` and `animation_saturn_rings`.
+* Reworked matrix operations in visualization routines to follow the Model-View-Projection paradigm.
+* Fixed an issues where unit tests would fail because a binary file was not deleted.
+
+### Version 4.1.1
+* Fixed python wheels for windows.
+
+### Version 4.1.0
+* New visualization feature that allows you to show past particle positions and orbits (keyboard commands p, u, and i).
+* After pausing a simulation, you can now advance it by a single timestep by pressing the down arrow or 50 timesteps by pressing the page down key.
+* Visualization now supports scroll to zoom.
+* Fixed memory leaks when using custom ODEs.
+* Fixed broken links in documentations.
+
+### Version 4.0.3
+* Default IAS15 timestepping criterion is now `adaptive_mode=2`. See Pham, Rein, and Spiegel (2024) for details. To use the old default timestepping criterion, set `adaptive_mode=1`.
+* Fixed a race condition that should improve the responsiveness of web based visualizations.
+* Removed the glad dependency from emscripten builds which reduces filesize and improves performance.
+
+### Version 4.0.2
+* Fixes an issue where the default Makefiles included white spaces after the SERVER and OPENGL variable definitions. This caused the main Makefile to ignore these settings.
+* Added `key_callback` function for customizing user interaction in visualizations.
+* Added `simulationarchive_viewer` example.
+* Included `-sGL_ENABLE_GET_PROC_ADDRESS` flag that is now needed for the latest version of emscripten.
+
+### Version 4.0.1
+* Include missing python packages
+
+### Version 4.0.0
+* Major API changes and new features! If you have used a previous version of REBOUND, then you will need to update your code. If you have trouble with the migration, open a GitHub issue!
+* Many function and variable names have changed. They now follow a coherent naming convention. See the naming convention section in the documentation for more information.
+* New visualization module! Previously, using OpenGL visualization required the GLFW library which led to problems on various operating systems. The new visualization module no longer requires ANY dependencies and is compatible with MacOS, Linux, and Windows. It works by running a local web server to which you can point your browser to. In your web browser, an emscripten compiled version of REBOUND handles the WebGL visualization while constantly updating simulation data over HTTP. You can use ssh and port forwarding to visualize simulations on remote servers. Check out the documentation for more details on this new module.
+* OpenGL for all the examples has been turned off by default so that new users don't get stuck at this step. To turn on OPENGL simply change the flag in the Makefile.
+* Added emscripten support. All C examples (including those using visualizations) are now automatically compiled with emscripten on readthedocs.org so you can run from within the browser. No download or installation required.
+* A race condition in OpenGL visualization has been removed. Visualizations run much smoother.
+* `reb_random` functions now callable with `r=NULL`. If `r=NULL` then the time and PID is used as a seed.
+* Removed support for Simulationarchives with version 2. Added some additional support for reading corrupt/old archives.
+* Fixed memory leak in `reb_simulation_copy`.
+* Consistent integer sizes for 32/64bit. This includes padding for `reb_particle` which is stored in the Simulationarchive.
+
+
+## Version 3.x
+
+### Version 3.28.4
+* WHFast512 now support the integration of 2 and 4 planet systems in parallel. Providing a speed up of up to 10x.
+* The sqrt7 function used by IAS15 now support a wider range of input arguments.
+
+### Version 3.28.3
+* Removed distutils requirement in preparation for python 3.12.
+* Removed rebound.InterruptiblePool as it no longer works with recent python version. Updated examples.
+* Added Holmberg example.
+* Added `adaptive_mode==3` for IAS15 (Aarseth 1985).
+
+### Version 3.28.2
+* Implemented own fmemopen implementation on MacOS. This is mainly to appease conda-forge builds.
+* Improved sqrt7 algorithm allows larger convergence interval.
+
+### Version 3.28.1
+* Improved support for reading old and corrupted Simulationarchives.
+* Renamed `ri_ias15.epsilon_global` to `ri_ias15.adaptive_mode`.
+* Added new timestep method for IAS15 `ri_ias15.adaptive_mode = 2`. This is experimental for now. Details to be described in Pham, Rein & Spiegel (in prep).
+* Added unit tests to check for fused multiply add instruction (these break reproducibility).
+* Added phony target in C Makefile to force rebuilding librebound whenever building examples.
+
+### Version 3.28.0
+- Native Windows support. REBOUND can now be built natively on Windows (without WSL) using the Microsoft Visual Studio Compiler.
+- Python Wheels are now provided for Linux, MacOS, and Windows. This should significantly speed up the installation process on a wide variety of systems.
+
+### Version 3.27.0
+* In python, Simulation and Particle objects are now picklable. Just like loading Simulations from a binary file, function pointers will need to be re-set manually after unpickling.
+* The difference between simulations can now be printed out in a human readable form. Python syntax: `sim.diff(sim2)`. C syntax: `reb_simulation_diff(sim2, sim1, 1)`.
+* Reading Simulationarchives with version < 2 is no longer supported.
+* The POSIX function fmemopen() is now required to compile REBOUND. This should not affect many users. However, if you are using macOS, the version needs to be >= 10.13 (this version of macOS, High Sierra, was released in 2017).
+* Internal changes on how Simulationarchives are written.
+* Internal variable names that represent the size of allocated buffers now consistently include the name `N_allocated`.
+* The TES (Terrestrial Exoplanet Integrator) has been removed. If you wish to use TES, you will need checkout an earlier version.
+
+### Version 3.26.3
+* A few more changes to reduce the number of compiler warnings. This should not affect any calculation.
+
+### Version 3.26.2
+* Fixed various signed/unsigned int issues. This should reduce the number of compiler warnings but not affect any calculation.
+
+### Version 3.26.1
+* Added support for `AVX512` and `FFP_CONTRACT_OFF` environment variables when using pip to install REBOUND.
+
+### Version 3.26.0
+* Added WHFast512 integrator (Javaheri, Rein, Tamayo 2023)
+
+### Version 3.25.1
+* Bug fixed that prevented the installation via PyPi
+
+### Version 3.25.0
+* MPI parts updated and unit tests added
+* Fixed machine independence bug in TES.
+
+### Version 3.24.3
+* Updated unit tests so they work on 32bit machines
+
+### Version 3.24.2
+* Fixed bug in TES ctypes structure
+
+### Version 3.24.1
+* Added CORS proxy for Horizons request in pyodide
+* Smoother OpenGL animations when using usleep
+* TES calculates orbital period automatically
+
+### Version 3.24.0
+* Added support for Simulationarchive larger than 4 GB.
+* Updated documentation for Lyapunov characteristic number.
+
+### Version 3.23.5
+* Added new units shortcuts (year,years,massist)
+* Rearranged some loops and switch statements (doesn't affect floating point numbers).
+
+### Version 3.23.4
+* Added pyproject.toml file
+
+### Version 3.23.3
+* Changed the way REBOUND reverses the integration direction when the sign of the timestep is inconsistent with respect to the requested final time.
+* Fixes a memory leak when a tree code is used
+* Fixes an issue where MERCURIUS was not bit-wise reproducible when safe mode was turned off.
+
+### Version 3.23.2
+* Minor changes to the python side of Vec3d to make it more compatible with numpy.
+
+### Version 3.23.1
+* Minor changes related to the REBOUND Rotations framework.
+
+### Version 3.23.0
+* Added the REBOUND Rotations framework.
+* Fixes an issue with showing an incorrect periastron location in OrbitPlot for high mass-ratio systems.
+* Adds pre and post timestep calls to the ode framework.
+
+### Version 3.22.0
+* OrbitPlot is now a class. Checkout the OrbitPlot.ipynb tutorial. This change allows for interactive plots and much faster updates to existing plots. This is great for rendering animations!
+
+### Version 3.21.0
+* Automatic rescaling of first order variational particles has been added. This will allow you to integrate chaotic systems for longer and obtain a more accruate measure of MEGNO and the Lyapunoc exponent.
+* Added `sim.stop()` / `reb_simulation_stop()` to end an integration from within the heartbeat function.
+
+### Version 3.20.1
+* Pal coordinates have been added to the `reb_orbit` struct.
+
+### Version 3.20.0
+* A new integrator has been added, the Terrestrial Exoplanet Simulation (TES).
+
+### Version 3.19.10
+* Fixes another bug int he BS integrator when additional forces are used.
+
+### Version 3.19.9
+* Two bugs fixed in the BS integrator. One was related to unitialized memory and the other to issues when the particle number changed.
+
+### Version 3.19.5
+* Workaround for urllib support in pyodide added
+* Silent warning when InterruptiblePool is not available
+
+### Version 3.19.4
+* InterruptiblePool is optional.
+* Fixed an issue that occured when switching integrators while using the Simulationarchive.
+* Renamed `srand_seed` to make it user accessible.
+
+### Version 3.19.3
+* Added several examples.
+* Changed how pypi is rendering the documentation.
+
+### Version 3.19.2
+* Fixes a bug relates to test particles of type 0 in MERCURIUS.
+
+### Version 3.19.1
+* Some compilers seem to complain that a constant cannot be initialized from a constant. Fixed this so that REBOUND works on colaboratory.
+
+### Version 3.19.0
+* Added a Gragg-Bulirsch-Stoer integrator (short BS for Bulirsch-Stoer). This is an adaptive integrator which uses Richardson extrapolation and the modified midpoint method to obtain solutions to ordinary differential equations. The version in REBOUND is based on the method described in Hairer, Norsett, and Wanner 1993 (see section II.9, page 224ff).
+* Added the ability to integrate arbitrary ordinary differential equations with REBOUND. The ODEs can be couple to the N-body simulation. This can be used to simulate spin, tides, and other physical effects. The user-defined ODEs are integrated with the new BS integrator.
+
+### Version 3.18.1
+* Various improvements and fixes relates to NASA Horizons: small bodies are retrieved correctly, the dates now work with fractional JD values and dates in the format YYYY-MM-DD HH:MM:SS are now supported.
+
+### Version 3.18.0
+* Fixes an issue in the Simulationarchive that prevented REBOUND from seeing more than one snapshot. This only affected simulations with a large number of particles.
+
+### Version 3.17.5
+* REBOUND will now uses the new HTTP API from NASA Horizons. This is significantly faster than the old telnet version. Thanks to Lukas Winkler for implementing this.
+
+### Version 3.17.4
+* REBOUND will now attempt to recover binary files and Simulationarchives which have been corrupted. Simulations can be restarted from corrupt files and in most cases the corrupt files will fix themselves.
+
+### Version 3.17.3
+* Allow for Horizon queries with future JD dates.
+
+### Version 3.17.2
+* Moved some function declarations to rebound.h. This is a temporary fix for REBOUNDx.
+
+### Version 3.17.1
+* Fixed an issue where the simulation struct in python did not match the one in C. This might have lead to unexpected behaviour in rare cases.
+* Fixed various typos in the documentation
+* MERCURIUS switching functions can now be set from Python. Also inluded more built-in switching functions from Hernandez (2019).
+
+### Version 3.17.0
+* Added new 'reb_simulation_add_fmt()' function. This makes adding particles in C as easy as in python.
+* Orbits can now also be initialized using the eccentric anomaly.
+* Fixed an issue which prevented one loop in the gravity routine form being parallelized with OpenMP.
+* Added a warning message when test particles have finite mass.
+* More reliable reading of corrupt Simulationarchive files.
+
+### Version 3.16.0
+* MERCURIUS: If encounters only involve test-particles (type 0), then the algorithm is now resetting the coordinates of all massive particles after the encounter step. This only changes the outcome at the machine precision, but it makes the trajectories of massive particles independent of the close encounter history. Thanks to Kat Deck for this feature!
+* MERCURIUS: The gravity routine is now $O(0.5 \cdot N^2)$ instead of $O(N^2)$ for non-OPENMP runs. This should lead to a noticable improvement in runtime.
+
+### Version 3.15.0
+* Orbital parameters of particles can now be changed in-place. For example: 'sim.particles[1].e += 0.1'.
+* Implemented more chatty repr functions for most object. Printing REBOUND objects should now give some useful information.
+* Improved support for adding/removing particle in MERCURIUS during collisions.
+* REBOUND now outputs an error message when one is trying to remove a particle with a negative index.
+* Small updates to the documentation.
+* New ipython example added, showing how to use a python collision resolve function.
+
+### Version 3.14.0
+* Due to a bug, WHFast was not thread-safe. It is now.
+* Random number generator seed is now stored in the Simulationarchive.
+ This allows you to get reproducible random number even after restarting a simulation.
+* Random numbers generated with the `reb_rand_*()` functions were not thread-safe.
+ They are thread-safe now. Note that this required an API change. All `reb_rand_*()`
+ functions now require the simulation structure as an argument. This is because the
+ random number generator seed is now stored in the simulation structure.
+
+### Version 3.13.2
+* Correct handling of test particles in reb_transformations.
+* Small bug fixes
+
+### Version 3.13.1
+* WHFast: Fixes multiple issues with testparticles in WHFast.
+
+### Version 3.13.0
+* IAS15: Fixes a bug which leads to a biased energy error in long term integrations with fixed timesteps (see Hernandez and Holman 2020). The old version of IAS15 can still be used for the time being by setting ri_ias15.neworder=0.
+* IAS15: Does not take variational particles into account when predicting new timesteps. This should be beneficial during close encounters.
+* A few improvements have been made to the Simulationarchives code including a more efficient loading procedure for large datasets.
+
+### Version 3.12.3
+* Various small bug fixes
+* Added a new function sim.cite() to automatically generate citations depending on the current simulation settings.
+
+### Version 3.12.2
+* Various bug fixes to MERCURIUS
+* Performance increase when using the BASIC Gravity Routine with OpenMP
+
+### Version 3.12.1
+* Bug fixes to LINE and LINETREE algorithms
+
+### Version 3.12.0
+* Added LINETREE collision search algorithm.
+ This algorithm uses a tree to check if any two particle trajectories overlapped during the last timestep. This
+ should be beneficial in large N, low density situation as it allows for much larger timesteps. A modification of the
+ collision resolve routine might be necessary to allow for multiple collisions of the same particle during one timestep.
+ This depends on the application and the default is to only allow one collision per timestep.
+
+### Version 3.11.1
+* Added support for test particles and first-order variational particles to the Embedded Operator Splitting (EOS).
+* BASIC Gravity routine changed from O(N^2) to O(0.5 N^2). This should lead to a speed-up in most cases but will break bit-wise reproducibility from earlier versions as the ordering of floating point operations has changed.
+
+### Version 3.11.0
+* This version adds the new Embedded Operator Splitting methods from Rein (2019). See the tutorial in the ipython_examples folder for how to use them.
+
+### Version 3.10.2
+* Updates to OrbitPlot. Includes better layout of plot and some syntax changes. See OrbitPlot documentation for the new syntax.
+
+### Version 3.10.1
+* Small syntax changes for SABA integrator family.
+* Includes high order integrators by Blanes et al. (2013).
+
+### Version 3.10.0
+* Changes for the new version of REBOUNDx.
+
+### Version 3.9.0
+* Added new high order symplectic integrators from Wisdom et al. (1996) and Laskar & Robutel (2001). The implementation of these integrators are discussed in Rein, Tamayo & Brown (2019).
+* Implemented new bit-wise comparison functions for simulations. Python syntax is simply sim1==sim2.
+* Fixed a bug in IAS15 which prevented a restarted simulation to reproduce the original simulation exactly.
+
+### Version 3.8.3
+* Improves and fixes various issues related to variational equations and MEGNO.
+
+### Version 3.8.2
+* Fixes a bug which resulted in duplicate snapshots in Simulationarchives when restarting simulations.
+
+### Version 3.8.1
+* Syntax change on the python side to create a simulation from a binary file or Simulationarchive:
+
+ ```python
+ rebound.Simulation.from_file("test.bin") becomes rebound.Simulation("test.bin")
+ rebound.Simulation.from_archive("test.bin",5) becomes rebound.Simulation("test.bin",5)
+ ```
+
+### Version 3.8.0
+* The hybrid integrator MERCURIUS has been completely rewritten. It can now much more easily be used in simulations where physical collisions occur. There are no more hidden particle arrays in the background, meaning adding and removing particles can occur in the same way as for other integrators. It also works reliably with any additional forces.
+* The old hybrid integrator HERMES has been removed. MERCURIUS should always be equal or better in performance and accuracy.
+
+### Version 3.7.1
+* Added getBezierPaths to Simulationarchive to allow for easy plotting of complicated trajectories. To do this, store a lot of snapshots in the Simulationarchive (several per orbit!).
+* Added functionality to add, subtract, multiply and divide simulations. This might be useful when developing new algorithms, but is most likely not useful for most users.
+
+### Version 3.7.0
+* Added a deep copy functionality: reb_simulation_copy() in C, and sim.copy() in python.
+* Refactored WHFast to enable calling only certain substeps.
+
+### Version 3.6.8
+* Added the rhill property to reb_orbit in C and the Orbit and Particle classes in Python. This parameter corresponds to the circular Hill radius of the particle: $ a (m/(3M)^{1/3}$.
+
+### Version 3.6.7
+* Fixes an issue related to collisions and the Mercurius integrator that prevented the last_collision property to be updated.
+
+### Version 3.6.6
+* New: Fancy plotting routine. Usage: rebound.OrbitPlot(sim, fancy=True)
+
+### Version 3.6.5
+* One can now add particles from NASA Horizons using Julian Days. For example: sim.add("Earth", date="JD2458327.500000")
+
+### Version 3.6.4
+* Fixes a memory leak when using the old Simulationarchive version. Thanks to Ian Rabago for reporting the issue.
+
+### Version 3.6.2
+* Fixes a memory leak in the Simulationarchive read function.
+
+### Version 3.6.1
+* Removed function calls to open_memstream and fmemopen which might not work on older Mac OSX versions. This only affects the internals and there are no changes to user interface.
+* Minor bug fixes
+
+### Version 3.6.0
+* Simulationarchive Version 2. With the new version of the Simulationarchive file format, you can now create snapshots of your simulations without any restrictions. You can change the number of particles, the timestep, even the integrator used during the integration. REBOUND automatically detects what has changed and only stores the differences in incremental snaphots. This reduces the filesize while keeping the format as flexible as possible. The old Simulationarchive Version 1 is still supported for now but might become deprecated in the future. All examples have been updated. As usual these are as usual good starting points for understanding the functionality and the syntax.
+
+### Version 3.5.12
+* Added REB_COLLISION_LINE. This is a collision detection routine which serves for collisions during the last timestep, assuming that all particles travel along straight lines. This can be useful in cases where not every collision needs to be detected exactly, but the overall collision rate should be reproduced. The algorithm is O(N**2).
+* Bug related to N_active and variational particles has been fixed.
+* A bug where WHFast might not converge in rare cases involving negative timesteps has been fixed.
+
+### Version 3.5.11
+* Changed default collision behaviour from hardsphere bouncing to halting the simulation. An exception is raised when using the python version. In C, you need to check the status flag after integrating the simulation.
+
+### Version 3.5.10
+* Refactored OrbitPlot.
+
+### Version 3.5.9
+* SIGINT handler added. Allows for garceful exit and keyboard interrupts (even from python).
+
+### Version 3.5.8
+* WebGL widget text overlay added.
+
+### Version 3.5.7
+* Bug fixes related to WebGL widget and ipywidgets version 6
+
+### Version 3.5.6
+* Updated WebGL widget to work with ipywidgets version 7
+
+### Version 3.5.5
+* Various fixed for Mercurius
+
+### Version 3.5.4
+* Bug fix for N_active=-1 (default)
+
+### Version 3.5.3
+* Allow for better parallelization of WHFast with OpenMP.
+* Addded example of the Solar System with Testparticles.
+* Made simulationarchive_append a public function (might be useful for some hacking projects).
+
+### Version 3.5.2
+* Fixes an issue with the WebGL widget.
+* Fixes an issue with external forces and MERCURIUS.
+
+### Version 3.5.1
+* MERCURIUS is not compatible with binary files and the Simulationarchive.
+
+### Version 3.5.0
+* The WHFast integrator now supports Jacobi coordinates (default), democratic heliocentric coordinates and WHDS coordinates. The previously separate WHFastHelio integrator has been removed. The coordinate system can now be changed by simply setting the coordinates flag in the ri_whfast struct.
+* Included an experimental new integrator MERCURIUS. This is similar to the hybrid integrator in Mercury but uses WHFast and IAS15. Not ready for production yet.
+
+### Version 3.4.0
+* Added a screenshot functionality for the WebGL ipython widget. This lets you take screenshots programmatically which is useful to create movies of simulations.
+
+### Version 3.3.1
+* Removed the march=native compiler flag as it seems to be problematic for some OSX/Sierra compilers.
+
+### Version 3.3.0
+* JANUS integrator added. This is a bit-wise reversible high-order symplectic integrator. At this time, it remains experimental. Details about this integrator will be published in an upcoming paper.
+
+### Version 3.2.4
+* Changes to the WHFastHelio integrator. This integrator now uses democratic heliocentric coordinates and a Hamiltonian splitted as proposed by Hernandez and Dehnen (2017), WHDS, which splits the Hamiltonian into three parts. It has the advantage that the integrator solves the two body problem exactly. It is not compatible with symplectic correctors, this functionality has been removed for WHFastHelio. For very high accuracy integrations of stable planetary systems, the WHFast integrator in Jacobi coordinated (and potentially symplectic correctors) should be better suited.
+
+### Version 3.2.3
+* Various minor bug fixes. Added pre-timestep modifications for REBOUNDx.
+
+### Version 3.2.2
+* Various minor bug fixes. One related to exact_finish_time=1.
+
+### Version 3.2.0
+* Added real-time interactive 3D visualizations using WebGL for Jupyter notebooks. This is an early release. Not everything might be working yet and new feature will be added to the widget class. To try it out, simply run `sim.widget()` in a Jupyter notebook. Note that you need to have ipywidgets installed and enabled.
+* Minor changes to the Visualization backend. This should not have any consequences for users.
+
+
+### Version 3.1.1
+* Now stores the first characters of the current githash in binary files. This is helpful when trying to restart simulations from a binary file and making sure one uses the same version of REBOUND than in the original run. Currently, the git hash is not automatically compared when reloading a binary file. To view the githash, use e.g. hexdump. The hash appears between the first and second zero character in the first 64 bytes of the file.
+
+### Version 3.1.0
+* Updated visualization. REBOUND now uses a modern version of OpenGL (3.3) that allows for custom shaders and therefore better looking visualizations. However, REBOUND now requires glfw3 to compile the visualization module. If you are on a Mac, then the easiest way to install the glfw3 library is with homebrew: `brew tap homebrew/versions && brew install glfw3`. If you are on Linux, you can install it with your package manager, for example with `sudo apt-get install libglfw3-dev`.
+
+### Version 3.0.0
+* Introducing the Simulationarchive. The Simulationarchive allows for exact (bit-by-bit) reproducibility in N-body simulations and a completely new way of analyzing simulations. See Rein&Tamayo (2017) for details.
+* The binary format has changed. Binary files created with an earlier version of REBOUND can not be loaded with this version. However, future binary files will be backwards compatible from this point forward.
+
+
+## Version 2.x
+### Version 2.20.6
+* Minor bug fixes in HERMES integrator and some examples.
+
+### Version 2.20.5
+* NASA Horizons changed a telnet command. This update implements those changes and restores access to NASA Horizons from within REBOUND.
+
+### Version 2.20.4
+* Improvements to the Kepler solver. This is typically only relevant for extremly long simulation (1e11 timesteps or more) and extremely accurate simulation with symplectic correctors and a relative energy error of less than 1e-10.
+
+### Version 2.20.3
+* Small changes to HERMES integrator. It now has a Solar Switch Factor SSF to allow for close encounters with the central object.
+
+### Version 2.20.2
+* Added adaptive HSF for HERMES integrator. More documentation and paper to follow.
+
+### Version 2.20.1
+* Added symplectic correctors for WHFastHelio integrator. See Wisdom (2006).
+* Improved accuracy of symplectic corrector coefficients for WHFast and WHFastHelio.
+
+### Version 2.20.0
+* Added new WHFastHelio integrator. This integrator uses the WHFast Kepler solver, but uses democratic heliocentric coordinates (WHFast itself uses Jacobi coordinates). Heliocentric coordinates are advantages if planets swap positions.
+
+### Version 2.19.2
+* Changes to how particle hashes are handled.
+
+### Version 2.19.1
+* This version removes the old SWIFTER based Wisdom-Holman routine, INTEGRATOR_WH. It wasn't working correctly for a while and the WHFast (INTEGRATOR_WHFAST) should be superior in any possible case we can think of.
+
+### Version 2.19.0
+* Added warning/error message system. This allows warning messages to be shown directly in iPython/python programs, rather than being shown on the console. To hide the warning messages, use a filter, e.g.
+.. code:: python
+
+ with warnings.catch_warnings(record=True) as w:
+ warnings.simplefilter("always")
+ # Execute a command which triggers a warning message.
+ # The message will not show up.
+* Improvements regarding the WHFast logic for hyperbolic orbis. No changes should be noticeable to users.
+
+### Version 2.18.9
+* Added the reb_simulation_get_serialized_particle_data function for fast access to particle data via numpy array. The full syntax is explained in the documentation. Here is a short example:
+.. code:: python
+
+ import numpy as np
+ a = np.zeros((sim.N,3),dtype="float64")
+ sim.serialize_particle_data(xyz=a)
+ print(a)
+
+
+### Version 2.18.5
+* When loading a simulation from a binary file, REBOUND now checks if the version of the binary file is the same as the current version.
+* When saving a simulation to a binary file, all the auxiliary arrays for IAS15 are now stored. This allows for bit-by-bit reproducibility in simulations that are making use of checkpoints.
+
+
+### Version 2.18.0
+* We replaced the old HYBRID integrator with the new and better HERMES integrator. Details of the HERMES integrator will be explained in an upcoming paper Silburt et al (2016, in prep).
+
+### Version 2.17.0
+* What used to be called ``id`` in the particle structure is now called ``hash``. This can be used to uniquely identify particles in a simulation. In many cases, one can just identify particles by their position in the particle array, e.g. using ``sim.particles[5]``. However, in cases where particles might get reordered in the particle array (e.g. when using a tree code), when particles can merge (by using the ``collision_resolve_merge`` routine), or when particles get added or removed manually.
+* The syntax is as follows:
+.. code:: python
+
+ sim = rebound.Simulation()
+ sim.add(m=1)
+ sim.add(m=1e-3,a=1)
+ # Setting a hash using a string:
+ sim.particles[1].hash = "planet1"
+ # Finding a particle using a string:
+ p = sim.get_particle_by_hash("planet1")
+ # Setting a random unique hash:
+ sim.particles[1].hash = sim.generate_unique_hash()
+ # Save unique hash to find particle later
+ uhash = sim.particles[1].hash
+ # Find particle using the hash
+ p = sim.get_particle_by_hash(uhash)
+
+
+
+### Version 2.0.0
+* We made many changes to the code. Most importantly, REBOUND is now thread-safe and does not use global variables anymore. All the variables that were previously global, are now contained in the ``reb_simulation`` structure. This has many advantages, for example, you can run separate simulations in parallel from within one process.
+* We also made it possible to choose all modules at runtime (compared to the selection in the ``Makefile`` that was used before). This is much more in line with standard UNIX coding practice and does not severely impact performance (it might even help making REBOUND a tiny bit faster). This makes REBOUND a fully functional shared library. We added a prefix to all public functions and struct definitions: ``reb_``.
+* There are still some features that haven't been fully ported. Most importantly, the MPI parallelization and the SWEEP collision detection routine.
+* The best way to get an idea of the changes we made is to look at some of the example problems and the new REBOUND documentation. If you have trouble using the new version or find a bug, please submit an issue or a pull request on github.
+
diff --git a/rebound/source/docs/chaos.md b/rebound/source/docs/chaos.md
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+++ b/rebound/source/docs/chaos.md
@@ -0,0 +1,102 @@
+# Chaos indicators
+REBOUND supports different chaos indicators.
+All of these make use of variational equations, but most of the complexity is hidden.
+
+## Initialization
+If you want to use a chaos indicator in REBOUND, first add all the particles to your simulations.
+Then, initialize the variational particles and MEGNO variables with
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ // ... add particles ...
+ reb_simulation_init_megno(r);
+ ```
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ # ... add particles ...
+ sim.init_megno()
+ ```
+
+REBOUND uses random numbers to initialize the variational particles.
+The initial seed is chosen based on the current time and the process id.
+This ensures the seed is different every time you run the simulation.
+See the discussion on [random sampling](c_randomsamplingfunctions.md) for more details.
+
+If you want to have reproducible result, you can specify the seed manually:
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ // ... add particles ...
+ reb_simulation_init_megno_seed(r, 0); // 0 is the initial seed
+ ```
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ # ... add particles ...
+ sim.init_megno(seed=0) # 0 is the initial seed
+ ```
+## Accessing chaos indicators
+Once you've initialized the chaos indicators, you can integrate the simulation normally.
+To print out the MEGNO value or the largest Lyapunov characteristic number (LCN), use the following syntax:
+
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ // ... add particles ...
+ reb_simulation_init_megno_seed(r);
+ // ... integrate ...
+ printf("MEGNO = %f\n", reb_simulation_megno(r));
+ printf("LCN = %f\n", reb_simulation_lyapunov(r));
+ ```
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ # ... add particles ...
+ sim.init_megno()
+ # ... integrate ...
+ print("MEGNO", sim.calculate_megno())
+ print("LCN", sim.lyapunov())
+ ```
+!!! Note
+ Using chaos indicators is not always straightforward.
+ It can be particularly tricky to figure out how long to integrate for.
+ If the integration time is too short, you might not capture the Lyapunov timescale accurately.
+ On the other hand, if the integration time is too long, you can run into problems as well because quantities tend to grow exponentially with time in chaotic systems.
+
+!!! Note
+ There are different definitions of the LCN which might differ by a factor of order unity.
+ Here, we're following Eq. 24 of [Cincotta and Simo (2000)](https://aas.aanda.org/articles/aas/abs/2000/20/h1686/h1686.html).
+
+## Re-scaling of variational equations
+
+!!! Important
+ This is a new feature, first implemented in version 3.21
+
+REBOUND will automatically re-scale first order variational equation once any coordinate of a variational particle becomes larger than $10^{100}$.
+This is only possible for first order variational equations because they are linear.
+It is not possible to re-scale second order equations.
+For the calculation of MEGNO, all this is done behind the scenes and no user intervention is needed.
+However, should you be interested in the actual value of the variational particles, for example to calculate a Lyapunov exponent manually, then you need to take the value of the `lrescale` variable into account.
+This variable contains the natural logarithm of all re-scaling factors that have been applied throughout the integration to a given set of variational particles.
+
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ // ... add particles ...
+ reb_simulation_init_megno_seed(r);
+ // ... integrate ...
+ struct reb_variational_configuration* vc = &(r->var_config[0]);
+ double log_x = log(r->particles[vc->index].x) + vc->lrescale; // log of x coordinate of variational particle
+ ```
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ # ... add particles ...
+ sim.init_megno()
+ # ... integrate ...
+ vc = sim.var_config[0]
+ log_x = vc.particles[0] + vc.lrescale // log of x coordinate of variational particle
+
+Note that above the calculations involving the rescaling factors have been done in log space as floating point numbers cannot be used to represent a number larger than $10^{308}$.
+For a more complete example, check out the [iPython Variational Equation example](ipython_examples/VariationalEquations.ipynb).
diff --git a/rebound/source/docs/collisions.md b/rebound/source/docs/collisions.md
new file mode 100644
index 0000000000000000000000000000000000000000..72aa116313c14e4a099c7e7672ed4f37e46a1d95
--- /dev/null
+++ b/rebound/source/docs/collisions.md
@@ -0,0 +1,246 @@
+# Collisions
+
+## Detecting collisions
+
+REBOUND comes with several collision detection modules.
+These modules check for physical collisions (the distance between two particles is closer than the sum of the radii), not close encounters.
+For a collision to occur between two particles, at least one of them needs to have a finite radius and collision detection needs to be turned on (it is turned off by default).
+
+
+### No collisions
+By default REBOUND does not search for collisions.
+You can manually set the collision routine to NONE with the following code:
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ r->collision = REB_COLLISION_NONE;
+ ```
+
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.collision = "none"
+ ```
+
+### Direct
+The direct collision detection module is a brute force collision search and scales as $O(N^2)$.
+It checks for instantaneous overlaps between every particle pair.
+The following code enables this module:
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ r->collision = REB_COLLISION_DIRECT;
+ ```
+
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.collision = "direct"
+ ```
+
+!!! Important
+ This method checks for instantaneous overlaps. It does this only after each timestep.
+ This means that if the timestep is large enough for particles to pass completely through each other, then the collision will be missed.
+
+
+
+### Line
+This is a brute force collision search and scales as $O(N^2)$ but compared to the direct method described above, this algorithm checks for overlapping particles during the timestep (not just at the end).
+It assumes particles travelled along straight lines during the timestep and might therefore miss some collisions.
+
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ r->collision = REB_COLLISION_LINE;
+ ```
+
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.collision = "line"
+ ```
+
+### Tree
+This method uses an oct-tree to check for overlapping particles at the end of the timestep.
+When a large number of particles $N$ is used, this method scales as $O(N log(N))$, rather than $O(N^2)$ for the direct search.
+Note that you need to initialize the simulation box whenever you want to use the tree.
+Below is an example on how to enable the tree based collision search.
+
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ reb_simulation_configure_box(r, 10, 1, 1, 1); # confine the simulation to a box of size 10
+ r->collision = REB_COLLISION_TREE;
+ ```
+
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.configure_box(10) # confine the simulation to a box of size 10
+ sim.collision = "tree"
+ ```
+
+
+### Linetree
+Similar to the tree method, this method also uses an oct-tree and has a scaling of $O(N log(N))$.
+It checks for overlapping trajectories during the last timestep, not only for overlapping particles at the end of the timestep.
+It might still miss some collisions because it assumes that particles travel along straight lines.
+
+
+Below is an example on how to enable the line-tree collision search.
+
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ reb_simulation_configure_box(r, 10, 1, 1, 1); # confine the simulation to a box of size 10
+ r->collision = REB_COLLISION_LINETREE;
+ ```
+
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.configure_box(10) # confine the simulation to a box of size 10
+ sim.collision = "linetree"
+ ```
+
+## Resolving collisions
+
+Once a collision has been detected, you have a choice on what to do next.
+You might just want to merge particles, let them bounce off each other, or simply keep a log of all collisions that occurred.
+
+REBOUND comes with several built-in collision resolve functions.
+You can also write your own.
+
+Internally this functionality is implemented using a [function pointer](https://www.cprogramming.com/tutorial/function-pointers.html).
+You can set this pointer to a function that should be called when a collision occurs, whether it be a built-in function or your own.
+
+### Halt
+
+This function resolves a collision by simply halting the integration and setting the `status` flag in the simulation to `REB_STATUS_COLLISION`.
+In python this will raise the `Collision` exception.
+This is the default.
+It can also be set manually using the following syntax:
+
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ r->collision = REB_COLLISION_DIRECT;
+ r->collision_resolve = reb_collision_resolve_halt;
+ ```
+
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.collision = "direct"
+ sim.collision_resolve = "halt"
+ ```
+
+### Hard-sphere
+
+This assumes a hard-sphere collision and uses the `coefficient_of_restitution` function pointer in `struct reb_simulation` to determine coefficient of restitution which can be velocity dependent
+It conserves momentum and mass.
+Depending on the coefficient of restitution, it also conserves energy.
+
+The following example shows how to set up a hard-sphere collision resolve function and a direct collision detection routine.
+
+=== "C"
+ ```c
+ double coefficient_of_restitution_constant(const struct reb_simulation* const r, double v){
+ // v is the normal impact velocity.
+ // Here, we just use a constant coefficient of restitution
+ return 0.5;
+ }
+ struct reb_simulation* r = reb_simulation_create();
+ r->collision = REB_COLLISION_DIRECT;
+ r->coefficient_of_restitution = coefficient_of_restitution_constant;
+ r->collision_resolve = reb_collision_resolve_hardsphere;
+ ```
+
+=== "Python"
+ ```python
+ def coefficient_of_restitution_constant(r, v):
+ # v is the normal impact velocity.
+ # Here, we just use a constant coefficient of restitution
+ return 0.5
+ sim = rebound.Simulation()
+ sim.collision = "direct"
+ sim.coefficient_of_restitution = coefficient_of_restitution_constant
+ sim.collision_resolve = "hardsphere"
+ ```
+
+
+### Merge
+
+This function merges the two colliding particles.
+It conserves mass, momentum and volume, but not energy.
+The particle with the higher index will be removed.
+
+The following example shows how to set up a hard-sphere collision resolve function and a direct collision detection routine.
+
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ r->collision = REB_COLLISION_DIRECT;
+ r->collision_resolve = reb_collision_resolve_merge;
+ ```
+
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.collision = "direct"
+ sim.collision_resolve = "merge"
+ ```
+
+### Custom function
+You can write your own collision resolve function.
+In your function, you can update the properties of the particles involved in the collision.
+The return value of your function (of type `enum REB_COLLISION_RESOLVE_OUTCOME`) determines if a particle gets removed.
+
+- `REB_COLLISION_RESOLVE_OUTCOME_REMOVE_NONE` or `0`: don't remove either particle from the simulation
+- `REB_COLLISION_RESOLVE_OUTCOME_REMOVE_P1` or `1`: remove the first particle (`p1`) from the simulation
+- `REB_COLLISION_RESOLVE_OUTCOME_REMOVE_P2` or `2`: remove the second particle (`p2`) from the simulation
+- `REB_COLLISION_RESOLVE_OUTCOME_REMOVE_BOTH` or `3`: remove both particles from the simulation
+
+Here is a short example on how to write a simple custom collision resolve function:
+
+=== "C"
+ ```c
+ enum REB_COLLISION_RESOLVE_OUTCOME collision_print_only(struct reb_simulation* const r, struct reb_collision c){
+ printf("%f\t", r->p);
+ printf("%f\t", r->particles[c.p1].x); // x position of particle 1
+ printf("%f\n", r->particles[c.p2].x); // x position of particle 2
+ return REB_COLLISION_RESOLVE_OUTCOME_REMOVE_NONE; // Don't remove either particle
+ }
+
+ int main(int argc, char* argv[]){
+ struct reb_simulation* r = reb_simulation_create();
+ r->collision = REB_COLLISION_DIRECT;
+ r->collision_resolve = collision_print_only;
+ }
+ ```
+
+=== "Python"
+ ```python
+ def collision_print_only(sim_pointer, collision):
+ sim = sim_pointer.contents # get simulation object from pointer
+ print(sim.t) # print time
+ print(sim.particles[collision.p1].x) # x position of particle 1
+ print(sim.particles[collision.p2].x) # x position of particle 2
+ return 0 # Don't remove either particle
+
+ sim = rebound.Simulation()
+ sim.collision = "direct"
+ sim.collision_resolve = collision_print_only
+ ```
+The first argument of the collision resolve function is a pointer to the simulation.
+The second argument is a `reb_collision` structure.
+It contains information about which particles are involved in the collision and, for periodic or shear-periodic [boundary conditions](boundaryconditions.md), if the collision occurred across a boundary:
+
+`int p1`
+: Index corresponding to one of the colliding particles
+
+`int p2`
+: Index corresponding to one of the colliding particles
+
+`struct reb_vec6d gb`
+: Shift of particle p1 due to a collision across periodic and shearing sheet boundaries. All entries are zero if a normal collision occurs.
diff --git a/rebound/source/docs/examples.md b/rebound/source/docs/examples.md
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+# Examples in REBOUND
+We provide a lot of examples for REBOUND. We think examples are the easiest way to learn how to use REBOUND.
+This page contains a list of all examples that come with REBOUND.
+The examples are sorted by topic.
+Note that some examples use the C version, other the python version of REBOUND.
+Often, the syntax is very similar and you might want to look at the C examples even if you want to write python code and vice verse.
+!!! Info
+ You can find the source code for all examples in the `examples/` and `ipython_examples/` directories.
+
diff --git a/rebound/source/docs/generate_python_docs.py b/rebound/source/docs/generate_python_docs.py
new file mode 100644
index 0000000000000000000000000000000000000000..b0098c790437b790ba17be52f7663858de25a15c
--- /dev/null
+++ b/rebound/source/docs/generate_python_docs.py
@@ -0,0 +1,39 @@
+import rebound
+import inspect
+import docstring_to_markdown
+def convert_code_blocks(doc):
+ new_doc = ""
+ lines = doc.split("\n")
+ first = True
+ for line in lines:
+ if first:
+ if line[:3]==">>>":
+ first = False
+ new_doc += "```python\n"
+ new_doc += line[3:]+"\n"
+ else:
+ new_doc += line+"\n"
+ else:
+ if line[:3]==">>>":
+ new_doc += line[3:]+"\n"
+ else:
+ new_doc += "```\n"
+ new_doc += line+"\n"
+ first = True
+ if first==False:
+ new_doc += "```\n"
+
+ return new_doc
+
+def render_class(cls, functions=None):
+ d = "## Class `"+cls+"`\n"
+ d += convert_code_blocks(inspect.cleandoc(eval(cls).__doc__))
+ for function in functions:
+ f = getattr(eval(cls),function)
+ d += "## Function `"+cls+"."+function+"`\n"
+ d += convert_code_blocks(inspect.cleandoc(f.__doc__))
+
+ return d
+
+print(render_class("rebound.Simulation",["copy"]))
+
diff --git a/rebound/source/docs/gravity.md b/rebound/source/docs/gravity.md
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+# Gravity solvers
+
+## Basic
+`REB_GRAVITY_BASIC`
+
+The basic gravity routine works is the default. It works in most cases.
+It uses direct summation to calculate gravitational forces between all particle pairs.
+OpenMP parallelization is implemented. If OpenMP is turned on, the scaling is $O(N^2)$, otherwise, it is $O(\frac12 N^2)$, where $N$ is the number of particles.
+
+## Compensated
+`REB_GRAVITY_COMPENSATED`
+
+This routine also uses direct summation but in addition makes use of compensated summation to minimize round-off errors.
+There are only a few special cases where the round-off error in force calculations has a dominant effect. In most cases, the basic gravity routine is faster and equally accurate.
+
+## Tree
+`REB_GRAVITY_TREE`
+
+This method uses an oct tree (Barnes and Hut 1986) to approximate self-gravity. It scales as $O(N \log(N))$.
+
+## Tree
+`REB_GRAVITY_JACOBI`
+
+Direct summation, scales as $O(N^2)$, includes special terms needed for some symplectic integrators.
+
+## None
+`REB_GRAVITY_NONE`
+
+By using this gravity routine, no self-gravity calculated. It is still possible to include additional forces.
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+version https://git-lfs.github.com/spec/v1
+oid sha256:296d298b253a126e4803c81f9025b4ccbdceb65e3b5e3f8be6b0723a4ad04a90
+size 710010
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+# Welcome to REBOUND
+
+
+
+REBOUND is an N-body integrator, i.e. a software package that can integrate the motion of particles under the influence of gravity. The particles can represent stars, planets, moons, ring or dust particles. REBOUND is very flexible and can be customized to accurately and efficiently solve many problems in astrophysics.
+
+## Features
+
+
+* No dependencies on external libraries.
+* Runs natively on Linux, MacOS, and Windows.
+* Symplectic integrators ([WHFast](integrators/#whfast), [SEI](integrators/#sei), [LEAPFROG](integrators/#leapfrog), [EOS](integrators/#embedded-operator-splitting-method-eos))
+* Hybrid reversible integrators for planetary dynamics with arbitrary close encounters ([TRACE](integrators/#trace))
+* Hybrid symplectic integrators for planetary dynamics with close encounters ([MERCURIUS](integrators/#mercurius))
+* High order symplectic integrators for integrating planetary systems ([SABA](integrators/#saba), WH Kernel methods)
+* High accuracy non-symplectic integrator with adaptive time-stepping ([IAS15](integrators/#ias15))
+* Can integrate arbitrary user-defined ODEs that are coupled to N-body dynamics for tides, spin, etc
+* Support for collisional/granular dynamics, various collision detection routines
+* The computationally intensive parts of the code are written entirely in C, conforming to the ISO standard C99, and can be used as a thread-safe shared library
+* Easy-to-use Python module, installation in 3 words: `pip install rebound`
+* Real-time, 3D visualization, for both C and Python.
+* Extensive set of example problems for both C and Python. You can run examples directly from your browser without the need to download or install anything.
+* Parallelized [WHFast512](integrators/#whfast512) integrator for super fast integrations of planetary systems with SIMD AVX512 instructions
+* Parallelized with OpenMP (for shared memory systems)
+* Parallelized with [MPI](mpi/) is supported for some special use cases only (using an essential tree for gravity and collisions)
+* The code is 100% open-source. All features are included in the public repository on [github](https://github.com/hannorein/rebound)
+
+## Contributors
+
+* Hanno Rein, University of Toronto,
+* Dan Tamayo, Harvey Mudd College
+* David S. Spiegel, Institute for Advanced Study Princeton,
+* Garett Brown, University of Toronto,
+* Shangfei Liu, Kavli Institute for Astronomy and Astrophysics at Peking University,
+* Ari Silburt, Penn State University,
+* Pejvak Javaheri, University of Toronto,
+* Ruth Huang, University of Toronto,
+* and many others! Check the git history to find out who contributed to the code.
+
+REBOUND is open source and you are invited to contribute to this project!
+
+## YouTube tutorials
+
+There are several short YouTube videos describing various aspects of REBOUND available at .
+
+## Related projects
+
+### Additional physics
+To easily incorporate additional physics modules such as migration forces, GR effects and spin into your REBOUND simulations, see REBOUNDx at .
+
+### Analytical and semianalytical tools
+If you're interested in comparing numerical simulations to analytical and semianalytical tools for celestial mechanics, see Celmech at .
+
+### Ephemeris-quality integrations of test particles
+To generate ephemeris-quality integrations of test particles in the Solar System with a precision on par with JPL's small body integrator, see ASSIST at .
+
+
+## Papers
+
+There are several papers describing the functionality of REBOUND.
+
+1. Rein & Liu 2012 (Astronomy and Astrophysics, Volume 537, A128) describes the code structure and the main feature including the gravity and collision routines for many particle systems.
+
+2. Rein & Tremaine 2011 (Monthly Notices of the Royal Astronomical Society, Volume 415, Issue 4, pp. 3168-3176) describes the Symplectic Epicycle integrator for shearing sheet simulations.
+
+3. Rein & Spiegel 2015 (Monthly Notices of the Royal Astronomical Society, Volume 446, Issue 2, p.1424-1437) describes the versatile high order integrator IAS15 which is now part of REBOUND.
+
+4. Rein & Tamayo 2015 (Monthly Notices of the Royal Astronomical Society, Volume 452, Issue 1, p.376-388) describes WHFast, the fast and unbiased implementation of a symplectic Wisdom-Holman integrator for long term gravitational simulations.
+
+5. Rein & Tamayo 2016 (Monthly Notices of the Royal Astronomical Society, Volume 459, Issue 3, p.2275-2285) develop the framework for second order variational equations.
+
+6. Rein & Tamayo 2017 (Monthly Notices of the Royal Astronomical Society, Volume 467, Issue 2, p.2377-2383) describes the Simulationarchive for exact reproducibility of N-body simulations.
+
+7. Rein & Tamayo 2018 (Monthly Notices of the Royal Astronomical Society, Volume 473, Issue 3, p.3351–3357) describes the integer based JANUS integrator.
+
+8. Rein, Hernandez, Tamayo, Brown, Eckels, Holmes, Lau, Leblanc & Silburt 2019 (Monthly Notices of the Royal Astronomical Society, Volume 485, Issue 4, p.5490-5497) describes the hybrid symplectic integrator MERCURIUS.
+
+9. Rein, Tamayo & Brown 2019 (Monthly Notices of the Royal Astronomical Society, Volume 489, Issue 4, November 2019, Pages 4632-4640) describes the implementation of the high order symplectic integrators SABA, SABAC, SABACL, WHCKL, WHCKM, and WHCKC.
+
+10. Javaheri, Rein & Tamayo 2023 (The Open Journal of Astrophysics, Volume 6, July 2023) describes the WHFast512 integrator which uses AVX512 instructions.
+
+## Acknowledgements
+
+If you use this code or parts of this code for results presented in a scientific publication, we would greatly appreciate a citation.
+The simplest way to find the citations relevant to the specific setup of your REBOUND simulation is:
+
+```python
+sim = rebound.Simulation()
+-your setup-
+sim.cite()
+```
+
+!!! Info
+ When you cite one of the REBOUND papers, your paper will receive an automatic shout-out from the [REBOUND Citation Bot](https://botsin.space/@reboundbot).
+
+## License
+
+REBOUND is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
+
+REBOUND is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along with REBOUND. If not, see .
+
diff --git a/rebound/source/docs/integrators.md b/rebound/source/docs/integrators.md
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+# Integrators
+
+
+
+Numerical integrators are the backbone of any N-body package.
+A numerical integrator evolves particles forward in time, one timestep at a time.
+To do that, the integrator needs to know the current position and velocity coordinates of the particles, and the equations of motion which come in the form of a set of ordinary differential equations.
+
+Because an exact solution to these differential equations is in general unknown, each integrator attempts to approximate the true solution numerically.
+Different integrators do this differently and each of them has some advantages and some disadvantages.
+Each of the built-in integrators of REBOUND is described in this section.
+
+## IAS15
+
+
+
+IAS15 stands for **I**ntegrator with **A**daptive **S**tep-size control, **15**th order. It is a very high order, non-symplectic integrator which can handle arbitrary forces (including those who are velocity dependent).
+It is in most cases accurate down to machine precision (16 significant decimal digits).
+The IAS15 implementation in REBOUND can integrate variational equations.
+The algorithm is described in detail in [Rein & Spiegel 2015](https://ui.adsabs.harvard.edu/abs/2015MNRAS.446.1424R/abstract) and also in the original paper by [Everhart 1985](https://ui.adsabs.harvard.edu/abs/1985ASSL..115..185E/abstract).
+
+
+IAS15 is the default integrator of REBOUND, so if you want to use it, you don't need to do anything.
+However, you can also set it explicitly:
+
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ r->integrator = REB_INTEGRATOR_IAS15;
+ ```
+
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.integrator = "ias15"
+ ```
+
+The setting for IAS15 are stored in the `reb_integrator_ias15` structure.
+
+`epsilon` (`double`)
+: IAS15 is an adaptive integrator. It chooses its timesteps automatically. This parameter controls the accuracy of the integrator. The default value is $10^{-9}$. Setting this parameter to 0 turns off adaptive timestepping and a constant timestep will is used. Turning off adaptive time-stepping is rarely useful.
+
+ !!! Important
+ It is tempting to change `epsilon` to achieve a speedup at the loss of some accuracy. However, that makes rarely sense. The reason is that IAS15 is a very high (15th!) order integrator. Suppose we increase the timestep by a factor of 10. This will increase the error by a factor of $10^{15}$. In other words, a simulation that previously was converged to machine precision will now have an error of order unity.
+
+`min_dt` (`double`)
+: This sets the minimum allowed timestep. The default value is 0. Set this to a finite value if the adaptive timestep becomes excessively small, for example during close encounters or because of finite floating point precision. Use with caution and make sure the simulation results still make physically sense as you might be in danger of ignoring small timescales in the problem.
+ The following code sets the smallest timestep to $10^{-3}$ time units:
+ === "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ r->ri_ias15.min_dt = 1e-3;
+ ```
+
+ === "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.ri_ias15.min_dt = 1e-3
+ ```
+
+`adaptive_mode` `(unsigned int`)
+: This flag determines how the adaptive timestep is chosen. The previous name of this flag was `epsilon_global`.
+ The default is 2 which corresponds to the timestep criterion described in Pham, Rein, and Spiegel (2024).
+ This should be optimal in almost all cases.
+ If set to 0, the fractional error is estimated via `max(acceleration_error/acceleration)` and the timestep criterion of Rein and Spiegel (2015) is used.
+ If set to 1, IAS15 estimates the fractional error via `max(acceleration_error)/max(acceleration)` where the maximum is taken over all particles. As before, the timestep criterion of Rein and Spiegel (2015) is used. This was the default until January 2024.
+ If set to 3, then the criterion of [Aarseth 1985](https://ui.adsabs.harvard.edu/abs/1985IAUS..113..251A/abstract) is used.
+
+All other members of this structure are only for internal IAS15 use.
+
+
+## WHFast
+
+
+
+WHFast is an implementation of the symplectic [Wisdom-Holman](https://ui.adsabs.harvard.edu/abs/1991AJ....102.1528W/abstract) integrator.
+It is the best choice for systems in which there is a dominant central object and perturbations to the Keplerian orbits are small.
+It supports first and second symplectic correctors as well as the kernel method of [Wisdom et al. 1996](https://ui.adsabs.harvard.edu/abs/1996FIC....10..217W/abstract) with various different kernels.
+The basic implementation of WHFast is described in detail in [Rein & Tamayo 2015](https://ui.adsabs.harvard.edu/abs/2015MNRAS.452..376R/abstract).
+The higher order aspects of it are described in [Rein, Tamayo & Brown 2019](https://ui.adsabs.harvard.edu/abs/2019MNRAS.489.4632R/abstract).
+WHFast also supports first order variational equations which can be used in chaos estimators ([Rein & Tamayo 2016](https://ui.adsabs.harvard.edu/abs/2016MNRAS.459.2275R/abstract)).
+The user can choose between Jacobi, Democratic Heliocentric, WHDS, and barycentric coordinates.
+
+The following code enables the WHFast integrator.
+Because WHFast is not an adaptive integrator, you also need to set a timestep.
+Typically, this should be a small fraction (a few percent) of the smallest dynamical timescale in the problem.
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ r->integrator = REB_INTEGRATOR_WHFAST;
+ r->dt = 0.1;
+ ```
+
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.integrator = "whfast"
+ sim.dt = 0.1
+ ```
+
+
+The setting for WHFast are stored in the `reb_integrator_whfast` structure, which itself is part of the simulation structure.
+
+`unsigned int corrector`
+: This variable turns on/off different first symplectic correctors for WHFast.
+ By default, it is set to zero and symplectic correctors are turned off.
+
+ First symplectic correctors remove error terms up to $O(\epsilon \cdot dt^p)$, where $p$ is the order of the symplectic corrector, and $\epsilon$ is the mass ratio in the system.
+ The following first correctors are implemented in REBOUND:
+
+ Order | Number of stages
+ ------- | ----------------
+ 0 | Correctors turned off (default)
+ 3 | 2
+ 5 | 4
+ 7 | 6
+ 11 | 10
+ 17 | 16
+
+ For most cases you want to choose the 17th order corrector.
+ You only want to consider lower order correctors if frequent outputs are required and speed is an issue.
+ Symplectic correctors are turned on as follows.
+
+
+ === "C"
+ ```c
+ r->ri_whfast.corrector = 17;
+ r->ri_whfast.safe_mode = 0;
+ ```
+
+ === "Python"
+ ```python
+ sim.ri_whfast.corrector = 17
+ sim.ri_whfast.safe_mode = 0
+ ```
+
+ Note that the above code also turns off the safe mode.
+ Most likely, you want to do that too (see below for a description of the safe mode).
+
+`unsigned int corrector2`
+: This variable turns on/off second symplectic correctors for WHFast.
+ By default, second symplectic correctors are off (0).
+ Set to 1 to use second symplectic correctors.
+
+ !!! Info
+ The nomenclature can be a bit confusing.
+ First symplectic correctors are different from second symplectic correctors.
+ And in REBOUND first symplectic correctors have different orders (see above).
+ Second symplectic correctors on the other hand can only be turned on or off.
+ See [Rein, Tamayo & Brown 2019](https://ui.adsabs.harvard.edu/abs/2019MNRAS.489.4632R/abstract) for more on high order symplectic integrators.
+
+`unsigned int kernel`
+: This variable determines the kernel of the WHFast integrator.
+ The following options are currently supported:
+
+ - The standard Wisdom-Holman kick step. This is the default.
+ - Exact modified kick. This works for Newtonian gravity only. Not additional forces.
+ - The composition kernel.
+ - Lazy implementer's modified kick. This is often the best option.
+
+ Check [Rein, Tamayo & Brown 2019](https://ui.adsabs.harvard.edu/abs/2019MNRAS.489.4632R/abstract) for details on what these kernel methods are.
+ The syntax to use them is
+
+ === "C"
+ ```c
+ r->ri_whfast.kernel = REB_WHFAST_KERNEL_DEFAULT; // or
+ r->ri_whfast.kernel = REB_WHFAST_KERNEL_MODIFIEDKICK; // or
+ r->ri_whfast.kernel = REB_WHFAST_KERNEL_COMPOSITION; // or
+ r->ri_whfast.kernel = REB_WHFAST_KERNEL_LAZY;
+ ```
+
+ === "Python"
+ ```python
+ sim.ri_whfast.kernel = "default" # or
+ sim.ri_whfast.kernel = "modifiedkick" # or
+ sim.ri_whfast.kernel = "composition" # or
+ sim.ri_whfast.kernel = "lazy"
+ ```
+
+`unsigned int coordinates`
+: WHFast supports different coordinate systems.
+ Default are Jacobi Coordinates.
+ Other options are democratic heliocentric coordinates, and the WHDS coordinates ([Hernandez & Dehnen, 2017](https://ui.adsabs.harvard.edu/abs/2017MNRAS.468.2614H/abstract))
+ The syntax to use them is
+
+ === "C"
+ ```c
+ r->ri_whfast.coordinates = REB_WHFAST_COORDINATES_JACOBI; // or
+ r->ri_whfast.coordinates = REB_WHFAST_COORDINATES_DEMOCRATICHELIOCENTRIC; // or
+ r->ri_whfast.coordinates = REB_WHFAST_COORDINATES_WHDS; // or
+ r->ri_whfast.coordinates = REB_WHFAST_COORDINATES_BARYCENTRIC;
+ ```
+
+ === "Python"
+ ```python
+ sim.ri_whfast.coordinates = "jacobi" # or
+ sim.ri_whfast.coordinates = "democraticheliocentric" # or
+ sim.ri_whfast.coordinates = "whds" # or
+ sim.ri_whfast.coordinates = "barycentric"
+ ```
+
+`unsigned int recalculate_coordinates_this_timestep`
+: Setting this flag to one will recalculate the internal coordinates from the particle structure in the next timestep.
+ After the timestep, the flag gets set back to 0. If you want to change particles after every timestep, you also need to set this flag to 1 before every timestep. Default is 0.
+
+`unsigned int safe_mode`
+: If this flag is set (the default), WHFast will recalculate the internal coordinates (Jacobi/heliocentric/WHDS/barycentric) and synchronize every timestep, to avoid problems with outputs or particle modifications between timesteps.
+ Setting it to 0 will result in a speedup, but care must be taken to synchronize and recalculate the internal coordinates when needed. See also the AdvWHFast.ipynb tutorial.
+
+`unsigned int keep_unsynchronized`
+: This flag determines if the inertial coordinates generated are discarded in subsequent timesteps (cached Jacobi/heliocentric/WHDS/barycentric coordinates are used instead). The default is 0. Set this flag to 1 if you require outputs and bit-wise reproducibility
+
+All other members of the `reb_integrator_whfast` structure are for internal use only.
+
+## Gragg-Bulirsch-Stoer (BS)
+The Gragg-Bulirsch-Stoer integrator (short BS for Bulirsch-Stoer) is an adaptive integrator which uses Richardson extrapolation and the modified midpoint method to obtain solutions to ordinary differential equations.
+
+The version in REBOUND is based on the method described in Hairer, Norsett, and Wanner 1993 (see section II.9, page 224ff), specifically the JAVA implementation available in the [Hipparchus package](https://github.com/Hipparchus-Math/hipparchus/blob/master/hipparchus-ode/src/main/java/org/hipparchus/ode/nonstiff/GraggBulirschStoerIntegrator.java). The Hipparchus as well as the REBOUND version are adaptive in both the timestep and the order of the method for optimal performance.
+The BS implementation in REBOUND can integrate first and second order variational equations.
+
+The BS integrator is particularly useful for short integrations where only medium accuracy is required. For long integrations a symplectic integrator such as WHFast performs better. For high accuracy integrations the IAS15 integrator performs better. Because BS is adaptive, it can handle close encounters. Currently a collision search is only performed after every timestep, i.e. not after a sub-timestep.
+
+The following code enables the BS integrator and sets both the relative and absolute tolerances to 0.0001 (the default is $10^{-8}$):
+
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ r->integrator = REB_INTEGRATOR_BS;
+ r->ri_bs.eps_rel = 1e-4;
+ r->ri_bs.eps_abs = 1e-4;
+ ```
+
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.integrator = "BS"
+ sim.ri_bs.eps_rel = 1e-4
+ sim.ri_bs.eps_abs = 1e-4
+ ```
+
+The BS integrator tries to keep the error of each coordinate $y$ below $\epsilon_{abs} + \epsilon_{rel} \cdot \left|y\right|$. Note that this applies to both position and velocity coordinates of all particles which implies that the code units you're choosing for the integration matter. If you need fine control over the scales used internally, you can set the `getscale` function pointer in `r->ri_bs.nbody_ode` (this is currently undocumented, search the source code for `getscale` to find out more).
+
+!!! Info
+ The code does not guarantee that the errors remain below the tolerances. In particular, note that BS is not a symplectic integrator which results in errors growing linearly in time (phase errors grow quadratically in time). It requires some experimentation to find the tolerances that offer the best compromise between accuracy and speed for your specific problem.
+
+
+You can limit the timestep with both a maximum and minimum timestep:
+
+=== "C"
+ ```c
+ r->ri_bs.min_dt = 1e-5;
+ r->ri_bs.max_dt = 1e-2;
+ ```
+
+=== "Python"
+ ```python
+ sim.ri_bs.min_dt = 1e-5
+ sim.ri_bs.max_dt = 1e-2
+ ```
+
+Compared to the other integrators in REBOUND, BS can be used to integrate arbitrary ordinary differential equations (ODEs), not just the N-body problem. We expose an ODE-API in REBOUND which allows you to make use of this. User-defined ODEs are always integrated with BS. You can choose to integrate the N-body equations with BS as well, or any of the other integrators.
+
+If you choose BS for the N-body equations, then BS will treat all ODEs (N-body + all user-defined ones) as one big system of coupled ODEs. This means your timestep will be set by either the N-body problem or the user-defined ODEs, whichever involves the shorter timescale.
+
+If you choose IAS15 or WHFast for the N-body equation but also have user-defined ODEs, then they cannot be treated as one big coupled system of ODEs anymore. In that case the N-body integration is done first. Then the user-defined ODEs are advanced to the exact same time as the N-body system using BS using whatever timestep is required to achieve the tolerance set in the `ri_bs` struct. During the integration of the user-defined ODEs, the coordinates of the particles in the N-body simulation are assumed to be fixed at their final position and velocity. This introduces an error. However, if the system evolves adiabatically (the timescales in the user-defined ODEs are much longer than in the N-body problem), then the error will be small.
+
+The following code sets up a REBOUND simulation in which a harmonic oscillator is driven by the phase of a planet orbiting a star:
+
+=== "C"
+ ```c
+ void derivatives(struct reb_ode* const ode, double* const yDot, const double* const y, const double t){
+ struct reb_orbit o = reb_orbit_from_particle(ode->r->G, ode->r->particles[1], ode->r->particles[0]);
+ const double omega = 1;
+ double forcing = sin(o.f);
+ yDot[0] = y[1];
+ yDot[1] = -omega*omega*y[0] + forcing;
+ }
+
+ void run(){
+ struct reb_simulation* r = reb_simulation_create();
+ reb_simulation_add_fmt(r, "m", 1.);
+ reb_simulation_add_fmt(r, "m a e", 1e-3, 1., 0.1);
+
+ r->integrator = REB_INTEGRATOR_BS;
+
+ struct reb_ode* ho = reb_ode_create(r,2); // Add an ODE with 2 dimensions
+ ho->derivatives = derivatives; // Right hand side of the ODE
+ ho->y[0] = 1; // Initial conditions
+ ho->y[1] = 0;
+ }
+ ```
+
+=== "Python"
+ ```python
+ import numpy as np
+
+ def derivatives(ode, yDot, y, t):
+ omega = 1.0
+ sim_pointer = ode.contents.r
+ orbit = sim_pointer.contents.particles[1]
+ forcing = np.sin(orbit.f)
+ yDot[0] = y[1]
+ yDot[1] = -omega*omega*y[0] + forcing
+
+ sim = rebound.Simulation()
+ sim.add(m=1)
+ sim.add(m=1e-3, a=1, e=0.1)
+
+ sim.integrator = "BS"
+
+ ho = sim.create_ode(length=2) # Add an ODE with 2 dimensions
+ ho.derivatives = derivatives # Right hand side of the ODE
+ ho.y[0] = 1.0 # Initial conditions
+ ho.y[1] = 0.0
+ ```
+
+
+## Mercurius
+
+MERCURIUS is a hybrid symplectic integrator very similar to MERCURY ([Chambers 1999](https://ui.adsabs.harvard.edu/abs/1999MNRAS.304..793C/abstract)).
+It uses WHFast for long term integrations but switches over smoothly to IAS15 for close encounters.
+The MERCURIUS implementation is described in [Rein et al 2019](https://ui.adsabs.harvard.edu/abs/2019MNRAS.485.5490R/abstract).
+
+
+The following code enables MERCURIUS and sets the critical radius to 4 Hill radii
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ r->integrator = REB_INTEGRATOR_MERCURIUS;
+ r->ri_mercurius.r_crit_hill = 4.;
+ ```
+
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.integrator = "mercurius"
+ sim.ri_mercurius.r_crit_hill = 4.
+ ```
+
+The `reb_integrator_mercurius` structure contains the configuration and data structures used by the hybrid symplectic MERCURIUS integrator.
+
+`double (*L) (const struct reb_simulation* const r, double d, double dcrit)`
+: This is a function pointer to the force switching function.
+ If NULL (the default), the MERCURY switching function will be used.
+ The argument `d` is the distance between two particles.
+ The argument `dcrit` is the maximum critical distances of the two particles.
+ The return value is a scalar between 0 and 1.
+ If this function always returns 1, then the integrator effectively becomes the standard Wisdom-Holman integrator.
+
+ The following switching functions are available:
+
+
+ - Mercury switching function
+
+ This is the same polynomial switching function as used in MERCURY.
+
+ ```c
+ double reb_integrator_mercurius_L_mercury(const struct reb_simulation* const r, double d, double dcrit);
+ ```
+ - Smooth switching functions
+
+ These two polynomials switching functions are 4 and 5 times differentiable.
+ Using smooth switching functions can improve the accuracy.
+ For a detailed discussion see [Hernandez 2019](https://ui.adsabs.harvard.edu/abs/2019MNRAS.490.4175H/abstract).
+
+ ```c
+ double reb_integrator_mercurius_L_C4(const struct reb_simulation* const r, double d, double dcrit);
+ double reb_integrator_mercurius_L_C5(const struct reb_simulation* const r, double d, double dcrit);
+ ```
+
+ - Infinitely differentiable switching function
+
+ This is an infinitely differentiable switching function.
+
+ ```c
+ double reb_integrator_mercurius_L_infinity(const struct reb_simulation* const r, double d, double dcrit);
+ ```
+
+ The switching function can be set using this syntax:
+
+ === "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ r->ri_mercurius.L = reb_integrator_mercurius_L_infinity;
+ ```
+
+ === "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.ri_mercurius.L = "infinity"
+ ```
+
+`double r_crit_hill`
+: The critical switchover radii of particles are calculated automatically based on multiple criteria. One criterion calculates the Hill radius of particles and then multiplies it with the `r_crit_hill` parameter. The parameter is in units of the Hill radius. The default value is 3.
+
+`unsigned int recalculate_coordinates_this_timestep`
+: Setting this flag to one will recalculate heliocentric coordinates from the particle structure at the beginning of the next timestep. After a single timestep, the flag gets set back to 0. If one changes a particle manually after a timestep, then one needs to set this flag to 1 before the next timestep.
+
+`unsigned int recalculate_r_crit_this_timestep`
+: Setting this flag to one will recalculate the critical switchover distances dcrit at the beginning of the next timestep. After one timestep, the flag gets set back to 0. If you want to recalculate `dcrit` at every timestep, you also need to set this flag to 1 before every timestep.
+
+`unsigned int safe_mode`
+: If this flag is set to 1 (the default), the integrator will recalculate heliocentric coordinates and synchronize after every timestep to avoid problems with outputs or particle modifications between timesteps. Setting this flag to 0 will result in a speedup, but care must be taken to synchronize and recalculate coordinates manually if needed.
+
+## TRACE
+
+TRACE is a hybrid time-reversible integrator, based on the algorithm described in [Hernandez & Dehnen 2023](https://ui.adsabs.harvard.edu/abs/2023MNRAS.522.4639H/abstract).
+It uses WHFast for long term integrations but switches time-reversibly to BS or IAS15 for all close encounters. TRACE is appropriate for systems with a dominant central mass that will occasionally have close encounters.
+The TRACE implementation is described in [Lu, Hernandez & Rein](https://ui.adsabs.harvard.edu/abs/2024MNRAS.533.3708L/abstract).
+
+
+The following code enables TRACE and sets the critical radius to 4 Hill radii
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_create_simulation();
+ r->integrator = REB_INTEGRATOR_TRACE;
+ r->ri_trace.r_crit_hill = 4;
+ ```
+
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.integrator = "trace"
+ sim.ri_trace.r_crit_hill = 4
+ ```
+
+The `reb_integrator_trace` structure contains the configuration and data structures used by the hybrid symplectic TRACE integrator.
+
+`int (*S) (const struct reb_simulation* const r, const unsigned int i, const unsigned int j)`
+: This is a function pointer to the switching function for close encounters between non-central bodies.
+ If NULL (the default), the default switching function will be used.
+ The arguments `i` and `j` are the indices of the two particles considered.
+ The return value is either 0 or 1.
+ A return value of 1 means a close encounter has been flagged.
+ If the return values of both this function and the central switching function below are always 0, then the integrator effectively becomes the standard Wisdom-Holman integrator.
+
+ - Default switching function
+
+ This is a similar (but slightly modified) switching function used in MERCURY. It uses a modified Hill radius criteria, with heliocentric distance replacing semimajor axis
+
+ ```c
+ int reb_integrator_trace_switch_default(const struct reb_simulation* const r, const unsigned int i, const unsigned int j);
+ ```
+
+ The switching function can be manually set using this syntax:
+
+ === "C"
+ ```c
+ struct reb_simulation* r = reb_create_simulation();
+ r->ri_trace.S = reb_integrator_trace_switch_default;
+ ```
+
+ === "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.ri_trace.S = "default"
+ ```
+
+`int (*S_peri) (const struct reb_simulation* const r, const unsigned int j)`
+: This is a function pointer to the switching function for close encounters involving the central body.
+ If NULL (the default), the default switching function will be used.
+ The argument `j` is the index of the non-central particle considered.
+ The return value is either 0 or 1.
+ A return value of 1 means a close encounter has been flagged.
+
+ - Default switching function
+
+ This switching function checks if a body is close to its pericenter by considering a timescale derived from high-order derivatives of the particle's herliocentric position, inspired by [Pham, Rein, and Spiegel 2024](https://ui.adsabs.harvard.edu/abs/2024OJAp....7E...1P/abstract).
+
+ ```c
+ int reb_integrator_trace_switch_peri_default(const struct reb_simulation* const r, const unsigned int j);
+ ```
+ The switching function can be manually set using this syntax:
+
+ === "C"
+ ```c
+ struct reb_simulation* r = reb_create_simulation();
+ r->ri_trace.S_peri = reb_integrator_trace_switch_peri_default; // default
+ r->ri_trace.S_peri = reb_integrator_trace_switch_peri_none; // Turn off pericenter switching
+ ```
+
+ === "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.ri_trace.S_peri = "default" # Following Pham et al 2024
+ sim.ri_trace.S_peri = "none" # Turn off pericenter switching
+ ```
+
+`double r_crit_hill`
+: The critical switchover radii of non-central particles are calculated based on a modified Hill radii criteria. This modified Hill radius for each particle is calculated and then multiplied by the `hillfac` parameter. The parameter is in units of the modified Hill radius. This value is used by the `default` switching function. The default value is 4.
+
+`double peri_crit_eta`
+: The criteria for a pericenter approach with the central body. This criteria is used in the `default` pericenter switching condition. It flags a particle as in a close pericenter approach if the ratio of the timestep to the condition described in [Pham, Rein, and Spiegel 2024](https://ui.adsabs.harvard.edu/abs/2024OJAp....7E...1P/abstract). The default value is 1.
+
+ The switching criteria can be manually set using this syntax:
+
+ === "C"
+ ```c
+ struct reb_simulation* r = reb_create_simulation();
+ r->ri_trace.peri_crit_eta = 0.5; // or
+ ```
+
+ === "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.ri_trace.peri_crit_eta = 0.5 # or
+ ```
+`unsigned int peri_mode`
+: This variable determines how TRACE integrates close approaches with the central star.
+ The following options are currently supported:
+
+ - Integrating the entire system with BS. This is the default.
+ - Integrating only the Kepler Step with BS.
+ - Integrating the entire system with IAS15.
+
+ Check [Lu, Hernandez & Rein 2024](https://ui.adsabs.harvard.edu/abs/2024MNRAS.533.3708L/abstract) for details on what these pericenter switching modes entail.
+ The syntax to use them is
+
+ === "C"
+ ```c
+ r->ri_trace.peri_mode = REB_TRACE_PERI_PARTIAL_BS; // or
+ r->ri_trace.peri_mode = REB_TRACE_PERI_FULL_BS; // or
+ r->ri_trace.peri_mode = REB_TRACE_PERI_FULL_IAS15; // or
+ ```
+
+ === "Python"
+ ```python
+ sim.ri_trace.peri_mode = "PARTIAL_BS" # or
+ sim.ri_trace.peri_mode = "FULL_BS" # or
+ sim.ri_trace.peri_mode = "FULL_IAS15" # or
+ ```
+## SABA
+
+SABA are symplectic integrators developed by [Laskar & Robutel 2001](https://ui.adsabs.harvard.edu/abs/2001CeMDA..80...39L/abstract) and [Blanes et al. 2013](https://ui.adsabs.harvard.edu/abs/2012arXiv1208.0689B/abstract).
+The implementation in REBOUND supports SABA1, SABA2, SABA3, and SABA4 as well as the corrected versions SABAC1, SABAC2, SABAC3, and SABAC4.
+Different correctors can be selected.
+In addition, the following methods with various generalized orders are supported: SABA(8,4,4), SABA(8,6,4), SABA(10,6,4).
+See [Rein, Tamayo & Brown 2019](https://ui.adsabs.harvard.edu/abs/2019MNRAS.489.4632R/abstract) for details on how these methods work.
+
+The `reb_integrator_saba` structure contains the configuration and data structures used by the SABA integrator family.
+
+`unsigned int type`
+: This parameter specifies which SABA integrator type is used.
+ The following SABA integrators are supported:
+
+ Numerical value | C constant name | Description
+ ------------------- | ------------------- | ----------------------------------
+ 0x0 | `REB_SABA_1` | SABA1 (Wisdom-Holman)
+ 0x1 | `REB_SABA_2` | SABA2
+ 0x2 | `REB_SABA_3` | SABA3
+ 0x3 | `REB_SABA_4` | SABA4
+ 0x100 | `REB_SABA_CM_1` | SABACM1 (Modified kick corrector)
+ 0x101 | `REB_SABA_CM_2` | SABACM2 (Modified kick corrector)
+ 0x102 | `REB_SABA_CM_3` | SABACM3 (Modified kick corrector)
+ 0x103 | `REB_SABA_CM_4` | SABACM4 (Modified kick corrector)
+ 0x200 | `REB_SABA_CL_1` | SABACL1 (lazy corrector)
+ 0x201 | `REB_SABA_CL_2` | SABACL2 (lazy corrector)
+ 0x202 | `REB_SABA_CL_3` | SABACL3 (lazy corrector)
+ 0x203 | `REB_SABA_CL_4` | SABACL4 (lazy corrector)
+ 0x4 | `REB_SABA_10_4` | SABA(10,4), 7 stages
+ 0x5 | `REB_SABA_8_6_4` | SABA(8,6,4), 7 stages
+ 0x6 | `REB_SABA_10_6_4` | SABA(10,6,4), 8 stages, default
+ 0x7 | `REB_SABA_H_8_4_4` | SABAH(8,4,4), 6 stages
+ 0x8 | `REB_SABA_H_8_6_4` | SABAH(8,6,4), 8 stages
+ 0x9 | `REB_SABA_H_10_6_4` | SABAH(10,6,4), 9 stages
+
+ SABA(10,6,4) is the default integrator. It has a generalized order of $O(\epsilon dt^{10} + \epsilon^2 dt^6 + \epsilon^3 dt^4)$.
+
+ Below is an example on how to enable the SABA integrators in REBOUND and set a specific type.
+
+ === "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ r->integrator = REB_INTEGRATOR_SABA;
+ r->ri_saba.type = REB_SABA_10_6_4;
+ ```
+
+ === "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.integrator = "saba"
+ sim.ri_saba.type = "(10,6,4)"
+ ```
+ One can also use the following shorthand:
+ ```python
+ sim = rebound.Simulation()
+ sim.integrator = "SABA(10,6,4)"
+ ```
+
+`unsigned int safe_mode`
+: This flag has the same functionality as in WHFast. Default is 1. Setting this to 0 will provide a speedup, but care must be taken with synchronizing integration steps and modifying particles.
+
+`unsigned int keep_unsynchronized`
+: This flag determines if the inertial coordinates generated are discarded in subsequent timesteps (cached Jacobi coordinates are used instead). The default is 0. Set this flag to 1 if you require outputs and bit-wise reproducibility
+
+
+
+
+## JANUS
+Janus is a bit-wise time-reversible high-order symplectic integrator using a mix of floating point and integer arithmetic.
+It is described in [Rein & Tamayo 2018](https://ui.adsabs.harvard.edu/abs/2018MNRAS.473.3351R/abstract).
+
+The following code shows how to enable JANUS and set the length and velocity scales.
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ r->integrator = REB_INTEGRATOR_JANUS;
+ r->ri_janus.scale_pos = 1e-10;
+ r->ri_janus.scale_vel = 1e-10;
+ ```
+
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.integrator = "janus"
+ sim.ri_janus.scale_pos = 1e-10
+ sim.ri_janus.scale_vel = 1e-10
+ ```
+
+
+The `reb_integrator_janus` structure contains the configuration and data structures used by the bib-wise reversible JANUS integrator.
+
+`double scale_pos`
+: Scale of the problem. Positions get divided by this number before the conversion to an integer. Default: $10^{-16}$.
+
+`double scale_vel`
+: Scale of the problem. Velocities get divided by this number before the conversion to an integer. Default: $10^{-16}$.
+
+`unsigned int order`
+: The order of the scheme. Default is 6.
+
+`unsigned int recalculate_integer_coordinates_this_timestep`
+: If this flag is set, then JANUS will recalculate the integer coordinates from floating point coordinates at the next timestep.
+
+All other members of this structure are only for internal use and should not be changed manually.
+
+
+## Embedded Operator Splitting Method (EOS)
+This is the Embedded Operator Splitting (EOS) methods described in [Rein 2019](https://ui.adsabs.harvard.edu/abs/2020MNRAS.492.5413R/abstract).
+
+The `reb_integrator_eos` structure contains the configuration and data structures used by EOS.
+
+`unsigned int phi0`
+: Outer operator splitting scheme (see below for options)
+
+`unsigned int phi1`
+: Inner operator splitting scheme (see below for options)
+
+`unsigned int n`
+: Number of sub-timesteps. Default: 2.
+
+`unsigned int safe_mode`
+: If set to 0, always combine drift steps at the beginning and end of `phi0`. If set to 1, `n` needs to be bigger than 1.
+
+
+
+The following operator splitting methods for `phi0` and `phi1` are supported in the EOS integrator.
+
+Numerical value | Constant name | Description
+--------------- | --------------------- | -------------------------------------------------
+0x00 | `REB_EOS_LF` | 2nd order, standard leap-frog
+0x01 | `REB_EOS_LF4` | 4th order, three function evaluations
+0x02 | `REB_EOS_LF6` | 6th order, nine function evaluations
+0x03 | `REB_EOS_LF8` | 8th order, seventeen function evaluations, see Blanes & Casa (2016), p91
+0x04 | `REB_EOS_LF4_2` | generalized order (4,2), two force evaluations, McLachlan 1995
+0x05 | `REB_EOS_LF8_6_4` | generalized order (8,6,4), seven force evaluations
+0x06 | `REB_EOS_PLF7_6_4` | generalized order (7,6,4), three force evaluations, pre- and post-processors
+0x07 | `REB_EOS_PMLF4` | 4th order, one modified force evaluation, pre- and post-processors, Blanes et al. (1999)
+0x08 | `REB_EOS_PMLF6` | 6th order, three modified force evaluations, pre- and post-processors, Blanes et al. (1999)
+
+
+The following code shows how to enable EOS and set the embedded methods.
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ r->integrator = REB_INTEGRATOR_EOS;
+ r->ri_eos.phi0 = REB_EOS_LF4;
+ r->ri_eos.phi1 = REB_EOS_LF4;
+ r->ri_eos.n = 6;
+ ```
+
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.integrator = "eos"
+ sim.ri_eos.phi0 = "LF4"
+ sim.ri_eos.phi1 = "LF4"
+ sim.ri_eos.n = 6
+ ```
+
+## Leapfrog
+`REB_INTEGRATOR_LEAPFROG`
+
+This is the standard leap frog integrator. It is symplectic. By default it is second order with one force evaluation per step. Higher orders of 4, 6, and 8 can be selected as well. These correspond to the 4th order Yoshida integrator and the 8th order by Blanes & Casa (2016), p91. The higher order methods have more function evaluations and are therefore slower. Note that some substeps of the higher order methods move particles backwards. Therefore higher order methods might not give accurate results when a collision search is turned on.
+
+`unsigned int order`
+: Set the order of the leapfrog integrator:
+ === "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ r->integrator = REB_INTEGRATOR_LEAPFROG;
+ r->ri_leapfrog.order = 8; // 2, 4, 6, or 8
+ ```
+
+ === "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.integrator = "leapfrog"
+ sim.ri_leapfrog.order = 8 # 2, 4, 6, or 8
+ ```
+
+## Symplectic Epicycle Integrator (SEI)
+`REB_INTEGRATOR_SEI`
+
+Symplectic Epicycle Integrator (SEI), mixed variable symplectic integrator for the shearing sheet, second order, Rein & Tremaine 2011. The `reb_integrator_sei` structure contains the configuration and data structures used by the Symplectic Epicycle Integrator (SEI).
+
+`double OMEGA`
+: Epicyclic/orbital frequency. This can be set as follows:
+ === "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ r->integrator = REB_INTEGRATOR_SEI;
+ r->ri_sei.OMEGA = 1.0;
+ ```
+
+ === "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.integrator = "sei"
+ sim.ri_sei.OMEGA = 1.0
+ ```
+
+`double OMEGAZ`
+: Epicyclic frequency in vertical direction. Defaults to `OMEGA` if not set.
+
+All other members of this structure are only for internal use and should not be changed manually.
+
+
+## No integrator
+Sometimes it might make sense to simply not advance any particle positions or velocities. By selecting this integrator, one can still perform integration steps, but particles will not move.
+
+Here is how to do that:
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ r->integrator = REB_INTEGRATOR_NONE;
+ ```
+
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.integrator = "none"
+ ```
+
+## WHFast512
+
+WHFast512 is a symplectic Wisdom-Holman integrator.
+It is using Single Instruction Multiple Data (SIMD) parallelism and 512-bit Advanced Vector Extensions (AVX512) to speed up the integration of planetary systems by up to 4.7x compared to the standard version of WHFast.
+
+!!! warning "Important"
+
+ To use WHFast512 you need to compile and run REBOUND on a computer that has a CPU which supports AVX512 instructions.
+ You will see an error message if you try to use WHFast512 but have not compiled REBOUND with the AVX512 flag.
+ We describe below how to do this for both the C and python versions of REBOUND below.
+
+ To find out if your CPU supports AVX512 instructions, check for the AVX512 flags by running
+ ```bash
+ cat /proc/cpuinfo | grep avx512
+ ```
+
+ Note that you can read Simulationarchives of simulations which used WHFast512 on machines that do not support AVX512 instruction.
+ If a synchronization is required, it will be performed with the standard WHFast integrator.
+
+
+=== "C"
+ To turn on the AVX512 flag, go to the Makefile in problem directory. Add this line at the top:
+ ```
+ export AVX512=1
+ ```
+ To explicitly turn AVX512 off, add
+ ```
+ export AVX512=0
+ ```
+ Also make sure to add the `-march=native` flag to the compiler. This will optimize your code (and enable AVX512 instruction) for the specific CPU you're using.
+ ```
+ export OPT=-march=native
+ ```
+ Then, clean your build directory and (re)-build REBOUND with
+ ```bash
+ make clean
+ make
+ ```
+
+=== "Python"
+ To use WHFast512 from python, you need to compile REBOUND with AVX512 instructions enabled.
+ They are disabled by default and enabled with the AVX512 environment variable.
+ To install the latest release of REBOUND on pypi use:
+ ```bash
+ export AVX512=1
+ pip install rebound
+ ```
+ Alternatively, you can download the latest development version of REBOUND.
+ Then set the AVX512 environment variable and install REBOUND by running
+ ```bash
+ export AVX512=1
+ pip install -e .
+ ```
+ from the main directory.
+
+Once you have compiled REBOUND with AVX512 enabled, you can use WHFast512 like any other integrator:
+
+=== "C"
+ ```c
+ struct reb_simulation* r = reb_simulation_create();
+ r->integrator = REB_INTEGRATOR_WHFAST512;
+ ```
+
+=== "Python"
+ ```python
+ sim = rebound.Simulation()
+ sim.integrator = "whfast512"
+ ```
+
+See also [this example](../c_examples/whfast512_solar_system) on how to use WHFast512.
+If you are interested in integrating 2 or 4 planet systems in parallel, see [this example](../c_examples/whfast512_2_planets).
+
+To allow for the best performance, WHFast512 has certain limitations that WHFast does not have.
+
+- The number of particles cannot exceed 9 (1 star and 8 planets) and needs to be constant.
+- Although you can use WHFast512 with any number of planets (up to 8), the performance is best if the system has either 2, 4, or 8 planets.
+- The gravitational constant needs to be exactly equal to 1. Note that you can always [rescale](../units/) your system such that G=1.
+- The integrator always combines the first and last drift step (`safe_mode=0` for WHFast).
+- No variational or test particles are supported (although a particle can have mass 0).
+- MEGNO and other chaos indicators are not supported.
+- WHFast512 always uses democratic heliocentric coordinates. Jacobi coordinates are not supported.
+- The timestep needs to be constant and the `exact_finish_time` flag needs to be set to 0. To change the timestep, first synchronize the simulation, then call `reb_simulation_reset_integrator()`.
+- The masses of all particles need to be constant. To change the masses, first synchronize the simulation, then call `reb_simulation_reset_integrator()`.
+- Additional forces (other than the GR potential) and REBOUNDx are not supported.
+
+
+The setting for WHFast512 are stored in the `reb_integrator_whfast512` structure, which itself is part of the simulation structure.
+The following settings are available:
+
+`unsigned int keep_unsynchronized`
+: This flag determines if democratic heliocentric coordinates are re-used after subsequent calls to `reb_simulation_integrate()`. The default is 0. This makes WHFast512 recalculate democratic heliocentric coordinates at the beginning of each `reb_simulation_integrate()` call. Set this flag to 1 if you want to continue an integration using unsynchronized democratic heliocentric coordinates. This is useful if you require outputs (and therefore synchronization) but don't want the integration to be affected by the output to allow for bit-wise reproducibility.
+
+`unsigned int gr_potential`
+: This flag determines if an additional $1/r^2$ potential is included in the force calculation. The default is 0. Set to 1 to turn on the potential. This can be used to mimic general relativistic precession. Note that this feature assumes [units](../units/) of AU and year/2pi.
+
+`unsigned int N_systems`
+: This flag determines how many systems are integrated in parallel. Possible values are 1, 2, or 4. By default this is set to 1 which means WHFast512 is integrating only one system at a time. If your system has fewer than 5 planets, then you can use WHFast512 to integrate 2 systems in parallel. If your system has fewer than 3 planets, then you can use WHFast512 to integrate 4 systems in parallel. If multiple systems are integrated at the same time, particles must be added in the following order: Star 1, Planet, Planet, Star 2, Planet, Planet, ... For more information see the [this example](../c_examples/whfast512_2_planets).
+
diff --git a/rebound/source/docs/ipython_examples/AdvWHFast.ipynb b/rebound/source/docs/ipython_examples/AdvWHFast.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..d29ae810ce809ab2f6d6c2130145359a44a334c6
--- /dev/null
+++ b/rebound/source/docs/ipython_examples/AdvWHFast.ipynb
@@ -0,0 +1,440 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "deletable": true,
+ "editable": true
+ },
+ "source": [
+ "# Advanced settings for WHFast: Extra speed, accuracy, and additional forces\n",
+ "\n",
+ "There are several performance enhancements one can make to WHFast. However, each one has pitfalls that an inexperienced user can unwittingly fall into. We therefore chose safe default settings that make the integrator difficult to misuse. **This makes the default WHFast substantially slower and less accurate than it can be**. Here we describe how to alter the integrator settings to improve WHFast's performance.\n",
+ "\n",
+ "**TL;DR**\n",
+ "\n",
+ "As long as \n",
+ "\n",
+ "1. you don't add, remove or otherwise modify particles between timesteps\n",
+ "2. you get your outputs by passing a list of output times ahead of time and access the `particles` pointer between calls to `sim.integrate()` (see, e.g., the Visualization section of [WHFast.ipynb](../WHFast))\n",
+ "\n",
+ "you can set `sim.ri_whfast.safe_mode = 0` to get a substantial performance boost. Under the same stipulations, you can set `sim.ri_whfast.corrector = 11` to get much higher accuracy, at a nearly negligible loss of performance (as long as there are many timesteps between outputs).\n",
+ "\n",
+ "If you want to modify particles, or if the code breaks with these advanced settings, read below for details, and check out the Common mistake with WHFast section at the bottom of [WHFast.ipynb](../WHFast)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "deletable": true,
+ "editable": true
+ },
+ "source": [
+ "**The Wisdom-Holman algorithm**\n",
+ "\n",
+ "In order to understand and apply the various integrator flags, we need to first understand the Wisdom-Holman scheme (see, e.g., Wisdom & Holman 1991, or Rein & Tamayo 2015 for more details).\n",
+ "\n",
+ "The Wisdom-Holman algorithm consists of alternating *Keplerian* steps that evolve particles on their two-body Keplerian orbits around the star with *interaction* steps that apply impulses to the particles' velocities from the interactions between bodies. The basic algorithm for a single timestep $dt$ is a Leapfrog Drift-Kick-Drift scheme with an *interaction* kick over the full $dt$ sandwiched between half timesteps of *Keplerian* drift:\n",
+ "\n",
+ "$H_{Kepler}(dt/2)\\:H_{Interaction}(dt)\\:H_{Kepler}(dt/2)$\n",
+ "\n",
+ "Timesteps like the one above are then concatenated over the full integration:\n",
+ "\n",
+ "$H_{Kepler}(dt/2)\\:H_{Interaction}(dt)\\:H_{Kepler}(dt/2)$ $H_{Kepler}(dt/2)\\:H_{Interaction}(dt)\\:H_{Kepler}(dt/2)$ ... $H_{Kepler}(dt/2)\\:H_{Interaction}(dt)\\:H_{Kepler}(dt/2)$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "deletable": true,
+ "editable": true
+ },
+ "source": [
+ "**Combining Kepler steps and synchronizing**\n",
+ "\n",
+ "It turns out that Kepler steps take longer than interaction steps as long as you don't have many planets, so an obvious and important performance boost would be to combine adjacent Kepler half-steps into full ones, i.e.:\n",
+ "\n",
+ "$H_{Kepler}(dt/2)\\:H_{Interaction}(dt)\\:H_{Kepler}(dt)\\:H_{Interaction}(dt)\\:H_{Kepler}(dt) ... \\:H_{Interaction}(dt)\\:H_{Kepler}(dt/2)$\n",
+ "\n",
+ "The issue is that if you were to, say, output the state of the particles as the simulation progressed, the positions would not correspond to anything real, since the beginning (or end) of one of the full $H_{Kepler}(dt)$ steps corresponds to some intermediate step in an abstract sequence of calculations for a given timestep. In order to get the particles' actual positions, we would have to calculate to the end the timestep we want the output for by splitting a full *Kepler* step back into two half-steps, e.g.,\n",
+ "\n",
+ "$H_{Kepler}(dt/2)\\:H_{Interaction}(dt)\\:H_{Kepler}(dt)\\:H_{Interaction}(dt)\\:H_{Kepler}(dt/2) \\text{**PRINT OUTPUT**} H_{Kepler}(dt/2) H_{Interaction}(dt)\\:H_{Kepler}(dt)$...\n",
+ "\n",
+ "We call this step of reinserting half-Kepler steps to obtain the physical state of the particles *synchronizing*. This must be done whenever the **actual** states of the particles are required, e.g., before every output, or if one wanted to use the particles' states to compute additional changes to the particle orbits between timesteps. It is also necessary to synchronize each timestep whenever the MEGNO chaos indicator is being computed.\n",
+ "\n",
+ "**Conversions between Jacobi and Inertial Coordinates**\n",
+ "\n",
+ "It turns out that the most convenient coordinate system to work in for performing the Kepler steps is often Jacobi coordinates (see, e.g., 9.5.4 of Murray & Dermott). WHFast therefore works in Jacobi coordinates by default, converting to inertial coordinates when it needs to (e.g. for output, and for doing the direct gravity calculation in the interaction step, which is most easily done in inertial coordinates).\n",
+ "\n",
+ "One feature of WHFast is that it works in whatever inertial coordinate system you choose for your initial conditions. This means that whatever happens behind the scenes, the user always gets the particles' inertial coordinates at the front end. At the beginning of every timestep, WHFast therefore has to somehow obtain the Jacobi coordinates. The straightforward thing would be to convert from the inertial coordinates to Jacobi coordinates every timestep, but these conversions slow things down, and they represent extra operations that grow the round-off error.\n",
+ "\n",
+ "WHFast therefore stores the Jacobi coordinates internally throughout the time it is running, and only recalculates Jacobi coordinates from the inertial ones if told to do so. Since Jacobi coordinates reference particles to the center of mass of all the particles with indices lower than their own (typically all the particles interior to them), the main reason you would have to recalculate Jacobi coordinates is if between timesteps you choose to somehow change the particles' positions or velocities (give them kicks in addition to their mutual gravity), or change the particles' masses. \n",
+ "\n",
+ "**Overriding the defaults**\n",
+ "\n",
+ "Let's begin by importing rebound, and defining a simple function to reset rebound and initialize a new simulation with a test case,"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
+ "outputs": [],
+ "source": [
+ "import rebound\n",
+ "import numpy as np\n",
+ "def test_case():\n",
+ " sim = rebound.Simulation()\n",
+ " sim.integrator = 'whfast'\n",
+ " sim.add(m=1.) # add the Sun\n",
+ " sim.add(m=3.e-6,e=0.99, a=1.) # add Earth\n",
+ " sim.move_to_com()\n",
+ " sim.dt = 0.2\n",
+ " return sim"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "deletable": true,
+ "editable": true
+ },
+ "source": [
+ "By default WHFast synchronizes and recalculates the Jacobi coordinates from the inertial ones every timestep. This guarantees that the user always gets physical particle states for output, and ensures reliable output if the user decides to, e.g., grow the particles' masses between timesteps. \n",
+ "\n",
+ "Now that you understand the pitfalls, if you want to boost WHFast's performance, you simply set"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
+ "outputs": [],
+ "source": [
+ "sim = test_case()\n",
+ "sim.ri_whfast.safe_mode = 0"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "deletable": true,
+ "editable": true
+ },
+ "source": [
+ "Now it becomes the user's responsibility to appropriately synchronize and recalculate jacobi coordinates when needed. You can tell WHFast to recalculate Jacobi coordinates for a given timestep (say after you change a particle's mass) with the `sim.ri_whfast.recalculate_coordinates_this_timestep` flag. After it recalculates Jacobi coordinates, WHFast will reset this flag to zero, so you just set it each time you mess with the particles."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "safe_mode = 1\n",
+ "---------------------------------\n",
+ "REBOUND version: \t3.4.0\n",
+ "REBOUND built on: \tMay 31 2017 11:53:50\n",
+ "Number of particles: \t2\n",
+ "Selected integrator: \twhfast\n",
+ "Simulation time: \t6.2831853071795858e+05\n",
+ "Current timestep: \t0.200000\n",
+ "---------------------------------\n",
+ "\n",
+ "\n",
+ "---------------------------------\n",
+ "Safe integration took 1.4043679237365723 seconds\n",
+ "---------------------------------\n",
+ "REBOUND version: \t3.4.0\n",
+ "REBOUND built on: \tMay 31 2017 11:53:50\n",
+ "Number of particles: \t2\n",
+ "Selected integrator: \twhfast\n",
+ "Simulation time: \t6.2831853071795858e+05\n",
+ "Current timestep: \t0.200000\n",
+ "---------------------------------\n",
+ "\n",
+ "\n",
+ "---------------------------------\n",
+ "Manual integration took 0.8836901187896729 seconds\n"
+ ]
+ }
+ ],
+ "source": [
+ "import time\n",
+ "Porb = 2*np.pi # orbital period for Earth, using units of G = 1, solar masses, AU and yr/2pi\n",
+ "\n",
+ "sim = test_case()\n",
+ "print(\"safe_mode = {0}\".format(sim.ri_whfast.safe_mode))\n",
+ "start_time = time.time()\n",
+ "sim.integrate(1.e5*Porb)\n",
+ "sim.status()\n",
+ "print(\"Safe integration took {0} seconds\".format(time.time() - start_time))\n",
+ "\n",
+ "sim = test_case()\n",
+ "sim.ri_whfast.safe_mode = 0\n",
+ "start_time = time.time()\n",
+ "sim.integrate(1.e5*Porb)\n",
+ "sim.status()\n",
+ "print(\"Manual integration took {0} seconds\".format(time.time() - start_time))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true,
+ "deletable": true,
+ "editable": true
+ },
+ "source": [
+ "In our test case with a single planet, there is effectively no interaction step, and by combining Kepler steps we get almost the full factor of 2 speedup we expect. Because Kepler steps are expensive (by virtue of having to solve the transcendental Kepler equation), this will always be an important performance boost for few-planet cases.\n",
+ "\n",
+ "Note that one case where REBOUND needs to synchronize every timestep is if you're using the MEGNO chaos indicator. So if you call"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": true,
+ "deletable": true,
+ "editable": true
+ },
+ "outputs": [],
+ "source": [
+ "sim.init_megno()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "deletable": true,
+ "editable": true
+ },
+ "source": [
+ "REBOUND will synchronize every timestep even if you set `sim.ri_whfast.safe_mode = 0` and never explicitly call `sim.synchronize()`."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true,
+ "deletable": true,
+ "editable": true
+ },
+ "source": [
+ "**Modifying particles/forces**\n",
+ "\n",
+ "Again, if performance is a factor in your simulations, you would not want to write a custom stepper in python that modifies the particles, since this will be very slow. You could either write a modified C version of `reb_simulation_integrate` in `src/librebound.c` (the flags are defined in `librebound.h`, and have the same name as the python ones, just without `sim.` in front), or you can use the REBOUNDXF library, which takes care of this for you and supports many typically used modifications. We again illustrate a simple scheme with python code:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": true,
+ "deletable": true,
+ "editable": true
+ },
+ "outputs": [],
+ "source": [
+ "sim = test_case()\n",
+ "sim.ri_whfast.safe_mode = 0\n",
+ "def integrate_mod(sim, t_final):\n",
+ " while sim.t < t_final:\n",
+ " sim.step()\n",
+ " sim.particles[1].m += 1.e-10\n",
+ " sim.ri_whfast.recalculate_coordinates_this_timestep = 1\n",
+ " sim.synchronize()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "deletable": true,
+ "editable": true
+ },
+ "source": [
+ "Here, because we grow the mass of the planet every timestep, we have to recalculate Jacobi coordinates every timestep (since they depend on the masses of the particles). We therefore manually set the flag to recalculate them the next timestep every time we make a change. Here we would actually get the same result if we just left `sim.ri_whfast.safe_mode = 1`, since when recalculating Jacobi coordinates, WHFast automatically has to synchronize in order to get real positions and velocities for the planets. In this case WHFast is therefore synchronizing and recalculating Jacobi coordinates every timestep.\n",
+ "\n",
+ "But imagine now that instead of growing the mass, we continually add an impulse to vx:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
+ "outputs": [],
+ "source": [
+ "sim = test_case()\n",
+ "sim.ri_whfast.safe_mode = 0\n",
+ "def integrate_mod(sim, t_final):\n",
+ " while sim.t < t_final:\n",
+ " sim.step()\n",
+ " sim.particles[1].vx += 1.e-10*sim.dt\n",
+ " sim.ri_whfast.recalculate_coordinates_this_timestep = 1\n",
+ " sim.synchronize()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "deletable": true,
+ "editable": true
+ },
+ "source": [
+ "This would not give accurate results, because the `sim.particles[1].vx` we access after `sim.step()` isn't a physical velocity (it's missing a half-Kepler step). It's basically at an intermediate point in the calculation. In order to make this work, one would call `sim.synchronize()` between `sim.step()` and accessing `sim.particles[1].vx`, to ensure the velocity is physical."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "deletable": true,
+ "editable": true
+ },
+ "source": [
+ "**Symplectic correctors**\n",
+ "\n",
+ "Symplectic correctors make the Wisdom-Holman scheme higher order (without symplectic correctors it's second order). The great thing about them is that they only need to get applied when you synchronize. So if you just need to synchronize to output, and there are many timesteps between outputs, they represent a very small performance loss for a huge boost in accuracy (compare for example the green line (11th order corrector) to the red line (no corrector) in Fig. 4 of Rein & Tamayo 2015--beyond the right of the plot, where the round-off errors dominate, the two lines would rise in unison). We have implemented symplectic correctors up to order 11. You can set the order with (must be an odd number), e.g.,"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": true,
+ "deletable": true,
+ "editable": true
+ },
+ "outputs": [],
+ "source": [
+ "sim.ri_whfast.corrector = 11"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "deletable": true,
+ "editable": true
+ },
+ "source": [
+ "By default, WHFast does not use correctors, i.e., sim.integrator_whfast_corrector = 0. This is because the default is also to synchronize every timestep. An Nth order corrector does N-1 Kepler steps of various sizes, so an 11th order corrector done every timestep would increase the number of Kepler steps by an order of magnitude, making WHFast unacceptably slow. So keep in mind that if you're doing modifications that require recalculating jacobi coordinates or synchronizing every timestep, you should turn off symplectic correctors (the default) unless you really need the accuracy."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Changing the internal coordinate system**\n",
+ "\n",
+ "WHFast by default uses Jacobi coordinates internally. This works well for planetary systems which are stable and orbits are not crossing. However, in some cases a different coordinate system might perform better. WHFast also support so-called democratic heliocentric coordinates and the so called WHDS coordinates. For more information on these coordinates systems [see Hernandez and Dehnen (2016)](https://arxiv.org/abs/1612.05329). To select a different coordinate system, use the following syntax:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "sim.ri_whfast.coordinates = 'jacobi' #default\n",
+ "sim.ri_whfast.coordinates = 'democraticheliocentric' \n",
+ "sim.ri_whfast.coordinates = 'whds' "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Note that symplectic corrector are only compatible with Jacobi coordinates because both democratic heliocentric and WHDS include a so called jump step."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "deletable": true,
+ "editable": true
+ },
+ "source": [
+ "**Warning messages**\n",
+ "\n",
+ "If you choose a timestep that is larger than the smallest dynamical timescale and WHFast has difficulties to solve the Kepler problem, you will receive a warning message."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false,
+ "deletable": true,
+ "editable": true
+ },
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/Users/rein/git/rebound/rebound/simulation.py:305: RuntimeWarning: WHFast convergence issue. Timestep is larger than at least one orbital period.\n",
+ " warnings.warn(msg[1:], RuntimeWarning)\n"
+ ]
+ }
+ ],
+ "source": [
+ "sim = test_case()\n",
+ "sim.dt = 1000.\n",
+ "sim.integrate(1000.)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true,
+ "deletable": true,
+ "editable": true
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.5.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/rebound/source/docs/ipython_examples/ChaoticHyperion.ipynb b/rebound/source/docs/ipython_examples/ChaoticHyperion.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..b5e8f454f8fbe7439e1c8bf26d7ab1d35eae5f34
--- /dev/null
+++ b/rebound/source/docs/ipython_examples/ChaoticHyperion.ipynb
@@ -0,0 +1,250 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "6882e778",
+ "metadata": {},
+ "source": [
+ "# Chaotic Hyperion\n",
+ "In this example, we simulate the spin of Hyperion. The spin evolution is governed by an ordinary differential equation that is coupled to the moon's orbit. \n",
+ "\n",
+ "We start by importing REBOUND, numpy and matplotlib."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "e350dbbb",
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [],
+ "source": [
+ "import rebound\n",
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0bc568b2",
+ "metadata": {},
+ "source": [
+ "The right hand side of ODEs can be implemented in either python or in C. Although not absolutely necessary for this example, we here show how to implement the RHS in C. This is often significantly faster than using a python callback function. \n",
+ "\n",
+ "We use a simple spin model which is one second order ODE, or a set of two coupled first order ODEs. For more details on the physics behind this model, see Danby (1962), Goldreich and Peale (1966), and Wisdom and Peale (1983). The RHS of this set of ODEs implemented in C is:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "79a48333",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Overwriting rhs.c\n"
+ ]
+ }
+ ],
+ "source": [
+ "%%writefile rhs.c\n",
+ "#include \"rebound.h\"\n",
+ "void derivatives(struct reb_ode* const ode, double* const yDot, const double* const y, const double t){\n",
+ " struct reb_orbit o = reb_orbit_from_particle(ode->r->G, ode->r->particles[1], ode->r->particles[0]);\n",
+ " \n",
+ " double omega2 = 3.*0.26; \n",
+ " yDot[0] = y[1];\n",
+ " yDot[1] = -omega2/(2.*o.d*o.d*o.d)*sin(2.*(y[0]-o.f));\n",
+ "}\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "33cd1c9c",
+ "metadata": {},
+ "source": [
+ "We now compile this into a shared library. We need the REBOUND headers and library for this. The following is a bit of hack: we just copy the files into the current folder. This works if you've installed REBOUND from the git repository. Otherwise, you'll need to find these files manually (which might depend on your python environment). "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "7d3c176a",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "!cp ../src/librebound.so .\n",
+ "!cp ../src/rebound.h .\n",
+ "!gcc -c -O3 -fPIC rhs.c -o rhs.o\n",
+ "!gcc -L. -shared rhs.o -o rhs.so -lrebound "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2421c0e7",
+ "metadata": {},
+ "source": [
+ "Using ctypes, we can load the library into python"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "11736a91",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from ctypes import cdll\n",
+ "clibrhs = cdll.LoadLibrary(\"rhs.so\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "37ac5371",
+ "metadata": {},
+ "source": [
+ "The following function is setting up the N-body simulation as well as the ODE system that governs the spin evolution. Note that we set the `derivatives` function pointer to the C function we've just compiled. You could also set this function pointer to a python function and avoid all the C complications."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 133,
+ "id": "18043d1d",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def setup():\n",
+ " sim = rebound.Simulation()\n",
+ " sim.add(m=1) # Saturn\n",
+ " sim.add(a=1, e=0.123233) # Hyperion, massless, semi-major axis of 1\n",
+ " sim.integrator = \"BS\"\n",
+ " sim.ri_bs.eps_rel = 1e-12 # tolerance\n",
+ " sim.ri_bs.eps_abs = 1e-12\n",
+ " \n",
+ " ode_spin = sim.create_ode(length=2, needs_nbody=True)\n",
+ " ode_spin.y[0] = 0.01 # initial conditions that lead to chaos\n",
+ " ode_spin.y[1] = 1\n",
+ " ode_spin.derivatives = clibrhs.derivatives\n",
+ " \n",
+ " return sim, ode_spin"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "85c097cf",
+ "metadata": {},
+ "source": [
+ "We will create two simulations that are slightly offset from each other."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "8182b908",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "sim, ode_spin = setup()\n",
+ "sim2, ode_spin2 = setup()\n",
+ "ode_spin2.y[0] += 1e-8 # small perturbation"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c597773f",
+ "metadata": {},
+ "source": [
+ "With these two simulations, we can measure the growing divergence of nearby trajectories, a key feature of chaos."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 149,
+ "id": "4eb25927",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "times = 2.*np.pi*np.linspace(0,30,100) # a couple of orbits\n",
+ "obliq = np.zeros((len(times)))\n",
+ "obliq2 = obliq.copy()\n",
+ "\n",
+ "for i, t in enumerate(times):\n",
+ " sim.integrate(t, exact_finish_time=1)\n",
+ " sim2.integrate(t, exact_finish_time=1) \n",
+ " obliq[i] = ode_spin.y[0]\n",
+ " obliq2[i] = ode_spin2.y[0]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "98a92abf",
+ "metadata": {},
+ "source": [
+ "Finally, let us plot the divergence as a function of time."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 150,
+ "id": "13ac8f3a",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots(1,1)\n",
+ "ax.set_xlabel(\"time [orbits]\")\n",
+ "ax.set_ylabel(\"obliquity difference [degrees]\")\n",
+ "ax.set_yscale(\"log\")\n",
+ "ax.set_ylim([1e-8,1e2])\n",
+ "o1 = np.remainder((obliq-obliq2)*180/np.pi,360.)\n",
+ "o2 = np.remainder((obliq2-obliq)*180/np.pi,360.)\n",
+ "ax.scatter(times/np.pi/2.,np.minimum(o1,o2))\n",
+ "ax.plot(times/np.pi/2.,1e-8/np.pi*180.*np.exp(times/(np.pi*2.)/1.2),color=\"black\");"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c2bc381f",
+ "metadata": {},
+ "source": [
+ "On a log-linear scale, we see that the divergence follows a straight line, indicating exponential growth. The Lyapunov timescale is approximately 1.2 orbits. About 25 days! (Wikipedia says ~30 days which is close enough given the very simplistic model)"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.8.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/rebound/source/docs/ipython_examples/Cheartbeat.ipynb b/rebound/source/docs/ipython_examples/Cheartbeat.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..29d1b36f8a3499e0cef721a91fca144cb1d9c100
--- /dev/null
+++ b/rebound/source/docs/ipython_examples/Cheartbeat.ipynb
@@ -0,0 +1,300 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Using a C Heartbeat function\n",
+ "The heartbeat function of a REBOUND simulation gets called after every timestep. There are many different things you can do in a heartbeat function, for example creating outputs, adding particles, adjusting parameters that depend on time, etc. REBOUND supports heartbeat functions in both its C and python interface. \n",
+ "\n",
+ "A python heartbeat function can sometimes become the bottleneck of a simulation because it gets called every single timestep. This tutorial shows you how to implement the heartbeat function in C, then link it to REBOUND using python. Note that alternatively you can of course always just use the C version of REBOUND directly and never bother with python at all.\n",
+ "\n",
+ "We start by creating a REBOUND simulation which contains the planets of our Solar System as a test case."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import rebound\n",
+ "sim = rebound.Simulation()\n",
+ "rebound.data.add_solar_system(sim)\n",
+ "sim.integrator = \"whfast\"\n",
+ "sim.dt = sim.particles[1].P/30.13 # About 30 steps for each Mercury Orbit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let us first create a simple heartbeat function in python. It simply calculates the eccentricity of Mercury (you could do something with it, here we just calculate it and then ignore it)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Eccentricity: 0.205636 \n"
+ ]
+ }
+ ],
+ "source": [
+ "# We use a global variable to store the value of the eccentricity\n",
+ "e = 0 \n",
+ "def heartbeat(sim_pointer):\n",
+ " global e\n",
+ " # The function argument is a pointer to the simulation:\n",
+ " # Here we get its contents:\n",
+ " sim = sim_pointer.contents \n",
+ " e = sim.particles[1].e\n",
+ "sim.heartbeat = heartbeat\n",
+ "sim.integrate(sim.t+1)\n",
+ "print(\"Eccentricity: %f \" %e)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's measure how long it takes to integrate 1000 orbits:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Runtime: 0.474900 s\n"
+ ]
+ }
+ ],
+ "source": [
+ "import time\n",
+ "start = time.time()\n",
+ "sim.integrate(sim.t + sim.particles[1].P*1000)\n",
+ "stop = time.time()\n",
+ "print(\"Runtime: %f s\"%(stop-start))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We now implement this in C. For this to work, it is best to download and work with a full REBOUND repository (download the package from github, rather than just installing the python package with pip install). \n",
+ "\n",
+ "We first write our heartbeat function in C. The following cell writes to a new file in the current directory, `heartbeat.c` (you can also use an external editor and terminal window to do the same without the jupyter magic commands):"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Overwriting heartbeat.c\n"
+ ]
+ }
+ ],
+ "source": [
+ "%%writefile heartbeat.c\n",
+ "#include \"rebound.h\"\n",
+ "double e =0; // global variable\n",
+ "void heartbeat(struct reb_simulation* sim_pointer){\n",
+ " struct reb_orbit orbit = reb_orbit_from_particle(sim_pointer->G, sim_pointer->particles[0], sim_pointer->particles[1]);\n",
+ " e = orbit.e;\n",
+ "}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Before we compile and link our heartbeat function as a shared library, we need the REBOUND header file and the shared library file. Different operating systems and compilers handles the paths to shared libraries differently. This can quickly get rather frustrating. If you're familiar with C, by all means go ahead and do it the proper way. A hack to get around most of these difficulties is to simply copy the REBOUND header and library to the current folder."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "!cp ../src/librebound.so .\n",
+ "!cp ../src/rebound.h ."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "If you installed REBOUND with pip, you can look up the paths to the two files in python and e.g. create symlinks to them into your working directory."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "/path/to/your/venv/lib/python3.9/site-packages/rebound/../librebound.cpython-39-x86_64-linux-gnu.so\n",
+ "/path/to/your/venv/lib/python3.9/site-packages/rebound/rebound.h\n"
+ ]
+ }
+ ],
+ "source": [
+ "from pathlib import Path\n",
+ "print(rebound.__libpath__)\n",
+ "print(Path(rebound.__file__).parent / \"rebound.h\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Next we can compile and link the code. `-fPIC` instructs gcc to create Position Independent Code, which might not be needed on your operating system."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "!gcc -c -O3 -fPIC heartbeat.c -o heartbeat.o"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "!gcc -L. -shared heartbeat.o -o heartbeat.so -lrebound "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we load the library using ctypes."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from ctypes import cdll\n",
+ "clibheartbeat = cdll.LoadLibrary(\"heartbeat.so\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can now finally set the function pointer in our simulation to the new heartbeat function and then run the simulation."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "sim.heartbeat = clibheartbeat.heartbeat"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Runtime: 0.153589 s\n"
+ ]
+ }
+ ],
+ "source": [
+ "start = time.time()\n",
+ "sim.integrate(sim.t + sim.particles[1].P*1000)\n",
+ "stop = time.time()\n",
+ "print(\"Runtime: %f s\"%(stop-start))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Note that the simulation runs significantly faster using the C heartbeat function as we avoid all the python overhead.\n",
+ "\n",
+ "We can print out the value of the global variable `e` in the heartbeat library (using global variables in a shared library is not the best way to store data - all simulations will see the same variable and you could end up with unexpected behaviour if you are running multiple simulations in one python program)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0.2057293010348337\n"
+ ]
+ }
+ ],
+ "source": [
+ "from ctypes import c_double\n",
+ "print(c_double.in_dll(clibheartbeat,\"e\").value)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.7"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/rebound/source/docs/ipython_examples/Checkpoints.ipynb b/rebound/source/docs/ipython_examples/Checkpoints.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..d22ee84be9779acbafd80bf8fa204ed6be26f6a2
--- /dev/null
+++ b/rebound/source/docs/ipython_examples/Checkpoints.ipynb
@@ -0,0 +1,120 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Checkpoints\n",
+ "You can easily save and load a REBOUND simulation to a binary file. The binary file includes all information about the particles (mass, position, velocity, etc), as well as the current simulation settings such as time, integrator choice, etc.\n",
+ "\n",
+ "Let's add three particles to REBOUND and save them to a file."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "---------------------------------\n",
+ "REBOUND version: \t3.8.0\n",
+ "REBOUND built on: \tFeb 3 2019 13:37:32\n",
+ "Number of particles: \t3\n",
+ "Selected integrator: \twhfast\n",
+ "Simulation time: \t0.0000000000000000e+00\n",
+ "Current timestep: \t0.001000\n",
+ "---------------------------------\n",
+ "\n",
+ "\n",
+ "\n",
+ "---------------------------------\n"
+ ]
+ }
+ ],
+ "source": [
+ "import rebound\n",
+ "sim = rebound.Simulation()\n",
+ "sim.add(m=1.)\n",
+ "sim.add(m=1e-6, a=1.)\n",
+ "sim.add(a=2.)\n",
+ "sim.integrator = \"whfast\"\n",
+ "sim.save_to_file(\"checkpoint.bin\")\n",
+ "sim.status()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The binary files are small in size and store every floating point number exactly, so you don't have to worry about efficiency or losing precision. You can make lots of checkpoints if you want!\n",
+ "\n",
+ "Let's delete the old REBOUND simulation (that frees up the memory from that simulation) and then read the binary file we just saved."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "---------------------------------\n",
+ "REBOUND version: \t3.8.0\n",
+ "REBOUND built on: \tFeb 3 2019 13:37:32\n",
+ "Number of particles: \t3\n",
+ "Selected integrator: \twhfast\n",
+ "Simulation time: \t0.0000000000000000e+00\n",
+ "Current timestep: \t0.001000\n",
+ "---------------------------------\n",
+ "\n",
+ "\n",
+ "\n",
+ "---------------------------------\n"
+ ]
+ }
+ ],
+ "source": [
+ "del sim\n",
+ "sim = rebound.Simulation(\"checkpoint.bin\")\n",
+ "sim.status()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Note that you will have to re-set any function pointers manually (if you're using them)"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.6.5"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/rebound/source/docs/ipython_examples/Churyumov-Gerasimenko.ipynb b/rebound/source/docs/ipython_examples/Churyumov-Gerasimenko.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..d2d7b2d50c7e9f0a472abf50239107f38a397638
--- /dev/null
+++ b/rebound/source/docs/ipython_examples/Churyumov-Gerasimenko.ipynb
@@ -0,0 +1,355 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# The comet 67P/Churyumov–Gerasimenko\n",
+ "\n",
+ "This tutorial teaches you how to use the IAS15 integrator (Rein and Spiegel, 2015) to simulate the orbit of 67P/Churyumov–Gerasimenko. We will download the data from NASA Horizons and visualize the orbit using matplotlib.\n",
+ "\n",
+ "This tutorial assumes that you have already installed REBOUND."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**NASA Horizons**\n",
+ "\n",
+ "If you're interested in Solar System dynamics, you have probably heard of NASA Horizons. It's a large database of Solar System objects, their orbits and physical properties. It includes planets, moons, satellites, asteroids, comets and spacecrafts. With REBOUND, you can easily import data from NASA Horizons. As an example, let's pull in the present day positions of Jupiter, Saturn and the Sun:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Searching NASA Horizons for 'Sun'... \n",
+ "Found: Sun (10) \n",
+ "Searching NASA Horizons for 'Jupiter'... \n",
+ "Found: Jupiter Barycenter (5) (chosen from query 'Jupiter')\n",
+ "Searching NASA Horizons for 'Saturn'... \n",
+ "Found: Saturn Barycenter (6) (chosen from query 'Saturn')\n"
+ ]
+ }
+ ],
+ "source": [
+ "import rebound\n",
+ "sim = rebound.Simulation()\n",
+ "sim.add(\"Sun\")\n",
+ "sim.add(\"Jupiter\")\n",
+ "sim.add(\"Saturn\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now all the data is in REBOUND! Let's have a look at the orbits of the two planets."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "for orbit in sim.orbits():\n",
+ " print(orbit)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Although there are three bodies, the `orbits()` function only returns two objects as the orbit for the Sun would be a little boring. The function returns the orbits in Jacobi coordinates. Since we didn't specify a value for $G$, REBOUND assumes that $G=1$. The unit of length is one astronomical unit, the unit of time is one year/$2\\pi$.\n",
+ "\n",
+ "Let's add something more interesting to our simulation: the comet 67P/Churyumov-Gerasimenko. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Searching NASA Horizons for 'Churyumov-Gerasimenko'... \n",
+ "Found: 67P/Churyumov-Gerasimenko (chosen from query 'Churyumov-Gerasimenko')\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/Users/rein/git/rebound/rebound/horizons.py:165: RuntimeWarning: Warning: Mass cannot be retrieved from NASA HORIZONS. Set to 0.\n",
+ " warnings.warn(\"Warning: Mass cannot be retrieved from NASA HORIZONS. Set to 0.\", RuntimeWarning)\n"
+ ]
+ }
+ ],
+ "source": [
+ "sim.add(\"Churyumov-Gerasimenko\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "When searching for a body by name, REBOUND takes the first dataset that Horizons offers. In this case, it's a set of parameters from 1962. You probably want to go to the Horizons website and check that the values you are using are up-to-date and appropriate for what you want to do. You can also use more complicated Horizons queries, for example, to get the most recent apparition solution for the comet, use\n",
+ "\n",
+ " sim.add(\"NAME=Churyumov-Gerasimenko; CAP\")\n",
+ "\n",
+ "You can also use the IAU asteroid number for numbered asteroids, or the database record numbers from Horizons for objects not yet numbered by the IAU (but note that database record numbers can change as the database gets rearranged with new discoveries, see https://ssd.jpl.nasa.gov/?horizons_doc#sb for details). In our case the current database record number is 900647, so you could use `sim.add(\"900647\")` to get the newest set of orbital parameters for Churyumov-Gerasimenko.\n",
+ "\n",
+ "NASA Horizons doesn't have masses for all bodies. If REBOUND doesn't find a mass, you get a warning message (see above). In our case, we don't need the mass of the comet (it's really small). However, it you want, you can add it manually using the syntax `sim.add(\"Churyumov-Gerasimenko\", m=5.03e-18)`.\n",
+ "\n",
+ "Before we integrate the orbits, let's plot the instantaneous orbits using the built-in REBOUND class `OrbitPlot`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig = rebound.OrbitPlot(sim, unitlabel=\"[AU]\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Integration with IAS15**\n",
+ "\n",
+ "We will integrate backwards in time for 70 years. Because we don't know what will happen yet (hint: a close encounter) we will use the IAS15 integrator. It is fast, accurate and has adaptive timesteps to capture any potential close encounters. \n",
+ "\n",
+ "To integrate backwards, we could set a negative timestep or multiply all velocities with $-1$. We'll choose the first option:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "sim.dt = -0.01"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "While we're integrating, let's store the positions of Jupiter and the comet at 10000 times during the interval. We'll need to prepare a few variables to do that:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "Noutputs = 10000\n",
+ "year = 2.*np.pi # One year in units where G=1\n",
+ "times = np.linspace(0.,-70.*year, Noutputs)\n",
+ "x = np.zeros((2,Noutputs))\n",
+ "y = np.zeros((2,Noutputs))\n",
+ "z = np.zeros((2,Noutputs))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we're ready to start the integration:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "sim.integrator = \"ias15\" # IAS15 is the default integrator, so we actually don't need this line\n",
+ "sim.move_to_com() # We always move to the center of momentum frame before an integration\n",
+ "ps = sim.particles # ps is now an array of pointers and will change as the simulation runs\n",
+ "\n",
+ "for i,time in enumerate(times):\n",
+ " sim.integrate(time)\n",
+ " x[0][i] = ps[1].x # This stores the data which allows us to plot it later\n",
+ " y[0][i] = ps[1].y\n",
+ " z[0][i] = ps[1].z\n",
+ " x[1][i] = ps[3].x\n",
+ " y[1][i] = ps[3].y\n",
+ " z[1][i] = ps[3].z"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Visualization with matplotlib**\n",
+ "\n",
+ "Let's plot the orbits of Jupiter (blue) and the comet (green) to get an idea of what was going on during our integration."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "fig = plt.figure(figsize=(5,5))\n",
+ "ax = plt.subplot(111)\n",
+ "ax.set_xlim([-6,6])\n",
+ "ax.set_ylim([-6,6])\n",
+ "plt.plot(x[0], y[0]);\n",
+ "plt.plot(x[1], y[1]);"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As you can see in the above image, the comet 67P had a rather strong encounter with Jupiter a few years ago. Of course, if you wanted to do a realistic simulation of that encounter, you'd need to include all the other planets and maybe even some non-gravitational effects for the comet. However, let's stick with our simplistic model and try to find out when exactly the two bodies had a close encounter. We already stored the data, so we can just plot their distance as a function of time."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Minimum distance (0.047401 AU) occured at time: -63.790379 years.\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig = plt.figure(figsize=(12,5))\n",
+ "ax = plt.subplot(111)\n",
+ "ax.set_xlabel(\"time [yrs]\")\n",
+ "ax.set_ylabel(\"distance [AU]\")\n",
+ "distance = np.sqrt(np.square(x[0]-x[1])+np.square(y[0]-y[1])+np.square(z[0]-z[1]))\n",
+ "plt.plot(times/year, distance);\n",
+ "closeencountertime = times[np.argmin(distance)]/year\n",
+ "print(\"Minimum distance (%f AU) occured at time: %f years.\" % (np.min(distance),closeencountertime))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can see that the minimum distance occured approximately 56 years ago (as of writing this tutorial). Let's see what date that was using some python magic and the datetime module:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "'1959-02-04 08:09'"
+ ]
+ },
+ "execution_count": 10,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "import datetime\n",
+ "encounterdate = datetime.datetime.today() + datetime.timedelta(days=365.25*closeencountertime)\n",
+ "encounterdate.strftime(\"%Y-%m-%d %H:%M\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "If you check [Wikipedia](https://en.wikipedia.org/wiki/67P/Churyumov–Gerasimenko) or [JPL](https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=67P;old=0;orb=0;cov=0;log=0;cad=1#cad), the encounter happened on 1959-Feb-04 06:24, so we are not far off (it turns out that's because of jets and other non-gravitational forces from the comet!)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.6"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}
diff --git a/rebound/source/docs/ipython_examples/CloseEncounters.ipynb b/rebound/source/docs/ipython_examples/CloseEncounters.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..1ad3c8c95c12153247168fda59da057f13310c84
--- /dev/null
+++ b/rebound/source/docs/ipython_examples/CloseEncounters.ipynb
@@ -0,0 +1,332 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Catching close encounters using exceptions\n",
+ "Sometimes one is interested in catching a close encounter between two planets. This can easily be done with REBOUND. What you do when a close encounter happens is up to you.\n",
+ "\n",
+ "Some integrators are better suited to simulate close encounters than others. For example, the non-symplectic integrator IAS15 has an adaptive timestep scheme that resolves close encounters very well. Integrators that use a fixed timestep like WHFast are more likely to miss close encounters.\n",
+ "\n",
+ "Let's start by setting up a two-planet system that will go unstable on a short timescale:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import rebound\n",
+ "import numpy as np\n",
+ "def setupSimulation():\n",
+ " sim = rebound.Simulation()\n",
+ " sim.integrator = \"ias15\" # IAS15 is the default integrator, so we don't need this line\n",
+ " sim.add(m=1.)\n",
+ " sim.add(m=1e-3,a=1.)\n",
+ " sim.add(m=5e-3,a=1.25)\n",
+ " sim.move_to_com()\n",
+ " return sim"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's integrate this system for 100 orbital periods."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "sim = setupSimulation()\n",
+ "sim.integrate(100.*2.*np.pi)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Rebound exits the integration routine normally. We can now explore the final particle orbits:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "for o in sim.orbits():\n",
+ " print(o)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We see that the orbits of both planets changed significantly and we can already speculate that there was a close encounter.\n",
+ "\n",
+ "Let's redo the simulation, but this time set the `sim.exit_min_distance` flag for the simulation. If this flag is set, then REBOUND calculates the minimum distance between all particle pairs each timestep. If the distance is less than `sim.exit_min_distance`, then the integration is stopped and an exception thrown. Here, we'll use the [Hill radius](https://en.wikipedia.org/wiki/Hill_sphere) as the criteria for a close encounter. It is given by $r_{\\rm Hill} \\approx a \\sqrt{\\frac{m}{3M}}$, which is approximately 0.15 AU in our case. \n",
+ "\n",
+ "This setup allows us to catch the exception and deal with it in a customized way. As a first example, let's catch the exception with a `try`-`except` block, and simply print out the error message. Additionally, let's store the particles' separations while we're integrating:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Two particles had a close encounter (d"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "fig = plt.figure(figsize=(10,5))\n",
+ "ax = plt.subplot(111)\n",
+ "ax.set_xlabel(\"time [orbits]\")\n",
+ "ax.set_xlim([0,sim.t/(2.*np.pi)])\n",
+ "ax.set_ylabel(\"distance\")\n",
+ "plt.plot(times/(2.*np.pi), distances);\n",
+ "plt.plot([0.0,12],[0.2,0.2]); # Plot our close encounter criteria;"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We did indeed find the close encounter correctly. We can now search for the two particles that collided and, for this example, merge them. To do that we'll first calculate our new merged planet coordinates, then remove the two particles that collided from REBOUND and finally add the new particle."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Number of particles at the beginning of the simulation: 3.\n",
+ "Two particles had a close encounter (d"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "%matplotlib inline\n",
+ "op = rebound.OrbitPlot(sim,Narc=300)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Finally, let's simulate our system for and check that our final relative energy error is small. The energy error is a key measure of whether the integration was performed accurately or not."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "5.390879254005452e-07\n"
+ ]
+ }
+ ],
+ "source": [
+ "sim.integrate(tmax)\n",
+ "dE = abs((sim.energy() - E0)/E0)\n",
+ "print(dE)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.6"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/rebound/source/docs/ipython_examples/EmbeddedOperatorSplittingMethods.ipynb b/rebound/source/docs/ipython_examples/EmbeddedOperatorSplittingMethods.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..990a65500ce13d2577bb290fd1bd5213e06e2939
--- /dev/null
+++ b/rebound/source/docs/ipython_examples/EmbeddedOperatorSplittingMethods.ipynb
@@ -0,0 +1,557 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Embedded Operator Splitting (EOS) Methods\n",
+ "\n",
+ "This examples shows how to use the Embedded Operator Splitting (EOS) Methods described in Rein (2019). The idea is to embedded one operator splitting method inside another. The inner operator splitting method solves the Keplerian motion, whereas the outer solves the planet-planet interactions. The accuracy and speed of the EOS methods are comparable to standard Wisdom-Holman type methods. However, the main advantage of the EOS methods is that they do not require a Kepler solver. This significantly simplifies the implementation. And in certain cases this can lead to a speed-up by a factor of 2-3x."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import rebound\n",
+ "%matplotlib inline\n",
+ "import matplotlib.pylab as plt\n",
+ "import numpy as np\n",
+ "import time\n",
+ "linestyles = [\"--\",\"-\",\"-.\",\":\"]\n",
+ "labels = {\"LF\": \"LF\", \"LF4\": \"LF4\", \"LF6\": \"LF6\", \"LF8\": \"LF8\", \"LF4_2\": \"LF(4,2)\", \"LF8_6_4\": \"LF(8,6,4)\", \"PLF7_6_4\": \"PLF(7,6,4)\", \"PMLF4\": \"PMLF4\", \"PMLF6\": \"PMLF6\"}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We first create a function to setup our initial conditions of two Jupiter-mass planets with moderate eccentricities . We also create a function to run the simulation and periodically measure the relative energy error. The function then runs the simulation again, this not only measuring the runtime. This way we don't include the time required to calculate the energy error in our run time measurements. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def initial_conditions():\n",
+ " sim = rebound.Simulation()\n",
+ " sim.add(m=1)\n",
+ " sim.add(m=1e-3,a=1,e=0.05,f=0.)\n",
+ " sim.add(m=1e-3,a=1.6,e=0.05,f=1.)\n",
+ " sim.move_to_com()\n",
+ " return sim\n",
+ " \n",
+ "def run(sim):\n",
+ " simc = sim.copy() # Use later for timing\n",
+ " tmax = 100.\n",
+ " \n",
+ " # First run to measure energy error\n",
+ " Emax = 0\n",
+ " E0 = sim.energy()\n",
+ " while sim.t"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig,ax = plt.subplots(1,2,figsize=(8,3),sharey=True)\n",
+ "plt.tight_layout()\n",
+ "for _ax in ax:\n",
+ " _ax.set_xscale(\"log\")\n",
+ " _ax.set_yscale(\"log\")\n",
+ "ax[0].set_xlabel(\"timestep\");\n",
+ "ax[1].set_xlabel(\"runtime\");\n",
+ "ax[0].set_ylabel(\"error\")\n",
+ "\n",
+ "for m, method in enumerate(methods):\n",
+ " ax[0].plot(dts/np.pi/2.,results[:,m,0],label=method,color=\"black\",ls=linestyles[m])\n",
+ " ax[1].plot(results[:,m,1],results[:,m,0],label=method,color=\"black\",ls=linestyles[m]) \n",
+ "\n",
+ "ax[0].legend(loc='upper center', bbox_to_anchor=(1.1, -0.2), ncol=5);"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**EOS with $\\Phi_0=\\Phi_1=LF$**\n",
+ "\n",
+ "We now run several EOS methods where we set both the inner and outer operator splitting method to the standard second order leapfrog method. Our resulting EOS method will therefore also be a second order method. We vary the number of steps $n$ taken by $\\Phi_1$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "ns = [1,2,4,8,16]\n",
+ "results_lf = np.zeros((len(dts), len(ns), 2))\n",
+ "for i, dt in enumerate(dts):\n",
+ " for j, n in enumerate(ns):\n",
+ " sim = initial_conditions()\n",
+ " sim.dt = dt\n",
+ " sim.integrator = \"eos\"\n",
+ " sim.ri_eos.phi0 = \"lf\"\n",
+ " sim.ri_eos.phi1 = \"lf\"\n",
+ " sim.ri_eos.n = n\n",
+ " sim.ri_eos.safe_mode = 0\n",
+ " results_lf[i,j] = run(sim)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can see in the following plot that for $n=1$, we recover the LEAPFROG method. For $n=16$ both the accuracy and efficiency of our EOS method is very similar to the standard WH method."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig,ax = plt.subplots(1,2,figsize=(8,3),sharey=True)\n",
+ "plt.tight_layout()\n",
+ "for _ax in ax:\n",
+ " _ax.set_xscale(\"log\")\n",
+ " _ax.set_yscale(\"log\")\n",
+ "ax[0].set_xlabel(\"timestep\");\n",
+ "ax[1].set_xlabel(\"runtime\");\n",
+ "ax[0].set_ylabel(\"error\")\n",
+ "colors = plt.cm.viridis(np.linspace(0,1,len(ns)))\n",
+ "\n",
+ "for j, n in enumerate(ns):\n",
+ " label = \"$\\Phi_0=\\Phi_1=LF$, $n=%d$\"%n\n",
+ " ax[0].plot(dts/np.pi/2.,results_lf[:,j,0],label=label,color=colors[j])\n",
+ " ax[1].plot(results_lf[:,j,1],results_lf[:,j,0],label=label,color=colors[j])\n",
+ "\n",
+ "for m, method in enumerate(methods):\n",
+ " ax[0].plot(dts/np.pi/2.,results[:,m,0],label=method,color=\"black\",ls=linestyles[m])\n",
+ " ax[1].plot(results[:,m,1],results[:,m,0],label=method,color=\"black\",ls=linestyles[m]) \n",
+ "\n",
+ "ax[0].legend(loc='upper center', bbox_to_anchor=(1.1, -0.2), ncol=4);"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**An extra factor of $\\epsilon$**\n",
+ "\n",
+ "We now create EOS methods which are comparable to the Wisdom-Holman method with symplectic correctors. For the same timestep, the error is smaller by a factor of the mass ratio of the planet to the star, $\\epsilon$. We set $\\Phi_1$ to the fourth order LF4 method and use $n=2$. For $\\Phi_0$ we try out LF4, LF(4,2) and PMLF4. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "phi0s = [\"LF4\", \"LF4_2\", \"PMLF4\"]\n",
+ "results_4 = np.zeros((len(dts), len(phi0s), 2))\n",
+ "for i, dt in enumerate(dts):\n",
+ " for j, phi0 in enumerate(phi0s):\n",
+ " sim = initial_conditions()\n",
+ " sim.dt = dt\n",
+ " sim.integrator = \"eos\"\n",
+ " sim.ri_eos.phi0 = phi0\n",
+ " sim.ri_eos.phi1 = \"LF4\"\n",
+ " sim.ri_eos.n = 2\n",
+ " sim.ri_eos.safe_mode = 0\n",
+ " results_4[i,j] = run(sim)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can see in the following plot that the EOS methods using LF(4,2) and PMLF4 do approach the accuracy and efficiency of the Wisdom-Holman method with symplectic correctors for small enough timesteps. To achieve a better accuracy for larger timesteps, we could increase the order of $\\Phi_1$ or the number of steps $n$. Note that the EOS method with $\\Phi_0=LF4$ is a true 4th order method, whereas the methods with LF(4,2) and PMLF4 have generalized order (4,2). "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig,ax = plt.subplots(1,2,figsize=(8,3),sharey=True)\n",
+ "plt.tight_layout()\n",
+ "for _ax in ax:\n",
+ " _ax.set_xscale(\"log\")\n",
+ " _ax.set_yscale(\"log\")\n",
+ "ax[0].set_xlabel(\"timestep\");\n",
+ "ax[1].set_xlabel(\"runtime\");\n",
+ "ax[0].set_ylabel(\"error\")\n",
+ "\n",
+ "for j, phi0 in enumerate(phi0s):\n",
+ " label = \"$\\Phi_0=%s, \\Phi_1=LF4, n=2$\" % labels[phi0]\n",
+ " ax[0].plot(dts/np.pi/2.,results_4[:,j,0],label=label)\n",
+ " ax[1].plot(results_4[:,j,1],results_4[:,j,0],label=label)\n",
+ "\n",
+ "for m, method in enumerate(methods):\n",
+ " ax[0].plot(dts/np.pi/2.,results[:,m,0],label=method,color=\"black\",ls=linestyles[m])\n",
+ " ax[1].plot(results[:,m,1],results[:,m,0],label=method,color=\"black\",ls=linestyles[m]) \n",
+ " \n",
+ "ax[0].legend(loc='upper center', bbox_to_anchor=(1.1, -0.2), ncol=4);"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**High order methods**\n",
+ "\n",
+ "Next, we will construct arbitrarily high order methods using LF, LF4, LF6, and LF8 for both $\\Phi_0$ and $\\Phi_1$. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "phis = [\"LF\", \"LF4\", \"LF6\", \"LF8\"]\n",
+ "results_2468 = np.zeros((len(dts), len(phis), 2))\n",
+ "for i, dt in enumerate(dts):\n",
+ " for j, phi in enumerate(phis):\n",
+ " sim = initial_conditions()\n",
+ " sim.dt = dt\n",
+ " sim.integrator = \"eos\"\n",
+ " sim.ri_eos.phi0 = phi\n",
+ " sim.ri_eos.phi1 = phi\n",
+ " sim.ri_eos.n = 1\n",
+ " sim.ri_eos.safe_mode = 0\n",
+ " results_2468[i,j] = run(sim)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The following plots show that the methods are indeed 2nd, 4th, 6th, and 8th order methods. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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6xcrAtHE/NPi2I3o1qYHOce4oeXcDZGEJgN1AoPk0wKRcblc5S549e4YOHTrgwYMHMDY2RmBgIEqXLp3b1coTEhISsH37dtjb22PChAnJ+8uaFsasTjUx5uuqcLn4DGs9LiG6UGmMHz8eq1avhtOyZWjb9r/PpzNnzoSbmxu8vb2hq/vBpP/CxYG+O4HzS9STwYPvq9MQlKySk7cpCHlarsxhehcwebwfkpPJZD0BtCU57N33AwE4khyTyvktAHQHYAjgLknnFI4ZAWAEAFhYWNTz9/fX/o0IghYFBQXB1XULdu/zQL2Ri+D5MAyRPudhZVkeI/t0RKdaJWHq7ar+oxYfDtTqBrT8H2CWiWSGeYhKpcLUqVOxfPlySJKEOnXq4MiRIyhTpozGZWTnHKa80JaQRPfu3eHh4QFPT080adIkxeOiEhRYevwhVm/Zg0jPjUgMD0THjp2wb9+/0NXVxcuXL6Gnp4eyZcumfrHHJ9VZwSUJ6L4WsGqXTXclCHlPmm0JyRzfAFgC8P7g+55Qz1t6//1AACu1db169epREPKixMREuru78+vW7aijo0sANCxfgzZTd3LeIR8+CopSH3jvH3JJDfI3E3JLV/LVzdytuJacO3eO5ubmBMBChQpx48aNmSoHgBdzoO3KzbYkIiKCVatWZdmyZRkUFJTmsfdfRbLrck8Wb/k9q7UewHsBESTJ2NhYkqRSqeTmzZupUqlSLiD8Obmmqfr1dvpPUpK0ei+CkFel1ZbklbQCrwBU/OD7Cu/2CUKBpFQqEa8k5q/bg/njB0LXuASK1u+Gb7v0wYhOTdDS2hz6ujqAIh44MA646QqUraNOPFi5eW5XP8siIiIwePBgHDhwAADQunVr7N27FyYmJrlcs7zL1NQUbm5uaNCgAfr27YsTJ05ATy/lJrxmORO4j20O98ZVMf/IA3ReeQHNTcNxcMkk/D5nDszNzTF06FCULFky5cV9i1cCvj8OHJoEnF2gTnrZbEo236Eg5G15JWC6DqCaTCb7CupAqS+A/rlbJUHQrsjISOzYsRMrVq9DEUtbxNbui7hEE9QZvhAj+nZBD4dKMC/6wWPhbx4DewcDwd5Ak0lAyxn5PiszSezYsQMjR45ETEwMTE1NsWPHDrRv3z63q5Yv2NraYu3atRg0aBBmzJiBhQsXpnqsTCZDj3oV8G3N0lh24hE2HPBHonF5jB49GnIbGzg5OaUcLL2nX0idCVxSAqf/AIqUAuoNzoa7EoR8IrWup+zaAOwE8BqAAkAAgB/e7W8P4BGAJwBmaPOaYkhOyE3nz59n5559qW9YiACob1aJ5TtP4i9ud3jDP5xSSsMdd/eS88qRCyzJR8dzvtLZwNfXly1atCAA2tjYcNCgQclDRFmFL2BI7kMjR44kALq7u2t8jverCPZYdYFmXX5hoeKlCYDDhw/n7du3ef/+/dRPVCaRW7uTs4uRPge1UHtByLvSakvyZeLKjMrtZHPClyc0NBSSYVHsv/0Ksyf9hKB7F1G0VnO06NQHI3q0wjc1Sqe8NIkiATg2HfDaBFR0BHpuAkwr5PwNaFFMTAwWLlyIP//8Ezo6OlixYgVGjBjx8VNaWfSlJK58LzExEU2aNMGjR4/g5eWFatWqaXQeSRz1DsLc/bdx/+hWVKtYBsGX/4Whvh4uXLiQ+lOJSbGAa2cg6B4w8F/AsrEW70YQ8o602hIRMAmCligUCvzz734s+XsNbl70RLmhK6BXyhLWJkr0aFgdPepXQYkiBqkXEPYE2DsECLoLNBoHfDNLPXckn0pISMDatWsxb948hIaGws7ODs2bN8fixYuho6PdFHBfWsAEAP7+/rCzs0P58uVx5coVGBkZaXxuolKFrZf9sfyUH8Ke3EXQjukoYmSEHTu2o2PHjiknDY0LBza1AaKDgaGHgTLyz48RhHwuzz0ll9NbXulGFwqmkJBQ9h82hkamJQiAusYlWKFlP87acZZPQqI1K8TbnZxXnpxvQfoezt4KZzOFQsENGzawYsWKBMA6derwypUr2XpNfGFDcu8dOXKEMpmMgwcPTnloNx1hMYmc6X6bOoZG1DE0IgC2btOGDx48SPmEty/UT2suqkaGP8ta5QUhD0qrLcmNTN+CkO8lJibi8q37WHnaD51XX8aurZuhV9YaPX9difO3HuDFqe2Y068ZKpcyTrsgZSJwaIq6Z6mUFTDyfL7NeyNJEnbv3o1atWph2LBhMDY2RuHChaFSqWBvn+2dP1+ktm3bYubMmXB1dcWGDRsyfH6JIgZobvIGUmIcWvwwE8W/HoZTZy5AbmODv/766/MTilUEBripX7dbuwExoVq4C0HIH0TAJAgZcNf7ProP/hGmZqXRok1HLDr2EF+VLYUdnrcQfPcc9s4bjYZVzTVbBy38GbCxNXB9PdBgNDD0CFDMIvtvQstI4tChQ7Czs0Pfvn1hYGCAOXPmwN/fH5UqVcLRo0e1Ol9J+NisWbPQunVrjB07Fjdv3szw+W5ubjAyMsLBRePgsXY+mv1vBwrX/Bpuj5W49eItFAoFJEn67wTzGkD/PUDUa2B7TyAxWot3Iwh5WGpdTwVpy2vd6EL+47J7Hy1r1SMAQkeXxeVNOfzPjXweGpO5Ar3/Jf+sqN7y8ZNHZ8+eZePGjQmAlStX5rZt23jw4EEaGhrSxsaGwcHBOVIPfKFDcu+FhoayQoUKtLS0ZHh4uMbnKZVKli5dmj179vxvn0rirmv+rPfHCVaa5sEGvUaxdl07Xrp06eOTHx4lZxcnXTuTigRt3Yog5Kq02hLRwyQIqfC6dQeunt7oveYyJm85i4DA16jfeyz2nrmNkNtnsG7696hklsFFbhOjgX2j1PmVSlYGfjwL1EhxucQ87fr162jbti2aN2+OZ8+eYc2aNfD19YWxsTF69OiBWrVqwdPTE+bm5rld1S+CmZkZ9u7di1evXmHQoEEf9wil4dKlSwgODkaPHj2S9+nqyNDHwQJnprbAmJZV4a8sCm8/fzRq1Aj9vxuAwMBA9YHV2wBdnIGnZ4A9gwFlUjbcmSDkIalFUgVpy6ufCoW8JywsjD//sYhlq8kJgMVbfs8Wizz590lfBkXGZa1w/yukk606n83J39X5bfKR0NBQLl++nHXr1iUAlixZkosXL2ZcnPr3smfPHurp6dHR0ZFv377N0brhC+9hem/FihUEwP79+yf/v6Rl/PjxNDQ0ZFRUVKrHBLyN48jNF2jSoBdluvo0LGzEza6u/x1wdZ16CZXdA0mlQhu3IQi5Jq22JNeDmZzY8nojJ+S+p8FRrNuiPWW6+ur13My/YvNBk3n0+sNMPX30EWUSeWquOlBaJiefX0r/nDwiKSmJ+/btY7du3aivr/7d2NnZcfny5YyMjEw+buvWrdTR0WGTJk0+2p9Zj98+ztDxImBSkySJ8+bNIwA6Ojry9evXaR6/fv16/vzzz1SoFHwS8STNY2/4h7PNnN00qt6I9catpsedQEZERFChUJAX/1YHTW7DSZVSm7ckCDlKBEx5vJETcseVG7c4YsZC9lp9iZWmedCoRlNafdObi7YfZUyClj4pv3lMrmup/mPi/iMZH6GdcrPZrVu3OGHCBJYqVYoAWLp0aU6ePJl3795N8fjt27ezVatWjInJ5Jyud55EPOG4U+Mod5HzRtANjc8TAdPH3N3daWRkxAoVKvDmzfQXana+5Uz7rfY8+uxomsdJksQT94PYaukZVprmwYoNOtCyqhUPHjxI6cxf6tf5/jFkaov6CkIeJwKmfNLICdkvKDiE42bOp3nlmgRAmZ4Bm/1xkM6efnz1NotDbh+SJNLLhZxbVp1b6Z6b9srOJsHBwVy2bBlr165NADQwMGDPnj158OBBJiWlPHz4/Pnz5H9npScuNC6Uv1/6nbVda9NxuyPX3F7D2CTNl00RAdPnbt26xYoVK9LIyIhubp+//u7cuZM8FBcaF8rvDn1HuYucK2+tpEpKO+BRqiTu9XpJqwFzqFe8HAHQoWETXl81Uh00eUxWvwcEIZ8RAVM+auQE7ZMkid6vItj3l2XJQ26FylRm6+9/5umbj7I+5PapmFByRz/1Hw6XTmREgHbL17KbN2+ye/fu1NPTU//hc3DgypUr+ebNmzTP27FjBw0MDLKUlDI2KZbOt5zpsM2BdVzrcN6VeXwTl/Z1UyICppS9fv2aDRo0IADOnj2bqnc9P5IksUqVKmzfvn3ysYnKRM44P4NyFzknek7UKGCNT1Jy9Wlflm8/mjqFTQiAS39qrX7tH5shgiYh3xEBUz5r5ISskySJ+495smmX71h76DxWmuZByzGulLfuR+d/TjBRkU1DBo9OqLMg/25GXlqZp4cmbt68yS5duhAAixUrxilTptDb21vj89++fctff/2ViYmJGb52kiqJu313s/mu5pS7yDnJcxL9I/0zXM57ImBKXXx8PAcNGkQAbNeuHcPCwihJEs+dO8eLFy9+dKwkSXT1dqWtqy177O/BV9GvNLpGZHwS/3DzYsnGfWkxejMvLB/Ch2OKMGDXz9lxS4KQbUTAlA8bOSFzbt71YfdhE2lcqkLykJu82yhuvfyc4TEZ/8OusaQ48tAU9Sdr5wbk63vZd60s+jRQ+v333xkRodncqjdv3nDixIkaPYGVEkmSePL5SXZ070i5i5yDDg/inZA7mSrrQyJgSpskSVy9ejUNDAxYqVIlenl5pXn8+YDzbLi9IZvtapahuWTBUfH8bb83q//qwdpVzFlIDxzXsylDQ0OzeguCkCNEwJRPGzlBM2+jYnj4biCHu16ngZkFARmLV63L76Yu4P1naT8lpBXBPuRKR3WwdGQ6mRSf/dfMhKwESiR54sQJlitXjvr6+jx16lSGr38r+BYHHBpAuYucnf/tTM8XnlobDhUBk2auXr1KCwsLGhgYcNSoUZw/f36qxz6NeMoO7h1YZ0sduj3K2By8V2/j+JOzB1valqeODDQqZMBpv87UyhOUgpCdClzABKAFgPMA1gBokd7x+b2REz4XFxfPeSs3s6pDS+oambLiJDfazz3B4Yt28Pi1+9qfl5SS9xO7/yhN/lWF9DuZ/dfMhFu3brFr164EQFNTU86ZMydDeZISEhI4ZcoUAmCNGjV469atDF0/NimWEz0nUu4iZ8vdLbn34V4qVKk/hRhz8SKfDxlCZQbqKAImzYWGhrJ169YEQB0dHT55kno6gYiECA4/NpxyFzmXei3N8LWeh0Tw394ObF+6MAGw/feTGBmfv/KPCV+WPBUwAdgEIASA9yf72wJ4COAxgF/SKaM5gCMAXABUTe+aBaGRE9TOe3mzSZcB1DMqSgDUMy7Beh0H0uPaQyqUOThfKD6C3DNY3avk2oWMCsq5a2soq4ESSfr4+LBOnToEwFGjRjE2VvMn10j1UNDUM1Np62rL1bdXpzmROO7uPfoPHUofK2s+atmScamkMEiJCJgyRqlUcsyYMQRAc3Nz+vn5pXqsQqXgrIuzKHeR826I5v8n74WuXEkfK2vusynPST+NYu05xzh24Qb+7bwq1acvBSG35LWAqRkAuw8DJgC6AJ4AqAzAAMAdADUB2ADw+GQzB6Dz7rzSALand82C0sh9qZ69DOSqg1fYe80llhm0lNDVZ6X6rThr5TZGxeXCGlYvr5PLbNTraJ1bkqcmdsfGxnLnzp1s165dcqA0e/bsDAdK7+e8FC5cmGZmZjx4MHPr3e18sJNyFznX3VmX6jEJT5/y5fgJ9LGy5sMGDRnm4kJVBieSi4ApcxwdHSmTyVi0aFG6uLik2jMbkxTDpjubctixYZm6TtSxI/S1rcmHttXp8vNkFpF/o87vVaESXV23UKkUyS6FvCFPBUzq+sDyk4CpIYBjH3w/HcB0DcoxAPBPescVtEbuS5CQkMiFa7awqkNLQkeXxrat2fyv01xx8iHvPw/MnUqpVOQFJ3JOCXKpnHxxNXfq8QmlUsnjx49z0KBBNDY2JgCWL18+U4ESqX6qqnPnzgTANm3apJstOjX3Qu+x7pa6/OnETynm9UkKCmbgzFn0qVmLD+raMWT5CiqjozN1LREwZc7p06cJgFWqVCEAfvPNN7x27VqKx7p6u1LuIueVwMylkUJcqDYAACAASURBVEjwvcfHjeT0sbbi3V/G037EQuqbVyYAflXNmseOHcvKrQiCVuSHgKkngA0ffD8QwMo0zu8OYC2A3anNYQIwAoAXAC8LCwtt/06FbPIiLJbth0ygvnFx9ZBbkeJ06DSYu49fzJl5SamJDiG3dFMPwe0aQMbl7Fppn5IkiV5eXpwwYQLLlClDADQxMeEPP/zA06dPZ+kTuyRJHDx4MJcvX56ctyejIhIi2Hpva7ba24pv4z/+XSkjIxm8eAkf1K5DH7kNX//+BxWhoVSpVNy0aVOac2pSk50BU0FuSyRJYu3atVmrVi2uWrWKRYoUoZ6eHufPn//ZcFmCMoHf7v2W/Tz6Zfq9qHoTwJcdbeljZc0XP3xH9/O+tOo/k3olyrPR97N4LyCCSqUyd9/rwhetwAVMGd0K2qfCgubl62COmrWIfVZfZKVpHizq0JUV6jbn9GWbGBGjxezbmfX49LvcSqXIaxtyNRnfkydP+Mcff9DKyio5G3e3bt34zz//MD4+80/nxcfHc/LkyXzw4EGW66iSVBx9cjTrbKnz0ZwXVXw832zYQN/6jvSxsmbA5ClMfPEi+eeBgYEsUqQIp0+fnuFrih6mzHNxcSEAHjt2jH5+fuzWrVtyr5O7u/tHx7o9cqPcRc6T/pl/wEGKCuabobb0sbbi49bfMOqRH9d6PmLt3w6z0jQPNvluIhs0bpZqT5cgZKf8EDBlakhO060gNnL5nUKh4LJNu2nVsDVluuoM07VHO3P5yUd8EZa19ci0RplEnpxD/mZK/u2Qa7mVXr58yRUrVrBRo0YEQABs3rw5161bx/DwcK1cIzAwkGZmZly6NONPQn1qw90NlLvIud1nO0l1L8bbf9z4qFlz+lhZ03/4cMb7+JAkX716RWdn5+Rz79/P3BOOImDKvISEBJYuXZodO3ZM3ufm5pac+X3UqFEMDFQPgytUCnZ078gu/3ahMiuL7EYEMGZKTT60taJv3bqMOnWKkfFJXHjkAct0mkgdI1MCYNcevTLV4ygImZUfAiY9AE8BfPXBpO9a2rpeQWzk8quAt3H8deNhGpiUJADqFjahXbt+dD1wOm91w7/1Jze0Ug/B7RtNJuZsEOfn58eFCxfS0dExOUiSy+VcsGAB/f0znxE7LdpILnjt9TXautpy8pnJyf+fUSdO0MfKmk9792bM1Y/nff3+++80NDTM8j2JgClrRo4cSVNT04/eg3fu3GHfvn2po6NDfX19DhkyhI8fP+aRZ0cod5HzwOMDWbto2FMmzbbi08ZWfGBjk5xGIigynpO3XWKxxn0p0zekrp4+Fy11ytq1BEFDabUlMvXPc45MJtsJdR4lMwDBAH4juVEmk7UH4AT1E3ObSM7T1jXt7e3p5eWlreKEDAoKDcfvKzbgVkA0gso0gKRUAGed0btnL0wf+R1KmBTJ7Sp+zOcAcGAMIElAJyfApme2X5IkvL294e7uDnd3d9y9excAYG9vj+7du6Nbt26wtrbW+nWVSiWcnJzw/fffo0SJElkq6038G/Q62AvG+sbY1XEXiugXAVUqPOvaFVQoUdnjIKCri/3796NcuXKoX78+4uLiEBQUhMqVK2fp2jKZ7AZJ+ywVooGC2pZcuHABDx48wJAhQ6Cvr//Rz548eYLevXvj5s2bkMlk6N2nN8IbhEOngg4Odj0IfV39VErVQOhDJCxuj2f7DVDm53Eo/v1PyT969iYWv++5iH/WLUXpeq3w8+Cu6FqrBIoaFULhwoUzf01BSEOabUlqkVRB2grqp8K8TKFQcOVWN9Zs2p4yPUMCYHGr+lx24iFfhGUsl0+OSYonPSape5XWNifDsncoQJIkXr16ldOmTWO1atXUS7nIZGzatCmXLVvG58+fZ+v1SdLV1ZUAPpurklEKlYJDjw6l/VZ7Pgx/mLw/4sAB+lhZM8LDgyQZFxfH8uXLs3///lm63qcgepiy1blz5zh27Fj+/PPPLFpUnQPN2NaYs7bOynLZ0qtbfOJYnc+a1SCjPn8i815ABAdtvMpK0zxYukEXljAvyw2bNolUBEK2SKstyfVgJie2L7WRyw1PQqK55JgvSzu0V2cSLmTM2q16cYPbcSpzMrFkRoU+Ilc1/m95E0X2rTt3+/ZtTpo0iRUqqNe709PTY+vWrblmzRoGBeVcAkyFQsGqVauyTp06WR4OXX5jOeUucu7z25e8T0pKol/r1nzYsRMXLVqU/MSdr68vFYrUM31nhgiYss7Hx4d37qS/rt+dO3dYo0YNGhQ1IAA2atyIZ8+ezdK13yyaRR8raybOtSdjw1I85tLjN2w8bgUNyqg/XJStVIWuW7eLwEnQKhEwFeBGLi+49+gp+4yeTpPyVVlu+Fpa/uLBNr9s4MT5qxjyNiq3q5e+W9vJuWXJBZak75FsuURgYCAXL15MW1tbAqC+vj47d+5MV1dXrU3czqj3T0ft27cv/YPTcPblWcpd5Pzt4m8f7Q/fs4c+VtbcPmcOAfDMmTNZuk5aRMCUdTVr1vxo4ndq3NzcaGNjw+XblrPsgLIsZl6MANihQwfezUB29g8lBQXRx7oGQ3pakGuaqTPpp0CSJB73DqTDD39Q38yCANi673DGJGg3ABe+XGm1JTk+hyk3FNR5B7npbVQM/vh7E3bv3IFAn+sAJZhWqomffvkd4/t1QBnTQrldxfQlRgOHpgB3dwGVmgA91gMm5bRWfHx8PPbv3w9XV1ccP34ckiTB0dERgwYNQp8+fVCyZEmtXSujlEolrK2tYWJighs3bkAmk2WqnMCYQPQ62AvljMtha7utKKSn/n+XkpLwpE1b6JUqhUq7duLKlSto2LBhpq+THjGHKesuXLgAMzOzDM2VG31qNLxeeqH9q/ZYtmgZoqKiMGjQIPz++++wsLDI0PVffP8Dkh77oso3vpBVdAAGuAEGKc9vJImLfqGYtngdnsMcpSpYom05JeTGsfiuT89se50JBZ+Yw1SAPxXmpMTEJO6/cI9T995mjal7CV09GhYvw5Z9f+LhCzdyu3oZE3ibXF6XnF2M9JxPZuUR6Q+oVCqePXuWP/zwA01MTAiAFStW5K+//qqVHEfasnnzZgLg/v37M11GojKR/Tz6scH2BvSP/PgptzDXLfSxsmbkuXNZrapGIHqYcoVvmC/lLnI63XBiWFgYp06dSkNDQxoaGnLy5Ml88+aNxmVF7NtHHytrxu5Zon5funZRzytMxw3/cP7gco3GddXTAMpVqcGtu93y1lO3Qr6RVluS68FMTmyikcua05dvsWXv4dQvWpKG5Wuw5swjnLznNrcfvZSzC95qgySRV9aQv5uRi63IZ+e1Uqyfnx9nzpxJS0tL9YRYY2MOGTKEp0+fznS27OyiUChYpUoV1q1bN0t/VOZdmUe5i5wnnp/4aL8qNpYPGzXmjV69WalSJR44kMXHzzUgAqasi4qK4oYNG+jzLkdWWtatW0cbGxuqVCpOPTuVDtscGBqnTkvx4sULDh06lDo6OjQxMeGff/7JuLj0E9CqYmL4oK4dA/83k7y5TT2fcEdfdT40Ddx9EcZvRs6hXrGyBEAL69o85Zm1uVXCl0cETAW4kcsusYkKTlu6iSUry9V5gGQ6rFC7KactXsfY/DpfIDaM3NFP3RBv60XGaP7pNyUxMTF0cXFhs2bNkp9wa926Nbdt28aYmDySfDMF2uhdOvJUnYtn4bWFn/0sdO06+lhZ8/6BA2zfvn2O9KyJgCnrwsLCCIALF37+f/opNzc39u7dm5GRkfSP9Gdt19qce3nuR8fcu3ePnTp1Uq8V99VX3L9/f7oB+qufp9HX3oGqhATy6jr1e3Xv0Az1APu+CmfL4TOpa1yC5Zr35YHbr0Rvk6AxETAV4EZOm5RKJdfs3M+xLudYc+YRlmg9ikbmldj1x2m8/fBpblcva55fJJfUJOeUJC85Z3p5E0mSeOnSJQ4bNix5oduqVavyzz//5MuXL7Vcae1TKpWsUqUK7ezsMv1H5JT/KTpsc+CAQwOYpPr4078yKoq+9R3pP3y4NqqrMREwaYeFhQX79u2b4fNmX5r92VI47506dYo1a9YkALZv355+fn6plhNz8aJ6KPfIu4cvzi99lzx2lHrx6ww44/2CrRYeZaVpHmw6din7DB7G4ODgDJUhfHlEwFTAG7msunbXlx2GjGOhEuqu7DLtx3DKntu8+Cg4zw0nZZhKSXouUM+JcKpNBmRurtXr16+5cOFCWltbEwCLFCnCIUOG8Ny5c/nu0+uFCxd48eLFDJ+nklR0vuVMuYucfQ72YUhsyGfHhCxfQR8ra27480+tZA7XlAiYtKNLly60trbW+Pj3r/3w+HC2+acNm+1qxoDogM+OS0pK4pIlS1i0aFEaGBhwxowZKfbCSkolHzVrzhc/jvxv56k/1EHToSkZ/qCjVEnccdWf5Vr9QMh0aFC4CGfMmsPY2DyaC07IdSJgKuCNXGbEJynpdu0Jy9asT0BGADS3tufY35czJDwyt6unHREB5Kb26sb2n2FkfMbuKykpif/++y87depEXV1dAmDjxo25ceNGRkXlg3QJWhSdGM0xp8ZQ7iLnr+d/ZYIy4bNjFOHh9K1rx6tDhlJXV5ezZmU9qaGmRMCkHbNnz6ZMJtNoSLljx47s169f8vdP3j5hw+0N2eXfLoxKTPn9ERgYyAEDBiQ/DLF3797PPnAEL15Mn5q1qHg/YVySyKO/qt/Hx/6Xqd7hiLgkjl11kEbV1EsNFStVhtt37s5wOULBJwKmAt7IaUqpVHL1zv1sPfxXyn9Td1WXtG3JVgPG8PyN+7ldPe16cIhcUEmdX+nWdo0bWUmSePPmTU6YMIHm5ubqBHlly3LatGn09fXN3jpnM1dXV/74448aTcD90LOIZ+z8b2fWdq3NbT7bUu1RC1r4F32sazDBz4/e3t6MiEg5l052EAGTduzbt48AeOnSpXSP/fPPP+nk9PEab1cCr7COax0OPzb8s+HaD507dy45J9nXX3/N69evJ/8s4dEj+lhZM8x1y38nSBJ5cKI6aPKcn/Ebe8cvOIqtf15Dg7LVaNllPF0vPWNsQmL+70kXtEYETAW8kUvP6Su32Kr/TzQsXlq94K2RCcduu8oLfqFUqvLXcFK6kuLJQ1PVDevqJmRo6vMlPhQQEMCFCxdSLpcnJ5bs3r07PTw8tJ6VOrfMnTuXjRs3ztAQ4tmXZ9lwe0M23dmU115fS/W4pKBgPrCtTf8pU7RR1QwTAZN2+Pv7EwBXrVqV6TLcH7knJzJN67WmUCj4999/s2RJ9ULcvXr14sOH6mV1nnbrzqfde3x8gkpF/vuT+r19flmm60eSF/xC2NP5PCtN86Bl57G0tJJz/0GPfDe8LmifCJgKeCOXkoi4JO646s+6fackP+VWVt6AE+b+XXCG3D4V+ohc/W55k8PTSMXnw0Yfio6O5pYtW9iqVSvKZOphyYYNG3L16tUMC0t5eYb8TtNlJCRJ4ro762jjYsNeB3rxVfSrNI9/PWcOvWvWYv26dTl37tw0j80OImDSDkmSWKJECQ7XcNK+UqlkYuLnywg53XCi3EXOTfc2pVtGZGQkZ82axSJFilBXV5cjRoygt5MTfaysmfDpBHGVUv3U3G8m6vQgWSBJEi/4hdJx+Dzqmao/TFrVduApzzNZKlfI30TAVMAbuffi4hP4h7MrKzt8w3J95rDSNA82+GUbu42cxhs+j3O7etlHktR5WzRY3kSpVPLkyZMcNGgQixQpQgC0tLTkrFmz+OjRoxysdM5JSkrK0CTv2KRYTvScSLmLnD+f/ZlxirSH8BJfBtBHbsPHv0znyJEjuX379qxWOcNEwKQ9X3/9Ne3t7dM97uXLlyxcuDA3btz42c9UkoqTz0ym3EXO48+Pa3TdoKAgjh07lvr6+ixcuDCHlTTjw9//+PxAZRK5s786aPJy0ajstEiSxJP3AmjbZzJ1jUuon+br9wOT8luOOUErRMBUwBu5g56X2bjrYOoVUa/ppFfElF3Gz+Odl28LfhdzfCT5zw/qxnNzBzIy5Z4Qb29vTps2LXnBWxMTEw4bNoznzp0r8PMX1q9fTwAaBU0vIl+w676utHW1pYu3i0avn1fTf+UDG1smvf58pfmcIgIm7Zk8eTKNjY3T7Y1UqVScPHkyL1++nOLP4xXx7H+oP+ttrZdiuoHUPHnyhN999x1lAE309Dh//vzP590pEsit3cnfTMk72pm8LUkSD996xppdR9G8z1y2WOTJPRd8kocJhS9DlgImALoAJqZ3XE5uAJoCWANgA4BL6R1fEBu50MhYbr38nJ3+Pk9d09KEjh4t7Vty9kpXxsSlPRRVYAR4kU625Ozi5Jm/PktuFxQUxGXLltHOzk49d0tXlx06dODu3bszPPE5v0pMTKSlpSXr16+fbvBz8dVFNtrRiI12NOLFV5r1SCU8eUqfGjW5bfDgXF36RQRM2vP27VvGx6e/JIkm3sS9YZt/2rD5rubpDut+6sLKlWz2rhe4QoUK3LRp08dBXFKc+kPS7OLk/awtIP0hSZJ4/H4Qv1lyhiYNelKmo8se3w1hYGCg1q4h5F1Z7mECcE2T4zQsaxOAEADen+xvC+AhgMcAftGwrK4AfkzvuILSyCUlKbh44y5Wa9CaeialaDHlX7ZeepbT17jR99nnuU8KLEkiL/5NzilBLq1F+v/3CTc2NpY7duxgu3btklMB1KtXj05OTgwKCsrFSueO971Lhw8fTvO4rfe30tbVlt32d+OLqBcalx8wcSLv16nLKl99xVatWmW1upkmAqbcIUkSX758mWYw/j7dQNd9XRmdGK1x2ar4ePrWs+c//frTwcGBACiXy3no0KH/rpcQTW5orU5I+/BYVm/nIwqliqsPe7GUY2dCR5d6BoU4euLUHH36U8h52giYlgFY+a5nx+79psm5KZTV7N353h/s0wXwBEBlAAYA7gCoCcAGgMcnm/kH5+0BUDS9a+b3Ru7SHV9+0/dHGpiWUveUFC5K+/b9eP7es4I/5Pap2DBye2/1ENzO/mRsGFUqFU+fPs2hQ4eyaNGiyTlefvnlF96/X8DSJWRAYmIiK1WqREdHxzRfJ95vvCl3kXPcqXGMTdI8oV/8gwf0sbJm8NJlDAkJ4ePHuTdPTgRM2jVjxgyuXr063eNWrVpFAOn2vlx6dYlyFzk339ucoXoE/u9/fFDXjsqYGO7Zs4dVq1YlALZo0YLXrr17ajM+glzTjPzDnHyq/cWeYxMVnOFygia1mhMAbZp34JvoL6QX/wukjYDJM4XttCbnplKe5ScBU0MAxz74fjqA6emUYQFgvSbXy4+N3OvQcG44fou91lxi6X7zCZkOy9k05M9/rWFE9Beapdb/yn/Lm1xeTZ/79zl9+nRWrFiRAFi0aFEOHTo0Ty54mxvWrVtHADxyJPVJ8JIkcejRoWy2q1mGPv2T5IuRP9G7nj2VeeATtwiYtKt58+YcOXJkusc9ePCAK1euZHh4eLrHDjg0gJ3+7ZShD3mx16/Tx8qaEe8WcE5MTOTff//NUqXUHx779OmjDtRj3pAr65PzypEvr6dTauaERCXw+8W7WPHHdaw16yhnup7g2vUbNX7yVMgf8tyk7xQCpp4ANnzw/UAAK9MpYw6ARppcL780cgqFksu3uLFG0w6U6RuyaL1ObP7Xaf596hFvPijAT7mlR6VSryk1uzhjFsq5aclvbNiwYfK8pHbt2nHnzp1iuYMPJCYm0sLCIt3epdP+pyl3kXPng50ZKj/u9m36WFlzaLNm7Nq1a64HqCJg0q7s6Ll+n5/pZvBNzeuhUtHv62/o//0PH+2PjIzkzJkzaWRkRAMDA/7vf/9jbNAT9fJH8y3I1/e0Xf1kfsHRHOZ6nSYNeqoT21aqyh279nx5vf0FlDZ6mEwBLAXg9W5bAsBUk3NTKS/LAZMG1xjxvr4WFhba/61q0bPQGHb4fjINiqkzS+sYFmGd1j3psu+EeBPGhJJbu9NreBH++G315CE3a2trLl68+Iucl6SJtWvXEgCPHj2a6jFJqiR2dO/ITv92SjMr86ckSeLzIUP4sEFD/jXvT06fPl0bVc6S7AyY8lNbkhvCwsI0mvAfmxRLx+2OnHF+RobKD1m+nD41ajIphfd6YGAgBw4cmJwe5ODOTeSSGuRfVdR52bLRjedhbPbTn9QroX7y1tLahoeOpP5+E/IHbQRMbu96dCq/234D4K7JuamUl+UhuYxsefFT4cugUI75fQV7rLrAStM8aFynLcvJG3LKglUMj8zY0EhBFXHnKJ27mbNuWT0CYKFChTho0CCeP39eBJJpePToEfX09NigQYM0f087H+yk3EVOzxeeGpetionhy7HjPl+6IpeJHibtCggIYKNGjThhwoR032tt27Zl7dq1NSp39qXZdNjmkOpacylJfP6cPjVr0X/YcEqpZN339PRkzZo1CYBd2n3L59Mt1IFT+HONr5NZFx4F037QDOqalmbZRt245/oLKkQOp3xLGwHTbU32abqlEDDpAXgK4KsPJn3Xymz5n255pZFLfPeUW/VGbSnTMyAAOkxcT2dPP756K4aTyHfZd8+d5eA29VhYDwTAOrWs6OzszLdv3+Z29fKsHTt2cNGiRSTVv8OFCxemORE3KjGKTXc25dCjQzUOPhNfvOCTTp3pU6Mmz8yezePHNUtImBNEwKRdkiRx3LhxBMBJkyal+Ro5c+YMT548qVG590LvUe4i527fjOVOCt+zhz5W1gycOSvVuiQmJnLhwoU0MjJi4UKF+GcbUyYutiGjsj8/mCRJPH73Jdv+dYyVpnmwzsilrNf4a16/7pXt1xa0SxsB02UATT74vjGAy5qcm0JZOwG8BqAAEADgh3f72wN4BPXTcjMyU3ZqW243ck9DYzhx1T4amJip590UMma9tn249cDJXJ/7kVcEBwdzyZIlrGFVjQBobACOaGXF6xfPiN6kVHw4HDl06FA6ODho/Hpa5rWMchc577/R7CnCmIsX+bC+I33rOzL6wgX279+fpUqVyjPzxkTApH2SJHHs2LEEwMmTJ2vlfShJErvt78Y+B/tk+NzgpcvoY2XNN+vXp3mcv78/u3fvrl7qxEyPx0ZbqSeF5wBJknjU+zVtBsykTiFjAmDTVu15+/btHLm+kHXaCJhqv+v1ef5uuwXAVpNz88KWG43cq5Awjvh1IR2/Vy9RUmmyGyvVa8lpi77gp9w+kZiYSHd3d3bu3Jl6euphtwYWhtzYtSijz69V51sSPiJJEs+ePcuePXtSV1c3eZX36Ohojf+gvYp+Rbstdpx+Lv25R5Ik8c3mzfSpUZNPOnZkor8/STI+Pp63bt3K/I1omQiYsockSRwzZky6QdOzZ884depUjQL2bT7bKHeR80FYxhKdSioVAyZOoo+VNSPTyStGkocPH2Zli3IEwFY1ivHm5bMZul5WKFUSt531YcVvB1NmqE6+2WvA0By7vpB5WQqYAOgA6P3u3yYATNI7J69tOdXIKRRKrtjqTuumHSjTMyQAmtVqxFWejxkUqZ3MuQXBrVu3OH78eJqZqXvcypQpw6l9mtL7J2Pybwcy6MvNnZSa2NhYrl+/nrVr1yYAFi9enFOnTmVAQMYTlk47N431ttbj65i0hypU8fF89fPP9LGy5ssxY3jt/AX26tWLCQl5LweNCJiyz4dB05QpU1IMmlatWsVixYpptIxIREIE7bbYcd6VeRmuiyohgc/6f8cHNraMvXEj3eMTEhK4dPqPLFFYvbj2gH59+OzZswxfN7MSFEquOHybpVsMYInWozhu500+DY7kvXvZ9xSfkDXa6GHKkcYou7bsbuRehMVy2YmHNLdr9cFTbr3osu+4GHJ7JyQkhMuWLUv+g29gYMCePXvy0N6tVGxop05E6T6STIzJ7armKcHBwZw1axZLlixJALS1teX69eszPRTmHapOUrn8xvI0j0t6/ZpPe/Skj5U1Q5ydKalUdHNzY8WKFen36QryeYAImLKXJEkcPXo0AXDQoEGfvf4kSeLrDKwlOPXsVDbc0ZDxiox/kFSEh/Nx6zZ86NiAic+fa3TO2ys7+EuTQiykr0MDAwNOmjSJb97kzDAdSUbEJXHhkQesPuMwS3eaTADs1KUb797VfI09IWdoI2BaAGAKgIoASrzfNDk3L2zZ0cgFh73lmNlLaW5Vj+V/cqHlLx78dsoqTvpzJcMixFNuJJmUlMR9+/axa9euyUNu9vb2XLlypbqx8jtJLqxMzi1D3sr5Fe7zup9//pmGhoaUyWTs0qULz5zJ2nwuSZI4+MjgdJNUxt64wYeNm9DXrh7fHD2aPOxHMs+uwScCpuwnSRLnzJlDmUzGOXPmpHrcli1b6OWV9mTnK4FXKHeR8+CTg5mqS+Lz53zo2IB+rVtToUHSTJLk/X18OdGU3zcpTx0dHZqamnLBggU5+pp+HRHPsZvOsVijvtQxMFIHTl275+o6jMLHtBEwPUthe6rJuXlh01Yjp1Ao6bx9H2u16EyZfiH1o+4ly3OC004GvM2bf0hymiRJvHbtGseOHZucjdfc3JyTJ0/+79OUUkGenKNeaXylIxksGgtS/bu7dOlScq/knDlzOGLECPr6+mql/FP+pyh3kXPXg12pHhO+cxd95DZ83LoNE/z8OGrUKBobGzMkJEQrdcguImDKOWfOnElenDcm5uMe4ZiYGFpYWHDAgAFplqGSVGz7T1sOPZr5eT2xN27ygY0tn/XrT5Wmw8Te/5Kzi/PenMbs2L4tAbB8+fJctWpVjg41PwyK4gDnkzRt1Icyg8IsUbEqzz0MoUol5m3mNm3MYWqc3nF5ectqI/f49VsuO/GQ9f+3l5DpUMfAiLbfdOf6vYfFkNs7z58/59y5c2llZUUANDQ0ZM+ePXngwAEmJX2QFDEigNzYVj0EqJ6uBAAAIABJREFUt28UmSgmwL/n4eFBADx4MHOfutPyYZJKherzXDZSYiIDf/uNPlbW9B82nIp3y50EBATQzc1N6/XRNhEw5byIiAhWr16df/3110f7nz179vF7PhXr7qyj3EVO/0j/TNch8vBh+lhZM2DiJEqatsXe7uTs4uSmdjx74gibNGlCALSwsOD69es1qru2+L+J5a87L7D6yFWsNM2DTf/wYLvvRvLx81c5VgfhY9roYbqlyXF5dctMIxf05i1H/baEparXZSHLurT8xYPfrb/COat38c1bzZOuFWQRERFcv349mzVrRkCdM6lp06Zct25dyjmTHh0nF1iSc8uSt1Pv5fhSREdHc8WKFdywYQNJ9RDmhg0bsuVR/e0+2yl3kfPMizOf/UySJPoPHapeSHfxYjotW8YffvghX6VzEAFTzouPj+fIkSN5/vz5FH8eHR1NZ2fnVF9HwbHBtHW1pdMNpyzVI3TdOvpYWTN07TrNT7r3Dzm7GLmpPaWEaB47doyOjo4EwMqVK9PFxYWKVJJkZof4JCXdb76k44j57z6UF2aj3iN5+cHLHKuDoKaNgGkxgB4AZJocn9c2TRs5lUriBrfjrNmsI2X66qfcCptVYKdhk/kyXPSEkOo/6gcOHGCvXr1oaKj+HVWvXp1//PEHnz59mvJJyiTy+Ex1r5JzQzIk/SdpCiqVSsULFy5w/PjxLF68OAGwR48e2XrNqMQoNtnZhN8f/T7FP17RFy6o89ts3kySnD17Nrt27Zonn4ZLjQiYct+iRYvo5uaW/Bpzdnamjo4Ob6TxNNuYk2PYYneLFHs9NaUO+L+n39ffZCzIv7tXHTRt7kAmxlCSJHp4eNDOzo4AWK1aNW7bti3HF9fdf+Yqqzt+o36AqLAJa3Ufy11XnzM+SSzymxO0ETBFA1ABSAIQ9e77KE3OzQubpo3c1adhLN7ye+oYGrFOqx7c6HZEDLlR3SBdv36dY8eOTU4FYGZmxjFjxvDq1atpN1JvX5AbWqmDpQPjyKQvb66XSqXiuXPnOHbsWJYrVy75KcEePXrw4sWL2X79JV5LaONiQ583Pin+/MWIH3m8rh3v3LyZXN/81LtEioApt0VHR1MulxMAHR0d6enpSZVKlWawRP63+PP/2Tvv+BrvL46/n5spCTETI0KIVbFXxd7ULB20dlUHqkVrtEZ/qkXRopQajT1r1wxq702sJBKRLXvfdX5/XFKKyLhZ3Pfr9bx4nvsd517uuZ/n+5zvOYf8D2Vp/sgNG8SrSlVJupXBm7ErG58QTYabYr1eL1u3bpWaNWsKINWqVZNNmzbl+G/BoaMn5I167lK0cgMpN3aXzNhjivXMCYwhmFQYCuJOenTuDDRKT9+8cGRkhemv096mXW6PCAgIkJ9++kmqVauWGpf07rvvPhuX9CJu7RGZXk5kWmnD3dxryPr166VUqVKpn1+PHj1kzZo1EhMTkyPzP4h7IHVX1pUJxyY89/WUe/fkauUqUqZwEalfv36+E0qPMQmm3Eer1cry5cvFyclQjLZTp06pGa7v3bv33BVLjU4jLTe0lOGew7M0tzo01PBY7vffM975ygaDaPLo8lRMpU6nk40bN6b6v7p168revXtz/DsSFxcnJ70fSqBpY1GOYAzB9DuwALj56LwIcC49ffPCYXJy6ScuLk5Wrlwpbdu2FUUxJHtr2rTpi+OSnocmWWTPeMOq0sImIg+9s9foPERQUJB8/vnnqXfWR44ckZ49e8q6deskNjbnY9++PvJ1mkkqg6f+IF5uNcTvypV8vbXZJJjyDomJifLzzz9LkSJFRFEUadfOkJ9u9wuyc/9y/hepuaKmhMSHPPf19OL77nvi+867met8eb1h1+6qXiKalKde0mq1smLFCilfvrwA0rx5czl+/HiWbDWRdzGGYLr46M9LT1y7kp6+eeEwObm00Wq14unpKf379xdbW9vUwMcpU6aIt3cGxc5Db5FFzQ1i6e8xIupXO8P541QA//zzj4iIREVFSeHChcXDwyOXLRO5GnY1zSSV2thYuVWnrjz4+usctsz4mART3iMyMlLGjh0rVlZWolKpZPDg58fQ+cX4iZuHm/xxJQNB288h/PdF4lWlqqhDQjM3wHkPg9/aOEBE92y8UEpKivz222/i6OgogLz11lt5qjyQCeOQli9RkT40iqKYPdoJhaIoJQB9OvuayKPcvHmTCRMmUL58edq2bcv27dv58MMPOX78ON7e3kyePJmKFSumf8Crm2Bxc4jyg/fXwFs/g4V1ttmfm9y+fZtJkybh6uqKu7s7kyZNAqBw4cKEhoYyYMCAXLVPRJh1fhZFrYvyUY2PntsmZssWTj0M58tr1wgNDc1hC0286hQpUoTp06fj4+PDkCFDsLCwQFEUAO7evZvarlyhcjQo2YAtd7egl8z/rNi1bgVA/D//ZG6AegOg/Q9wYyvs+hIMCwOpWFpaMmzYMHx8fJg+fTqnTp2iTp069O7dm9u3b2fabhP5iBcpqScP4ENgB/AAmAbcBt5NT9+8cJjuCv8lKChIZs+enboTxMzMTLp06SIbN25MTUaXYVLiRbZ+brg7W9bBEOj9ChISEiK//vqrNGjQQABRFEXatm0rf/75Z47FJKUXTz9PcfNwkw23Njz3db1WK3fbtpOfGzaSSpUqZf7fPo+AaYUpT6NWq2Xfvn1y7949OXfunACybt261Nd3+uwUNw83OR10OtNz6PV6udumrdwf+knWjD041eDL9k5IswB4VFSUfPvtt2JraysqlUr69euXrlp6JvI2afmSdDsKoCowDBgOVEtvv7xwvO5OLjY2VlasWCHt2rUTlUolgDRo0EDmzp0rISFZixuQ4Ksi8+oZnv8f/MGQxfsV49ChQ9KhQwcxMzMTQOrUqSOzZs3KVOHbnCAsIUzabmor3bZ2e+F27diDB1Orvr8KO0FNgilvExoamlpSJSoqSqZPn556k7Fnzx5Zt3GdvLn6Tfnc8/MszRM8bZrcrFFTdFnJZabXG8IJJhcSOTLzpc1DQ0NlzJgxUqBAAZNwegUwimDKz8fr6OTUarXs2rVLevfuLQUKFEiNS5o4caJxSm3o9SJn/hD5XwmRnyuL+B7J+ph5BK1WK/v27ZOgoCAREVm7dq2UK1dOJkyYIDdu3Mhl69ImLiVOem3vJQ1WN5DrD6+/sJ3fgIFyorG76HMwOV92YhJMeZ+jR48+Nylr165dBRDH8o5S9vOy4unvmek54k+dMtwI7N+fFVNFdDqRv4YaRNPpxenqEhISYhJOrwCvnGAC3gA2Yti9987L2r8uTk6v18upU6dk2LBhqfmSihUrJp9//rmcPHnSeNthEyJE1n1gcCareonEhxtn3Fzm8bZnb29vAVJLPmg0mnyxCqPWquWjfR9J7RW15diD52dfFhFJunVbzrpWEjtra5k6dWoOWph9mART/kWj0cj69eulZi1D3qPSbUpLeEzmfIperZZbDRpK4LjxWTdMqxFZ28fg5y6tTXe3kJAQGT16dKpw6t+/v9y5cyfr9pjIEfKUYAKWA2HA9f9c7/goNsobGPeSMUYDzR79fcfL5nzVndzDhw9l9uzZqXXcrK2t5b333pMdO3ZISkrKywfICP6nRGa/IfJ9MZET8w13YvmYqKgoWbx4sTRu3Fjefvvt1Ouenp75KtO1Tq+Tr498LW4ebrLt7rY02wZ9951ccKshM6dOlYuPklXmd0yCKe+j0Whk/vz58vfff7/w9UEjBgkgpVxLZXp15sHoMXL7zcaiN0aGbnWSIT/TlCIiXhmr8fhf4fTFF19I9KMajSbyLnlNMDUH6j4pmAAzwAeoAFgCVx6tItUAdv3ncHh0LAB+Bk68bM5X0cnp9Xo5evSofPjhh6klSho3bizLli3LngBknU7kyM8Gx/FrTZEH540/Rw6h1Wpl79690qdPH7G2thZA3njjDfnll19y27RM8/PZn8XNw02WXF2SZjtNZKTcrFlLgiZOyiHLcgaTYMr76PV6qVChggwZMiTNdn1n9xUzOzOxsbV5KjA8vcT8/bd4VakqCS/JMp5ukmNF/mgt8r/iIj6HM9w9JCREPvvsM1EURRwdHWXlypX5NkHs60CeEkwGeyj/H8HUGNj3xPl4YHw6xjEDtr+s3avk5CIiIuSXX35JzT5bqFAhGTZsmFy9ejX7Jo0LE1nZw7A0vWmQSFLe2hGWXm7duiXjxo2TMmXKCCBFihSRYcOGyblz5/K1A1txfYW4ebjJD6d+eOn7CF+0WNY6l5Otixfni8eM6cUkmPIHERERL20TnRwtDX9rKMWrGcIKJk3KmLjXxsaKV3U3Cf3558ya+SwJESIL3jQUDg/I3M3i+fPnUwv8Nm3aNHt9tolMkx8E0zvA0ifO+wG/vaT/H8AaoOkL2gwFzgPnnZ2djf2Z5ih6vV6OHz8u/fr1S10RadSokSxfvlzi4+Ozd/J7x0VmVTEEd5//M81ttnmZlStXGopZqlTSuXNn2bRpU7565PYidvvuFjcPN/nq8FeifU6yvSfRq9Vyp3kL6eriImXKlElfeZt8QnYKplfJl+QXdvrslOpLq0vXj7qm1lvMiMD3HzRIvDt2Mq5RscEiv9QQmV5eJCxzG2d0Op0sWbJEihUrJmZmZvLll1/muZQkrzuvnGDK6JFf7wojIyNl3rx5Ur16dQGkYMGC8tlnn6XWZ8pWUh/BFRaZV9eQPiAfERcXJ8OHD5fNmzeLiGHr74wZM1J3vr0KnAk6I3VW1pH+u/tLsvbl4i961y7xqlJVHu7bJ15ezy/Em18xrTDlH7777juZMOH5tQ0fo9frZci+IfLmmjclLCFMRERGjhwpAwcOTJdwili1WryqVJVkH1+j2PzvwD4iP1cSmVVVJMo/08M8fPhQPvnkE1EURUqWLCmrVq16pVZ88zNp+ZL0ZvrObgKBsk+cOz269tqh0+nYu3cv77//PiVLluSLL77AxsaGJUuWEBQUxMKFC6lVq1b2GpHwENb0gkNToXpPGPoPlKyRvXMagfj4eE6fPg2AjY0Nhw8fTs3A6+DgwDfffEOpUqVy00SjcTvyNiMPj6RcoXLMaz0PKzOrl/aJWrkKi3LOFG3blmrVquWAlSZMPEtwcDDBwcFptlEUhe/e/A61Ts3MczMBsLe3p3DhwqhUhp8tw2/b8ynYqiUA8YcPG8foxxStAH23gDoBVvaA+PBMDVOsWDEWLVrEmTNncHJyol+/ftSpU4ctW7ag15uKaORZXqSksvPg2RUmc8AXcOHfoO/qxpovP9wV3r59W8aPH58aX1O0aFEZMWJEzu9i8jvx7yO4c8vz/CM4vV4v586dk48//ljs7OykaNGiqVmrNa9IjqH/EhgXKK02tJLWG1u/sKjuf0m8ckVOulaSuhUqyJEjr07OrMdgWmF6JVl4eaG4ebjJ8QdPF7s9efKkNGrUKLXI9fPw6d5D7n34YfYY5n9KZKqjyO9NsxzTqdVqZdWqVVKpUiUBpFatWrJlyxbTilMukZYvyfEVJkVR1gGngCqKojxQFOUjEdFiyCC+D7gJbBSRGzltW04TGxvLkiVLaNKkCVWqVGHGjBnUrl2bzZs3ExQUxLx586hTp07OGKPXw7HZ4NEFLGxgiCfUHwSPaj/lNaKjo1m4cCF169alQYMGrF69ml69erFz506srAyrLebm5rlspfGJTo7mU89PSdYls6jtIkralkxXv8iVqwi3sEBvZ0eRIkWy2UoTJl6OTqd7aZuP3D6ifKHy/HD6B5K1yanXo6Ki8PPzo0GDBnzxxRfExMQ807dg61YkXbyENirKqHYD4PwmvL8KwrxgXR/QJGV6KDMzM/r27YuXlxcrV64kMTGRnj17Uq9ePbZt25bmSpqJHOZFSupVOvLSXaFOpxNPT0/p27dvagbuatWqycyZM3MvviY+XGRVz0eVugfm2V1wer1eDh8+LH379k0Nfq9du7YsWLBAoqKictu8bCdJkyR9/+4rdVfWlXPB59LdTx0SKl7V3STkxx/z9W7AtMC0wpSvGD9+vNSpUyddbc8EnRE3DzeZe2HuU9ejoqJk2LBhqdv1V61a9dT/78Sr18SrSlWJ2rLVqLY/xdVNhrJQa3sbrSyURqORFStWiKura2oppm3btr2y3928Rlq+JNfFTE4cecHJXbt2TSZMmCDlypUTQOzt7eXTTz+V06dP5+4Xwe+kIYDxfyVEzi3Lk4/gHi9NX716NTWVwqeffprv0wFkBI1OIyMOjpAaHjVkv1/Gyj6E/vqreFZ0lThv72yyLvcxCab8xerVq2X06NHpfmw+4dgEqb2ytvhE+Tzz2vnz56Vhw4YCSIsWLeT6dUNJIL1eL3eaNZeA4SOMavsznPnDcLO55VOjJvLVaDTi4eEhFStWFEDq1q0ru3fvfm18Xm5hEky55OR8fHxk2rRp4ubmJoCYmZlJ+/btZe3atZKYmJgrNqWi04kcnW1IRDm3tkjQldy15wV8+OGHMmjQoNTz7du3P7ce1auMXq+X/538n7h5uMkarzUZ6qtLTpbbjd2lfsmS0qRJk2yyMPcxCaZXm4eJD8V9rbsM2DNAdPpnRYlOp5PFixdL0aJFxdzcXEaPHi1xcXESNHmy3KxTV3TZnULk8HSDaNo91ug3nY+Fk4uLiwDSrFkzOXbsxaWPTGSNtHxJXtkl98oQHBzM3LlzefPNN6lYsSLffvst9vb2/PbbbwQFBbFv3z769OlDgQIFcs/I+DDDLriD38Mb3WHoEShVM/fseYJbt27x008/GdQ8UKFCBVxcXFJf79atGzY2NrllXq6w5NoSNt7ZyGC3wXxQ7YMM9Y3d9TfaiAi+GzuWr7/+OpssNGEi44gI9+7dS1fbYgWKMbr+aC6EXmC79/ZnXlepVAwdOpTbt28zYMAAVq1ahUajoWDr1khiIolnzhjb/Kdp8Q28+Tmc+R0OTAIxXtyRubk5AwYM4NatWyxcuBBvb2+aNWvGW2+9xaVLl4w2j4l08CIl9Sod2X1XGBkZKUuWLJHWrVuLSqVKja2ZMWOG+Pn5ZevcGcbnH0MekakOeWYXnF6vl71790qzZs0EEHNzc7l582Zum5Un2Hp3q7h5uMn4o+MzvBSv1+vFp3sP8enS9ZVfxse0wpTv+PHHH8XMzEwiIyPT1V6n10n/3f3Ffa27PEx8mGbbxzGNKfHx0rdECbk0alSW7X0per3IrlGGlaYDU7LNtyYkJMiMGTOkSJEiAsj777+f6bp7Jp4lLV+S62ImJ47scHJJSUmyceNG6datm1hYWAgglSpVkkmTJuXNH3utRuTgD4YAxfn1RUKu57ZFotfrxdPTU9zd3QUQZ2dnmTlzpoSEhOS2aXmCYw+OSa0VtWTIviGi1mY8K3f8mTNypKKrTPnww1c+KN4kmPIfN27ckMWLF0tsbGy6+/hE+UjtlbVl7NGx6Wp/+fJlKWBuLr9WrSb6nNimr9OJ7BhpEE0Hf8jWqaKiouS7774TW1tbMTMzk48++kju3buXrXO+DpgEk5GcnF6vl2PHjsnHH38s9vb2AkiZMmVk9OjRcv78+bx7Fx8TKLK8k+FLvPUzkZRsLqeSDv755x9p3rx56mf4+++/S0pKSm6blWe4/vC6NFjdQN7Z8Y7EpcRlaoyA4cNlmksFURRF7ty5Y2QL8xYmwfT6MP/ifHHzcJMTgSfS1f7msmXiVaWqJF69JidOnMh+P6PTiWwfbvC3h3/K3rnEUMVg5MiRYmVlJebm5vLxxx+bhFMWMAmmLDq5u3fvyqRJk1KD7mxtbaV///7i6ekpWm3a9btyndv7DLWPfiglcjnjlb+zgz59+gggpUqVkvnz56cmmjRh4H7sfWm+vrm039Q+tSxERkkJeCBe1d6Q0NlzXgvnaRJM+ZO4uDj566+/MlTXMFmbLF22dJFOf3WSJM3LfYcmMlK8qr0hV77/XqysrKRhw4bi62vkkin/RacT2fq5QTT9MzN753rEgwcPZPjw4WJpaWkSTlnAJJgy4eQiIiJk4cKF0rhxYwFEURRp166drFy5UuLiMnfHn6NoUkT2fWv4wi50FwnP3RWGc+fOpW4hXrp0qfzyyy+5v1MwDxKZFCmdt3SWJuuaiE/0s1uo00vI9Bly443qog5OXybw/I5JMOVPtm7dKoAcPHgwQ/0e52b69cKv6Wp/78MPxad7D9m4caPY29tLoUKFZOPGjZkxOf3otCJbPjH44KOzs3euJzAJp6xhEkzpdHIpKSmydetW6dmzp1haWgog1atXl5kzZ8qDBw/SNUaeIPKeyB+tDF/UXaNE1Lm7gnP8+HEBxMPDI1ftyOskahLlg10fSL1V9eRiaOZL4mijouRmnbriXraszJ6dc446NzEJpvxJfHy8HD58OEMrTI+ZcGyC1F5RW+5Evvxm8OGy5eJVpaqk3Lsnvr6+0qhRIwHkk08+yd4bN51WZPMQgy8+nj5xZyxMwilzmARTOp3ciRMnBBAHBwf56quv5OLFi3k3LulF3Ngm8mNZkR+dRK5nY4bbNAgPD5c///xTFixYICKG2K+MBne+bmh0GhnuOVxqrqgpnv6eWRorbO48uVCpsvTu2lWWLVtmJAvzNibB9PoRmRQpTdc1lb5/931ubqYnUQcHi1fVahI2/zfDuVotX3/9tQDyxhtvyKZNm7IvvEKrEdk0yCCaTv6WPXOkQUBAQKpwatasWY7Pn98wCaZ0Ojm9Xi/79+/Pn0Vb1Ukiu0YbvpSLW4pEZPMz+v/g4+Mjc+bMkebNm6emVqhfv36O2pBf0ev1MuXkFHHzcJN1N7MWZ6aNiZFb9RtIwIgvjGRd/sAkmPIv4eHh8uOPP2ZqY8J27+3i5uEmG25teGlbv/4D5G779k/dBO/Zs0cqVKgggLi4uMiJE+kLJM8wWo3Ihv4G/3x6cfbM8RICAgLk6tWruTJ3fiItX2JKXPkEiqLQrl27/Fe0NcIHlrWFc0vgzWEweB8UdXl5vywgIly4cIFJkyZRs2ZNKlasyKhRo4iOjua7777j4sWLnD17NltteFX44+ofbL6zmSE1htC7au8sjRW5chUBkZEkdO9mJOtMmMhe1Go13377LUeOHMlw364VutKoZCN+vfAr4Ynhaba179oFjf99kq9dS73WsWNH7ty5w19//YWzszPlypUDwMvLi8DAwAzb80LMzKHXUqjaBfZ8DVc2GG/sdOLk5ESNGjVyfN5XihcpqVfpeKXvCq9sFJlWWmR6OZFbu7N1KrVanbr69uOPPwogKpVKWrRoIb/88kv27zx5BdlyZ4u4ebjJhGMTsvz4VxsbK7caNJS3K1eWIkWKvFZB9ZhWmPI1oaGhme57L/qe1F1ZV0b/MzrNdtqYGLlZo6YET315fqS2bduKi4tLah1Lo6FOEvHoYihJlc3+2kTmSMuXmFaY8ivqRNg+HLYMAUc3+PQ4VOmUbdNdu3YNJycnDhw4AEDPnj35888/CQ0N5Z9//uHLL798qoSJiZdz7MExvj/1Pe6l3ZniPgVFUbI0XtTq1ehjY5mxcCF//vln7pbfMWEiAzg4OGS6b3n78nxc82P2+e3j6IOjL2xnVqgQdi1bErtnD6LVpjnmH3/8wdKlS1GpVKjVar766isePHiQaRtTsbCG3muhdG3YOADuHcv6mCZyjDwvmBRFqaAoyjJFUTande21IuwWLGkNl1ZB01Ew8G+wdzLqFCLC0aNH2b7dULepSpUqtG/fHkdHx9TzgQMHUrx4caPO+7pwI+IGo4+MpnKRysxpOQcLlUWWxtPFxxPhsQK7Vq2o1KYN3bt3N5KlJkxkP0lJSQwePJjVq1dnqv9Hbh9Rwb4C005PI1GT+MJ29t26oouIIOHUqTTHc3FxoXXr1gCcP3+eRYsWUbVqVWbOnIlarc6UjalYFYQPNxvCJtb1gcCLWRvPRI6RrYJJUZTliqKEKYpy/T/XOyqKcltRFG9FUcalNYaI+IrIRy+79logApfWwJJWkBAOff+CtpMNz8eNREJCAkuWLKF27dq0aNGCKVOmAGBpacmqVauoW7eu0eZ6XQlNCGXEwREUsSrCgjYLsLWwzfKYUWvW4hMexhh/P+PcCZswkYNYW1tz48YNQkJCMtXfwsyCSY0nEZQQxNJrS1/YzrZ5c1SFChGzY2e6x3Z3d8fLy4s2bdowduxYatWqxaFDhzJlZyo2RaHfVrApAqt7QfjtrI1nIkfI7hUmD6DjkxcURTEDFgCdgDeAPoqivKEoSg1FUXb958j8Ou2rRko8bP0Utn8OZerBZyfAta3Rhvf19WXMmDE4OTkxdOhQFEVh6dKlnDhxwmhzmIBkbTIjD48kQZPAb21+o4RNiSyPqU9IIPLPP/GvWJEjFy9iZWVlBEtNmMg5FEXh9OnTjBkzJtNj1HOsR+cKnVlxYwUBcQHPbaOytKRQhw7EeXqiT0hI99guLi5s376dnTt3olaradOmDX369MlaYHih0tBvG6jMYdXbEH0/82OZyBGyVTCJyFEg8j+XGwLej1aJ1MB6oLuIXBORLv85wrLTvnxDyHX4oyVc2wgtJ0D/7VCwZJaH1ev17Nu3jy5duuDq6srcuXPp0KEDx44d49KlS3z00UfY2Nhk3X4TgOEx56QTk/CK8GJ6s+lUKlLJKONGrVuHLjqagbNn4+/vT4kSWRdhJkzkNI9j+HQ6XabH+KruV5ipzJh1btYL29h364okJRGXiVWiLl26cOPGDaZMmcLWrVupWrUqs2fPRqPRZM7gYhUNK03qeFjZA+JNP3l5mdyIYSoDPCn/Hzy69lwURSmmKMoioI6iKONfdO05/YYqinJeUZTz4eFpbzfNs4jA+eWGeKWUOOi/A1qOBZVZlobVPgp4PHnyJB07duT8+fNMnDgRPz8/1q9fT9OmTbMcgGziWZZcW8Ievz2MrDuSVs6tjDKHrSjAAAAgAElEQVSmPjGRiOV/ElG7FgVq1jStLmUDr4QvySe8/fbbDBgwINP9HW0d+bjGxxwKOMSpoOfHKRWoVw/zUqWI2Zn+x3JPYm1tzeTJk/Hy8qJFixaMGTMGT0/PTNtMSTf4YBPEBcPqnpAUnfmxTGQreT7oW0QiRORTEakoIj+96Npz+v0hIvVFpH6+vONOjoXNg2HXV1C+qWEXnEuzLA2p1+tp3rx56rK3u7s7GzduxN/fn++//54yZV6oW01kkYP+B5l/aT5dKnRhsNtgo40btW49PiEhtNy8mT/++MNo45r4l3zvS/IRDRo0yHKcZP/q/XGyc2LG2Rlo9M+u/CgqFfZdupBw4iTaiIhMz1OhQgV27drF4cOH6djREHmyZMkSdmZGiDk3gvdXGTb0rH3PEIJhIs+RG4IpECj7xLnTo2smHhN0CRY3B6/t0GayYUeFXcYddWJiIuvXr2f06NEAqFQqmjRpgpubW+r5u+++a1qVyGZuR95m/PHx1ChewyjpAx6jT0oiYvlyyjVpwg8//GDaGWci3zNhwgRGjRqVpTGszKwY02AMPjE+bLy98bltCnXtAjodsbv3ZGkugJYtW6IoCnq9nkWLFrFy5crMDeTaFt5ZBg/OwbreoEnKsm0mjEtuCKZzQCVFUVwURbEEegM7csGOvIcInFkMy9qDTg2DdkOzUaBK/z+TTqfD09OTgQMH4ujoSJ8+fdi0aRMxMTEA/PTTTwwZMiS73oGJ/xCRFMGIQyMoaFmQua3mYmVmPHEatWEDuogIyn/1JePGjUtN+WDCRH5Gp9Ph5+eXpTFal23Nm6XeZMHlBUQlRz3zunXlylhVqULMrsw9lnseKpWK06dPs2jRIoDUnXUZ2jjzRnd4ezH4HYcNfUGbYjT7TGSd7E4rsA44BVRRFOWBoigfiYgWGA7sA24CG0XkRnbakS9IijJ8QfZ8AxVbGx7BOb+Z7u6+vr6MHz8eZ2dn2rVrx9atW3n//ff5559/8PPzw97ePhuNN/E81Do1o/4ZRVRyFPNazzPKjrjH6JOTiVi2jNV2dpx5JIZNmHgVGDx4ME2bNsWQdDlzKIrCuIbjSNQk8tul357bxr5bV5KvXEWdRXH2JBYWFhQrVgwAf39/bty4QdOmTencuTNeXl7pG6Tme9BtHnh7wqZBoMtkQLkJo5Pdu+T6iEgpEbEQEScRWfbo+m4RqfwoBmladtqQLwg4B4uaw5190OFH6LPekKcjHfj7+9OxY0dcXV2ZOXMm9erVY9OmTYSGhrJ06VJatGiBKgMrVCaMg4gw9fRULoZdZGrTqVQvVt2o40dv3ERiaBhrggLZscO0QGvi1WHw4MHMmjUrS7vlACoWrkifqn3YfHcztyOfzXNUqHNnUBRidv2dpXleRKdOnfDx8WH69OmcPHmSmjVrMmLECCLSEzdVtz+8NQtu/w1bhoI+a5+FCSPxopopr9KRZ+s/6XQix+eKfF9U5Bc3kYDz6eoWEBAgp06dEhGRhIQEcXNzkylTpkhAQEB2WmsiA6y4vkLcPNxk/sX5Rh9bl5wsd5o1F7++/SQ5OVliYmKMPkd+A1MtORPPISYlRpqtayYD9gx4bq1Gv/4DxLt9hyzXcXwZ4eHh8vnnn4tKpZIiRYrI3LlzRa1Wv7zj8bkikwuJbPnE8HthIttJy5eYlh5yi4QIQ2DfgYmGGnCfHAOnei9sLk8sT/fu3ZvBgwcjItjY2HD16lUmT56Mk5Nxy6OYyBzHA48z+8Js2jq35fPanxt9/OhNm4kJCaHoZ59hZWVFoUKFjD6HCRO5ycOHD/nrr7+yPE4hy0KMqDuCC6EX2Oe/75nX7bt2Qe3vT/K1a1meKy2KFy/OggULuHLlCvXq1WPkyJHUqlWLS5cupd2xyRfQ6lu4sg7+HmWIczWRa5gEU27gfxIWNQXfw4Zl1/dWQYHCz20aFhbG9OnTqV69eupS7ty5c9m1a1fqbitTzqS8g2+ML18f+ZpKhSsxrek0VIpxv2J6tZqIJUuYpdfRbtRXWX5sYcJEXmT16tW88847+Pr6Znmsnq49qVa0GrPPzyZJ+/TOs4Lt26NYWhKzc1eW50kPbm5u7N+/nx07dmBlZZVadDjN73Hzr6HpV3DhT9g73iSachGTYMpJ9Ho4+jN4dDZUrR7iCQ0/hv8InoSEBNavX0+PHj1wcnJi/PjxODo68jhpXr169ahQoUJuvAMTaRCTEsOIgyOwNLNkXut52FgYP0t6zF9/oQ0NpUO/fvTs2RMzs6wlMTVhIi/ywQcfcOHCBVxcXLI8lpnKjLENxxKSEMKf1/98+rVChbBr2ZLY3buRRwl9sxtFUejatSsXL16kTJkyiAgdO3Zk4sSJL+pgSC/T6DM48zsc/N4kmnIJ41VtNZE2cSGG4L17R8CtF3T5Faz/fZSSlJTEnj172LBhAzt37iQpKYnSpUszfPhwhg4dStWqVXPReBMvQ6PXMPrIaIITglneYTml7UobfQ5Rq3n4xxIK1KnDwEmTTCuLJl5ZHBwcUldfjEE9x3p0Kt+J5deX08O1x1Pfz0JduxC3fz8Jp05h1yxryYEzwuPvr1qtpmrVqpQta0hPmJKSgre3N9WrV3+yMXT8CbTJcPwXsLCFFl/nmK0mDJhWmLKAiKCNiHj59te7B+D3JhBwFrrOg17LnhJLiYmJlClThl69enH48GEGDhzIkSNHCAgIYM6cOSaxlMfR6XVMOTmFM8FnmNR4ErUdamfLPNFbt+F//z57XVxMj+JMvPL4+/szYcIEjFWOZlT9USgoTDsz7SmfbdeiBapChYjZYbycTBnBysqK+fPnM3ToUABWrVqFm5sbPXr04Ny5c/82VBToPAdq9obDP8DpRblib15C1Gr0iYk5Np9JMGUQ0etJvHiJ0Okz8GnbjrtNmuLbsROhP/9M4qVLiF7/b2OtGvZ9C2veATtHGPoP1BsAisL3339Pr169ALCxseG7775j//79BAUFsXDhQpo3b25KB5AP0Og1jD82nh0+Oxheezg9XHtkyzyiVhOxeDG7C1gzcvYsQkJCsmUeEybyChEREcycOfNp0ZAFStqWZGTdkRx9cJR1t9alXldZWlKoQwfiDh7M0R/fF9GzZ08mT57M0aNHadiwIe3bt+fIkSMGkadSQfcFULUL7B0Ll1bntrm5gjYykvAFC7jbqjV3GrsTPGWKUfNpvQjlpasjrwD169eX8+fPZ7q/aLUknr9A3P79xHl6og0LQ7GwwNbdnQJ16pB47hwJZ86AVot5iRLYtWlNwYbVsfX/DSX0MjQYQkS9r1i6Yg2jRo3CwsKCWbNmcf36dZYvX24SRvkUtU7NN0e/4eD9g4yqN4pBboOyba6oTZsImTgJp8WL8C9WLLW8jQkDiqJcEJH62T1PVn2JifQjIkRFRVG0aPpy0qV3zOGHhnM66DRrO6+lStEqACSeO4d/v/6U/vln7Lt2Mdp8WSEuLo7ff/+d2bNnExYWRsuWLVmyZAmurq6GDODreoPvP/DOcqj+dm6bmyOk+PgQ6bGCmB07kJQUbFs0x7xECWJ37EQ0Ggq2bUvRwYOwqVMn03Ok5UtMgukFiFpNwpmzBpF08CC6yEgUa2vsmjWlYPsO2LVsgcrOjlh1LPZW9uhiY4k/coS4A57EHzmMpGhQWQiJtarikWLBsj17SEhIwNPTkzZt2hj1/YlWiyYwkBRfX8yLF6dAjRpGHd/Es6ToUvjq8FccCzzGuIbj+LDah9k2V9yhQwSOGo1F5UpU2LDBFLv0HEyCyUR6iUyO5J0d72Bnacf6zuuxsbBB9Hp8OhgK6Lps2ohZ4efvWs4NkpKSWLp0KRMnTkSr1TJ79myGDh2KokmE1b3gwXnovRYqt89tU58i6coV9ImJSNWKWNsXxVyVuZBpESHx9GkiPDxIOHIUxcoK++7dKTqgP1YVKwKgffiQyNWriVq3Hn1MDAXq1qXYR4Oxa9UKJYMLEibBlE4np09JIeHECeL27Sfu8GH0sbGobGywa9mSgu3bY920MXdTArgYetFwhF0kMjkS54LONCnThKYO9ah/6S+sL27gdnRVZp1MYc3lq2hEeMu+MCM7tKdu9+5YODhgVrjwv4e9PYqFxcvtS0gg5Z4f6nu+pPj4oPa9h/qeL2o/f0TzKH2+olBi5BcU++QT0w9rNpGkTeKLQ19wJvgMExtP5N3K72bbXJFr1xL6wzQiXFzoe+0qyz08aN26dbbNl18xCaZXk9DQUIYNG8aQIUPo2LGj0cY9HXyaofuH0rNST6a4TwEg8dIl/PsPwPbNNym76HeUPLYDNSAggEGDBnHw4EF2795Np06dIDkGVnSF8NvQ9y8o3zS3zQQg7uwZAgYNRtHp0QNBjmZoqrrg1LgNlZp2xrpCxecKGRFBHxuLNiwMTWgY6vv+RG/cRMqtW5gVK0aRDz+gSO/emL9g1VGfkED0X38R6bECTVAQli4uFB00EPvu3VGls8i8STCl08klXbmC3/u9UdnbU7BVK6zbtsK3kh0XY65zMfQil8Mvk6BJAKCMXRnqOtTFxd6Fy+GXORd0hiR9CvrQFHT7EvA+GoqCQv9+/Rj5Vmcc7tw2PM4LCn7u3Cpb26cE1OO/A6j97pHiew/tk3ErZmZYli2LZYUKWFVwwdKlApYu5Ylau47YXbso9FYnSk2bhqpAgSx/fib+JUGTwLCDw7gUdon/uf+P7q7ds2Ue0esJnzOHiKXLsGvVitiPh/DVuHEsXboUZ2fnbJkzP2MSTK8mGo2G2rVrM27cOPr162fUsedenMvSa0uZ1WIWHcp3ACBqw0ZCJk+m2NChOIz6yqjzGQO9Xs+uXbvo2rUriqJw//59nIvZgsdbEPMA+u9IMwFydhMQG8CekyuoPWEdsdZ6tnayp22iC7a3H1DU9yG2yYZ2GhtLLGpUp0jl6ugio9CGhqIJC0MbFoYkJz81plUlV4oOHEihLl3SLXpEqyV27z4ili8jxesmpWdMx757+ny1STCl08klpMRzbd9azpaM53zEZa4/vI5Gb1i5cS3sSj3HetR1qEtdx7qUtC1p6CQCZxaRcmASn58Q/jwQiWKmULh5YYp3Ko6TsxNNyzSlSekmNCrVCJuIBLRRUeiio9HHxKCNjkb33yMm5tHfY0Cnw9LF5V9RVMEFqwoVsHR2RrG0fOY9iAgRS5cSPucXrKtVw2nBb1iUKmXUz/N1JU4dx2een3H94XV+avYTnVw6Zcs8erWa4HHjid29myIf9MFhwgRU5qYMIGlhEkwmMopGr2HgnoHci7nH5m6bU1MNBE+cRPSmTZT59VcKdeyQy1a+mHv37lGjRg2+//57Rn/8AfzZEZKiYdBucDRu7cq0SNIm4envyZa7W7h+/xw/rNLjEG9G9ILxNG30LhZmhqcnccmxnDi1kTvHd6G6cZdKgXpKRivoihbEtpQzdqXLYu7giLmDA+aODlg4OmLu6IiFk1Omn5aICIlnzmBTt+5zfy+fh0kwpdPJ3Xh4g95/98ZcMeeNYm9Q17EudR3qUsehDoWt//NMWwQCL3Jp5Xhc405TsEYnNus7cuaKF6NGjUIppHAy6CTHA49zOug0cZo4zBQzKhepjI2FDZYqSyzNDIe5yvypcwuVBRYqCyzNLClRoARty7XF3so+Q+857vBhgsZ8jWJtjdP8edjUrfvU64maRA7eP4hOdLRxbkNBy4IZGv91IyYlhk8OfMLtqNvMaj6LNuWMG4f2GF1MDA+GDSfx/HkcxoxmeVQU169fZ9myZZibRNMLMQmmV5/9+/fTunVro34PHsQ94N2d7+Ja2JU/O/6JucocvVrN/X79Sb57F5cN67GqVMlo8xkTjUbDjBkzGDBgAGXLlkUb7o35yi6g15Hyrgd7tQ8pbVeaBiUbZGp8EeFk0EmuPbxGsjaZZF0yydpkkrRJT53fibpDvCYeZ1snxm8zo9ile5T94w/smjR54dhRyVEc8D/Annt7uBB6gRolarDmrTWZ/SiMikkwpdPJafVazoeep2bxms/P0vxIJCVf3oT13b9ZedSbAduS+enT7oxbuPWZjN1Pjnvt4TWOBx7nRsQNUrQpqPVqNDoNGr0GtU6NWq9GrXviml6NXgwpCixVlrR2bs3brm/TqFQjzFTpe7ae4uNDwOefowkKptTkSdj36sXVh1fZencre/32pj5etDKzomXZlnSt0BX3Mu5YqF4eT/U6EZkcycf7P8Yvxo9fWv1Cc6fm2TKPJjCQ+0M/QXP/PqV++gn7Lp2ZOnUq169fZ+3ataas3mlgEkyvNidOnKBp06YsWbKEIUOGGHXs3b67GXtsLJ/U/IThdYYDoAkN4947vVDZ2OCyaRNmebxeo16vp1OnTphLCg3f8OWImw3hj+Jim5Ruwlf1vkrdEZgezgSfYf6l+VwJvwKAucqcAmYFsDa3Tj0en5e2K023it1wXnecyMV/YDZiBJWHpb+GZkhCCFHJUVQrVi1jbzqbyNeCSVGUCsC3gL2IvPPoWjVgJFAcOCgiv6c1Rpac3CORdHPvEjZt3sqmi+FUd7Rg/bhufLgmiJtB8Rz65wiFCxcmOTkZa2vrzM3zHLR6LXej7rLNext/3/ubmJQYHG0c6VaxGz1ce+Bc6OWxLLqYGO6NHIHm9DlOuhdmXrM4rCxtaF+uPW9XehsLlQU7fXay128v0SnRFLUuSsfyHelasSvVi1XPUuC4Tq9Lt7jLq4QnhvPx/o8JjA9kbuu5uJd2z5Z5km7cIODTT5EUNU6/zceidm0sHy0h6/V6U+qJl2ASTK82IsLmzZvp0aMHFunYIJNRJp6YyHbv7SzrsCx1RSbx4kVDEHgTd8ouXJijQeAigiDprkWZlJzEkHFD2LR8E5o4DcUr2TOmRUEcquhZWrwocQp0rdCF4XW+oJTdi0M0LoddZv6l+ZwNOYujjSOf1vqUrhW7YmWWduxQ6F9biPz2W2LbtqXdyhXMmTPH6MI2p8g1waQoynKgCxAmIm5PXO8IzAXMgKUiMj0dY21+LJieuKYCVopI37T6ZtjJiSAPLnB99x9s3rKNzZci8Ao3rPZYW1owZeJ4xn73PQ8fPqRQoUJYWlri6+tLo0aN8PDwoHPnzumfK52odWoOBxxmm/c2TgadRC966jnW423Xt2lXrt0zK2JavZYTgSfY6r2VY/7/0Pugmi7nhPhaFajy2x8UKlHmqfYanYbjgcfZ6buTIwFHUOvVlC9Unm7l3qJDvAvWl26TePoMmKkoUL061o8Oy/LlidbEci/m3r9HrOHPwPhAqhSpwiC3QbQr1y7T20pzi5CEEIbsH0JYYhgL2izI9NL2y4g/epQHX36FWWF7nP/4A8/bt/niiy84cOCAqWZgOjEJptcHtVqNhYWFUXcBJ2oSeX/X+yRqEtncbTNFrIsAELVuHSHf/49in32Kw8iRRpsvLc6FnON/p/7Hw6SHVC9enZrFa1KzRE1qFK9BsQLFnmorInje92TBpQX4xPjgautKuVvl2L5sO35+flR1Kc0wd0sS6+jYUMweVGZ8UKU3Q2p/9lSYx42IG/x26TdOBByjVrQ9/dX1qOyvQSKiKNStK/bde2BmZ/tcew+tWEGfIUNY3q4dzVevZsq0aXz55ZeULVs2X97s5aZgag7EYxA1bo+umQF3gHbAA+Ac0AeDePrpP0MMFpGwR/2eEkyKonQDPgNWicjatOxIt5OLCeTmpqms2bCFzZciuB2hRwEa1XSl78ChNGzakrFjxzJv3rxnEgf6+/vzzTffMGfOHMqUKUNcXBx2dnbZsrU/NCGUnb472Xp3K/fj7mNjbkNHl470cO1BEasibPPexg6fHYQnhVPUuijdKnbjbde3KXrwMiFTpmBeqhRlF/z23GfzIkLkrStc+XsVCSdP4HQ3BmsN6BVIruSEhZkFZj4BqNSGQpXJFuDnCL4lFXxLKjwoY4WFS3nKF6lAadvSHA44jF+sH2XsytDvjX687fp2thSlNTYBsQF8fOBjYlJi+L3t79lW7iRq0yZCpnyPVZXKlF20CAsHBy5dusTEiRNZu3YthfL4o4C8gkkwvR7cv3+fdu3aMXXqVN577z2jjn0z4iYf7v6QJqWbMLf1XFSKChEh+LvviPlrC2Xmz6NQu3ZGnfNJEjWJ/HLhF9bfXk/ZgmVpXKox1x5e407UHXRiKIVUxq5MqoAqVqAYHjc88IrwwsXehWG1h9GuXDtUigqtVsumTZuYMWMGV65cobRDMT5qXoTkN9XsLVYQO5UlQ2p8TKPS7uzY9Svx589S84EZbwQqmCeqAbBwdkZlY0PKrVuo7Oywf/ttinzQB6snCiJrQkM536073/r48MdBT1xr1XrqPfXr1w8HBwdmz56dbZ+bscnVR3KKopQHdj0hmBoDU0Skw6Pz8QAi8l+x9N9xnllhenT9bxFJc0kn3U4uwocZvWsy4WAirRpUp/v7/ZkybQadO3dm5cqVL+//BO+99x4RERF4enpmWz4kEeFS2CW2eW9jr99ekrRJAJgpZjQr04welXrQ3Kn5UzFJiZcu8WDEF0hiIqVnzaJg61ZoHz4k4dQpEk6cJOHkSbRhYQBYlHOG+rW4XF7YYHuDW5oAAFR6oXqcPXWji1A5zIxSAYnY+oehJBu+aEqBAlhXrYp19epYlHXitlk4u2JOcEZzF30xe3q69eaDqh88c7dktM9FrUb78CHa8HC04eGG7arh4UhiIjaN3sS2iXua21NPBZ1izJExKIrC4raLqV7c+DtORITwefOI+H0Rts2a4fTrL0SnpBg1q/HrhEkwvR7odDp69+7NZ599li35yNbcXMP0s9MZ8MYAxjQYAxjy8/n364/a25vymzamJks0JqeDTzPlxGSKXQ+kT1QV6rm1w7Z8RSydy6ErVZzbSX5cDb/K1YdXuRp+ldDEUMAgoD6r9RmdK3R+7gq+iHDgwAFmzJjB+fPnub3yF6LPrOF0UCDWISqqBArWj1L4mbuUx65hI2zq18emQX0sShp2gidduULk6jXE7t0LGg22zZph+967bPX2prXnQTT37lFu3Tqsq1R+am6dTsfo0aMpVqwYEydONPpnll3kNcH0DtBRRIY8Ou8HNBKR4S/oXwyYhmFFaqmI/KQoSkugJ2AFXBWRBc/pNxQYCuDs7FzP398/XfZ67t6O59FTTJ9ueEq4efNmatWqRaUM7pRYsWIFsbGxjBgxAoDw8HBKlCiRoTHSS3JyMgnqBI6HHScgKAD/ff58POBjKleujEajQafTPRVbpQkJ4cGw4SR7eWFZoQJqHx8AzOztsWncGFv3xti6N8HS6d/HdiLCzcibqHVqXOxdntm1Jzodal9fkr28SLpxg+QbXiTfvIk8pzZTvDXE2CmYOzhQulx1CpdxwbxECcxLlAAzcxA9otOBXkCvQx7/+eia6B/9qdWgi4hE+0gQPT500dHPfkgqFYqFBZKSgsrWFrtWrSjYoT12TZum5qoSEVZ5rWL2hdlUsK/AvFbzKFuorDH+iQCD4026eJGEk6eIP36clJs3KfzuO5ScNIm79+7h7u7O7NmzGTBggNHmfF3ITsGUWV9iIv8hIkw/O521t9Yypv4YBlQ3fBc1ISHc6/UOqBSKvPc+9j26Y1k2674hXh3PL2dnEbhjE++cM6dMsBosLOBxIuJHmJcogYWzM5bOzlg6lyXBCiI1MZS1L4e5hSWYmaE8OlCZGao/PAjA58oVHnj7UCMxkZDQUCK1WkqYm1PU3BxdhbJEVHGkcuu3KdG4OebFi6dpqzY8nKiNG4lev4Et3t6MCwnGo6wzPT3+pGAa4lVEUBSFs2fPsmLFCmbMmIGdnV2WP7vsIl8LJmOQkbvCn376iVmzZnH79m2Kv+Q/UHo5ceIEbdq0YdeuXbRt2zbL4+l0OpKTk7G1tcXHxwc3NzcWL15M//79OXHiBM2aNePAgQO0adOGI0eO0LJlSw4fPkzLli25ceMGy5cv54tPP8Vq3TrUfn6GVRd3d6zfqGbUwEYRQRcdjTYs/F9RExZGZKAP/r6XSAwJonC8nmIJCmbaTP4/tLDAvHjxVMFlXuKJvzs4/Pv3YsVApyPhzBli9+0j3vMguuholAIFsGvRAuu2rZhndZytQXto69yWaU2nZfnRoeh0JN+8RcKpkySeOkXihYtISgpYWGBTqxaFunSm8PvvoygKycnJfPnll4wdOxaXJ5a8TaQP0wrT64VOp2P+/Pk0bNgQd3fjbsTQ6XV8c/Qb9vvvZ0azGbxV4S0Akq7fIHzOHBJOnQIRbBo0wL5HDwp26PDC+J60OOF9iEO/T6DF8RhKxICFS3mKDR6MfbduSEoK6vsBaO77o74fgPr+fTT376O+fz/1CcDzOBgXx8WkJL52cABgbGQEFxMTOfvll1iWK0fH2bPB0pKzp0+jsrEhISEBW9v0267T6VDpdMQeOIDnwoW06t2Hov3SDCFOZc6cOcydO5erV69ib5+xNDk5SZq+RESy9QDKA9efOG8M7HvifDwwPjttqFevnqSXuLg4iYuLS3f79PDgwQP54osvJD4+XkREFixYID179hS9Xi8iIteuXZOzZ8++sL9er0/tm5KSIg4ODjJhwgQREdHpdPLNN9/IhQsXUtunpKSIWq0WERFvb2+ZOnWqBAUFiYjI1q1bpUCBAnL79m0REdm2bZt06NBBgoODjfqe00N4YrjMvTBX3Nc0ljcXVpdRy96RNTt/lGNH18r9qycl2cdXUvz8JCUgQNQPHog6OFjUIaGiCQ8XTUSEaKOjRa/TZWpuvUYj8SdPStDkyXLTvbF4Vakql6tXlaN9O0vU9u2ijY3N+Jh6vaT4+0vkuvUS8MVIud2wkXhVqSpeVaqKT7fuEvLTdIk7ckR0j/4tRUQCAwMlMTExU+/BxL8A5yWbfZlk0JeYyD7i4uKkbNmyMnLkyGwZP1mbLM8KBGcAACAASURBVAP3DJTaK2vLycCTT72mDgqS8N8XiXf7DuJVparcrF1HAr8ZK/GnTr/UH4Unhsv+S5tk7aiucraWwTdcf6e7xB48mG5fpktKEk1kpGjCwiQlOFj+Wr5cEu/dk2RfXxk/fLiULV1a4r28RJeQIFeuXHnqt+XSpUty5MgRERHRaDTi4OAgU6ZMee48Go1Grl27JhqNRkREli5dKq6urln6rTD2b2t2kJYvyY0VJnMMQd9tgEAMQd8fiMiN7LIhr90Vzpkzh/3797N3717AEBh39OhRHi/1jxs3jsDAQFatWgVAs2bNcHR0ZPPmzQD88MMPNGjQgA4dMpeF9vG/uaIorF27lvnz53Ps2DHMzc05fvw4jo6OGX4EmRUSNYls9d7K+lvr8Yv1S71uZ2GHa2FXXIu4UqlwJSoVqUTlIpUznMQzLS6HXeargyNxuhfPyNiG2J+6iTY0FMXCggK1a6NYWYFeDzwS+HoxpJoQQUQPguF1EUP9o6AgAMxLlTI82mzsju2bjZ673K1Wq6lVqxaVK1dm+/btRntPryOmFabXj+DgYEqWLJltMaKx6lgG7h1IYFwgHh09nskTJCIkXb5MzNZtxO7ejT4+HvNSpQyxPyoViqKQIhritAnEauKI0cSSokmmaoBgroPw+uWp89X32NdrmGkb//77b7p06cLmzZvp1atXhnalJSQkMHv2bJo0aUKbNm0ICwujR48ebNy4EScnJ1atWkX//v25fv061atX5+jRo2zevJmxY8dSpkyZl0+QT8nNXXLrgJYY8iWFApNFZJmiKG8Bv2LYGbdcRKZlmxHkfSfn7e1NaGgoTR5lRv3+++8JDg5m0aJFACxcuBA7Ozv69++f7bbUqlWLAgUKcPr0aeDf5885RZw6Du9ob+5G3TUc0YY/Y9WxqW0cCjgYxFPRyjQu1Zj6jvVT0+9nhM13NjPtzDRK25Zmbqu5uBZxRfR6kq5cIW7/AZIuXkQQFBRQqQyJSVWK4Vz595qiUgAFVaFC2DRsgG3jxliWL5+uz239+vU4OTnRtGneKJqZXzEJpteXhw8fkpSURFkjxBT9l9CEUPrt6Ydap2bVW6soW/D5c+iTk4k7eJDYfft4+DCAqKQI4pJj0ehSUOnBXDGjoLkddmY22FSvTvlPvsC2QuZuSn18fPD396d169aICNu2baNbt25ZTmx7+fJlPvroI6ZMmULXrl0JDAzk8OHDvPXWW6/VZpR8nbjSGJicXPoJCgoiLCyM2rVrk5ycTM2aNfnuu+9yRKy9CBEhLDEsVTw9FlI+0T5o9BrsLOxoWqYpLcq2oFmZZi9dgdLoNcw8O5P1t9fjXtqdmc1nGnXVKi20Wi1z5syhbNmy9OnTJ0fmfB0wCabXE61WS9WqVXF2dubQoUPZModvtC/99/bH3tKelZ1WPnd3b7w6nq3eW1lzcw2B8YEUtS5KPcd61HesTz3HelQqUindSShfRosWLQgODubWrVv5LsdRfiBXY5jywmGKO8gcwcHB8v7778uhQ4dSz4cNG5YaD3Xs2DHp3bt36jPtvXv3Stu2bSU0NFRERDZv3iwffPCBhISEZIt9iZpEOXz/sEw+MVlarG8hbh5uUmtFLRm0d5CsuL5C7sfcf6ZPRFKEDNwzUNw83GT2udmi1Wmzxbb/otUa5tHr9dKgQQMZMmRIjsz7uoAphum15cSJE3LixAkRMcR0pqSkGH2OS6GXpN6qetJ7Z29JUCekXg+MC5Sfz/4sb655U9w83KT/7v5ywO9AhvzKlStXpGnTpnLgwAH5f3t3Ht9Ulf4P/HPSdC90J0AX2kLbdK+2FIWCICOCyiKrIIvC4AACOh3FwQVRUUE2QZQR+QmWWhyQTUAREMSOgEDB0sWuQCmFlha670nO748s35Au6ZKkTfO8X6++yF3Pcw8nJ0/uPbmXc86vXbvGJ0yYwP/44w/OOefXr1/nixYtUo3/SUtL4/n5+To8OqKupb7EuG69TAyqd+/e+O6771TTP/zwA+Lj47Fo0SL06dMH9+/fR2JiImpq5Pd/amhoQFVVFaRS+U3WLC0t8fvvv6t+EbFt2zYcP34c8fHxqsd+dIS10BrDPYZjuMdwyLgMKcUp+DXvV/x661esvbQWay+tRX/7/qp1LMws8OrpV3G/9j4+HvoxnvF5psMxtMbOnTuxatUqXL16FTY2Njh16lSX/lktIcZE/VdyGzZswO7du/HLL7/AwcGhha3aJrxXONYOW4tXf30V/zrzL7wU+hK+/etbnMw9CQAY5TUKswNnI9glWMue5GMXv/76a/Tv3x9PPPEEvLy8wDlX3fqluroaOTk5qFbckuXu3bvYvXs3Bg0ahNmzZyMgoGs8c80U0SU5YjCbNm3CkSNHcOLECQDAv/71LxQWFiIuLg5A4/FS2dnZMDc3R79+/QAAsbGxcHd3V92w7qWXXkJ0dLTqcuH69esRHh6OkSNH4lbFLWyI3YCbljeRY5EDCZegvqge7p7u2DxyM4KcdX8zSnU3b95Ez5494eDggP/973/44osvsHHjRohEIr2Wa6rokhwBgEOHDuHw4cP46quvdDr28ubNm8jIyEBZvzK8d+49VKZVQpItwT/f/CdmiGfgz4Q/ceHCBbzzzjtgjCE3NxfV1dWq5Ka2tlb+qBKxGDKZDN7e3hg9ejS+/PJLncVIdIMuydFp9C7pvffe44sXL1ZNP/HEE3z27NmqaR8fH/7888+rpj08PPgLL7ygmo6KiuLvvvuuatra2pq/9tprnHP5pS8zMzP+5ptv8rK6Mn4k+wgHwF99/VXV8qysLNWtHXTp9u3b3MLC4oHYiH6BLskRDYWFhfy5557jt27davO2VVVV/Ntvv1VdSv/www85AF5bW8sPZB3gkxZP4kKhULV82bJl3MHBQbX9okWLuKOjo2r6H//4B/fz81P1NwUFBXrpe0jHtdSXdHoyY4g/6uSMw9tvv823b9+umj569OgD9xApKCjgVVVVTW3KOee8vr6e19bWcs7lCdGff/7J8/LyOOfyMURffvml6n5V6enpHADfsWMH51zeQd64caNN8aqPlTh58iT/5ptvVNPbtm3jN282HkNF9IMSJqLp2LFj3NnZmaekpHDOOc/Ly+NlZWUtbqNMYr7//nsOgB8/fpxzzvmNGzd4QkKC6p5EDQ0NjRIe5TLOOb969So/fPiwajouLo6fOHGCkiQjQAkTdXJEQ3FxMd+6dasqqTl06BAHoBo8WlRUxNPS0lTr//TTT6qzV5xz/uqrr3KRSKSanj9/Pu/Vqxevqakx0BEQdZQwkaZUqt0kdty4cTwoKEg1HRsby/fv388557y0tJQ/8sgj/PPPP+ecy798nTlzhhIcE9RSX0K/SSQmydnZGQsWLFDdu+Whhx7Cpk2bEBERAQDYsWMHAgMDUVtbCwC4ePEiduzYgfp6+QOGn3jiCSxdulT+rQPAmjVrkJub+8Az+wghnUv9sR+vvPIKPvjgA9X0hg0bsHPnTgBAz5494enpCUdHRwCAubk5hg0bZtB70JGujwZ9E9KEzMxMXLhwAZMmTYK1tXWb7qBLDI8GfZO2kkqlKC8vVyVJhAAt9yV0WwFCmuDn5wc/Pz/VNCVLhHQvZmZmlCyRNqFPAUIIIYQQLShhIoQQQgjRghImQgghhBAtKGEihBBCCNGCEiZCCCGEEC0oYSKEEEII0cIk7sPEGCsCkAvAHkCZYrb6a81pFwDFOipes5yOrNvS8qaWtXSMmtP6Ov7mYmvvus0tb83xa84zxjbQ0jqm3Ab6cc5d2xNYWyj6klJF+e2pI321b22vlf+29/9VV3G3tv0ZY9xNzdNHG2luHWojuom7+b6kuVuAd8c/ANuaet3EMp09ZkGznI6s29Lyppa1dIwt1Ycuj99QddCa4+8ObaCjddCd24Ch/pTlt6eO9NW+tb3uSMy6jLsN7c/o4m5mns7bSGvaA7UR3da38s/ULskdbuZ1U9P6KLOj67a0vKll2o6xpfrQJUPUQWuOX3OeMbaBltYx9TZgKB0pX1/tW9vrjtaZruJubfszxrh19V5qbx9AbaR9Wr29SVySayvG2CVugMcsdFWmfvwA1YGpH39rGGMdGWPMAMVtSMYYM2CYuE3tDFNrbevsADqZqR8/QHVg6sffGsZYR8YYM0BxG5IxxgwYIG46w0QIIYQQogWdYSKEEEII0YISJkIIIYQQLShhaiPGmC1j7BJj7JnOjqUzMMYCGGP/YYx9zxhb2NnxGBpjbAJj7CvG2H8ZY6M6O57OwBjzYYz9P8bY950dS1fEGBvOGEtQvE+Gd3Y8bWGM/Zux9knG2JcY03tf0Za/UdTx87rYp8kkTIyxrxljdxljKRrzRzPGMhhj2Yyxf7diV28A2KOfKPVLF3XAOf+Lc74AwFQAQ/QZr67p6PgPcs7nA1gAYJo+49UHHdXBNc75PP1G2jl01E9wAJUArADc0les6oy1fzPWPskY+5Lu8N5v4zFMBPC9oo7H6aR8Uxn0zRgbBnknFss5D1bMMwOQCeAJyDu2iwCmAzAD8LHGLuYCCAPgDHlHWMw5P2KY6HVDF3XAOb/LGBsHYCGAXZzzeEPF31G6On7FdusBfMs5v2yg8HVCx3XwPed8sqFiNwQd9RPFnHMZY0wEYAPnXCffbg0Qt8H7N2Ptk4yxL+kO7/02HsN4AD9xzv9kjMVzzmd0tHxhR3dgLDjnvzHGvDRmRwHI5pxfAwDG2HcAxnPOPwbQ6JS04vS6LYBAADWMsR855zJ9xq1LuqgDxX5+APADY+woAKNJmHTUBhiA1ZC/EY0qWQJ01wa6Kx3XTwkAS33EqclY+zdj7ZOMsS/pDu/9thwD5MmTO4A/oaOraSaTMDXDDUCe2vQtAIOaW5lz/hYAMMZegOJbpF6jM4w21YGiU50I+QfBj3qNzDDadPwAlgD4GwB7xtgAzvl/9BmcgbS1DTgD+BDAQ4yx5YrOtTtra/1MBPAkAAcAW/QbWouMtX8z1j7JGPuS7vDeb+4YNgPYwhh7Gjp6OoCpJ0ztwjnf2dkxdBbO+a8Afu3kMDoN53wz5G9Ek8U5vwf5uAvSBM75fgD7OzuO9jK2/s1Y+yRj7EuM6b3POa8C8KIu92kyg76bkQ/AQ23aXTHPlJh6HZj68QNUB9oYa/1Q3IZljHEbY8yaDHYMpp4wXQTgyxjzZoxZAHgOwA+dHJOhmXodmPrxA1QH2hhr/VDchmWMcRtjzJoMdwycc5P4A7AbwB0ADZBf45ynmP8U5CPscwC81dlxUh3Q8VMdUP1Q3BQ3xdz1jsFkbitACCGEENJepn5JjhBCCCFEK0qYCCGEEEK0oISJEEIIIUQLSpgIIYQQQrSghIkQQgghRAtKmAghhBBCtKCEiXQqxpgDY2yR4nVfxtj3eiwrnDH2lL72TwjpHhhjXoyxGWrTkYwxo3qMCdE9SphIZ3MAsAgAOOe3OeeT9VhWOOQ3OCOEmAgm19bPOi8AqoSJc36Jc75Up4ERo0MJE+lsqwH0Z4z9yRjbyxhLAeRPTGeMHWSMnWCM3WCMLWaMxTDGrjDGzjPGnBTr9WeMHWOMJTLGEhhjYsX8KYyxFMZYEmPsN8Ut898HME1R1jTGmC1j7GvG2AXFfserlX2IMfYrYyyLMfZuJ9UNIaQdFGeIMhhjsQBSAEjVlk1mjO1UvN7JGNvMGDvLGLvGGFN+YVsNYKiir/gnY2w4Y+yIYpuVjLFvFP1NLmNsImPsE8ZYsqIvMlesF8EYO6Pom35mjPUxaCUQnaOEiXS2fwPI4ZyHA3hdY1kwgIkABgL4EEA15/whAOcAzFassw3AEs55BIDXAHyhmL8CwJOc8zAA4zjn9Yp5/+Wch3PO/wvgLQCnOOdRAEYAWMsYs1VsHwVgEoBQAFMYY5G6PnBCiF75AviCcx4EoKqF9foAiAbwDOSJEiDvlxIUfcXGJrbpD+BxAOMAxAE4zTkPAVAD4GlF0vQZgMmKvulryPswYsSEnR0AIS04zTmvAFDBGCsDcFgxPxlAKGPMDsBgAHsZY8ptLBX//g5gJ2NsD4D9zex/FIBxjLHXFNNWADwVr09wzu8BAGNsP+Qd6iXdHBYhxAByOefnW7HeQc65DEAaY0zUyn3/xDlvYIwlAzADcEwxPxnyy3n+kH/hO6Hom8wgfwYaMWKUMJGurE7ttUxtWgZ52xUAKFWcnXoA53wBY2wQgKcBJDLGIprYPwMwiXOe8cBM+XaaD1mkhy4SYlzUzyqpv3+tNNZT72cYWqcOADjnMsZYA/+/h7Iq+yYGIJVz/mgb4iVdHF2SI52tAkCP9mzIOS8HcJ0xNgVQDe4MU7zuzzn/g3O+AkARAI8myvoZwBKm+ArIGHtIbdkTjDEnxpg1gAmQn7EihBinQsZYgGLw97OtWL/d/ZJCBgBXxtijAMAYM2eMBXVgf6QLoISJdCrFZa/fFYO917ZjF88DmMcYSwKQCmC8Yv5axSDMFABnASQBOA0gUDnoG8AHAMwBXGWMpSqmlS4A2AfgKoB9nHO6HEeI8fo3gCOQ9wWtuTR2FYBU8aORf7a1MMWYyckA1ij6pj8hHz5AjBj7vzOJhBBA/is5AJGc88WdHQshhJCugc4wEUIIIYRoQWeYCCGEEEK0oDNMhBBCCCFaUMJECCGEEKIFJUyEEEIIIVpQwkQIIYQQogXd6VsPEhMTewmFwu2Q3xqfklJCCCGk65ABSJFIJH+PiIi429qNKGHSA6FQuL13794Brq6uJQKBgH6GSAghhHQRMpmMFRUVBRYUFGyH/AHKrUJnP/Qj2NXVtZySJUIIIaRrEQgE3NXVtQzyq0Ct305P8Zg6ASVLhBBCSNek+IxuUw5ECRMhhBBCiBaUMBFCCCGEaEEJkwmYOnVqv9WrV7saaxlr1651mTVrlqfmPFdX11CxWBwoFosDx48f762PsjVNmTLFy8nJKczX1zfIEOV1NabUloqLi81Gjx7t4+3tHeTj4xN08uRJW33EpKk7tzEbG5uHNOfFxMT07dWrl6r+xWJxYHFxsZly+dy5cz169eoVKpVKVdts3rzZ2dHRMUwsFgf2798/aP369S6a88ViceCzzz7rBQCTJk3ycnNzCxGLxYH+/v6Bhw4d6qHcV21tLZs7d66Hp6dncL9+/YJHjhzZPycnx1y5PC8vTzh27Fhvd3f3kKCgoIDw8HBxbGysg35qyLDmzZvn8f777/dSTkdHR/tOmzatn3J6/vz57itXrhRptsWYmJi+K1asECmnV6xYIfL29g4Si8WBwcHBAVu2bHE2zBEYFiVM3VhcXJyDu7t7yIkTJxw2bNjQJzg4OODSpUtWxlZGcnKyTUhISI3mvDfffPN2enp6Wnp6etqhQ4eu67LM5sydO7f4hx9+yDJEWV2JKball156yWPUqFHl169fT01LS0sLDw+v1WUszTHFNrZgwYJCZf2np6enubi4SAFAKpXi2LFjDn369Kn/8ccfe6hvM3bs2JL09PS03377LWPVqlVueXl5QvX56enpaQcOHLihXH/VqlW30tPT09atW5e3dOlSVVKwdOlSt8rKSsG1a9dScnNzU8aNG1c6YcKEATKZDDKZDGPHjh0wdOjQylu3biWnpqb+tWfPnmt5eXkWBqoavYqOjq48f/68HSCv65KSEmFGRoa1cvnFixfthg4dWtnSPj755BPXU6dO9UxMTPxL+f/RXZ9RS7cV6KZSU1MtY2JiPE+ePJmxbt06UWRkZJW9vb106tSp/TMzM1OFwo7/1xuiDABIS0uznjlz5j3NefPnzy9uzfajRo3qLxaLa86ePdsjPz/fYuvWrTcmTJhQ0Z5YxowZU5mRkdEtOsvWMsW2dO/ePbM//vijx/fff38DAKysrLiVlZUUzaA2ph9Hjx7t4evrWzN58uSS+Ph4p7FjxzaqUzc3N4mnp2dddnZ2q+ps5MiRlXfv3jUHgIqKCsGePXtcrl27dlXZxl555ZV7sbGxLocPH+4BAObm5nzZsmVFyu39/Pzq33rrrVbfu6crGzFiROXy5cs9ACAxMdHa39+/prCw0LyoqMjMzs5OlpOTY+Xq6ippaR8bN27s/csvv2Q4OTnJAMDJyUm2ZMmSey1tY6zoDFM3deTIkZ6jRo0qDQ0NrVPOmzNnTqlAIEBycnKL39ojIiL81U+PK/8OHjz4wDc8Q5QBAFlZWdYREREPfLvPzs62njdvnpdYLA4cPHiwX0tlZWRkWDs4OEgvXbqUsWbNmry4uLgHThe3JRZTZIptKSMjw8LJyUkyZcoUr4CAgMBp06b1Ky8vb7a/1NbG2hqnqfnPf/4jUtbHoEGDVO/n+Ph4p6lTp95//vnnS3755Rf7uro6prltWlqaRV5enmVgYGAdABw+fNhRua9NmzY1+n/Yt2+f/d/+9rdSxbaWffr0qVd+2CuFh4dXJycnWycnJ1uHhoZW6/6IuwYvL68GMzMznpWVZXHmzBnbRx55pCoyMrLq1KlTdgkJCTZ+fn41lpaWPC8vz1K9zcbGxroCwP379wVVVVVmgYGB9Z19LIZAZ5j07PXvkzwyCypsdLlPv949qtdODstr7/ZSqRQTJ070srCw4I899ljFwoUL76svT0xMzOhojFKpFFOnTu1XXl5uduzYsWuay1tbRnZ2trmtra3U2dlZqj7PxcWlITMzM03b9hUVFYKKigqzFStWFAJAfX09s7e3f+BMgS6O1xDe+f0dj+ySbJ22pQGOA6o/GPIBtSWNtiSRSNhff/1ls2nTppuPP/541Ysvvujxzjvv9N60adNtzf22po21JU5DiYqK8tecN3HixPv//ve/iyoqKgQjR4701Vw+c+bM4qVLl967c+eOcPz48f3Vl124cKHdx7dgwYLC999/v1B9Xm1tLTt16pT91q1b8xwdHWXh4eFV+/fv7zl9+vQyQJUY2VlYWMg+/fTTXJFIJAXkl+RiY2Nvapbx9ttvu7/33ntuhYWF5qdOnUpvT5yzZs3yvHDhgp25uTlPSUn5qz37aElT/yeaRo8eXaqsq6ioKP+O/p9ERERUnj592vbcuXN2r7/+euHNmzctfv/9d1t7e3vpoEGDKgHAw8OjLj09XfUeiYmJ6dv2ozN+lDB1U0899VT5+vXr+6Smpqo6obi4OAeJRMLOnTtnO3ny5JIZM2aUPf300z6aH3IRERH+VVVVZpr7XL16dZ76ZYaWyggPD6/ds2dP7ujRo32aiq+1ZSQmJtr4+/s/MOYkMTHRxs/Pr0Zz26ZcuXLFKjg4uFp5uv3q1avWwcHBD2zb2lhMlSm2JS8vr3qRSFT/+OOPVwHAtGnTSlavXt27qfJb08baEieR279/f8+Kigqz4ODgIACoqakRWFlZyZQJU3OJUXNWrVp168UXXyz58MMPe/3973/3Sk1N/SsgIKDuzp07FiUlJQJHR0fVWaakpCSbcePGlQLAoUOHHJXzd+3adfPOnTvCyMjIAN0daecaPHhw5dmzZ+3S09OtBw4cWOPj41P/6aefiuzs7KQvvPBCi8MenJycZDY2NrK0tDQLUzjLRAmTnnXkTFBHhISE1K1du/bmqFGj/GprawXHjx93sLe3l+zZsyfnwIED9hEREdWA6uZdD2jtN+GWytA25qS1ZSQlJVkHBgbWaM4LCAhoMmF69NFH/eLj4697e3s3AMCVK1esQ0JCVKfUU1JSbCZNmlTanlg6W0fOBHWEKbYlT09PSe/eveuTkpIsw8LC6o4fP97T39+/FmhfG2tLnIbS0tmHHj16yFpa3qdPH0lHzii1xu7du50+/fTT3H/84x/3AaC8vFzg5eUVUlFR0aGhJMuXL78bFxfnsm/fvp6TJk0qnzx5cvHChQs94uLicoVCIbZs2eJcW1srUI6Xeuedd9iaNWtc33jjjSIAqKys1NtQlrbWqfr67f0/GTZsWOWWLVt6e3p61gmFQohEIml5eblZVlaWdWxsbG5Ll6IB4NVXX72zYMGCfgcPHsxxcnKSlZWVCXbt2uW4ePHibjeOicYwdWNz5swpzcvLSx4xYkTZkiVLCjIyMtKioqJq3N3d63Nzcy0AgHPeaEyALsrQzREAKSkp1t9++62rm5tbiJubW0h4eLg4JSXFOigoqNEvlqRSKXJzcy3VBykmJydbh4eHqz7MMjMzrSMiItod39ixY72jo6PF169ftxSJRKEbN250ae++jImptSUA+Oyzz24+//zzPn5+foFXr161XrVq1R1qYx1TW1srEIlEocq/lStXioAHxzCJxeLAxMREq99++81+ypQpqsSzZ8+essjIyMrvvvvOviMxCAQCvPHGG7fXrVvXGwA+++yzfEtLS5m3t3dwv379gvfv3+948ODBbIFAAIFAgMOHD+ckJCT0cHNzCwkJCQmYOXOm18qVK291rCa6jqioqJrS0lJhZGSk6tdwYrG4xs7OTtqnT58WB3wDwLJly4qGDRtW/vDDDwf6+voGPfLII+Lu+qQL1l1//teZkpKSboSFhbXqF1ydoby8XDB37lxPS0tLWXR0dKXmZRRdKCgoMIuJiXFLSEjoOXPmzOKPP/64QNdlaLp48aLVl19+6bJ9+/Zu05l1dd21LTWH2hgh3UdSUpJLWFiYV2vXp4RJD7p6wkQIIYSYurYmTHRJjhBCCCFEC0qYCCGEEEK0oISJEEIIIUQLSpgIIYQQQrSghIkQQgghRAtKmAghhBjEvHnzPN5///1eyuno6GjfadOm9VNOz58/333lypUiX1/fIPXtYmJi+q5YsUJkyFgJ0UQJEyGEEIOIjo6uPH/+vB0gv9FsSUmJMCMjw1q5/OLFi3ZDhw6tbH4PRB/eeOON3gMGDAjy8/MLFIvFgadOnbIFgDt37giFQuHDn3zyiav6+m5ubiHKdf38/ALj4uIc1Jfv2rXLgTEWceXKlQcenJ2bm2s+mxrYqgAADY1JREFUYsSIAQBQV1fHJk6c6OXn5xfo4+MTtHz58iYfPVRbW8umT5/ez8vLK9jb2zto586dDk2tBwBnzpyxEQqFETt27HAEgNu3bwuHDh3a6JmI7UUJEyGEEIMYMWJE5eXLl+0AIDEx0drf37/G1tZWWlRUZFZTU8NycnKs1O+iTvTv5MmTtj///LNDcnJyWmZmZtrp06czfXx86gEgNjbWMSwsrGrv3r1OmtudOXMmMz09PW3v3r05y5Yt81Bf9t133zk9/PDDlbGxsQ9s99FHH4nmzZtXDAA7duxwrK+vF2RmZqYlJSX9FRsb65qRkWGhWc7y5cv7uLq6Nty4cSMlOzs79cknn2wyoZZIJHjjjTfchwwZUqac17dvX4lIJGo4fvy4bftq50GUMBFCCDEILy+vBjMzM56VlWVx5swZ20ceeaQqMjKy6tSpU3YJCQk2fn5+NZaWljwvL89S/VEpsbGxrtr3TtojPz/f3MnJSWJtbc0B+TPpvLy8GgBg7969TuvWrcsrLCw0z8nJMW9q+9LSUrOePXtKldNlZWWCixcv2u3YsePGgQMHHkiYjh496jhp0qQyAGCMobq6WtDQ0ICqqipmbm7OHRwcpJr73717t8uqVasKAMDMzAzNPa7lo48+6jV+/PgSFxeXB5ZPmDChNDY21rlttdI0SphMwNSpU/utXr1arx2OPstYu3aty6xZszw157m6uoYqO9Tx48d7K5dJJBIEBAQEKk/9GsKUKVO8nJycwjTHXnQ3ptSW3nvvvV4DBgwI8vX1DRo7dqx3dXV1h56V11qGaEtz5871iIqK8tfl39y5cz20lwxERERUnj592vbcuXN2Q4cOrRw8eHDV77//bpuQkGA3aNCgSgDw8PCoS09PT1P+zZ49u0hfddGVREVF+W/evNkZkF+yioqK8v/iiy+cAKCiokIQFRXl/9VXXzkCwL1798yioqL8v/nmGwdAfvksKirKPz4+3h4Abt682fJTqxUmTJhQfvv2bQsvL6/gmTNneh49etQOALKzs82LiorMR4wYUT1u3LgSzbNFjz32mJ+vr2/Q6NGj/d9999185fz4+HiH4cOHl4WGhtY5OjpKEhISbAAgPT3dwt7eXpWYvfDCCyU2NjayXr16hXl7e4cuXry4QCQSPZAwFRcXmwHyMWyBgYEBY8aM8cnLy2t0XNevXzc/fPiw47Jlyxq1kyFDhlRduHDBrjV1oQ0lTN1YXFycg7u7e8iJEyccNmzY0Cc4ODjg0qVLVtq37FplJCcn24SEhNRoznvzzTdvKzvUQ4cOXVcuW7VqlWjAgAE6e2hra8ydO7f4hx9+yDJkmYZkam3p+vXr5tu2bRP9+eefaVlZWalSqZRt37690WUJfejubWnw4MGVZ8+etUtPT7ceOHBgzfDhwysvXrxod/78ebshQ4bQ+CUDs7e3l6WkpKRt2bIl19XVVTJnzpz+mzdvdo6NjXUaN25cCQDMmjXr/r59+x5o/2fOnMnMyspKvXTpUtprr73mWVZWJgCAPXv2OE2fPr0EACZNmnR/165dTgCQl5dn7uTkJFHb3kYgEPCCgoKr2dnZyVu2bOmdlpb2wCW5hoYGVlhYaD5kyJCqtLS0vwYNGlS1ZMmSRon5okWLPFavXn3LzMys0fH17dtXcvfu3UaX+tqjVRkoMT6pqamWMTExnidPnsxYt26dKDIyssre3l46derU/pmZmalCYcf/6w1RBgCkpaVZz5w5857mvPnz5zd6Xl9OTo75zz//bL98+fI7GzdubPFXNaNGjeovFotrzp492yM/P99i69atNyZMmFDRnhjHjBlT2dT19+7AVNuSVCplVVVVAktLS2lNTY3A3d29obn9Gltb+vrrr/P0uf+WDBs2rHLLli29PT0964RCIUQikbS8vNwsKyvLOjY2Nre8vNxkv8hfuHAhQ/na0tKSq0/36NFDpj7t7OwsVZ/u06ePRH3a09Oz1WPBhEIhnnnmmYpnnnmmIjQ0tGbXrl3OhYWF5kVFReb79+93AoC7d++aJycnW4aEhNSpbxsUFFTn7OzccPnyZavAwMC68+fP98jIyLBevHgxpFIpY4xxmUx2y8bGRlZXV6f6v921a5fzk08+WWZpacnd3NwkAwcOrDx79qxtYGBgvXIdkUgksbKyks2ePbsEAGbOnHk/Li7ORTP+q1ev2s6ePdsHAEpKSoSnT5+2FwqFfNasWaXV1dXM0tJS1tq6aInJNszu7siRIz1HjRpVGhoaqmrcc+bMKRUIBEhOTm7xW3tERIS/+vgB5d/Bgwd7GLoMAMjKyrKOiIioVZ+XnZ1tPW/ePC+xWBw4ePBgP+X8l19+2eOTTz65JRBob9oZGRnWDg4O0kuXLmWsWbMmLy4urtF17rbE2V2ZYlvy9vZuePnllwu8vb1De/XqFdajRw/pxIkTy5uLgdpS60VFRdWUlpYKIyMjVWeTxGJxjZ2dnbS58SlEf5KSkiyTk5MtldNXrlyxlkqlqKqqMrt79+7V/Pz85Pz8/OTFixcXfPPNN43Osubn5wtv3bplOWDAgPpdu3Y5Pvvss/dv376dnJ+fn1xQUHDV3d29/ueff7YLCQmpy8/PV30R8PT0rD99+nRPACgvLxdcvnzZNiQkpBYAHn30Ub/r16+bCwQCjBw5suzo0aM9AODHH3/s6evrWwMAsbGxDi+//LKbIoZk5d+YMWNK1q9ff3PWrFmlAJCSkmLl5+enkysOdIZJ3w6+7IG7aTY63WevwGpM+Lzd3xClUikmTpzoZWFhwR977LGKhQsX3ldfnpiYmNHctm0pY+rUqf3Ky8vNjh07dk1zeWvLyM7ONre1tZU6OztL1ee5uLg0ZGZmpqmvu3v3bnsXFxfJ0KFDq48cOdLih1BFRYWgoqLCbMWKFYUAUF9fz+zt7RsNONRFXejK7Tff8qjLytJpW7L09a3u+9GH1JY02lJRUZHZ0aNHHbKzs5OdnZ2lTz/9tM8XX3zhtGjRovua+zXGttSZhEIhKisrr6jP27dv3w3la39///qsrKxU9eUbNmy4baDwTE55ebnZ0qVLPcvLy83MzMy4l5dXXWRkZFVQUNADScZzzz1XMn36dJ9169bdAeRjmAQCASQSCVuxYsUtDw8Pyd69e51ef/31AvXtxo8fXxIXF+c0ZsyYSk9Pz7qUlBTL4ODgumXLlt197rnnvAYMGBDEOceMGTOKBw0aVCOVSpGbm2up/LXkhg0bbs2YMcP7tddeM3N2dpbExsbeAIDs7GxL9cHmzTlx4kSP0aNHl2lbrzUoYeqmnnrqqfL169f3SU1NLVTOi4uLc5BIJOzcuXO2kydPLpkxY0bZ008/7aP5IRcREeFfVVXV6GLw6tWr89QvM7RURnh4eO2ePXtyR48e7dNUfK0tIzEx0cbf3/+BN25iYqJNU98Y/ve//9mdOHHCwc3Nzb6urk5QVVUlGD9+vLf6+CalK1euWAUHB1crL/VcvXrVOjg4uNE+Wxtnd2aKbenw4cM9PT096/r27SsB5L+0OXv2rF1TCRO1JWLMhg4dWn3lypV0besNGjSo5tq1a6mA/IxOU+v88ccfmZrz3n777bvK1wsXLry7bds2582bN9+2t7eX/fTTT42+AF2+fNnqqaeeKrGzs+MA4OfnV3/p0qVGXzaSkpJstm7d2ujLnnryDQA//vijw08//ZSt7fhagxImfevAmaCOCAkJqVu7du3NUaNG+dXW1gqOHz/uYG9vL9mzZ0/OgQMH7CMiIqoBQCAQcM1tW/tNuKUytI05aW0ZSUlJ1oGBgTWa8wICAhp9IH3++ef5n3/+eT4AHDlypMf69etFymTp0Ucf9YuPj7/u7e3dAMhPO4eEhFQrt01JSbGZNGlSaXvjNISOnAnqCFNsS15eXvWXL1+2q6ioENja2spOnTrVQ3mc3aEtEdIZZs+eXVpcXNziG3rgwIG1AwcOvKVtX019EdZ0+/Zt4SuvvFLo6uqq9UxUa9AYpm5szpw5pXl5eckjRowoW7JkSUFGRkZaVFRUjbu7e31ubq4FAHDOO/RT6ebK0M0RACkpKdbffvutq5ubW4ibm1tIeHi4OCUlxTooKKhW+9Zymqd4ASA5Odk6PDxc9SGXmZlpHRER0e64x44d6x0dHS2+fv26pUgkCt24cWOjgYnGzNTa0uOPP141duzYktDQ0AB/f/8gmUzGYmJiiqgtEdIxMTExjX5goS99+/aVKMcy6QLjvNGXQtJBSUlJN8LCwgzWKNqqvLxcMHfuXE9LS0tZdHR0peZlFF0oKCgwi4mJcUtISOg5c+bM4o8//rhA+1b6cfHiRasvv/zSZfv27Vq/tZC2obZECDFWSUlJLmFhYV6tXZ8SJj3o6gkTIYQQYuramjDRJTlCCCGEEC0oYSKEEEII0YISJkIIIYQQLShhIoQQQgjRghIm/ZDJZDKDPNmcEEIIIW2j+Ixu0zPmKGHSj5SioiJ7SpoIIYSQrkUmk7GioiJ7AClt2Y7u9K0HEonk7wUFBdsLCgqCQUkpIYQQ0pXIAKRIJJK/t2Ujug8TIYQQQogWdPaDEEIIIUQLSpgIIYQQQrSghIkQQgghRAtKmAghhBBCtKCEiRBCCCFEi/8Pjzn9So0j/6EAAAAASUVORK5CYII=\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig,ax = plt.subplots(1,2,figsize=(8,3),sharey=True)\n",
+ "plt.tight_layout()\n",
+ "for _ax in ax:\n",
+ " _ax.set_xscale(\"log\")\n",
+ " _ax.set_yscale(\"log\")\n",
+ "ax[0].set_xlabel(\"timestep\");\n",
+ "ax[1].set_xlabel(\"runtime\");\n",
+ "ax[0].set_ylabel(\"error\")\n",
+ "\n",
+ "for j, phi in enumerate(phis):\n",
+ " label = \"$\\Phi_0=\\Phi_1=%s, n=1$\" % labels[phi]\n",
+ " ax[0].plot(dts/np.pi/2.,results_2468[:,j,0],label=label)\n",
+ " ax[1].plot(results_2468[:,j,1],results_2468[:,j,0],label=label)\n",
+ "\n",
+ "for m, method in enumerate(methods):\n",
+ " ax[0].plot(dts/np.pi/2.,results[:,m,0],label=method,color=\"black\",ls=linestyles[m])\n",
+ " ax[1].plot(results[:,m,1],results[:,m,0],label=method,color=\"black\",ls=linestyles[m]) \n",
+ " \n",
+ "ax[0].legend(loc='upper center', bbox_to_anchor=(1.1, -0.2), ncol=4);"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Modified potentials**\n",
+ "\n",
+ "We can use operator splitting methods which make use of derivatives of the acceleration, or the so called modified potential. For the same order, these methods can have fewer function evaluations, and thus better performance. Let us compare using the sixth order methods LF6 (nine function evaluations) and PMLF6 (three modified function evaluations) for $\\Phi_0$. We keep using LF6 for $\\Phi_1$. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "phis_m = [\"LF6\", \"PMLF6\"]\n",
+ "results_m = np.zeros((len(dts), len(phis_m), 2))\n",
+ "for i, dt in enumerate(dts):\n",
+ " for j, phi in enumerate(phis_m):\n",
+ " sim = initial_conditions()\n",
+ " sim.dt = dt\n",
+ " sim.integrator = \"eos\"\n",
+ " sim.ri_eos.phi0 = phi\n",
+ " sim.ri_eos.phi1 = \"LF6\"\n",
+ " sim.ri_eos.n = 1\n",
+ " sim.ri_eos.safe_mode = 0\n",
+ " results_m[i,j] = run(sim)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In the following plot, we see that the method using PMLF6 is indeed about a factor of 2 faster than the one using LF6. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig,ax = plt.subplots(1,2,figsize=(8,3),sharey=True)\n",
+ "plt.tight_layout()\n",
+ "for _ax in ax:\n",
+ " _ax.set_xscale(\"log\")\n",
+ " _ax.set_yscale(\"log\")\n",
+ "ax[0].set_xlabel(\"timestep\");\n",
+ "ax[1].set_xlabel(\"runtime\");\n",
+ "ax[0].set_ylabel(\"error\")\n",
+ "\n",
+ "for j, phi in enumerate(phis_m):\n",
+ " label = \"$\\Phi_0=%s, \\Phi_1=LF6, n=1$\" % labels[phi]\n",
+ " ax[0].plot(dts/np.pi/2.,results_m[:,j,0],label=label)\n",
+ " ax[1].plot(results_m[:,j,1],results_m[:,j,0],label=label)\n",
+ "\n",
+ "for m, method in enumerate(methods):\n",
+ " ax[0].plot(dts/np.pi/2.,results[:,m,0],label=method,color=\"black\",ls=linestyles[m])\n",
+ " ax[1].plot(results[:,m,1],results[:,m,0],label=method,color=\"black\",ls=linestyles[m]) \n",
+ " \n",
+ "ax[0].legend(loc='upper center', bbox_to_anchor=(1.1, -0.2), ncol=4);"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**High order methods for perturbed systems**\n",
+ "\n",
+ "We can do better than above by making use of high order methods for $\\Phi_0$ which were specifically designed for perturbed systems such as LF(8,6,4) and PLF(7,6,4). "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "phi0s_8 = [\"LF8\", \"LF8_6_4\", \"PLF7_6_4\"]\n",
+ "results_8 = np.zeros((len(dts), len(phi0s_8), 2))\n",
+ "for i, dt in enumerate(dts):\n",
+ " for j, phi0 in enumerate(phi0s_8):\n",
+ " sim = initial_conditions()\n",
+ " sim.dt = dt\n",
+ " sim.integrator = \"eos\"\n",
+ " sim.ri_eos.phi0 = phi0\n",
+ " sim.ri_eos.phi1 = \"LF8\"\n",
+ " sim.ri_eos.n = 1\n",
+ " sim.ri_eos.safe_mode = 0\n",
+ " results_8[i,j] = run(sim)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can see in the following plot that these methods indeed perform very well. With $\\Phi_0=LF(8,6,4)$, $\\Phi_1=LF8$ and $n=1$ we achieve an accuracy and efficiency comparable to SABA(8,6,4). In contrast to SABA(8,6,4) we do not require a Kepler solver. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig,ax = plt.subplots(1,2,figsize=(8,3),sharey=True)\n",
+ "plt.tight_layout()\n",
+ "for _ax in ax:\n",
+ " _ax.set_xscale(\"log\")\n",
+ " _ax.set_yscale(\"log\")\n",
+ "ax[0].set_xlabel(\"timestep\");\n",
+ "ax[1].set_xlabel(\"runtime\");\n",
+ "ax[0].set_ylabel(\"error\")\n",
+ "\n",
+ "for j, phi0 in enumerate(phi0s_8):\n",
+ " label = \"$\\Phi_0=%s, \\Phi_1=LF8, n=1$\" % labels[phi0]\n",
+ " ax[0].plot(dts/np.pi/2.,results_8[:,j,0],label=label)\n",
+ " ax[1].plot(results_8[:,j,1],results_8[:,j,0],label=label)\n",
+ "\n",
+ "for m, method in enumerate(methods):\n",
+ " ax[0].plot(dts/np.pi/2.,results[:,m,0],label=method,color=\"black\",ls=linestyles[m])\n",
+ " ax[1].plot(results[:,m,1],results[:,m,0],label=method,color=\"black\",ls=linestyles[m]) \n",
+ " \n",
+ "ax[0].legend(loc='upper center', bbox_to_anchor=(1.1, -0.2), ncol=4);"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.0"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/rebound/source/docs/ipython_examples/EscapingParticles.ipynb b/rebound/source/docs/ipython_examples/EscapingParticles.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..91f457b65e7d69c8e683a236ecf1a1a57d54d44b
--- /dev/null
+++ b/rebound/source/docs/ipython_examples/EscapingParticles.ipynb
@@ -0,0 +1,242 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "# Escaping particles\n",
+ "\n",
+ "Sometimes we are not interested in particles that get too far from the central body. Here we will define a radius beyond which we remove particles from the simulation. Let's set up an artificial situation with 3 planets, and the inner one moves radially outward with $v > v_{escape}$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "---------------------------------\n",
+ "REBOUND version: \t2.19.1\n",
+ "REBOUND built on: \tJul 8 2016 19:40:49\n",
+ "Number of particles: \t4\n",
+ "Selected integrator: \tias15\n",
+ "Simulation time: \t0.000000\n",
+ "Current timestep: \t0.001000\n",
+ "---------------------------------\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "---------------------------------\n"
+ ]
+ }
+ ],
+ "source": [
+ "import rebound\n",
+ "import numpy as np\n",
+ "def setupSimulation():\n",
+ " sim = rebound.Simulation()\n",
+ " sim.add(m=1., hash=\"Sun\")\n",
+ " sim.add(x=0.4,vx=5., hash=\"Mercury\")\n",
+ " sim.add(a=0.7, hash=\"Venus\")\n",
+ " sim.add(a=1., hash=\"Earth\")\n",
+ " sim.move_to_com()\n",
+ " return sim\n",
+ "\n",
+ "sim = setupSimulation()\n",
+ "sim.status()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now let's run a simulation for 20 years (in default units where $G=1$, and thus AU, yr/2$\\pi$, and $M_\\odot$, see [Units.ipynb](../Units) for how to change units), and set up a 50 AU sphere beyond which we remove particles from the simulation. We can do this by setting the `exit_max_distance` flag of the simulation object. If a particle's distance (from the origin of whatever inertial reference frame chosen) exceeds `sim.exit_max_distance`, an exception is thrown.\n",
+ "\n",
+ "If we simply call `sim.integrate()`, the program will crash due to the unhandled exception when the particle escapes, so we'll create a `try`-`except` block to catch the exception. We'll also store the x,y positions of Venus, which we expect to survive."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "A particle escaped (r>exit_max_distance).\n"
+ ]
+ }
+ ],
+ "source": [
+ "sim = setupSimulation() # Resets everything\n",
+ "sim.exit_max_distance = 50.\n",
+ "Noutputs = 1000\n",
+ "times = np.linspace(0,20.*2.*np.pi,Noutputs)\n",
+ "xvenus, yvenus = np.zeros(Noutputs), np.zeros(Noutputs)\n",
+ "for i,time in enumerate(times):\n",
+ " try:\n",
+ " sim.integrate(time) \n",
+ " except rebound.Escape as error:\n",
+ " print(error)\n",
+ " for j in range(sim.N):\n",
+ " p = sim.particles[j]\n",
+ " d2 = p.x*p.x + p.y*p.y + p.z*p.z\n",
+ " if d2>sim.exit_max_distance**2:\n",
+ " index=j # cache index rather than remove here since our loop would go beyond end of particles array\n",
+ " sim.remove(index=index)\n",
+ " xvenus[i] = sim.particles[2].x\n",
+ " yvenus[i] = sim.particles[2].y"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Went down to 3 particles\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(\"Went down to {0} particles\".format(sim.N))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "So this worked as expected. Now let's plot what we got:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "fig,ax = plt.subplots(figsize=(15,5))\n",
+ "ax.plot(xvenus, yvenus)\n",
+ "ax.set_aspect('equal')\n",
+ "ax.set_xlim([-2,10]);"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This doesn't look right. The problem here is that when we removed `particles[1]` from the simulation, all the particles got shifted down in the `particles` array. So following the removal, `xvenus` all of a sudden started getting populated by the values for Earth (the new `sim.particles[2]`). A more robust way to access particles is using hashes (see [UniquelyIdentifyingParticlesWithHashes.ipynb](../UniquelyIdentifyingParticlesWithHashes))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "A particle escaped (r>exit_max_distance).\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "sim = setupSimulation() # Resets everything\n",
+ "sim.exit_max_distance = 50.\n",
+ "Noutputs = 1000\n",
+ "times = np.linspace(0,20.*2.*np.pi,Noutputs)\n",
+ "xvenus, yvenus = np.zeros(Noutputs), np.zeros(Noutputs)\n",
+ "for i,time in enumerate(times):\n",
+ " try:\n",
+ " sim.integrate(time) \n",
+ " except rebound.Escape as error:\n",
+ " print(error)\n",
+ " for j in range(sim.N):\n",
+ " p = sim.particles[j]\n",
+ " d2 = p.x*p.x + p.y*p.y + p.z*p.z\n",
+ " if d2>sim.exit_max_distance**2:\n",
+ " index=j # cache index rather than remove here since our loop would go beyond end of particles array\n",
+ " sim.remove(index=index)\n",
+ " xvenus[i] = sim.particles[\"Venus\"].x\n",
+ " yvenus[i] = sim.particles[\"Venus\"].y\n",
+ "\n",
+ "fig,ax = plt.subplots(figsize=(15,5))\n",
+ "ax.plot(xvenus, yvenus)\n",
+ "ax.set_aspect('equal')\n",
+ "ax.set_xlim([-2,10]);"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Much better! We solved the problem by assigning particles hashes and using those to access the particles for output."
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.5.1"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/rebound/source/docs/ipython_examples/Forces.ipynb b/rebound/source/docs/ipython_examples/Forces.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..6ddae65ebb7d90a689cc17a8858c6126c79825be
--- /dev/null
+++ b/rebound/source/docs/ipython_examples/Forces.ipynb
@@ -0,0 +1,297 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Additional forces\n",
+ "REBOUND is a gravitational N-body integrator. But you can also use it to integrate systems with additional, non-gravitational forces.\n",
+ "\n",
+ "This tutorial gives you a very quick overview of how that works. Implementing additional forces in python as below will typically be a factor of a few slower than a C implementation. For a library that has C implementations for several commonly used additional effects (with everything callable from Python), see [REBOUNDx](https://github.com/dtamayo/reboundx).\n",
+ "\n",
+ "**Stark problem**\n",
+ "\n",
+ "We'll start by adding two particles, the Sun and an Earth-like planet, to REBOUND."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": true,
+ "jupyter": {
+ "outputs_hidden": true
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import rebound\n",
+ "sim = rebound.Simulation()\n",
+ "sim.integrator = \"whfast\"\n",
+ "sim.add(m=1.)\n",
+ "sim.add(m=1e-6,a=1.)\n",
+ "sim.move_to_com() # Moves to the center of momentum frame"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We could integrate this system, and the planet would go around the star at a fixed orbit with $a=1$ forever. Let's add an additional constant force that acts on the planet and points in one direction $F_x = m\\cdot c$, where $m$ is the planet's mass and $c$ a constant. This is called the Stark problem. In python, we can describe this with the following function"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false,
+ "jupyter": {
+ "outputs_hidden": false
+ }
+ },
+ "outputs": [],
+ "source": [
+ "ps = sim.particles\n",
+ "c = 0.01\n",
+ "def starkForce(reb_sim):\n",
+ " ps[1].ax += c"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Next, we need to tell REBOUND about this function. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false,
+ "jupyter": {
+ "outputs_hidden": false
+ }
+ },
+ "outputs": [],
+ "source": [
+ "sim.additional_forces = starkForce"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we can just integrate as usual. Let's keep track of the eccentricity as we integrate as it will change due to the additional force."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false,
+ "jupyter": {
+ "outputs_hidden": false
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "Nout = 1000\n",
+ "es = np.zeros(Nout)\n",
+ "times = np.linspace(0.,100.*2.*np.pi,Nout)\n",
+ "for i, time in enumerate(times):\n",
+ " sim.integrate(time, exact_finish_time=0) # integrate to the nearest timestep so WHFast's timestep stays constant\n",
+ " es[i] = sim.particles[1].e "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "And let's plot the result."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false,
+ "jupyter": {
+ "outputs_hidden": false
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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e0VmkeMxYlLQCv4I7f4/OI31nxk3ASe5cHp1FiseMTYFzgFXzgq3ITLTjVhxj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\nROw64LMLy3w/EhHHNRO1RiIipkXE8oh4MCJ+FhF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+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "fig = plt.figure(figsize=(15,5))\n",
+ "ax = plt.subplot(111)\n",
+ "plt.plot(times, es);"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "You can see that the eccentricity is oscillating between 0 and almost 1. \n",
+ "\n",
+ "Note that the function `starkForce(reb_sim)` above receives the argument `reb_sim` when it is called. This is a pointer to the simulation structure. Instead of using the global `ps` variable to access particle data, one could also use `reb_sim.contents.particles`. This could be useful when one is running multiple simulations in parallel or when the particles get added and removed (in those cases `particles` might change). The `contents` has the same meaning as a `->` in C, i.e. follow the memory address. To find out more about pointers, check out the [ctypes documentation](https://docs.python.org/3/library/ctypes.html#pointers).\n",
+ "\n",
+ "\n",
+ "**Non-conservative forces**\n",
+ "\n",
+ "The previous example assumed a conservative force, i.e. we could describe it as a potential as it is velocity independent. Now, let's assume we have a velocity dependent force. This could be a migration force in a protoplanetary disk or PR drag. We'll start from scratch and add the same two particles as before."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": true,
+ "jupyter": {
+ "outputs_hidden": true
+ }
+ },
+ "outputs": [],
+ "source": [
+ "sim = rebound.Simulation()\n",
+ "sim.integrator = \"ias15\"\n",
+ "sim.add(m=1.)\n",
+ "sim.add(m=1e-6,a=1.)\n",
+ "sim.move_to_com() # Moves to the center of momentum frame"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "But we change the additional force to be"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": true,
+ "jupyter": {
+ "outputs_hidden": true
+ }
+ },
+ "outputs": [],
+ "source": [
+ "ps = sim.particles\n",
+ "tau = 1000.\n",
+ "def migrationForce(reb_sim):\n",
+ " ps[1].ax -= ps[1].vx/tau\n",
+ " ps[1].ay -= ps[1].vy/tau\n",
+ " ps[1].az -= ps[1].vz/tau"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We need to let REBOUND know that our force is velocity dependent. Otherwise, REBOUND will not update the velocities of the particles. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": true,
+ "jupyter": {
+ "outputs_hidden": true
+ }
+ },
+ "outputs": [],
+ "source": [
+ "sim.additional_forces = migrationForce\n",
+ "sim.force_is_velocity_dependent = 1"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now, we integrate as before. But this time we keep track of the semi-major axis instead of the eccentricity."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false,
+ "jupyter": {
+ "outputs_hidden": false
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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GYQ3gdcAsYB3gL51cTNLzy+SGTD4JvBz4DKX/320R/CSC10cwqdkKJUmS1EtGM9N3dWZu\nHRHXZuaWETEZ+E1mvmp8SnSmT6o2ejmYMgO4LvAjyvLP65qsS5IkSeOj7pm+gXv35kfEFsAU4CWd\nXExSZzJ5qOr992pgd2Ah8PNq988PRfDihkuUJElSlxpN6Ds6IlYD/gU4E7gB+EqtVUlaokxuzOQw\nyvLPfwF2Am6N4OQI9o9gcrMVSpIkqZt0tHvneHN5p/TcIpgCHETZ/XN9SvP3H9r8XZIkqR3GvWXD\neDP0SaMXwcaUe/8OBR6mbMZ0QiZ3NlqYJEmSOmbok7SYCCZQdv48FHgTcCVlA5hTMnm0ydokSZK0\ndGoLfRExAdgxM3/baXFjwdAnLZsIXgDsR+n9txtwDmUG8PxMFjRZmyRJkp5f3c3Zr87MrTuqbIwY\n+qSxE8HqlPYPh1Lu/zuRMgM4O5Pun/qXJEnqQ3W3bLggIt4SEYYuqQUyuT+Tb1btH3YGHgJOAOZG\n8C8RrNdshZIkSRpLo5np+wvwQuBp4Inq5czMlWuubWgNzvRJNYoggB0pyz8PAuZSln+elMlDTdYm\nSZIkN3KRNIYiWA7Yh7L8c2/gAsryz3MyebLJ2iRJkvpV7aEvIt5A2QUwgV9m5lmdXKxThj6pGVX/\nv7dQZgC3AE6jLAW9KJOnm6xNkiSpn9S9kcsRwHRKs+cA3gbMzszDOrlgJwx9UvMiWIeyAczfAGsB\nPwF+DFzmBjCSJEn1qjv0zQG2zsynq+cTgaszc4tOLtgJQ5/UXaoG8IdUxyTK7N8JmVzfaGGSJEkt\nVffunQlMGfJ8SvWapD6VybxMDgc2Ad4KrAD8PIJrIvhUBOs2WZ8kSZIGjWam7xDgCGBW9dJuwKcy\n88R6SxtWgzN9UpeLYAKwC2X27y3APMryz5My+VOTtUmSJPW68djIZS3KfX0JXJaZ93ZysU4Z+qTe\nUu0Auhfl/r99gd9RloCelskjTdYmSZLUi2oJfRGxaWbOjYjtKGFv4AJZHQ9m5h86uehSF2nok3pW\nBCsC+1NmAGcA51NmAM/JfLb3pyRJkp5DXaHv6Mx8f0TMYuR7+F4MXJuZh3Zy4aVh6JPaIYLVgDdR\nZgC3Ac4G/gc4zx6AkiRJS9ZYc/aIOC8z9+74A0Z/HUOf1DIRvAx4M3AQpQfgWZQAeEEmTzVZmyRJ\nUrcZj3v6tgA2pezQB0Bm/r9OLtgJQ5/UbhGsRdn85SDK3zVnUALgLzJZ0GRtkiRJ3aDuPn2HU3bs\nnEZZirUP8JvMfEsnF+yEoU/qHxFMZTAAbgicRmkEPyuThU3WJkmS1JS6Q991wFbAlZm5VUSsARyf\nmXt2csFOGPqk/hTBKyh9AA8CXgGcSgmAv8rk6SZrkyRJGk91N2f/a2Y+DSyMiFWAPwFTO7mYJC2N\nTP6QyVcz2QF4NXA78FXgrgiOimDXqj+gJEmSlmA0/1m6PCJWBY4GZgNXAb+ttSpJWkQmt2by5Uy2\nozSBvxv4BnBHBP8ZwU4GQEmSpMUt1e6dEbEesFJmXltfSSNe1+WdkkYUwSaUJaAHA6sAJwGnAJdk\n8kyTtUmSJI2V8di9cytgXWAipUl7ZuapnVywE4Y+SaMRwTRKAHwzpZfoqZQA+Gs3gZEkSb2s7o1c\njqX00LoeBn9qnpnv6eSCnTD0SVpaEWxMCX9vptyHfAZwMnCRfQAlSVKvqTv03QBMy2Xp4r6MDH2S\nlkUE6wFvogTAjYGfUmYAz8vkiSZrkyRJGo26d++8HNiskw+XpG6QyW2ZfC2T11Ba0MwG/hG4N4IT\nI3hLBCs2W6UkSVI9RjPTNwM4E7gXeLJ6OTNzy3pLG1aDM32SxlwELwUOpDSDfxVwIWUG8KeZzG+y\nNkmSpKHqXt55C/Ax4DqG39N3eycX7IShT1LdIlgNOICyBHQ34FeUAHhmJg80WZskSVLdoe+SzHx1\nR5WNEUOfpPEUwcrAfpQAuCdwGYMB8O4ma5MkSf2p7tD3LWAKcBY8u+PdqFo2RMRM4EhKq4fvZeaX\nRzhnBvB1YDJwf2bOGOEcQ5+kRlT3+s2kBMB9gBuB04HTM5nXZG2SJKl/1B36fgAsdtLztWyIiInA\nPMpPye+ibAhzSGbOHXLOFOBi4HWZeWdErJ6Z94/wWYY+SY2LYDnK0s83Am8A5lMFQGC2zeAlSVJd\nam/O3tEHR7wa+GxmzqyefwogM48Ycs4HgZdl5mee57MMfZK6SgQTgO0pAfBAYCVKL8DTgVmZLGiw\nPEmS1DJ1t2wYeqErl+L0tYE7hjy/s3ptqI2A1SLiooiYHRHvWJp6JKkpmTyTyWWZHJbJppRVDX8E\nPg/cF8GPqlYQL2q2UkmS1O+WKvQBS5MsRzOFOBnYFng98DrgXyNio6WsSZIal8mNmXw5kx2BzYHf\nAP8LuDuCsyJ4X9UiQpIkaVxNWsrzz1mKc+8Cpg55PpUy2zfUHZTNW/4K/DUifkVpnHzToh8WEYcP\neTorM2ctRS2SNG6qHT6/DXw7gimUDWAOBL4WwRzgNMpGMLc2WKYkSepi1YaXM8bks2q8p28SZSOX\nPYC7KVueL7qRyybAUZRZvuWBS4GDM/OGRT7Le/ok9bwIlqf8nXggpSfg/cCZ1XGZG8FIkqQlqWUj\nl4i4ODN3ioi/sPhSzczMlUdR2D4Mtmw4JjO/FBEfqD7gO9U5HwfeQ2n8fnRmfmOEzzH0SWqVaiOY\nHYD9KQHwpcBPKe1xzs/ksQbLkyRJXaYrd+8cS4Y+SW0XwXoMBsAdgF9RAuBZNoSXJEm1h76IWJVy\nT96z9wBm5tLs5LlMDH2S+kl1H+BMSgjcB7iFsgT0LOCazFFtlCVJklqk7ubsnwfeDdwKg/ebZObu\nnVywE4Y+Sf0qgsnAzpQZwAMoux4PBMBZmTzZYHmSJGmc1B36fg9snplPdXKBsWDokySIIIBNKeFv\nf2AacAElBJ6Tyf0NlidJkmpUd+g7Dfi7zLyvkwuMBUOfJC2u6vu3LyUEvha4Hji7OlwGKklSi9Qd\n+qYDZwDXwbPLiDIzD+jkgp0w9EnSc6vaQexGCYH7UdrgnEMJgBe4G6gkSb2t7tA3F/hvSugbuKcv\nM/OXnVywE4Y+SRq9ahnoxpQAuC8wHfgtpSXE2TaFlySp99Qd+i7PzOkdVTZGDH2S1LkIVgH2ogTA\nfYCHGFwG+ptMFjRYniRJGoW6Q99/UJZ1nsng8k5bNkhSD6qawm/H4CzghpTNYM4GfpZJY/dvS5Kk\nJas79M2CxTcDsGWDJPW+CF5Gmf3bF9gT+D3VMlDgqszBVj2SJKk5tTdnb5qhT5LqF8FylJ6AA7OA\nU4Bzq+O8TB5ssDxJkvpa3TN9LwO+CKydmTMjYjPg1Zl5TCcX7IShT5LGXwQbAK+jzATuRmkJcS7w\nM+CKTJ5usDxJkvpK3aHvXOBY4J8zc8uImAxclZmbd3LBThj6JKlZVUuInSkBcCbwMuA8SgA8z3sB\nJUmqV92hb3Zmbh8RV2XmNtVrV2fm1p1csBOGPknqLhFMpYS/mcAewM0MLgX9XSYLGyxPkqTWWZZM\nNGEU5/wlIl485GI7AvM7uZgkqR0yuSOTozN5M/AS4B8p/6b8F/DnCE6K4H0RrN1ooZIkaVQzfdtR\n/hGfRrmf4yXAWzLzmvrLe7YGZ/okqUdEsCawN2Up6F7AXZRloOcCF2fyVIPlSZLUk2rfvbO6j2/j\n6um8zBzXRr6GPknqTRFMBKYzeC/gJsBFDO4IemuD5UmS1DPqvqfvIODczHwkIv4V2Ab4gs3ZJUlL\nK4LVKbN/A7OAjwHnUzaFuSiThxssT5KkrlV36JuTmVtExM7AF4CvAp/JzB06uWAnDH2S1D4RBLA5\nZSnoXsBOwBxKADwPuMwNYSRJKuoOfVdn5tYRcQQwJzOPH7qT53gw9ElS+0WwAqUtxEAIXBeYRRUC\nM7mlseIkSWpY3aHvbMpN+HtRlnY+AVyamVt1csFOGPokqf9EsAawJ4Mh8AkGZwF/4VJQSVI/qTv0\nrUi5+f7azLwpItYEtsjM8zq5YCcMfZLU36qloNMoAXBvylLQ6xi+FHRcNxmTJGk81b57Z9MMfZKk\noaqloDsxGALXA34JXABcCMzNpPv/gZMkaZQMfZKkvhbBSylLQfeojuWAX1AC4IWZ/LHB8iRJWmaG\nPkmSKtVS0PUZDICvBR6iCoCU1hAPNFehJElLz9AnSdISRDAB2JLBELgzcDODIfDXmTzWXIWSJD0/\nQ58kSaMUwXLADgyGwG2BKxm8H9BNYSRJXcfQJ0lShyJYEdiFwRC4AfAbBmcC52TyTHMVSpJk6JMk\nacxEsDqwO4MhcBXgIgZD4K3uDCpJGm+GPkmSahLByxm+KcxCYBYlCM7K5LbmqpMk9QtDnyRJ46Da\nGXQjykzgjOrrEwwPgX9oqj5JUnsZ+iRJakAVAjdmMADOAB6jhMBZlPYQdzRTnSSpTQx9kiR1gSoE\nbkoJfwPHowyfCbyzmeokSb3M0CdJUheqQuBmDM4C7gY8zPAQeHdT9UmSeoehT5KkHlA1ip/G4HLQ\n3YAHqAIgJQTe01R9kqTuZeiTJKkHVSFwc4bPBN4P/GrI8QdbREiSDH2SJLXAkJnAXYccCxkeAm80\nBEpS/zH0SZLUQtU9gRsyPASuCPyawRB4bSZPN1akJGlcGPokSeoTVbP4XapjV2At4GIGQ+AVmTzV\nXIWSpDoY+iRJ6lMRvBTYmcGZwI2AyxgMgZdm8nhzFUqSxoKhT5IkARDBFOA1DIbALYFrKUtCfwP8\nNpMHmqtQktQJQ58kSRpRBC8EXg3sRJkRfBVwF2VJ6MWUIHiLm8NIUncz9EmSpFGJYBKwBYMhcCdg\nMsND4FWZLGisSEnSYgx9kiSpY9XmMAMBcGdgfWA2gyHwkkzmN1ehJMnQJ0mSxkwEqzB8Sej2wK0M\nhsCLgT+6JFSSxo+hT5Ik1SaCycDWDJ8NXMDwJaH2C5SkGhn6JEnSuKmaxq/P8BC4NnApJQReQmkV\n4ZJQSRojhj5JktSoCF7M4JLQVwPbAX+gBMCBY14mzzRWpCT1MEOfJEnqKtWS0C0oAXDgWI0yGzgQ\nAp0NlKRRMvRJkqSuF8EawI4MhsDtgNtxNlCSnpehT5Ik9ZxqNnBLhs8GTmHx2cBHGitSkrqEoU+S\nJLVCBC9j+GzgtsBtDIbA3+FsoKQ+ZOiTJEmtVM0GbsXis4GXU2YEL6XMBv65sSIlaRwY+iRJUt+o\n7g3cAXhVdUwHHgQuYzAIXpXJXxsrUpLGWNeGvoiYCRwJTAS+l5lfXsJ50ylLNg7KzFNHeN/QJ0mS\nRhTBBOCVlAA4EAY3BW5kyGwg8HuXhUrqVV0Z+iJiIjAP2BO4i7IM45DMnDvCeecDjwPHZuYpI3yW\noU+SJI1aBC8AtmH4jOBqDF8Welkm9zVWpCQthWXJRJPGupghdgBuzszbASLiROANwNxFzvswcDJl\naYYkSdIyq5Z2/rY6AIjgJQyGwA8BO0QwnyoAVl+vzOTx8a9YkupTZ+hbG7hjyPM7KX/JPisi1qYE\nwddSQl/332AoSZJ6UrXZy9nVQQQBbMTgstCDgWkR3ATMpswKzgbmZPJUI0VL0hioM/SNJsAdCXwq\nMzMiAnAJpyRJGheZJPD76jgOIILlKb0DpzM4I7h+BNczGAIvB+Zm8nQTdUvS0qoz9N0FTB3yfCpl\ntm+o7YATS95jdWCfiFiQmWcu+mERcfiQp7Myc9aYVitJkvpeJk9SQt3lA69FsCLl/sDtKXsVHAas\nGcHVDA+Ct7hRjKSxEhEzgBlj8lk1buQyibKRyx7A3ZS18ott5DLk/GOBs9y9U5IkdbsIplB+eL09\nZVZwe2AV4AqGLw39YzWjKEnLpCs3csnMhRHxIeDnlJYNx2Tm3Ij4QPX+d+q6tiRJUp0yeRi4sDoA\niOCllCA4HXgXcBQwMWJYCLw8k3vHv2JJ/czm7JIkSTWoNopZixICB2YDt6e0qboCuHLgayb3NFWn\npN7QlX36xpKhT5IktUEVBNcHtq2O7aqvCxgMggPHHS4NlTTA0CdJktSjqiA4lcEAOBAGJzI8BF4J\n3GoQlPqToU+SJKllIliLwRA4cKwEXMVgCLwCuMldQ6X2M/RJkiT1gWqzmG0YPiP4EuBqhtwjCNyY\nycKm6pQphyFNAAAK90lEQVQ09gx9kiRJfSqCVRkMggNLRNcB5jAYAq8Crq/6EErqQYY+SZIkPSuC\nlYGtGAyCWwMbAjdTZgUHjmsyeaCpOiWNnqFPkiRJzymCFYDNKAFw4NgKeIThQfBq4DbvE5S6i6FP\nkiRJSy2CCcC6DA+CWwNTgGsYHgSvz+SJZiqVZOiTJEnSmIngxZRZwKFBcCNGXh56f1N1Sv3E0CdJ\nkqRaDVkeumgYHLo8dGB28FaXh0pjy9AnSZKkcVc1ll+X4SFwG2BV4Hrg2uqYA8zJ5MFmKpV6n6FP\nkiRJXSOCKcAWwJaLfH2YwRA4EAjnZbKgoVKlnmHokyRJUlerNo15BSUADg2DrwB+z+Jh8J5Muv8/\nqtI4MfRJkiSpJ0XwAsq9gkPD4FbABAYD4EAgvD6TxxoqVWqUoU+SJEmtUd0ruAaDs4EDYXAT4E6G\nzwjOwY1j1AcMfZIkSWq9CCZTWkcMDYNbAi+mbBxzPXBddVwP3O0SUbWFoU+SJEl9q9o4Zlp1bF4d\n04DlGAyAz37N5M8NlSp1zNAnSZIkLSKCl7B4ENwceIrFZwWvz+ThhkqVnpehT5IkSRqF6n7BNVk8\nCG4GzGd4ELwOuMHNY9QNDH2SJEnSMqhaSryc4UFwc2Bj4F4WXyY6L5O/NlOt+pGhT5IkSapBBBOB\nDRgeBDcDNgTuBm6ojrkDXzN5tJlq1WaGPkmSJGkcRTCJEgY3pYTAzarHmwAPsngYvCGTB5upVm1g\n6JMkSZK6QLVM9BUsHgY3A55ghDAI3GdrCT0fQ58kSZLUxaoNZNZieAgcOCYychi8wzCoAYY+SZIk\nqUdVrSUWnRXcDFgJmAfcOOSYB9yUyRPNVKumGPokSZKklqmazm9K2UF0Y8r9gpsA6wF3MTwQDjz+\nk7OD7WTokyRJkvpEBJMpwW8gBA4NhBMYHgIHHt+SyVONFKwxYeiTJEmSRASrM3IYnAr8gRGWi2by\nQDPVamkY+iRJkiQtUQTLU1pMjBQIn2Lk2cHbMlnYSMFajKFPkiRJ0lKrdhVdg5HD4JrAbcDvhxzz\nqq+2mRhnhj5JkiRJYyqCF1BmB19ZHRsPebw8w0Pgs0cmjzZScMsZ+iRJkiSNmwhWYzAADg2EGwE/\nz+SNDZbXSoY+SZIkSY2LYAKwciYPN11L2xj6JEmSJKnFliUTTRjrYiRJkiRJ3cPQJ0mSJEktZuiT\nJEmSpBYz9EmSJElSixn6JEmSJKnFDH2SJEmS1GKGPkmSJElqMUOfJEmSJLWYoU+SJEmSWszQJ0mS\nJEktZuiTJEmSpBYz9EmSJElSixn6JEmSJKnFDH2SJEmS1GKGPkmSJElqMUOfJEmSJLWYoU+SJEmS\nWszQJ0mSJEktZuiTJEmSpBarPfRFxMyIuDEiboqIT47w/tsj4pqIuDYiLo6ILeuuSZIkSZL6Ra2h\nLyImAkcBM4HNgEMiYtNFTrsV2DUztwQ+D3y3zprUfSJiRtM1qB6Obbs5vu3l2Lab49tejq2WpO6Z\nvh2AmzPz9sxcAJwIvGHoCZl5SWbOr55eCqxTc03qPjOaLkC1mdF0AarVjKYLUG1mNF2AajWj6QJU\nmxlNF6DuVHfoWxu4Y8jzO6vXluR9wDm1ViRJkiRJfWRSzZ+foz0xInYH3gvsVF85kiRJktRfInPU\nuWzpPzxiR+DwzJxZPT8MeCYzv7zIeVsCpwIzM/PmET6nviIlSZIkqQdkZnTyfXXP9M0GNoqIdYG7\ngYOBQ4aeEBEvpwS+Q0cKfND5L06SJEmS+l2toS8zF0bEh4CfAxOBYzJzbkR8oHr/O8BngFWB/44I\ngAWZuUOddUmSJElSv6h1eackSZIkqVm1N2dfFs/X2F3dLyK+HxH3RcScIa+tFhHnR8TvI+K8iJgy\n5L3DqvG+MSL2bqZqjUZETI2IiyLi+oi4LiI+Ur3u+LZARKwQEZdGxNURcUNEfKl63fFtiYiYGBFX\nRcRZ1XPHtiUi4vaIuLYa38uq1xzfloiIKRFxckTMrf5+fpXj2/siYuPqz+zAMT8iPjJWY9u1oW+U\njd3V/Y6ljOFQnwLOz8xXAhdWz4mIzSj3fW5Wfc+3IqJrf4+KBcDHMnMasCPwD9WfUce3BTLzCWD3\nzNwa2BLYPSJ2xvFtk48CNzC407Zj2x4JzMjMbYbcMuP4tsd/Audk5qaUv59vxPHteZk5r/ozuw2w\nHfA4cBpjNLbdPOjP29hd3S8zfw08tMjLBwA/rB7/EDiwevwG4ITMXJCZtwM3U34fqAtl5r2ZeXX1\n+C/AXEofTse3JTLz8erhcpT7sh/C8W2FiFgHeD3wPWBgszTHtl0W3QTP8W2BiFgF2CUzvw9l/4zM\nnI/j2zZ7UnLQHYzR2HZz6Fvaxu7qHWtk5n3V4/uANarHa1HGeYBj3iOqHXq3AS7F8W2NiJgQEVdT\nxvGizLwex7ctvg58AnhmyGuObXskcEFEzI6I91evOb7tsB7w54g4NiKujIijI2JFHN+2eRtwQvV4\nTMa2m0OfO8z0gSw7CT3XWPv7oMtFxIuAU4CPZuajQ99zfHtbZj5TLe9cB9g1InZf5H3HtwdFxH7A\nnzLzKhafDQIc2xbYqVoitg9l6f0uQ990fHvaJGBb4FuZuS3wGNVyvwGOb2+LiOWA/YGTFn1vWca2\nm0PfXcDUIc+nMjzNqnfdFxEvA4iINYE/Va8vOubrVK+pS0XEZErgOy4zT69ednxbplo6dDblHgPH\nt/e9BjggIm6j/CT5tRFxHI5ta2TmPdXXP1PuCdoBx7ct7gTuzMzLq+cnU0LgvY5va+wDXFH9+YUx\n+rPbzaHv2cbuVeI9GDiz4Zo0Ns4E3lU9fhdw+pDX3xYRy0XEesBGwGUN1KdRiIgAjgFuyMwjh7zl\n+LZARKw+sENYRLwA2Au4Cse352XmpzNzamauR1lC9IvMfAeObStExAsjYqXq8YrA3sAcHN9WyMx7\ngTsi4pXVS3sC1wNn4fi2xSEMLu2EMfqzW2tz9mWxpMbuDZelpRQRJwC7AatHxB3AZ4AjgJ9ExPuA\n24GDADLzhoj4CWU3uYXAB9NGkt1sJ+BQ4NqIuKp67TAc37ZYE/hhtRPYBMps7oXVWDu+7TIwTv7Z\nbYc1gNPKz+WYBByfmedFxGwc37b4MHB8NSlyC/Aeyv+VHd8eV/2gZk/g/UNeHpO/m23OLkmSJEkt\n1s3LOyVJkiRJy8jQJ0mSJEktZuiTJEmSpBYz9EmSJElSixn6JEmSJKnFDH2SJEmS1GKGPklS34qI\nVSLi76vHa0bESU3XJEnSWLNPnySpb0XEusBZmblFw6VIklSbSU0XIElSg44ANoiIq4CbgE0zc4uI\neDdwIPBCYCPga8AKwN8ATwKvz8yHImID4CjgJcDjwPszc974/zIkSVoyl3dKkvrZJ4FbMnMb4BOL\nvDcNeCMwHfgi8EhmbgtcAryzOue7wIczc/vq+781LlVLkrQUnOmTJPWzWMJjgIsy8zHgsYh4GDir\nen0OsGVErAi8Bjgp4tlvXa7OYiVJ6oShT5KkkT055PEzQ54/Q/n3cwLwUDVLKElS13J5pySpnz0K\nrLSU3xMAmfkocFtEvAUgii3HuD5JkpaZoU+S1Lcy8wHg4oiYA3wFGNjSOoc8ZoTHA8/fDrwvIq4G\nrgMOqLdiSZKWni0bJEmSJKnFnOmTJEmSpBYz9EmSJElSixn6JEmSJKnFDH2SJEmS1GKGPkmSJElq\nMUOfJEmSJLWYoU+SJEmSWszQJ0mSJEkt9v8Bh4vTbEqwOfcAAAAASUVORK5CYII=\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "Nout = 1000\n",
+ "a_s = np.zeros(Nout)\n",
+ "times = np.linspace(0.,100.*2.*np.pi,Nout)\n",
+ "for i, time in enumerate(times):\n",
+ " sim.integrate(time)\n",
+ " a_s[i] = sim.particles[1].a \n",
+ "fig = plt.figure(figsize=(15,5))\n",
+ "ax = plt.subplot(111)\n",
+ "ax.set_xlabel(\"time\")\n",
+ "ax.set_ylabel(\"semi-major axis\")\n",
+ "plt.plot(times, a_s);"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The semi-major axis decays exponentially on a timescale `tau`.\n",
+ "\n",
+ "In the above example, REBOUND is calling a python function at every timestep. This can be slow. Note that you can also set `rebound.additional_forces` to a c function pointer. This let's you speed up the simulation significantly. However, you need to write your own c function/library that knows how to calculate the forces. Or, you use Dan Tamayo's new migration library (in preparation)."
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/rebound/source/docs/ipython_examples/FourierSpectrum.ipynb b/rebound/source/docs/ipython_examples/FourierSpectrum.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..f9310c471fa63602044b826cfe17eb16421a5488
--- /dev/null
+++ b/rebound/source/docs/ipython_examples/FourierSpectrum.ipynb
@@ -0,0 +1,407 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Fourier analysis & resonances\n",
+ "\n",
+ "A great benefit of being able to call rebound from within python is the ability to directly apply sophisticated analysis tools from scipy and other python libraries. Here we will do a simple Fourier analysis of a reduced Solar System consisting of Jupiter and Saturn. Let's begin by setting our units and adding these planets using JPL's horizons database:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Searching NASA Horizons for 'Sun'... Found: Sun (10).\n",
+ "Searching NASA Horizons for 'Jupiter'... Found: Jupiter Barycenter (5).\n",
+ "Searching NASA Horizons for 'Saturn'... Found: Saturn Barycenter (6).\n"
+ ]
+ }
+ ],
+ "source": [
+ "import rebound\n",
+ "import numpy as np\n",
+ "sim = rebound.Simulation()\n",
+ "sim.units = ('AU', 'yr', 'Msun')\n",
+ "sim.add(\"Sun\")\n",
+ "sim.add(\"Jupiter\")\n",
+ "sim.add(\"Saturn\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now let's set the integrator to whfast, and sacrificing accuracy for speed, set the timestep for the integration to about $10\\%$ of Jupiter's orbital period."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "sim.integrator = \"whfast\"\n",
+ "sim.dt = 1. # in years. About 10% of Jupiter's period\n",
+ "sim.move_to_com()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The last line (moving to the center of mass frame) is important to take out the linear drift in positions due to the constant COM motion. Without it we would erase some of the signal at low frequencies.\n",
+ "\n",
+ "Now let's run the integration, storing time series for the two planets' eccentricities (for plotting) and x-positions (for the Fourier analysis). Additionally, we store the mean longitudes and pericenter longitudes (varpi) for reasons that will become clear below. Having some idea of what the secular timescales are in the Solar System, we'll run the integration for $3\\times 10^5$ yrs. We choose to collect $10^5$ outputs in order to resolve the planets' orbital periods ($\\sim 10$ yrs) in the Fourier spectrum."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "Nout = 100000\n",
+ "tmax = 3.e5\n",
+ "Nplanets = 2\n",
+ "\n",
+ "x = np.zeros((Nplanets,Nout))\n",
+ "ecc = np.zeros((Nplanets,Nout))\n",
+ "longitude = np.zeros((Nplanets,Nout))\n",
+ "varpi = np.zeros((Nplanets,Nout))\n",
+ "\n",
+ "times = np.linspace(0.,tmax,Nout)\n",
+ "ps = sim.particles\n",
+ "\n",
+ "for i,time in enumerate(times):\n",
+ " sim.integrate(time) \n",
+ " # note we used above the default exact_finish_time = 1, which changes the timestep near the outputs to match\n",
+ " # the output times we want. This is what we want for a Fourier spectrum, but technically breaks WHFast's\n",
+ " # symplectic nature. Not a big deal here.\n",
+ " os = sim.orbits()\n",
+ " for j in range(Nplanets):\n",
+ " x[j][i] = ps[j+1].x # we use the 0 index in x for Jup and 1 for Sat, but the indices for ps start with the Sun at 0\n",
+ " ecc[j][i] = os[j].e\n",
+ " longitude[j][i] = os[j].l\n",
+ " varpi[j][i] = os[j].Omega + os[j].omega"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's see what the eccentricity evolution looks like with matplotlib:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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gsM7RuMY76NYQHBgMGktRpUgVUfvEzRMxb+88RlFxnDHdeHBDtr11xdYIDAjU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UK0w/GVGGOMMcaYckII5TuTVc+gLwVQxzvI/gdAHwC32srMBDAQwDTvgP5o9uDci7x/gtLxP4ox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\nRU5ErkJggg==\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "%matplotlib inline\n",
+ "labels = [\"Jupiter\", \"Saturn\"]\n",
+ "import matplotlib.pyplot as plt\n",
+ "fig = plt.figure(figsize=(12,5))\n",
+ "ax = plt.subplot(111)\n",
+ "plt.plot(times,ecc[0],label=labels[0])\n",
+ "plt.plot(times,ecc[1],label=labels[1])\n",
+ "ax.set_xlabel(\"Time (yrs)\")\n",
+ "ax.set_ylabel(\"Eccentricity\")\n",
+ "plt.legend();"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now let's try to analyze the periodicities in this signal. Here we have a uniformly spaced time series, so we could run a Fast Fourier Transform, but as an example of the wider array of tools available through scipy, let's run a Lomb-Scargle periodogram (which allows for non-uniform time series). This could also be used when storing outputs at each timestep using the integrator IAS15 (which uses adaptive and therefore non-uniform timesteps).\n",
+ "\n",
+ "Let's check for periodicities with periods logarithmically spaced between 10 and $10^5$ yrs. From the documentation, we find that the lombscargle function requires a list of corresponding angular frequencies (ws), and we obtain the appropriate normalization for the plot. To avoid conversions to orbital elements, we analyze the time series of Jupiter's x-position."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 10,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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g2MWSevanBQAAACpqsFS8Ky1txfuQmY1QTKiUmR2jaP8AAADAIMNyguVJW/FeJOluSbPM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\n+ID0zW/GJdqlqGavWhX3ly2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5PXtinH/5l9Jf/EVsSyrY06ZJ3/xm3K+vz1Sszzkn/882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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "from scipy import signal\n",
+ "Npts = 3000\n",
+ "logPmin = np.log10(10.)\n",
+ "logPmax = np.log10(1.e5)\n",
+ "Ps = np.logspace(logPmin,logPmax,Npts)\n",
+ "ws = np.asarray([2*np.pi/P for P in Ps])\n",
+ "\n",
+ "periodogram = signal.lombscargle(times,x[0],ws)\n",
+ "\n",
+ "fig = plt.figure(figsize=(12,5))\n",
+ "ax = plt.subplot(111)\n",
+ "ax.plot(Ps,np.sqrt(4*periodogram/Nout))\n",
+ "ax.set_xscale('log')\n",
+ "ax.set_xlim([10**logPmin,10**logPmax])\n",
+ "ax.set_ylim([0,0.15])\n",
+ "ax.set_xlabel(\"Period (yrs)\")\n",
+ "ax.set_ylabel(\"Power\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We pick out the obvious signal in the eccentricity plot with a period of $\\approx 45000$ yrs, which is due to secular interactions between the two planets. There is quite a bit of power aliased into neighbouring frequencies due to the short integration duration, with contributions from the second secular timescale, which is out at $\\sim 2\\times10^5$ yrs and causes a slower, low-amplitude modulation of the eccentricity signal plotted above (we limited the time of integration so that the example runs in a few seconds). \n",
+ "\n",
+ "Additionally, though it was invisible on the scale of the eccentricity plot above, we clearly see a strong signal at Jupiter's orbital period of about 12 years. \n",
+ "\n",
+ "But wait! Even on this scale set by the dominant frequencies of the problem, we see an additional blip just below $10^3$ yrs. Such a periodicity is actually visible in the above eccentricity plot if you inspect the thickness of the lines. Let's investigate by narrowing the period range:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 12,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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i8Q/fubaOeCiaEnLEx40D3v524E9/SuYfMUL/ud+B64i70RRfiC9bphEW3zkP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+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig = plt.figure(figsize=(12,5))\n",
+ "ax = plt.subplot(111)\n",
+ "ax.plot(Ps,np.sqrt(4*periodogram/Nout))\n",
+ "ax.set_xscale('log')\n",
+ "ax.set_xlim([600,1600])\n",
+ "ax.set_ylim([0,0.003])\n",
+ "ax.set_xlabel(\"Period (yrs)\")\n",
+ "ax.set_ylabel(\"Power\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This is the right timescale to be due to resonant perturbations between giant planets ($\\sim 100$ orbits). In fact, Jupiter and Saturn are close to a 5:2 mean-motion resonance. This is the famous great inequality that Laplace showed was responsible for slight offsets in the predicted positions of the two giant planets. Let's check whether this is in fact responsible for the peak. \n",
+ "\n",
+ "In this case, we have that the mean longitude of Jupiter $\\lambda_J$ cycles approximately 5 times for every 2 of Saturn's ($\\lambda_S$). The game is to construct a slowly-varying resonant angle, which here could be $\\phi_{5:2} = 5\\lambda_S - 2\\lambda_J - 3\\varpi_J$, where $\\varpi_J$ is Jupiter's longitude of pericenter. This last term is a much smaller contribution to the variation of $\\phi_{5:2}$ than the first two, but ensures that the coefficients in the resonant angle sum to zero and therefore that the physics do not depend on your choice of coordinates.\n",
+ "\n",
+ "To see a clear trend, we have to shift each value of $\\phi_{5:2}$ into the range $[0,360]$ degrees, so we define a small helper function that does the wrapping and conversion to degrees:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def zeroTo360(val):\n",
+ " while val < 0:\n",
+ " val += 2*np.pi\n",
+ " while val > 2*np.pi:\n",
+ " val -= 2*np.pi\n",
+ " return val*180/np.pi"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we construct $\\phi_{5:2}$ and plot it over the first 5000 yrs. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 13,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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qWrnaKdUvTi452ctSegBvZ4+MNwHOsdZeBqwC6rqIK1XdusFBB8FTT7mORPml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\nPvdc2il1wQI44ojaxmT1x4V4QXR0Vr5vH9x6a1qD2Bpb+/5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+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "phi = [zeroTo360(5.*longitude[1][i] - 2.*longitude[0][i] - 3.*varpi[0][i]) for i in range(Nout)]\n",
+ "fig = plt.figure(figsize=(12,5))\n",
+ "ax = plt.subplot(111)\n",
+ "ax.plot(times,phi)\n",
+ "ax.set_xlim([0,5.e3])\n",
+ "ax.set_ylim([0,360.])\n",
+ "ax.set_xlabel(\"time (yrs)\")\n",
+ "ax.set_ylabel(r\"$\\phi_{5:2}$\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We see that the resonant angle $\\phi_{5:2}$ circulates, but with a long period of $\\approx 900$ yrs (compared to the orbital periods of $\\sim 10$ yrs), which precisely matches the blip we saw in the Lomb-Scargle periodogram. This is approximately the same oscillation period observed in the Solar System, despite our simplified setup!\n",
+ "\n",
+ "This resonant angle is able to have a visible effect because its (small) effects build up coherently over many orbits. As a further illustration, other resonance angles like those at the 2:1 will circulate much faster (because Jupiter and Saturn's period ratio is not close to 2). We can easily plot this. Taking one of the 2:1 resonance angles $\\phi_{2:1} = 2\\lambda_S - \\lambda_J - \\varpi_J$,"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 14,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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kNqi7oGvEh2H4OIBvn/j7XQC+e6bPtQCulcbuOYMlgIUmNehh3VuHtqbDal9L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\ngg==\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "phi2 = [zeroTo360(2*longitude[1][i] - longitude[0][i] - varpi[0][i]) for i in range(Nout)]\n",
+ "fig = plt.figure(figsize=(12,5))\n",
+ "ax = plt.subplot(111)\n",
+ "ax.plot(times,phi2)\n",
+ "ax.set_xlim([0,5.e3])\n",
+ "ax.set_ylim([0,360.])\n",
+ "ax.set_xlabel(\"time (yrs)\")\n",
+ "ax.set_ylabel(r\"$\\phi_{2:1}$\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "In this case, since we are far from this particular resonance (the 2:1), the corresponding resonance angles vary on fast (orbital) timescales, and their effects simply average out."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.10"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/rebound/source/docs/ipython_examples/FrequencyAnalysis.ipynb b/rebound/source/docs/ipython_examples/FrequencyAnalysis.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..6086f459d2be7df64457aaba3227276637eafa02
--- /dev/null
+++ b/rebound/source/docs/ipython_examples/FrequencyAnalysis.ipynb
@@ -0,0 +1,254 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Frequency Analysis\n",
+ "This examples shows how to perform a Modified Fourier Transform (MFT), or a Frequency Modified Fourier Transform (FMFT) on timeseries data using REBOUND. This can be used to determine the fundamental or secular frequencies of planetary systems. The (Frequency) Modified Fourier Transform is much more accurate in determining the frequencies than a simple Fourier Transform. For more information on these methods see: [Laskar (1988)](https://ui.adsabs.harvard.edu/abs/1988A%26A...198..341L/abstract), [Laskar (1990)](https://ui.adsabs.harvard.edu/abs/1990Icar...88..266L/abstract), and [Sidlichovsky and Nesvorny (1996)](https://ui.adsabs.harvard.edu/abs/1996CeMDA..65..137S/abstract).\n",
+ "\n",
+ "In this example, we will determine the secular frequencies present in the outer Solar System. Throughout the example, we work in units where $G=1$ and one year is equivalent to $2\\pi$ code units."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import rebound\n",
+ "import numpy as np\n",
+ "sim = rebound.Simulation()\n",
+ "rebound.data.add_outer_solar_system(sim)\n",
+ "sim.integrator = \"whfast\"\n",
+ "sim.dt = sim.particles[1].P/30.13 # About 30 steps per Jupiter orbit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We now integrate forward in time, taking snapshots every 120000 days using the Simulationarchive."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "step = int(120000.0/365.25*np.pi*2/sim.dt)\n",
+ "sim.save_to_file(\"output.bin\",step=step,delete_file=True)\n",
+ "Nsamples = 2**13 # Needs to be a power of 2\n",
+ "sim.integrate(step*sim.dt*(Nsamples-1),exact_finish_time=False)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We now have a Simulationarchive with $2^{13}$ snaphots."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "sa = rebound.Simulationarchive(\"output.bin\")\n",
+ "print(sa)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We next extract the eccentricity e and the periastron $\\bar \\omega$ of Jupiter from this archive."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "inp = np.zeros(Nsamples*2)\n",
+ "for i, sim in enumerate(sa):\n",
+ " o = sim.particles[1].orbit()\n",
+ " inp[i*2+0] = o.e*np.cos(o.pomega)\n",
+ " inp[i*2+1] = o.e*np.sin(o.pomega)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's quickly plot this dataset."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "fig, ax = plt.subplots()\n",
+ "ax.set_xlabel(\"Time [Myrs]\")\n",
+ "ax.set_ylabel(\"Eccentricity of Jupiter\")\n",
+ "ax.plot(np.arange(Nsamples)*step*sim.dt/np.pi/2.0/1e6,np.sqrt(inp[::2]**2+inp[1::2]**2));"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Next, we perform the Frequency Modified Fourier Transform algorithm on this time series to extract the secular frequencies, amplitudes, and phases. We specify a minimum and maximum frequency to ensure the FMFT only returns modes in this range. Here, we choose the range of -60\"/year to +60\"/year."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "minfreq = 60.0/1296000.0*step*sim.dt\n",
+ "freq, amp, phase = rebound.frequency_analysis(inp, type=1, minfreq=-minfreq, maxfreq=minfreq)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can now print out the 10 most dominant frequencies in the signal. Also shown are the amplitudes and the phases."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "nu = 4.24\"/yr A = 0.0441150 phi = 30.0°\n",
+ "nu = 28.24\"/yr A = 0.0156774 phi = 306.1°\n",
+ "nu = 3.09\"/yr A = 0.0018430 phi = 119.5°\n",
+ "nu = 52.25\"/yr A = 0.0005711 phi = 42.2°\n",
+ "nu = 29.29\"/yr A = 0.0002578 phi = 253.3°\n",
+ "nu = 27.18\"/yr A = 0.0002552 phi = 183.9°\n",
+ "nu = 5.35\"/yr A = 0.0000729 phi = 135.4°\n",
+ "nu = 53.36\"/yr A = 0.0000541 phi = 325.2°\n",
+ "nu = 4.17\"/yr A = 0.0000483 phi = 75.7°\n",
+ "nu = 51.18\"/yr A = 0.0000191 phi = 282.4°\n"
+ ]
+ }
+ ],
+ "source": [
+ "nfreq = len(freq)\n",
+ "for i in range(nfreq):\n",
+ " print(\"nu = %5.2f\\\"/yr A = %.7f phi = %5.1f°\" % (freq[i]*1296000.0/step/sim.dt, amp[i], phase[i]/np.pi*180.0))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can also use these few dominant modes to create a very accurate approximation of the input data. Note that we don't need to worry about converting units in the following code."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "approx = np.zeros(Nsamples*2)\n",
+ "for i in range(nfreq):\n",
+ " approx[0::2] += amp[i]*np.cos(freq[i]*np.arange(Nsamples)+phase[i])\n",
+ " approx[1::2] += amp[i]*np.sin(freq[i]*np.arange(Nsamples)+phase[i])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The following plot shows the original signal (blue) and the reconstructed signal consiting of 10 modes (orange). They are a very good match."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots()\n",
+ "ax.set_xlabel(\"Time [Myrs]\")\n",
+ "ax.set_ylabel(\"Eccentricity of Jupiter\")\n",
+ "ax.plot(np.arange(Nsamples)*step*sim.dt/np.pi/2.0/1e6,np.sqrt(inp[::2]**2+inp[1::2]**2), label=\"input signal\")\n",
+ "ax.plot(np.arange(Nsamples)*step*sim.dt/np.pi/2.0/1e6,np.sqrt(approx[::2]**2+approx[1::2]**2),label=\"reconstruction\")\n",
+ "ax.legend();"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.13.7"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/rebound/source/docs/ipython_examples/HighOrderSymplectic.ipynb b/rebound/source/docs/ipython_examples/HighOrderSymplectic.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..0ff58ef0fc719586ba3f3672672382db7a7e3e81
--- /dev/null
+++ b/rebound/source/docs/ipython_examples/HighOrderSymplectic.ipynb
@@ -0,0 +1,278 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# High Order Symplectic Integrators\n",
+ "\n",
+ "These notebooks show how to use the high order symplectic integrators of Wisdom et al. (1996) and Laskar & Robutel (2001) with REBOUND. See Rein, Tamayo & Brown (2019) for an overview of these integrators. \n",
+ "\n",
+ "Let us start by importing REBOUND, as well as numpy and matplotlib."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import rebound\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "High order symplectic integrators with a fixed timestep are well suited for planetary systems in which planets orbit the primary mass on almost Keplerian orbits. The planet-planet interactions need to be a perturbation. If they are not, a different integrator, such as IAS15 or MERCURIUS is better suited.\n",
+ "\n",
+ "On system that we know is stable is the outer Solar System. So we will use this as our test case. We can either import accurate data from NASA Horizons, or, because this is just a test, use some of the initial conditions which come with REBOUND to setup a simulation."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 2,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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vvIL9+/dj1apVUKlUbMciLVBBElYYjUb861//wr59+/Dee+/ho48+onUriVWaNWsWPvzwQyiVSjz//POor69nOxL5P1SQpNcZjUasWLECGzduxPLly/HCCy/QTFVi1YYPH44XXngBxcXFWL9+PRoaGtiOREAFSXqZ0WjE008/je3bt2Pr1q144okn2I5ECCdERETg448/xpUrV/Daa69Bo9GwHcnqUUGSXmMwGLBs2TL873//w44dO/Doo4+yHYkQTunTpw/+85//4Pr163jrrbeg1+vZjmTVqCBJrzAYDFiyZAm+++47fPXVV5g/fz7bkQjhpP79+2Pt2rVITk7GunXrYDQa2Y5ktaggSY8zGAx4+eWX8eOPP+Kbb77Bgw8+yHYkQjht2LBhePPNN3H8+HF89tlndJ0kS6ggSY9iGAb//Oc/sXPnTnz33Xe4//772Y5ECC+MGzcOL730Evbt24ft27ezHccqidkOQCzb22+/ja1bt+LLL7/EnDlz2I5DCK9Mnz4d9fX1+OKLL+Do6EhHX3oZFSTpMZ9//jnee+89rFu3Do8//jjbcQjhpQceeAB1dXXYvHkzHB0dMWPGDLYjWQ0qSNJt4uPjsXr1apSUlEAqleLmzZt46aWX8K9//YvtaITw2uLFi1FfX48PP/wQDg4OtJB/L6GCJN3iiSeewM6dO9vcX1lZyUIaQiyLQCDAypUr0dDQgHfffRfr1q3DsGHD2I5l8WiSDumy+Ph4s+UIADt27MDRo0d7OREhlkcoFGLVqlWIiYnBm2++iYyMDLYjWTwqSNJlq1evvuPn33jjjV5KQohlE4vFePvtt9G/f3989tlnKC0tZTuSRaOCJF1WUlLSpc8TQtpPJpNhzZo1aGpqwttvv42mpia2I1ksKkjSZb6+vl36PCGkYxwdHfHuu+9CpVLhk08+oYUEeggVJOmyd955546fX7t2bS8lIcR6BAUF4fHHH8fx48fxxx9/sB3HIlFBki67++67sXjxYrOfW7x4MSZPntzLiQixDhMnTsSsWbOwceNG3Lx5k+04FocKknSLbdu2ISEhASNHjkRgYCBGjhyJhIQEbNu2je1ohFi0p556Cv7+/li7di1UKhXbcSyKgKGD1yZ1dXWQy+VQKpVwcnJiOw4hhLRLUVERnnnmGYwePRqvvPIKbUB+Bx15nacRJCGE8Jy/vz+ee+45HD16FIcOHWI7jsWglXQI6WFqtRoKhQINDQ2mW319fauPm++zsbGBUCiEUqmETCaDjY0NZDLZbf8sl8vh4uICPz8/ODo60sjBik2aNAlXr17Fxo0b0a9fPwQHB7MdiffoEGsLdIiVdEVtbS1yc3ORl5dn+u/NmzdhZ2eH4uLiNuUllUrh6OgIBwcH083LywtSqRS1tbVQq9XQaDSm//71z3q9HmFhYcjPzwcA2Nvbw9fXF35+fvD19W11c3d3p/K0AhqNBitWrIBer8fGjRtha2vLdiTO6cjrPBVkC1SQf49hGKt/oW1sbERWVhays7Nx8+ZNUyEqlUoAgEgkQkBAAEJCQhASEoLAwEC4uLjAycmpVSFKJJIu5TAYDKivr0dlZSVKSkpQUlKC4uJi059broMrlUoxcOBABAYGIjg4GNHR0QgICLD6/5eWqLCwEM888wzGjh2Ll19+me04nEMF2UlUkHfGMAwYhoFQaF2nrrVaLVJTU3Hu3DmcO3cOCoUCNjY2KCkpQVBQEEJCQhAcHIzQ0FCEhITA398fYjH7Zy+0Wi3KyspMxVlbW4usrCykpaXBaDRCLpdjwIABiI6ORnR0NEJDQyESidiOTbrB0aNH8f7772PVqlWYNGkS23E4hQqyk6gg78xoNEIgEFj8qMNoNOLGjRumQrx06RLUajWcnZ0RGxuL4cOHY/DgwQgODublmwWVSoXMzEykpqYiNTUVmZmZ0Gq1sLW1xYABAxAVFYXo6GhERER0eZRL2LNp0yYkJCRgy5Yt8PDwYDsOZ1BBdhIV5O0ZjUYA4GUhtIdCoUBiYiLOnDmD8+fPo6amBlKpFEOHDsWIESMwYsQIhIeHW+S/X6fT4fr166bCTE9Ph1AoRGBgIAIDAzFhwgQMGjSIRpc809DQgGXLliEsLAzvvPOOxb+xbS8qyE6igjTPUg+t6nQ6nD59Gvv27UN5eTkEAgHEYrGpEAcNGgSpVMp2zF5nMBhw8+ZNXLx4EcePH0dxcTGcnZ0xduxYjB8/HpGRkfRiyxOJiYlYs2YNXn75ZVrR6v9QQXYSFaR5lnZoNSsrC/v27cNvv/0GhUKBAQMGYPbs2YiLi4Obmxvb8TiFYRjcvHkTJ06cwMmTJ1FdXQ1PT0+MHz8eEyZMoEsJeGDdunVITk7Gl19+CRcXF7bjsI4KspOoINuylEOrCoUCv/32G/bt24esrCy4ublh1qxZuOeee9CnTx+24/ECwzBIS0vDyZMncebMGdTX1yMoKAgTJkzApEmT4O7uznZEYoZSqcTSpUsxaNAgvP7662zHYR0VZCdRQbZmNBrBMAxvzz0ZjUYkJSVh9+7dOHXqFABgwoQJmD17Nu666y7e/ru4QK/X4/Llyzh58iRu3LgBlUqFwYMHY86cOQgKCmI7HvmL48eP48cff8TixYsxfPhwtuOwigqyk6gg/z+GYWAwGCAUCnk3ejQYDDh48CB+/fVXFBYWws3NDXPmzMH06dPh7OzMdjyL09jYiGPHjmHv3r2oqqrCsGHDcN9996Ffv34Wc1ie7xiGwapVq1BVVYXNmzdz4jIktlBBdhIV5P9nMBjAMAyvfpH0ej0OHDiALVu2oLCwEJMmTcKSJUswaNAgtqNZBYPBgFOnTuGXX35BQUEBIiMjMXfuXMTGxlJRckBeXh6WL1+OJ554Avfddx/bcVhDBdlJVJC3NI8eRSIRL17Y9Ho99u3bh61bt6KoqAhxcXF4+umnERkZyXY0q8QwDC5evIhffvkFGRkZ8Pf3x9y5czF+/HheveGyRF988QXi4+Oxfft2q52wQwXZSVSQt+j1eggEAs6fo9PpdNi7dy+2bt2KkpISTJkyBU8//TT69u3LdjTyfzIzM/Hzzz/j/PnzcHNzw0MPPYSJEyfSAgQsqa+vx5IlSzBixAi88MILbMdhBRVkJ1FB3prYYjQaOT161Ol02LdvHzZv3oyysjJMnToVTz31FMLDw9mORm6jsLAQv/zyC3Jzc6HX6/HEE09g6NChbMeySr/99hs+//xzfPLJJ4iIiGA7Tq+jguwkay9IhmGg0+kgEok4O3o8e/YsvvnmG9TU1CAwMBBPPvkkXabBI4WFhdi+fTtSU1MxfPhwLFq0CF5eXmzHsipGoxErVqyARCLBxx9/zNk3wj2FNkwmnWIwGDh7aLWmpgYvvfQSFi1aBJ1Oh3feeQcffPABlSPPBAQE4K233sK//vUv5ObmYuXKldi1axc0Gg3b0ayGUCjE008/DYVCgTNnzrAdh9NoBNmCNY8gm0ePYrGYU5d1MAyDX375Bf/5z38AAK+++irmzJljde96LZFGo8HPP/+Mffv2wdnZGYsWLcKIESPo/20veeedd1BUVIQvvviCk2+KewqNIEmHNY8euVSON27cwMKFC/Haa69h4sSJOHToEObOnUsvoBZCJpNh/vz5+PTTTxEcHIwPPvgAb7/9NoqKitiOZhXmz5+P4uJi0yIapC3uvBoS1rScmMMFGo0Gn376Ke655x5UVFTg66+/xn/+8x+4urqyHY30AG9vb6xatQqvvfYaKisr8cILL+DXX3+FTqdjO5pF69OnD0aMGIEffvgBBoOB7TicRAVJODV6TEpKwj/+8Q9s3boVy5Ytw4EDBzBy5Ei2Y5FeEBMTg08++QQPPvggDh06hDfeeAOlpaVsx7JojzzyCIqLi3Hy5Em2o3AS+6+IhFUGgwFGo5H1C7h1Oh02bNiA9957D+7u7ti/fz9WrlwJmUzGai7SuyQSCe677z6sWrUKGo0Gr776Kk6fPs12LIsVFhZGo8g7oIK0cs2LArB5Xq+0tBQPP/wwNm/ejAcffBDffvstwsLCWMtD2BccHIz3338fsbGx+Pzzz7Fp0yao1Wq2Y1mkRx55BCUlJTSKNIMK0opxYb3Vs2fP4h//+AfKysrw/fffY8GCBZw41EvYZ2Njg+XLl2P58uVISkrCqlWrkJ+fz3YsixMWFoaRI0fSKNIMeiWyYmzu1mE0GrFp0yY89thjiIqKwoEDB2hRcWLWuHHj8J///AdSqRSvv/46Dh8+DLo6rXvNnz8fJSUlOHHiBNtROIUK0ko1z1xlY/SoVCrx5JNP4qOPPsLy5cuteuFk0j4+Pj5Yu3YtJk+ejB07duC///0vGhsb2Y5lMcLCwjBq1Cjs37+fRpEtUEFaKb1ez8roMSMjA7Nnz0ZycjK2b9+O5557jjOXlxBuk0gkWLRoEV566SWkp6dj/fr1KCgoYDuWxXjwwQeRl5eHpKQktqNwBhWkFWJr9Lh7927cd999kMvl2L9/PyZMmNCr359YhmHDhmH9+vUQCAR49913ce3aNbYjWYTw8HD0798f+/btYzsKZ1BBWqHmC7B7a/RoNBrx6aef4vvvv8fcuXPx008/wd/fv1e+N7FM7u7uePXVVxEaGor3338f58+fZzuSRZg9ezauXbuG69evsx2FE6ggrUzzZsi9NXo0GAx4+eWXsXXrVsyZMwfvvfceXdtIuoWNjQ1eeuklxMbG4rPPPkN8fDzbkXgvNjYWPj4+OH78ONtROIEK0srodDoIBIJeKUidTocVK1bgl19+wXvvvYdHH320x78nsS5isRjPPPMMpk6diq+++gq7d++mGa5dIBQKMW3aNMTHx9MkKFBBWpXeHD2q1WosXboUR44cwRdffIF77723x78nsU4CgQALFizA/PnzsXfvXnz55Zc0E7MLJkyYAL1ejz///JPtKKyjgrQivbUwQGNjIx577DEkJSVh586dmDp1ao9+P0IEAgFmzpyJp59+GmfOnMHHH38MrVbLdixecnV1xeDBg+kwK6ggrYper4dIJOrRZeUUCgXmz5+PtLQ0fPPNNxg7dmyPfS9C/mrMmDF48cUXkZGRgX//+99oaGhgOxIvTZo0CRkZGSgrK2M7CquoIK2EwWCAXq/v0dFjVVUVHnroIeTn5+PHH3/E8OHDe+x7EXI7gwYNwhtvvIGqqips3rwZTU1NbEfinREjRsDW1tbqR5G8Kch169Zh+PDhcHR0hKenJ+69915kZWW1+hq1Wo3ly5fDzc0NDg4OuO+++1BeXs5SYm5pXhigpy7KLy0txbx581BdXY3du3cjKiqqR74PIe0RGhqKV199Ffn5+diwYQMdbu0gmUyGu+66C8ePH7fqSU+8KciTJ0+aFi2Oj4+HTqfDlClTWs20ev7553HgwAHs3r0bJ0+eRElJCebOnctiam5gGKZHR4+VlZVYsmQJvL29sWfPHoSHh/fI9yGkI/z9/bFy5Urk5eVh69atMBqNbEfilYkTJ6K8vNyqF2IQMDx9e1BZWQlPT0+cPHkS48aNg1KphIeHB77//nvcf//9AIDMzEz069cPiYmJ7dp0t66uDnK5HEqlEk5OTj39T+g1er0earUadnZ23b44QFNTE+6//36IRCJs2rQJAQEB3fr4hHRVSkoKNmzYgDFjxuDRRx9ldWs3PmEYBsuWLcOgQYPw7LPPsh2n23TkdZ43I8i/UiqVAG7NuAKA5ORk6HQ6xMXFmb4mMjISgYGBSExMNPsYGo0GdXV1rW6WSKfTQSQSdXs5GgwGPPvss8jOzsa6deuoHAknDRw4EIsWLcKpU6ewd+9etuPwhkAgwMSJE/Hnn39a7SFqXhak0WjEc889h7vuust0rqusrAxSqRTOzs6tvtbLy+u2M7HWrVsHuVxuulniC3xPXvv47rvvIj4+Hps3b6ZzjoTTRo8ejXnz5uHgwYM4evQo23F4Y8KECWhqasK5c+fYjsIKXhbk8uXLkZaWhl27dnXpcVatWgWlUmm6FRYWdlNC7uiplXN27tyJL7/8Eu+++y4mT57crY9NSE+YNm0apk6dih9++IHWbm0nX19fREZGWu1sVt4V5LPPPouDBw/i+PHjrRa89vb2hlarhUKhaPX15eXl8Pb2NvtYMpkMTk5OrW6WpieufUxISMDq1auxdOlSPP744932uIT0tHnz5mHkyJHYtm0bMjIy2I7DC5MmTcKlS5dQW1vLdpRex5uCZBgGzz77LH799VccO3YMISEhrT4fExMDiUTS6vBJVlYWCgoKMGrUqN6Oywk9ce1jamoqnnrqKUydOhVvvvlmtz2uNTIYDNBoNGhqakJ9fT3q6uqgUChQU1OD6upqVFdXo6qqClVVVaaPa2pqUFtbC6VSibq6OtTX16OpqQlqtRparRZ6vZ5ma96BQCDAokWLMGDAAGzcuBFFRUVsR+K8u+66C2KxGCdPnmQ7Sq/jzSzWZ555Bt9//z327duHiIgI0/1yuRy2trYAgKeffhq///47vvrqKzg5OWHFihUAgLNnz7bre1jaLFaNRgOtVgtHR8duebySkhLMnDkTvr6+2LNnj+l5J39Pq9VCp9OZ/tu85VjzyF4kEkEsFps2sRYIBK2uWW2eYNXy15VhGFMZtvxz899vvu61+dbbm2NzmVarxaZNm1BZWYk33niDfpb/xoYNG6DRaPCvf/2L7Shd1pHXed4U5O0OEe7cudN0mE+tVuPFF1/EDz/8AI1Gg6lTp2LTpk23PcT6V5ZWkA0NDRCJRN3yy9/Q0IAFCxagrKwMBw4cgIeHRzcktFxarRYqlQoajQYajQYMw0AoFEIikbS6icXibj0E3rwZttFohMFggNFobFWqzd+PCvPWyk9r165Fv379sGzZMrr84w5OnDiBzz//HDt37uy2N9xs6cjrfO9uKd8F7elxGxsbbNy4ERs3buyFRNzW/CJpY2PT5cdiGAYffvghKioq8NVXX1E5msEwDFQqFVQqFZqammAwGCAQCGBrawu5XA6ZTAapVNrjL8LNI9C/ai5Lo9EIvV7favKWtZalu7s7Hn30UWzZsgWnTp3C+PHj2Y7EWVFRUWAYBunp6e26ptxS8KYgScd05+zVPXv24IsvvsCXX36JyMjIbkhnOVQqFRoaGtDY2Aij0QipVAp7e3vY2dlBJpNxZlTSPGps1nKE2bw1VMtDvNZi6NChmDBhAn766SeEhoZa5KVe3cHd3R0+Pj5ISUmxqoK0nt8EK6PT6brlha6wsBCrVq3CvHnzcM8993RDMv4zGAxQKBTIz89HcXExVCoV5HI5/P394e/vD1dXV9jY2HCmHM1pPtwrk8kgk8kgFotNSxLqdDqr2k/x/vvvh4+PD7Zu3Qq1Ws12HM6Kjo5Gamoq2zF6FRWkBequtVebV8qRy+X497//3U3p+Euj0aCsrAy5ubmorq6GjY0N/Pz8EBgYCBcXF0ilUrYjdkrzkYbm86ICgcB0KLZ5D1FLJpFIsGzZMiiVSnz33XcW/+/trOjoaJSUlKCmpobtKL2GCtIC6fV6ALd+8bti48aNOHfuHDZu3GgRk5Y6S6VSobi4GPn5+WhqaoKbmxuCg4Ph5eVlcbMfW5alUCg0rcRk6UXp6emJhQsX4vz58+2e9W5tmlfLsqZRJBWkBWre2qorh1hTUlLwn//8BytWrLCqcw4tqdVqFBUVIT8/H1qtFt7e3ggJCYGLi0uPbRvGJUKhsNUkHoZh2pRkfHw8Ro0ahaCgIIwaNQrx8fEspe264cOHY8yYMfjhhx9QUlLCdhzOcXJyQnBwMFJSUtiO0muoIC2QTqfr0uFVlUqFZ555Bv369cPLL7/cjcn4QafTobi4GHl5edBqtfD19UVISAicnJw4fV6xpwgEAtOtZUk+8cQTmDJlCpKSklBQUICkpCRMmTIFS5YsYTlx5z344IPw8PDA1q1brXaB7juJjo5GWlqaRR9NaIkK0sI0T+XvyuHVd955BwUFBfjiiy+6fJiWT4xGIyorK5GTk4PGxkb4+PiYipHAtPiAQCBAfHw8du7cafbrtm/fztsFwaVSKZYuXQqxWIw//viD7TicEx0djaqqqttuAGFpqCAtTPP5x86OII8ePYodO3ZgzZo1VrXxcWNjI3JyclBVVQU3Nzf06dMHcrncKkeM7bF69eo7fv6NN97opSTdz9fXFzExMUhISEB5eTnbcTilf//+EAqFVnOYlQrSwnRlcfK6ujps2LAB99xzDxYtWtQD6bjHYDCguLgYubm5kEgkCAsLg6enp1VdC9gZf3eOju/n8OLi4uDq6oqffvrJag4ntoetrS3Cw8ORlpbGdpReQa8CFkan03X6sOiHH34Ig8GANWvWWMXIqb6+Hjk5OVAqlabzjHy9VKO3+fr6dunzXCeRSDBv3jxkZmbiypUrbMfhlKioKKSmplrFGwcqSAvSPB2/M4dXc3NzsXXrVkycOBF+fn49kI47GIZBSUmJadQYHh4OV1dXtmPxyjvvvHPHz3t5eUGlUvVSmp4RFRWFgQMHYs+ePdBoNGzH4Yzo6GjU19cjPz+f7Sg9jgrSgjSff+zMJQhr1qyBp6cnnnnmme6OxSk6nQ45OTmorq6Gr68vQkNDrWoiUne5++67sXjxYrOfGz16NI4ePYrHH38cOTk5vZyse91///1obGzEoUOH2I7CGZGRkZBIJFaxnyYVpAXp7PnHs2fP4uDBg3jzzTe7ZXFzrmpsbMT169eh1WoRGhoKd3d3tiPx2rZt25CQkICRI0ciMDAQI0eOREJCAv78808kJiYiPT0do0ePxu+//8521E5zc3PDlClTcPToUZqw838kEgkiIyORlZXFdpQex5vtrnoD37e7UiqVEIvFsLe3b/ffMRqNiIuLg1AoxJEjRyx2ckp1dTWKiopgZ2eH4OBgGjX2AqVSiSeeeAI1NTWYPXs2Vq5cyctz2zqdDmvXroW7uzueffZZXv4buttXX32F5ORkbNiwge0oHdaR13nLfDW0QgzDQKfTdfjw6p49e3D16lWsXbvWYsuxuLgYBQUFcHV1RZ8+fagce4lcLsfu3bsxbtw4rFq1Ci+++CIvF0FvOWHn6tWrbMfhhNDQUJSVlaGpqYntKD3KMl8RrVDLLYvaq6mpCe+88w5mz55tkcvJMQyD3NxclJeXw8/PDwEBAfTuv5cJhUK8/fbb+Pzzz7F161Y8/PDDvHxRjYqKQnR0NPbv308TdgAEBwfD398fBQUFbEfpUVSQFqIzE3Q2btyI6urqv73om48YhsHNmzdRU1ODkJAQeHp6sh3Jqi1evBh79uxBRkYGHn/8cdTX17MdqcPmzp0LhmGQmJjIdhTW+fj4oLS0lPfXu/4dKkgLYTAYOjRBp6ysDJ9++imefPJJBAcH92y4XmY0GpGTkwOFQoE+ffrAxcWF7UgEwLRp07Bjxw6cOXMGs2bNgkKhYDtSh3h6eiIsLAzHjx/n5aHi7iSRSODu7o7S0lK2o/QoKkgL0VyQ7bVlyxZERUXh+eef78FUva+5HOvr6xEeHg65XM52JNJCbGwsfv/9dygUCixdupR3I8m4uDgoFApcvHiR7Sis8/Hxsfg1WakgLURHNkguKyvDsWPHcO+991pUgTAMY1poPDw8nJczka3B4MGD8b///Q9//vknHnzwQajVarYjtZu3tzeio6ORkJAAo9HIdhxWeXt70wiScB/DMDAaje0eQW7fvh3Z2dmYP39+DyfrXTdv3oRSqURYWBgcHR3ZjkPuYNCgQfj5559x8eJFPPbYY6Zz6Hxw9913o6Kiwqo2DjaneQRpyVcKUkFagI5M0FGr1di+fTsWLFhgUSOsoqIiVFZWIjQ01KL+XZZs1KhR+Oabb3DkyBGsWbOGNy+0QUFBCA8PR0JCAm8y9wQfHx/odDpUV1ezHaXHUEFagI5c4rF7927U1NTgySef7OlYvaaqqgpFRUUIDAyEm5sb23FIB0ydOhU7duzApk2b8OGHH7Idp93uvvtuFBQU4Pr162xHYY23tzcAWPRhVipIC9C8xNzfYRgGX3zxBaZNm4awsLBeSNbz6uvrcePGDXh4ePB+BwlrNWfOHLzyyitYu3Ytb9Y87du3L/z9/ZGQkMB2FNZ4enpCJBJRQRJua29Bnjp1Cunp6RazILlGo0F2djYcHR0RGhrKdhzSBS+//DKefPJJLFmyhBcLnAsEAtx99924fv26VexqYY5IJIKnp6dFz2SlgrQA7S3ITZs2YcCAARg7dmwvpOpZDMPg+vXrYBgGffv2pRVyeE4gEGD16tXw8fHB448/zouZrQMHDoSnp6dVjyItfSYrFSTPtXcG640bN3Do0CE888wzFlEm+fn5aGxsRERERKf2vyTc4+DggK+//ho5OTl45ZVX2I7zt4RCISZNmoTq6mrU1NSwHYcVgYGBFr1oAhUkzxmNRhiNxr8tvc2bN8Pd3R33339/LyXrOXV1dSgqKoK/vz8cHBzYjkO6Uf/+/fHRRx/hm2++wf79+9mO87diYmJQW1uL5ORktqOwwtHRETdu3GA7Ro+hguS55ouV77QTR11dHb777jssXryY9/s9GgwGXL9+HU5OTvDz82M7DukBjzzyCJYuXYp//vOfKCoqYjvOHUmlUkRFReHSpUtWecmHk5MTmpqaeHUda0dQQfJcewpy//79cHV1xaJFi3orVo/Jzc2FTqej844W7rXXXoOjoyPWrl3L+eKJiYlBRUWFxS/cbU7zNcd1dXUsJ+kZVJA8156C/PbbbxEVFQUfH5/eitUjampqUFpaipCQEN6PhMmdyeVyfPbZZ/jll1/wyy+/sB3njvr27QsHBwdcunSJ7Si9rrkg+bambntRQfJc8/nH242mKisr8eeff2L69Om9nKx7GY1GZGdnw8XFxXSBMrFsEydOxD/+8Q+8+eabnB6hCIVCDB48GJcuXbK69Vmb13JWKpUsJ+kZVJA8ZzQa7zh6PHDgAAQCAWbNmtWLqbpfQUEBNBqNxSxwQNpn7dq1aGpqwrp169iOckdDhw5FXV0dbt68yXaUXtW85jGX38B0BRUkzzEMc8eC3Lt3L8aMGcPrJdi0Wi0KCwvh5+cHW1tbtuOQXuTj44NXXnkFO3bs4PTi4M3LHFrbbFaZTAZfX1+oVCq2o/QIKkieu9MIUqFQ4OTJk5g9e3Yvp+peubm5EAqFCAoKYjtKjzAajdBoNGhsbIRSqURdXV2rW2NjI1QqFbRarcXOFryTJUuW4O6778ZHH33E2Qk7AoEAQ4cORUpKitX9P1KpVGhoaGA7Ro+gK6x57k6LBPz222/Q6/W45557ejlV92lsbERZWRnCwsIsZkEAlUqFpqYmqFQqqFQqGAyGVm9yZDIZRCKR6byyUCg0FYNIJIJQKIRYLIZEIoFUKoVEIrHoGb0SiQSLFy/GQw89hCNHjmDq1KlsRzJr6NChiI+PR0ZGBgYOHMh2nF4jlUqh1WrZjtEjLOMVx4oZjUZIJBKzn9u7dy9GjhzJ69mrN27cgI2NDe8XIm9oaIBCoUBdXR30ej0kEgns7Ozg5OQEGxsbyGQyiMXiVsXYUvOCEEajEXq9Hnq9HhqNBhqNBgKBABKJBDKZzGLLcsKECXjwwQexZcsWTJkyhZP/Rk9PT/j7++PSpUtUkBaCCpLnbneItaGhAUePHsWaNWt6P1Q3USgUUCgU6Nev3x3Ps3KVwWBAVVUVqqqqoNfrIZPJ4OLiAicnJ9jZ2XXoRV4oFJqeA6lUarrfaDRCp9NBp9NBpVJBrVabRpbt3UCbDwQCAR5++GHMnTsXx44dw+TJk9mOZFZMTAwuXLgAvV5vMUc8/o5UKoVOp2M7Ro/g36sOaeV2BXno0CFoNBpeH17Nz8+Hra0tPDw82I7SIXq9HoWFhUhNTUVJSQns7e3Rp08fREZGwsfHB/b29t02AhIKhZDJZHBwcDCNRg0Gg6ksLemyg5EjR2L48OH49NNPOXsusk+fPqioqEBhYSHbUXqNJY8gqSB5rPmQmzkHDx7E4MGDERwc3LuhuklTUxMqKyt5tZwcwzAoLS3F1atXUV5eDnd3d0RFRSE4OBj29vY9/v0FAgGkUikcHBxMs33VajW0Wi1nC6UjBAIB/vnPf+LChQtISkpiO45Z3t7esLW1tarLPaRSKTQaDdsxegQVJM+ZK0i9Xo/U1FTMmzePhUTdo7CwEBKJhDeLAjQ0NCA1NRWFhYVwc3PDoEGD4O/vf9vzwz1NJBKZzm0CgE6ns4hdFyZPnoz+/fvj008/ZTuKWUKhEMHBwRa9gPdf0SFWwivp6elIS0vDkCFD2I7SKXq9HiUlJfD39+f8uUeGYVBQUICUlBQAwIABAxAcHMxaMf6VSCQynY80GAzQ6/Wm0WR8fDxGjRqFoKAgjBo1CvHx8Syn/XsCgQDPPfcciouLkZmZyXYcs0JDQ1FQUGARb0jao/mcuiXq8KvPY489hlOnTvVEFtJNzp8/D5FIhOHDh7MdpVNKSkpgNBrh7+/PdpQ70ul0SE1NRUFBAQICAhAdHd0rh1I7QyQSmWa4Go1GPPHEE5gyZQqSkpJQUFCApKQkTJkyBUuWLGE76t+aPn06GhoasGfPHrajmBUaGgqdTmc15yEbGxvR1NTEdowe0eGCVCqViIuLQ3h4OP7973+juLi4J3KRLjh//jyio6N5+a6OYRgUFRXBy8vLdHiQixoaGnDp0iU0NTUhOjoaAQEBnLz0oCWBQACRSISjR49i586dZr9m+/btOHr0aC8n6xixWIyFCxfi+++/5+TkEF9fX8hkMqs5D2nJM3Y7XJB79+5FcXExnn76afz4448IDg7G9OnTsWfPHos9Ds0358+fR2xsLNsxOqW2thaNjY2cvu5RqVTiypUrkEqlGDJkiGnBZr5466237vj5N954o5eSdN4999yD+vp6HDt2jO0obTSfh8zNzWU7Sq+ggvwLDw8PvPDCC7h69SrOnTuHPn36YOHChfD19cXzzz+P7Ozs7s5J2kmhUCAzM5O3h1fLysoglUrh6urKdhSzamtrceXKFTg6OmLgwIGcHuXezt/tW8iHfQ379OmD6Ohozm6FFRoairy8PKs4D6nX6y3qmtuWujQDorS0FPHx8YiPj4dIJMKMGTOQmpqK/v374+OPP+6ujKQDmhdLHjFiBMtJOo5hGJSXl8PLy4vtKGYplUqkp6dDLpcjOjqaty8Kfzc65/LovaU5c+YgISGBkztJhIaGQqvVWsUpKBpBtqDT6fDzzz9j1qxZCAoKwu7du/Hcc8+hpKQEX3/9NRISEvDTTz/hnXfe6Ym85G+cP38ecrkc4eHhbEfpMIVCAY1Gw8mCbGpqQkpKCmxsbBAdHc352bV38ne/m2vXru2lJF0ze/ZsGAwG/Pbbb2xHacPPzw9SqdQqDrMaDAYqyGY+Pj5YunQpgoKCcP78eVy8eBFPPfWUaWdp4NZGp87Ozt2Zk7TTuXPnMHz4cF6+gJeXl0Mmk3HuZ0ev1+Py5csQCAQYNGgQb0eOze6++24sXrzY7Ofi4uI4u4zbX3l6emLOnDm4cOEC21HaEIlEiIiIQHV1NdtRehyNIFv4+OOPUVJSgo0bN2Lw4MFmv8bZ2dkq3jlxDcMwuHDhAm8n6JSXl8PT05Nzs0HT0tKg0+kwZMiQHrm+kWEY03ZXdXV1pi2v6uvrTdtcdfdKONu2bUNCQgJGjhyJwMBAjBw5EvPmzcOlS5dw7dq1bv1ePWno0KE4ceIEJ7dbcnZ2RkFBAdsxepwlF2SH/1ULFy7siRykG+Tl5aGqqoqXBVlXVweVSsW5lXMKCwtRWVmJgQMHdus1jgaDAUqlEo2NjaZluoRCIUQikWlLq5bbXQmFQkilUtOtO0axkydPbjVabGpqwpIlS7BkyRIcO3aMFxOQxo0bh9WrV+P8+fOYNGkS23FacXd3x/nz5++4Z6slsORJOpZZ+1ai+QW0eXSRmpqK0aNHIyYmhs1YnVJZWQmRSMSp2atqtRrXrl2Dt7d3t50X1Wq1qKiogFKphEAggL29PVxcXGBnZ2e2+BiGMa2Ao9frodVqodVqTdtbdecLk52dHV599VVMnjwZW7ZswT//+c9ue+yeEhQUBB8fHyQlJXGuIN3c3ExvhFxcXNiO02Ps7OxMa/9aGst9W2MljEajqSCzs7NhMBjg6enJcqqOq62thaOjI6cOr6anp0MqlaJfv35dfiyj0YiioiJkZGRAoVDAw8MDffv2RVBQENzc3GBra2u27AQCAcRiMWxsbODg4AC5XA47OzsIhUJoNBrT4dfuWjZu4MCBeOWVV/DWW2/x4lCrQCDAiBEjcO7cObajtOHm5gYAFn8esqKiotUWbJaECpLHBAKBaekwALh+/TpUKhXLqTqntraWU5NzqqqqUF5ejr59+3b5vGNjYyPS0tJQUVEBLy8v9O/fH56enp0+byORSEwLkQsEAixatKhbl41bsWIFpk6dypuZ6CNGjEB6ejoaGxvZjtKKs7MzhEKhRRdk88bdXF1isauoIC1A88XIhYWFnF+/1ByVSgWNRsOZw1AMwyA9PR1OTk5dviawsrISGRkZEIlEGDBgAHx8fLrtfJRIJMKJEyfw9ddfm/18Z5eNk8lkWLhwIRISEnD69OmuxuxxI0aMgMFgwMWLF9mO0opQKISrqyuqqqrYjtJjmidHOTg4sJykZ1BB8pxQKDSNIAsLCxEYGMhyoo6rra0FAM6MIMvKytDY2NjlQ6ulpaXIzs6Gs7Mz+vfv3yOTXlavXn3Hz3d22bgZM2ZgzJgxePfddzm/l2RISAh8fHyQlpbGdpQ23NzcUFNTw3aMHtM8aqcRJOGk5m2MmrddCggIYDtSh9XW1sLOzo4zsyZzcnLg5ORkOofUGeXl5cjOzoa3tzfCw8N77NxqTy0bJxAI8PTTTwMAZzcnbiYQCBAdHc3JnG5ubhY9glQoFHB1deXdesTtRQXJc80FqVQq0dDQwMsRpEKh4Mzh1draWlRUVCAsLKzTj1FXV4fs7Gx4eHggNDS0G9O11ZPLxt19992or6/H5s2bO/0YvWXgwIGcXNbNzc0NtbW1Zjc2twTV1dVQKpWcmn3enaggea65IJv3nuPjOUiFQsGZQzR5eXlwdHTs9PWYBoMBGRkZsLGxQURERDena6snl40TCAR49tlnceXKFVRUVHT6cXqDn58fCgsLOTdJreWlHpaooqICLi4uFrtQABUkzzVP1HjggQdgNBqxYsUKXuwM30yr1UKlUnFi70qDwYD8/Hz4+/t3+pBoTk4OmpqaMGDAgF65OPxOy8aFh4dj9OjRXXr8mTNnorq6mpPrnbYUFBQEAMjPz2c5SWvNhx+bz7NbmqqqKnh4eLAdo8dQQfLcihUrsGDBAmRmZgIALl26xJud4QGYdiLnwgiyrKwMADp9HrepqQnFxcUICQnp1QunzS0b99VXX6G6uhpbtmzp0mM7Oztj5syZ2L17dzel7RnNBcm1pd0cHBxgNBpNP+eWprKykgqScFN8fDy++eYbs5/jw87wwP8vSC6sxFFSUgIbGxs4Ojp26u/n5OSAYRjTi3Vvmjx5MhITE5Gfn4/ExEQ89thjeO6553Dy5Emo1eouPXZcXBwAcPowq4uLCxwcHDg3gpRKpabLmCxRZWUl3N3d2Y7RY6ggeaynpvj3pqamJgiFQtjY2LAdBSUlJZ0+96jValFWVobAwEDOrLu5cOFCnD59usubCk+YMAGXL1/GmTNnuilZ9xMIBAgKCuJcQQoEAkgkEuh0OrajdDuNRoP6+npertzVXtz4TSadYgk7wzc1NXHi/GNDQwM0Gk2nf9mLi4uh0WhYGT3eTnBwMB555BHs37+/S4/j4eGBadOm4fr1692UrGcMGjSIk7NFpVIptFot2zG6XWVlJQDQCJJwkyXsDN/Y2MiJgqyuroZer+/0tY9lZWXw8PDg3JqUI0aMwJ9//tnlSSLu7u6cP2Tv7OyMuro6tmO0YakjyOaCpHOQhJMsYWd4vV7PifOPCoUCTk5OnVqswGg0dvu5GKPRiB9++KHLjzNhwgTY2Nh0+SL6IUOGQKFQQK/XdzlTTzEYDMjOzmY7RhuWPIKUSCQWu0gAYKEFuXHjRgQHB8PGxgYjRozA+fPn2Y7UI+40xX/x4sW82BmeK9etNa/m0xlKpRJGo7FbFzv4+OOPMX/+fHz00UddehxfX1/4+PggJyenS48TEhKCsrIy5OXldelxepKNjU2XJyT1BEsdQTZf4sGlHXi6m8UV5I8//ogXXngBb731Fi5duoRBgwZh6tSpnJ6B1xXbtm3Dnj17MGTIENMU/4SEBGzbto3taO3Clc1kNRpNp2ev1tfXQ6vVdus76e3btwMAduzY0eXHCgsLQ3p6epceIygoCC4uLqYFKbjI1taWkwVpqSPIiooKiz7/CFjghsn//e9/sXTpUixatAgAsHnzZvz222/YsWMHXn31VZbT9Yy4uDgMHjwYoaGhvHs3x5WCVCgU8PPz69TfbWpqgkwm6/JqIk888QRKS0sBwHRd67Vr1zB9+nQAgI+PT6cKMzg42HSNZ2d5eXnBxcWF0xe8y2QyThakRCKxyIKsqqpCZGQk2zF6lEUVpFarRXJyMlatWmW6TygUIi4uDomJiW2+XqPRtLo+iYsn+NtDIpHAYDBAp9NxbpLI3+FCQTIMA4PB0OnF0rvjGreGhgZ89dVXbXbOYBgGhw4dAnDrkoHPPvusw1sL2dra4ubNm13KJxKJUFdXh/Ly8i49Tk+ytbWFVqvlxM9US1Kp1OIWCmjeqL2zbyr5gjs/Rd2gqqoKBoMBXl5ere738vIy+w563bp1kMvlphsfd8IAYCpFPr5L5cKLmV6vh1ar7fQIUCAQQCQSdSmDg4MDzp8/f9vDtHK5HBcvXuzUvnsODg7d8rPdG2vLdkXzGxyu/R5Y4iHW8vJy1NTUtHmttTQWVZAdtWrVKiiVStONy+dX7kQsFkMkEvFytQ6GYVgvSIPBAJFI1OnD0wKBoFtGCMOGDbvtodCysjIMHTq0U49bU1PTLbvaV1VVcXrRbalUipiYGM5NiBGLxZyYqd2d8vLyoNfrERwczHaUHmVRBenu7g6RSNTmMFB5ebnZFVJkMhmcnJxa3fhKKpXysiBFIhEnLu5mGKbTGwPb2NjAYDB0y7/j22+/NXv/d99916XH7d+/f5f+PnBrJiuXp/Q3Njbi6tWrnLiutiWtVguDwcB2jG6VnZ0NPz8/zj3X3c2iCrL5HWTLC5qNRiOOHj2KUaNGsZis58lkMl4exjEYDKznFovFpnNXneHg4ACVSoX6+vouZ/nf//4H4NaC6WfPnjVtX/b11193+jGvXLnSLSOYzMxMTr8Jq6urg729fZcPd3c3jUbDmc3Au0t2djbCw8PZjtHjLGqSDgC88MILeOyxxzBs2DDExsbik08+QWNjo2lWq6WSSqVQKBScOKfXETY2NpwoyK6MwJ2dnSGVSlFeXt7lEdby5csxcuRIvP/++xAKhcjPz8err76KmJiYTj2eWq2Gvb09Bg4c2KVcwK09F7m87mZdXR0njwJpNBpO5uqs+vp6lJWVYdasWWxH6XEWV5APPvggKisrsXr1apSVlWHw4ME4dOiQxZ9MFovFYBgGWq2WEwt/txdXpuYLhcJOL1pga2sLGxsblJaWom/fvl3K8eCDD+LBBx9slWv9+vWdfrzk5GSkpaVhzZo1Xcql0Whw+fJlPPTQQ116nJ5UX1/PySKytBFk86ITNILkqWeffRbPPvss2zF6VfMvoEql4l1BcuHyGldX1y5NtAkODsa1a9c4N4K/fPkyxo0b1+XJFCUlJXBxceH0tH6lUtnpxR56kqUVZHZ2NlxdXeHq6sp2lB7Hnd9k0iXN2+pwYTTWEVwZQcpksi7N9AwODkZ9fT2nlmJTqVTYt28fIiIiuryARGFhIZRKpemcKBdxdQSpVqstqiBzcnKsYvQIUEFaDIFAAFtbW86sbdpeMpmMExM/3Nzc0NjY2Om/7+7uDn9/f1y6dKkbU3XN4cOH4evri3vuuafLj5WdnQ0PDw9On4M0GAycXPpMo9Hw6qjOnWg0GuTn51NBEv6xsbGBXq/n3HVgd2Jrawu9Xs/6NHhXV1fT9bCdFRUVhdLSUk5s2qtWq3Ho0CGEhYV1y7ZnxcXFiIqK4twM0Zby8vLg4+PDdoxW9Ho9jEajxYwgc3NzYTQa0adPH7aj9AoqSAshEAhM71L5NIp0cHAAwzDdcolEV3h6ekIsFndpk+nQ0FAEBgbi+PHjrBf+119/DYZhsHTp0i4/FsMwOHnyJKdHDUqlEhUVFZxbDav56IilFGR2djbs7Ox4sddsd6CCtCAikQgSiYRXBSmXy6HT6VhfBNvGxgZOTk4oLi7u0uPcdddd0Gg0OHv2bDcl67i0tDQkJSVhwoQJ3TKiysvLg7u7O2JjY7shXc+4ceMGgFs7l3BJ8/l1SyrIPn368G5ThM6igrQQzT+wfDsPKZPJYGdnx3pBAre2dMrNze30ijrArXORMTExSExMxPXr17sxXftUV1fjo48+QnBwMB544IFuecxTp04hNze309di9oabN29CKBQiMDCQ7SitqFQqyOVyi1hqzmg04ubNm5w+ktDdqCAtTPOF92wf4usIrmyjFBISAoZhUFRU1KXHGTZsGAYNGoQjR46goKCgm9L9vfr6eqxfvx729vZYvnx5t50vTE5OxuzZszk90eTGjRsIDAzk3G42dXV1YBiGk5efdFRBQQE0Gg0VJOGf5hGknZ0djEYjr7bX4UpBenl5QSwWm/Zi7IrJkyfDzc0NBw8eRHZ2djeku7Pq6mq8++67UKlUeOmll7ptNmdBQQH+/PNPTo8egVsFybXDq8CtheIBWMQIMjs7GxKJBEFBQWxH6TVUkBZGJBJBJpOhoaGB7Sjt5uLigoaGBtZn3woEAkRFRaGgoKDLy9+JxWLMmzcPPj4+2LVrF86ePdulQ7d3kpGRgfXr16OxsREvvPBCt76A7du3D35+fpgwYUK3PWZP4GpBVldXw83Nje0Y3SIvLw+DBw/u8sbgfEIFaUEYhoHRaIS9vX2XrunrbW5ubhAKhaiqqmI7Cvr374+6ujqkpaV1+bHEYjHuvfdejB07FqdPn8Z3333Xrf9GlUqFb775Bm+99RYcHR2xdu3abt1+SKvVIikpCePGjeP04dWysjL4+voiOjqa7ShtVFVVWURBajQa5ObmWtXhVYAK0uIYDAbY29vDYDBwYoWa9miexHC7vRB7k4ODA6KionDx4sVu2b5KIBBgwoQJmDdvHlQqFTZt2oTffvutS6v2NF/j+MYbb+DKlSt47LHHsGrVKri4uHQ5b0v79+9HTk4Op9dfBYCLFy8iKyuLcwXJMAxqamosoiBTUlJQW1vbLYve84n1jJWtgFAohE6ng52dnenaQi6/828mEAjg4uKCoqIiDBkyhO04GDJkCDIyMpCent5tL7qhoaHw9/dHUlISkpOTcfLkSfTr1w/9+vVDZGQknJ2d7/j31Wo1srKykJKSgrS0NGi1WkRHR2PWrFk9srqNRqPBwYMH8cADD3B6eTkASEpKQr9+/Ti3V2V9fT10Oh0nV/fpqIsXLyI0NNQiyr4jqCAtSMtFsh0dHVFfXw8PDw8WE7Wfv78//vzzT2i1WtZnIrq7uyMsLAynT59GZGQkJBJJtzyuVCrFuHHjMHLkSFPR7du3D/v374dMJoOXlxccHR1Nb3C0Wi3q6upQVVWF8vJyMAwDJycnjBgxAuPGjevRF949e/YgKysL7777bo99j+5gNBpx7tw5zJ07l+0obTQfTud7qTQ1NSE9PR333Xcf21F6HRWkBWkuSKPRCCcnJxQWFnKicNrD398fDMOguLgYISEhbMfB2LFj8cMPPyAxMRHjxo3r1seWSqUYNmwYhg0bhoaGBuTl5aGwsBDV1dWoqqqCVquFTqeDSCSCvb09goODMXr0aPTt2xc+Pj49fpF2VVUVvv32WyxatIhzK9P8VVZWFhQKBUaOHMl2lDaqq6shFos5N7LtqMuXL8NoNGLo0KFsR+l1VJAWRCAQQCAQwGg0wsHBAUKhEHV1dbw4xOPg4ABnZ2fOFKRcLkdUVBTOnTuHyMjIHluku/mcZ1RUVI88fkcxDIMtW7bAy8uL8+ceAeDcuXOws7PjzPPXUnV1NVxdXXm/6szFixcRHh7O+6LvDJqkY2GEQiGMRiMEAgEcHBw4sddie/n7+3d5qbfuNHLkSLi4uODAgQO8WnihKxISEvD777/j0Ucf5eTWUX+VlJSEmJiYbjsM3p2qqqp48eb0Turq6pCVlYXhw4ezHYUVVJAWprkgAcDJyQlqtbrL1/T1lsDAQCiVSk5c7gHcukxjxowZaGhowIkTJ9iO0+NKSkqwbds2zJkzB5MmTWI7zt+qq6uDWq3GxIkT2Y5iVn19Pe8L8vLlyxAIBJyYPMcGKkgLIxQKwTAMGIaBg4MDBAIB6ztltJe3tzecnZ2Rk5PDdhQTb29vjBw5EufOnUNGRgbbcXqMWq3Ghx9+CLlcjqeeeortOO0SHx+PnJwc3HXXXWxHaaOurg5GoxFeXl5sR+mSCxcuoH///rC3t2c7CiuoIC1My4k6QqEQjo6OvDnMKhQK4e/vj6ysrG65BrG7jBgxAlFRUdi7dy+nDgF3F4ZhsHbtWmRkZOCVV16Bg4MD25Ha5cCBAxg9ejRcXV3ZjtJGYWEhGhsb4efnx3aUTqupqcGNGzes9vAqQAVpcVpO1AFuXe6hUqlYX8atvSIjI6FSqTix6XBLM2bMgJ+fH3799VfOHALuDgzD4LPPPkNRURHefPNNTi7XZk52djaysrLwj3/8g+0oZuXl5cHT0xN2dnZsR+m05ORkSCQSq1scoCUqSAskEAhMk0ocHR0hEomgVCpZTtU+rq6u8PT0xLVr19iO0krz2qoikQi7d+9GZWUl25G6jGEYfP7557hw4QLmzZvHyUOVt7N//364u7tj9OjRbEcxKz8/n/eLel+8eBFRUVG8WGykp1BBWiCBQGAaMQqFQtjZ2Zl2FeCDfv36mQ5RcYmdnR0WLlwIo9GIHTt28Ppwq8FgwBdffIF9+/bhoYcewsyZM9mO1G5arRaHDx/GjBkzum1Lr+5UU1ODhoYGXhdkeXk5CgoKrPrwKkAFaZHEYjEYhjGNIl1cXKBWqzlXOLcTFhYGe3t7zo0igVvXLS5atAh+fn7Ytm0bJzP+nYaGBnzwwQc4ePAgXnvtNcyaNYvtSB1y4sQJ1NfXczZ3fn6+6Xw6X124cAGBgYGcvL60N1FBWiCRSASBQAC9Xg/g1ou6TCbr0gLZvUkqlSIwMBCpqamcvP7Qzs4ODzzwAKKjo/Htt98iPj6eU5OK7uTmzZt49tlnceHCBfz73//mxeUcLTEMg99//x3Tp0/n7Co/+fn58PHx4cUKVubo9XqcOXMGYWFhnLy+tDdRQVoosVjcamKOm5sblEolbybrNE8MSE9PZzmJeVKpFHPmzMHUqVNx4cIFfPnll5yevGM0GnHgwAG88cYbcHV1xeeff47BgwezHavDLl26hKtXr2L69OlsRzGLYRgUFBTw+vBqSkoK6uvrMWbMGLajsI4K0kKJxWIYjUbTyMbFxQUCgYA35yKdnZ3h7++P5ORkTo4igVvneseNG4f58+fDYDDgk08+wYkTJziXNzc3Fy+++CK2bNmC6dOn4/3334ePjw/bsTqMYRhs27YN4eHhGDZsGNtxzKqoqIBareZ1QZ45cwZDhw6Fr68v21FYRwVpoZp3/W4+zCoSieDi4oLq6uoe29m+uw0fPty0kwCXBQcHY8mSJRg1ahSOHDmCDRs2IDU1lfXnuaqqCtu3b8f69euhVqvxwQcfYOHChbw99Hf+/HmkpaVh8eLFnF3fND8/H2KxmLflcuPGDWRnZ2PEiBFsR+EEWqzcQgkEAojFYuj1etMLopubG6qrq6FUKv92/0EucHZ2RkREBJKTk9G/f39T6XORVCrFzJkzERMTg/j4eOzcuRM+Pj6Ii4vDoEGDWm1F1tPKysqwb98+HDlyBDY2NnjooYcwbdo0Xp9Pah49RkVFITY2lu04t1VUVAR/f39Ozq5tj/j4ePj4+GDAgAFsR+EE7r7ikC4Ti8VQq9VgGAYCgQA2NjZwcHBAVVUVLwoSuDWKzMrKQlpaGi/OmXl7e2PhwoUYM2YM4uPj8dtvvyEhIQGRkZGIjY3tsaXHtFotzp07h2PHjqGqqgq2trZ4+OGHMXPmTNja2vbI9+xNf/75JzIzM/HJJ59wdvSo1WpRUVHB29FXSUkJ0tPTsXDhQs4+x72NCtKCNY+4DAaD6c9ubm7Iz8+HSqXixQunXC7HgAEDTNtO8eWi5ZCQECxbtgyFhYU4d+4czp49i4SEBISGhiI4OBh9+/ZFWFhYpw93MgyDsrIypKamIjU1FRUVFcjJyUG/fv0wZ84c3HXXXZDJZN38r2KH0WjE/v37MXjwYE7vSZiVlQWVSoXw8HC2o3RKQkICXFxcEBMTw3YUzqCCtGBCoRBCoRB6vd5UkE5OTpBIJKiurubNdVqxsbHIzMzE+fPnu33z4p4WEBCAgIAA3HvvvcjMzMS1a9eQlJSEI0eOQC6Xw93dHY6OjvDy8oKHhwfs7e0hk8lgY2MDoVAIrVYLlUqFpqYm1NTUoKSkBCUlJVCpVMjJyYFIJEJ4eDjGjRuH559/Ht7e3mz/k7vdoUOHcPnyZXz66aecHtlkZGQgMDCQN2vZtlRTU4Pk5GTMmTOHt4eHewIVpIUTi8XQarWmkZdAIICbmxvKy8vh4+PDi18GOzs7jBgxAidPnkTfvn15WQJisdi0MfL999+P8vJy5ObmIi8vDyUlJcjOzoaDg0OrNWi9vLxardbj7u4OiUQCPz8/REdH44EHHkDfvn15cSSgs6qrq7Fp0ybMmDED/fv3ZzvObSmVShQXF3P28pO/c+zYMdjY2HB26T62UEFaOIlEgqamJuh0OtMkDVdXV1RWVqKqqoo32/EMGjQI165dQ0JCAubPn9+rk166m0AggLe3N7y9vTFq1CjT/RqNBiqVChqNBhqNBgaDARKJBLa2trC1tYVMJuPFG5ruwjAMPvnkE0ilUixZsoTtOHeUkZEBqVTKy8OrDQ0NOHv2LOLi4ng7w7mn8PdVhrSLSCSCSCSCWq023ScWi+Hk5ITKykrerAAjFAoRFxeH6upqJCcnsx2nR8hkMjg7O8PLywuBgYEICQmBv78/3NzcYGdnZ1XlCACnTp3CmTNnsHLlSjg6OrId57YYhkFGRgb69u3L6ZnWt3Pq1CnTNb2kNSpIK2BjYwOdTteqDD09PaHX63m1K4WnpyeGDh2K8+fP82bBA9I59fX1+OSTTzB27FjOv3AXFxdDqVRy+hDw7Wg0Gpw8eRKjRo3i5bnTnkYFaQWkUikEAgE0Go3pPplMBldXV5SXl3Nu5Zc7GTVqFORyOQ4dOsSb0S/puG3btkGn02HlypWcnpgD3Dq8KpfLebk5clJSEvR6Pe/W5O0tVJBWQCAQQCaTtSpIAPDx8YHBYEBFRQVLyTpOLBYjLi4O5eXlSEpKYjsO6QEnTpzAwYMH8cILL8DNzY3tOHek1+tx/fp19O/fn/NF/ldqtRqHDx9GbGwsXF1d2Y7DSVSQVkImk8FoNEKr1Zruk0gk8PT0RHl5uWlJOj7w9vbG2LFjcfbsWdy4cYPtOKQb5efnY9OmTbjnnnswceJEtuP8rezsbGi1Wl4eXj1+/Di0Wi2mTp3KdhTOooK0EiKRCGKxuM0o0svLCwKBAGVlZSwl65yYmBiEhYXh999/h0KhYDsO6QYNDQ146623IJfLsWzZMl6MyLKzsxEUFAS5XM52lA6pr6/HsWPHMG7cON6sqsUGKkgr0jxZp+U5R7FYDE9PT1RWVrYaXXKdQCDAjBkzYGtri3379vFmGy9iHsMweP/996FUKvH222/z4trOqqoqVFRU8HJT4cOHD0MkEiEuLo7tKJxGBWlFzE3WAW7NDhWJRLwbRcpkMtx7771oaGjAkSNHWN89g3Te119/jfPnz+O1117jzU4YFy9ehFgs5t21j6Wlpbhw4QJmzJgBOzs7tuNwGhWklWmerNOyTEQiEby9vVFdXd2mPLnO3d0dU6ZMQXp6Ok6fPs12HNIJp06dwv79+7F48WIMHz6c7TjtUlNTg+vXr2PYsGG8WrSCYRj8/PPPkMvltGpOO/Dn/yzpFjY2NjAaja0WDgBuFY1YLG61tBlfhIeHY+LEibhy5QouXrzIdhzSAVevXsV//vMfjB07Fg888ADbcdrt4sWLcHBwQL9+/diO0iGXL1/GjRs3cN999/FyUYPeRgVpZYRCISQSCRobG1uNIoVCIXx9fVFTU4OGhgYWE3bO8OHDERUVhYSEBKSkpLAdh7RDRkYG1qxZgwkTJmDFihW8mJQDAAqFAllZWYiJieHV6kZqtRr79u3DoEGDEBERwXYcXqCCtEL29vYwGo1QqVSt7ndzc4O9vT3y8/N5eT5v0qRJGDx4MP744w9cu3aN7TjkDq5du4Y33ngDffv2xYoVK3g1mrl48SJsbW15t6nw4cOHoVarMXv2bLaj8AYVpBUSiUSwtbVtM4oEgMDAQKhUKl4tQdfS1KlT0b9/fxw8eBCZmZlsxyFmZGVl4Y033kBYWBjWrFnDmz0+AaCurg6ZmZkYOnQor0q9tLQUp06dwt133w0XFxe24/AGFaSVsre3BwA0NTW1ud/d3R3FxcW8vHRCIBBg5syZ6N+/P3799VekpaWxHYm0kJWVhddffx3BwcF45513eHE5R0vJycmQyWSIjo5mO0q7NU/McXNzw4QJE9iOwytUkFZKKBTC1tYWTU1NbdY0bd5IubCwkI1oXSYUCjFjxgxER0fjwIEDNHGHI65cuYLXXnsNMTExePfdd3lXjg0NDcjIyMCQIUNMW8fxAU3M6TwqSCvWPIpsbGxsdb9YLEZAQACqqqqgVCrZiNZlzSPJUaNG4dChQ3SdJMvi4+Oxbds2DBgwAM8//zwvr79LTk6GWCzGwIED2Y7Sbk1NTTh+/DiGDBlCE3M6gQrSigkEAtjb20OlUrXZ0cPd3R1OTk7Izc3l1W4fLQkEAkyYMAHTpk3DhQsXsHv3bl4eNuYzg8GAbdu24bPPPkO/fv3w1ltv8eqcYzOlUomsrCwMHz6cV5sK//rrr6itrcU999zDdhReooK0cra2thAKhW1GkQAQEhICvV6PoqIiFpJ1n2HDhuHBBx9Ebm4uvv/+e9TW1rIdySo0Njbi3XffxYEDB/Dkk0/imWee4dVlES2dPn0a9vb2vBo9pqam4tKlS5gzZw6tt9pJVJBWrnkUqVar2+zoIZPJ4O/vj/Lycl5eG9lSnz59sGjRItTV1eHLL79EdnY225EsWn5+Pv79738jMzMTb7/9NmbNmsWb6xz/KicnBwUFBbjrrrt4cw6voaEBe/bsQVRUFIYOHcp2HN6igiSwtbWFSCRCXV1dm895eXnBwcEBN2/e5P0GxZ6enli6dCkCAwPx22+/4fDhw7za5osPGIbBkSNH8K9//QtqtRofffQRBg8ezHasTtNqtThz5gxCQ0MRHBzMdpx2++WXX8AwDO6//37evjHhAipIAgBwcHCAWq1uc9mHQCBASEgI1Go18vPzWUrXfWxsbPDggw9i5MiROH/+PL788kuUl5ezHcsiVFdX47333sNPP/2EiRMnYt26dfDz82M7VpckJSVBp9NhzJgxbEdptytXriA9PR1z586Fo6Mj23F4jQqSALh1ONXW1hZ1dXVtJuXY2toiKCgI5eXlFnH+TiAQYOTIkVi2bBkYhsHWrVtx5swZ3k5GYhvDMDh+/DhWrlyJGzdumM438mkyizkVFRVIS0tDbGwsHBwc2I7TLpWVldizZw+GDh3K65E7V/DjgDrpFXK5HJWVlVAqlXB1dW31OS8vLygUCty4cQMDBw7k/YsfcOvftGzZMpw+fdq0hus999xjug6U/L3Kykp88803OH36NMaPH48lS5bwpkzuxGg04sSJE3B3d+fNogB6vR7ffvstnJyccO+997IdxyLQCJKYCIVCyOVys4daASAsLAwCgQA3btxgIV3PEIvFmDhxIpYtWwahUIgffvgBe/fu5f2kpJ6m1Wqxe/du/POf/0RxcTFeffVVPPfccxZRjgCQlpaGqqoqTJgwgTfbWe3fvx8VFRVYsGABZDIZ23EsAo0gSSs2NjamQ60ymazVtHyxWIw+ffrg2rVrKC0thY+PD4tJu5evry+WLVuGixcvIiEhAampqRg7dizuuusuXq2a0tMMBgNOnjyJn376CTY2Npg+fTrmzZvHu1Vx7qShoQHnzp1DVFQUPD092Y7TLlevXkViYiLuu+8+3mw4zQdUkKSNOx1qlcvl8PX1RUFBARwdHS1mxADcGkHHxsYiOjoaJ0+exPHjx5GSkoLY2FgMGzaMN1P8ewLDMDh//jx++OEHFBcXY/To0XjwwQct8sU4MTEREokEI0eOZDtKu1RVVWH37t0YPHgwRowYwXYciyJgaP0tk7q6OsjlciiVSjg5ObEdh1VqtRo1NTVwdnZusywYwzBIT0+HVqvFwIEDLbY4ampqcOzYMVy5cgWOjo4YO3YsYmJirOrwlcFgQFJSEg4cOICSkhJERETg4YcfRmhoKNvRekRmZiYSExMxYcIEhISEsB3nb+n1emzYsAFarRYrV67k5SpFva0jr/NUkC1QQbZWW1sLjUYDDw+PNiugqNVqpKSkwNHRkXe7qndUdXU1Tp48icuXL0MkEmH48OEYPXq0RW8bVF9fjxMnTuDixYvIzMzEwIEDMXfuXIv+f11dXY29e/ciPDwc48aNYzvO32IYBr/++ivS09OxePFiixzN9wQqyE6igmzNaDSioqICUqm0zaFW4FaBXrt2DX5+fggKCmIhYe9SKpVISkrCuXPnIBAI4O/vj2HDhqF///68XUKtJYZhkJmZiWPHjiEpKQkCgQDjx4/H5MmTeXWRfGdotVr88ssvkEgkmD17Ni+Oipw+fRoHDx7EAw88gJiYGLbj8AYVZCdRQbalVqtRWVkJZ2dnsxcdFxUVIS8vD3379uXNhIau0ul0SElJQVJSEgoKCmBnZ4fo6GgMHDgQoaGhvJn1CNwqxeLiYiQmJuLs2bMQCARgGAZxcXEYN26c1VxoHh8fj+LiYsydO5cXv/uZmZn46quvMH78eEyfPp3tOLzSkdd57r9NIqyysbGBo6MjamtrIZFI2pzj8Pf3h0qlQnZ2NmQyGeRyOUtJe49EIkFMTAxiYmJQXl6Oq1ev4sKFC0hMTDQtaB0eHo4+ffpwcnanXq/HtWvXcOXKFVy5cgVCoRAKhQIjRozAmDFjEBERYVXLk6WmpiI3NxdTpkzhRTmWl5fj+++/R79+/TBt2jS241g0GkG2QCPI26usrIRGo4G3t3ebw0/Nk3YaGhowaNAgTpZCT2MYBkVFRUhNTUV+fj5ycnJMh2HDwsIQEhKCoKAgVkZkGo0GN2/eRHZ2NrKyslBZWYnS0lK4ublh0KBBiImJQb9+/azycpaysjIcPHgQUVFRvJi12tjYiM8//xwymcwiVitiAx1i7SQqyNszGo0oLy8HwzDw9vZucxhRr9cjJSUFRqMRgwYNssoX25Zqa2tx/fp13Lx5E9euXUN9fT0AwMfHB66urvD29oaPjw88PDzg6uoKe3v7Lo/aNBoNKisrUVFRgZKSEhQWFqKgoADl5eWQy+VQqVTo27cvoqOjERkZCX9/f6saKf6VSqXCzz//DCcnJ8yaNYvzh8b1ej22b9+OiooKPPvssxY9SawnWVxB5uXl4d1338WxY8dQVlYGX19fLFiwAK+//nqrd1ApKSlYvnw5Lly4AA8PD6xYsQIvv/xyu78PFeSd6fV6lJWVQSqVmj3fqFarcfXqVdja2iIqKorzLzi9hWEYKBQK5Ofno7S0FLm5uSgrK4NSqYSdnR0aGhogkUjg4uICuVwOmUwGOzs7ODk5wWAwQCQSQSgUQiwWQ6VSQafTQa/Xo76+3nTTaDSoqqoyfU8vLy84OTkhMDAQgYGBCA4Ohq+vL/0/+T8Mw+D3339HTU0N7rvvvjaXMnGN0WjE999/j8LCQsyfP98qJsX1FIs7B5mZmQmj0YgtW7agT58+SEtLw9KlS9HY2IgPP/wQwK1/9JQpUxAXF4fNmzcjNTUVTzzxBJydnbFs2TKW/wWWQSwWw93dHRUVFaitrW3zDtbGxgb9+/dHamoqrl+/jsjISJaScotAIICLiwtcXFxaLSCtUqlQWVmJ2tpa062urg6NjY0oLy+HQqFAVVUVjEYjDAYDnJ2doVQqIZVK4eDgAKFQCBcXFwQFBcHJyQlyuRyenp7w8PCAo6OjVY8O/05ycjJKSkowc+ZMzpcjwzDYu3cvrl27hgULFlA59iJejCDN+eCDD/DFF1/g5s2bAIAvvvgCr7/+ummEAwCvvvoq9u7di8zMzHY9Jo0g26e+vh61tbVwc3ODvb19m89XVVUhMzMTAQEB9MtMOCc7OxtnzpzB8OHDERUVxXacv3X48GGcOHEC8+bNo82Pu0FHXud5e7zlr8ugJSYmYty4ca0OuU6dOhVZWVm33aJJo9Ggrq6u1Y38veYl5mpqaqDRaNp83t3dHcHBwSgsLERZWRkLCQkxLy8vD2fOnEFERAQvyvH06dM4ceIEZs6cSeXIAl4WZE5ODjZs2IAnn3zSdF9ZWRm8vLxafV3zx7d7kV63bh3kcrnpFhAQ0HOhLYyLiwukUimqqqrM7qPo7+8Pb29vZGZm0obEhBOKi4tx4sQJBAcHY9SoUWzH+VvJycn4/fffMWHCBF5t2GxJWC3IV199FQKB4I63vx4eLS4uxrRp0zBv3jwsXbq0S99/1apVUCqVplthYWGXHs+aCAQCuLu7QyAQoKSkxGxJhoWFwcPDA2lpaVSShFUVFRU4evQofH19MX78eM6fn01JSUF8fDyGDx+OKVOmsB3HarE6SefFF1/E448/fsevabkocklJCSZOnIjRo0dj69atrb7O29u7zYtw88fe3t5mH1smk1nVwtPdTSQSwcPDA6WlpSgpKYGvr2+rJdcEAgH69+8P4Nb+es2XiBDSm2pqanDkyBG4u7tj0qRJnJ/Je/XqVdPuHPfeey/ny9ySsVqQHh4e8PDwaNfXFhcXY+LEiYiJicHOnTvb/JCPGjUKr7/+OnQ6nekavPj4eERERND1Qj1IIpHAx8fHVJI+Pj6tFhJoWZLp6ekAbv+GhZDuplQqcejQITg5OeHuu+/m/Bqrly5dwi+//IKhQ4fi3nvv5XyZWzpePPvFxcWYMGECAgMD8eGHH6KyshJlZWWtzi3Onz8fUqkUixcvRnp6On788Ud8+umneOGFF1hMbh2aS5JhGJSWlkKv17f6fHNJ+vj4ID09HaWlpSwlJdakoaEBhw4dgo2NDaZMmcL5xSsuXLiAX375BcOGDcOcOXOoHDmA22+n/k98fDxycnKQk5MDf3//Vp9rvkpFLpfjyJEjWL58OWJiYuDu7o7Vq1fTNZC9RCKRwNfXFyUlJSgtLTU7kmzeKql5JOnj48NKVmL5VCoVDh8+DIFAgGnTpnF+n8Rz585h//79GDlyJGbNmkWHVTmCt9dB9gS6DrLr9Ho9SkpKIBAI2pQkcOsNzbVr11BSUoIBAwZQSZJu19jYiCNHjsBoNGLKlCmc35EkMTERBw8exOjRozFjxgwqxx5mcSvpEP4Qi8XtGkkKBAKkp6fDaDTCz8+PxcTEkigUChw9ehRSqZTz23UxDIP4+HicPn0akyZNwqRJk6gcOYYKknS79pRkZGQkBAIBrl27Br1eTyvukC4rKyvD8ePH4eDggMmTJ3N6CTm9Xo9ff/0VqampmD59OkaPHs12JGIGFSTpES1LsqCgAL6+vq3OAzWXpEgkQlZWFjQaDcLDw+kdNOmUGzduIDExEd7e3hg/fjynJ+So1WrTwuMPPPAAL1b0sVZUkKTHiMVi+Pn5obi4GIWFhaYdJloKDw+HTCZDTk4OGhsbMXDgwFbXUhLyd1JSUnDlyhX06dMHI0eO5PTsz7q6Ovzvf/+DUqnEY489huDgYLYjkTvg7k8SsQgikQgBAQFwdHREWVkZKisr23xNYGAgoqKiUFVVhXPnzkGtVrOQlPCN0WjE2bNnceXKFQwePBijR4/mdDkWFxfj+++/h0qlwtKlS6kceYC7P03EYggEAnh7e8PDwwO1tbUoLi6G0Whs9TWenp4YOXIktFotEhMToVAo2AlLeEGn0+Ho0aO4efMmxowZg4EDB7Id6Y4uX76MHTt2QCQS4amnnjK7nyrhHrrMowW6zKPnNTU1obS0FCKRCL6+vq12XwEArVaLS5cuoa6uDlFRUfD19WUpKeGqxsZGHDt2DI2NjZgwYQKnV2YyGAw4fPgwzp07h6FDh2LmzJmcX83H0nXkdZ4KsgUqyN6h0+lQXFwMvV4PHx+fNntKGo1GpKeno7i4GKGhoTR5h5gUFRUhOTkZIpEIY8aMgbOzM9uRbquhoQE//fQTCgsLMWPGDAwbNox+jjmAroMknCaRSBAYGIiysjIUFxfD3d291d6eQqEQ0dHRcHBwQHZ2Nurq6jBw4MA2o01iPfR6PS5duoScnBwEBARgxIgRnP55KC4uxq5du2A0GrFo0SIEBgayHYl0Ao0gW6ARZO+rrq5GVVUV7OzszK68U1VVhStXrkAoFGLIkCG08LwVqqmpwZ9//gmVSoWhQ4eiT58+bEe6LYZhcOHCBSQmJsLW1hYPPfQQvZZwDB1i7SQqSHY0NjaiqKgIwK2dPuRyeavPq9VqXL58GQqFAn379kVoaCgdqrICzcsSXr16FS4uLhg9ejSnfy8bGxuxb98+XL9+HbGxsZgyZQqdb+QgKshOooJkj16vR1lZGerq6uDo6NhmNMkwDK5fv44bN27Aw8MDgwYN4vQhNtI1TU1NOHv2LCoqKtC/f38MHDiQ05dw3Lx5E7/++isMBgPuvfde9O3bl+1I5DaoIDuJCpJ9dXV1KCsrM22u/NfRZGVlJVJSUgAA0dHRNF3eAuXn5+PChQsQi8UYNWoUvLy82I50WwaDAceOHcOff/6J0NBQzJkzh9PrvxIqyE6jguQGg8GAsrIyKJVKODg4wMfHp9XSYRqNBlevXkVFRQUCAwPRv39/OpRlAdRqNa5cuYKbN28iMDAQsbGxnD5KUFpaiv3790OpVOKuu+7C6NGj6dA/D1BBdhIVJLfU19ejtLQURqMR3t7ebab05+fnIyMjAzKZDIMGDYKbmxs7QUmXGI1GZGdnIyMjAxKJBNHR0ZxevF6v1+PEiRNITEyEl5cX7rnnHk5fi0lao8s8iEVwdHSEnZ0dysvLUVJSAqVSCS8vL9Oi50FBQXB3d0dKSgr+/PNP02iSy6MO0lpxcTGuXLmCpqYmhIWFISoqitP///Lz83HgwAEolUpMnDiR88vbka6hEWQLNILkroaGBpSUlECj0cDFxQVeXl6mw64MwyA/Px/Xrl2DQCBA//79ERAQQIe7OKy2thZXrlxBZWUlfHx8MGjQIE7/zmk0Ghw9ehQXL15EQEAA/vGPf8Dd3Z3tWKQT6BBrJ1FBchvDMKiurkZFRQUMBgPc3Nzg6elpOv+o0WiQnp6OoqIiuLm5YeDAgTRhgmPUajVSU1ORm5sLJycnDBo0CD4+PmzHuqP09HT8+eefqK6uRlxcHK2Iw3NUkJ1EBckPRqMRVVVVqKysBMMwcHd3h4eHh2mbrKqqKqSkpKCxsRFhYWGIiIigLbRYZjAYTOcZhUIhoqKiEBoayunDk2VlZTh8+DAKCwvRr18/xMXFtZlVTfiHCrKTqCD5xWAwoKKiAtXV1RAIBPD09ISbmxuEQiGMRiNycnJw/fp1yGQyREdH00QKFuj1euTl5SErKwsqlQphYWEYMGAAp88zNjU14fjx47h8+TLc3d0xdepUhISEsB2LdBMqyE6iguQnnU6HiooK1NTUQCQSwcvLCy4uLhAKhWhsbERqaioqKyvh4uKCAQMG0HJ1vaCpqQk3btxAXl4e9Ho9AgMD0bdvX04f8tbr9UhOTsapU6cgEAgwfvx4xMTEcHqUSzqOCrKTqCD5TavVory83LSXpJubG9zd3SGVSlFWVobMzEzU1NTAx8cH/fr14/ROEHxVW1uL7OxsFBcXQywWIyQkBGFhYbC1tWU72m0ZjUZcvXoVZ86cgV6vR79+/TBu3DjY2dmxHY30ACrITqKCtAzNRVlTUwODwQAnJye4u7vDyckJRUVFyMzMRENDAxVlN2EYBiUlJcjJyUF1dTXs7e3Rp08fBAUFcXoBB4ZhkJaWhtOnT0OhUGDAgAEYO3Zsq51liOWhguwkKkjLYjQaUVtbi6qqKjQ2NkIikZi21iovLzcVpa+vL/r160cTMDpIp9MhLy8PN2/eRGNjI9zd3REeHg5vb29Oz/JkGAaZmZk4deoUqqur0bdvX4wbN46WLbQSVJCdRAVpuVQqFSorK1FbWwuDwQC5XA43NzcoFApkZWWhsbGRirIddDodysrKUFpaiurqagAwFSPXR+J6vR5paWk4f/48NBoNPDw8MH78eM5fZkK6FxVkJ1FBWj6j0YiamhpUVVWhqakJYrEYTk5OqK+vR3FxMZqamuDn54eIiAjOv+D3Fq1Wi7KyMpSUlKCqqgpGoxGurq7w9fWFr6+vaWUjrlKpVLh8+TIuXryIpqYmREREIDY2Fn5+fmxHIyygpeYIuQ2hUAh3d3e4u7ujqakJ1dXVqK6uhlarhaurK2xsbJCfn4/c3Fz4+voiJCQEfn5+VjeTUavVorS01FSKDMPAzc0NAwYMgI+PD+dLEbg1YejixYtISUkBwzCIjo5GbGwszWIm7UYjyBZoBGm9mpqaoFQqoVAoUF9fj7KyMlRWVkKj0cDV1RWRkZHo06cPHBwc2I7aI4xGI5RKJWpra1FRUYHKykoAt2YC+/r6wsfHBzKZjOWUf89oNOLGjRumZex0Oh1iYmIwdOhQmpVKANAh1k6jgiTArXNVdXV1UCgUKCoqQkFBAcrLyyGRSODn54d+/fqhT58+nL7Y/e+oVCooFArU1tZCoVBAqVSCYRhIpVLI5XJ4eHjwphQBQKlUIiUlBampqaYZyoMHD0a/fv04PZOW9D46xEpIF4jFYri6usLV1RWhoaFobGxEdXU1rl+/jszMTGRkZEAqlZoufvf09ISdnR3s7e05eejRYDCYRsfNpajRaAAAdnZ2cHZ2hp+fH5ydneHk5MTpGagtqdVqZGdnIycnB9nZ2ZBKpYiKisLAgQNpRirpFjSCbIFGkOTvMAyD8vJyZGRkICcnByqVCiKRCG5ubvD29oadnZ2pLGUyGaRSKSQSSatbdxeQVquFWq2GSqWCWq023Zo/1ul0MBgMEAgEkMvlcHFxgbOzM5ydnXkzQmym1WqRk5ODzMxM5OXlwWg0mrY5i4iIaLWxNiHm0CHWTqKCJB1hMBhQXFyM/Px8FBYWQqVSwd7eHnK5HE5OThAKhdDpdG3+nlgshkQiaVWeYrEYzb+KRqMRDMO0urW8z2AwwGAwQKVSQaVSwWg0mh5bKBTC1tYWNjY2sLGxMf3Z0dERDg4OvBkdtqTT6XDjxg1kZWXh5s2bMBgM8PX1RWRkJCIiImBvb892RMIjdIiVkF4gEokQGBiIwMBAaLVaFBcXo7i4GEVFRaitrYWjoyO8vLzg4eEBFxcXGAwG6HQ66HQ6aLVa05/VajWMRiO0Wi0EAoHZm1AobPVnqVRqOqTbshD5fF60JYVCgdzcXOTm5qKoqAg6nQ5eXl4YM2YMIiIi6A0s6RU0gmyBRpCkO+j1epSXl6O4uBglJSVoamqCRCKBl5cXfHx84OnpSYsR/EXzdajFxcUoKChAbW0tRCIR/P39Teu50nNGugONIAlhkVgshp+fn+lC9NraWpSUlKCsrAznz58HwzCQyWTw9PSEp6enafcRPh7+7AyGYVBTU2N6A1FcXIz6+noAgIuLC0JDQ+Hv74/AwEA6p0hYRQVJSA9zcXExbbWl1+tRWVmJiooKVFRU4MqVKzAYDLC1tYWDgwPc3Nzg6uoKNzc3Xs0ovZOGhgZUVVWhoqLCtPiARqOBUCiEp6cnwsPDTavy0LWKhEvoEGsLdIiV9DaDwYCamhpUVlaisrISNTU1ptGUra0tpFIpHB0d4eTk1OrGtSJpbGxEXV0dlEollEql6c8qlQq1tbUAAJlMZjrM7OvrC29vbxohkl5Hh1gJ4QmRSAQPDw94eHiY7tNqtaipqUFtba2pbPLy8tDQ0GD6GrFYbCrO5ktLbGxs2lxS0vLW3uXyjEYjdDod9Hp9q1vzhKLmRQaaS7Curg56vd709+3s7CCXy+Hs7IzQ0FA4OzvDw8OD05slE2IOFSQhHCOVSuHt7Q1vb+9W9xsMBjQ0NKCurs50a2pqQlFREZqamgDAtACAOUKhsE1pNl8n2bIIb3dQSSQSQafTwd7eHiKRCE5OTvDz80P//v1Nl7Y4OTnRqJBYDCpIQnhCJBJBLpffdjZny8tImkuv5cd/vQG3Rotisdh0bWbzn293k8lkvFtcgJDOooIkxEKIRCKIRCJOLndHCB9Z1x4+hBBCSDtRQRJCCCFmUEESQgghZlBBEkIIIWZQQRJCCCFmUEESQgghZlBBEkIIIWZQQRJCCCFmUEESQgghZlBBEkIIIWZQQRJCCCFmUEESQgghZlBBEkIIIWZQQRJCCCFmUEESQgghZlBBEkIIIWZQQRJCCCFmUEESQgghZlBBEkIIIWZQQRJCCCFmUEESQgghZlBBEkIIIWZQQRJCCCFmUEESQgghZlBBEkIIIWbwriA1Gg0GDx4MgUCAK1eutPpcSkoKxo4dCxsbGwQEBGD9+vXshCSEEMJ7vCvIl19+Gb6+vm3ur6urw5QpUxAUFITk5GR88MEHWLNmDbZu3cpCSkIIIXwnZjtAR/zxxx84cuQIfv75Z/zxxx+tPvfdd99Bq9Vix44dkEqlGDBgAK5cuYL//ve/WLZsGUuJCSGE8BVvRpDl5eVYunQpvvnmG9jZ2bX5fGJiIsaNGwepVGq6b+rUqcjKykJtba3Zx9RoNKirq2t1I4QQQgCeFCTDMHj88cfx1FNPYdiwYWa/pqysDF5eXq3ua/64rKzM7N9Zt24d5HK56RYQENC9wQkhhPAWqwX56quvQiAQ3PGWmZmJDRs2oL6+HqtWrerW779q1SoolUrTrbCwsFsfnxBCCH+xeg7yxRdfxOOPP37HrwkNDcWxY8eQmJgImUzW6nPDhg3DI488gq+//hre3t4oLy9v9fnmj729vc0+tkwma/OYhBBCCMByQXp4eMDDw+Nvv+6zzz7D2rVrTR+XlJRg6tSp+PHHHzFixAgAwKhRo/D6669Dp9NBIpEAAOLj4xEREQEXF5ee+QcQQgixWLyYxRoYGNjqYwcHBwBAWFgY/P39AQDz58/H22+/jcWLF+OVV15BWloaPv30U3z88ce9npcQQgj/8aIg20Mul+PIkSNYvnw5YmJi4O7ujtWrV9MlHoQQQjpFwDAMw3YIrqirq4NcLodSqYSTkxPbcQghhHSzjrzO8+IyD0IIIaS3UUESQgghZlBBEkIIIWZQQRJCCCFmUEESQgghZljMZR7doXlCLy1aTgghlqn59b09F3BQQbZQX18PALRoOSGEWLj6+nrI5fI7fg1dB9mC0WhESUkJHB0dIRAIzH5NXV0dAgICUFhYSNdKthM9Zx1Hz1nH0XPWcdb4nDEMg/r6evj6+kIovPNZRhpBtiAUCk1L1/0dJycnq/mB6i70nHUcPWcdR89Zx1nbc/Z3I8dmNEmHEEIIMYMKkhBCCDGDCrKDZDIZ3nrrLdpHsgPoOes4es46jp6zjqPn7M5okg4hhBBiBo0gCSGEEDOoIAkhhBAzqCAJIYQQM6ggCSGEEDOoIDtBo9Fg8ODBEAgEuHLlSqvPpaSkYOzYsbCxsUFAQADWr1/PTkgOyMvLw+LFixESEgJbW1uEhYXhrbfeglarbfV19Jy1tXHjRgQHB8PGxgYjRozA+fPn2Y7ECevWrcPw4cPh6OgIT09P3HvvvcjKymr1NWq1GsuXL4ebmxscHBxw3333oby8nKXE3PP+++9DIBDgueeeM91Hz5l5VJCd8PLLL8PX17fN/XV1dZgyZQqCgoKQnJyMDz74AGvWrMHWrVtZSMm+zMxMGI1GbNmyBenp6fj444+xefNmvPbaa6avoeesrR9//BEvvPAC3nrrLVy6dAmDBg3C1KlTUVFRwXY01p08eRLLly9HUlIS4uPjodPpMGXKFDQ2Npq+5vnnn8eBAwewe/dunDx5EiUlJZg7dy6LqbnjwoUL2LJlCwYOHNjqfnrOboMhHfL7778zkZGRTHp6OgOAuXz5sulzmzZtYlxcXBiNRmO675VXXmEiIiJYSMpN69evZ0JCQkwf03PWVmxsLLN8+XLTxwaDgfH19WXWrVvHYipuqqioYAAwJ0+eZBiGYRQKBSORSJjdu3ebvubatWsMACYxMZGtmJxQX1/PhIeHM/Hx8cz48eOZlStXMgxDz9md0AiyA8rLy7F06VJ88803sLOza/P5xMREjBs3DlKp1HTf1KlTkZWVhdra2t6MyllKpRKurq6mj+k5a02r1SI5ORlxcXGm+4RCIeLi4pCYmMhiMm5SKpUAYPqZSk5Ohk6na/X8RUZGIjAw0Oqfv+XLl2PmzJmtnhuAnrM7oYJsJ4Zh8Pjjj+Opp57CsGHDzH5NWVkZvLy8Wt3X/HFZWVmPZ+S6nJwcbNiwAU8++aTpPnrOWquqqoLBYDD7nFjj83EnRqMRzz33HO666y5ERUUBuPUzI5VK4ezs3Oprrf3527VrFy5duoR169a1+Rw9Z7dn9QX56quvQiAQ3PGWmZmJDRs2oL6+HqtWrWI7Muva+5y1VFxcjGnTpmHevHlYunQpS8mJJVm+fDnS0tKwa9cutqNwWmFhIVauXInvvvsONjY2bMfhFavf7urFF1/E448/fsevCQ0NxbFjx5CYmNhmzcJhw4bhkUcewddffw1vb+82M7+aP/b29u7W3Gxq73PWrKSkBBMnTsTo0aPbTL6xluesvdzd3SESicw+J9b4fNzOs88+i4MHD+LUqVOttqjz9vaGVquFQqFoNSKy5ucvOTkZFRUVGDp0qOk+g8GAU6dO4fPPP8fhw4fpObsdtk+C8kV+fj6Tmppquh0+fJgBwOzZs4cpLCxkGOb/TzjRarWmv7dq1SqrnnBSVFTEhIeHMw899BCj1+vbfJ6es7ZiY2OZZ5991vSxwWBg/Pz8aJIOwzBGo5FZvnw54+vry1y/fr3N55snnOzZs8d0X2ZmplVPOKmrq2v12pWamsoMGzaMWbBgAZOamkrP2R1QQXZSbm5um1msCoWC8fLyYhYuXMikpaUxu3btYuzs7JgtW7awF5RFRUVFTJ8+fZjJkyczRUVFTGlpqenWjJ6ztnbt2sXIZDLmq6++YjIyMphly5Yxzs7OTFlZGdvRWPf0008zcrmcOXHiRKufp6amJtPXPPXUU0xgYCBz7Ngx5uLFi8yoUaOYUaNGsZiae1rOYmUYes5uhwqyk8wVJMMwzNWrV5kxY8YwMpmM8fPzY95//312AnLAzp07GQBmby3Rc9bWhg0bmMDAQEYqlTKxsbFMUlIS25E44XY/Tzt37jR9jUqlYp555hnGxcWFsbOzY+bMmdPqTRlpW5D0nJlH210RQgghZlj9LFZCCCHEHCpIQgghxAwqSEIIIcQMKkhCCCHEDCpIQgghxAwqSEIIIcQMKkhCCCHEDCpIQgghxAwqSEIIIcQMKkhCCCHEDCpIQqxQZWUlvL298e9//9t039mzZyGVSnH06FEWkxHCHbQWKyFW6vfff8e9996Ls2fPIiIiAoMHD8bs2bPx3//+l+1ohHACFSQhVmz58uVISEjAsGHDkJqaigsXLrTZFJwQa0UFSYgVU6lUiIqKQmFhIZKTkxEdHc12JEI4g85BEmLFbty4gZKSEhiNRuTl5bEdhxBOoREkIVZKq9UiNjYWgwcPRkREBD755BOkpqbC09OT7WiEcAIVJCFW6qWXXsKePXtw9epVODg4YPz48ZDL5Th48CDb0QjhBDrESogVOnHiBD755BN88803cHJyglAoxDfffIPTp0/jiy++YDseIZxAI0hCCCHEDBpBEkIIIWZQQRJCCCFmUEESQgghZlBBEkIIIWZQQRJCCCFmUEESQgghZlBBEkIIIWZQQRJCCCFmUEESQgghZlBBEkIIIWZQQRJCCCFmUEESQgghZvw/uvaVnOlXE3cAAAAASUVORK5CYII=\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "from rebound import data\n",
+ "sim = rebound.Simulation()\n",
+ "data.add_outer_solar_system(sim) # either this, or add the planets manually\n",
+ "rebound.OrbitPlot(sim)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We'll integrate the outer Solar System for 1000 years into the future and measure the energy error along the way. We do that at random intervals to make sure we don't have any aliasing with an orbital period. The following function runs the simulation, and then returns the error."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def measure_energy(sim):\n",
+ " Nsamples = 1000\n",
+ " tmax = 2.*np.pi*1e3 # 1000 years\n",
+ " t_samples = tmax*np.sort(np.random.random(Nsamples))\n",
+ " E0 = sim.energy() # initial energy\n",
+ " Emax = 0. # maximum energy error\n",
+ " for t in t_samples:\n",
+ " # we do not want to change the timestep to reach t exactly, thus \n",
+ " # we need to set exact_finish_time=False and slighlty overshoot.\n",
+ " sim.integrate(t,exact_finish_time=False) \n",
+ " E = sim.energy()\n",
+ " Emax = max(Emax, np.abs((E-E0)/E0))\n",
+ " return Emax"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To get an idea how our integrators are behaving, we want to run this simulation for various timesteps. So let us set up an array of timesteps from 0.001 to 1 orbital periods of Jupiter."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "N_dt_samples = 100\n",
+ "dt_samples = sim.particles[1].P * np.logspace(-3,0.,N_dt_samples)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's run the simulations with the standard WH integrator first. We set `safe_mode` to 0 to speed up the calculation."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "Emax_wh = np.zeros(N_dt_samples)\n",
+ "for i, dt in enumerate(dt_samples):\n",
+ " sim_run = sim.copy() # make a copy of the simulation so we don't need to set a new one up every time\n",
+ " sim_run.integrator = \"whfast\"\n",
+ " sim_run.dt = dt\n",
+ " sim.ri_whfast.safe_mode = False\n",
+ " Emax_wh[i] = measure_energy(sim_run)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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DZ+fDhQX6uNSWWfZQtz6NiIiIuLyiUjMfrT1AfrEZbw83a7J2PusK1XOGU2f8sAuAW2KbW7fnOl8f67y4EzVamVpbqMSIiIiIXBHHc4v4aM1+PvzlAFl5ZTss9IpqVGUP2fnDqZsPnWbJzmO4mWDCtW2rvE/fto3579oDrNqTRdPAsnl1dW0+HCiJExEREQezWAye+3o7H685QPHZfU3DAn24++qW3BXfssrrynva0rPysFgMZvywG4ARsc1pXUUvHECfs7st7MzIZcvZLbjqWnkRUBInIiIiDvbDjkzmnN0aKyaiIfdc04qhXcLwvMQctRaNfPF0N1FYYmHRtgx+LO+FG9zuotc1buBNx7AAdmbk8v32TKDulRcBJXEiIiLiYD+f3cv0zt4RTB/VrdrXebi70bKxP2nH8pi8YCsAI7o3p1XIhefQnevqNiHszMi19vzVxZ44LWwQERERhypP4gZ2aGrzta3PJmxZecW4u5l48NqL98KVu/q80iN1cWFDnU/iTp8+Ta9evYiNjaVLly68/fbbzg5JRESkzsgpLKHkbG/XhRw5fYa9x/NxM8FVrRtXeV5Vzp37NiK2OVHV6IUDiG8djLvbb7tAaGFDLRQQEMDy5cvx8/MjPz+fLl26MGrUKBo3tv1BEhERkd/8tOs4932wge6RDfl4/FUXPKe8Fy4moiFBvp4236N8haq7m+miK1LPF+DjSdfmQaQcPE2wvxd+XnUv5anzPXHu7u74+ZVNZiwqKsIwDAzDcHJUIiIitduqPVn86f31nCkxs2rPCdKO5V3wvJVnk7hrzu6kYKtBHZrSPrQBD17brtq9cOX6ti3rsKmLQ6ngAknc8uXLGTZsGOHh4ZhMJubPn1/pnOTkZKKiovDx8SE+Pp61a9fadI/Tp08TExNDixYteOyxxwgJqdmDJCIiIrBu30numbOeolILHmeHLL/cdKTSeRaLYU3i+tYwiWsS4M3ivw7goYTqzYU716geLWga4M3N3ZrV6N6uzulJXH5+PjExMSQnJ1/w/blz55KUlMSzzz7Lxo0biYmJYciQIRw7dsx6Tvl8t/O/jhwpe6AaNmzIpk2bSE9P5+OPPyYzM7PKeIqKisjJyanwJSIiImV+PXCKsbPXcabETP/2TZg2qisAX6YcrjTSlZqZS1ZeMb6e7vSIbHTFY23TpAFrn0rgzwPaXPF7XwlOHyAeOnQoQ4cOrfL9119/nfHjxzN27FgAZs2axcKFC3n33XeZOHEiACkpKdW6V2hoKDExMaxYsYLbbrvtgudMnz6dqVOn2vYhRERE6oGth7O5+9215BWV0qd1Y/79x56YLQbPLtjGvhMFbD6UTUxEQ+v5P+8u64WLbx2Ml4fT+43qHJf+jhYXF7NhwwYSEhKsx9zc3EhISGD16tXVaiMzM5Pc3FwAsrOzWb58OR06dKjy/EmTJpGdnW39Onjw4OV9CBERkTrgVH4xd7+7ltzCUuKiGvGfMb3w8XTH39uD66JDAViQUnFI9efLnA8nF+fSSVxWVhZms5nQ0NAKx0NDQ8nIyKhWG/v376dfv37ExMTQr18/JkyYQNeuXas839vbm8DAwApfIiIi9d3XW45yMr+Y1k38eXdMXIXVnrfEhgPw1eYjmC1lQ6pFpWbWpp8E4Jp2SuIcwenDqY7Wu3fvag+3nis5OZnk5GTMZrP9gxIREallvtl8FIA7ekUQ4FOxVEi/dk1o6OfJ8dwiftl7gr5tQ9i4/zRnSsyENPCiQ2iAM0Ku81y6Jy4kJAR3d/dKCxEyMzMJCwtz6L0TExPZvn0769atc+h9RERErqTiUstFi/NeSFZeEWvSTwBwY9fKKz29PNysxxekHAaosCrVZDJVukYun0sncV5eXvTs2ZMlS5ZYj1ksFpYsWUKfPn0ceu/k5GSio6OJi4tz6H1ERESulJzCEvq/vJTfv/2LTTVTF23NwGJAtxZBRARfeCP5W2LKhlS/3ZpBYYlZ8+GuAKcPp+bl5ZGWlmZ9nZ6eTkpKCsHBwURGRpKUlMTo0aPp1asXvXv3ZsaMGeTn51tXqzpKYmIiiYmJ5OTkEBQU5NB7iYiI2GJXZi6e7m7V2gj+XOvST5KRU0hGTiGHTp2pMiE738KzQ6k3XaAXrlxcVDDNgnw4ml3IlylH2HzoNFDz+nByaU5P4tavX8+gQYOsr5OSkgAYPXo0c+bM4Y477uD48eNMnjyZjIwMYmNjWbRoUaXFDiIiIvVBdkEJI5NX4uXhxupJg/HxdK/2tRv2n7L+efWeE9VK4i41lFrOzc3E8Jhw/rV8Ly8t2onFKNsyK7yO7pbgCpw+nDpw4EDrVljnfs2ZM8d6zgMPPMD+/fspKipizZo1xMfHOzwuDaeKiIgr2nz4NPnFZk4VlLDxnKSsOtafc/4ve09U65rqDKWWG352lerJ/GIA+qkXzqGcnsS5Ki1sEBERV7TlcLb1zyv3ZFX7uhKzhU0HT1tf/7L3RLXmxX2zpWwo9WK9cOWimwXStmkD62sNpTqWkjgREZFaZOs5SdyqPdXrTQPYfiSHolILgT4eeLqbOJJdyIGTBRe9JiuvyNpjd7H5cOVMJpN1gYO7m4mr2jSudnxiOyVxIiIitci5PXGbD2WTW1hSrevK58PFRQUTe3ZrrEsNqdoylFru1p4taOzvxU1dmxF4Xj05sS8lcVXQnDgREXE1pwuKOXjyDABNA7wxWwzW7D1ZrWvLk7geLRtxVeuyHrJfLnGtLUOp5cIb+rLuqQTevLN7ta+RmlESVwXNiRMREVdT3gvXsrEfgzuVVWmozpCqYRis31+WsPU8J4lbvafqeXG2DqWey81NxX2vBCVxIiIitUR5EteleRB925YlYquqsbjhSHYhmTlFeLiZiGnRkB6RjfB0N5GRU8j+ExeeF/fdtrKh1K7Nqz+UKleWkjgREZFaonxRQ9fmQfQ525u2MyOXrLyii163fl9ZL1zn8EB8vdzx9XKne0QjoOp5ceUFfm0ZSpUrS0lcFTQnTkREXM2Wc5K4xg286RhWtrH86ksMqW48Zz5cuataB5dde4EkLiO7sMZDqXLlKImrgubEiYiIKzl3UUOX8LLtIMvrsF1qSHXDgbIkrmeFJK58cUPleXGvfJeKxYDeUcFENtZQqqtSEiciIlILbD2cA0BksB9BfmWlO8rnxa1Mq7onLr+olB1Hc4GKSVyPlo3wcncjM6eIfefMi9tyKJvPNx4CYNKNHe37IcSulMSJiIjUAucOpZaLiwrG3c3EgZMFHKyicO+mg6cxWwyaN/SlWdBv+5j6eLoTG9kQ+G041jAMnvt6GwAjYsPpHtmoUnviOpTEiYiI1AJbz1mZWi7Ax5OYFmWvq5oXt+EC8+HKnTukCvDt1gzW7TuFj6cbj9+gXjhXpySuClrYICIiruRCPXHw27y4qvZRtc6HO9vrdq7yxQ2/7D1BYYmZad/sAODP/dsQ3tC30vniWpTEVUELG0RExFWcLii27nN6fhLXp015vbjKCxQsFsO6MrVXVHCldntENsLLw41juUU8M38rh06dITTQmz8PaO2IjyF2piRORETExV1oUUO5HpGN8PZw43huEWnH8iq8l3Y8j5zCUnw93a3lSM7l4+lO97P7qH66oWwxwxM3dMTPy8MBn0LsTUmciIiIi6tqKBXKErG4s71sK9MqDqmWz4eLjWiIh/uF/8svnxcHZRvdj4htbpeYxfGUxImIiLi4Cy1qOFf5kOry3VmYLb8NqZYncT0vsKih3LlJ3OSbo7XvaS2i/lIREREXd7GeOChb3PDKd6n8uPMYXad8R+fwQLo0D+Ln3WU9cz2jqk7iercK5o9XtaR5I98LzpsT16UkrgrJyckkJydjNpudHYqIiNRj2QUl1kUNXZoHXvCcbs2DGBYTzg/bMykoNrNu3ynW7Ttlfb9HRNVJnLubiedHdLFv0HJFKImrQmJiIomJieTk5BAUdOHffERERBxt65GyXriIYF8a+nld8Bw3NxNv3dkds8Vgz/E8thzKZsvhbLYfzeGqVsGVFkNI3aAkTkRExIVdaij1XO5uJtqHBtA+NIBbe7ZwdGjiZFrYICIi4sK2XGJRg9RfSuJERERc2JZD1e+Jk/pFSZyIiIiL2pWZ+9uihnAlcVKRkjgREREXZBgGz3+9HYAhnUNp5H/hRQ1SfymJExERcUFLU4+xYncWXu5uPHljJ2eHIy5ISZyIiIiLKTFbeOHrHQCMvSaKlo39nRyRuCIlcSIiIueZ8cMu7v9oA6Vmi1Pu//7q/ezNyiekgRcPDGrrlBjE9SmJq0JycjLR0dHExcU5OxQREbmCSs0Wkpem8c2WDDYdOn3F738yv5g3ftgFwCPXdyDAR4V65cKUxFUhMTGR7du3s27dOmeHIiIiV9CR04WUmMs2kd+ZkXvF7z/jh13kFJbSMSyA23tFXPH7S+2hHRtERETOse9EvvXPO486LolLO5bLvqwCIoL9iAj2xc/Lg12ZuXy05gAAk4dF4+5mctj9pfZTEiciInKOc5O4VAf1xGXmFDJ85koKis3WYyENvDGZwGwxuD46lKvbhDjk3lJ3KIkTERE5R3rWb0ncjowcDMPAZLJvj9gbS3ZTUGwmyNcTwzDIKSwlK68IQCVFpNqUxImIiJxj/4kC659zC0s5kl1I84a+dms/PSufuesOAvDO6F7ERQWTXVDCgZMFHDhZQMvGfkSFqKSIXJqSOBERkXPsO9sTZzKBYcDOozl2TeJe/34XZovBoA5NiIsKBiDIz5OufkF0baGttaT6tDpVRETkrFKzhYOnynri4lqWJVj2XKG69XA2X206AsBjQzrarV2pn5TEiYiInFVeXsTLw42BHZsAsONojt3af+W7VABuiQ0nOjzQbu1K/aQkTkRE5Kzylaktg/3o1KwsybLXCtVf9p7gp13H8XAzkXRde7u0KfVbvUniCgoKaNmyJY8++qizQxERERdlTeIa+9MprCyJ25uVT2GJ+WKXXZJhGLy8aCcAv+sdob1QxS7qTRL34osvctVVVzk7DBERcWHl5UVahfgRGuhNQz9PzBaDtGN5l9XuDzuOsfHAaXw83Xjw2nb2CFWkfiRxu3fvZufOnQwdOtTZoYiIiAsrLy8SFeKPyWSiY1gAcHmLG0rMFl75rqwXbmzfVjQN9Ln8QEVwgSRu+fLlDBs2jPDwcEwmE/Pnz690TnJyMlFRUfj4+BAfH8/atWttusejjz7K9OnT7RSxiIjUVeXlRaLODnd2PDukuvMyFjfM/DGNXZl5NPTz5L7+bS4/SJGznF4nLj8/n5iYGMaNG8eoUaMqvT937lySkpKYNWsW8fHxzJgxgyFDhpCamkrTpk0BiI2NpbS0tNK1ixcvZt26dbRv35727duzatWqS8ZTVFREUVGR9XVOjv1WJYmIiOs6t7xIebHdTs0urydu6+FskpemAfDcLV0I8vO0Q6QiZZyexA0dOvSiw5yvv/4648ePZ+zYsQDMmjWLhQsX8u677zJx4kQAUlJSqrz+l19+4ZNPPuHTTz8lLy+PkpISAgMDmTx58gXPnz59OlOnTq35BxIRkVrp3PIizc4OeXYo74mrQRJXVGom6X8plFoMhnYJY1i3ZnaNV8Tpw6kXU1xczIYNG0hISLAec3NzIyEhgdWrV1erjenTp3Pw4EH27dvHq6++yvjx46tM4AAmTZpEdna29evgwYOX/TlERMT1pZ9TXsTNrWyv1PahDTCZICuviOO5RRe7vJI3ftjNrsw8Gvt78cKILnbff1XEpZO4rKwszGYzoaGhFY6HhoaSkZHhkHt6e3sTGBhY4UtEROq+/WeTuHP3LfXz8rDOj7OlXtyvB04x66c9ALw4sguNG3jbMVKRMk4fTr2SxowZU+1zk5OTSU5Oxmy+vNpAIiJSO6RbFzX4VTjeMSyA9Kx8dmbkcE27kEu2U1hi5pFPN2ExynZmuKGLhlHFMVy6Jy4kJAR3d3cyMzMrHM/MzCQsLMyh905MTGT79u2sW7fOofcRERHXcG55kXOVr1DdcfTSPXFmi8GLC3ew93g+TQO8mTq8s/0DFTnLpZM4Ly8vevbsyZIlS6zHLBYLS5YsoU+fPg69d3JyMtHR0cTFxTn0PiIi4hrOLy9SrqN1herFqxVsOniaEckr+eCX/QC8dGtXGvp5OSBSkTJOH07Ny8sjLS3N+jo9PZ2UlBSCg4OJjIwkKSmJ0aNH06tXL3r37s2MGTPIz8+3rlZ1lMTERBITE8nJySEoKMih9xIREecqNVs4cLKqnriyJG73sTxKzRY83Cv2f5wuKOaV71L5eO0BDAMCfDx48sZOXNux4nxuEXtzehK3fv16Bg0aZH2dlJQEwOjRo5kzZw533HEHx48fZ/LkyWRkZBAbG8uiRYsqLXYQERGpqSOnCym1VCwvUi6ikR9+Xu4UFJvZdyKftk0DrO8tSDnM1K+2czK/GIBR3Zsz6cZONAnQQgZxPJuSuNLSUqZNm8a4ceNo0aKFXQIYOHAghmFc9JwHHniABx54wC73qy4tbBARqT8uVF6knJubiQ5hAfx64DQ7jubStmkAhmHw1o9pvP79LqCsFMnzt3QhvnXjKx671F82zYnz8PDglVdeueDuCHWNFjaIiNQ9G/afYt6vhyp1HlyovMi5rNtvZeRgthhMXrDNmsD9ZWAbFj7YTwmcXHE2D6dee+21/PTTT0RFRTkgHBEREcewWAz+/MEGsvKK8PV0r1D6o6ryIuXKt9/afCibCf/dyDdbMjCZYMqwzoy+OsrhsYtciM1J3NChQ5k4cSJbtmyhZ8+e+PtX/K1l+PDhdgtORETEXvYczyMrr2zXhdcW7+K66DDczw6dVlVepFx5T9yK3VkAeLqb+PsdsdzcLdzRYYtUyeYk7v777wfK9jQ9n8lkqjNzyDQnTkSkblm375T1z7uP5bEg5TCjepTN766qvEi5DqG/LWbw93Ln33f3om/bSxf+FXEkm+vEWSyWKr/qUsKjOXEiInXL+n0nAQgNLFs5OuOH3RSXWi5aXqRckJ8nAzs0oXlDX+b+uY8SOHEJTi8xIiIiciWsPZvETR3ehafnb+XAyQL+t/4g/ds1qbK8yLlmj4nDMKi0elXEWWq0Y8NPP/3EsGHDaNu2LW3btmX48OGsWLHC3rGJiIjYxdHsMxw6dQY3E/Rt25gJ17YF4K0fd7Pj7E4MFyovci6TyaQETlyKzUnchx9+SEJCAn5+fjz44IM8+OCD+Pr6MnjwYD7++GNHxOgU2nZLRKTuKJ8PFx0eSICPJ7/rHUHzhr5k5hTx8qKdQNVDqSKuymRcqtLueTp16sSf/vQn/vrXv1Y4/vrrr/P222+zY8cOuwbobOXbbmVnZxMYGOjscEREpAYmL9jK+6v3M+bqKKac3ZT+f+sP8vhnm63njO/XiqduinZWiCKAbXmHzT1xe/fuZdiwYZWODx8+nPT0dFubExERcbi16WXz4Xq3CrYeG9W9Oa2b/Nb7pp44qW1sTuIiIiJYsmRJpeM//PADERERdglKRETEXrLPlJCamQtAr6hG1uMe7m4kXdfe+rqq8iIirsrm1amPPPIIDz74ICkpKVx99dUArFy5kjlz5vDGG2/YPUAREZHLsfHAKQyjbDeGpgEVV5/e2KUZ17Q9yO5juXRtEeSkCEVqxuYk7i9/+QthYWG89tpr/O9//wPK5snNnTuXW265xe4BOouK/YqI1A3rzg6l9ooKrvSem5uJ98b1xoRKh0jtY1MSV1payrRp0xg3bhw///yzo2JyCYmJiSQmJlonGIqISO20/uzK1N4XSOIA69ZbIrWNTXPiPDw8ePnllyktLXVUPCIiInZTVGom5dBpoOJ8OJG6wOaFDYMHD+ann35yRCwiIiJ2teVQNsWlFkIaeNFKq0+ljrF5TtzQoUOZOHEiW7ZsoWfPnvj7V/xHMXz4cLsFJyIicjnKt9rq1TIYk0nDplK32JzE3X///UBZcd/zmUwmLQQQERGXUT4fTkOpUhfZPJxqsViq/KpLCZy23RIRqd0sFoP1+yoX+RWpK2xK4kpKSvDw8GDr1q2OisdlJCYmsn37dtatW+fsUEREpAZ2Hcslp7AUPy93optp20Spe2xK4jw9PYmMjKxTPW4iIlI3lW963yOyER7uNg88ibg8m5/qp556iieffJKTJ086Ih4RERG7+K3Ir+bDSd1k88KGmTNnkpaWRnh4OC1btqy0OnXjxo12C05ERKQmlqUe47ttGUDVRX5Fajubk7gRI0Y4IAwRERH7+HbLUR785FdKzAaDOzblqtaNnR2SiEOYDMMwnB2EKyvfdis7O5vAQE2MFRFxZZ9vOMRjn23CYsBN3Zrx99tj8fLQfDipPWzJO2r0ZJ8+fZp33nmHSZMmWefGbdy4kcOHD9ekORERkcv2wep9PPJpWQJ3e68WvPm77krgpE6zeTh18+bNJCQkEBQUxL59+xg/fjzBwcF88cUXHDhwgPfff98RcYqIiFyQYRj8Y9keXvkuFYAxV0cx+eZo3LSxvdRxNv+KkpSUxJgxY9i9ezc+Pj7W4zfeeCPLly+3a3DOpGK/IiKur7DEzCP/22RN4BIHteHZYUrgpH6weU5cUFAQGzdupE2bNgQEBLBp0yZat27N/v376dChA4WFhY6K1Sk0J05ExDUdyylk/Acb2HTwNO5uJibfHM3oq6OcHZbIZbEl77B5ONXb25ucnJxKx3ft2kWTJk1sbU5ERMRmmw+d5k/vbyAjp5AgX0/+cVcP+rYNcXZYIleUzUnc8OHDee655/jf//4HlG16f+DAAZ544gluvfVWuwcoIiJiGAaZOUVsPZxNysHTvL1iL0WlFto2bcA7d/ciKsT/0o2I1DE2D6dmZ2dz2223sX79enJzcwkPDycjI4M+ffrwzTffVCr+W9tpOFVExHl+2J7J+7/sZ9vhbE7kF1d4b1CHJrxxZ3cCfTydFJ2I/Tl0ODUoKIjvv/+elStXsmnTJvLy8ujRowcJCQk1DlhEROR8CzcfZcJ/N2I529Xg7maibZMGdG4eSHyrYG7rGYG7FjBIPWZzEleub9++9O3b156xiIiIALBkRyYPffIrFgNGdW/O6Kuj6BAWgI+nu7NDE3EZNU7iREREHGFlWhZ/+WgjpRaDW2LDeeX/YtTjJnIBKmUtIiIuY/2+k9z73nqKSy1cHx3Kq0rgRKqkJE5ERFzClkPZjJ29jjMlZvq3b8Jbv++Op7v+mxKpioZTRUTE6RZtzSDpfykUFJvp3SqYf/2hJ94emv8mcjE2/4ozYMAA3n//fc6cOeOIeBwiKiqKbt26ERsby6BBg5wdjoiInGWxGLzxw27u+3ADBcVmrm7TmHfHxOHrpQRO5FJsTuK6d+/Oo48+SlhYGOPHj+eXX35xRFx2t2rVKlJSUli6dKmzQxERESC/qJTEjzfy9x92AWUb178/rjcNvDVIJFIdNidxM2bM4MiRI8yePZtjx47Rv39/oqOjefXVV8nMzHREjCIiUsccPFnArf9cxbdbM/B0N/Hyrd2YMrwzHpoDJ1JtNfrX4uHhwahRo1iwYAGHDh3i97//Pc888wwRERGMGDGCH3/8sdptLV++nGHDhhEeHo7JZGL+/PmVzklOTiYqKgofHx/i4+NZu3atTfGaTCYGDBhAXFwcH330kU3XioiIfS3deYyb3/qZnRm5hDTw5pM/XcXtcRHODkuk1rmsPuu1a9cye/ZsPvnkE5o2bcqYMWM4fPgwN998M/fffz+vvvrqJdvIz88nJiaGcePGMWrUqErvz507l6SkJGbNmkV8fDwzZsxgyJAhpKam0rRpUwBiY2MpLS2tdO3ixYsJDw/n559/pnnz5hw9epSEhAS6du1Kt27dLhhPUVERRUVF1tc5OTnV/XaIiMhFmC0GM37YxVs/pgEQ0yKIf/6hJ+ENfZ0cmUjtZPPeqceOHeODDz5g9uzZ7N69m2HDhnHvvfcyZMgQTKayWj4///wzN9xwA3l5ebYFYzIxb948RowYYT0WHx9PXFwcM2fOBMBisRAREcGECROYOHGiTe0DPPbYY3Tu3JkxY8Zc8P0pU6YwderUSse1d6qISM2dyCvioU9S+DktC4A/XtWSp2/upBWoIudx6N6pLVq0oE2bNowbN44xY8bQpEmTSud069aNuLg4W5uupLi4mA0bNjBp0iTrMTc3NxISEli9enW12sjPz8disRAQEEBeXh4//vgjt99+e5XnT5o0iaSkJOvrnJwcIiLUzS8iUlPr9p1kwse/kpFTiK+nOy/d2pVbYps7OyyRWs/mJG7JkiX069fvoucEBgbaZRVoVlYWZrOZ0NDQCsdDQ0PZuXNntdrIzMxk5MiRAJjNZsaPH3/RBNPb2xtvb2+Sk5NJTk7GbDbX/AOIiNRjhSVmXv9+F2+v2IthQJsm/sz6Q0/ahQY4OzSROsHmJO5SCZyrad26NZs2bbL5usTERBITE63dmiIiUn2bDp7mkU83kXasbFrNbT1bMGV4Z5UPEbEjm/81de/e3Tr37VwmkwkfHx/atm3LmDFj7FJUNyQkBHd390qlSzIzMwkLC7vs9kVExL6KSy28uWQ3//xpD2aLQZMAb14a1ZXBnUIvfbGI2MTmEiM33HADe/fuxd/fn0GDBjFo0CAaNGjAnj17iIuLs64AXbBgwWUH5+XlRc+ePVmyZIn1mMViYcmSJfTp0+ey27+Y5ORkoqOj7TK3T0SkPliz9wQ3vbmCmUvTMFsMhseEs/jh/krgRBzE5p64rKwsHnnkEZ555pkKx1944QX279/P4sWLefbZZ3n++ee55ZZbLtleXl4eaWlp1tfp6emkpKQQHBxMZGQkSUlJjB49ml69etG7d29mzJhBfn4+Y8eOtTV0m2g4VUSkerLyipj2zQ6+2HgYgMb+Xjw/ogs3dm3m5MhE6jabS4wEBQWxYcMG2rZtW+F4WloaPXv2JDs7m507dxIXF0dubu4l21u2bNkFh15Hjx7NnDlzAJg5cyavvPIKGRkZxMbG8uabbxIfH29L2DVmy1JfEZH6xGIx+O+6A7y8KJXsMyWYTHBn70geH9KBhn5ezg5PpFZyaIkRHx8fVq1aVSmJW7VqFT4+PkDZkGf5ny9l4MCBXCqPfOCBB3jggQdsDfWyaHWqiEjVdmfm8sTnm9l44DQA0c0CeXFkF7pHNnJuYCL1iM1J3IQJE7jvvvvYsGGDdb7YunXreOedd3jyyScB+O6774iNjbVroFeahlNFRCorLrUw66c9zPwxjWKzBX8vdx4d0oE/XtVS+56KXGE2D6cCfPTRR8ycOZPU1FQAOnTowIQJE/j9738PwJkzZ6yrVWs7DaeKiJTZdPA0T3y+mZ0ZZVNlru3YlBdGdNG2WSJ25LDh1NLSUqZNm8a4ceO46667qjzP17f2/4PWcKqISJnCEjN/P1u012JAsL8Xzw6LZnhM+AVLTonIlWFzT1yDBg3YunUrUVFRDgrJtagnTkTqs82HTvPI/zax+2zR3hGx4Uwe1plgfy1cEHEEhy5sGDx4MD/99FO9SeJEROqj4lILb/24m38sKyvaG9LAm+mjunJdtGq+ibgKm5O4oUOHMnHiRLZs2ULPnj3x9/ev8P7w4cPtFpyIiFx524/k8Minm9hxNAeAYTHhPDe8M43U+ybiUmweTnVzq3r1kclkqnNzyDScKiL1RYnZwj+W7uGtH3dTajFo5OfJCyO6clM3Fe0VuVIcOpxqsVhqHFhtooUNIlKf7Diaw6OfbmLbkbLet+ujQ3lxZFeaBHg7OTIRqUqNSoyUKywsrBNlRC5GPXEiUpeVmC38c1lZ71uJ2aChnydTh3fWylMRJ7El77C5MqPZbOb555+nefPmNGjQgL179wLwzDPP8J///KdmEYuIyBW3+dBphs9cyevf76LEbHB9dCiL/9qfW2KbK4ETqQVsTuJefPFF5syZw8svv4yX12+TXLt06cI777xj1+BERMT+zhSbmfbNDkYkr2TH0Rwa+nnyxu9i+dcfe9I0oG6ProjUJTbPiXv//ff597//zeDBg7nvvvusx2NiYti5c6ddgxMREftamZbFpC+2cOBkAQDDY8KZPCyakAaa+yZS29icxB0+fJi2bdtWOm6xWCgpKbFLUK5ACxtEpC45XVDMiwt38OmGQwA0C/LhhRFdGNxJdd9Eaiubk7jo6GhWrFhBy5YtKxz/7LPP6N69u90Cc7bExEQSExOtEwxFRGojwzD4ZksGz365jay8IgDu7tOSx4Z0IMDH08nRicjlsDmJmzx5MqNHj+bw4cNYLBa++OILUlNTef/99/n6668dEaOIiNTA0ewzPDN/Gz/syASgbdMGvDSqK72igp0cmYjYQ41KjKxYsYLnnnuOTZs2kZeXR48ePZg8eTLXX3+9I2J0KpUYEZHaxmIx+HjtAV76did5RaV4upu4f2Bb7h/UBm8Pd2eHJyIXYUvecVl14uoDJXEiUpukZ+XzxOebWZt+EoDukQ35263daB8a4OTIRKQ6HLpjQ7ni4mKOHTtWaQeHyMjImjYpIiI1VGq28J+f03n9+10UlVrw9XTn8Rs6cHefKNzdVPNNpC6yOYnbvXs348aNY9WqVRWOG4ZRp/ZO1epUEaktdhzN4YnPN7P5UDYA/dqFMG1kVyKC/ZwcmYg4ks3DqX379sXDw4OJEyfSrFmzSlW9Y2Ji7Bqgs2k4VURcVWGJmbd+3M2/ftpLqcUg0MeDp2+O5v96ttCOCyK1lEOHU1NSUtiwYQMdO3ascYAiInJ5ftl7gie/2MLerHwAbugcxnO3dKZpoHZcEKkvalQnLisryxGxiIjIJWSfKeGlb3fy37UHAGga4M1zt3Thhi5hTo5MRK40m5O4v/3tbzz++ONMmzaNrl274ulZsVikhhxFRBzjh+2ZPDV/C5k5ZUV77+wdycShHQnyVdFekfrI5jlxbm5uZReeN9+iri1sKKc5cSLibCfzi5n61TYWpBwBoFWIP9NHdeWq1o2dHJmI2JtD58QtXbq0xoGJiEj1GYbBwi1HeXbBNk7kF+NmgvH9WvPX69rj46mivSL1nc1J3IABAxwRh4iInONYTiFPz9/K4u1lW2Z1CA3g5du6ERPR0LmBiYjLcKvJRStWrOAPf/gDV199NYcPHwbggw8+4Oeff7ZrcCIi9Y1hGPxv/UESXv+Jxdsz8XAz8eDgdnw14RolcCJSgc1J3Oeff86QIUPw9fVl48aNFBWVTbDNzs5m2rRpdg/QWZKTk4mOjiYuLs7ZoYhIPXHwZAF3v7uWxz/bTE5hKV2bB/HVhGtIuq49Xh41+p1bROowmxc2dO/enb/+9a/cfffdBAQEsGnTJlq3bs2vv/7K0KFDycjIcFSsTqGFDSLiaKVmC++t3s9ri1MpKDbj7eFG0nXtueeaVni4K3kTqU8curAhNTWV/v37VzoeFBTE6dOnbW1ORKRe+/XAKZ6at5XtR3MA6B0VzEu3dqV1kwZOjkxEXJ3NSVxYWBhpaWlERUVVOP7zzz/TunVre8UlIlKnZZ8p4ZXvdvLRmgMYBgT5ejJxaEfu6BWBmzasF5FqsDmJGz9+PA899BDvvvsuJpOJI0eOsHr1ah599FGeeeYZR8QoIlJnGIbB15uPMvWrbWTlFQMwqkdznryxEyENvJ0cnYjUJjYncRMnTsRisTB48GAKCgro378/3t7ePProo0yYMMERMYqI1AmZOYU8NW8rP+woKxvSuok/L4zowtVtQpwcmYjURjYvbChXXFxMWloaeXl5REdH06BB3Zy/oYUNInK5DMNg7rqDvPjNDnILS/F0N3H/wLbcP6gN3h4q2isiv3HowoZyXl5eREdH1/RyEZF64cCJAiZ+sZlVe04AENMiiL/d1o2OYfqlUEQuT42TOBERqZrZYjB7ZTqvLk6lsMSCj6cbj1zXgXHXtMJdCxdExA6UxImI2FlqRi5PfL6ZlIOnAbiqdTAvjepGVIi/cwMTkTqlXiRx6enpjBs3jszMTNzd3fnll1/w99cPUxGxr+JSC/9Ylkby0jRKzAYB3h48eVMnfhcXgcmk3jcRsa96kcSNGTOGF154gX79+nHy5Em8vbWMX0Tsa8P+U0z6YjO7MvMASOjUlBdGdCUsyMfJkYlIXVWj/Vw++OAD+vbtS3h4OPv37wdgxowZLFiwwK7B2cO2bdvw9PSkX79+AAQHB+PhUS9yVxG5AvKKSnl2wVZum7WKXZl5NPb34s07u/P23b2UwImIQ9mcxP3zn/8kKSmJG2+8kdOnT2M2mwFo2LAhM2bMsDmA5cuXM2zYMMLDwzGZTMyfP7/SOcnJyURFReHj40N8fDxr166tdvu7d++mQYMGDBs2jB49ejBt2jSbYxQRuZAlOzK57vWfeG/1fgwDbu3Rgh+SBjA8JlzDpyLicDZ3Sb311lu8/fbbjBgxgpdeesl6vFevXjz66KM2B5Cfn09MTAzjxo1j1KhRld6fO3cuSUlJzJo1i/j4eGbMmMGQIUNITU2ladOmAMTGxlJaWlrp2sWLF1NaWsqKFStISUmhadOm3HDDDcTFxXHdddfZHKuICMCxnEKmfrWdhVuOAhAR7Mu0kV3p166JkyMTkfrE5iQuPT2d7t27Vzru7e1Nfn6+zQEMHTqUoUOHVvn+66+/zvjx4xk7diwAs2bNYuHChbz77rtMnDgRgJSUlCqvb968Ob169SIiIgKAG2+8kZSUlCqTuKKiIoqKiqyvc3JybP1IIlJHWSwGH689wN8W7SS3sBR3NxP3XNOKvya0x9dLRXtF5MqyeTi1VatWF0yaFi1aRKdOnewRk1VxcTEbNmwgISHBeszNzY2EhARWr15drTbi4uI4duwYp06dwmKxsHz58ovGOX36dIKCgqxf5cmfiNRvqRm53DZrFU/P30puYSndWgSxILEvT97YSQmciDiFzT1xSUlJJCYmUlhYiGEYrF27lv/+979Mnz6dd955x67BZWVlYTabCQ0NrXA8NDSUnTt3VqsNDw8Ppk2bRv/+/TEMg+uvv56bb765yvMnTZpEUlKS9XVOTo4SOZF67Eyxmbd+3M2/l++l1GLg7+XOo0M6cHefKBXtFRGnsjmJu/fee/H19eXpp5+moKCA3//+94SHh/PGG2/wu9/9zhExXrZLDdmey9vbG29vb5KTk0lOTrYu3BCR+uenXcd5Zv5WDpwsAOD66FCm3tKZZkG+To5MRKSGdeLuuusu7rrrLgoKCsjLy7MuMLC3kJAQ3N3dyczMrHA8MzOTsLAwh9yzXGJiIomJidaNaEWk/jieW8TzX2/ny01HAGgW5MOU4Z0Z0tmxP3dERGxh85y4F154gfT0dAD8/PwclsABeHl50bNnT5YsWWI9ZrFYWLJkCX369HHYfUWkfrJYDP679gCDX1vGl5uO4GaCsX2j+D5pgBI4EXE5NvfEffrppzz77LPEx8fzhz/8gdtvv52QkJAaB5CXl0daWpr1dXp6OikpKQQHBxMZGUlSUhKjR4+mV69e9O7dmxkzZpCfn29dreooGk4VqV92Zeby5BdbWL//FABdmgcybWRXurVo6NzARESqYDIMw7D1om3btvHRRx/xySefcOjQIa677jruuusuRowYgZ+fn01tLVu2jEGDBlU6Pnr0aObMmQPAzJkzeeWVV8jIyCA2NpY333yT+Ph4W8OukfLh1OzsbAIDA6/IPUXkyiksKVu48K+fyhYu+Hm588j1HRjdpyUe7jXa1EZEpMZsyTtqlMSda+XKlXz88cd8+umnFBYW1rm6akriROqun3dn8dT8Lew/UbZw4broUKYO70x4Qy1cEBHnsCXvuOxNRP39/fH19cXLy4vc3NzLbc5laDhVpO46mV/MCwu388XGwwCEBfow9RYtXBCR2qVGPXHp6el8/PHHfPzxx6SmpjJgwAB+//vfc9ttt9W5lZzqiROpOwzDYH7KYZ7/egcn84sxmWB0nygeub49AT6ezg5PRMSxPXFXXXUV69ato1u3bowdO5Y777yT5s2b1zhYEZEr4eDJAp6ct4UVu7MA6BgWwPRRXeke2cjJkYmI1IzNSdzgwYN59913iY6OdkQ8LkPDqSJ1g9li8P7qfby8KJUzJWa8PNx4aHA7/tS/NZ5auCAitdhlL2yo6zScKlJ7pR3L44nPN7PhbNmQ3q2C+dut3WgV4u/kyERELszuw6lJSUk8//zz+Pv7V9hX9EJef/316kcqIuIAJWYL/16+lzeW7Ka41EIDbw8mDu3I73tH4qb9TkWkjqhWEvfrr79SUlJi/bOIiKtav+8kT83bSmpm2Wr5gR2aMG1kV5UNEZE6R8OpVTh3TtyuXbs0nCri4k7lF/O3RTv5ZN1BAIL9vXj6pk6M7N4ck0m9byJSO9gynGrzrN5x48ZdsB5cfn4+48aNs7U5l5WYmMj27dtZt26ds0MRkYswDIPPNhxi8Os/WRO438VFsCRpAKN6tFACJyJ1ls09ce7u7hw9erTSxvdZWVmEhYVRWlpq1wCdTQsbRFzXnuN5PPnFFtaknwSgQ2gAL47sQq+oYCdHJiJSMw6pE5eTk4NhGBiGQW5uLj4+Ptb3zGYz33zzTaXETkTEEYpKzfxz2R7+sXQPxWYLPp5uPJzQnnuuaaWyISJSb1Q7iWvYsCEmkwmTyUT79u0rvW8ymZg6dapdgxMROd+avSd4ct4W9hzPB2BA+ya8MKILEcF+To5MROTKqnYSt3TpUgzD4Nprr+Xzzz8nOPi34QovLy9atmxJeHi4Q4J0BhX7FXEtpwuKmf7NTuauL5v3FtLAm2eHRXNzt2aa9yYi9ZLNc+L2799PREQEbm71Y8hCc+JEnMswDL7cdITnv95OVl4xAHf2jmTiDR0J8tN+pyJStzh079SWLVsCUFBQwIEDByguLq7wfrdu3WxtUkTkgg6cKOCp+b/td9quaQOmjepKnBYuiIjYnsQdP36csWPH8u23317wfQ0/isjlMlsMZq9M59XFqRSWWPDycOPBa9vyp/5t8PKoH6MAIiKXYvNPw4cffpjTp0+zZs0afH19WbRoEe+99x7t2rXjyy+/dESMIlKP7MvK53f/Xs0LC3dQWGLh6jaN+e7h/jxwbTslcCIi57C5J+7HH39kwYIF9OrVCzc3N1q2bMl1111HYGAg06dP56abbnJEnCJSx1ksBnNW7ePl73ZSWGLB38udp26K5s7eEVq4ICJyATYncfn5+dZ6cI0aNeL48eO0b9+erl27snHjRrsHKCJ1X9qxPJ6ct4W1Z4v29m3bmL/d2o0WjVQ2RESkKjYncR06dCA1NZWoqChiYmL417/+RVRUFLNmzaJZs2aOiNEpVGJExPHOFJuZuXQ3/16+lxKzgZ+XO0/e2Im74iPV+yYicgk2lxj58MMPKS0tZcyYMWzYsIEbbriBkydP4uXlxZw5c7jjjjscFatTqMSIiGP8sD2TZ7/cxuHTZwC4tmNTpg7vrKK9IlKv2ZJ32JzEna+goICdO3cSGRlJSEjI5TTlkpTEidjX4dNneHbBNn7YkQlA84a+PDssmuuiQ9X7JiL1nkPrxJ3Pz8+PHj16XG4zIlLHmc8uXHhtcSoFxWY83EyM79+aCde2xc/rsn8UiYjUO9X6yZmUlFTtBl9//fUaByMiddPWw9lM+mILWw5nAxAX1YhpI7vSLjTAyZGJiNRe1Urifv3112o1pqEQETlXQXEpM37YzX9+TsdsMQjw8eDJGztxR68I3Nz080JE5HJUK4lbunSpo+MQkTpmWeoxnp6/lUOnyhYu3NytGZOHRdM0wMfJkYmI1A01noiSlpbGnj176N+/P76+vhiGoZ44ESErr4jnv97OgpQjQNnChedHdObajqFOjkxEpG6xOYk7ceIEt99+O0uXLsVkMrF7925at27NPffcQ6NGjXjttdccEaeIuDjDMPh0wyFeXLiD7DMluJlgbN9WJF3XHn9vLVwQEbE3mzci/Otf/4qnpycHDhzAz++3ek533HEHixYtsmtwzpScnEx0dDRxcXHODkXE5aVn5fP7t9fw+GebyT5TQufwQBYkXsMzN0crgRMRcRCb68SFhYXx3XffERMTQ0BAAJs2baJ169bs3buXbt26kZeX56hYnUJ14kSqVlxq4e0Ve3ljyW6KSy34eLqRdF17xvVthYe7NqsXEbGVQ+vE5efnV+iBK3fy5Em8vb1tbU5EaqmNB04x6fMtpGbmAtCvXQjTRnbVjgsiIleIzb8q9+vXj/fff9/62mQyYbFYePnllxk0aJBdgxMR15NTWMIz87dy6z9XkZqZS7C/FzPuiOX9cb2VwImIXEE298S9/PLLDB48mPXr11NcXMzjjz/Otm3bOHnyJCtXrnREjCLiAgzD4LttGTz75TYyc4oAuLVHC56+qRON/L2cHJ2ISP1jcxLXpUsXdu3axcyZMwkICCAvL49Ro0aRmJhIs2bNHBGjiDjZkdNnmHzOfqdRjf2YNrIrV7ete/sli4jUFjYlcSUlJdxwww3MmjWLp556ylExiYiLMAyDj9ceYNrCHeQXm/F0N3HfgDYkDmqLj6e7s8MTEanXbEriPD092bx5s6NiEREXcvj0GSZ+vpkVu7MA6NmyEdNHdaW99jsVEXEJNi9s+MMf/sB//vMfR8QiIi7AMAzmrjvAkL8vZ8XuLLw93Hjm5mg+/XMfJXAiIi7E5jlxpaWlvPvuu/zwww/07NkTf3//Cu+//vrrdgtORK6sfVn5PPvlNn7adRyAHpENefX/YmjdpIGTIxMRkfPZnMRt3bqVHj16ALBr164K77ni3qmpqanccccdFV7/97//ZcSIEc4LSsTF5BeVMnNpGv9ZkU6x2YKXhxuPXt+ee65pjbub6/27FhGRGuzYUJvl5eURFRXF/v37K/UgVkU7NkhdZhgG81MO89K3O61lQ/q3b8Kzw6Jpo943EZErzqE7NtRmX375JYMHD652AidSl6Vm5PLUvC2s338KgMhgPybfHM3gTk1dslddREQqcvrmhsuXL2fYsGGEh4djMpmYP39+pXOSk5OJiorCx8eH+Ph41q5dW6N7/e9//6swtCpSHxWWmHnlu53c9OYK1u8/hZ+XO48N6cDiv/YnITpUCZyISC3h9J64/Px8YmJiGDduHKNGjar0/ty5c0lKSmLWrFnEx8czY8YMhgwZQmpqKk2bNgUgNjaW0tLSStcuXryY8PBwoKx7ctWqVXzyyScXjaeoqIiioiLr65ycnMv5eCIuZWVaFk/N28K+EwUAXB8dytRbOtMsyNfJkYmIiK1cak6cyWRi3rx5FRYdxMfHExcXx8yZMwGwWCxEREQwYcIEJk6cWO22P/jgA7777js+/PDDi543ZcoUpk6dWum45sRJbXYyv5gXFm7ni42HAQgL9GHqLZ0Z0jnMyZGJiMi5bJkT5/Th1IspLi5mw4YNJCQkWI+5ubmRkJDA6tWrbWqrukOpkyZNIjs72/p18OBBm+MWcRWGYfDp+oMMfm0ZX2w8jMkEo/u05Puk/krgRERqOacPp15MVlYWZrOZ0NDQCsdDQ0PZuXNntdvJzs5m7dq1fP7555c819vbG29vb5tjFXE1e4/n8dS8razeewKAjmEBTB/Vle6RjZwcmYiI2INLJ3H2EhQURGZmpk3XJCcnk5ycjNlsdlBUIo5RVGpm1rK9JC9No9hswcfTjYcT2nPPNa3wdHfpzncREbGBSydxISEhuLu7V0rAMjMzCQtz7FBQYmIiiYmJ1rFpkdpgbfpJJn2xmT3H8wEY0L4JL4zoQkSwn5MjExERe3PpX8u9vLzo2bMnS5YssR6zWCwsWbKEPn36ODEyEddyuqCYJz7bzO3/Ws2e4/mENPDmzTu7M2dsnBI4EZE6yuk9cXl5eaSlpVlfp6enk5KSQnBwMJGRkSQlJTF69Gh69epF7969mTFjBvn5+YwdO9ahcWk4VWoDwzD4ctMRnvtqOyfyiwG4s3ckE2/oSJCfp5OjExERR3J6iZFly5YxaNCgSsdHjx7NnDlzAJg5cyavvPIKGRkZxMbG8uabbxIfH39F4tO2W+KqjuUW8uQXW/lhR9l0g3ZNGzBtVFfiooKdHJmIiNSULXmH05M4V6ckTlxNee/bs19u43RBCZ7uJiZc2477BrTBy8OlZ0iIiMglaO9UO9BwqriirLwinp63lUXbMgDoHB7Iq/8XQ6dm+gVDRKS+UU/cJagnTlyB2WLw8doDvLY4ldMFJXi4lfW+3T+ojcqGiIjUIeqJE6lDftl7gilfbmNnRi4AnZoF8ur/daNzuErfiIjUZ0riqqDhVHG2Q6cKmP7NThZuOQpAkK8nSde15674SDzU+yYiUu9pOPUSNJwqV5rFYvDBL/t56dudnCkx42aC38dH8sh1HWjk7+Xs8ERExIE0nCpSSx08WcATn29m1Z6y/U57RwUz9ZbOWrggIiKVKIkTcQGGYfDftQd5ceF28ovN+Hq6M3FoR/54VUvc3EzODk9ERFyQkrgqaE6cXCnpWflMXrCVFbuzAOjVshGv/l8MUSH+To5MRERcmebEXYLmxImj5BeVMnNpGv9ZkU6x2YK3hxuPDenA2L6tcFfvm4hIvaQ5cSIuzDAMvt58lBcX7iAjpxCAAe2bMGV4Z1qp901ERKpJSZzIFZSelc+TX2xh9d6yhQsRwb5MvrkzCZ2aYjKp901ERKpPSZzIFVBitvDv5Xt5Y8luikvLhk4TB7XlT/1b4+Pp7uzwRESkFlISVwUtbBB7STl4momfb7buuNCvXQjTRnYlItjPyZGJiEhtpoUNl6CFDVJTeUWlvLY4lfdW7cNiQCM/TyYPi2ZEbHMNnYqIyAVpYYOIExmGwaKtGUz9art14cKI2HCeuTmaxg28nRydiIjUFUriROzowIkCJn+5lWWpxwGIDPbjuVs6M7BDUydHJiIidY2SOBE7KF+48OaS3RSVWvB0N/GXAW24f1BbLVwQERGHUBIncpm2HcnmsU83s/1oDgBXt2nM8yO60KZJAydHJiIidZmSOJEaKio1k/xjGv9YtodSi0FDP08m3xzNyO5auCAiIo6nJK4KKjEiF5Ny8DSPf7aJXZl5AAztEsZzt3ShSYAWLoiIyJWhEiOXoBIjcq68olJe/S6V91bvwzAgpIEXz93ShRu7NnN2aCIiUgeoxIiIA3y/PZPJC7ZyNPu3siGTh3Um2N/LyZGJiEh9pCRO5BIycwqZ8uU2vt2aAZSVDXlhRBf6t2/i5MhERKQ+UxInUgWzxeDDX/bz6nep5BaV4u5m4k/9W/Pgte3w9VLZEBERcS4lcSIXsPVwNk/O28LmQ9kAxEY0ZPqornRqpnmRIiLiGpTEiZwjt7CE1xbv4v3VZfudBvh48PgNHfl970jc3VQ2REREXIeSOBHK9jv9dmsGU7/aRmZOEQDDY8J5+uZONA3wcXJ0IiIilSmJk3rvwIkCnlmwlZ92le132rKxH8/fooULIiLi2pTEVUHFfuu+olIzby/fy1s/plFUasHL3Y37Brbh/oFttN+piIi4PBX7vQQV+62bNh44xeOfbSbtWNmOC9rvVEREXIGK/YpU4UyxmdcWp/KflenWHReeuTma4THh2u9URERqFSVxUm+s3nOCiV9sZv+JAgBG9WjO5JujaeinHRdERKT2URIndd7pgmJe/i6Vj9ccAKBZkA/TRnZlUMemTo5MRESk5pTESZ1lsRh8tuEQLy3aycn8YgDu7B3JpBs7Eujj6eToRERELo+SOKmTth7OZvKCrWw8cBqA9qENeO6WLlzVurFzAxMREbETJXFSp+QVlfLqd6nWHRf8vdx5OKE9Y/pG4enu5uzwRERE7EZJnNQZP+7M5Ol5WzmSXQjAzd2a8fRN0YQFaccFERGpe5TESa2XlVfE1K+289WmIwBEBPsybWRX+rXTjgsiIlJ31Ysk7u9//zvvvPMOhmGQkJDAG2+8oZpgdYBhGHy+8TAvLNzO6YIS3Exwb7/WPJzQDj+vevFoi4hIPVbn/6c7fvw4M2fOZNu2bXh6etK/f39++eUX+vTp4+zQ5DIcOFHAk/O28HNaFgDRzQL5263d6NoiyMmRiYiIXBl1PokDKC0tpbCwbJ5USUkJTZuqPlhtVWq28O7KdF7/fheFJRa8Pdx4OKE99/ZrpYULIiJSrzj9f73ly5czbNgwwsPLtj2aP39+pXOSk5OJiorCx8eH+Ph41q5dW+32mzRpwqOPPkpkZCTh4eEkJCTQpk0bO34CuVK2HclmxD9WMu2bnRSWWOjTujHfPdyfvwxsowRORETqHaf3xOXn5xMTE8O4ceMYNWpUpffnzp1LUlISs2bNIj4+nhkzZjBkyBBSU1OtPWqxsbGUlpZWunbx4sX4+vry9ddfs2/fPnx9fRk6dCjLly+nf//+F4ynqKiIoqIi6+ucnBw7fVKpqRKzheSlacz8MY1Si0GgjwdP3xTN//VqobmNIiJSb5kMwzCcHUQ5k8nEvHnzGDFihPVYfHw8cXFxzJw5EwCLxUJERAQTJkxg4sSJl2zz008/ZdmyZSQnJwPwyiuvYBgGjz/++AXPnzJlClOnTq10PDs7m8DAwBp8KrkcqRm5PPJpClsPlyXTQ7uEMfWWzjQNUNkQERGpe3JycggKCqpW3uHSY1DFxcVs2LCBhIQE6zE3NzcSEhJYvXp1tdqIiIhg1apVFBYWYjabWbZsGR06dKjy/EmTJpGdnW39Onjw4GV/DrFdqdnCP5alMeytn9l6OIeGfp68eWd3/nFXDyVwIiIiuMBw6sVkZWVhNpsJDQ2tcDw0NJSdO3dWq42rrrqKG2+8ke7du+Pm5sbgwYMZPnx4led7e3vj7e19WXHL5Vm/7yRTvtpm7X1L6NSUaSO70jRQyZuIiEg5l07i7OXFF1/kxRdftOma5ORkkpOTMZvNDopKznc0+wzTv9nJl2eL9gb4ePDssM7c2qO55r6JiIicx6WTuJCQENzd3cnMzKxwPDMzk7CwMIfeOzExkcTEROvYtDhOYYmZfy/fyz+X7eFMiRmTCX4XF8Ej13cgpIF6RUVERC7EpefEeXl50bNnT5YsWWI9ZrFYWLJkicOL9SYnJxMdHU1cXJxD71PfLd91nOv/vpzXv9/FmRIzcVGN+OqBa5g+qpsSOBERkYtwek9cXl4eaWlp1tfp6emkpKQQHBxMZGQkSUlJjB49ml69etG7d29mzJhBfn4+Y8eOdWhc6olzrKy8Ip7/ejsLUsqGTpsF+fDkjZ24uVszDZ2KiIhUg9OTuPXr1zNo0CDr66SkJABGjx7NnDlzuOOOOzh+/DiTJ08mIyOD2NhYFi1aVGmxg9QOFovBpxsOMu2bnWSfKdvvdMzVrUi6vj0NvJ3+OIqIiNQaLlUnzpWcu7Bh165dqhNnB7syc3l63lbW7jsJQOfwQKaP6kq3Fg2dG5iIiIiLsKVOnJK4S7DlmykXdqbYzJs/7ubt5XsptRj4erqTdF17xvaNwkPbZYmIiFjZkndo/Eoc6sedmUxesI1Dp84AcF10KM8Oi6ZFIz8nRyYiIlK7KYkThziWW8iUL7fxzZYMAMKDfJgyvDPXd3ZsaRgREZH6QklcFVTst2YMw+DT9Yd4YeF2cgpLcXczce81rXhwcDv8tXBBRETEbjQn7hI0J676Dpwo4Ml5W/g5LQuArs2D+Nut3YgO1/dNRESkOjQnTq6oErOFOSv3WQv2enu4kXRde+65ppUWLoiIiDiIkji5LBv2n+KpeVvYmZELwFWtg3lpVDeiQvydHJmIiEjdpiSuCpoTd3GnC4r526Kd/HftQQAa+nkyaWhHbu8VoR0XRERErgDNibsEzYmryDAMvtx0hOe+2s6J/GIA/q9nCybd2Ilgfy8nRyciIlK7aU6cOMSx3EKemreV77dnAtCuaQNeGNGF+NaNnRyZiIhI/aMkTi6pvPft2S+3cbqgBE93ExOubcd9A9rg5aGFCyIiIs6gJE4u6nhuEc/M38qibWVFe6ObBfLa7TF0aqahZREREWdSEleF+r6wwWwx+HjtAV5ZtJOcwlI83Mp63+4f1AZPlQ0RERFxOi1suIT6uLBh86HTPD1/K5sPZQPQpXkgf7u1G53Dg5wcmYiISN2mhQ1SI9lnSnj1u1Q+XLMfw4AAbw8eu6EDd8W3xN1NZUNERERciZI4wTAMvtp8lOe+2k5WXhEAI2LDefKmTjQN8HFydCIiInIhSuLquQMnCnh6wVaW7zoOQOsm/rwwogtXtwlxcmQiIiJyMUri6qkSs4V3VqTzxpJdFJZY8HJ3I3FQW+4b2BpvD3dnhyciIiKXoCSuCnV5deqmg6d54vPN1v1O+7RuzIsju9C6SQMnRyYiIiLVpdWpl1CXVqcWFJfy2uJdzF6ZjsWARn6ePH1TNKN6NNd+pyIiIi5Aq1Olkp92HeepeVs4dOoMACO7N+fpmzrRuIG3kyMTERGRmlASV8edLijmua+388XGwwA0b+jLiyO7MLBDUydHJiIiIpdDSVwd9s2Wo0xesJWsvGJMJhhzdRSPXt8Bf2/9tYuIiNR2+t+8DjqWU8jkBdus+522bdqAl2/rRo/IRk6OTEREROxFSVwdYrYY/G/9QaZ/s8O63+n9A9uQeG1blQ0RERGpY5TE1RHr951kylfb2Ho4B4CuzYP4263diA6v3StqRURE5MKUxNVyGdmFvPTtDuanHAEgwMeDhxPaM7pPSzzc3ZwcnYiIiDiKkrgquHqx31Kzhdkr9/H3H3ZRUGzGZII7ekXw6JAOhKhsiIiISJ2nYr+X4IrFfncczeGJzzez+VA2AD0iGzJleGe6tWjo3MBERETksqjYbx1VVGpm5o9p/HPZHkotBgE+Hjx1Yydu7xWBm5t2XBAREalPlMTVEuv3neSJzzez53g+AEM6h/LcLV0IDfRxcmQiIiLiDEriXFxOYQl/+3YnH605AEBIA2+ev6UzQ7s2c3JkIiIi4kxK4lzYoq1HmbxgG8dyiwC4vVcLnryxEw39vJwcmYiIiDibkjgXdDT7DM8u2Mbi7ZkAtArx58WRXbi6TYiTIxMRERFXoSTOhZSYLbz7czpvLNlNQbEZDzcT9w1owwPXtsXHUzsuiIiIyG+UxLmI1XtOMHnBVnYfywOgZ8tGvDiyCx3DXKOsiYiIiLgWJXFOdiy3kGkLf9txIdjfi4lDO3JbjxYqGyIiIiJVUhLnZH/+YAO/HjiNyQS/7x3JY0M6aOGCiIiIXFK92Fzz1VdfpXPnznTp0oUPP/zQ2eFU8Nj1HejWIoj59/flxZFdlcCJiIhItdT5nrgtW7bw8ccfs2HDBgzDYNCgQdx88800bNjQ2aEBcHXbEBYk9sVk0tCpiIiIVF+d74nbsWMHffr0wcfHB19fX2JiYli0aJGzw6pACZyIiIjYyulJ3PLlyxk2bBjh4eGYTCbmz59f6Zzk5GSioqLw8fEhPj6etWvXVrv9Ll26sGzZMk6fPs2pU6dYtmwZhw8ftuMnEBEREbnynD6cmp+fT0xMDOPGjWPUqFGV3p87dy5JSUnMmjWL+Ph4ZsyYwZAhQ0hNTaVp06YAxMbGUlpaWunaxYsXEx0dzYMPPsi1115LUFAQV111Fe7uVddcKyoqoqioyPo6JyfHDp9SRERExL5MhmEYzg6inMlkYt68eYwYMcJ6LD4+nri4OGbOnAmAxWIhIiKCCRMmMHHiRJvvce+99zJy5EhuuummC74/ZcoUpk6dWul4dnY2gYGq2SYiIiKOk5OTQ1BQULXyDqcPp15McXExGzZsICEhwXrMzc2NhIQEVq9eXe12jh07BkBqaipr165lyJAhVZ47adIksrOzrV8HDx6s+QcQERERcRCnD6deTFZWFmazmdDQ0ArHQ0ND2blzZ7XbueWWW8jOzsbf35/Zs2fj4VH1x/b29sbb25vk5GSSk5Mxm801jl9ERETEUVw6ibMXW3rtyiUmJpKYmGjt1hQRERFxJS49nBoSEoK7uzuZmZkVjmdmZhIWFuakqEREREScz6WTOC8vL3r27MmSJUusxywWC0uWLKFPnz4OvXdycjLR0dHExcU59D4iIiIiNeH04dS8vDzS0tKsr9PT00lJSSE4OJjIyEiSkpIYPXo0vXr1onfv3syYMYP8/HzGjh3r0Lg0nCoiIiKuzOlJ3Pr16xk0aJD1dVJSEgCjR49mzpw53HHHHRw/fpzJkyeTkZFBbGwsixYtqrTYQURERKQ+cak6ca7k3NWpu3btUp04ERERcThb6sQpibsEW76ZIiIiIpejzhT7FREREZELc/qcOFdX3lGpPVRFRETE0crzjeoMlCqJq0L5nLji4mIAIiIinByRiIiI1Be5ubmXrI6hOXGXYLFYOHLkCAEBAZhMpirPi4uLY926dTa/n5OTQ0REBAcPHqz1c+4u9T2oDfe83PZqcr0t11T33Jo+j1B3nsm68Dzao01XeCYv55y68jxC3Xgm68LzWJ3znPkz0jAMcnNzCQ8Px83t4rPe1BN3CW5ubrRo0eKS57m7u1/0L/NS7wcGBtb6H1CX+oy14Z6X215Nrrflmuqee7nPI9T+Z7IuPI/2aNMVnkl7nFPbn0eoG89kXXgeq3Oes39GVrc+rRY22EliYuJlvV8XOOMz2vuel9teTa635ZrqnqvnsW48j/Zo0xWeSXudU9vVhWeyLjyP1TmvtjyPGk51MpUwEVejZ1JciZ5HcTWu9EyqJ87JvL29efbZZ/H29nZ2KCKAnklxLXoexdW40jOpnjgRERGRWkg9cSIiIiK1kJI4ERERkVpISZyIiIhILaQkTkRERKQWUhInIiIiUgspiatFTp8+Ta9evYiNjaVLly68/fbbzg5J6rGDBw8ycOBAoqOj6datG59++qmzQxJh5MiRNGrUiNtuu83ZoUg99PXXX9OhQwfatWvHO++84/D7qcRILWI2mykqKsLPz4/8/Hy6dOnC+vXrady4sbNDk3ro6NGjZGZmEhsbS0ZGBj179mTXrl34+/s7OzSpx5YtW0Zubi7vvfcen332mbPDkXqktLSU6Oholi5dSlBQED179mTVqlUO/T9aPXG1iLu7O35+fgAUFRVhGAbKwcVZmjVrRmxsLABhYWGEhIRw8uRJ5wYl9d7AgQMJCAhwdhhSD61du5bOnTvTvHlzGjRowNChQ1m8eLFD76kkzo6WL1/OsGHDCA8Px2QyMX/+/ErnJCcnExUVhY+PD/Hx8axdu9ame5w+fZqYmBhatGjBY489RkhIiJ2il7rmSjyP5TZs2IDZbCYiIuIyo5a67Eo+kyK2utzn88iRIzRv3tz6unnz5hw+fNihMSuJs6P8/HxiYmJITk6+4Ptz584lKSmJZ599lo0bNxITE8OQIUM4duyY9Zzy+W7nfx05cgSAhg0bsmnTJtLT0/n444/JzMy8Ip9Nap8r8TwCnDx5krvvvpt///vfDv9MUrtdqWdSpCbs8XxecYY4BGDMmzevwrHevXsbiYmJ1tdms9kIDw83pk+fXqN7/OUvfzE+/fTTywlT6glHPY+FhYVGv379jPfff99eoUo94cifkUuXLjVuvfVWe4Qp9VRNns+VK1caI0aMsL7/0EMPGR999JFD41RP3BVSXFzMhg0bSEhIsB5zc3MjISGB1atXV6uNzMxMcnNzAcjOzmb58uV06NDBIfFK3WaP59EwDMaMGcO1117LH//4R0eFKvWEPZ5JEUepzvPZu3dvtm7dyuHDh8nLy+Pbb79lyJAhDo3Lw6Gti1VWVhZms5nQ0NAKx0NDQ9m5c2e12ti/fz9/+tOfrAsaJkyYQNeuXR0RrtRx9ngeV65cydy5c+nWrZt17sgHH3ygZ1JqxB7PJEBCQgKbNm0iPz+fFi1a8Omnn9KnTx97hyv1THWeTw8PD1577TUGDRqExWLh8ccfd3j1CCVxtUjv3r1JSUlxdhgiAFxzzTVYLBZnhyFSwQ8//ODsEKQeGz58OMOHD79i99Nw6hUSEhKCu7t7pYUImZmZhIWFOSkqqa/0PIqr0TMprsxVn08lcVeIl5cXPXv2ZMmSJdZjFouFJUuWqKtfrjg9j+Jq9EyKK3PV51PDqXaUl5dHWlqa9XV6ejopKSkEBwcTGRlJUlISo0ePplevXvTu3ZsZM2aQn5/P2LFjnRi11FV6HsXV6JkUV1Yrn0+Hrn2tZ5YuXWoAlb5Gjx5tPeett94yIiMjDS8vL6N3797GL7/84ryApU7T8yiuRs+kuLLa+Hxq71QRERGRWkhz4kRERERqISVxIiIiIrWQkjgRERGRWkhJnIiIiEgtpCROREREpBZSEiciIiJSCymJExEREamFlMSJiIiI1EJK4kRERERqISVxIlJty5Ytw2Qycfr0aWeHcsWYTCZMJhMNGzZ0+L2ioqKYMWOGw+/j6qZMmWL9vuv7IVI1JXEickEDBw7k4YcfrnDs6quv5ujRowQFBTknKJyTSM6ePZtdu3ZZX8+ZM8chSd26dev405/+ZH1tMpmYP3++3e/j6h599FGOHj1KixYtnB2KiEvzcHYAIlJ7eHl5ERYW5uwwrriGDRvStGlTh9+nSZMmDmm3pKQET09Ph7Rtq+LiYry8vC56ToMGDWjQoAHu7u5XKCqR2kk9cSJSyZgxY/jpp5944403rMNa+/btq9QLVt4j9fXXX9OhQwf8/Py47bbbKCgo4L333iMqKopGjRrx4IMPYjabre0XFRXx6KOP0rx5c/z9/YmPj2fZsmXW9/fv38+wYcNo1KgR/v7+dO7cmW+++YZ9+/YxaNAgABo1aoTJZGLMmDEAWCwWpk+fTqtWrfD19SUmJobPPvvM2mZ57AsXLqRbt274+Phw1VVXsXXrVrt8v0aMGFHh2MMPP8zAgQOtrwcOHMgDDzzAAw88QFBQECEhITzzzDMYhmE959zh1KioKABGjhyJyWSyvgZYsGABPXr0wMfHh9atWzN16lRKS0ut75tMJv75z38yfPhw/P39efHFFyvF/Nxzz9GlS5dKx2NjY3nmmWesr9955x06deqEj48PHTt25B//+EeF85944gnat2+Pn58frVu35plnnqGkpMT6/pQpU4iNjeWdd96hVatW+Pj4APDZZ5/RtWtXfH19ady4MQkJCeTn51/4GywiF6SeOBGp5I033mDXrl106dKF5557DijrJdq3b1+lcwsKCnjzzTf55JNPyM3NZdSoUYwcOZKGDRvyzTffsHfvXm699Vb69u3LHXfcAcADDzzA9u3b+eSTTwgPD2fevHnccMMNbNmyhXbt2pGYmEhxcTHLly/H39+f7du306BBAyIiIvj888+59dZbSU1NJTAwEF9fXwCmT5/Ohx9+yKxZs2jXrh3Lly/nD3/4A02aNGHAgAHWeB977DHeeOMNwsLCePLJJxk2bBi7du26Ij1V7733Hvfccw9r165l/fr1/OlPfyIyMpLx48dXOnfdunU0bdqU2bNnc8MNN1h7pVasWMHdd9/Nm2++Sb9+/dizZ491CPbZZ5+1Xj9lyhReeuklZsyYgYdH5R/148aNY+rUqaxbt464uDgAfv31VzZv3swXX3wBwEcffcTkyZOZOXMm3bt359dff2X8+PH4+/szevRoAAICApgzZw7h4eFs2bKF8ePHExAQwOOPP269V1paGp9//jlffPEF7u7uHD16lDvvvJOXX36ZkSNHkpuby4oVKyoktCJSDYaIyAUMGDDAeOihhyocW7p0qQEYp06dMgzDMGbPnm0ARlpamvWcP//5z4afn5+Rm5trPTZkyBDjz3/+s2EYhrF//37D3d3dOHz4cIW2Bw8ebEyaNMkwDMPo2rWrMWXKlAvGdX4MhmEYhYWFhp+fn7Fq1aoK595zzz3GnXfeWeG6Tz75xPr+iRMnDF9fX2Pu3LlVfh8AY968eRWOzZ492wgKCrK+Hj16tHHLLbdUOOehhx4yBgwYYH09YMAAo1OnTobFYrEee+KJJ4xOnTpZX7ds2dL4+9//ftF7Dx482Jg2bVqFYx988IHRrFmzCtc9/PDDVX6mckOHDjX+8pe/WF9PmDDBGDhwoPV1mzZtjI8//rjCNc8//7zRp0+fKtt85ZVXjJ49e1pfP/vss4anp6dx7Ngx67ENGzYYgLFv376Lxnf+90NEKlJPnIhcFj8/P9q0aWN9HRoaSlRUFA0aNKhw7NixYwBs2bIFs9lM+/btK7RTVFRE48aNAXjwwQf5y1/+wuLFi0lISODWW2+lW7duVcaQlpZGQUEB1113XYXjxcXFdO/evcKxPn36WP8cHBxMhw4d2LFjh42fumauuuoqTCZThVhee+01zGZzted/bdq0iZUrV1YYIjWbzRQWFlJQUICfnx8AvXr1umRb48ePZ9y4cbz++uu4ubnx8ccf8/e//x2A/Px89uzZwz333FOhp7C0tLTCwpa5c+fy5ptvsmfPHvLy8igtLSUwMLDCfVq2bFlhvl9MTAyDBw+ma9euDBkyhOuvv57bbruNRo0aVet7ICJllMSJyGU5fxjSZDJd8JjFYgEgLy8Pd3d3NmzYUClxKU/87r33XoYMGcLChQtZvHgx06dP57XXXmPChAkXjCEvLw+AhQsX0rx58wrveXt71/zDVZObm1ulocBz54XZU15eHlOnTmXUqFGV3iufbwbg7+9/ybaGDRuGt7c38+bNw8vLi5KSEm677TbrfQDefvtt4uPjK1xX/ve2evVq7rrrLqZOncqQIUMICgrik08+4bXXXqtw/vmxuLu78/3337Nq1SoWL17MW2+9xVNPPcWaNWto1apVNb4LIgJK4kSkCl5eXhUWI9hL9+7dMZvNHDt2jH79+lV5XkREBPfddx/33XcfkyZN4u2332bChAnWlY3nxhYdHY23tzcHDhyoMP/tQn755RciIyMBOHXqFLt27aJTp06X9ZmaNGlSaYFESkpKpWR2zZo1lWJp165dlb1wnp6elf4OevToQWpqKm3btr2smAE8PDwYPXo0s2fPxsvLi9/97nfWOYahoaGEh4ezd+9e7rrrrgtev2rVKlq2bMlTTz1lPbZ///5q3dtkMtG3b1/69u3L5MmTadmyJfPmzSMpKemyP5dIfaEkTkQuKCoqijVr1rBv3z4aNGhAcHCwXdpt3749d911F3fffTevvfYa3bt35/jx4yxZsoRu3bpx00038fDDDzN06FDat2/PqVOnWLp0qTXRatmyJSaTia+//pobb7wRX19fAgICePTRR/nrX/+KxWLhmmuuITs7m5UrVxIYGGidhA9lqzIbN25MaGgoTz31FCEhIZVWltrq2muv5ZVXXuH999+nT58+fPjhh2zdurXSUO6BAwdISkriz3/+Mxs3buStt96q1Gt1rqioKJYsWULfvn3x9vamUaNGTJ48mZtvvpnIyEhuu+023Nzc2LRpE1u3buWFF16wOfZ7773X+r1duXJlhfemTp3Kgw8+SFBQEDfccANFRUWsX7+eU6dOkZSURLt27Thw4ACffPIJcXFxLFy4kHnz5l3ynmvWrGHJkiVcf/31NG3alDVr1nD8+PHLTqZF6huVGBGRC3r00Udxd3cnOjqaJk2acODAAbu1PXv2bO6++24eeeQROnTowIgRI1i3bp21h8xsNpOYmEinTp244YYbaN++vbW0RfPmzZk6dSoTJ04kNDSUBx54AIDnn3+eZ555hunTp1uvW7hwYaXhuZdeeomHHnqInj17kpGRwVdffXXJumXns1gsFVZ8DhkyhGeeeYbHH3+cuLg4cnNzufvuuytdd/fdd3PmzBl69+5NYmIiDz30UIXivud77bXX+P7774mIiLAmhEOGDOHrr79m8eLFxMXFcdVVV/H3v/+dli1b2vQZyrVr146rr76ajh07Vho2vffee3nnnXeYPXs2Xbt2ZcCAAcyZM8f6PR0+fDh//etfeeCBB4iNjWXVqlUVypNUJTAwkOXLl3PjjTfSvn17nn76aV577TWGDh1ao88gUl+ZjPMncoiI1EHLli1j0KBBnDp1yqbdFkwmE/PmzavQW/fSSy9Ze9uqa+DAgcTGxrrcNlKGYdCuXTvuv/9+lxvKjIqK4uGHH660c4iIlFFPnIjIJdx55520aNGCgoICNm7cyOzZs0lISHB2WJft+PHjzJw5k4yMDMaOHevscKymTZtGgwYN7Nr7K1IXaU6ciMhF7N69GyhbUfnvf/+b5557joSEBCZPnuzkyC5f06ZNCQkJ4d///rdLlfe47777uP322wHHbUUmUhdoOFVERESkFtJwqoiIiEgtpCROREREpBZSEiciIiJSCymJExEREamFlMSJiIiI1EJK4kRERERqISVxIiIiIrWQkjgRERGRWuj/Absj9QK2JzZNAAAAAElFTkSuQmCC\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f,ax = plt.subplots(1,1,figsize=(7,5))\n",
+ "ax.set_xscale(\"log\")\n",
+ "ax.set_yscale(\"log\")\n",
+ "ax.set_xlabel(\"timestep [Jupiter years]\")\n",
+ "ax.set_ylabel(\"relative energy error\")\n",
+ "ax.plot(dt_samples/sim.particles[1].P,Emax_wh,label=\"WH\")\n",
+ "ax.legend();"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can see that the WH converges quadratically and reaches a precision of $10^{-9}$ at a timestep of 0.001 Jupiter years. Let's try the same with the WHCKL, SABACL4, and SABA(10,6,4) integrators."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/Users/rein/git/rebound/rebound/simulation.py:724: RuntimeWarning: WHFast convergence issue. Timestep is larger than at least one orbital period.\n",
+ " warnings.warn(msg[1:], RuntimeWarning)\n"
+ ]
+ }
+ ],
+ "source": [
+ "Emax_saba4 = np.zeros(N_dt_samples)\n",
+ "for i, dt in enumerate(dt_samples):\n",
+ " sim_run = sim.copy() # make a copy of the simulation so we don't need to set a new one up every time\n",
+ " sim_run.integrator = \"SABACL4\"\n",
+ " sim_run.ri_saba.safe_mode = False\n",
+ " sim_run.dt = dt\n",
+ " Emax_saba4[i] = measure_energy(sim_run)\n",
+ "Emax_saba1064 = np.zeros(N_dt_samples)\n",
+ "for i, dt in enumerate(dt_samples):\n",
+ " sim_run = sim.copy() \n",
+ " sim_run.integrator = \"SABA(10,6,4)\" \n",
+ " sim_run.ri_whfast.safe_mode = False\n",
+ " sim_run.dt = dt\n",
+ " Emax_saba1064[i] = measure_energy(sim_run)\n",
+ "Emax_whckl = np.zeros(N_dt_samples)\n",
+ "for i, dt in enumerate(dt_samples):\n",
+ " sim_run = sim.copy() \n",
+ " sim_run.integrator = \"WHCKL\" \n",
+ " sim_run.ri_whfast.safe_mode = False\n",
+ " sim_run.dt = dt\n",
+ " Emax_whckl[i] = measure_energy(sim_run) "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We get a warning message because the largest timestep we try is larger than the innermost orbital period. You would not want to use such a large timestep in an actual simulation, but we can ignore the message for this test."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f,ax = plt.subplots(1,1,figsize=(7,5))\n",
+ "ax.set_xscale(\"log\")\n",
+ "ax.set_yscale(\"log\")\n",
+ "ax.set_xlabel(\"timestep [Jupiter years]\")\n",
+ "ax.set_ylabel(\"relative energy error\")\n",
+ "ax.plot(dt_samples/sim.particles[1].P,Emax_wh,label=\"WH\")\n",
+ "ax.plot(dt_samples/sim.particles[1].P,Emax_saba4,label=\"SABACL4\")\n",
+ "ax.plot(dt_samples/sim.particles[1].P,Emax_whckl,label=\"WHCKL\")\n",
+ "ax.plot(dt_samples/sim.particles[1].P,Emax_saba1064,label=\"SABA(10,6,4)\")\n",
+ "ax.legend();"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can see that the higher order SABA4, WHCKL, and SABA(10,6,4) integrators are doing significantly better than the standard WH method. For very small timesteps the methods are limited by double floating point precision. The SABA methods appear to be slightly better than the WHCKL method above, but note that the SABA methods are also much slower than the WHCKL per timestep. Taking this into account, the WHCKL has a slight advantage for timesteps larger than 1% of the shortest orbital period. For extremely high accuracy, the SABA(10,6,4) method is faster."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Note that by default all integrators set `safe_mode=False` and `keep_unsynchronized=False`. Depending on your application, you might want to change these flags."
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.6"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}
diff --git a/rebound/source/docs/ipython_examples/Holmberg.ipynb b/rebound/source/docs/ipython_examples/Holmberg.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..107bb6b1f83effa7bdbe42f071e62cd4ee114ca6
--- /dev/null
+++ b/rebound/source/docs/ipython_examples/Holmberg.ipynb
@@ -0,0 +1,233 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Holmberg\n",
+ "In 1941, Erik Holmberg performed arguably the first N-body simulation on the dynamics of interacting galaxies. He used light bulbs to simulate the gravitational interaction of stars as both gravitational force and light intensity fall of as $1/r^2$ with distance. This notebook recreates Holmberg's N-body simulation. Instead of lightbulbs, we use REBOUND. More information about Erik Holmberg can be found on [wikipedia](). His paper can be found on [ADS](http://adsabs.harvard.edu/abs/1941ApJ....94..385H)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2023-09-24T14:23:10.051870Z",
+ "start_time": "2023-09-24T14:23:09.708792Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import rebound\n",
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "First, we setup the initial conditions of one galaxy. The velocities are chosen such that the particles are initially on approximately circular orbits. The arrangement roughly matches that of Holmberg's experiment."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2023-09-24T14:23:10.058351Z",
+ "start_time": "2023-09-24T14:23:10.053319Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "sim = rebound.Simulation()\n",
+ "\n",
+ "sim.add(m=1) # central object\n",
+ "\n",
+ "# 4 rings\n",
+ "lamps = [{\"N\": 6, \"m\": 1, \"r\": 1, \"v\": np.sqrt(4.1/2)},\n",
+ " {\"N\": 8, \"m\": 1, \"r\": 2, \"v\": np.sqrt(9/2)},\n",
+ " {\"N\": 10, \"m\": 0.7, \"r\": 3, \"v\": np.sqrt(15/2)},\n",
+ " {\"N\": 12, \"m\": 0.3, \"r\": 4, \"v\": np.sqrt(16/2)}]\n",
+ "\n",
+ "for l in lamps:\n",
+ " for i in range(l[\"N\"]):\n",
+ " phi = i/l[\"N\"]*2*np.pi\n",
+ " x, y = l[\"r\"]*np.sin(phi), l[\"r\"]*np.cos(phi)\n",
+ " vx, vy = l[\"v\"]*np.cos(phi), -l[\"v\"]*np.sin(phi)\n",
+ " sim.add(m=l[\"m\"], x=x, y=y, vx=vx, vy=vy)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let us plot the galaxy we just created."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2023-09-24T14:23:10.413945Z",
+ "start_time": "2023-09-24T14:23:10.290734Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f, ax = plt.subplots(1, 1, figsize=(5,5))\n",
+ "ax.set_aspect(\"equal\")\n",
+ "coords = np.zeros((sim.N, 6))\n",
+ "sim.serialize_particle_data(xyzvxvyvz=coords)\n",
+ "ax.scatter(coords[:,0],coords[:,1])\n",
+ "ax.quiver(coords[:,0],coords[:,1],coords[:,3],coords[:,4], alpha=0.5);"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Next, we add the second galaxy and put the two galaxies on a collision course. To do that, we simply copy the first galaxy and offset it."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2023-09-24T14:23:10.561114Z",
+ "start_time": "2023-09-24T14:23:10.557749Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "N = sim.N\n",
+ "for i in range(N):\n",
+ " p = sim.particles[i].copy() # make a copy of the particle in the simulation\n",
+ " p.x += 8 # offset\n",
+ " p.y += 8 # offset\n",
+ " p.vx -= 6 # set up collision course\n",
+ " sim.add(p) # add the copy\n",
+ "sim.move_to_com() # Move to the center of mass frame"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Next, let's run the simulation and take snapshots of the particle positions and velocities at 9 intervals. We set a smoothing length to smear out gravity on small scales so that close encounters between particles don't slow down our simulation. The physical size of the lightbulbs would have had the same effect."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2023-09-24T14:23:11.094329Z",
+ "start_time": "2023-09-24T14:23:10.829736Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "sim.softening = 0.2 # smoothing length\n",
+ "N = 9\n",
+ "coords = np.zeros((N,sim.N,3))\n",
+ "times = np.linspace(0,4.,N)\n",
+ "for i,t in enumerate(times):\n",
+ " sim.integrate(t)\n",
+ " sim.serialize_particle_data(xyz=coords[i])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Finally, let's plot the results."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2023-09-24T14:23:11.824081Z",
+ "start_time": "2023-09-24T14:23:11.193361Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f, axarr = plt.subplots(3, 3, figsize=(15,15))\n",
+ "for i,axs in enumerate(axarr):\n",
+ " for j,ax in enumerate(axs):\n",
+ " ax.set_aspect(\"equal\")\n",
+ " ax.set_xlim([-10,10])\n",
+ " ax.set_ylim([-10,10])\n",
+ " ax.scatter(coords[i*3+j,:sim.N//2,0],coords[i*3+j,:sim.N//2,1],facecolors='none', edgecolors='b')\n",
+ " ax.scatter(coords[i*3+j,sim.N//2:,0],coords[i*3+j,sim.N//2:,1],facecolors='b')\n",
+ " ax.set_title(\"t=%.1f\"%(times[i*3+j]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "Holmberg pointed out the aparent spiral arms in the post collision snapshots in his paper. You can see them in the above plots as well. However, note that this simulation is very rudimentary and a claim that it explains the occurance of spiral arms in galaxies would not hold up. One of the most obvious shortcomes of our model is that a typical galaxy contains 100 billion stars but our model contains only 37 particles."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.6"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}
diff --git a/rebound/source/docs/ipython_examples/Horizons.ipynb b/rebound/source/docs/ipython_examples/Horizons.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..f382c626da6c345ad3f97cce801b4a9d5360fc8b
--- /dev/null
+++ b/rebound/source/docs/ipython_examples/Horizons.ipynb
@@ -0,0 +1,355 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Adding particles using NASA JPL Horizons system\n",
+ "\n",
+ "REBOUND can add particles to simulations by obtaining ephemerides from NASA's powerful HORIZONS database. HORIZONS supports many different options, and we will certainly not try to cover everything here. This is meant to serve as an introduction to the basics, beyond what's in [Churyumov-Gerasimenko.ipynb](../Churyumov-Gerasimenko). If you catch any errors, or would either like to expand on this documentation or improve REBOUND's HORIZONS interface (`rebound/horizons.py`), please do fork the repository and send us a pull request.\n",
+ "\n",
+ "**Adding particles**\n",
+ "\n",
+ "When we add particles by passing a string, REBOUND queries the HORIZONS database and takes the first dataset HORIZONS offers. For the Sun, moons, and small bodies, this will typically return the body itself. For planets, it will return the barycenter of the system (for moonless planets like Venus it will say barycenter but there is no distinction). If you want the planet specifically, you have to use, e.g., \"NAME=Pluto\" rather than \"Pluto\". In all cases, REBOUND will print out the name of the HORIZONS entry it's using.\n",
+ "\n",
+ "You can also add bodies using their integer NAIF IDs: [NAIF IDs](https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/MATLAB/req/naif_ids.html). Note that because of the number of small bodies (asteroids etc.) we have discovered, this convention only works for large objects. For small bodies, instead use \"NAME=name\" (see the SMALL BODIES section in the [HORIZONS Documentation](https://ssd.jpl.nasa.gov/?horizons_doc))."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Searching NASA Horizons for 'Sun'... \n",
+ "Found: Sun (10) \n",
+ "---------------------------------\n",
+ "REBOUND version: \t4.0.3\n",
+ "REBOUND built on: \tJan 12 2024 08:52:18\n",
+ "Number of particles: \t1\n",
+ "Selected integrator: \tias15\n",
+ "Simulation time: \t0.0000000000000000e+00\n",
+ "Current timestep: \t0.001000\n",
+ "---------------------------------\n",
+ "\n",
+ "---------------------------------\n",
+ "The following fields have non-default values:\n",
+ "N:\n",
+ "\u001b[31m< 0\u001b[0m\n",
+ "---\n",
+ "\u001b[32m> 1\u001b[0m\n",
+ "python_unit_l:\n",
+ "\u001b[31m< 0\u001b[0m\n",
+ "---\n",
+ "\u001b[32m> 4097248214\u001b[0m\n",
+ "python_unit_m:\n",
+ "\u001b[31m< 0\u001b[0m\n",
+ "---\n",
+ "\u001b[32m> 2145773914\u001b[0m\n",
+ "python_unit_t:\n",
+ "\u001b[31m< 0\u001b[0m\n",
+ "---\n",
+ "\u001b[32m> 1864791206\u001b[0m\n",
+ "rand_seed:\n",
+ "\u001b[31m< 886170\u001b[0m\n",
+ "---\n",
+ "\u001b[32m> 676381\u001b[0m\n",
+ "particles:\n",
+ "\u001b[32m> (128 bytes, values not printed)\u001b[0m\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "import rebound\n",
+ "sim = rebound.Simulation()\n",
+ "sim.add(\"Sun\")\n",
+ "## Other examples:\n",
+ "# sim.add(\"Venus\")\n",
+ "# sim.add(\"399\")\n",
+ "# sim.add(\"Europa\")\n",
+ "# sim.add(\"NAME=Ida\")\n",
+ "# sim.add(\"Pluto\")\n",
+ "# sim.add(\"NAME=Pluto\")\n",
+ "sim.status()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Currently, HORIZONS does not have any mass information for solar system bodies. `rebound/horizons.py` has a hard-coded list provided by Jon Giorgini (10 May 2015) that includes the planets, their barycenters (total mass of planet plus moons), and the largest moons. If REBOUND doesn't find the corresponding mass for an object from this list (like for the asteroid Ida below), it will print a warning message. If you need the body's mass for your simulation, you can set it manually, e.g. (see [Units.ipynb](../Units) for an overview of using different units):"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Searching NASA Horizons for 'NAME=Ida'... \n",
+ "Found: 243 Ida (A884 SB) \n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/Users/dtamayo/Documents/workspace/rebound/rebound/horizons.py:167: RuntimeWarning: Warning: Mass cannot be retrieved from NASA HORIZONS. Set to 0.\n",
+ " warnings.warn(\"Warning: Mass cannot be retrieved from NASA HORIZONS. Set to 0.\", RuntimeWarning)\n"
+ ]
+ }
+ ],
+ "source": [
+ "sim.add(\"NAME=Ida\")\n",
+ "print(sim.particles[-1]) # Ida before setting the mass\n",
+ "sim.particles[-1].m = 2.1e-14 # Setting mass of Ida in Solar masses\n",
+ "print(sim.particles[-1]) # Ida after setting the mass"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Time**\n",
+ "\n",
+ "By default, REBOUND queries HORIZONS for objects' current positions. Specifically, it caches the current time the first time you call `rebound.add`, and gets the corresponding ephemeris. All subsequent calls to `rebound.add` will then use that initial cached time to make sure you get a synchronized set of ephemerides.\n",
+ "\n",
+ "You can also explicitly pass REBOUND the time at which you would like the particles ephemerides: "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Searching NASA Horizons for 'Venus'... \n",
+ "Found: Venus Barycenter (299) (chosen from query 'Venus')\n",
+ "Searching NASA Horizons for 'Venus'... \n",
+ "Found: Venus Barycenter (299) (chosen from query 'Venus')\n",
+ "---------------------------------\n",
+ "REBOUND version: \t4.0.3\n",
+ "REBOUND built on: \tJan 12 2024 08:52:18\n",
+ "Number of particles: \t2\n",
+ "Selected integrator: \tias15\n",
+ "Simulation time: \t0.0000000000000000e+00\n",
+ "Current timestep: \t0.001000\n",
+ "---------------------------------\n",
+ "\n",
+ "\n",
+ "---------------------------------\n",
+ "The following fields have non-default values:\n",
+ "N:\n",
+ "\u001b[31m< 0\u001b[0m\n",
+ "---\n",
+ "\u001b[32m> 2\u001b[0m\n",
+ "python_unit_l:\n",
+ "\u001b[31m< 0\u001b[0m\n",
+ "---\n",
+ "\u001b[32m> 4097248214\u001b[0m\n",
+ "python_unit_m:\n",
+ "\u001b[31m< 0\u001b[0m\n",
+ "---\n",
+ "\u001b[32m> 2145773914\u001b[0m\n",
+ "python_unit_t:\n",
+ "\u001b[31m< 0\u001b[0m\n",
+ "---\n",
+ "\u001b[32m> 1864791206\u001b[0m\n",
+ "rand_seed:\n",
+ "\u001b[31m< 829806\u001b[0m\n",
+ "---\n",
+ "\u001b[32m> 210256\u001b[0m\n",
+ "particles:\n",
+ "\u001b[32m> (256 bytes, values not printed)\u001b[0m\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "sim = rebound.Simulation()\n",
+ "date = \"2005-06-30 15:24\" # You can also use Julian Days. For example: date = \"JD2458327.500000\"\n",
+ "sim.add(\"Venus\")\n",
+ "sim.add(\"Venus\", date=date)\n",
+ "sim.status()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We see that the two Venus positions are different. The first call cached the current time, but since the second call specified a date, it overrode the default. Any time you pass a date (with time in UTC), it will overwrite the default cached time, so: "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Searching NASA Horizons for 'Venus'... \n",
+ "Found: Venus Barycenter (299) (chosen from query 'Venus')\n",
+ "Searching NASA Horizons for 'Earth'... \n",
+ "Found: Earth-Moon Barycenter (3) (chosen from query 'Earth')\n",
+ "---------------------------------\n",
+ "REBOUND version: \t4.0.3\n",
+ "REBOUND built on: \tJan 12 2024 08:52:18\n",
+ "Number of particles: \t2\n",
+ "Selected integrator: \tias15\n",
+ "Simulation time: \t0.0000000000000000e+00\n",
+ "Current timestep: \t0.001000\n",
+ "---------------------------------\n",
+ "\n",
+ "\n",
+ "---------------------------------\n",
+ "The following fields have non-default values:\n",
+ "N:\n",
+ "\u001b[31m< 0\u001b[0m\n",
+ "---\n",
+ "\u001b[32m> 2\u001b[0m\n",
+ "python_unit_l:\n",
+ "\u001b[31m< 0\u001b[0m\n",
+ "---\n",
+ "\u001b[32m> 4097248214\u001b[0m\n",
+ "python_unit_m:\n",
+ "\u001b[31m< 0\u001b[0m\n",
+ "---\n",
+ "\u001b[32m> 2145773914\u001b[0m\n",
+ "python_unit_t:\n",
+ "\u001b[31m< 0\u001b[0m\n",
+ "---\n",
+ "\u001b[32m> 1864791206\u001b[0m\n",
+ "rand_seed:\n",
+ "\u001b[31m< 433115\u001b[0m\n",
+ "---\n",
+ "\u001b[32m> 842290\u001b[0m\n",
+ "particles:\n",
+ "\u001b[32m> (256 bytes, values not printed)\u001b[0m\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "sim = rebound.Simulation()\n",
+ "date = \"2005-06-30 15:24\" # You can also use Julian Days. For example: date = \"JD2458327.500000\"\n",
+ "sim.add(\"Venus\", date=date)\n",
+ "sim.add(\"Earth\")\n",
+ "sim.status()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "would set up a simulation with Venus and Earth, all synchronized to 2005-06-30 15:24 UTC. All dates should either be passed in the format Year-Month-Day Hour:Minute or in JDxxxxxxx.xxxx for a date in Julian Days.\n",
+ "\n",
+ "For reference HORIZONS interprets all times for ephemerides as [Coordinate (or Barycentric Dynamical) Time](https://en.wikipedia.org/wiki/Barycentric_Dynamical_Time)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Origin**\n",
+ "\n",
+ "REBOUND queries for particles' positions and velocities relative to the Solar System barycenter"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Searching NASA Horizons for 'Sun'... \n",
+ "Found: Sun (10) \n",
+ "---------------------------------\n",
+ "REBOUND version: \t4.0.3\n",
+ "REBOUND built on: \tJan 12 2024 08:52:18\n",
+ "Number of particles: \t1\n",
+ "Selected integrator: \tias15\n",
+ "Simulation time: \t0.0000000000000000e+00\n",
+ "Current timestep: \t0.001000\n",
+ "---------------------------------\n",
+ "\n",
+ "---------------------------------\n",
+ "The following fields have non-default values:\n",
+ "N:\n",
+ "\u001b[31m< 0\u001b[0m\n",
+ "---\n",
+ "\u001b[32m> 1\u001b[0m\n",
+ "python_unit_l:\n",
+ "\u001b[31m< 0\u001b[0m\n",
+ "---\n",
+ "\u001b[32m> 4097248214\u001b[0m\n",
+ "python_unit_m:\n",
+ "\u001b[31m< 0\u001b[0m\n",
+ "---\n",
+ "\u001b[32m> 2145773914\u001b[0m\n",
+ "python_unit_t:\n",
+ "\u001b[31m< 0\u001b[0m\n",
+ "---\n",
+ "\u001b[32m> 1864791206\u001b[0m\n",
+ "rand_seed:\n",
+ "\u001b[31m< 629898\u001b[0m\n",
+ "---\n",
+ "\u001b[32m> 447379\u001b[0m\n",
+ "particles:\n",
+ "\u001b[32m> (128 bytes, values not printed)\u001b[0m\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "sim = rebound.Simulation()\n",
+ "sim.add(\"Sun\")\n",
+ "sim.status()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The reference plane is the ecliptic (Earth's orbital plane) of J2000 (Jan. 1st 2000 12:00 GMT), with the x-axis along the ascending node of the ecliptic and the Earth's mean equator (also at J2000). "
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.10.4"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/rebound/source/docs/ipython_examples/HybridIntegrationsWithTRACE.ipynb b/rebound/source/docs/ipython_examples/HybridIntegrationsWithTRACE.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..4c974cd8d272ed6c3b97213f5f3430636beae6af
--- /dev/null
+++ b/rebound/source/docs/ipython_examples/HybridIntegrationsWithTRACE.ipynb
@@ -0,0 +1,198 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Hybrid integrations with TRACE\n",
+ "REBOUND comes with several integrators, each of which has its own advantages and disadvantages. TRACE is a time-reversible hybrid integrator (Lu, Hernandez & Rein 2024) that is an improvement on the older MERCURIUS hybrid integrator. It uses a symplectic Wisdom-Holman integrator when particles are far apart from each other and switches over to a high order integrator during close encounters. Specifically, TRACE uses the efficient WHFast and Bulirsch-Stoer/IAS15 internally."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's start out by showcasing the problem with traditional fixed timestep integrators such as WHFast. We setup a simulation of the outer solar system and increase the masses of the planets by a factor of 50. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import math\n",
+ "import rebound, rebound.data\n",
+ "%matplotlib inline\n",
+ "sim = rebound.Simulation()\n",
+ "rebound.data.add_outer_solar_system(sim) # add some particles for testing\n",
+ "for i in range(1,sim.N):\n",
+ " sim.particles[i].m *= 50.\n",
+ "sim.integrator = \"WHFast\" # This will end badly!\n",
+ "sim.dt = sim.particles[1].P * 0.002 # Timestep a small fraction of innermost planet's period\n",
+ "sim.move_to_com()\n",
+ "E0 = sim.energy() # Calculate initial energy \n",
+ "rebound.OrbitPlot(sim);"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let us integrate this system for a few hundred years. An instability will occur. We can then measure the energy error, which is a good estimate as to how accurate the integration was."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Relative energy error with WHFast: 41.850545\n"
+ ]
+ }
+ ],
+ "source": [
+ "sim.integrate(600*2.*math.pi)\n",
+ "E1 = sim.energy()\n",
+ "print(\"Relative energy error with WHFast: %f\"%((E0-E1)/E0))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "An energy error that large means we basically go it wrong completely. Let's try this again but use TRACE."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Relative energy error with TRACE: 3.591519e-07\n"
+ ]
+ }
+ ],
+ "source": [
+ "sim = rebound.Simulation()\n",
+ "rebound.data.add_outer_solar_system(sim) # add some particles for testing\n",
+ "for i in range(1,sim.N):\n",
+ " sim.particles[i].m *= 50.\n",
+ "sim.integrator = \"trace\" \n",
+ "sim.dt = sim.particles[1].P * 0.002 # Timestep a small fraction of innermost planet's period\n",
+ "sim.move_to_com()\n",
+ "E0 = sim.energy() # Calculate initial energy \n",
+ "sim.integrate(600*2.*math.pi)\n",
+ "E1 = sim.energy()\n",
+ "print(\"Relative energy error with TRACE: %e\"%((E1-E0)/E0))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As you can see, TRACE is able to integrate this system with much better accuracy. When a close encounter occurs, it automatically (and reversibly!) switches to the BS integrator. When there is no close encounter, you still get all the benefits in terms of speed an accuracy from a symplectic integrator."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "There are a few options to adjust TRACE. First of all, close encounters with the central star are treated differently than close encounters between planets. This becomes important in systems that deal with highly eccentric orbits. \n",
+ "\n",
+ "You can switch between two prescriptions that use the BS integrator:\n",
+ "* `PARTIAL_BS`, the fastest and least accurate method\n",
+ "* `FULL_BS`, which provides a good compromise between speed and accuracy (this is the default)\n",
+ "\n",
+ "Or you may use the IAS15 integrator\n",
+ "* `FULL_IAS15`, which is the most accurate but slowest prescription (in most cases, this will have no significant accuracy advantage over `FULL_BS`)\n",
+ "\n",
+ "See Lu, Hernandez & Rein (2024) for more details on these prescriptions."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Sets the pericenter switching prescription\n",
+ "sim.ri_trace.peri_mode = \"PARTIAL_BS\" # or\n",
+ "sim.ri_trace.peri_mode = \"FULL_BS\" # or\n",
+ "sim.ri_trace.peri_mode = \"FULL_IAS15\" # or"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "You also may want to change the criteria at which TRACE switches over from pure WHFast to BS/IAS15. For planet-planet encounters, this is expressed in units of a slightly modified Hill radii criteria. The default is 3 Hill radii, in the following we change it to 5 Hill radii (larger values result in more accurate but slower simulations):"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "sim.ri_trace.r_crit_hill = 5"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "For star-planet encounters, this is expressed as a parameter $\\eta$, which is related to the ratio between the timestep and an adaptive timescale described in Dang, Rein & Spiegel (2024). The default is $\\eta = 1$, we set it to $\\eta = 0.1$ here (lower values result in more accurate but slower simulations):"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "sim.ri_trace.peri_crit_eta = 0.1"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.6"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/rebound/source/docs/ipython_examples/HyperbolicOrbits.ipynb b/rebound/source/docs/ipython_examples/HyperbolicOrbits.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..47ab16cc1b2bfa0cada585535e3a10f3e1716e6b
--- /dev/null
+++ b/rebound/source/docs/ipython_examples/HyperbolicOrbits.ipynb
@@ -0,0 +1,251 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Loading Hyperbolic Orbits into REBOUND\n",
+ "\n",
+ "Imagine we have a table of orbital elements for comets (kindly provided by Toni Engelhardt)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from io import StringIO\n",
+ "import numpy as np\n",
+ "import rebound\n",
+ "epoch_of_elements = 53371.0 # [MJD, days]\n",
+ "c = StringIO(u\"\"\"\n",
+ "# id e q[AU] i[deg] Omega[deg] argperi[deg] t_peri[MJD, days] epoch_of_observation[MJD, days]\n",
+ "168026 12.181214 15.346358 136.782470 37.581438 268.412314 54776.806093 55516.41727\n",
+ "21170 2.662235 2.013923 140.646538 23.029490 46.292039 54336.126288 53673.44043 \n",
+ "189298 15.503013 11.550314 20.042232 203.240743 150.855761 55761.641176 55718.447145 \n",
+ "72278 34.638392 24.742323 157.984412 126.431540 178.612758 54382.158401 54347.240445\n",
+ "109766 8.832472 9.900228 144.857801 243.102255 271.345342 55627.501618 54748.37722\n",
+ "\"\"\")\n",
+ "comets = np.loadtxt(c) # load the table into a numpy array"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We want to add these comets to a REBOUND simulation(s). The first thing to do is set the units, which have to be consistent throughout. Here we have a table in AU and days, so we'll use the gaussian gravitational constant (AU, days, solar masses). "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "sim = rebound.Simulation()\n",
+ "k = 0.01720209895 # Gaussian constant\n",
+ "sim.G = k**2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We also set the simulation time to the epoch at which the elements are valid:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "sim.t = epoch_of_elements"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We then add the giant planets in our Solar System to the simulation. You could for example query JPL HORIZONS for the states of the planets at each comet's corresponding epoch of observation (see [Horizons.ipynb](../Horizons)). Here we set up toy masses and orbits for Jupiter & Saturn:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "sim.add(m=1.) # Sun\n",
+ "sim.add(m=1.e-3, a=5.) # Jupiter\n",
+ "sim.add(m=3.e-4, a=10.) # Saturn"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "Let's write a function that takes a comet from the table and adds it to our simulation:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def addOrbit(sim, comet_elem):\n",
+ " tracklet_id, e, q, inc, Omega, argperi, t_peri, epoch_of_observation = comet_elem\n",
+ " sim.add(primary=sim.particles[0], \n",
+ " a = q/(1.-e),\n",
+ " e = e,\n",
+ " inc = inc*np.pi/180., # have to convert to radians\n",
+ " Omega = Omega*np.pi/180.,\n",
+ " omega = argperi*np.pi/180.,\n",
+ " T = t_peri # time of pericenter passage\n",
+ " )"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "By default, REBOUND adds and outputs particles in Jacobi orbital elements. Typically, orbital elements for comets are heliocentric. Mixing the two will give you relative errors in elements, positions etc. of order the mass ratio of Jupiter to the Sun ($\\sim 0.001$) which is why we pass the additional `primary=sim.particles[0]` argument to the `add()` function. If this level of accuracy doesn't matter to you, you can ignore the `primary` argument.\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can now set up the first comet and quickly plot to see what the system looks like:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "addOrbit(sim, comets[0])\n",
+ "%matplotlib inline\n",
+ "op = rebound.OrbitPlot(sim,xlim=[-20.,20],ylim=[-20.,20])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we just integrate until whatever final time we’re interested in. Here it's the epoch at which we observe the comet, which is the last column in our table:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "tfinal = comets[0][-1]\n",
+ "sim.integrate(tfinal)\n",
+ "op = rebound.OrbitPlot(sim,xlim=[-20.,20],ylim=[-20.,20])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "REBOUND automatically find out if you want to integrate forward or backward in time."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "For fun, let's add all the comets to a simulation:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "sim = rebound.Simulation()\n",
+ "sim.G = k**2\n",
+ "sim.t = epoch_of_elements \n",
+ "sim.add(m=1.) # Sun\n",
+ "sim.add(m=1.e-3, a=5.) # Jupiter\n",
+ "sim.add(m=3.e-4, a=10.) # Saturn\n",
+ "for comet in comets:\n",
+ " addOrbit(sim, comet)\n",
+ "op = rebound.OrbitPlot(sim,xlim=[-50.,50],ylim=[-50.,50])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.6"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}
diff --git a/rebound/source/docs/ipython_examples/IntegratingArbitraryODEs.ipynb b/rebound/source/docs/ipython_examples/IntegratingArbitraryODEs.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..433cb054ee8adccdbb0e118d659c99a399c9bfc0
--- /dev/null
+++ b/rebound/source/docs/ipython_examples/IntegratingArbitraryODEs.ipynb
@@ -0,0 +1,429 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "ac2c0891",
+ "metadata": {},
+ "source": [
+ "# Integrating arbitrary ODEs\n",
+ "\n",
+ "Although REBOUND is primarily an N-body integrator, it can also integrate arbitrary ordinary differential equations (ODEs). Even better: it can integrate arbitrary ODEs in parallel with an N-body simulation. This allows you to couple various physical effects such as spin and tides to orbital dynamics.\n",
+ "\n",
+ "In this example, we are integrating a two planet system and a decoupled harmonic oscillator which is governed by the following ODE:\n",
+ "\n",
+ "$$ y_0(t)'' = -\\frac km y_0(t)$$\n",
+ "\n",
+ "or equivalently as a set of 2 first order differential equations\n",
+ "\n",
+ "$$ \\begin{pmatrix} y_0(t)\\\\y_1(t)\\end{pmatrix}' = \\begin{pmatrix} y_1(t)\\\\- \\frac k m y_0(t)\\end{pmatrix}\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "e350dbbb",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import rebound\n",
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "37ac5371",
+ "metadata": {},
+ "source": [
+ "We first set up our N-body simulation. Note that we are using the Gragg-Bulirsch-Stoer integrator (BS)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "18043d1d",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "sim = rebound.Simulation()\n",
+ "sim.add(m=1)\n",
+ "sim.add(a=1.2,m=1e-3,e=0.1)\n",
+ "sim.add(a=2.3,m=1e-3,e=0.1)\n",
+ "sim.integrator = \"BS\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "55150ae8",
+ "metadata": {},
+ "source": [
+ "We now create an ODE structure. Note that the ODE is linked to the simulation. If you run multiple simulations in parallel, you need to create an ode structure for each of them."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "39c5337d",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "ode_ho = sim.create_ode(length=2, needs_nbody=False)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f5766f9e",
+ "metadata": {},
+ "source": [
+ "Next, we setup the ODE structure with the initial conditions and the right hand side (RHS) of the harmonic oscillator:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "id": "265f8c39",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Mass and spring constants\n",
+ "m = 1.\n",
+ "k = 10.\n",
+ "\n",
+ "# Initial conditions\n",
+ "ode_ho.y[0] = 1. \n",
+ "ode_ho.y[1] = 0. # zero velocity\n",
+ "\n",
+ "# RHS\n",
+ "def derivatives_ho(ode, yDot, y, t):\n",
+ " yDot[0] = y[1]\n",
+ " yDot[1] = -k/m*y[0]\n",
+ "\n",
+ "ode_ho.derivatives = derivatives_ho "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2f9b90c7",
+ "metadata": {},
+ "source": [
+ "To keep track of how accurate the integration of the harmonic oscillator is, we can calculate the energy which is conserved in the physical system."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "id": "ebc52cd3",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def energy_ho(ode):\n",
+ " return 0.5*k*ode.y[0]**2 + 0.5*m*ode.y[1]**2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6bff9751",
+ "metadata": {},
+ "source": [
+ "Now we can run the simulation, keeping track of a few quantities along the way."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "id": "4eb25927",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "times = np.linspace(0.,60.,1000)\n",
+ "energies_nbody = np.zeros(len(times))\n",
+ "energies_ho = np.zeros(len(times))\n",
+ "r_nbody = np.zeros(len(times))\n",
+ "x_ho = np.zeros(len(times))\n",
+ "\n",
+ "for i, t in enumerate(times):\n",
+ " sim.integrate(t)\n",
+ " \n",
+ " r_nbody[i] = sim.particles[1].d\n",
+ " x_ho[i] = ode_ho.y[0]\n",
+ " energies_nbody[i] = sim.energy()\n",
+ " energies_ho[i] = energy_ho(ode_ho)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "439539a6",
+ "metadata": {},
+ "source": [
+ "Let's plot the relative energy error over time for both the N-body and the harmonic oscillator integration."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "id": "0411c827",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 7,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots(1,1)\n",
+ "ax.set_xlabel(\"time\")\n",
+ "ax.set_ylabel(\"relative energy error\")\n",
+ "ax.set_yscale(\"log\")\n",
+ "ax.plot(times,np.abs((energies_nbody-energies_nbody[0])/energies_nbody[0]), label=\"N-body\")\n",
+ "ax.plot(times,np.abs((energies_ho-energies_ho[0])/energies_ho[0]), label=\"harmonic oscillator\")\n",
+ "ax.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6421232c",
+ "metadata": {},
+ "source": [
+ "Let us also plot the radius of the inner planet and the position coordinate of the harmonic oscillator."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "id": "bf8928b4",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots(1,1)\n",
+ "ax.set_xlabel(\"time\")\n",
+ "ax.plot(times,r_nbody, label=\"planet\")\n",
+ "ax.plot(times,x_ho, label=\"harmonic oscillator\")\n",
+ "ax.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2ef6fafa",
+ "metadata": {},
+ "source": [
+ "The above example is using the BS integrator for both the N-body and the harmonic oscillator integration. The BS integrator has default tolerance parameters set to $10^{-5}$. You can change the relative or absolute tolerance with to get more accurate results:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "id": "1d3c7ced",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "sim.ri_bs.eps_rel = 1e-8\n",
+ "sim.ri_bs.eps_abs = 1e-8"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1e2b0d95",
+ "metadata": {},
+ "source": [
+ "Note that in this example, the harmonic oscillator has a period that is shorter than any orbital timescale. Therefore the timestep is limited by the harmonic oscillator, not the N-body integration. As a result, the N-body integration has an error much smaller than the tolerance parameters. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9bb09a10",
+ "metadata": {},
+ "source": [
+ "Let us change the simple harmonic oscillator to a forced harmonic oscillator where the forcing depends on phase of a planet."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "id": "03c94568",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def derivatives_ho_forced(ode, yDot, y, t):\n",
+ " # Now we can access particles and their orbital parameters during sub-steps\n",
+ " forcing = np.sin(sim.particles[1].f)\n",
+ " \n",
+ " # Note that we are using the global sim variable.\n",
+ " # Alternatively, one can also access the simulation via\n",
+ " # sim = ode.contents.r.contents \n",
+ " \n",
+ " yDot[0] = y[1]\n",
+ " yDot[1] = -k/m*y[0] + forcing\n",
+ "\n",
+ "ode_ho.derivatives = derivatives_ho_forced"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c592c246",
+ "metadata": {},
+ "source": [
+ "We explicitly set `needs_nbody = False` during initialization. We therefore need to tell REBOUND that our ODE now needs access to the particle state during the integrations:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "id": "61034468",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "ode_ho.needs_nbody = True"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3dfafc1d",
+ "metadata": {},
+ "source": [
+ "Running the integration a bit further, now with the forced harmonic oscillator:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "id": "4305edc4",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "times = np.linspace(65.,120.,1000)\n",
+ "\n",
+ "for i, t in enumerate(times):\n",
+ " sim.integrate(t)\n",
+ " \n",
+ " r_nbody[i] = sim.particles[1].d\n",
+ " x_ho[i] = ode_ho.y[0]\n",
+ " energies_nbody[i] = sim.energy()\n",
+ " energies_ho[i] = energy_ho(ode_ho)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "191064cf",
+ "metadata": {},
+ "source": [
+ "The harmonic oscillator is now getting forced by the planet."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "id": "9f90e0fb",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 13,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots(1,1)\n",
+ "ax.set_xlabel(\"time\")\n",
+ "ax.plot(times,r_nbody, label=\"planet\")\n",
+ "ax.plot(times,x_ho, label=\"harmonic oscillator\")\n",
+ "ax.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "80beed0f",
+ "metadata": {},
+ "source": [
+ "In addition to using BS, it is also possible to integrate arbitrary ODEs in conjunction with other REBOUND integrators such as IAS15 and WHFast. In that case, only the user-defined ODEs are integrated with BS **after** a successfull N-body integration step. This type of switching back and forth the different ODEs will lead to an error. However, if the timescale involved in the user-defined ODEs are much longer than the timestep of the N-body integration, then this will be a small error. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "15c2b8e3",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.8.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/rebound/source/docs/ipython_examples/Megno.ipynb b/rebound/source/docs/ipython_examples/Megno.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..12cff135dfb3cb0989a6607c18a0b7419e7ad4b4
--- /dev/null
+++ b/rebound/source/docs/ipython_examples/Megno.ipynb
@@ -0,0 +1,200 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Stability map with MEGNO and WHFast\n",
+ "In this tutorial, we'll create a stability map of a two planet system using the chaos indicator MEGNO (Mean Exponential Growth of Nearby Orbits) and the symplectic integrator WHFast (Rein and Tamayo 2015).\n",
+ "\n",
+ "We will integrate a two planet system with massive planets. We vary two orbital parameters, the semi-major axis $a$ and the eccentricity $e$. Let us first define a function that runs one simulation for a given set of initial conditions $(a, e)$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2023-09-24T21:08:23.195270Z",
+ "start_time": "2023-09-24T21:08:23.181079Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "def simulation(par):\n",
+ " a, e = par # unpack parameters\n",
+ " sim = rebound.Simulation()\n",
+ " sim.integrator = \"whfast\"\n",
+ " sim.ri_whfast.safe_mode = 0\n",
+ " sim.dt = 5.\n",
+ " sim.add(m=1.) # Star\n",
+ " sim.add(m=0.000954, a=5.204, M=0.600, omega=0.257, e=0.048)\n",
+ " sim.add(m=0.000285, a=a, M=0.871, omega=1.616, e=e)\n",
+ " sim.move_to_com()\n",
+ " \n",
+ " sim.init_megno()\n",
+ " sim.exit_max_distance = 20.\n",
+ " try:\n",
+ " sim.integrate(5e2*2.*np.pi, exact_finish_time=0) # integrate for 500 years, integrating to the nearest\n",
+ " #timestep for each output to keep the timestep constant and preserve WHFast's symplectic nature\n",
+ " megno = sim.megno() \n",
+ " return megno\n",
+ " except rebound.Escape:\n",
+ " return 10. # At least one particle got ejected, returning large MEGNO."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's try this out and run one simulation"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2023-09-24T21:08:24.035399Z",
+ "start_time": "2023-09-24T21:08:23.946126Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "2.0535548978104345"
+ ]
+ },
+ "execution_count": 2,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "import rebound\n",
+ "import numpy as np\n",
+ "simulation((7,0.1))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The return value is the MEGNO. It is about 2, thus the system is regular for these initial conditions. Let's run a whole array of simulations. We will use the multiprocess module to run the simulations in parallel. If the following line throws you an ImportError, install the module with `pip install multiprocess`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2023-09-24T21:08:24.770700Z",
+ "start_time": "2023-09-24T21:08:24.757093Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from multiprocess import Pool"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2023-09-24T21:08:25.796868Z",
+ "start_time": "2023-09-24T21:08:25.182288Z"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "with Pool() as pool:\n",
+ " Ngrid = 80\n",
+ " par_a = np.linspace(7.,10.,Ngrid)\n",
+ " par_e = np.linspace(0.,0.5,Ngrid)\n",
+ " parameters = []\n",
+ " for e in par_e:\n",
+ " for a in par_a:\n",
+ " parameters.append((a,e))\n",
+ " results = pool.map(simulation,parameters)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "On my laptop, this takes only half a second.\n",
+ "\n",
+ "Let's plot it!"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "ExecuteTime": {
+ "end_time": "2023-09-24T21:08:26.697801Z",
+ "start_time": "2023-09-24T21:08:26.263972Z"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "results2d = np.array(results).reshape(Ngrid,Ngrid)\n",
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "fig = plt.figure(figsize=(7,5))\n",
+ "ax = plt.subplot(111)\n",
+ "extent = [min(par_a),max(par_a),min(par_e),max(par_e)]\n",
+ "ax.set_xlim(extent[0],extent[1])\n",
+ "ax.set_xlabel(\"semi-major axis $a$\")\n",
+ "ax.set_ylim(extent[2],extent[3])\n",
+ "ax.set_ylabel(\"eccentricity $e$\")\n",
+ "im = ax.imshow(results2d, interpolation=\"none\", vmin=1.9, vmax=4, cmap=\"RdYlGn_r\", origin=\"lower\", aspect='auto', extent=extent)\n",
+ "cb = plt.colorbar(im, ax=ax)\n",
+ "cb.set_label(\"MEGNO $\\\\langle Y \\\\rangle$\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.6"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}
diff --git a/rebound/source/docs/ipython_examples/OrbitPlot.ipynb b/rebound/source/docs/ipython_examples/OrbitPlot.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..89e5ae1796a9b40bac494d5abab1e53d5ea7c963
--- /dev/null
+++ b/rebound/source/docs/ipython_examples/OrbitPlot.ipynb
@@ -0,0 +1,542 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Orbit Plot\n",
+ "*Note that OrbitPlot has changed from being a function to a class in REBOUND version 3.22.* \n",
+ "\n",
+ "REBOUND comes with a simple way to plot instantaneous orbits of planetary systems. To show how this works, let's setup a test simulation with 4 planets."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import rebound\n",
+ "sim = rebound.Simulation()\n",
+ "sim.add(m=1)\n",
+ "sim.add(m=0.1, e=0.041, a=0.4, inc=0.2, f=0.43, Omega=0.82, omega=2.98)\n",
+ "sim.add(m=1e-3, e=0.24, a=1.0, pomega=2.14)\n",
+ "sim.add(m=1e-3, e=0.24, a=1.5, omega=1.14, l=2.1)\n",
+ "sim.add(a=-2.7, e=1.4, f=-1.5,omega=-0.7) # hyperbolic orbit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To plot these initial orbits in the $xy$-plane, we can simply create an `OrbitPlot` instance and give it the simulation as an argument during initialization."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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vuLgYixYtwp133onY2FgcO3YMb7/9NmdrNhLXFRAQgLVr1+Lvf/876uvr8eCDD2LLli0wGo1cl+Y2tFotTCYThSMh9mIwGPDGG29gwoQJEAqF+Oabb7B9+3YMGzaM69KIixs/fjw2bdqEO++8E1u2bMGqVau6LFNJrl9raysAbkeqAhSOxE0VFhZi7ty52LJlC1avXo0vvvgCN998M10jIjYjkUiwatUqfPLJJ/Dx8cHrr7+Of//737QU3SC1trbC29ub8wX8KRyJW2FZFv/+97+Rnp6OlpYWbNmyBa+++iot9UbsJiEhAR988AFuu+02fPfdd3j88cet08vIwGk0GoSEhHBdBoUjcR+NjY1YunQp/vCHP+Dee+/FsWPHMG7cOK7LIh5AIBBg2bJl+Oijj6DX6/HII49gx44doMkAA9fY2Mh5lypA4UjcxO7duzF+/HhkZ2fj+++/x/vvvw8fHx+uyyIeZsiQIfjXv/6F+fPn4/3338fbb78NtVrNdVkuQ6vVQq/XIygoiOtSKByJa+vs7MSaNWuwcOFCpKWl4dSpU7jlllu4Lot4MIlEgj/84Q94/fXXkZ2djccee4xW1+mn5uZmAKBwJGQw8vLyMHXqVGzatAnvvPMOtm/fftUWZYRwZfLkyfj4448RHByMp556Cj/++CN1s15DU1MT/Pz8nGLzB7deeJy4J5ZlsXHjRnz77bcQCoU4cuQIp6v3E9KbkJAQvPPOO/jkk0/wwQcfoLq6GitXrnSKk78zam5udopWI0AtR+JiOjs78cgjj+Dxxx/H8OHD8dtvv1EwEqcmFArx+9//Hs8//zz27NmDP//5z9a5fOT/YxgGra2tCA4O5roUABSOxIVUV1fjrrvuwjfffIPPPvsM7733Hn0CJy4jIyMDb775Jurr6/GHP/wBFRUVXJfkVFpbW8EwDLUcCRmI3NxcTJ06FSqVCocOHcI999zDdUmEDNjQoUPx/vvvw9fXF08++SRycnK4LslpNDU1gc/nO8U0DoDCkbiAX375BRkZGYiIiMC3336L1NRUrksi5LqFhobi3XffxciRI7Fu3Tr88ssvXJfkFJqbmxEYGAg+3zliyTmqIKQXH330ERYvXow5c+Zg3759CA8P57okQgbN29sbf/3rX7FgwQK8//77+OSTT8AwDNdlcaqpqclprjcCNFqVOCmz2Yw//elP+PDDD/HUU09h/fr1EAgEXJdFBohlWRgMBhgMBhiNRvD5fAiFQohEIgiFQo/+mQoEAvz+979HVFQUPv74Y3R2duKxxx6DWCzmujSH0+v1aGtrc5rrjQCFI3ECmZmZePHFF1FbWwuFQoFnn30Wmzdvxs6dO/Hhhx/ikUce4bpEcgWGYdDQ0ICqqirU1NSguroaNTU1aGhoQG1tLVQqFSIjI5GXl9dlK6dhw4ahsLDQ+u/o6Gg0NzfDz88P/v7+GDlyJAwGAxQKBSIiIhAeHo6IiAhERUUhMDDQbReNv+222xAeHo7XX38d1dXVeOWVVzxuLWDL5H9najnyWJqV2qeB7BxNBu7BBx/Epk2brrpfJBLhxx9/xLx58zioilh0dnYiPz8fubm5OHPmDBiGwe7du7vsPCGTyRAVFQWFQoHw8HDI5XKEhISAx+NBLBZDIpFY/8swDIxGI4xGI8xmM9rb26FWq6HRaAAAly5dQl1dHZRKJfR6PYDLg1jq6+sxY8YMBAQEYNSoURg1ahRiY2Od5vqULVy4cAH//ve/wefz8dprr3lUQObl5aGoqAhLliyx63EGcj6ncLwGCkf7yczMxE033dTr1/fu3YtZs2Y5sCLPxrIsioqKcPLkSZw5cwa5ubkoKCiA2WyGRCLBqFGjcMMNNyAkJATR0dGIjo5GZGQkpFKpXWpRqVSoq6tDbW0tSktLUV9fj+PHj6O8vBwAIJVKMXz4cIwaNQppaWlITU11qm6563Hp0iU8//zziI+Px8svv+wxAbl//37weDxkZGTY9TgUjjZE4Wg/6enpOH78eK9fnzx5Mo4dO+bAijxPZ2cnDh06hN27d6OmpgYHDhyAXC6HQqFAWloaxowZg7S0NCQnJ0MkEnFdLoDLi1Pn5+dbb+fOnYNcLrdew8zIyMCMGTMwZMgQl+yKLSgowLp165CUlIS//vWvnO9raG8sy2LHjh0YOnSo3Rf0oHC0IQpH+4mNje1z37uYmBiaKG0HTU1N2L17N3bt2oUDBw5Ap9MhISEBCxYswA033IDx48fD19eX6zIHpL6+HidOnMDBgwdx5MgRdHR0ICIiAhkZGcjIyMC4ceOcJtz748KFC3jhhReQnJyMv/71r249SEetVmPPnj2YPn263ddGpnC0IQpH+6GWo+N0dHTgl19+wbfffouCggLU19dj0qRJmDt3LubNm4ekpCSuS7QZg8GAU6dO4eDBgzhw4ACUSiV8fX2xePFipKenIz093SWuVebn5+PFF1/EiBEj8MILL7htQBYXF+PMmTNYtGgRhEL7jhGlcLQhCkf7oWuO9pefn4/PPvsMhYWFOH78OCZPnoylS5fi5ptvRmhoKNfl2R3Lsrh06RIOHjyIgoICHDx4EBEREVi8eDFuv/12p79GmZeXh5deegmjR4/GunXrXKr121/Hjh1DR0eHQ/7WKRxtiMLRvh566CFs3LjxqvtXrlyJTz/9lIOKXJ/RaLROgzl16hTCwsKwYsUKLFu2DHFxcVyXxxmWZZGfn4+tW7diz549MJlMmDlzJhYvXowJEyY4bWsyNzcXf/3rXzF27Fg899xzdm9dOdqPP/6IuLg4jB492u7HonC0IQpH+8vKysK6deus8xxfe+01ajFeh87OTmzZsgUffPABamtrMX/+fCxbtgxz5851yxbHYGg0GuzcuRNbt25FaWkpoqOjcd9992HevHlOeb01JycHr7zyCiZMmIC1a9e6zeIJWq0Wv/76K6ZPn+6Q1a8oHG2IwpE4O5VKhU8++QQbNmyASqXC4sWL8eSTT2LkyJFcl+b0WJZFbm4utm7diqNHjyI8PBwzZ87E7373O6cLyRMnTuCLL75AWloaHnzwQZccidtdaWkpcnJyHHK9ERjY+dy92ueEeJD29nZ8/PHHeP/99xEWFobFixfjiSeeQGxsLNeluQwej4cxY8ZgzJgxaGxsxA8//IAtW7bg22+/xfLly3HHHXc4zVzDiRMnQqfT4a233oJcLseiRYu4LmnQGhoaEBgY6JRdxc7ZyU7cEnVSDFxmZibS09MRGxuL9PR0ZGZmgmVZ6+4kmZmZuOeee/Dzzz/jrbfeomAchJCQEDzyyCP44YcfMGfOHGzYsAGLFy/Gt99+C4PBwHV5AIDp06fjzjvvxOeff46TJ09yXc6gNTY2IiQkhOsyekTdqtdA3aq2wbIsWJZ12kEPzqi3pfUiIiKgVqtx++234/XXX0d8fDwH1bm/2tpabNy4ETt37kRoaCgef/xxzJ49m/PfYZZl8be//Q25ubl48803XfYDUVtbG3bu3Ilp06ZBoVA45JgDOZ/TmYrYnSUY3eEaiaNkZmb2GIwAUFdXh1deeQVfffUVBaMdKRQKvPDCC/j666+Rnp6Ol156CatWrUJBQQGndfF4PDz11FMIDw/Ha6+9BrVazWk916uxsRE8Hs9pW44UjsSurgxGCsf+e/HFF/v8+vfff++gSkhsbCyeffZZ/POf/7QG03vvvYfOzk7OavLy8sLzzz8PvV6PN954o8tC8K6ioaEBAQEBTjuSmsKR2A0F4/Wrra0d1NeJ7aWlpeGTTz7BihUr8OOPP+Kee+7pc4UnewsNDcVzzz2HwsJCbNiwweWu6Tvz9UaAwpHYCcuyMJvNAEDBeB2udQ3GUddoSFd8Ph933303/vOf/yAmJgZPP/00XnnlFc66NlNSUvD73/8emZmZ+Pnnnzmp4Xq0t7ejo6ODwpF4HrPZDB6Px/ngBVf1yiuv9Pn11157zUGVkJ4oFAq8++67eP7553H06FGsXbsWR44c4aSWWbNmYdGiRdi4cSPy8vI4qWGgGhsbAYDCkXgWS4vRXVbx4MKcOXOwcuXKHr+2cuVKWkHICfB4PNx888348ssvIZfL8eyzz+Ltt9+GTqdzeC3Lly9HRkYG3nrrLTQ3Nzv8+APV2NiIgIAAp15MncKR2BTDMGBZloLRBj799FPs3bsXkydPRkxMDCZPnoy9e/fSmrNOJigoCK+++iqefvpp/Prrr3jxxRdRVVXl0Br4fD5WrlwJsViMt99+2/oB1Vm1tLQ4ZLm4waBwJDbDsiwYhgGfz6frjANgGbjUk1mzZuHYsWOoqKjAsWPHqMXopHg8HhYuXIhPPvkEdXV1eOSRRxzezern54c//elPKCwsxI4dOxx67IHQarXQarVO3aUKuGA4fvTRR4iLi4OXlxcmTZqEEydO9PrYzZs3W0dKWm7uvqs2VywDcOg648BYWtrEPSQkJGDDhg3WHTQ2btwIhmEcdvyUlBTcd999+Oqrr1BYWOiw4w5EfX09+Hw+haMtffPNN1izZg1eeuklnD59GqmpqZg7dy4aGhp6fY6/vz/q6uqsN9pZ3j5MJhN4PB51pw6A5aRJLW334uvri1dffRUPP/ww/vOf/+Avf/kL2traHHb8BQsWYMiQIXj//feh1+sddtz+UiqVCA4Odsr1VK/kUuH4zjvvYNWqVXjggQcwfPhwbNiwAT4+Pvjss896fQ6Px0N4eLj1FhYW5sCKPYPJZKKl4QbA0v0MgL5nborH4+Gee+7B3//+d3R0dODxxx9HXV2dQ44tEAjwxBNPoKWlBV988YVDjtlfDMOgsbHRJc7DLvOXaTAYkJOTg9mzZ1vv4/P5mD17No4dO9br89ra2hAbG4vo6GjcfvvtOH/+vCPK9RgMw4BhGAiFQmr99IOl+5k+THiG8ePHY+3atTCZTPj973/vsKXnFAoFli9fjl9//RVnz551yDH7o6mpCWaz2ekH4wAuFI6Wb2r3TxxhYWFQKpU9Pic5ORmfffYZduzYgf/85z9gGAZTpkxBdXV1r8fR6/XQaDRdbqRnLMvCZDKBz+fTib4fGIaxXpel7mfPERUVhY8++si6kXdf4yRsad68eRg1ahQ+/PBDtLe3O+SY11JfXw8vLy/IZDKuS7kmtz6jpaenY/ny5UhLS8OMGTPwww8/ICQkBP/61796fc769eshk8mst+joaAdW7Fos1xmd/dqBM7AEI5/Pp2D0QAEBAXjnnXeQnJyMF154Ab/99pvdj8nj8bB69Wp0dnZi48aNdj9efyiVSpfoUgVcKByDg4MhEAhQX1/f5f76+vp+N9FFIhHGjBmD4uLiXh+zdu1aqNVq683R85VchaVrkILx2hiGoRY2gUQiwdq1a3HDDTfglVdewd69e+1+zODgYKxcuRKXLl1CTk6O3Y/XF51OB7VaTeFoa2KxGOPGjUNWVpb1PoZhkJWVhfT09H69htlsxrlz5xAREdHrYyQSCfz9/bvcSFcsy8JoNNIoy34wm80wmUwQCATUYiQQCoV47rnnMHfuXPztb39zyHqoM2bMQFhYGDZu3Mjp6FVLw4bC0Q7WrFmDf//73/j8889x8eJFPPbYY2hvb8cDDzwA4PISSmvXrrU+/pVXXsGePXtQWlqK06dP495770VFRQUeeughrt6CWzAajdSd2g8Mw1g/RFAwEgs+n4+nn34aCxcuxPbt2/HTTz/Z/XirVq2CSqXC1q1b7XqsviiVSgQGBkIikXBWw0C41NntrrvuQmNjI1588UUolUqkpaVh165d1k8ilZWVXbqtWltbsWrVKusPZdy4cTh69CiGDx/O1VtweWazGQzDOPWaiM6AYRgYDAYIBAL6EEGuwuPx8Pjjj+Pjjz/GBx98AB8fH7uufhQeHo5FixZh69atmDFjBiIjI+12rJ6wLIuGhgaX2pybx9LyHH3SaDSQyWRQq9Ue38XKsiz0ej0EAoHTblDqDFiWhcFgAI/How8RpE8sy+Kdd97Bnj178MILL2DatGl2O5bRaMSaNWsQFBSEl156yaGXRFpbW5GVlYWMjAwEBwc77LjdDeR87lLdqoRblu5UCsbeWYIRAH2fyDXxeDw89dRTmD59Or788ku7zkkUiURYtWoVCgsLkZ2dbbfj9KS+vh4+Pj6Qy+UOPe5gUDiSfrF0p9IJv2+WAQ9isZgGK5F+4fP5+POf/wx/f3+88sorqKystNuxRo8ejcmTJ2PLli0OHZxTV1eHoKAglxqtTd2q10DdqpdbQzqdDgKBgLoJ+6DT6cCyLCQSiUudBAZKp9OhpqYGDQ0NaGxshEqlgslkgsFggEajAcMw8Pf3tw688PPzQ1BQEIKCghAWFobQ0FAaoNSD9vZ2PPXUU9Dr9fjHP/6BgIAAuxxHqVRizZo1WLp0KRYtWmSXY1yps7MTv/76KyZMmMD5vPGBnM8pHK+BwvHy0n1msxleXl7UGuqF0WiEXq+HRCJxu9a1wWBAYWEhLly4gKKiIiiVSoSEhKCjowO+vr4IDAxESEiI9ffDMjrXZDJBrVZDq9VCr9ejs7MT7e3tEAgEiI+PR3x8PJKSkhAZGUm/V//T0NCAP/zhDwgLC8Obb75pt5Gdn3/+Ofbt24f333/f7qvVlJaW4uzZs7j11ls5/9ugcLQhTw9HhmGg0+kgEok4/8V2VgzDoKOjAyKRyGWGqV+L0WhEfn4+8vLycPLkSfj5+UEsFmP48OGIiYlBbGwswsLCBtQCNBgMqKurQ01NDaqrq1FaWorOzk74+/tj5MiRSE1NdYk1N+3t0qVLWLduHW644QasXr3aLh8c2tra8Ic//AFTpkyx+9S2I0eOgGEY3HDDDXY9Tn8M5HxOY8xJn2gQzrXpdDrw+Xy3CEaNRoMDBw7gxIkTUCqVGD16NBYsWIC0tLRBT94Wi8WIjY1FbGwsgMsfKqqqqnDp0iWUlpYiOzsb0dHRmDhxIoYNG+bWXdN9GTp0KJ544gn83//9H6Kjo7Fw4UKbH0MqlWLx4sXYtWsXamtroVAobH4M4PISk42NjRg5cqRdXt+eKBxJr8xmM8xms1uc9O1Fr9eDYRj4+PhwXcqgaDQa7Nq1Czk5OVCr1Zg6dSoeeeQRu14j4vP51rBkGAaFhYU4efIkMjMzceLECUyePBnDhg2z2/Gd2Q033IAlS5bg3//+N5KSkuwSLjfddBN27tyJbdu24fHHH7f56wOXR6kyDGO38LUn6la9Bk/uVu3s7HSbFpE9mEwm6HQ6l77OaDKZsGfPHuzYsQOhoaEYO3Ys5syZA6lUyllNSqUShw4dQnFxMRQKBebMmePwSevOwGw247nnnkNNTQ0++OADBAYG2vwYu3fvxueff4533nnHLl3aJ0+ehEajsesCBwNB8xzJoBmNRloJpw+Wa7FCodBlg7GoqAjPP/88Dh48iBtuuAF//vOfsWjRIk6DEbi8msudd96Je+65B3w+Hz/99BOysrJgMpk4rcvRBAIBnn32WQQGBuKdd96BPdoxN954I2QyGbZv327z12YYBkqlss+1rJ0ZhSO5imUiO21g3LuOjg7rtA1XYzQa8d///hevvPIKgoOD8cQTT+Dee++Fn58f16V1ERsbi/vuuw/jxo3D2bNn8fnnn1+1K4+7CwwMxAMPPIDTp0/bZQ1WkUiE2267Db/99hsaGhps+trNzc0wGo0UjsR9GI1GsCzrsi0iezMYDDCZTC45taWxsRGvvfYajh49ijvvvBNPP/00oqKiuC6rVzweDxMmTMCKFSsgFAqxc+dO5Ofnc12WQ40dOxa33XYbPvvsM1RUVNj89W+88Ub4+fnZvPVYV1cHb29vu3QHOwKFI+nCsh2VSCTy2NGCfWFZFp2dnS45teXSpUtYv349NBoN/vjHP2LBggUu8zMOCgrCvffei+joaOzZsweHDx+2Szejs3rggQegUCjw97//HUaj0aavLZFIsGDBAhw6dAhNTU02e93GxkaXvlbsGn8ZxGEsrUa61tgznU4HAPD29ua4koE5ceIEXn31Vfj5+eHll19GUlIS1yUNmEAgwOzZszFjxgycOHECmZmZMJvNXJflEGKxGM888wx0Oh2+//57m7/+7Nmz4ePjgx07dtjk9VpbW6HT6Vy2SxWgcCRXuLLV6GrdhY5gNpuh1+vh5eXlMi0uADh8+DDeeustTJ8+HevWrXP5Udfjxo3DrbfeivLycmRmZnpMCzI+Ph5z5szB119/jbKyMpu+tqX1WFRUhNbW1kG/Xm1tLQQCAac7cAyW6/yFE7ujVmPfOjo6IBAIXGoQzqFDh/Dee+/h1ltvxUMPPeRyXcG9GTp0KGbNmoWioiJkZWV5TEAuWbIEUVFR+OCDD8AwjE1fe9asWWhsbMTevXsH9Tosy1oXFnDlD9kUjgTA/x+hSrtJ9Eyv18NkMrnUZP9Tp07h66+/xsyZM3Hfffe53c81MTERc+bMwfnz53Hq1Cmuy3EIoVCIJ554AsXFxfj1119t+to+Pj6YMWMG9u7da9127Xq0trais7PTpa83AhSO5H8MBgNtSdULyyAcsVjsMrtJlJaWYsOGDYiNjcVjjz3mdsFokZKSgunTp+PkyZMoKSnhuhyHSElJwaJFi/Df//4XarXapq89b948SKVSnDhx4rpfo6amBl5eXi61d2NPKBwJAFCrsQ86nQ5ms9llBuFoNBqsX78eISEheOqpp1zq+uj1GDNmDJKSkrBv3z6oVCquy3GIJUuWwGw246uvvrLp64aGhiIsLAz79++/rue7S5cqQOFIQNca+8KyLDo6Olxmj0aWZbFx40aYTCasWbPGY36mM2fOhFQqxb59+zxiBKu/vz+WLVuG3bt323zu4/Tp03Hp0iXU1dUN+LnNzc3Q6/Uu36UKUDgSXL6eJhQKXeLk72idnZ1gWdZlrjXu2bMH+/btw+rVqxESEsJ1OQ4jEokwZ84ctLa2Ijc3l+tyHOLmm29GREQENm3aZNMBSePGjYOvry8OHTo04OfW1tbCx8fHZSf+X4nOhh7OZDKBYRiXGoHpKJZrja4ydUOpVGLDhg1YtGgRxo0bx3U5DhccHIzRo0fjzJkzNr8W54yEQiHuv/9+nDlzBmfOnLHZ64pEIkyZMgW//fbbgFrhDMPYdfsrR3P+v3hiV5a9CF1loIkj6XQ6l2k1siyLLVu2ICAgAMuWLeO6HM6MGTMGUqkUR44c4boUh5g4cSKmTp2Kr776yqatxxkzZkCtViMvL6/fz2lqaoLBYHCLLlWAwtGjMQwDk8nkMdelBoJlWbS3t7vMtcZjx45h//79+P3vf+8yA4fsQSgUIj09HSqVCtXV1VyXY3c8Hg8LFixASUkJjh8/brPXteyzefDgwX4/p6amBlKpFDKZzGZ1cMn5/+qJ3RgMBvB4PJq+0QNX2sTYbDZj8+bNmDlzJiZMmMB1OZyLjY2Fn58fzp49y3UpDjFs2DCkpqbi66+/tnnrMTc3t19d1AzDoKmpyW1ajQCFo0ej6Ru96+jocJl5jfv27UNFRQUWLVrEdSlOIzU1FfX19VAqlVyX4hB33303dDqdTRdDSE9PB4/H61cXtVKphF6vd+odXgaKwtFD0WbGvTMajS6zGg7Lsvjpp58wd+5cDBkyhOtynEZMTAyCgoJw6dIlrktxiJSUFISGhtp02ympVIrx48fj0KFD12yRVlVVQS6Xw9fX12bH5xqFo4cyGAwQCAQu0TJytI6ODvD5fJf44HDy5Em0tbVh/vz5XJfidIYPH47y8nJ0dHRwXYpDLFiwAAUFBSgqKrLZa06fPh2tra0oLy/v9TE6nQ5NTU1u1WoEKBw9EsMwMBqNNH2jBwzDQKfTucyglh07dkAikWDYsGFcl+J0YmNjIRAI+jyxu5Px48cjLCwMP//8s81ec8SIERCLxTh9+nSvj6murgafz3ebKRwWFI4eiAbi9M4yfcMVwrGpqQkXL17ELbfcwnUpTkksFiMqKspj1lzl8/m45ZZbcPToUZttWszn8zF+/HicPHmy18dUVVUhPDwcQqHQJsd0FhSOHkin09Gejb2wDMRxhekb+/btQ3t7O2bOnMl1KU4rLi4OBoMBbW1tXJfiEDfeeCMkEolNd+wYPXo06uvr0dDQcNXXWltb0d7ejujoaJsdz1k4/xmA2JRlRRxqNV7NbDbDYDC4RKsRAI4ePYoZM2a41SAIW1MoFDAYDKivr+e6FIfw9vbGvHnzcP78+UFtO3WlYcOGgc/n49y5c1d9raqqCt7e3ggKCrLJsZwJhaOHMRgM4PP5FI496OzsBI/Hg5eXF9elXJNWq8XZs2cxatQorktxaiKRCIGBgR4TjsDlTYtLSkoGte3Ulby8vDB06NCrwtFsNqO2thZRUVFu2QtF4ehhLHMbydV0Oh0kEolL/KHn5eUhJiaGJv33Q1hYGJqbm7kuw2EiIiIwbNgw7Nu3z2avOWrUKFy8eBFGo9F6n1KphMlkcssuVYDC0aNYulQpHK/mal2qBQUFEAgECA8P57oUpxcUFASz2QydTsd1KQ5z4403QqVS2WxgzqhRo2AwGLrMG62uroZcLneJ+cDXg8LRg1i6VN1tVJktWE6crjK9JScnx+3mldmLTCbzqEE5wOUFyevr623WtRoVFYWAgABr12pHRweam5sRExNjk9d3RhSOHsQySpVcraOjAyKRyCVGqTIMg6KiIloRp5+kUikAeFQ4+vj4YPTo0cjOzrbJ6/F4PIwaNcoajpWVlRCJRIiIiLDJ6zsj5z8TEJswm800SrUXDMO4VJdqY2MjwsLCkJiYyHUpLkEgEMDPz89jVsqxmDRpEgoLC6FSqWzyeqNHj0ZtbS0aGxtRXV2NqKgot15hi8LRQ9DE/94ZDAaYzWaX6VKtr68Hj8dzqhVJGIbBf//7X67L6JW3t3eXwSSeYPz48eDz+TbrWh0+fDj4fD4OHDgAg8Hg1l2qgAuG40cffYS4uDh4eXlh0qRJ1/zBf/fdd0hJSYGXlxdGjRqFnTt3OqhS52IwGGjify/0er1LTW9pbGzEpUuXnGpu2bvvvovf/e53ePvtt7kupUcCgcBm8/5chVQqxYgRI2zWterj44PExEQcPXoUwcHBbj+/1qXC8ZtvvsGaNWvw0ksv4fTp00hNTcXcuXN7XLkBuDxJetmyZVi5ciXOnDmDhQsXYuHChcjPz3dw5dxiWRZGo9FlTv6OptfrXabVCFxelUQoFFqvpTmDjRs3AgA+++wzjivpmUAggMlk4roMh5s0aRIuXLgArVZrk9dLTExEeXm5U/Va2ItLheM777yDVatW4YEHHsDw4cOxYcMG+Pj49PoH+Y9//APz5s3DM888g2HDhuHVV1/F2LFj8eGHHzq4cm5ZupNoCkfPXC0cOzo6EBsby3kvwIMPPoj58+dj/vz5KCgoAABcvHjRet+DDz7IaX1XcpXBVrY2YcIEREREIC8vzyavJ5VK4eXl5RFd1C4zpt9gMCAnJwdr16613sfn8zF79mwcO3asx+ccO3YMa9as6XLf3Llz+9zzTK/XQ6/XW/+t0WgGV7gToO2pemcwGMCyrEuFI8MwnJ/o29rasHnz5qv2+WNZFrt27QJweYTj+++/7zQtXK6/Z1yQyWTw9vbG6dOnMXXq1EG9lqXlzbIsKisrER8fb4sSnZbL/LY0NTXBbDYjLCysy/1hYWG97vatVCoH9HgAWL9+PWQymfXmDqs/UJdq7/R6PXg8nku1qg0Gg80md18vqVSKEydOQCaT9fh1mUyGU6dOOU0wGo1GjwxH4PIo07q6umtuWHwtNTU14PP5SEpKQlVVlY2qc16e+dvSh7Vr10KtVltvrv5LYDabYTabXerk70h6vR5isZjzLsqB4PP5TnH9bPz48X1+MB07dqyDK+qdJ39AHDZsGCoqKga1vizLsqiurkZERATi4+NRWVlpwwqdk8uEY3BwMAQCwVU/4Pr6+l6X0AoPDx/Q44HLK6T4+/t3ubkyS7ehp54YrsUVF0aQSqVO0w38n//8p8f7v/zySwdX0jeGYVxiQXl7sMyHLS4uvu7XaGpqglarRWxsLGJiYlBdXQ2GYWxVolNymXAUi8UYN24csrKyrPcxDIOsrCykp6f3+Jz09PQujweAzMzMXh/vjoxGI4RCoUu1jByFZVkYDAaXW07Pz88P1dXV6Ozs5LoUbNmyBQAQHR2No0ePWpe0+/zzz7ksqwuGYWAymVxmkQdb8/X1RURExKA2fS4vL4dMJkNgYCCio6NhNBrdfqcTlzorrFmzBitWrMD48eMxceJEvPfee2hvb8cDDzwAAFi+fDkiIyOxfv16AMAf//hHzJgxA2+//TZuueUWfP311zh16hQ++eQTLt+GQxmNRqdpZTgbS9ekq7UcLdfR6+vrERcXx2ktjz/+OCZPnoy//e1v4PP5qKiowLPPPotx48ZxWteVOjo6YDQa3X5eXl8SExOvu+Wo1WrR3NyM1NRUALCOw6isrHTr5eNcKhzvuusuNDY24sUXX4RSqURaWhp27dplPVlUVlZ2ueg+ZcoUfPXVV1i3bh2ee+45DBkyBNu3b8fIkSO5egsOZbne6Gonf0exDEd3te9PWFgYwsLCUFdXx3k43nXXXbjrrrus/+bz+XjzzTc5rOhqljVVnWVwEBeSkpJw7Nix67r2Wl5eDi8vL+vlKF9fX8jlclRVVWHSpEn2KNcpuFQ4AsDq1auxevXqHr924MCBq+5bunQpli5daueqnJOrtowcxWg0gsfjuVy3akREBIKCglBdXc11KS5BrVbD19fXowelJSYmwmw2o6KiAklJSf1+nl6vR21tLZKTk7tcmomJiXH5wYrX4jLXHMnAWdZT9dQh7NdiMplcLhgBQCgUwmw248yZM1yX4hI0Gg0CAwO5LoNTMTExEIlEA+5araiogEAguGp7tOjoaFRWVg56eogzo7OmG3PVk7+juPLw/tGjR9ts1RN3ZjaboVKpPD4chUIhYmNjUVpa2u/nmM1mVFVVISoq6qrzSHR0NNra2qBWq21dqtOgcHRjlpGqpGeuHI7jxo2Dl5cXWltbuS7FqbW0tACAUy3SzpXExMQBzU+sqamByWRCbGzsVV+z7MjhzvMdKRzdFMMwtH/jNZhMJpf9/owbNw4NDQ347bffuC7FqTU0NMDX1xc+Pj5cl8I5hUIBo9HYr67QKyf99zQFRi6XIzo6Go2NjfYo1SlQOLopy2Acajn2zGQywWw2u+x6s6GhoQgNDcXevXu5LsVpMQyDpqamPhf98CSBgYFoamqyjt7tS319PTo6OnpdP9UykK2mpsbWZToNCkc3ZTKZXHIkpqNYWtauPFhpzpw5OHTokFMsBuCMGhsbYTabKRz/Ry6XA/j/Xc29YVkWZWVlCA4Ohp+fX6+Pi4iIQHt7u01rdCaue2YgfaLrjX2zLH3lyuE4b948DB8+HPv27eO6FKekVCoRGBhIXar/YxmUdK3r1I2NjWhvb7/mrhsymazPTRxcneueGUifaKRq39whHC17Om7atInrUpyOZSRlZGQk16U4DX9/f/D5/Gu2HMvKyiCXy3vdceXK13OHLf1647pnBtInCse+WQYluHI4AsADDzyAM2fO4OzZs1yX4lQqKyvh7e2NkJAQrktxGnw+HwEBAX22HC0LjPdnr0Z/f3/odLou+9+6E9c+M5Aemc1msCxL4dgHS8vR1RdknzlzJkaOHIkdO3ZwXYrTaGtrQ1NTE2JiYlz+52trcrm8z3AsKytDQEBAv+aFWnYs0mq1NqvPmVA4uiHLcG1XnabgCO7QrQoAAoEAK1aswGeffYb8/Hyuy3EKZWVlkEqlCA0N5boUpxMYGNhrt2pLSwvUanW/Wo0ArN2u7tq16tpnBtIjyzQOVz/x25Orj1S90m233YbExES8+uqrbr2cV380Nzejra0NcXFx1GrsQV8tx/Lycvj7+/d7wQTLSFZ3XSXHPc4OpAtXnr/nKAzDuM3JUygU4vnnn8exY8eQmZnJdTmcMZvNKCsrQ2BgoHXaAukqMDCwxw9QLS0tUKlUSEhI6Pdr+fr6gs/nU8uRuA6z2UzXG6+BZVm3amXNnDkT9913H5577jmoVCquy+FEWVkZeDxev7sFPZG3tzeampquur+kpAT+/v4IDg7u92vxeDz4+/vTNUfiOiwLAJC+Wa47ugMej4fVq1ejvb0dzz33HNflOFxTUxNaWloQExNDm3v3gc/nX/XBsLGxEVqtFomJiQN+PX9/f+pWJa6DulWvjcfjuVU4ApdXLFm/fj127NiBH374getyHKazsxPl5eUIDg6mqRvX0P06O8uyKC0thVwuv66dS9x5riOFoxtyp8Em9sLn890uHAFg4cKFePTRR/Hkk096xNxHk8mEoqIi+Pj4IC4ujutynJ6lR8nScqyvr0d7e/uArjVeyZ13O6EzqJuxdJlQOPbN8v1xx4B85plnkJKSgmXLlqG2tpbrcuzGbDajuLgYLMsiMTGRfuf7wRKOlrWFy8rKEBISYp2zOFD9WXHHVdFvk5txl/l79ubO4ejl5YUvv/wSIpEIa9asccsBOgzDoKSkBHq9HkOHDqXrjP10Zcuxrq4OnZ2d191qBACJRAKDwWCr8pwKnUHdDIVj/1i+P+40YvVKISEh+Pbbb1FWVoZbb721xxGKrspsNqO0tBR6vR6JiYk97jdIemb5vTeZTKisrER4eDh8fX2v+/XEYjEtH0dcA4Vj/7hzy9EiOTkZmzZtQn19PW655Ra32EHBaDRagzEhIQFSqZTrklyKpeVYWVkJo9E46GkvYrEYXl5etijN6dAZ1M1QOPaPZTSvZTUhdzV8+HDs3LkTfn5+ePTRR5Gbm8t1Sdets7MTJSUlMJlMSExMHFSLx1PxeDyYzWZUVVUhMjLSJq3ujo4OG1TmfOgM6mYoHPtHIBCAYRiYzWauS7G7IUOGYMuWLWhubsasWbPw5ZdfWr+WmZmJ9PR0xMbGIj093WlX2GlpaUFpaSnEYjGSkpLctrVibzweDxKJBHw+H7GxsVyX49RoGRU3Q9M4+kcgEIDP58NoNHJdikMoFApkZmZizZo1eP7553HhwgVUVFR0CcrKykrcdNNNWLlyJT799FMOq/3/TCYTamtr0dbWBrlcjvDwcFrgYhBaW1tRXV2NoUOH0ipa10DfHTdD4dh/AoHAbUfa9cTLywsff/wxtm7dilWrVvW6APXGjRuxbNkyzJo1y8EV/n8sy0KtVqOxsRE8Hg/R0dHWha7J9SspKUFoaKjNNoFmWdZtP6zQWdTNUDj2nzuPtOvLkiVLrjkQY926dQ6q5mrt7e2oqKhAQ0MD/Pz8EB8fT8FoA01NTVAqlQgKCnLbQLMlajm6GQrH/pNIJGhra+O6DE5ca2oHF4sHtLe3o7W1FTqdDhKJBDExMXRt0UYs80KBy8sMkmujcHQzZrOZwrGfPLXlCFy+BllZWdnn1x3BZDKhvb0dGo0GRqMRXl5eUCgU8PHxccjxPUVNTQ1MJhPEYrF1k2LSNwpHN+Ouk9rtQSKRgGVZGI1GiEQirstxqFdeeQU33XRTn19nGMZ6TclyswWj0QidToeOjg7rhxMfHx+EhobSSjd2oNfrrRP+dTodhWM/UTi6IXee2G5LYrEYAKDT6TwuHOfMmYOVK1di48aNV31t5cqVmDNnDliWhdlstn7gsvyXz+eDx+NZ/9tbaJrNZut0GaPRCIPBAKPRaJ0+I5FIEBQUBG9vb+rtsKOSkhIIBALExsZCrVbbNBx5PJ7bbiw94HBcsWIFVq5cienTp9ujHjJIPB6PWo/9dGU4euKAj08//RTLli3DunXrUFtbC4VCgddee806SpXH41k/NFgWqjaZTDCZTNZ/dw9Oy32W/175uygUCuHr6wuJRAKRSESDQhygtbUVTU1NSElJgdlstnnLUa/Xu+0iAAMOR7VajdmzZyM2NhYPPPAAVqxYYbNhwWTw3HGfQnuxTIju7OzkuhTOzJo1q19TNvh8Pvh8vnVu3JUhCKDL/wOwtij5fD4EAgEFIQcYhkFxcTECAgIQGhqK+vp6CAQCm4ejuw6aGnBfxvbt21FTU4PHHnsM33zzDeLi4jB//nx8//33HjOh2pnRSWhgfHx8PDocr5cl9EQiEUQikXWNTctNIpFALBZDKBTS7yRHqqurodPpkJSUBABobm4Gy7I23RDaMrLYHV1XR39ISAjWrFmDs2fPIjs7G0lJSbjvvvugUCjw1FNPoaioyNZ1kn6ibtWB8fb2RmdnJ7W2iVvR6XSorKxEZGSkdeSvUqmESCRCYGCgzY6j1+spHHtSV1eHzMxMZGZmQiAQ4Oabb8a5c+cwfPhwvPvuu7aqkQwAhePA+Pr6gmEYtLe3c10KITZTUlICsVjcZf3Uuro6hIWF2XTwE4/Hs2nYOpMBf5eMRiO2bt2KW2+9FbGxsfjuu+/w5JNPora2Fp9//jn27t2Lb7/9Fq+88oo96iXXQOE4MF5eXhAIBB67GABxP42NjWhtbUViYqJ19xkA0Gg0SExMtOmxmpqa3HaN1gG/q4iICDAMg2XLluHEiRNIS0u76jEzZ85EQECADcojA0XhODA8Hg9SqZRajsQtWPa7DA4ORlBQkPV+hmFQWFiIBQsW2PR4Go0G/v7+Nn1NZzHgcHz33XexdOnSPkcoBQQEoKysbFCFketD4ThwUqkUdXV1br2IMvEMpaWlYFn2qhZiXV0djEajTbepYhgGWq3WbcNxwN2q9913HydDd1taWnDPPffA398fAQEBWLly5TW7wjIyMrqs7sHj8fDoo486qGJuUDgOnFQqBcMwbjtfi3iGlpYWNDY2IiEh4apFLSoqKsDj8RATE2Oz47W3t4NlWbcNR5fpLL7nnnusA4CMRiMeeOABPPzww/jqq6/6fN6qVau6XP909zUbKRwHztvbGzweDxqNhnaXJy7JbDajuLgYgYGBCA0Nverr5eXlUCgU1oUvbEGj0QAAhSOXLl68iF27duHkyZMYP348AOCDDz7AzTffjLfeeqvPRZJ9fHwQHh7uqFI5ZwlH6iLsPz6fD39/f6jVatqxgLiksrIymM1m65zG7srLy23apQq4fzi6xIKGx44dQ0BAgDUYAWD27Nng8/nIzs7u87lffvklgoODMXLkSKxdu/aaXWd6vR4ajabLzZVQIF4fmUyGtrY2mEwmrkshZEDUajWampoQGxvb45zDzs5OdHZ2YsiQITY9rlarBQC3XXrRJVqOSqXyqq4CoVAIuVwOpVLZ6/N+97vfITY2FgqFAnl5efjLX/6CwsJC/PDDD70+Z/369Xj55ZdtVrujWcKRWo4DI5PJwOPxoFKpEBwczHU5hPSLpTvVz8+v1x60S5cuQaVS9dqqvF6WyxBXThdxJ5y2HJ999tmrBsx0vxUUFFz36z/88MOYO3cuRo0ahXvuuQdbtmzBtm3brJt+9mTt2rVQq9XWW1VV1XUfnws8Hg9ms5laQAMkEong7e2NlpYWrkshpN/KyspgMpn6DL6LFy8iNDTU5rtnaDQaREVF2fQ1nQmnLcenn34a999/f5+PSUhIQHh4OBoaGrrcbzKZ0NLSMqDriZMmTQIAFBcX9zoZViKRuPRySEKhECzLWjc2Jf0XFBSEyspKmEwmt53YTNyHZceN+Pj4Xs9ZLMvi4sWLGDVqlM2PX19f79YDHDk9A4SEhPRrEdz09HSoVCrk5ORg3LhxAIB9+/aBYRhr4PVHbm4uALj1oAvLSZ0WgR84uVyOiooKtLa22nRxZkJszWg0oqSkBIGBgQgLC+v1cU1NTWhpaUFKSorNa2hqarKej92RSwzIGTZsGObNm4dVq1bhxIkTOHLkCFavXo27777b2s9eU1ODlJQUnDhxAsDltQVfffVV5OTkoLy8HD/++COWL1+O6dOnY/To0Vy+Hbuy7MFH3aoDJxKJ4O/vT12rxOmVlJSAx+MhISGhz8cVFBRALpfbfDCO0Wh0++vzLhGOwOVRpykpKZg1axZuvvlmTJs2DZ988on160ajEYWFhdbRqGKxGHv37sVNN92ElJQUPP3001iyZAl++uknrt6CwwiFQmo5Xie5XA61Wk3fP+K0lEolVCoVEhMTr5rs311ubi4iIiJsfqmoubkZANy6h8VlLqzI5fI+J/zHxcV1mfweHR2NgwcPOqI0pyMSiaDX67kuwyUFBQWhvLwcjY2Nfc6fJYQLHR0dqKqqQkRExDXXr9ZqtSgpKcHdd99t8zoaGhpsvjeks3GZliPpP5FIRC2f6yQQCCCXy68aAEYI1yzTNry9vREdHX3Nx+fl5YHH49ltMI5MJnPrFaUoHN2QSCQCwzC0ge91Cg0NhU6nc7kFIIh7q6iogMFgQFJSUr/2ZDx//jzS0tLsEmC1tbWIiIhw67nUFI5uiEasDo6/vz+8vb37XGCCEEdqampCU1MT4uLi+rXxQ319PS5evGi3wYfV1dWIjIy0y2s7CwpHN2S5SE/heP3CwsLQ3NxM124J53Q6HcrLyxEcHNzv0aHHjh2Dr6+vXbpUOzo6oFKpKByJ6xEIBODz+TSdYxBCQkIgEAhQW1vLdSnEgzEMg+LiYojFYsTFxfXrOSaTCSdPnsTEiRPtsphFTU0NAFA4EtdE0zkGRyAQWFdmog8ZhCuVlZUDus4IXB6I09HRgfT0dLvUVFNTA4lE4tZzHAEKR7dFI1YHLyIiAgzDoL6+nutSiAdqbGy07rYxkGXajh49iqSkJLtNs6iuroZCoXDrwTgAhaPbolVyBk8kEiE0NBR1dXU08pc4VHt7OyorKxEaGoqgoKB+P6+hoQElJSWYMmWK3Wqrra11+y5VgMLRbQmFQhgMhi4LI5CBi4yMhF6vR11dHdelEA9hWTfV19e3X/MZr5SdnY3w8HC7DMQBLod2S0uLzTdOdkYUjm5KIpGAYRgYDAauS3FpXl5eCAsLQ3V1NcxmM9flEDfHsixKS0vBsiwSExMH1HXZ3t6Oo0ePIjU11W67ypSVlYFl2X4PDnJlFI5uyrKWok6n47gS1xcdHQ2TyUStR2J31dXVaGtr69e6qd0dOnQIMpkMU6dOtVN1QGlpKeRy+TWXrnMHFI5uis/nQyQSobOzk+tSXJ5EIkF4eDiqq6tpkBOxm+bmZjQ0NCA6OhpSqXRAz9VoNPjtt9+QmpoKPz8/O1V4ueV4rZ1A3AWFoxvz9va27lJCBicmJgYMw6C8vJzrUogbamtrQ2VlJYKDgxEaGjrg5+/duxdCoRAZGRm2L+5/Ojs7UVdXh/j4eLsdw5lQOLoxHx8fGAwGulZmAyKRCLGxsairq0N7ezvX5RA3otfrUVpaCl9fX8TExAz4+U1NTcjOzsaNN94Ib29vO1R4meV6I7UcicuzzI2i1qNtKBQK+Pj4oKSkhOtSiJswm80oKSmBQCBAQkLCdc0d3LVrF/z8/Ox6rREAiouLERUVhcDAQLsex1lQOLoxoVAIkUhE4Wgjlp3XVSoVGhsbuS6HuDiWZVFWVgaj0YjExMTrGmFaXV2Ns2fP4qabbhrwAJ6BYFkWBQUFiImJcfvJ/xYUjm7Ox8eHBuXYkFwuR1BQEIqLi2mRBTIo1dXV0Gq1SEhI6NdOGz359ddfERoaivHjx9u4uq4aGxvR2tqKlJQUux7HmVA4ujkfHx/odDpa4cWGEhMTYTKZUFpaynUpxEVZloaLjo6+7tGlxcXFuHTpEubPn9/vdVevV0FBAUQikcdcbwQoHN2e5QI9da3ajpeXFxISElBbWwuVSsV1OcTFqFQq1NTUICws7LoX72YYBvv378eQIUMwYsQIG1d4tYKCAiQlJdm169bZUDi6ObFYDKFQSF2rNqZQKCCTyXDp0iUaDUz6ra2tDRUVFQgMDIRCobju1zl48CAqKipw88032/0aYEdHByoqKjyqSxWgcPQIPj4+1HK0MR6Ph+TkZHR2dqKoqIjrcogL6OzsRFlZGaRS6XVN2bBQKpXIysrCtGnTEBUVZcMKe1ZUVASGYSgcifvx9vam64524OPjgyFDhqC2tpZGr5I+GQwGlJaWQiwWIz4+/rpbe2azGd9++y2Cg4Mxe/ZsG1fZs6KiIkRFRcHf398hx3MWFI4ewNfXFwzDUOvRDhQKBUJCQnDx4kVax5b0yGQyoaSkxDoVaDCDZ/bv34/6+nrceeeddltc/EpGoxHnz593yHVNZ0Ph6AEs1x21Wi3XpbillJQUCAQCXLhwgbYII10wDIOysjKYzebrWkz8StXV1di/fz9mzpw5qOuVA1FQUACDwWC3LbCcGYWjh/Dz80NbWxvXZbglkUiEESNGoK2tjaZ3ECtLMBoMBiQmJlp3yrkeJpMJ3333HcLDwzFz5kwbVtm3vLw8REVFDWjDZXdB4egh/Pz8YDQaqevPTgICAhAdHY2ysjK6/kjAsiwqKirQ2dmJuLi4Qa95mpmZiebmZixduhQCgcBGVfZNp9OhsLAQqampDjmes6Fw9BA+Pj7g8/nUtWpH8fHxCA0NRX5+Pl3f9WCWYGxra0NcXBx8fX0H9XrFxcU4e/Ys5s6di/DwcBtVeW3nz58HwzAe2aUKUDh6DB6PB6lUSpPW7WzEiBHw9vbGmTNnaO9HD8SyLKqqqqDVahEbGzvgfRm7U6lU+OabbxAeHm73hcW7O3fuHOLj4+26P6Qzo3D0IDKZDHq9nrpW7UggEGD06NEwGo04ffo0LRDgYWpqaqBSqRATEzPoqQ9GoxHbt2+HWCzGnXfeafcl4q7U2tqK0tJSu6/Z6swoHD2IVCqFQCCg1qOd+fj4YMyYMdBqtTh37hyNYPUQtbW1UKvViI6OhkwmG9RrsSyL77//HpWVlbj33nut2885yqlTpyCRSDB8+HCHHteZUDh6EB6Ph4CAAKjVajph25lMJkNqaioaGxtRWFjIdTnEzmpra9HS0gKFQmGT/Q737NmDixcv4s4770RERIQNKuw/s9mMnJwcjBkzxqPWUu2OwtHDBAQEwGg00m72DhASEoJhw4ahsrIS5eXlXJdD7MQSjJGRkTYJxlOnTuHw4cOYP38+J0u2XbhwAe3t7ZgwYYLDj+1M7L/EAnEq3t7eEIvFUKvVgx4sQK4tKioKOp0OxcXFEAgEiI6O5rokYkOWnVlsFYzFxcX46aefMGnSJEyePNkGFQ7cyZMnERcXh5CQEE6O7yyo5eiBLF2rtNaqYyQlJUGhUOD8+fOoqanhuhxiAyzLWgff2CoYq6ursXPnTgwZMsQhu230pLGxEWVlZZg4caLDj+1sKBw9UEBAABiGoTmPDjRs2DBERUXhwoULqK6u5rocMgiWYNRoNIiKihr04Bvgcgv0iy++gK+vr8NHpl7p1KlT8PX1xbBhwzg5vjOhblUPJBaL4ePjg5aWFpv8YZNr4/F4GDFiBHg8HvLy8mAwGDxqV3V3wTAMampq0NHRgaioKJvMAayrq8OWLVsQHByMe++9F2Kx2AaVDpzBYEBxcTHGjx/vkEXNnR19BzxUYGAgqqqqYDAYOPtj9DSWgBQKhSgoKIDRaERycjLXZZF+MpvNqK6uhl6vR3R0tE2mV9TX12PLli0IDAzEfffdN6j1VwcrJycHLS0tHj8Qx8JlulVff/11TJkyBT4+PggICOjXc1iWxYsvvoiIiAh4e3tj9uzZtDHt/8hkMggEAjQ1NXFdisdJTk7GsGHDUFJSgvz8fJpW4wJMJhMqKythMBgQExNjk2Csra3F999/D5lMhuXLl8PLy8sGlV4fs9mMo0ePYtSoUdSb9D8uE44GgwFLly7FY4891u/nvPnmm3j//fexYcMGZGdnw9fXF3PnzqUVYgDw+XwEBQWhtbWVBuZwID4+HqNHj0ZVVRVyc3PpZ+DEDAYDKioqwDAMYmNjbRJiZWVl+PzzzyGRSLB8+fJBL0w+WOfOnYNGo8G0adM4rcOZuEw4vvzyy3jqqaf6vQguy7J47733sG7dOtx+++0YPXo0tmzZgtraWmzfvt2+xbqIoKAgMAyD1tZWrkvxSFFRURg7diwaGhqQnZ1Na7E6IZ1Oh4qKCvB4PMTExNjkEsSFCxfwn//8B1FRUVi+fLnDV7/pjmVZHDlyBEOHDkVoaCintTgTlwnHgSorK4NSqcTs2bOt98lkMkyaNAnHjh3r9Xl6vR4ajabLzV2JRCL4+/tT1yqHwsLCMGHCBGi1Wvz22280gtiJdHR0oLq6GiKRCLGxsYNeLYZlWRw6dAg//PADRo8ejWXLljnF9f6ioiI0NDRQq7Ebtw1HpVIJ4PLJ50phYWHWr/Vk/fr1kMlk1pu7T9oODg6GXq+nkzKH5HI5pk2bBpFIhEOHDtFUDyegVqtRU1MDb29vxMbGDnoPRYPBgO+++w4HDhzA9OnTcdtttznFiFCWZXH48GEkJycjJiaG63KcCqfh+Oyzz4LH4/V5KygocGhNa9euhVqttt6qqqocenxH8/X1hbe3N7UeOebj44MpU6ZAoVDg9OnTyM3NpR09ONLU1IT6+nr4+/tDoVAMejJ+S0sLNm7ciNLSUtx1112YPn06JxP8e1JYWIjKykpMnjzZaWpyFpx+dHn66adx//339/mY650LZtkUtL6+vsvCvfX19UhLS+v1eRKJhNPh1FwIDg5GVVUVdDodpyPmPJ1AIMCYMWMQHByMvLw8tLa2YsKECbTMn4OwLAulUgmtVouQkBCbrHpTUlKCrVu3wsfHBw899BCCg4NtUKltMAyDrKwsJCQk0JzbHnAajiEhIXZbvy8+Ph7h4eHIysqyhqFGo0F2dvaARrx6goCAANTW1qK+vh6xsbFcl+PxoqOjERAQgFOnTuHgwYNITU1FVFQU12W5NbPZjNraWuh0OkRERNhkcv/Ro0eRlZWFxMRELF682Ok+eJ47dw6NjY24/fbbuS7FKbnMNcfKykrk5uaisrISZrMZubm5yM3NRVtbm/UxKSkp2LZtG4DLE66ffPJJvPbaa/jxxx9x7tw5LF++HAqFAgsXLuToXTgnHo+HsLAwtLa2Qq/Xc10OAeDn54fp06d36WY1mUxcl+WWjEajdUEMW6x609bWhu+//x7Z2dmYOnUqli1b5nTBaDabceDAAaSkpNAHr15wf0W4n1588UV8/vnn1n+PGTMGALB//35kZGQAuNx/rlarrY/585//jPb2djz88MNQqVSYNm0adu3a5XS/qM5ALpejvr4e9fX1dGHeSVzZzXr+/Hk0NzdjxIgR1ksGZPA6OjqgVCohEAgQExMzqBGpLMsiNzcX+/btg1QqxYIFC5CUlGTDam0nJycHKpUKy5Yt47oUp8VjaXmOPmk0GshkMqjVavj7+3Ndjl01NjaitrYWKSkpHnfd1dm1t7fj7NmzUCqViIiIQGpqKufz41ydSqVCU1MTfHx8EB4ePqjFvpubm/Hrr7+isrISqampmDVrltN+CDcYDHj//feRmJiIRYsWcV2OQw3kfO4yLUdif0FBQaivr4dSqaRrj07G19cXU6ZMQU1NDfLy8pCZmYnk5GQMGTJk0NMMPA3LsmhoaIBWq0VgYCCCgoKu+7UYhsHx48fx22+/wd/fH7/73e8QFxdnu2LtIDs7G52dndYeN9IzCkdixefzERYWhqqqKoSGhnK+pBW5WmRkJMLCwlBQUICCggJUVFQgNTWVulr7yWQyQalUQq/XIywsbFDXF2tra7Fz5040NjZi8uTJuOGGG5xi7mJf2tracPjwYaSnp9tkNK47c+6fJHG44OBgNDY2orq6GkOGDOG6HNIDoVCIkSNHIjY2FmfPnsXRo0cRERGB0aNHw9fXl+vynJZer0ddXR2Ay0v3Xe+lA51OhyNHjiA7Oxvh4eF48MEHr1psxFnt3bsXQqEQU6dO5boUp0fhSLrg8XiIiopCcXExVCpVv3dAIY7n5+eHadOmWbtas7KyEB0djZSUFGr1d6PRaNDc3AyRSITw8PDrauEZDAacPn0a586dg16vx6xZszBhwgTONiYeqKqqKuTl5eHWW2+l349+oHAkV/H394e/vz9qamogk8lo5QwnZ+lqLSoqQkFBAUpKShAXF4eUlBSPX0CAZVk0Njaira0N/v7+CAoKGvDvs8FgQE5ODk6ePAmDwYAxY8Zg0qRJLvW9ZVkWu3btQkREhHWkP+kbhSPpUVRUFC5evIiGhgaX6TLyZEKhEMOGDUNSUhJKSkpw6dIllJWVISoqCsOGDfPIHgCj0Yj6+noYjUaEhoYOOMz0ej1ycnJw6tQpGI1GpKamYtKkSTZZIMDRTp8+jbq6Ojz44IP0YbefKBxJj7y8vBAcHAylUomgoCCnH2hALhOJREhJScGQIUNQXl6OgoIC7NmzB+Hh4Rg2bJjdVqRyNm1tbWhsbIRQKERkZOSAdr/o6OjA6dOnkZOTA7PZbA1FV2opXkmj0WDfvn2YNGkSTfgfADrjkV5FRESgpaUFtbW1tDCAixEIBEhMTERCQgKqqqpw8eJF7N+/H6GhoYiPj0dUVJRbTgFhWRbNzc3QaDSQSqUIDg7u9zXBuro65ObmoqCgAD4+Phg1ahQmTpzosqFosXPnTohEIsyYMYPrUlwKhSPplVAoREREBKqrqxESEkIX8V2QZZPemJgY1NXVoaioCMePH4dAIEBUVBRiY2MRHh7uFl1tJpMJ9fX1MBgMCA4O7teiHR0dHSgoKEBxcTEqKyvh7++PqVOnYtSoUW7x+56Xl4fi4mLcddddTrsogbOicCR9CgkJQVNTE03tcAMRERGIiIiAVqtFWVkZKioqUFpaCi8vL8TExCA2NhbBwcEuGZRtbW1oaWkBn8+HQqHoc5qG0Wi0Dl6qqKgAj8fDkCFDsGjRIiQkJLjk++9JW1sb9uzZg5EjR9Lf7nWgcCR94vF4iIyMRHFxMVpbW2nisBvw8/PD6NGjMXr0aLS0tKCiogIVFRW4dOkSfH19ERMTA4VCgZCQEKefpsAwDJqbm9He3g6pVAq5XN5jzWq1GuXl5SgvL0djYyM0Gg0iIyMxa9YsDB061C1bVTt37oRAIMDcuXO5LsUlUTiSa5LJZJDJZKiqqoK/v79bXqvyVHK5HHK5HGlpaWhsbERFRQWqqqpw/vx5CIVChIeHIywsDKGhoQgMDHSqsNTr9WhsbATDMAgJCemyAILRaERtba01EFtbW62tyvHjxyMhIcGt10rOz8/HpUuXcMcdd7hF9zAXKBxJv8TExCA/Px/V1dW07qob4vF4CA0NRWhoKFiWRWtrK2pra9HQ0ICcnBwwDAOhUIjg4GCEhIQgODgYQUFBnC1+rlKpoFKpIJFIIJfLodVqUVlZaV08v7GxEWKxGAKBAHFxcZg6dSpiYmIGNGrVVbW3t2P37t0YPnw4UlJSuC7HZVE4kn4Ri8WIiopCeXk5ZDKZR86b8xQ8Hs/aogQu7/3X0tKChoYGNDQ0oKioCIWFhdDpdBCLxQgICLDe/Pz8IJVKIZVKB7X9U090Oh0aGxtRWlqK+vp6mEwm6PV6tLe3Wx8TFhYGuVyOESNGIDIy0voePMmuXbvA4/Ewb948rktxaRSOpN9CQ0OhUqlQWlqKUaNG2fzkR5yTQCBASEgIQkJCMGLECAD/fwCMpQXX1NSEkpISMAwDs9kM4PKcS29vbwiFQohEIojFYohEoi43SzetXq+HwWDo9abX663XFwFAoVAgPDwccrkcgYGBkMvlCAgI8PjfybNnz6KkpAS33347bWk2SBSOZEASEhJw7tw5lJSUUJeNB7O0Dq+c/8qyLDo6OtDW1ob29na0t7dDp9NBr9fDaDTCYDCgra3N+v/A5dagl5cXjEYjxGIxxGIxJBIJfHx8EBAQAIlEAoFAAJ1OZ901ZrCbErurpqYm7N69GyNHjkRycjLX5bg8CkcyIEKhEImJiSgoKEBdXR0iIiK4Lok4CR6PB19fX5vuDNLe3g61Wg0ej4fAwEC3HFVqCyaTCdu3b0dAQADmzJnDdTluwXmGnhGX4e/vD4VCgerqarS1tXFdDnFDZrMZTU1NaG1thZeXF8LCwigY+7Bv3z60tLRg4cKF1Kq2EQpHcl0iIyPh6+uLkpIS6zUmQmyho6PDumB4cHBwr3MXyWW5ubnIycnBzTffjNDQUK7LcRv0G0euC4/HQ2JiIkwmE8rLy7kuh7gBs9mM5uZmtLS0UGuxn6qqqrBnzx6MHTsWI0eO5Loct0LhSK6bRCJBXFwcmpub0dTUxHU5xIW1t7ejoaEBJpOJWov9pFarsW3bNkRFRdF1RjugATlkUIKCgqDRaFBeXg6pVEqf9MmAGI1GqFQqGI1G+Pr6ws/Pj0KxH4xGI3744QeIRCIsWrSIvmd2QN9RMmiWlUeKi4vBsizX5RAXwLIsNBoNGhsbwbIsgoODIZPJ6CTfT7/88gtaWlqwZMkSWh7OTug3kQyaQCBAUlISOjs7UVVVxXU5xMnpdDo0NDSgvb0d/v7+CAkJ8Yhl3Wzl6NGjKCgowIIFC2gAjh1RtyqxCR8fH0RHR6Oqqgq+vr4ICgriuiTiZMxmMzQaDTo7OyGRSCCTySAU0iloIC5duoRDhw7hhhtuwNChQ7kux61Ry5HYTHh4OAIDA3Hp0iVotVquyyFOgmVZtLe3o6mpCQaDAYGBgQgKCqJgHKDGxkb8/PPPSE5OxpQpU7gux+1ROBKbSkhIgJ+fHy5evIjOzk6uyyEc0+v1aG5uhlarhbe3N0JCQuga2XVoa2vDTz/9hODgYNxyyy1usyGzM6NwJDbF5/ORkpICsViMCxcuWNfQJJ7FbDajtbXVuo9icHAw/P39acDNddDr9fjuu++g1+uxaNEiuj7rIPSbSmxOKBRi+PDhAIALFy7AZDJxXBFxFJZlodVq0dTUBJPJhICAAMjlcupCvU4mkwnbtm2DVqvF0qVL4efnx3VJHoPCkdiFWCzG8OHDYTAYUFBQAIZhuC6J2JlOp0NTUxM6Ojrg6+uL4OBgmvc6CEajEdu2bYNKpcIdd9yB4OBgrkvyKBSOxG68vb0xbNgwtLW1oaioiOZAuimj0Wjd21EkEiE4OBhSqZSuiw2CJRhra2txyy23QKFQcF2Sx6FwJHbl5+eHoUOHorm5GWVlZVyXQ2zIMjWjtbUVAKwbDgsEAo4rc22WYKyrq8OSJUsQHR3NdUkeiS4EELuTy+VITExESUkJxGIxoqKiuC6JDALDMOjo6EBHRwf4fD78/f2p+9RGLMvCKZVKLFmyhP5WOEThSBwiLCwMRqMRlZWVEIlECAsL47okMkAsy6KzsxPt7e0AAKlUCm9vb+o+tZErg/GOO+5AZGQk1yV5NApH4jBRUVEwGAwoKSmBUCikVXRciE6nQ1tbGxiGgbe3N3x9fWlahg0ZjUZs3boVDQ0NWLp0KV1jdAIUjsSh4uPjYTKZUFBQgJSUFApIJ2cwGNDW1gaTyQSJRAKpVErXFG3MYDBg69ataGxsxB133EHB6CQoHIlD8Xg8DBkyBAzDoKCgAMnJyTRE3QmZTCa0t7fDYDBAKBQiMDAQIpGI67LczpXBuHTpUkRERHBdEvkfCkficDweD8nJybh06RIKCwvBMAztLuAkTCYTOjs7YTQawefzIZPJaEUWO9Hr9dixYwcFo5NymYsGr7/+OqZMmQIfHx8EBAT06zn3338/eDxel9u8efPsWyjpFx6Ph6FDhyI0NBSFhYWoqanhuiSPZjKZoNVqodFowDAMpFIpAgICKBjtRKvV4ptvvoFKpaJgdFIu03I0GAxYunQp0tPTsXHjxn4/b968edi0aZP13xKJxB7lketg6WIVCoUoKSmBTqdDYmIi12V5FLPZjM7OThgMBggEAkilUgpEO6utrcXPP/8MqVSKJUuW0HV3J+Uy4fjyyy8DADZv3jyg50kkEoSHh9uhImIr8fHxkEgkKC4uhl6vR0pKCo2EtLMrQ5HP58PX15c+ODrAuXPnsH//fkREROCWW26Bj48P1yWRXrhMOF6vAwcOIDQ0FIGBgbjxxhvx2muv9flJTa/XQ6/XW/+t0WgcUabHUygUkEgkuHjxIvLy8jBixAgaAGIHFIrcMJvNOHjwIPLy8pCamorp06fTqF8n59Yfz+fNm4ctW7YgKysLb7zxBg4ePIj58+fDbDb3+pz169dDJpNZb7R0k+MEBQUhNTUVnZ2dyM3NhU6n47okt2EZfarVamE2m+Hr64uAgAAKRgdob2/H1q1bkZ+fj9mzZ2PmzJkUjC6Ax3K4GvSzzz6LN954o8/HXLx4ESkpKdZ/b968GU8++SRUKtWAj1daWorExETs3bsXs2bN6vExPbUco6OjoVar4e/vP+BjkoHr7OxEfn4+zGYzRo4cCalUynVJLstkMkGn08FkMkEgEEAikdA1RQeqr6/HTz/9BJZlceutt9LAG45pNBrIZLJ+nc857VZ9+umncf/99/f5mISEBJsdLyEhAcHBwSguLu41HCUSCX2a5pi3tzfS0tKQn5+PvLw8JCUl0VSPATIajdDpdDCbzRAIBPD19aVuage7ePEi9u7di5CQECxYsAC+vr5cl0QGgNNwDAkJQUhIiMOOV11djebmZvr05gJEIhFSU1Nx6dIlXLhwARqNBgkJCTRQ5xoMBgN0Oh0YhoFQKIRUKqWNhh2MYRj89ttvOHPmDEaMGIEbb7yRulFdkMucaSorK5Gbm4vKykqYzWbk5uYiNzcXbW1t1sekpKRg27ZtAIC2tjY888wzOH78OMrLy5GVlYXbb78dSUlJmDt3LldvgwwAn89HSkoKhgwZgpqaGuTm5nbp8iaXsSwLvV4PjUaDjo4OCAQC+Pn5UTByoLOzE9u2bcPZs2cxc+ZMzJkzh4LRRbnMX86LL76Izz//3PrvMWPGAAD279+PjIwMAEBhYSHUajUAQCAQIC8vD59//jlUKhUUCgVuuukmvPrqq9Rt6mIiIyPh5+eH8+fP49SpUxg+fDgCAwO5LotzllDU6/VgWRZisRgSiYROxhxRKpXYuXMnjEYjFi9eTNtNuThOB+S4goFcwCX2ZTQacfHiRbS2tiIuLg4xMTEeuV0SwzDQ6/UwGo0ALndBSyQS6nLmiNlsxunTp5Gbm4vAwEDMnTsXfn5+XJdFeuAyA3IIGQiRSIRRo0ahoqICZWVlaG1txbBhwzymJ8BkMsFgMMBkMoHH41lHnnriBwRn0dDQgKysLLS0tGDcuHGYMGECtdzdBIUjcSk8Hg9xcXHw9/fHhQsXcOLECSQnJ7vtaFaWZWE0GmEwGMAwDAQCAby9vWnkKcdMJhNOnDiBM2fOICgoCHfeeadDBxcS+6NwJC5JLpdj0qRJKCgoQH5+PsLDwzF06FC3GYDCMAwMBgOMRiNYloVIJIK3tze1SpxAXV0dsrKyoNVqMWnSJIwdO5a6tN2Qe5xJiEeydLMqlUpcunQJra2tLr8/pNlstoYij8eDWCyGSCSik68TMBqNOH78OM6ePYvw8HDcfPPNkMvlXJdF7ITCkbi88PBwBAQE4NKlS8jNzUVoaCiGDh0KLy8vrkvrN0vXqdlsBp/Ph5eXF0QiEV1PdBJVVVXYv38/Ojo6MG3aNKSmptLPxs3RaNVroNGqrqW+vh6XLl2C0WhEfHw8YmNjnbbVxbKsdZANy7Lg8/kQi8Vu0zXsDgwGAw4fPowLFy4gMjISN954I2QyGddlketEo1WJxwoLC0NwcDBKS0tRWlqKuro6JCcnO9WeeWazGSaTCWazGTweDyKRCEKh0GlD3FOVlpbi4MGDMBqNyMjIwIgRI6i16EEoHInbEQgEGDJkCBQKBQoKCnDmzBnOu1otrUSTyUStRCfX0tKCw4cPo7q6GvHx8bjhhhto8XsPRN2q10Ddqq6Py67W7q1EgUBArUQnpVarkZOTg6qqKgiFQkydOhVxcXFcl0VsiLpVCblCT12tQ4cOtduoVmoluhatVoucnBwUFhbC29sb48ePx7Bhw+gDjIejv1biEa7sai0sLERubi4CAgKQkJBgs+H4lhYitRJdQ1tbG06fPo2CggJIJBKkp6dj+PDh9CGGAKBwJB7G19cXY8eORWNjI0pKSpCdnQ25XI74+HiEhIQMeMAFwzAwm81gGAYMw1jnJtIJ1nl1dHTg9OnTuHDhAsRiMSZOnIiRI0fSz4x0Qb8NxCOFhIQgODgYjY2NKCsrw+nTp+Hr64v4+HgoFIo+W3ssy1pbiCzLWluJtM6pc+vs7ERubi7y8/MhFAoxfvx4jBo1ipbiIz2icCQei8fjITQ0FKGhoVCpVCgrK0N+fj6KiooQGxuL6OjoLidOSyAyDAPgcletQCCgblMnp9VqkZ+fj4sXL4JlWaSlpWH06NEes2A9uT4UjoQACAgIwJgxY9De3o7y8nIUFxejpKQEkZGRiI6Ohlgstg6usSznRq1E51ZXV4dz586hoqICYrEYaWlpGD58uEutnES4Q1M5roGmcngelmXR0dGBsrIyVFVVwWQyITIyEklJSfQ74OQMBgNKS0tRUFCAhoYGBAQEYNSoURgyZAhdUyQDOp9TOF4DhaPn6KnblGVZ1NbWory8HDqdDsHBwYiNjUVwcDC1HJ0Ey7JQKpUoLCxEeXk5zGYz4uLikJycjKioKK7LI06E5jkS0k+WUaaWwTWWbtMrt4aKi4tDbGws6urqUFVVhZMnT8LHxwehoaFQKBQICAjg7g14sLa2Nly6dAlFRUXQarWQyWQYM2YMkpKS4Ovry3V5xMVROBKPw7KsNRSvHG0qEAh6bQ3yeDwoFAooFAqo1WrU1NSgpqYGpaWl8Pb2RkREBAWlA+j1elRWVqKoqAi1tbUQiURISEjA0KFDERYWxnV5xI1Qt+o1ULeqe2BZtkso8ng88Pn8QQ2sYVkWLS0tqK2thVKphF6vtwZlREQEAgMDbfwuPFNbWxsqKipQWVkJpVIJlmURHh6OIUOGID4+nq4lkn6ja442ROHouiyBaLkBsE67sPX0CwpK22ppaUFFRQUqKirQ0tICPp8PhUJhnWLj4+PDdYnEBVE42hCFo2vpLRB5PJ7DBtBYgrKurg51dXXQ6/Xw8vKCXC5HcHAwQkJC4O3t7ZBaXEV7ezuUSqX1w4VGo4FYLEZ0dDRiY2MRFRVFk/XJoNGAHOJRegtEruYi8ng8BAUFISgoCCNGjEBrayuUSiWamppQXV0N4PIydpbHBAQEQCqVeszoV4ZhoFar0dLSgoaGBtTV1UGj0QAA5HI54uLiEBkZifDwcFpggXCGwpG4JGcLxN7weDzI5XLr4uYGgwHNzc1oampCS0sLysvLAQBCoRABAQEIDAy0/tcdug7NZjNaW1vR0tKC5uZmtLS0QKVSwWw2AwCCg4OhUCgwbtw4hIeH06o1xGlQOBKX0j0ULSNNnSkQ+yIWi63XIQHAaDRCpVKhtbUVKpUK1dXVKCoqsj7Wz88Pvr6+kEqlkEql8PX1ha+vr9MNQrEsnKDRaKBSqaxBqFarrT+ngIAAyOVyJCQkICgoCIGBgdRVSpyWc/2FEdKNpVV45aVxy/VDVwnEvohEIoSEhCAkJMR6n06ng0qlglqthlqthkqlQk1NDYxGo/UxXl5eXcJSIpHAy8sLEokEEonEusSd5TZQLMvCaDRCp9NBr9dbb1f+u/vXDAYDBAIBGIZBYGAgQkNDkZKSYu06vnLuKCHOjsKROJ2+AtETeHl5ITw8HOHh4V3u1+v1aG9vR1tbm/W/Wq0WTU1N0Gq1XR5rWeXH4sqg7OvW2dlpDbuexuqJxeIuISyXyyGRSODj4wNfX1/4+fl51PVT4r4oHIlT8PRA7I8rA6k7lmW7tOKMRmOXfSb7c+PxeJDJZNbjdG+NSiQS+nkQj0HhSDhz5WAawL26Sx2Nx+PBy8uLdpwgxEYoHIlD9RSIV/6XEEKcAYUjsTsKREKIq6EZtuSaMjMzkZ6ejtjYWKSnpyMzM3PAr9F9LVMKRkKIM6NwJH168MEHcdNNN+H48eOorKzE8ePHcdNNN+Ghhx7q92tQGBJCXA2FI+lVZmYmNm3a1OPXNm7ciKysLAdXRAghjkHhSHr14osv9vn1devWOagSQghxLBqQQ67CsiwuXryIgoKCPh9XW1vroIoIIcSxKBwJAKC5uRlZWVnYs2cPMjMzUV1d3eMKKVdSKBQOqo4QQhzLJbpVy8vLsXLlSsTHx8Pb2xuJiYl46aWXYDAY+nyeTqfD448/jqCgIEilUixZsgT19fUOqtq5GY1GHDp0CC+88AImT56MsLAwLFu2DCdOnMAdd9yBX3/9FTt27OjzNV577TUHVUsIIY7lEi3HgoICMAyDf/3rX0hKSkJ+fj5WrVqF9vZ2vPXWW70+76mnnsIvv/yC7777DjKZDKtXr8bixYtx5MgRB1bvHFiWRXFxMQ4dOoSffvoJ+/fvR1tbG4KCgjB79mw8+uijmDNnDiIjI7s8b+XKldi4ceNVr7dy5UrMmjXLUeUTQohD8dhr9Z05qb///e/45z//idLS0h6/rlarERISgq+++gp33HEHgMshO2zYMBw7dgyTJ0/u13EGsnO0s1Eqldi3b5/1VlVVhRkzZoBhGMyZMwdz5szB2LFjr7lrQ1ZWFtatW4fa2looFAq89tprFIyEEJczkPO5S7Qce6JWq3tcgNkiJycHRqMRs2fPtt6XkpKCmJiYAYWjK2lsbMRvv/2GgwcP4vTp0zh+/DgAYOTIkViyZAlmzZqFadOmQSqVDuh1Z82aRWFICPEoLhmOxcXF+OCDD/rsUlUqlRCLxQgICOhyf1hYGJRKZa/Ps+xqYKHRaAZdr700NTXh8OHDOHDgAA4dOoTz588DABITEzFjxgw88cQTmD59+lVbHxFCCOkbp+H47LPP4o033ujzMRcvXkRKSor13zU1NZg3bx6WLl2KVatW2bym9evX4+WXX7b569pCc3MzDh8+jIMHD+LgwYPIz88HACQkJGDGjBn405/+hBkzZlx13ZAQQsjAcHrNsbGxEc3NzX0+JiEhAWKxGMDleXUZGRmYPHkyNm/e3Oe1sn379mHWrFlobW3t0nqMjY3Fk08+iaeeeqrH5/XUcoyOjubkmmNra2uXluG5c+fAsizi4uKQkZGB6dOnY8aMGYiKinJoXYQQ4opc5ppjSEgIQkJC+vXYmpoazJw5E+PGjcOmTZuuOYhk3LhxEIlEyMrKwpIlSwAAhYWFqKysRHp6eq/Ps2zqyoXW1lYcOXLE2jLMy8sDy7KIjY3FjBkz8Mc//hHTp09HTEwMJ/URQoincIlrjjU1NcjIyEBsbCzeeustNDY2Wr9muZ5WU1ODWbNmYcuWLZg4cSJkMhlWrlyJNWvWQC6Xw9/fH0888QTS09OdZjCOWq22dpMeOnQIubm5YFkW0dHRyMjIwOrVqzFjxgzExsZyXSohhHgUlwjHzMxMFBcXo7i4+KouREuvsNFoRGFhITo6Oqxfe/fdd8Hn87FkyRLo9XrMnTsXH3/8sUNrv5JarUZ2djb27duHgwcPIjc3FwzDIDIyEhkZGXjsscesYUi7WBBCCHdcdp6jowxmnmNdXR2OHDliveXn5yM9PR2lpaXWa4YZGRmIi4ujMCSEEDtzmWuO7oRhGBQUFOD48eMoKirCjh07UFZWBgBISkrC1KlT8cQTT2DKlClISEigMCSEECdG4XidNBoNTp48iePHjyM7OxsnTpyAVquFQCDA9OnTMX/+fEybNg1TpkxBWFgY1+USQggZAArHfiopKcH58+eRnZ2N48eP4+LFi2BZFnK5HJMmTcKf/vQnTJo0CWPHjoWvry/X5RJCCBkEuuZ4DZY+am9vb/D5fAwbNgyTJ0/GpEmTMGnSJCQlJVEXKSGEuAC65mgHX3/9NTIyMlxu8XFCCCED5xL7OToDCkZCCPEcFI6EEEJINxSOhBBCSDcUjoQQQkg3FI6EEEJINxSOhBBCSDcUjoQQQkg3FI6EEEJINxSOhBBCSDcUjoQQQkg3FI6EEEJINxSOhBBCSDcUjoQQQkg3FI6EEEJINxSOhBBCSDcUjoQQQkg3FI6EEEJINxSOhBBCSDcUjoQQQkg3FI6EEEJINxSOhBBCSDcUjoQQQkg3FI6EEEJINxSOhBBCSDcUjoQQQkg3Qq4LcHYsywIANBoNx5UQQggZDMt53HJe7wuF4zVotVoAQHR0NMeVEEIIsQWtVguZTNbnY3hsfyLUgzEMg9raWvj5+YHH4131dY1Gg+joaFRVVcHf35+DCgfP1d+Dq9cPuP57cPX6Add/D65eP2D/98CyLLRaLRQKBfj8vq8qUsvxGvh8PqKioq75OH9/f5f9hbRw9ffg6vUDrv8eXL1+wPXfg6vXD9j3PVyrxWhBA3IIIYSQbigcCSGEkG4oHAdJIpHgpZdegkQi4bqU6+bq78HV6wdc/z24ev2A678HV68fcK73QANyCCGEkG6o5UgIIYR0Q+FICCGEdEPhSAghhHRD4UgIIYR0Q+E4QOXl5Vi5ciXi4+Ph7e2NxMREvPTSSzAYDH0+T6fT4fHHH0dQUBCkUimWLFmC+vp6B1Xd1euvv44pU6bAx8cHAQEB/XrO/fffDx6P1+U2b948+xbah+t5DyzL4sUXX0RERAS8vb0xe/ZsFBUV2bfQXrS0tOCee+6Bv78/AgICsHLlSrS1tfX5nIyMjKt+Bo8++qiDKgY++ugjxMXFwcvLC5MmTcKJEyf6fPx3332HlJQUeHl5YdSoUdi5c6eDKu3dQN7D5s2br/p+e3l5ObDarg4dOoQFCxZAoVCAx+Nh+/bt13zOgQMHMHbsWEgkEiQlJWHz5s12r7MvA30PBw4cuOpnwOPxoFQq7V4rheMAFRQUgGEY/Otf/8L58+fx7rvvYsOGDXjuuef6fN5TTz2Fn376Cd999x0OHjyI2tpaLF682EFVd2UwGLB06VI89thjA3revHnzUFdXZ73997//tVOF13Y97+HNN9/E+++/jw0bNiA7Oxu+vr6YO3cudDqdHSvt2T333IPz588jMzMTP//8Mw4dOoSHH374ms9btWpVl5/Bm2++6YBqgW+++QZr1qzBSy+9hNOnTyM1NRVz585FQ0NDj48/evQoli1bhpUrV+LMmTNYuHAhFi5ciPz8fIfU25OBvgfg8kotV36/KyoqHFhxV+3t7UhNTcVHH33Ur8eXlZXhlltuwcyZM5Gbm4snn3wSDz30EHbv3m3nSns30PdgUVhY2OXnEBoaaqcKr8CSQXvzzTfZ+Pj4Xr+uUqlYkUjEfvfdd9b7Ll68yAJgjx075ogSe7Rp0yZWJpP167ErVqxgb7/9drvWcz36+x4YhmHDw8PZv//979b7VCoVK5FI2P/+9792rPBqFy5cYAGwJ0+etN7366+/sjwej62pqen1eTNmzGD/+Mc/OqDCq02cOJF9/PHHrf82m82sQqFg169f3+Pj77zzTvaWW27pct+kSZPYRx55xK519mWg72Egfx+OBoDdtm1bn4/585//zI4YMaLLfXfddRc7d+5cO1bWf/15D/v372cBsK2trQ6p6UrUcrQBtVoNuVze69dzcnJgNBoxe/Zs630pKSmIiYnBsWPHHFGiTRw4cAChoaFITk7GY489hubmZq5L6reysjIolcouPwOZTIZJkyY5/Gdw7NgxBAQEYPz48db7Zs+eDT6fj+zs7D6f++WXXyI4OBgjR47E2rVr0dHRYe9yYTAYkJOT0+V7x+fzMXv27F6/d8eOHevyeACYO3cuZ7/v1/MeAKCtrQ2xsbGIjo7G7bffjvPnzzuiXJtwtp/BYKSlpSEiIgJz5szBkSNHHHJMWnh8kIqLi/HBBx/grbfe6vUxSqUSYrH4qmtjYWFhDuk7t4V58+Zh8eLFiI+PR0lJCZ577jnMnz8fx44dg0Ag4Lq8a7J8n8PCwrrcz8XPQKlUXtUtJBQKIZfL+6zld7/7HWJjY6FQKJCXl4e//OUvKCwsxA8//GDXepuammA2m3v83hUUFPT4HKVS6RTfa4vreQ/Jycn47LPPMHr0aKjVarz11luYMmUKzp8/36/NCLjW289Ao9Ggs7MT3t7eHFXWfxEREdiwYQPGjx8PvV6PTz/9FBkZGcjOzsbYsWPtemxqOf7Ps88+2+OF3ytv3f+IampqMG/ePCxduhSrVq3iqPLLrqf+gbj77rtx2223YdSoUVi4cCF+/vlnnDx5EgcOHHCZ92Bv9q7/4Ycfxty5czFq1Cjcc8892LJlC7Zt24aSkhIbvgtikZ6ejuXLlyMtLQ0zZszADz/8gJCQEPzrX//iujSPkZycjEceeQTjxo3DlClT8Nlnn2HKlCl499137X5sajn+z9NPP43777+/z8ckJCRY/7+2thYzZ87ElClT8Mknn/T5vPDwcBgMBqhUqi6tx/r6eoSHhw+mbKuB1j9YCQkJCA4ORnFxMWbNmmWT17Tne7B8n+vr6xEREWG9v76+Hmlpadf1mt31t/7w8PCrBoGYTCa0tLQM6Pdh0qRJAC73XiQmJg643v4KDg6GQCC4anR1X7+/4eHhA3q8vV3Pe+hOJBJhzJgxKC4utkeJNtfbz8Df398lWo29mThxIg4fPmz341A4/k9ISAhCQkL69diamhrMnDkT48aNw6ZNm665aea4ceMgEomQlZWFJUuWALg8+qqyshLp6emDrh0YWP22UF1djebm5i5BM1j2fA/x8fEIDw9HVlaWNQw1Gg2ys7MHPGq3N/2tPz09HSqVCjk5ORg3bhwAYN++fWAYxhp4/ZGbmwsANv0Z9EQsFmPcuHHIysrCwoULAVzeBDwrKwurV6/u8Tnp6enIysrCk08+ab0vMzPTZr/vA3U976E7s9mMc+fO4eabb7ZjpbaTnp5+1fQZLn8GtpKbm2v333kANFp1oKqrq9mkpCR21qxZbHV1NVtXV2e9XfmY5ORkNjs723rfo48+ysbExLD79u1jT506xaanp7Pp6elcvAW2oqKCPXPmDPvyyy+zUqmUPXPmDHvmzBlWq9VaH5OcnMz+8MMPLMuyrFarZf/0pz+xx44dY8vKyti9e/eyY8eOZYcMGcLqdDqXeA8sy7J/+9vf2ICAAHbHjh1sXl4ee/vtt7Px8fFsZ2enw+ufN28eO2bMGDY7O5s9fPgwO2TIEHbZsmXWr3f/HSouLmZfeeUV9tSpU2xZWRm7Y8cONiEhgZ0+fbpD6v36669ZiUTCbt68mb1w4QL78MMPswEBAaxSqWRZlmXvu+8+9tlnn7U+/siRI6xQKGTfeust9uLFi+xLL73EikQi9ty5cw6ptycDfQ8vv/wyu3v3brakpITNyclh7777btbLy4s9f/48J/VrtVrr7zkA9p133mHPnDnDVlRUsCzLss8++yx73333WR9fWlrK+vj4sM888wx78eJF9qOPPmIFAgG7a9cuTupn2YG/h3fffZfdvn07W1RUxJ47d4794x//yPL5fHbv3r12r5XCcYA2bdrEAujxZlFWVsYCYPfv32+9r7Ozk/3973/PBgYGsj4+PuyiRYu6BKojrVixosf6r6wXALtp0yaWZVm2o6ODvemmm9iQkBBWJBKxsbGx7KpVq6wnFS4M9D2w7OXpHC+88AIbFhbGSiQSdtasWWxhYaHji2dZtrm5mV22bBkrlUpZf39/9oEHHugS7N1/hyorK9np06ezcrmclUgkbFJSEvvMM8+warXaYTV/8MEHbExMDCsWi9mJEyeyx48ft35txowZ7IoVK7o8/ttvv2WHDh3KisVidsSIEewvv/zisFp7M5D38OSTT1ofGxYWxt58883s6dOnOaj6Msu0hu43S80rVqxgZ8yYcdVz0tLSWLFYzCYkJHT5e+DCQN/DG2+8wSYmJrJeXl6sXC5nMzIy2H379jmkVtqyihBCCOmGRqsSQggh3VA4EkIIId1QOBJCCCHdUDgSQggh3VA4EkIIId1QOBJCCCHdUDgSQggh3VA4EkIIId1QOBJCCCHdUDgSQggh3VA4EuKhGhsbER4ejv/7v/+z3nf06FGIxWJkZWVxWBkh3KO1VQnxYDt37sTChQtx9OhRJCcnIy0tDbfffjveeecdrksjhFMUjoR4uMcffxx79+7F+PHjce7cOZw8eRISiYTrsgjhFIUjIR6us7MTI0eORFVVFXJycjBq1CiuSyKEc3TNkRAPV1JSgtraWjAMg/Lycq7LIcQpUMuREA9mMBgwceJEpKWlITk5Ge+99x7OnTuH0NBQrksjhFMUjoR4sGeeeQbff/89zp49C6lUihkzZkAmk+Hnn3/mujRCOEXdqoR4qAMHDuC9997DF198AX9/f/D5fHzxxRf47bff8M9//pPr8gjhFLUcCSGEkG6o5UgIIYR0Q+FICCGEdEPhSAghhHRD4UgIIYR0Q+FICCGEdEPhSAghhHRD4UgIIYR0Q+FICCGEdEPhSAghhHRD4UgIIYR0Q+FICCGEdEPhSAghhHTz/wAh6dHlGl861gAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "%matplotlib inline\n",
+ "op = rebound.OrbitPlot(sim)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "You can access the matplotlib figure and axes using attributes `ob.fig` and `ob.ax`. This allows you for example to save the figure to a file:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "op.fig.savefig(\"orbit.png\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "There are various ways to customize the plot. Have a look at the arguments used in the following examples, which are pretty much self-explanatory (if in doubt, check the documentation!). "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "op = rebound.OrbitPlot(sim, unitlabel=\"[AU]\", color=True, periastron=True, xlim=[-2,2], ylim=[-2.5,1.5])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "op = rebound.OrbitPlot(sim, orbit_style=\"solid\", lw=2)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "op = rebound.OrbitPlot(sim, orbit_style=None)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "If you want to get a sense of the three dimensional architecture of a planetary system, you can use `OrbitPlotSet` which shows three different perspectives of the same system:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "ops = rebound.OrbitPlotSet(sim)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "# Primary particles\n",
+ "\n",
+ "Note that all orbits that we have drawn so far used the center of mass of all interior particles as their primary particle. This coordinate system is known as Jacobi coordinates. It requires that the particles are sorted by ascending semi-major axis within the REBOUND simulation's particle array. You can specify the primary particle manually, for example to show heliocentric orbits or specific s- or p-type orbits in binaries. For example, have a look at this planetary system:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "sim = rebound.Simulation()\n",
+ "sim.add(m=1.) # Star A\n",
+ "sim.add(m=1., a=1.) # Star B\n",
+ "sim.add(a=2.) # Circumbinary planet ABb\n",
+ "sim.add(a=0.2, primary=sim.particles[1]) # Planet Bb, orbiting star B \n",
+ "sim.move_to_com()\n",
+ "fig = rebound.OrbitPlot(sim)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Circumbinary Planet ABb is plotted correctly in orbit around the center of mass of A and B, but Bb's Jacobi orbit is also around the center of mass of the interior particles, which, in this case renders as a hyperbolic orbit ( Note that although the plot looks incorrect, IAS15 would correctly integrate their motions).\n",
+ "\n",
+ "One way to fix the visualization is to create two orbit plots using the same matplotlib figure and axes, but each showing different particles, around different primaries. Here's how this can be done:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "ob1 = rebound.OrbitPlot(sim, particles = [1,2])\n",
+ "ob2 = rebound.OrbitPlot(sim, particles = [3], primary=1, show_primary=False, fig=ob1.fig, ax = ob1.ax)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Kepler-Orrery style plots\n",
+ "\n",
+ "You can use a similar idea to show multiple planetary systems in the same figure. This time we're creating the matplotlib figure by hand and then adding one orbit plot for each system."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "fig, ax = plt.subplots()\n",
+ "ax.set_aspect(\"equal\") # this is needed if you don't want to get stretched orbits\n",
+ "ax.axis('off') # no axis ticks\n",
+ "for x in range(5):\n",
+ " for y in range(5):\n",
+ " sim = rebound.Simulation()\n",
+ " sim.add(m=1)\n",
+ " for i in range(3):\n",
+ " sim.add(a=3+2.2*i, f=\"uniform\")\n",
+ " sim.move_to_com()\n",
+ " rebound.OrbitPlot(sim, fig=fig, ax=ax, origin = [-x*20., -y*20.])\n",
+ "ax.set_xlim([-10,90])\n",
+ "ax.set_ylim([-10,90]);"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Manually adjusting plot components\n",
+ "\n",
+ "You can access the `PathCollection` and `LineCollection` structures that OrbitPlot uses internally to adjust their appearance. These are stored in the `primary`, `particles`, and `orbits` attributes. This gives you great flexibility when it comes to customizing your plot. For example:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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Hjx42b/Pzzz+jR48ekMvl6Nu3L3bu3OmiaklbCgoKUFxcDIFAgISEBApSO1RXVyM/Px+HDx/G77//jv379yM1NRUFBQXNghRoClt7t/SyNyAB+1ux9g6Q0el0qKqqQnZ2Nk6fPo3Tp0/j6tWrqK6uBsMwdtfVVYlEIgQGBoJl2WY9AcT1eNUy7d27N/bs2WP53lYX0dGjR3Hvvfdi/fr1uPXWW7F582bMnj0bZ8+eRZ8+fVxRLrGiqKgIhw8fRkxMDMLDw7kux61VV1ejoKAABQUFaGhoaNf5TXtDUqfT2d0iNBgMdo2yNhgMdrWSxGJxs65orVaLoqIiFBUVWVrX/v7+8Pf3h0KhsKvGrkYsFlOr1A0IWPN6VW5uzZo12LZtG1JSUuw6/u6770ZDQwN27NhhuWzEiBEYMGAAPv74Y7sfV61WQ6VSoba2lhYP6ATFxcU4cOAAIiIiMGbMGHoDaMWNAXo9uVxuGWlrD3vOSWo0GiiVyjbPuZlMJhiNRiiVyjbv02g02hXQ7TlnGhoaCrlcjpCQEJo2ZYXBYIBarYa/vz/9bXUSezOAVy3TzMxMREREQC6XY+TIkVi/fj1iYmJaPfbYsWNYvnx5s8umTZuGbdu22XwMnU7X7BP9jed4SMeVlpbi4MGDCAsLoyC9QV1dHXJycloN0OtptVooFAq7wrSxsbHNberEYjH8/PygUCggl8shFAohFAohEAha/N9kMlmmYhgMBhgMBuj1ehgMhmZdyizLwmAw2BWmRqPR7kDV6XSorKxEYWEh/Pz8EBISQvt+tsJgMKCqqgqBgYH0s3Eh3oTp8OHDsWnTJiQnJ6O4uBhr167F2LFjkZaW1uobRklJCUJDQ5tdFhoaipKSEpuPs379eqxdu7ZTaydNvLy8EBsbi6FDh1KQoil08vPzkZGRAaVSiaKiIrtup9fr7XqTZFkWJpMJ/v7+8PLygkKhgEKhsPzfy8sLEonE0acBAJaFBPR6PXQ6HTQaDfR6vWX6hrVzqHq93q4wFQqFzQZK1dTUoKamBhKJBMHBwQgJCaHBS2iahxoYGIjKykrLKF8KVNfgTZjecsstlv/369cPw4cPR2xsLH766ScsXLiw0x5nxYoVzVq0arUa0dHRnXb/XVFtbS28vLzg4+ODESNGcF0O54xGI7Kzs3HlyhVLK9RkMkEgEMCesy4NDQ1QKpUt3iQFAgH8/PwQEBBg+XLVeUahUAiZTAaZTNbqh9vrg9X8b01Njd33LxAIYDQaW1xuMBgs51h9fX0REhKCgICALv1hTSKRICAgwDLSOyAggOuSugTehOmN/Pz80L17d2RlZbV6fVhYGEpLS5tdVlpa2ubuI+Y3BNI5GhsbsXv3boSHh2P06NFcl8MpjUaDK1euIDs7u0VLraamBt7e3nZNUxGLxairq0NQUBACAgIQGBiIgIAA+Pn5ue1cQ6lUagl4M4ZhUFdXh5qaGlRXV6O+vt7q7c2rLtlinnoTHBwMpVKJkJCQLhuqUqkUgYGBXJfRpfA2TOvr65GdnY3777+/1etHjhyJvXv3YunSpZbLdu/ejZEjR7qoQsIwDA4cOACWZTFw4ECuy+FMdXU1Ll++jLy8PJstT3uC1N/fH1FRUQgODuZ9i8M8WlelUiE2NhZ6vd4SrOYdUgD7RwYDTS1YnU6H6upqlJSUIDw8HMHBwV0yVKVSqeX/BoOh07r0Set4E6b//ve/MXPmTMTGxqKoqAirV6+GSCTCvffeCwCYN28eIiMjsX79egDAk08+ifHjx+PNN9/EjBkz8MMPP+D06dP49NNPuXwaXcqpU6dQUVGBadOmwcvLi+tyXK66uhpFRUVITU2163jzwLcbe0bMARoVFWXXSFq+kkqlCAkJQUhICFiWRX19vWVurb0tbqlUaplqYzQakZ+fj9LSUoSHhyMoKKhLnj9sbGxEXV0d/P39KVCdiDdhWlBQgHvvvReVlZUIDg7GmDFjcPz4cQQHBwMA8vLymn36HDVqFDZv3oxVq1Zh5cqVSEpKwrZt22iOqYuUl5cjIyMDI0aMsLxGXYVWq0VKSgqysrKgUCjg4+Nj14R6kUiEhoYGyGSyLhOg1ggEAvj4+MDHxwcxMTHQaDQoKytDRUVFq+dOzYxGY4vA1Ov1yM3NtbRUu9qgHIVCAa1Wi9ra2i5/PtmZeDPPlCs0z7TjysrKEBISwnUZLmMymZCRkYHU1NRm50T9/f3tClO5XI6oqCj07NmzSwaoPRiGQVVVFcrKylpMWzMYDHYNuJLL5YiIiOB9N3l7mH9uIpEIfn5+XerDhKM8cp4pcX/mFWwSEhK6VJDm5+fj7NmzrYZmTU2NZb5ma1QqFZKTkxEbG+u2A4jchVAoRFBQEIKCgtDY2IiysjKUl5fDaDTavXyiVqu1zOcNCgrqEisrmc9P19TUtGvFK2I/ClPSaRiGwf79+6FWqxEVFdVsAISnqqmpwZkzZ1BcXGz1GPMiBjf+PMLCwpCcnExLKnaQQqFAbGwsoqOjUV5ejuLiYptdwNeTy+WWHXZCQ0MRGhrq8a01iUQCf39/2qnHSeinSjrN6dOnUV5ejmnTpnl8kBoMBmRlZeHs2bN2zQ01TwMxj1xNTk6Gn5+f8wvtAoRCoSUQa2pqUFhY2GLh/xuPN1/PsixKSkpQU1OD6Ohoj+9eNwepTqeDUCikAUmdiMKUdIrs7GxcvnwZw4cP9/ju3fLychw8eLBdYSiVSi17tnaFbkWu+Pn5wc/PD1VVVSgqKmp1uhHLsi0+AGm1WmRmZiI4OBjh4eEeP0hHo9HAZDLRgKRORGFKOkV2dja6deuG5ORkrktxGpZlceHCBaSkpFi2vAoKCmpzJZ/o6GgMGjSozXVySecJCAiAv78/KisrUVxcbJl2pNfrbX6YKS8vR21tLaKjoz369VKpVKiqqkJtbS0NSOokNJq3DTSa1z7mwR+eOoCmvr4ehw4darGqlq3zT35+fhgyZEibq24R52JZFhUVFcjLy4NWq7W7KzcwMBCRkZEe23IzGAyorq62TN8iraPRvMQljh8/jsTERI+eS3rt2jUcO3as1Y2xjUYjWJZtdu5JJpOhf//+SEpKok/8bkAgECA4OBj+/v4oLy9HWVmZXee5GxsbkZeXh7CwMI8c/SqRSODj4wONRgOWZel31UEUpqTDsrOzcfHiRURGRnJdilMYDAacOHHC6vrPZizLWj69Jicno1+/fh4/AIuPxGIxwsPD4efnh7y8PJuDlMzBUl9fj6tXryIyMhIqlcpVpbqMees9ClLHUZiSDtFqtTh+/DgSEhI8cled2tpa7Nmzx67FFoRCIUJCQjB16lQ6FcADCoUC3bt3R1lZGUpKSlptpYpEIktPBMMwyM/Ph1arRUhIiMcFj0AggMlksnsPWtI6ClPSIcePHwcAj9xS7erVq7h8+bJdG3ALBAIMHDgQffv29bg3WU8mEAgQGhoKlUqF/Pz8ZhuyMwzTardneXk5GhsbER0d7XFjA4xGIzQaDUQiEU2X6SDPPLNOnEqj0aCgoAAjRozwuE+yqamp2LdvH4qKiiCVSm0GpI+PD2bMmIF+/fpRkPKUXC5HUlISoqKiIBQKLRuvW3s9zbtV2bPDD5/IZDJIJBI0NDTYdT6ZtESjedtAo3lbp9VqPSpIWZbFsWPHcPHixWaXK5VKy7SK63Xr1g3Dhw+nT/EeRK/XIzMz064wEQqFiIqK8qj3BIZhUFtbC5lM1iV3ebLG3gyglilpl6ysLI9b29NoNGLPnj0tghRoaolcv2i9VCrF+PHjMWbMGApSDyOVStGrVy+7NtVmGAZ5eXltzjHmE6FQCIVCAZ1OR63TDqAwJXYrKSnBwYMHce3aNa5L6TRarRY7d+5Ebm5uq9cLBAIYDAbU1dUhNDQUt912G+Lj411cJXEVgUCA8PBwREVFtdl1L5PJUFlZ2WLuMZ/J5XKoVCo6bdEBNACJ2MVkMuHw4cMIDQ31mFWO1Go1/vzzzxZbed1IKpUiKSkJ48aNozeZLsLPzw8ymQx5eXnNeibMhEKhZQOD6upqsCzrMYtzmJ+b0Wik3pd2oJYpscu5c+fQ0NCAMWPGeESgVFZWYvv27W0GqUAgwOjRozF+/HiPeN7EfgqFAomJiS1WTGIYBgKBoNlo75qaGps7B/GNTqdDXV2d3dvaEQpTYgeNRoO0tDQMGDDAIyaul5WV4dSpU21+6haLxZgyZQp69uzposqIuxGLxYiLi7OcRzWHS2sfrGpraz0mUOVyOUQiUbMpQ8Q26uYlbfLy8sKtt96KgIAArktxWHV1NX7//XfodDoEBARALBa3ugemQqHA1KlTPXqZRGIf83lUhUKBrKwseHt7Wz22trYWLMsiPDyc9z0ZSqUSarXa40buOwu1TIlNVVVVYFkWQUFBvF/wu66uDjt27LBMdTE/txtHLqpUKtx2220UpKQZPz8/9OzZs82QVKvVKCoq4v2IWLFYDLlcjsbGRt4/F1fg97sjcSqdToft27fj3LlzXJfiMI1Gg99++61Ft5VOp4PBYLAsHWcesUu7aJDWKJVKu0b61tXVeUSgKhQKeHt7876V7QoUpsSqCxcugGEY3p8z1Ol02LFjh9XBRkKhEA0NDQgPD8ctt9wCmUzm4goJnyiVSkRHR7fZU2Me6ctnAoGARvTaic6ZklZptVqkpqaiT58+NjdTdndGoxE7d+5EVVWVzeP69++PKVOm0CdwV6mqAnbtAioqAIYB/PyASZOAqCiuK7OLl5cXoqOjkZ+f3+oazuYAMv/e8X28gXmHHT6/FzgbhSlpVUpKCgQCAfr168d1KR1mMpnw559/tjmpPjo6GpMmTaIgdSaGAT7+GHj3XeDaNaCVvWEBAGJxU6DOnw+sXAm48VZ2CoWi1UAVCASWeZpAU6BKpVKbA5fcnVgsRmNjI6RSqcct8t9ZqJuXtMrX1xdDhgzh7Sg+81q7BQUFNo8LDQ3FtGnT6A3CWYxGYMECQKEAHnsMyMiwHqTm43NygLVrAS8vYMYMoI25wFxSKBSIiYmx/P4YDIZWP5SVlpa2usYzX0gkEgiFQl4/B2ejMCWt6tWrF/r27ct1GR12+vRpVFVV2RxIFBAQgOnTp0Mspg4ap9i3DwgIADZtsh2g1phMwM6dQFAQ8PXXnV5eZ5HL5YiOjobBYIBMJmv1XCrLsiguLm51GhZfyGQyGI1GWsjBCgpT0kx9fT2OHDnC60+g+fn5OHHiBPLy8qDX61s9z+Pr64tbb72VBhs5y2OPNZ0DtWNz9TYZDE3dvrfc0tRd7Ibkcjm6detms4fDaDSiuLiYtyN8JRIJRCKRXfv8dkUUpqSZc+fOITs7m7dzShsaGvDXX381+76+vr7ZG5hSqcTMmTNpmyln+ec/gQ8/7Pz7/fNPYNQotw1UhULR5txknU7H64XxlUolje61gp/vmMQp1Go1MjIyMGDAAF7+wTAMg127dllGHpqZFySvqamBWCzGjBkzaB6psyxbBnz3nfPu/8QJYPp0592/g3x9feHn52fzmPr6+jZHl7szlmUt87LJ/0dhSizOnj0LuVyOXr16cV1Khxw/fhxFRUWtXicUCuHj44MJEybwfpqC2zp2DHj7bec/zq5dwBdfOP9xOigoKKjNXg+NRgOtVuuiijqXyWSCVqulc6c3oDAlAJr+uLOysjBgwABeDsi5du0azp49a/OYMWPGoFu3bi6qqIthmKaRt66yeDHgxhtzh4WFQWplWo9UKgXLsigvL+dlIInFYohEIt5+GHAWClMCoGkS+h133MHL1Y7UajX27Nlj85jExET079/fRRV1Qf/+N+DK1X4MBuDuu133eO0kFAoRHh7ebEASwzCWATwmkwkmkwmVlZUcVtlxMpkMJpOJ16OTOxuFKYHBYADLsggICODdfEvzwgy2Rh+rVCpMmjTJhVV1QZ9/7vrH3LMHcOPWkUQiseweY55/euMcVI1Gw8ttzsytUz6P+u9sFKYER44cwfbt27kuo0OuXLli89OxSCTCLbfcYrXLjTS1mMyL/et0Omi1WjQ2NkKj0VjO7Wm1Wuh0Ouh0Ouj1ehgMBphMpqZR0lu2dM4UmPYX3rS4gxuTy+Xw9/eHWCy2OqivsrKSl929crmcppZdh38nx0inMhgMyMzMxIABA7gupd3Ky8vx119/wdvbG0FBQaioqGhxzPjx4xEUFMRBde7HPKrZPPHe/C/DMBAIBJZeCXMLyvwlEoksU4uun2JkPl72+usQAuBkMcZvvgHWr+fike0WEBAAo9EIjUbT6vUMw6CiogKhoaEurswxfOvFcjYK0y4uKysLBoMBPXr04LqUdmFZFvv27QPLsqirq0NdXR0UCgW0Wq3lj7xHjx68HZncWQwGQ7MWJfD/u+jEYjGkUqnle5FI1K71iVmWBcMwEGZkOKv8thUXc/fY7RAYGAitVmt1wYPGxkbU19fzbv1ec6+GVCrt8mtbU5h2cRcvXkRMTAzv5l2mp6ej+IY30sbGRhiNRjQ0NCAmJgbjx4/nqDpuabVaaDQa6PV6S6tTKpXCx8cHMpms0+YQCwQCiAQCbkfVMgyQmQkkJXFXgx1EIhECAwNRXl5u9ZiqqirI5XJejaYXCASWwVR8qtsZuvaz7+K0Wi3q6up418Wr0Whw6NChVq8zt7LGjRvHy4UnOsr8IaKhoQFGoxFisRhKpRIKhQISicR5rYa0NOfcb3vs2uX2YQo0rR5ka8CRubs3LCzMxZV1nPk0gPl3rivr2s++i5PL5Zg3bx7XZbTb4cOHbY4iHDZsGGJiYlxYEXc0Gg3q6uqg0+kgEAigVCqhVCpdNzDERkvLZdx4vumNzN291gYcCYVCNDY28mrfULFYDJ1O19Tlz9NlSDsDhWkXZV7FRKlUcl1KuxQUFODixYtWr/f19cXw4cNdWBE3GhoaUFNTA51OB4VCgcDAQHh5ebn+vJU7nCdzhxrsJBQKERgYiLKyshaXSyQS6PV61NTUQC6X8+YcpPlcu9Fo7NKj5nnzMWL9+vUYOnQofHx8EBISgtmzZyOjjYEPmzZtajEyka/7c3a2q1ev4ptvvrE6wtAdmUwm7Nu3z+YxEyZM8OjupoaGBhQUFKC0tNSyMEB4eDiUSiU3b77uMAKVZ8tDenl5WQYamQckCYVCS2vVZDKhvr6es/o6ojPPxfMVb8L0wIEDeOyxx3D8+HHs3r0bBoMBU6dObXPCs6+vL4qLiy1fubm5LqrYvV28eBFhYWG82jnl7NmzNhcIT0xMREJCggsrch2dTof8/HyUlpZCJBIhIiIC4eHh3HcHusOKWW688L01AQEBliBt7cNfXV0dr7Y6EwqFvGlJOwtvPsL/+eefzb7ftGkTQkJCcObMGYwbN87q7QQCAa9O6LtCbW0tCgsLMXnyZK5LsZtGo2l1HqmZWCzGhAkTXFeQizAMg8rKSlRXV0Mmk7lHgF5PKGxqGXK1C4pIBMTGcvPYDhAKhQgLC7P64ZBhGKjV6jZ3oHEn5nnLXXUhB960TG9UW1sLAG3uAFJfX4/Y2FhER0dj1qxZSE9Pt3m8TqeDWq1u9uVpLl26BJlMxqtW3IkTJ3D58mWEhYW1ep535MiRvJve05aGhgbk5OSgpqYGQUFBiImJca8gNevdm7vHjozk7rEd5OXlZbNr1Dwymy/M02T41KLuTLwMU4ZhsHTpUowePRp9+vSxelxycjK+/PJL/Prrr/j222/BMAxGjRqFgoICq7dZv349VCqV5Ss6OtoZT4FTRqMRPXv25M25RY1Gg/Pnz8NkMqGgoABqtRoikQgGgwFA0wjJgQMHclxl52EYBsXFxSgsLIRMJkNcXBwCAgLctxvt+ee5e+xFi7h77E5gq+XJsiyvPsybByLxcWnEziBgr18fjCcWL16MP/74A4cPH0ZUVJTdtzMYDOjZsyfuvfdevPjii60eY14txkytViM6Ohq1tbXw9fV1uHbSfocOHcKJEydaXK7X66HVavHQQw+16/fAnel0OhQUFMBgMCA8PBwqlYrrkuwTEODSXWNYAAKRqGmhe558KLSmoqLC5nZmoaGhvBnco9frYTKZ3LMHpYPUajVUKlWbGcC7lumSJUuwY8cO/P333+1+A5VIJBg4cCCysrKsHiOTyeDr69vsy5MUFxdbWnR8oNVqre5TKpVKMWDAAI8JUrVajWvXrgEAEhIS+BOkALBkicsfsn7iRN4HKYA2X2fzKS0+EIvFYFm2S7ZOeROmLMtiyZIl+N///od9+/YhPj6+3fdhMpmQmpqK8PBwJ1To/oxGI7Zu3Yo0d1i1xk5nz561Gf4jRoxwYTXOwbIsSkpKUFBQAB8fH8THx/Nvvt6aNYCLBvqxAHQCAeaJRNi7d69LHtOZJBKJzVH15s0J+EAoFEKhUHTJRfB5E6aPPfYYvv32W2zevBk+Pj4oKSlBSUkJGhsbLcfMmzcPK1assHy/bt06/PXXX7h69SrOnj2Lf/7zn8jNzcWDDz7IxVPgXEFBAUwmE+Li4rguxS56vd5qqxQAYmJiEBER4cKKOh/DMMjNzUVVVRXCwsIQGRnJz1VkhEJg926XPJQAAPPVV5CoVLjrrrvw008/ueRxncnX17fFOXHzmsoSiQR1XGxx10Fue27fyXjzV/vRRx+htrYWEyZMsExUDw8Px48//mg5Ji8vr9ni59XV1Vi0aBF69uyJ6dOnQ61W4+jRo112J5Hc3Fz4+PjA39+f61LskpKSYvNc0siRI11YTeczmUy4du0a6uvrERMT0+bIdLfXp09TC9XZ7r4bXvffj++++w733HMPFi1ahA8++MD5j+tE5rWUgaYPWCzLQiQSgWEYGI1G6HQ63nSdmrf64+FwHIfw5oSDPS/M/v37m32/YcMGbNiwwUkV8U9ubi5vWqUGgwGnT5+2en1kZCSvR1qbTCZcvXoVer0eCQkJvFo8w6bVq5vmnL77rnPu/+abgR9+ANAUQO+//z6Cg4OxcuVKlJWVYc2aNbxtGfn6+qK2ttayPd6NNBoNL6Z/CQQCy/Z8Xam7lzdhShyj1+shlUoRy5MJ7qmpqTaXOuTzuVKDwYBr167BaDQiISHBo0Y+AgDeeQfw9wfWru3c+/3HP4Bvv212kUAgwJo1axASEoLXXnsNUqkUK1eu5GWgCoVC+Pv7W/29b2xshLe3Ny+em1AopDAlnkkqleKee+7hugy7sCyLoqIixMXFobCwsMUApNDQ0A4NQHMHRqMR2dnZYBgGiYmJnrtazJo1wB13AFOnAqWljt2XUgn8/DNwyy1WD3n00Ufh7e2NZcuWQS6X46mnnnLsMTni5eVlNUwZhoFWq+XFhy+hUMibQVOdhTfnTIlj+DSAIT8/HykpKbh8+bJlztr154v42iplWdbStevRQWrWrx9QVAQ89xzQke5JmQyYP7+p29hGkJrNmzcPK1euxMsvv4xvvvmmAwVzTywW2xzJzZeNKcyt5660GhKFaRdgMpnw7bffIiUlhetS7JKammr5v0ajQXV1NbRareV8Urdu3TisruNyc3PR0NDQNYLUTCgE1q8H1Gpg2zZg2DDA1txtpbIphD/5BNBogE2bgHZME1q+fDkWLlyI5cuXt1jPmy/amibDh3niAoEAEomEnyPTO4i6ebuAoqIiGAwGXixuYDQaW92vVCQSQSQSYcyYMbw4Z3Sj4uJiVFVVIT4+nnd7yHaaWbOavgDAaAROnAAqKpr+HxgIjBgBOLhFokAgwPr161FeXo5//etf2LlzJwYMGOB47S4kl8shEomsjt7VaDS8WNCDj3+njqAw7QJyc3OhVCoRFBTEdSltunLlSrPlHK8nFArRm8tF1TuoqqoKxcXFiIiI4M20JKcTi4HRo51y1yKRCB9//DGefPJJPPDAA9i3bx/vph0pFAqre5pqtVr4+Pi4favPvBKSec1eT+ferwbpFLm5ubwZxXvhwgWr13Xr1o13U0i0Wi2uXr2KgIAA2grQhWQyGVavXg2tVosnnniCd3Mebf2ei8ViXgzuEQgEYBimy5w3pTD1cHq9Hnq9nhdh2tDQgOzsbKvX9+vXz4XVOI5lWWRnZ0MqlSImJobrcrqc8PBwvPfee9i9ezc+++wzrstpF6FQCPkNXd5CodAyOIkvA5GEQiHvPsh0FIWph5NKpViwYAEvBu2kp6db/cOTy+VISkpycUWOKSwshEajQWJiott3yXmqKVOm4OGHH8a6detw/vx5rstpF6VSCb1eD4ZhIBQKLXM3WZaF0WjkRYvP3DrtCugv3MOZu4P4cM7CVhdv7969eTUBvK6uDkVFRYiMjOy6A47cxAsvvIBevXph5cqVvGnRAU0L4Pv4+EAqlbb6YUyv13NQVfuY6+4KgUph6uG+/PJLnDp1iusy2lRWVoaSkhKr1/ft29eF1TjGvOaut7d3l92hyJ1IJBJ8+OGHyM3NxXvvvcd1Oe1ia84pH8JUIBBALBZ3iZ4Zz3+GXZhWq0V9fT0v9mQtKSlB9+7dWx2kExAQwItpPWbm7t2EhARe9Ah0Bd26dcP8+fPx0UcfIScnh+ty7GYrTPmymHxXCFKAwtSjVVRUAAAvpsScPn0aFy9eREFBgWUVGL1eD61Wy6tWqU6nQ1FRESIiIloMICHcWrJkCUJCQrB69WquS7GbRCKx+oHMvDsLH/Ah9B1FYerBysvLIRKJ3H5uo16vR2FhoeV7rVYLjUYDoVAInU7Hi5HIZrm5uRCJRIiMjOS6FHIDhUKB1atXY8+ePbzaVJzvXb0sy1KYEn6rqKhAQECA23ez5OfnW13tJSwsjDdbrdXV1aGiogIxMTG8GizVlUyfPh1jxozBunXreBFEAP/DtKuc6nDvd1nikPHjx2PmzJlcl9Gma9euWb0uPj6eN3+MOTk5UCqVCAkJ4boUYoVAIMDatWuh1+uxZcsWrsuxi60wZRiGunrdBIWpB5NKpfDz8+O6jDa1FaZ8UF1dDbVajZiYGN6Ef1fVo0cP9O3bF59++qnVHhF3Yl403tp1fJh2wjAM8vLycOHCBRw7dgxpaWkoKiriuqxORWvzeii1Wo19+/Zh/Pjxbn3OVKvV2vyj4kuYFhYWQqFQuPXPmvx/ixcvxuzZs7F7927cfPPNXJfTJplMZmmBsixr2fhBIBDAYDC43S5EmZmZ+Pzzz3HkyBFcvnwZVVVVrbZMhUIhgoOD0bt3b4wbNw4PP/wwb5fdpJaphyorK8PVq1etfqJ1F7m5uVa7f/z9/XnRstZoNKiqqqJBRzwycOBAjBgxAh999BEvuh8lEomlFW3e2oxlWTAM4zata4Zh8MUXXyAxMRHdu3fHa6+9hiNHjqCystLqz5hhGJSWlmLfvn1Ys2YNwsPD0b9/f+zYscPF1TuOwtRDVVRUQC6Xw9vbm+tSbPKELt6ioiJIpVIEBwdzXQpph8WLFyMlJQUnTpzgupQ2iUQiyOVyiMUtOxPNu7Nw6dlnn4VSqcSDDz6Iq1evOnRfFy5cwMyZM+Hn54f333+/kyp0PgpTD1VRUcGL+aV8D1Oj0YiSkhKEh4e7/ajpDqvP5boCpxg/fjzGjBmDP/74g+tS7NJakJpxFaaXLl1CdHQ0XnvtNWi12k6979raWjz++OMYMGAAysrKOvW+ncFD//pJRUWF27eU9Ho9AgICrI5+jYuLc21BHVBaWgqWZREREcF1Kc5x7Vuwv8YB177lupJOJxAIMGXKFPzwww+oqanhupw22ZpuxUWYPvXUU+jduzcKCgqc+jjnz59HRESE2y8FSWHqoUaNGoWePXtyXYZNxcXFSEtLQ2lpKby8vKBQKCAUCqHRaCyLfLu7oqIi+Pv7u/256Q7LeBsCAYCMd7iuxCmmT58OhmGwa9curktpk7uEKcMwGDt2LN566y2XnW82mUx44oknsGDBApc8XkdQmHooa+vcuhPzcocMw6Curg719fWWkYmJiYkcV9c2rVaLuro6t+8B6DCGgb48BSYG0JefA3gwBaO9QkJCMHz4cPz2229cl9ImdwhThmEwaNAgHD582CWPd6NNmzbhzjvv5OSx20Jh6oHKyspw7tw5rstokzlMW+PuHwSApuUahUIhL85Nd0ju95CKTHjjd0AqMgF5P3JdkVPMnDkTx48fd/vzckKh0OY6va4I1HHjxnG+L+yWLVvwr3/9i9MaWkNh6oFyc3Nx4MABrstoU3l5udXr+BBQZWVlCAgI8NylAzM/RI0GWLMFqNUAuPIB1xU5xc033wyRSMSLgUhcDkJ69NFHceTIEac+hr02btyITz75hOsymqEw9UCNjY1QKBRcl9EmWy1Tdw9TvV6P2tpaz+7iLTuJrScBrQHYegrQl7n/FJKOUKlUmD17Ns6cOcN1KW3iqqs3JSUFH330kdPuvyOWLFli8z3E1ShMPRAfwtRkMqG6urrV6wQCAQIDA11cUftUVlZCIBC4feh3WOFvkAqN2PJ/+8pvOQVIhUagYDu3dTlJUlISDh48CKPRyHUpNl0fpizLQiAQQCQSWRZycAaGYTB16lSn3LcjjEYjpk2bxnUZFhSmHogPYVpVVWV1TVGVSuX2o2Orqqogl8vdvs4Oy3gb9VpgT1rTt7tTgQYdgMtvc1mV0wwePBiNjY24ePEi16XYJBKJLCEqkUgsSwo685zpkiVLbJ6S4dLZs2fdpsVMYeqBAgIC3H7eI5+7eIGmCeUqlYrrMpxGX3IUv54B9P/XUNMb0fR9qXucM+tsffr0gVwux+nTp7kuxSahUGgJ0Rs5Y5qK0WjEZ5991un325lWrVrFdQkAKEw90rhx4zB69Giuy7DJVpi6+3lIo9GI+vp6zw3Tot2QCvXYcrL5xVtOAlKBHijhz8ba9pJIJOjfv7/bhylgfX9QZ2zC/frrr7t913dVVZVbbPZOYeqBdDqd2y/ezeeWqVqtBgDPDdPLb6JRD/x5ofnFf5wHGvUALr3BSVnONmTIEKSkpLj9lma2tvjr7L/7d97hx2Idzz77LNclUJh6ovfeew8pKSlcl2GTj48PEhISEBERAT8/P0ilUhgMBlRXV7v9ykc1NTUQi8VQKpVcl+IU+uKD+D3l/4LzOo16YGcKYCh2/2lXHdGvXz9otVq3PT9o5qowPXbsGEpLSzvt/pzpzJkzqKqq4rQGClMPo9frwTCM2w9AunLlCq5cuYK8vDxUVFRAo9FAIBDA29vb7bddq6+vh7e3t2duAl5+BFJBI36xMgvml5OABI1AueedO42NjYVOp0NeXh7XpdjkqjB1l4E99tq4cSOnj09h6mEaGxsBwO3D1NoOEwKBwO1rr6+vh1wu57oM57j4GvRG4PeU1q/+PQUwGAFcfN2FRblGREQEBAIB8vPzuS7FJleF6alTpzrtvlxh3759nD4+hamH4UuY6nQ6q9fJZDIXVtJ+fJh61FGGor3YdQGot7KbVl0jsCu16ThPI5PJEBIS4vZhams+aWeGaU5OTqfdlyukpqZy+vjW16YivERh6lwMw0Cn07lny9SoBfOjN4COzzeUCJq6cm35+QRw68B6MN850s0tgvDuekDsXj/HmJgYtw9TWy3Tzho8VV9f3+n7kzpbUVERp49PYephYmNj8dhjj8HLy4vrUqxiWRZ6vb7V65y5kktnMH8IcMsPK2I5hOGTwBT/BZMJeGMnkNfO1dZ0RuD7o7aP+f4oIBICsna+e8QEAf+eDohEgDB8ktsFKQBER0fj6tWrXJdhkyvO1R86dMjpj9HZTCYTtFotZx90KUw9jFAodPtRpgaDwWp3lDu3SoH/3/J3y5YpANy0C8IrH8J04nE8NoXBgk+a1tXtTAYTsLGdA3rvGAq8ei8AgRDCYe8DSYs7t6hOEhgYiJMn22iac8wcpgKBoMVXZ30Q5cNm6a2pqqribMEa920CWPHBBx8gLi4Ocrkcw4cPb/MX/+eff0aPHj0gl8vRt29f7Ny500WVcuPixYv49ddfuS7DJlvdR+4epuYWtVvX2f1RSG7PgtIvHFuWAh//C1BIuSlFIQU++RewZSmg9IuA5PYstw1SAPDy8rLaa+IuBAIBxGIxRCJRs23ZOnPRhoaGhk65H1erq6vj7LF5FaY//vgjli9fjtWrV+Ps2bPo378/pk2bZnUfwqNHj+Lee+/FwoULce7cOcyePRuzZ89GWlqaiyt3ndraWrfvpuLr+VKgqSvJaDS6/7QY73iIbi8A4u7HgxOBs/8F+kS7toS+0U2Pu3AigLh5EN2eD3jHu7aIdpLL5TZ/P7sKtzyNYQcu56i3O0znz5+PgwcPOqOWNr311ltYtGgRFixYgF69euHjjz+Gl5cXvvzyy1aPf+edd3DzzTfj6aefRs+ePfHiiy9i0KBBeP/9911cueuIRCKXbBLsCD6HqfmTv9uHKQAIhcCoryGa8CsSw6U48xKweLJrHvrRKcDpl4DEcClEE34DRn3VVI+bk8lkvBt44wz+/v5cl9AhXM5Rb/dvd21tLSZPnoykpCS8/PLLKCwsdEZdLej1epw5cwaTJ///dwOhUIjJkyfj2LFjrd7m2LFjzY4HgGnTplk9Hmh6o1er1c2++IQPYSoSiRAXF4fQ0FB4e3tDKBRCq9VCrVZbzkm6K16FqVnUbZDMLYUksC8+XABsWw4EeDvnoQK8m+7/gwcASWBfSOaWAlG3OufBnEAmk8FkMrn935CzjRo1iusS2k0kEnE68LLdYbpt2zYUFhZi8eLF+PHHHxEXF4dbbrkFv/zyCwwGgzNqBNC0lqvJZEJoaGizy0NDQ1FSUtLqbUpKStp1PACsX78eKpXK8hUd7eK+MQfxIUx1Oh2uXbuGwsJC1NTUQK/XQywWQy6Xu+/Anv/DyzAFAKkfBDMuAL1XYsYAIP1VYFyPzn2I8T2b7nf6AAC9VzU9ntSvcx/Eycyjybt669TPz8/te4luFBYWxunjd6jfJTg4GMuXL8f58+dx4sQJdOvWDffffz8iIiKwbNkyZGZmdnadLrNixQrU1tZavtx9ztmNwsPDMWHCBLde6F4sFrca+EKh0O0XGedtmJr1/y/E008hKNAXf68C1s5pmubiCJEQWHcnsO95IChQBcn0U0D/FzunXg4IhUKIxTTRITY2lusS2qVPnz6cPr5Df0bFxcXYvXs3du/eDZFIhOnTpyM1NRW9evXChg0bOqtGAE07iYhEohYLL5eWllr9RBIWFtau44Gmbh5fX99mX3wSGhqKUaNGufWbva1PvHwZ/OHOH1baFDgE4jnlEIZNxqrbgYP/AZQdbIQoZU23f342IAyfAvGcMiBwSKeW60r19fWQSCSQSjka/uxGBg0axHUJ7TJhwgROH7/dYWowGLBlyxbceuutiI2Nxc8//4ylS5eiqKgIX331Ffbs2YOffvoJ69at69RCpVIpBg8e3GzfOoZhsHfvXowcObLV24wcObLFPne7d++2erwnaGhoQGZmplt39dp6o3L3aQlSqRRGo9Ht62yTWApM2g1h5K0YlQT4dXBqsp8SGJUECCNvBW76q+l+eayurg4+Pj5u/WHUVR/kFi1a5JLH6SwPPPAAp4/f7r6M8PBwMAyDe++9FydPnsSAAQNaHDNx4kSnjKpavnw55s+fjyFDhmDYsGF4++230dDQgAULFgAA5s2bh8jISKxfvx4A8OSTT2L8+PF48803MWPGDPzwww84ffo0Pv30006vzV0UFxfj559/xpNPPum2izfwuWVqrl2n0/HunFJrmKpzOJ8DFHZw96rCKiAlF+gnP8eveXZWmMOUADfddBMCAgI439rMHn379uX8nGm7w3TDhg2YO3euzYEifn5+uHbtmkOFtebuu+9GeXk5/vOf/6CkpAQDBgzAn3/+aRlklJeX12wFkFGjRmHz5s1YtWoVVq5ciaSkJGzbto3zvnVnEolEAMDblilfwlSr1fLuFEAL2gqwmkL8ZGW7NXv9dBzoE10IobYCkLv3xu5tqaur48Xrev0qSNf/29lLcT766KN46aWXOvU+ncEdamz3T/7+++/ndMTlkiVLkJubC51OhxMnTmD48OGW6/bv349NmzY1O37u3LnIyMiATqdDWloapk+f7uKKXYsPYSoUCiGRSFq9Tq/Xu/X5yOtbprx36TWIhMAWB1fP++UkIBYCuMT/bdnq6+vdvmUqEAggEoksKyCZV0FyRtf0Cy+84NZrZQOAr68vbrvtNq7L8IieGXIdc5gajUaOK7HNWuuUZVm3rt28jJsnhCmT+xMuFgCZ1meK2SWzBLhYCLC5P3VOYRwqKSlBZGQk12XYZOvDZmcHqlQqxb333tup99nZVq1axXUJAChMPY5UKkVgYKBbD6AAbC8U7+5BpVQqUV9fz3UZjtGrwdTl4sc2ungn9AJ2Pdv0ry0/HQdMdTmAnl+LnFyPYRhcu3aNd1NCnO3rr7/mdGUhW3r06IGnn36a6zIAUJh6nODgYDz88MMICnLvc1ettUwZhoFGo3H7oPLy8uLtrhoWl9+CWGS9i1csAl6aC+xdCUzuK8DelcCLc5sub82WU/933eXOnRLnSkVFRdDr9UhISOC6lA5zxodooVCIHTt2dPr9OkooFGL37t1cl2FBYUo40bdvX/To0QNRUVHw8fEBy7JoaGiAyWRy+yUc/fz8+B+mOZuRXQqkF7S8Ki4YOLIaWDELEIZPg/DuegjDp2LlLODwf4DYVj6npeUDV8sA5H7n9NKdxTxoMj7evRfj52JMwejRo3Hfffe5/HFtWb9+PaKiorguw4LC1MM0NjbijTfewOXLl7kuxaaysjKkpaUhJycH1dXVMJlMUCgUUCgUbj8U38/PD3q9HhqNhutSOsaogbE2Ez8eb3nVXSOA1FeAgfEiCId/Btz0JyD2atondfhnGJQgQuorTcfd6MfjgKEmEzDy8+dy7do1KJVKBAcHc12KW/rmm2/Qt29frssAANx+++145plnuC6jGQpTD6NQKKDX61FbW8t1KTbZesMqLy93YSXtZ95Rg7et04x3IRY1jcI185IBXywCfnwcUPhFQ3L7VaDbg81v1+1BSG6/Ci//KPz4OPD5oqbbmf1yApCIAFzh565MBQUF6NGjh9uPN3DlAKTrCYVCnD17FomJiU57DHtMmjQJW7du5bSG1lCYeiCVSuX2b/QhISFWr7O2P627UCgUkEqlbt+Ctura18ivBM7lNH3bPxZIeRmYPw5AwkKIZucAypjWb6uMgWh2LpCwAA+Ma7pd//8br3M2B8ivBHD1K6c/hc7GsixOnz6NHj06efV/DyMWi3H58mXOWqizZ8/Gnj17OHnstlCYeiA/Pz9qmTpZcHCwzd2H3JZRD0P1ZUsX7xPTgFPrgLhQGUQ37QRGfN72vqNCITDiS4hu2om4UBlOrQMen9Z01U8nAEP1JcDIr+UWCwoKUFpaiiFD+LuusKta1GKxGCkpKZg/f75LHg9oem6rV6/G//73P5c9ZntRmHogPgyQsTXauKKiwu13jwkODkZFRYVTtx10iqyPIBGxOHgZ2PE08M48QBI8CJK5ZUDELe27r4hbIJlbBknwQLw7r+n+DlwCJCIWyP7EOfU7ycmTJyEWizFw4ECuS2mTMxdpaE8NmzZtwvHjx52+kXh8fDyys7OxZs0apz6OoyhMPdCoUaNwxx13cF2GTTKZDCqVqtXrTCYTqqurXVxR+0RERIBhGP61Tq9+CYZpOj86ta8A6LMGuOUMIO3gEnpSX+CWs0Cf1ZjaV4AvFgEMAyD7i86s2ulOnTqFPn36QKFQcF2KTdlV2Xjx4ItYumsp/nPgPzhTcgZisRhisZiTlYqGDx+OiooKPPDAA5YFYzqLTCbDCy+8gKtXr7r9CGuAwtQj+fv7u/08U4DfXb3e3t7w9fVFUVER16XYjzHCUJkGoRDw9/eD5NazQL/VnXPf/dZAcutZ+Pv7QSgEDJWpAOO+K1ldz2g04syZMxg2bBjXpVj1fer3SHo3Cd3e64Y1B9bg/VPv4+VDL2PEFyMQ+kYoXjn8CmctVaFQiI0bN0Kr1eKll16yOR7CHvHx8fjss8+g0Wg6ffcxZ6Iw9UD19fX4/fff3b51x+dBSAAQGRmJwsJCt15LuBmjpqn1EH4zxHPLAf8BnXv//gOa7jf85qbH4ckUmdTUVISFhbltmP5jyz9w39b7kFWd1er1ZQ1lWLF3BQZ/MhhGDj/AiMViPP/88ygtLcXRo0exYMEC9O3bF15eXjZv5+vri8GDB+PRRx/FxYsXcfXqVTz44INuvybwjWg7eQ915swZdOvWzennMxxhrWVqNBqRmZmJcePGubii9omIiEBGRgYqKir4MTdR6gvhfU4eGCQUAxP/4NWn9L/++gt6vR7Jyclcl9LCQ789hM1pm+069mzJWYz6YhROLnJw54JOMHLkyGb7Rmu1Wpw5cwa1tbXQaDRQKpUICgrCwIEDIRZ7Rgx5xrMgzXh7e0MsFvNiRK9cLkdAQIBlKUG1Wo2Ghga37+YFmuqXSCS4evUqP8KUtNDY2Ih9+/bhvvvuc7uWUG5NLj47+1m7bnOq6BS+Pf8t/tn/n06qqmPkcjmCg4PRv39/eHt7c12OU7jXbw/pNHyYa5qYmIjAwEAUFBSgoKAAVVVVMBqNUCqVKCoqQmNjI9cl2iQUCpGYmIjs7Gz+jeolAJq2bdTpdLj55pu5LqWFZbuWdeh26w6653nGyZMn47PP2vfhgE8oTD0UH6bHyOVy1NfXtzoNhmVZXL16lYOq2icpKQkmk8myrivhlz/++AODBg1CaGgo16W0sONKxxaXz6zKRIG6lUWXOVRbW4va2lqP3pGHwtRD9evXzy3PAd0oKSnJ6nVXrlxxYSUdo1QqERkZyYtaSXMFBQU4f/48pk+fznUpLeiNehiYjvd2nChoY289F8vPzwcAxMRYWVnLA1CYeqi+ffuif//+XJfRJlthmpmZ6cJKOq579+6oqqpCRUUF16WQdtiyZQv69euHsWPHcl1KC/V6x7YhVOvca+elnJwcABSmhId0Oh0uX74Mvd69l3Xr3r271esKCgrc/rwp0DRFJiAgAKmpqVyXQuxUXl6OnTt3YuTIkZDJZG3fwMX85H4O3T5G5V6hVVpaCh8fH48eqEdh6qHUajW+//57FBS417mTG/n5+Vn9A2NZFllZrc+tcycCgQDdu3fHtWvXUFlZyXU5xA7ff/89FAoFZs+ezXUprRIKhYjwiejQbSVCCSbGTezkihyzcOFCZGZmuv2OPI6gMPVQQUFBUCgUyMvL47qUNnlCV2+3bt2gUqlw5swZrkshbaioqMDvv/+Ou+66q80FBbj01MinOnS725Jvc7tpPgDcfqlGR7nfT5x0CoFAgOjoaApTFxEKhRg0aJBl9xHivty9VWq2dPhSeEnaF/YCCPDWtLecVFHHlJWVoV+/fjh16hTXpTgVhakHi46ORkFBgdvvwGItTA0GA9LT091+io9ZXFwcAgMDcfr0aa5LIVYUFRUhLS0N9957r1u3SoGmD2hHFhyBgBUAdq5Y+fXsr93ufOnJkydRWFiIyMhIrktxKgpTDxYbG4ugoCBoNO69RqpKpbKs0+vl5YWgoCDI5XIYDAZ4eXnh/PnzHFdoH4FAgMGDB6O6upoXc2S7GpZl8e6776KxsRGzZs3iuhy79A/rj8jfIgHt/11gJVSlIim23rXV7VY+AprCNCoqChERHTsHzBcUph4sNjYWDz30EC+W75o8eTJ69uwJo9GIkpIS1NfXQyqVQiAQ4MQJ95ozZ0tUVBRCQkJw9OhR6HQ6rssh19m7dy/OnTuHJ554AnK5nOty7JKamoqSCyUQvymG8GchUAHAhKZQZYBwZTjevfldNK5sxO09b+e42tadOHECw4cP57oMp6O1eT0cy7Kor6+Hj48P16XYFBQUZHVqybVr11BeXs6bYfWjR4/Gzz//jGPHjmHChAlcl0PQtALPJ598gokTJ2LIkCFcl2O3X3/91fJ/YYYQwoz/3/4ZNmwYjhw5wkVZdtPpdDh//jzmzp3LdSlORy1TD/fXX3/hyy+/5LqMNnXr1g0BAQFWr+dT61SpVGLUqFG4cuUKLwaAdQWffvopGIbBww8/zHUp7bJ9+3ar1/Ghq1oikeDAgQNuP9irM1CYerjIyEhUVVWhvt6xFVWcTSAQ2NxP8uTJk/zZNxRNi1FER0fj4MGDbr9whqc7duwYLl++jIceesittyS80fnz55GSkmL1+ttuu811xXSQUChEcnIygoKCuC7F6ShMPVx0dDQAuP3iDQBshml5eTnvFpMfO3YsWJbFoUOHuC6lyyoqKsKGDRsQFxeHqVOncl1Ou2zbtg1CoRDdu3dvsVJYUlISL9beXrt2LTZt2sR1GS5BYerhVCoVVCoVL7obw8PDba7dyaeuXqBpX9lRo0YhIyMD586d47qcLken0+Hll1+GSqXC8uXLebX6jk6nwxdffAGhUIirV6/i6tWrSEhIwJ133olJkyZh7ty5bv98WJbFd999h5KSEq5LcQkK0y4gOjoaVVVVXJdhF1ut0zNnzsBoNLqwGsclJiZi0KBBOHbsGHJzc7kup8tgWRbvvfceioqK8Pzzz0OpVHJdUrts3boV5eXlzS7Ly8vDtm3bcPr0aSxevJijyuyXnZ2NyspKm3/TnoTCtAu4/fbbcc8993Bdhl2GDh1q9RN3Q0MDb+acXm/48OGIi4vD7t27ebMABd/9/vvv+Pvvv/Hkk08iLi6O63La7cMPP7R6Xf/+/REWFubCajrm5MmTEAgEvBo97QgK0y5ALG6aAeXuKyEBgK+vL3r16tXicpPJBK1Wi507d3JQlWMEAgEmT54MpVKJnTt3QqvVtn0j0mHHjx/H1q1bMXfuXIwfP57rctrt9OnTNlfRevTRR11YTcedOHECvXr1gq+vL9eluASFaRfAsiw+//xz7N27l+tS7GLuFhKLxYiMjIRSqQTDMBCLxcjLy7PsjcgnUqnUsgn19u3baYSvk5w7dw6vv/46evTogfvvv5/rcjrko48+snpdeHg4L0bxAsBdd92FZ599lusyXIbCtAsQCATw9/dHWloaL6aX9O/fH6NHj0ZwcDByc3NRW1vbrOuXj61ToGkw2OTJk1FdXY1ff/2VArWTpaen4+WXX8bAgQOxfPlyiEQirktqt/Lycvzyyy9Wr1+0aBEkEokLK+q40aNHY8aMGVyX4TIUpl1Enz59UFFRgbKyMq5LaZNMJoNcLkd+fn6r1587dw5FRUUurqpzhISE4Pbbb0dlZSUFaifKzMzEunXr0KNHDzzzzDOWUxt88+WXX1r9nZBIJFi4cKGLK+qY7777Dtu2beO6DJeiMO0iunXrBrlcbnXJPnczZcoUm2+IfG2dAhSonS09PR0ff/wx4uLi8Pzzz0MqlXJdUodotVp8+umnVq+fM2eOZUMId8ayLN544w0cP36c61JcisK0ixCJROjduzeuXLnCdSl2UalUGDNmjNXrT5482WLqAJ+Ehobi9ttvh1qtxi+//IK6ujquS+KlAwcOYO3atfD19cWaNWt4s4B9a7755hvodDqra1DzZeDR2bNnUVRUxJtzu52FwrQLmTZtGh566CGuy7DbzTffDKGw9V9RlmXx559/uriizhUaGopZs2ahoaEB3333HYqLi7kuiTdYlsUPP/yAd999F+PHj8fzzz8PhULBdVkdptFo8Nprr6G2thZVVVVITk5uNqVk0KBBvJli8uuvvyIkJKRL7BRzPV6EaU5ODhYuXIj4+HgoFAokJiZi9erVbXaPTZgwAQKBoNnXI4884qKq3Y9SqYRYLObFFBkACAwMxIgRI6xef/ToUd7P2wwKCsI//vEP+Pv746effkJ6ejrXJbk9g8GAd955Bz///DP+8Y9/4NFHH+XtOVKz999/37JSkEAgQHZ2NlJSUjB58mTcd999vFnBiWEY/Pbbb5g5cyYvB4A5ghdhevnyZTAMg08++QTp6enYsGEDPv74Y6xcubLN2y5atAjFxcWWr9dee80FFbuv48eP4/333+fFqF4AuOWWW6y+iRiNRuzatcvFFXU+Ly8v3HnnnejZsyd27dqFffv28eYDj6sVFhZi3bp1SE1NxVNPPYU77riDFyFjS3l5Od56661Wr9u/fz/Onj2L2293z71Kb8QwDFatWsXbaUmO4MXHuZtvvhk333yz5fuEhARkZGTgo48+whtvvGHztl5eXrxYLcRVAgMDUVpaiuLiYl7sfB8WFoZBgwbhzJkzzS5nWRYGgwHbt2/HTTfdxJu9Tq0RiUSYOnUqgoODcerUKeTn52P69Om8f16dhWVZ7Nq1C99++y2Cg4OxatUqxMfHc11Wp3jllVfQ0NBg9fpVq1ZZPd3hbsRiMebMmcN1GZzgxyvUitraWpv7X5p99913CAoKQp8+fbBixQpoNBqbx+t0OqjV6mZfniQhIQEKhQJpaWlcl2I382IHZt7e3pDL5RAIBJBKpfjuu+9409Juy8CBAzFz5kwYjUZ89dVXOHbsWJdvpVZXV2P9+vXYuHEjJk2ahFdeecVjgjQrK8vmfsODBw/GHXfc4cKKOo5hGDz77LO4dOkS16VwgpdhmpWVhffee6/NjX7vu+8+fPvtt/j777+xYsUKfPPNN/jnP/9p8zbr16+37LSiUqksW5h5CvOo3tTUVN4EUExMDPr27Yvw8HAkJyejrq4ODQ0Nlu69tvZ95Jvw8HA88MADGDZsGA4fPoxvvvmG1yOXO4plWezfvx9PP/008vLysHLlSixYsAAymYzr0jrNmjVrbG7e8NJLL/GmG/vEiRPYtGmT2++d7CwClsN31Oeeew6vvvqqzWMuXbqEHj16WL4vLCzE+PHjMWHCBHz++efterx9+/Zh0qRJyMrKQmJiYqvH6HQ66HQ6y/dqtRrR0dGora31mDUms7KysGnTJixdupQ3m/aaWyfWQiUwMBD//e9/PeqNFgCKi4uxc+dONDY2Ijk5GaNGjeLdDigdcfHiRXz33XfIycnBlClTMGfOHPj4+HBdVqc6ceIEJk+ebPX6W265BT/99JMLK3LMihUr8Oeff+LMmTO86Za2h1qthkqlajMDOA3T8vJyVFZW2jwmISHBMgm7qKgIEyZMwIgRI7Bp06Z2v2ANDQ3w9vbGn3/+iWnTptl1G3t/kHzCMAwaGxt596a8ceNGHDx40Or1M2bMwJ133unCilzDZDLh9OnTOHz4MFiWxbBhwzB8+HCP++AANP2Nf//99zh79iy6deuGf/zjHy02xvYEDMNg/PjxVntUhEIhTpw40awh4c5MJhP69++POXPmYO3atVyX06nszQBOByAFBwfbPcCisLAQEydOxODBg7Fx48YOffIx/+KGh4e3+7aeRCgUQqlUwmg0QigU8uZT5Ny5c3HmzBmrgzX+/PNPjB492uNeX5FIhOHDh6Nfv344evQojh07hjNnzmD06NEYOHAgb9ZqtaWwsBB79uzBnj17EBgYiMcffxzDhw/nTRdne23cuBHp6emIiIhodWnMefPm8SZIgaZWdnl5OWbNmsV1KZzhtGVqr8LCQkyYMAGxsbH46quvms1fMo/ULSwsxKRJk/D1119j2LBhyM7OxubNmzF9+nQEBgbiwoULWLZsGaKionDgwAG7H9sTW6YAUFNTgw8++AB33XUXkpKSuC7HbgcPHsTGjRutXt+zZ088/fTTHvsmDAB1dXU4dOgQMjIyYDAYMHDgQAwePNiuAXnuhGVZnD9/Hn/99RfS09OhUqkwc+ZMTJgwwSM+IFiTnZ2NsWPHorGxESzLonv37qivr7esRe3l5YWUlBRefSgsLCzE9u3b8cgjj3jc3x4vWqb22r17N7KyspCVlYWoqKhm15k/CxgMBmRkZFhG60qlUuzZswdvv/02GhoaEB0djTlz5mDVqlUur98dqVQqeHt74+DBg7wK07Fjx+LgwYPIzs5u9fpLly7h5MmTHr36io+PD6ZPn45Ro0bh1KlTSElJwbFjx5CQkIDBgwcjOTnZrXsb1Go1Tpw4gd27d6O0tBTx8fF45JFHMHToUN4vvtAWk8mExYsXo7GxEUDTAg2ZmZlQKpWYO3cu9u3bhwcffJBXQQoAkZGRWLx4MddlcIoXLVMueWrLFGjafeWHH37AsmXLeDUXNy8vD2vWrLE6GlkoFGLDhg0e93pZYzQacfHiRZw+fRoFBQUIDg5GZGQkkpOTER8f7xYLv1dVVeHs2bM4c+YMMjMzER4ejvDwcEydOhWJiYke15qx5u2337Z5TvEf//gHXnvtNXh5ebmwKsd88MEHkMvlvNnRpr14MQCJDzw5TE0mE1599VUkJSVh7ty5XJfTLps3b8bu3bubXWb+VW5oaMCoUaOwdOnSLvMmbVZSUoL09HSkp6ejsrISYrEY8fHx6N69O+Li4hAcHOySn4lGo0Fubi5ycnJw+vRp5OTkWKZlDRo0CAMGDPC40bltSU9Px8SJE2EwGKwes3XrVkycONGFVTmmrq4OQ4cOxf3334/nn3+e63KcwqO6eYlziEQijBkzBmfPngXDMG7dNXij22+/HSdPnkRtbS2A/78HamVlJeRyOc6ePYtdu3Y1WzmrKwgLC0NYWBgmTZqEyspKXLlyBRkZGfjjjz8ANHUrmluF4eHhiIiIQGBgYIdbryaTybI4e0FBAXJycnDt2jXLOrPmVvLUqVPRr18/Xi9G7widToeHH37YZpAuXLiQV0EKAD/88AMaGxs9tlXaHtQybYMnt0yBpjdDoVDIyxbc8ePH8cknn6B3797Izc1tsei9SCTCqlWr0K1bN24KdCNarRb5+fkoLi5GUVERiouLLdPS9Ho9ZDIZfHx84O3tDR8fHygUCohEIrAsC4ZhwLIsWJaF0WhEQ0MDampqUF1dDbVaDZZlIZVKodPpEBUVhfj4eMTHxyMuLg6hoaG8/N3qbOvWrcOGDRusXp+QkIBDhw7xqnvXaDRi1KhRGDlyJN555x2uy3Ea6ubtJJ4epmYlJSUICAhwi/Nr9jKv1/rjjz9aXUUmMDAQL730Ery9vV1cnfvT6XQoLS1FZWUl6urqUF9fj/r6etTV1UGr1aK2thYCgcAyfUogEEAikUAkEsHPzw/+/v7w9/e3/D84ONjjBxB1xIkTJzB9+nSry0IKhUL8+eefGDp0qIsrc8zu3bvxwAMPYPfu3ejVqxfX5TgNhWkn6Qph2tDQgJdeegkzZ87EqFGjuC6nXWpra/H8889buntbM2DAAN5sYUU8S3l5OaZMmYLS0lJotdpWj1m2bBn+85//uLgyx7Esi9TUVPTr14/rUpzK3gzgz0ky4jRKpRJ9+/bFoUOHeLeoukqlwqOPPmozKFNSUrBz504XVkVIU8t/3rx5KCwshMlkanUKWu/evfHss89yUJ1jtFotBAKBxwdpe1CYEgDAuHHjUFVVxcvNqXv16tXmzho//fQTrly54qKKSFfHsiyeeOIJnD592vL91atXMW7cOMsgLIlEgk8++YSXy0I+9NBDeOaZZ7guw61QmBIAQFRUlGUQBB/ddttt6NOnj9XrGYbBa6+91iV3XyGu9+abb2Lr1q3NLhMIBDh69CiGDx+OwYMHY+XKlejduzdHFXZcZmYm9u7dy7tzvM5GYUosJkyYgKioKJhMJq5LaTehUIjFixfD39+/1euNRiOqq6vx5ptvtrmnLSGO2LZtm83dsA4fPozBgwfj8ccfd2FVnefTTz9FaGgoZs+ezXUpboXClFgkJyfjtttua7b2MZ/4+vq2ev7U19fXspF4bm4uXn/9dej1eo6qJJ7szJkzWLJkic1junXrhhUrVvDy76y8vBw///wz/vWvf3n0+skdQWFKmjEajdi/fz+Ki4u5LqVDevTo0Ww1p+7du6O2trbZ0oOXL1/GO++8w8sWOHFfBQUFuP/++5vth3wjf39/bN68GX5+fq4rrBOdP38egYGBuP/++7kuxe1QmJIWjh07hu3bt1td+9bd3XrrrRg5ciTGjBmDy5cvtxqaZ8+exSeffMLb50jcS3l5Oe666y6b5+QlEgk2bdqE+Ph4F1bWuSZPnoyjR49CpVJxXYrboTAlzYjFYtx22224cuUKLl68yHU5HSIQCPDQQw8hOzvb5lSfQ4cO4ZtvvqFAJQ6pra3FvHnz2hzc9uabb/JuHvf1tm/fDo1Gw8vRx65AYUpa6NWrF7p3747t27dbXVnI3YnFYjz33HNtbj7/xx9/YNu2ba4pinic6upq3HnnnUhJSUF9fT2ioqIgl8tbHLdkyRLce++9HFTYOY4fP47HH38ce/bs4boUt0VhSloQCASYNWuWZdssvgoICMDKlSvbXLnqp59+wq5du1xUFfEUFRUVmDNnDtLS0iyXlZSUICYmptmWhrfccguv91E2mUxYs2YNBg4ciFtvvZXrctwWLSfYhq6wnKA1ubm5iImJ4f0yfDk5OVi3bp1lQ+YbMQyDxsZGLFq0CDNnznRxdYSPSkpKMHfuXGRlZbV6fd++fWEymcAwDHbs2AGlUuniCjvPd999h5UrV+LXX3/FgAEDuC7H5Wg5QeKw2NhYCAQCVFVVcV2KQ+Li4vD000+3OpTfvOOJTCbD119/ja+++orOoRKbioqKcMcdd1gNUgBITU1FUlISfvzxR14HaUNDA9544w3ceeedXTJI24PClNiUkZGBl19+GYWFhVyX4pCePXti6dKlLfZsDQ8Pb7YA+Y4dO/D222/b3HeSdF15eXmYPXs2rl27ZvO4uLg4vPDCCwgJCXFRZc6hVCrx9ttv09KBdqAwJTYlJSUhNDQU27Zt432LbdCgQXjkkUcAwLJId0FBQYvjjh49ipdeegkNDQ2uLpG4sVOnTmH27NnIz8+3eVy3bt3wv//9D5GRkS6qzDkaGhrAsizGjx+P0NBQrstxexSmxCahUIhZs2bh6tWrOH/+PNflOGzs2LF44IEHMGnSJJw7d87qcRcvXsQLL7xg2UCbdG179uzB/fff3+bKWT169MDWrVubDUDiI5ZlsXjxYl7uaMMVClPSpu7du6N3797YsWOHR3R/Tps2DTExMW0el5+fjxUrViA3N9cFVRF3xDAM3n77bSxYsAANDQ2oqamx+rvTu3dvbNmypc3pWHzw999/48CBA5g0aRLXpfAGhSmxi3lXFk9Zgm/KlClWByVdr7q6GqtWrcLevXtdVBlxF3V1dXjwwQfx5ptvWi4TCAQoLy9HcnJys2MHDBiALVu2ICAgwNVldjqDwYB169Zh9OjRmDp1Ktfl8AaFKbFLUFAQZs+e3eqEdL4aOnQo1qxZAx8fH5vH1dfX45133sE333zjMR8miG2ZmZm49dZbsXv37hbXGQwGNDQ0oFevXgCafo9++uknj1lib9OmTcjNzcXq1at5Py3OlShMSbucOnUKmzZt4v1gJLPu3bvjv//9r9VRl2KxGCzLQiQSYevWrXjuued4uwkAsc/OnTsxc+ZMXL161eoxJSUl8Pf3x/3334/vv/++zQ9kfGIymbBo0aIWrW9iG4UpaRcvLy+cO3cOhw8f5rqUThMeHo6XX34ZCQkJzS6XSqWQy+XNPp1nZWVh+fLl2L9/v4urJM6m1+vxyiuv4OGHH7ZrJHdcXBxeeuklXs8jbc0jjzyCFStWcF0G71CYknbp3bs3xo0bh23btqGoqIjrcjqNSqXC2rVrLRPTRSIREhMTUVNT0+JYrVaLd955Bxs2bKCNxj3ElStXcMcdd+CLL75o81ixWIyXX34Zr7/+OqRSqQuqc4333nsPH374IQBQ924HUJiSdrvtttsQHByMr776yiNG95rJ5XI899xzuOmmmzBx4kSkpqbaPP7gwYNYvnw5rly54qIKSWfT6/XYsGEDZsyYgfT0dLAsa3NQWkhICH7++Wfcf//9HhU4J0+exLvvvmtzlyViG4UpaTeJRIL58+dDoVB43MIGIpEIixcvRkJCAsRicZvHl5aWYsWKFfj444/bnINI3MuZM2cwY8YMvPvuu5bdkUwmU4vufrMhQ4bgjz/+wJAhQ1xZptPV1tZi+fLlGDx4MBYvXsx1ObxFC923oSsvdN8WlmU96tP5jXJycvDmm2+2ukrS9QwGAwwGA2JiYvDggw9i2LBhHv1z4buGhga89tprNveyHTVqFA4ePGj5ft68eVizZk2bU6n4hmVZPP744zhy5Ah+//13REREcF2S26GF7onTCQQClJWV4d1334Varea6nE4XFxeHN954w+ZcO5Zl4eXlBalUipKSErz00kv4z3/+0+aSc4Qbf//9N6ZMmYKvv/7a5oj0ixcvYujQoZBKpXjzzTfx3//+1+OCFGjq5jYYDHj55ZcpSB1ELdM2UMvUtvr6erz66qsIDw/H4sWLPbZFdvz4cXzwwQeor69vdnlkZGSrKyQJhULMmDED9913H7y9vV1VJrEiNzcXa9euxd9//233be677z7cfffd6NevnxMr456n9zA5ilqmxCW8vb3xz3/+ExkZGR49XWTEiBHYsGEDevfubbksJCTE6tq9DMPgt99+w0MPPYQ//viDBnZwpKCgAM899xymTZuGv//+GyKRqM3bCIVCLFq0CKtWrfLYINXr9XjggQdw+PBhCtJOQmFKHJacnIybbroJv/32W5vnF/ksKCgI69atw3333QeZTIb4+PgWLdUb1dXV4cMPP8SSJUvw119/ecxiF+6uqKgIL7zwAiZPnowtW7bAZDJBLBYjKirK5u169uyJbdu2YeXKlVAoFC6q1vXefPNNHDt2DP7+/lyX4jGom7cN1M1rH5PJhE8//RQ33XRTl1g5pbq6Gi+++CIyMzPtOt5oNIJlWcTFxWHOnDmYMGGCR56D41ppaSk+/vhj/Pjjj61O2zK/BtnZ2c0ul0qlWLp0KRYtWmTXKG4+O3jwIBYsWICVK1di4cKFXJfj9uzNAArTNlCYth/DMC024fZEDMPgr7/+wtdff426ujqrx5mXI7x+6kxAQABmzZqF6dOn0znVTlBcXIwvv/wSmzdvbnOKUr9+/ZCammoJ2+HDh2P9+vWIj493RamcqqysxPTp09GzZ098+eWXXeLv1FEUpp2EwrR9jEYjNm7ciJ49e2LMmDFcl+MS9fX1+P7777Fjx45Wz42GhIRYXS1KLpfj5ptvxuzZs2kD5nZiGAbHjx/HL7/8gj179qCxsdHu286aNQu7du3C888/j7vuuqvLhMrFixexZs0afPDBBx6xVZwrUJh2EgrT9mFZFr/88gsOHDiARx55BH369OG6JJfJz8/HZ5991mzTcZFIhNDQUOTl5dm8rUAgwNixYzFx4kQMHz6cBoXYUFJSgv/973/YsmULCgsLATT93slkMruWdxQKhVi2bBluv/32LvMBhmEYGI1GSKXSLtNz1FkoTDsJhWn7MQyDzz//HJcuXcKTTz6JuLg4rktyGZZlcfLkSXzxxRcoLi7GsGHDcPToUbtuq9frodPpEBcXh/Hjx2P8+PFISkqiYEXTwhj79+/HL7/8gsOHD7faAxATE2NzpxeBQIAZM2bgiSee6BJdutd74403cO7cOXz99dd2jWgm/x+FaSehMO0Yg8GAd955B+Xl5VixYgX8/Py4LsmlDAYDfv/9d6Snp9u9w45CoWhx7jU8PBzjx4/HhAkTkJCQ0KWC1WQyITU1Fb/88gv2799vdRqSmVAohL+/P0pLS1tcd/PNN+OJJ55AUlKSs8p1W9999x3WrVuHlStXYv78+VyXwzseF6ZxcXEtJsevX78ezz33nNXbaLVaPPXUU/jhhx+g0+kwbdo0fPjhh+3q2qEw7bj6+nocPnwYU6dO7bLdSo2Njdi1axf+97//oayszOaxKpXKZmBERUVh/PjxGD16NBITEz3yZ1paWoojR47gyJEjOHbsGOrq6qBUKlFbW2vX7SdOnNhsQ+/JkyfjySefRI8ePZxVslvbs2cPlixZgvnz59O2ah3kkWG6cOFCLFq0yHKZj4+Pzb0EFy9ejN9//x2bNm2CSqXCkiVLIBQKceTIEbsfl8K0c1y7dg1RUVFddjqIyWTC4cOH8csvvyArK6vF9aGhoZbzf20xGAwICAhAnz590LdvX/Tp0wdJSUm8nNKh0+lw9uxZHD58GEePHm31Z+Pl5WX3cpWxsbEwmUyIi4vDk08+2aXO2d+oqKgIN998MyZOnIgNGzZ45IcvV/DIMF26dCmWLl1q1/G1tbUIDg7G5s2bceeddwIALl++jJ49e+LYsWMYMWKEXfdDYeq4xsZGvPDCC+jevTsefPDBLv1HzbIsUlNTsWXLFpw8edJy+eDBg3HixAm77qO17mCpVIoePXpYwrV3797w8fHp1Nodpdfrce3aNWRlZSErKwtnz55Feno6dDqdzduxLAsfH59W95a9nlwux7Rp0/Dkk08iPDy8Eyvnr127dmHChAmQyWRcl8JbHhmmWq3WsjvHfffdh2XLlln9NL5v3z5MmjQJ1dXVzc7XxcbGYunSpVi2bFmrt9PpdM3+uNVqNaKjoylMHZSWloaPP/4Y48aNw9y5c7vUuT9r8vLysGXLFly4cAEymazFQgKtMa+jat4yzJbQ0FDEx8cjPDy8xZeXl1dnPIVWMQyDgoICZGZmIjs7G5mZmcjKykJeXl6zgUMikajNIDUbNGhQsw8f1+vduzfuvPNOzJgxw+0+QHChoqICx44dw8yZM7kuxSPYG6a86Rd64oknMGjQIAQEBODo0aNYsWIFiouL8dZbb7V6fElJCaRSaYuBL6GhoSgpKbH6OOvXr8fatWs7s3QCoE+fPrjnnnvw/fffIyAgAJMnT+a6JM7FxMRg2bJlMBgM2L59O6RSKS5dumTzNsHBwTZ/f69XU1NjdfCTr6+vJVhlMhlCQ0MhkUgsX1KptNm/EokEjY2NEAgEUKvVqK2ttXzd+H1dXZ1dcz51Ol2Hp2n4+Phg5syZuPPOO9GzZ892395TNTY24uGHH0ZpaSkmTJhAHy5ciNOW6XPPPYdXX33V5jGXLl1qdfDAl19+iYcffhj19fWtdmFs3rwZCxYsaPHJd9iwYZg4caLVx6WWqXNt374dp0+fxqpVqyCVSrkux+2Ulpbi4MGD2L9/P65cudLi+gEDBuD06dN23ZdUKrVr3qVcLm9zjWEAEIvF0Gq1bR7XnhanrQUtbqyxd+/eYFkWd955J6ZMmQK5XG7XY3QVJpMJjz76KE6ePInvvvsOvXr14rokj8CLlulTTz2FBx54wOYx1na9Hz58OIxGI3JyclpdCzYsLAx6vR41NTXNWqelpaUICwuz+ngymYzOLzjRzJkzMWnSJApSK0JDQzF37lzMnTsXxcXFOHDgAA4cOGAZmNOen5s9wQc0nYO1J0y9vLzsus/27JATGRlpM0xlMhmGDh2K0aNHY+bMmVCpVHbfd1fCsizWrFmDQ4cO4dNPP6Ug5QCnYRocHNzhJa1SUlIgFAoREhLS6vWDBw+GRCLB3r17MWfOHABARkYG8vLyMHLkyA7XTBwjEAigVCqh0WjwySefYMaMGejevTvXZbml8PBw3HPPPbjnnntQUFCAlJQUnD9/HmKxuM1zplFRUcjJybHrcext4Xl5eaGqqqrN4xiGgVQqbXONXACtjsbv1q0bRo8ejdGjR2PQoEH04dYODQ0NuHTpEv773/92mWU83Q0vzpkeO3YMJ06cwMSJE+Hj44Njx45h2bJl+Oc//2nZQqiwsBCTJk3C119/jWHDhkGlUmHhwoVYvnw5AgIC4Ovri8cffxwjR460eyQvcR6RSASBQIB33nkHDz30EPr37891SW4tKioKUVFRuPXWW/HMM8/gypUrSE1NRVpaGtLS0lrMw4yIiLA7TO0NK1vT0K4nEAgQFRVlczUiM41Gg4iICPTp08cSoF1lib/OYDKZUFNTg8DAQGzevJl6fDjEizCVyWT44YcfsGbNGuh0OsTHx2PZsmVYvny55RiDwYCMjIxm54jMc6vmzJnTbNEGwj2ZTIYlS5bg888/x8cff4z58+fThxw7SSQS9O7d27JROcuyKCwsbBaugYGBdt+fvW/A9oYp0NR921qYRkVFoVu3bpav5ORkxMbG0ujuDtDpdHj66aeRm5uLrVu3UpByjDdTY7hC80ydi2EYfPvttzhy5AheeOGFNjdvJvZpbGxEYWEhiouLW/0yj7aVSCRITExEWlpam/c5atQoHDx4sM3jhEIh7r77bmRkZCApKckSnAkJCU6dktOVNDQ04PHHH0dKSgo2bNiA8ePHc12Sx/K4eaZcoTB1PpZlcenSJRo04SIsy0KtVqO4uBjV1dVobGxEWVkZ9Ho9DAaD5d8b/9+jRw9kZGRApVJBpVLB19fX8v/rL1MqldTSdKLq6mo8/PDDyM3NxYcffojBgwdzXZJH48VoXkKApnNs5iA9ePAgiouLcdddd9EbspMIBAJL+BH+SU9PR3l5Ob766qsuu+awO6IwJW7n77//hkajwbx582i7KEL+T3l5OYKCgjBmzBj88ccfNM/WzXTdRVKJWxo3bhwefPBBnDx5Ep988gkMBgPXJRHCuYsXL+KOO+7AN998A8D+6UzEdShMidsZMmQIHnvsMVy8eBFbt27luhxCOHX69GksWLAAERERtN6uG6NuXuKW+vTpg6eeesrqohyEdAX79+/H8uXLMXDgQLz77rvtmp5EXItapsRtxcfHQ6lUoqamBq+88kqLzeEJ8XS//PILxo4di48++oiC1M1RmBK3ZzKZYDAY8PLLL+Pvv/8GzeYinkytVlt2D3r11Vfx1ltv0YIMPEBhStxeYGAgVqxYgfHjx+Pbb7/Fp59+avci7oTwSXp6Ou6++26sWLECDMNAqVTSiHaeoDAlvCAWi3Hfffdh8eLFSEtLQ35+PtclEdJpWJbF999/j/nz58Pf3x8ffvhhh/Z5JdyhAUiEV4YMGYLevXtDoVCAYRikpaWhX79+XJdFiEPefPNNfPPNN7jvvvuwfPlySCQSrksi7URhSnhHoVAAAC5cuID33nsPo0ePxj//+U86r0R4h2VZCAQC3HLLLejfvz+mTJnCdUmkg6gfgfDWgAEDsHDhQpw6dQovvfQSiouLuS6JELuwLIstW7Zg0aJFMBgM6N27NwUpz1GYEl4bNWoUXnjhBTAMgxdffBElJSVcl0SITRqNBs8//zzWrVuH2NhYMAzDdUmkE1A3L+G9iIgIvPDCCzh06JBlY2mTyUSjIInbyc7Oxr///W8UFxfj5ZdfxowZM7guiXQSapkSjyCTyTB58mQIBAKcP38eK1euRHp6OtdlEdLMqVOnIBAI8P3331OQehgKU+JxgoOD4efnh9deew0fffQRampquC6JdGEnTpzAl19+CQCYO3cuvv/+e8THx3NcFelsFKbE40REROC5557DQw89hPT0dDz77LO4fPky12WRLqa8vBwrVqzAo48+ihMnTsBoNEIkEkEmk3FdGnECOmdKPJJAIMDo0aMxYMAA/Pbbb4iNjQUA1NfXw9vbm+PqiKf74Ycf8MEHH0Aul2PdunWYPn06bXbv4ahlSjyaUqnEPffcA4VCgZqaGvz73//Gpk2b0NDQwHVpxINlZ2djxowZ2LJlC2bMmEFB2gUIWFo13Ca1Wg2VSoXa2lr4+vpyXQ5xAMMw2Lt3L7Zs2QKxWIx77rkHo0ePpjc64rDa2lq899576NmzJ+bMmWNZjIHwn70ZQC1T0mUIhUJMmTIFr7zyCnr37o3PPvsM33//PddlER5jGAa//vorbr/9duzevduyDCAFaddD50xJl+Pn54fFixdj3Lhx8Pf3BwDk5eUhICCAzqcSu1VUVOCZZ57B+fPnMX36dCxbtgwBAQFcl0U4QmFKuqzevXsDaFrabdOmTcjJycHkyZMxffp0+Pn5cVsccVs5OTmIi4uDn58fwsLC8Nhjj2Hw4MFcl0U4RudM20DnTLsGtVqNP//8E3/99ReMRiMmTJiAO++8k1qqBEDTB66TJ09i48aNSElJwU8//YSYmBiuyyIuQOdMCWkHX19f3HXXXXj33Xcxe/ZspKWlQSxu6rihkb9d2+HDh7FgwQI88cQT0Gq1ePXVVxEVFcV1WcTNUDcvIdfx8vLC7NmzMWvWLAgEAqjVaixbtgyDBg3CrFmz6E20i2AYBiaTCRKJBIcPH4ZcLse7776LYcOG0eAi0irq5m0DdfN2bQaDAQcOHMD27dtRWVmJIUOGYNasWUhISOC6NOIEBoMBf/zxB7766ivcfffduOuuu2AwGGiz7i6MunkJ6QQSiQSTJ0/Ghg0b8NBDD6GgoABbt24FANo6y4PodDr89NNPmDNnDv773/8iKSkJAwYMAAAKUmIX6uYlxA4ikQjjx4/H2LFjLedQT506hV9++QXjxo3DmDFjLNNsCD+wLAuNRgOlUon9+/djw4YNmDZtGubPn08L0ZN2o27eNlA3L7EmMzMTv//+O06fPg2j0Yi+ffti+vTpGDhwINelERsKCwuxa9cu7Nq1C8nJyVi3bh30ej3Ky8sRGRnJdXnEzdibAdQyJaSDkpKSsHTpUjQ0NODEiRM4ePAg8vPzMXDgQJSVlaG0tBS9e/eGUEhnU9xBVlYW3njjDaSmpkKhUGDChAmWPUWlUikFKXEIhSkhDlIqlbjppptw0003wdzRc+TIEfzwww/w9/fH2LFjMW7cOERHR3NcaddiMBhw7NgxNDQ04JZbboGfnx+USiVWr16NcePGQS6Xc10i8SDUzdsG6uYlHcGyLLKzs3Hw4EEcOXIE9fX1uPfeezF79myuS/NoLMsiPT0df/75J/bu3Qu1Wo0RI0bgzTff5Lo0wlP2ZgCFaRsoTImjjEYjUlJSEB4ejsjISPz+++84cOAA+vTpgz59+qBnz55QKBRcl8lbpaWlqKurQ7du3ZCWloaHH34YISEhmDp1Km6++WYaTEQcQmHaSShMSWc7f/489u/fj7S0NFRVVUEkEuGOO+7APffcA4PBAJZlIZVKuS7TbdXW1uLEiRM4d+4czp07h+LiYgwYMADvvPMOjEYj0tLS0K9fPzpXTToFDUAixE31798f/fv3B8uyKC4uRmpqKiIiIgAA586dw5tvvonu3bujb9++6NOnD5KSkrr0XMeqqiqcO3cOQUFB6N+/P9LS0vDf//4X8fHxGDlyJAYNGoT+/fsDAMRisWV+KCGuRC3TNlDLlLhSRUUFTp48idTUVKSnp6OhoQEDBw7EqlWroNPpkJ6ejqioKAQHB3v0snapqanYs2cPzp07h9zcXADAnXfeiccffxw6nQ4ajYbm9RKXoG7eTkJhSrjCMAxycnJgMpmQlJSEzMxM/Pvf/wbQNJUjPDwcUVFR+Pe//w2hUIjCwkLLiFU+SE1NRXZ2NgoKClBQUID8/Hw8/vjjGDFiBLZs2YItW7Zg4MCBGDRoEAYMGIDAwECuSyZdkEeF6f79+zFx4sRWrzt58iSGDh3a6nUTJkzAgQMHml328MMP4+OPP7b7sSlMibswmUwoLy9HYWGh5auurg7PPPMMAGDRokUoKyuDSqVCZGQkIiMjcccddyAiIgJqtRpGoxEKhQJyudyprVqWZSEQCGAwGJCZmWkJyoKCAhQVFeH999+HRCLB8uXLkZ6ejoiICERHRyMqKgpTpkxBfHw8TCYTRCKR02okxF4eFaZ6vR5VVVXNLnvhhRewd+9eZGdnW31jmDBhArp3745169ZZLvPy8mpXKFKYEr64evWqJbDMYbt06VLExMTgk08+wfbt2wEAAoEAcrkcU6dOxUMPPYTS0lJs2LABXl5eUCgUUCgUUCqVWLBgAQBg7969qKioQGNjIxobG6HRaDB9+nT07NkT+/fvx48//mi5rrGxEQMHDsTatWtRXV2NO++8EwAQHByMqKgoREdHY+HChfD29oZarYZSqaTQJG7NowYgSaVShIWFWb43GAz49ddf8fjjj7f5CdvLy6vZbQnxVAkJCVZ3szEvc3h96F2/uXVAQAAaGxtRWVkJjUbT7O9qx44dKCgogFwutwSuRqMBAPj7+6N3795QKBTw8vKCXC63bFOnUqnw2WefITw8vNWpP/ThlHgSXrRMb7RlyxbcddddyM3Ntbm/5IQJE5Ceng6WZREWFoaZM2fihRdegJeXl9Xb6HQ66HQ6y/dqtRrR0dHUMiWEkC7Io1qmN/riiy8wbdq0Njdqvu+++xAbG4uIiAhcuHABzz77LDIyMixbaLVm/fr1WLt2bWeXTAghxINx2jJ97rnn8Oqrr9o85tKlS+jRo4fl+4KCAsTGxlr2HmyPffv2YdKkScjKykJiYmKrx1DLlBBCiBkvWqZPPfUUHnjgAZvH3HgOaOPGjQgMDMRtt93W7scbPnw4ANgMU5lMBplM1u77JoQQ0nVxGqbBwcEIDg62+3iWZbFx40bMmzevQyvCpKSkAADCw8PbfVtCCCHEGl4tXrlv3z5cu3YNDz74YIvrCgsL0aNHD5w8eRIAkJ2djRdffBFnzpxBTk4Otm/fjnnz5mHcuHHo16+fq0snhBDiwXg1AOmLL77AqFGjmp1DNTMYDMjIyLAM2ZdKpdizZw/efvttNDQ0IDo6GnPmzMGqVatcXTYhhBAPx8upMa5EizYQQkjXZW8G8KqblxBCCHFHFKaEEEKIgyhMCSGEEAdRmBJCCCEOojAlhBBCHERhSgghhDiIwpQQQghxEIUpIYQQ4iAKU0IIIcRBFKaEEEKIgyhMCSGEEAdRmBJCCCEOojAlhBBCHERhSgghhDiIwpQQQghxEIUpIYQQ4iAKU0IIIcRBFKaEEEKIgyhMCSGEEAdRmBJCCCEOojAlhBBCHERhSgghhDiIwpQQQghxEIUpIYQQ4iAKU0IIIcRBFKaEEEKIgyhMCSGEEAdRmBJCCCEOojAlhBBCHERhSgghhDiIwpQQQghxEIUpIYQQ4iAKU0IIIcRBFKaEEEKIgyhMCSGEEAeJuS7A3bEsCwBQq9UcV0IIIcTVzO/95iywhsK0DXV1dQCA6OhojishhBDClbq6OqhUKqvXC9i24raLYxgGRUVF8PHxgUAg4Locq9RqNaKjo5Gfnw9fX1+uy+kweh7uhZ6He6Hn4Xosy6Kurg4REREQCq2fGaWWaRuEQiGioqK4LsNuvr6+bv/LaQ96Hu6Fnod7oefhWrZapGY0AIkQQghxEIUpIYQQ4iAKUw8hk8mwevVqyGQyrktxCD0P90LPw73Q83BfNACJEEIIcRC1TAkhhBAHUZgSQgghDqIwJYQQQhxEYUoIIYQ4iMKUp/bv3w+BQNDq16lTp6zebsKECS2Of+SRR1xYeUtxcXEtanrllVds3kar1eKxxx5DYGAgvL29MWfOHJSWlrqo4pZycnKwcOFCxMfHQ6FQIDExEatXr4Zer7d5O3d4PT744APExcVBLpdj+PDhOHnypM3jf/75Z/To0QNyuRx9+/bFzp07XVRp69avX4+hQ4fCx8cHISEhmD17NjIyMmzeZtOmTS1+7nK53EUVW7dmzZoWdfXo0cPmbdzt9QBa/5sWCAR47LHHWj3eXV+P9qAVkHhq1KhRKC4ubnbZCy+8gL1792LIkCE2b7to0SKsW7fO8r2Xl5dTamyPdevWYdGiRZbvfXx8bB6/bNky/P777/j555+hUqmwZMkS3HHHHThy5IizS23V5cuXwTAMPvnkE3Tr1g1paWlYtGgRGhoa8MYbb9i8LZevx48//ojly5fj448/xvDhw/H2229j2rRpyMjIQEhISIvjjx49invvvRfr16/Hrbfeis2bN2P27Nk4e/Ys+vTp47K6r3fgwAE89thjGDp0KIxGI1auXImpU6fi4sWLUCqVVm/n6+vbLHTdZbnQ3r17Y8+ePZbvxWLrb9Pu+HoAwKlTp2AymSzfp6WlYcqUKZg7d67V27jr62E3lngEvV7PBgcHs+vWrbN53Pjx49knn3zSNUXZKTY2lt2wYYPdx9fU1LASiYT9+eefLZddunSJBcAeO3bMCRV2zGuvvcbGx8fbPIbr12PYsGHsY489ZvneZDKxERER7Pr161s9/q677mJnzJjR7LLhw4ezDz/8sFPrbI+ysjIWAHvgwAGrx2zcuJFVqVSuK8pOq1evZvv372/38Xx4PViWZZ988kk2MTGRZRim1evd9fVoD+rm9RDbt29HZWUlFixY0Oax3333HYKCgtCnTx+sWLECGo3GBRXa9sorryAwMBADBw7E66+/DqPRaPXYM2fOwGAwYPLkyZbLevTogZiYGBw7dswV5dqltrYWAQEBbR7H1euh1+tx5syZZj9HoVCIyZMnW/05Hjt2rNnxADBt2jS3+7kDaPNnX19fj9jYWERHR2PWrFlIT093RXltyszMREREBBISEvCPf/wDeXl5Vo/lw+uh1+vx7bff4l//+pfN1qa7vh72om5eD/HFF19g2rRpbS7Kf9999yE2NhYRERG4cOECnn32WWRkZGDr1q0uqrSlJ554AoMGDUJAQACOHj2KFStWoLi4GG+99Varx5eUlEAqlcLPz6/Z5aGhoSgpKXFBxW3LysrCe++912YXL5evR0VFBUwmE0JDQ5tdHhoaisuXL7d6m5KSklaPd5efO8MwWLp0KUaPHm2zmzM5ORlffvkl+vXrh9raWrzxxhsYNWoU0tPTOd3YYvjw4di0aROSk5NRXFyMtWvXYuzYsUhLS2v11Ie7vx4AsG3bNtTU1OCBBx6weoy7vh7twnXTmDT37LPPsgBsfl26dKnZbfLz81mhUMj+8ssv7X68vXv3sgDYrKysznoKLMt27HmYffHFF6xYLGa1Wm2r13/33XesVCptcfnQoUPZZ555hvPnUVBQwCYmJrILFy5s9+M56/VoTWFhIQuAPXr0aLPLn376aXbYsGGt3kYikbCbN29udtkHH3zAhoSEOK3O9njkkUfY2NhYNj8/v1230+v1bGJiIrtq1SonVdYx1dXVrK+vL/v555+3er27vx4sy7JTp05lb7311nbdxl1fD1uoZepmnnrqKZuf4AAgISGh2fcbN25EYGAgbrvttnY/3vDhwwE0taQSExPbfXtrOvI8rq/JaDQiJycHycnJLa4PCwuDXq9HTU1Ns9ZpaWkpwsLCHCm7hfY+j6KiIkycOBGjRo3Cp59+2u7Hc9br0ZqgoCCIRKIWo6Bt/RzDwsLadbwrLVmyBDt27MDBgwfb3ZqRSCQYOHAgsrKynFRdx/j5+aF79+5W63Ln1wMAcnNzsWfPnnb3tLjr62ELhambCQ4ORnBwsN3HsyyLjRs3Yt68eZBIJO1+vJSUFABAeHh4u29rS3ufx/VSUlIgFApbHU0KAIMHD4ZEIsHevXsxZ84cAEBGRgby8vIwcuTIDtfcmvY8j8LCQkycOBGDBw/Gxo0bbW4kbI2zXo/WSKVSDB48GHv37sXs2bMBNHWT7t27F0uWLGn1NiNHjsTevXuxdOlSy2W7d+/u9J97e7Asi8cffxz/+9//sH//fsTHx7f7PkwmE1JTUzF9+nQnVNhx9fX1yM7Oxv3339/q9e74elxv48aNCAkJwYwZM9p1O3d9PWziumlMHLNnzx6rXaYFBQVscnIye+LECZZlWTYrK4tdt24de/r0afbatWvsr7/+yiYkJLDjxo1zddkWR48eZTds2MCmpKSw2dnZ7LfffssGBwez8+bNsxxz4/Ng2abuvJiYGHbfvn3s6dOn2ZEjR7IjR47k4ilYauzWrRs7adIktqCggC0uLrZ8XX+Mu70eP/zwAyuTydhNmzaxFy9eZB966CHWz8+PLSkpYVmWZe+//372ueeesxx/5MgRViwWs2+88QZ76dIldvXq1axEImFTU1NdVvONFi9ezKpUKnb//v3Nfu4ajcZyzI3PY+3ateyuXbvY7Oxs9syZM+w999zDyuVyNj09nYunYPHUU0+x+/fvZ69du8YeOXKEnTx5MhsUFMSWlZWxLMuP18PMZDKxMTEx7LPPPtviOr68Hu1BYcpz9957Lztq1KhWr7t27RoLgP37779ZlmXZvLw8dty4cWxAQAArk8nYbt26sU8//TRbW1vrwoqbO3PmDDt8+HBWpVKxcrmc7dmzJ/vyyy83O1964/NgWZZtbGxkH330Udbf35/18vJib7/99mbB5WobN260ek7VzF1fj/fee4+NiYlhpVIpO2zYMPb48eOW68aPH8/Onz+/2fE//fQT2717d1YqlbK9e/dmf//9d5fWeyNrP/eNGzdajrnxeSxdutTynENDQ9np06ezZ8+edX3xN7j77rvZ8PBwViqVspGRkezdd9/d7Pw5H14Ps127drEA2IyMjBbX8eX1aA/ago0QQghxEM0zJYQQQhxEYUoIIYQ4iMKUEEIIcRCFKSGEEOIgClNCCCHEQRSmhBBCiIMoTAkhhBAHUZgSQgghDqIwJYQQQhxEYUoIIYQ4iMKUENJCeXk5wsLC8PLLL1suO3r0KKRSKfbu3cthZYS4J1qblxDSqp07d2L27Nk4evQokpOTMWDAAMyaNQtvvfUW16UR4nYoTAkhVj322GPYs2cPhgwZgtTUVJw6dQoymYzrsghxOxSmhBCrGhsb0adPH+Tn5+PMmTPo27cv1yUR4pbonCkhxKrs7GwUFRWBYRjk5ORwXQ4hbotapoSQVun1egwbNgwDBgxAcnIy3n77baSmpiIkJITr0ghxOxSmhJBWPf300/jll19w/vx5eHt7Y/z48VCpVNixYwfXpRHidqiblxDSwv79+/H222/jm2++ga+vL4RCIb755hscOnQIH330EdflEeJ2qGVKCCGEOIhapoQQQoiDKEwJIYQQB1GYEkIIIQ6iMCWEEEIcRGFKCCGEOIjClBBCCHEQhSkhhBDiIApTQgghxEEUpoQQQoiDKEwJIYQQB1GYEkIIIQ6iMCWEEEIc9P8Akkeuh4Z3dfIAAAAASUVORK5CYII=\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "op = rebound.OrbitPlot(sim)\n",
+ "op.orbits[1].set_linewidth(5)\n",
+ "op.orbits[2].set_linestyle(\"--\")\n",
+ "op.particles.set_color([\"red\", \"green\", \"black\"])\n",
+ "op.particles.set_sizes([500,100,1000])\n",
+ "op.primary.set_sizes([1000])\n",
+ "op.primary.set_edgecolor(\"orange\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Alternatively, you can combine multiple orbit plots in one figure to give you a similar result. For example:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "op1 = rebound.OrbitPlot(sim, particles=[1,3])\n",
+ "op2 = rebound.OrbitPlot(sim, particles=[2], ax=op1.ax, fig=op1.fig, lw=5, color=\"red\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Updating plots\n",
+ "\n",
+ "You can update the simulation data in an OrbitPlot after integrating the simulation. For example, integrating the last simulation and then updating the plot (including the highlighted orbit) can be done with:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 13,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "sim.integrate(sim.t+3.2)\n",
+ "op1.update()\n",
+ "op2.update() # red planet orbit\n",
+ "op1.fig"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Animations\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Updating OrbitPlot is efficient. Only the underlying data is updated whereas the figure itself does not need to get recreated. This makes it possible to render animations. Let us first render a series of frames to files:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "for i in range(3):\n",
+ " sim.integrate(sim.t+0.31)\n",
+ " op1.update()\n",
+ " op2.update()\n",
+ " op1.fig.savefig(\"out_%02d.png\"%i)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "You could now convert these images to a gif or a movie, for example by using ImageMagick's `convert` or `ffmpeg`."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Interactive plots and animations in a jupyter notebook\n",
+ "You can update exisiting figures in a jupyter notebook if you use matplotlib's widget backend using `%matplotlib widget`. These figures are interactive, you can zoom in, move around, and resize them.\n",
+ "\n",
+ "Note that you might need to run `%matplotlib widget` before importing rebound or matplotlib. If the following cells don't work, restart your kernel."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%matplotlib widget\n",
+ "import rebound"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "b9b7d3cabefb435283eadde0631d4160",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "image/png": 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sssjNMdDJpQmCgPfeew9ZWVno7u7Gli1b8NJLL0numzc5H7Vajfvuuw9vvfUWGhsbsWTJEqxbt47H1kk0DHRyWY2NjbjpppvwX//1X7j11lutE4MQOVJaWhpee+01XHPNNXjzzTexbNkyNDU1iV0WuSEGOrmkzZs3Y8SIEdi9ezfWrl2LN954g6PXSTQqlQr33XcfXnjhBRQVFeGuu+7Cjh07xC6L3AwDnVxKV1cXli5dihkzZiAjIwMHDx7EtddeK3ZZRACAyy67DO+++y7S09OxZs0avPnmmzCZTGKXRW6CgU4u4+jRoxg7dizef/99vPLKK1i/fv0Zl84lEptGo8FTTz2Fa6+9Fj/++CMefPBB1NfXi10WuQEGOjk9QRDwP//zP7jiiiugUCiwc+dO/PWvf+Xc6+S0ZDIZZsyYgZUrV6K5uRlLlizBgQMHxC6LJI7noUPa5yW6Op1Oh7vuugvFxcW48sor8cwzz/CypuRSdDodXnzxRdTV1eHqq6/GnDlz+GVURFLe3yvFLoDoXPLz8zFnzhzU1dXhgw8+wHXXXSd2SUS95u/vj2effRZr1qzB+++/j+rqatx3331QKrn7JdvibxQ5pR9++AErV66Eh4cHdu3ahX79+oldElGfyWQyzJs3D9HR0Vi5ciVqamrwj3/8A76+vmKXRhLCY+jkdN566y3Mnj0bYWFh2LFjB8OcJGPy5MnWU9vuv/9+1NTUiF0SSQgDnZyG2WzGgw8+iAceeAD3338/PvnkE7ZgSHLS09Px2muvQRAE3H///cjLyxO7JJIIBjo5hfb2dtx4443497//jTfffBMvvfQS52EnyYqOjsZrr72G+Ph4PProo/jll1/ELokkgMfQSXTV1dWYOXMmTp48iQ0bNmDq1Klil0S9ZDKZoNPp0NnZCb1eD4PBYP2350QapVIJDw8PqFQqqNVq+Pv7w9fX122/uPn5+WHFihV49dVX8d5776GhoYEj4OmSMNDJobZs2YLly5ejuroaUVFRWLBgAVasWAFBEPDrr79iyJAhYpdI/0EQBDQ3N6OysvK0W1VVFSorKxEcHIxdu3bB29sber3+jNdnZmbi6NGj1p8HDhyIgoIC68+jRo1CS0sLIiIiEBkZicjISERERCAuLg5xcXEICwuTbMgplUosXboUn332GT788EPo9Xr85S9/kez2kn3xPHRI+7xEZ3LnnXfiww8/POP+4OBgHDlyBNHR0SJURf+poaEBOTk5OHz4MHJycqDT6WA0GnH8+HEAgI+PD6KjoxETE4Po6GgkJyfD19cX/v7+8PPzg5eXFzw9PeHp6QmVSgWFQgGLxQKTyQSj0Qij0Yj29na0tbVBp9Ohq6sL5eXlqKmpQU1NDWpra9HU1GQN/qFDh8LDwwODBw/G4MGDkZ6ejujoaMmF3vfff4/Vq1dj2rRpWLhwoeS2z1lIeX/PFjo5xJYtW84a5gDQ1NSEgoICBroIDAYDjh49ikOHDmHfvn3IyclBVVUVgD++aGVmZmLixIkYPHgwoqKiEBMTA41GY/ew0ev1qK6uRmlpKSorK3Ho0CFs3rwZq1evBvDH9Ko9AT9y5EhkZGTAy8vLrjXZW888C6tWrYJCocD8+fMZ6tQrbKFD2t/YnEVWVhb27NlzzsdHjx6N3bt3O7Ai99Xa2ors7Gxs2rQJJ06cQH5+PkaMGAGVSoXMzEwMHToUmZmZiImJcbpAaW5uRm5uLo4dO4bc3FyUlpbCw8MDdXV1GD16NCZMmIBx48YhJCRE7FL7bMOGDXjnnXcwd+5c3H777U73Gbg6Ke/v2UInh6iurr6kx+nSVFRU4KeffsLGjRuxe/dumM1mDBkyBNOmTcMrr7yCjIwMl5i5LCgoCOPHj8f48eMB/HF8v7i4GDt27MD27dvxzDPPwGKxID09HePHj8eECROQkpLiUqE4Y8YMmM1mvP/++1Aqlbj11lvFLolcBFvokPY3NmfBFrrjNTc347vvvsPatWtRWFiI7u5ujB07FlOnTsXVV1+NqKgosUu0udbWVmu479q1C52dnUhISMD111+PyZMnIz4+XuwSL9ratWuxevVq3HHHHZg7d67Y5UiGlPf3DHRI+wN2Flu2bMHVV199zse3bt2KSZMmObAiaRIEAfv27cMHH3yAiooKHDhwABMnTsScOXMwZcoU+Pn5iV2iwxgMBhw4cAD79u3D7t27cerUKYwYMQKzZ8/GxIkT4eHhIXaJF/T555/jk08+wYIFC3DjjTeKXY4kSHl/z0CHtD9gZ3LXXXfh/fffP+P+hQsX4r333hOhIuno6urChg0b8PrrryM/Px9JSUlYsGAB5s6di9DQULHLE53BYMC2bdvwzTff4NChQwgKCsL111+PWbNmOf1gzE8++QSff/457rrrLtxwww1il+PypLy/Z6BD2h+ws8nOzsYTTzxhPQ/92WefZcv8ErS2tuLdd9/FqlWrYLFYcMUVV+DOO+/EuHHjIJdzIsizKS4uxjfffIMff/wRbW1tGDVqFG677TZkZWU55XsmCALWrFmDr776CnfffTeuv/56sUtyaVLe3zPQIe0PmKSpuroa//73v/HBBx/AbDbjL3/5C/7rv/4LCQkJYpfmMrq7u7F161Zs2bIFu3btwrhx4zB9+nRMnDjR6YJdEAR8+OGH2LNnD+644w6MHTtW7JJclpT39wx0SPsDJmlpbGzEyy+/jI0bN6KlpQULFy7EPffcg7CwMLFLc2lHjhzBF198gW3btqF///64++67cfnllzvV6HhBEPDuu+9i06ZNeO655zBgwACxS3JJUt7fO9fXUCLCli1bkJWVhfj4eGRlZWHLli0wGAx4/fXXkZWVhQ0bNuCWW27BkSNHsHz5coa5DWRkZGDFihV4++234ePjg6VLl+Kuu+7C/v37xS7NSiaTYcGCBejfvz+ef/55NDQ0iF0SORm20CHtb2xisFgskMlkTtW6cRXnmh43KCgIBoMBixYtwn//938jODhYhOrcgyAI2L9/P1atWoW8vDwMGzYM999/v9O0iLVaLR5++GH4+PjghRdecPkZ8hxNyvt7Bjqk/QE7msViAQCnOwbpCi50at+7776Lu+66y4EVuTdBEPD777/j22+/xZ49ezB9+nT89a9/dYovU2VlZXj00UcxdOhQPPbYY/zy3AtS3t9zr0s2wzC/NMuXLz/v42c75Y/sRyaT4YorrsArr7yCRx99FHv27MF9992HDRs2WH/XxRIfH4+lS5diz549+Pzzz0WthZwH97xkEz0dPQzzvuP0uM5JLpfjhhtuwKeffoohQ4bgpZdewt/+9jdUVFSIWtfIkSNx++2348svv8Tvv/8uai3kHLj3pUtmsVisx82p7y40FasUp2p1JRqNBsuWLcNrr72Guro63HHHHfjkk09gNptFq2nWrFmYMGECXnvtNZw6dUq0Osg5MNDpkgiCwEFwNvL000+f9/Fnn33WQZXQ+YwYMQIff/wxZs+ejbfffhtLly5FcXGxKLXIZDLce++9SEhIwHPPPYfm5mZR6iDnwECnPhMEAWazGTKZjF3tNnDVVVdh4cKFZ31s4cKFnFHPiXh5eeG+++7Du+++C0EQsGjRInzzzTcQY4yxp6cn/v73vyM0NBSvvvqqqD0GJC7uhanPelrmCoVC7FIk47333sPWrVsxevRoxMXFYfTo0di6dSvnundSAwYMwEsvvYTrrrsOr776Kl588UXodDqH1xEYGIg777wTeXl5+Oyzzxy+fnIOPG0N0j6NwV7MZjMEQYBCoWBXex8IgsD3TWJ27tyJlStXQqlU4tlnn0VKSorDa1i3bh3WrFmD5cuXY+jQoQ5fvyuQ8v6eLXTqNYvFwjC/BD3vH0nL5ZdfjjfffBN+fn5YsmQJNm/e7PAaZs6ciXHjxuGdd94RpaeAxOW0gf7WW28hISEBXl5eGDVqFPbt23fO565evdo6KKvnxtmT7KNnRLtcLmeY91LPAEKAp/dJVUREBN58801MmjQJzz33HF599VUYjUaHrb9netiuri68/fbb/OLoZpxyr/Lll1/ioYcewpNPPolDhw4hIyMDU6ZMQX19/Tlf4+/vj5qaGuutrKzMgRW7h55BcAADqbcEQbB2s/O9kzaVSoXHHnsMDz30EDZv3oxnnnkGbW1tDlu/RqPB4sWLsWfPHuzYscNh6yXxOeWe5V//+hcWLVqEBQsWYODAgVi1ahXUajU++OCDc75GJpMhIiLCegsPD3dgxe7hz8fN6eL9+Tx99mq4B5lMhhkzZuCFF17AkSNHcO+996KmpsZh6x8zZgzGjh2Ld999F01NTQ5bL4nL6QLdYDDg4MGDmDx5svU+uVyOyZMnY/fu3ed8XXt7O+Lj4xEbG4sZM2YgLy/vnM/V6/XQ6XSn3ej8zGYzLBYLlEolQ6kXet43HqJwT0OGDMG///1vWCwW/PWvf8WJEycctu5FixZBpVLhrbfeYte7m3C6QG9sbITZbD6jhR0eHo7a2tqzviY1NRUffPABNmzYgE8++QQWiwVjxoxBZWXlWZ+/YsUKBAQEWG+xsbE23w4p6elqVygU7C7uBZ4JQAAQHR2Nt956C4MGDcIjjzyCI0eOOGS9vr6+uPfee3HkyBFRBuiR40li75yVlYU77rgDmZmZGD9+PL799luEhobi7bffPuvzly1bBq1Wa72JPSezszOZTDzfvJdMJhMsFgvDnAAAAQEBeOKJJ5CamorHH3/8vIN8bWno0KG4+uqrsWbNGtTV1TlknSQepwv0kJAQKBSKM3756urqEBERcVHL8PDwwNChQ885t7FKpYK/v/9pNzq7nmBSKpVil+Iy/vyeMcyph5eXF5599lmMGDEC//jHPxw2YG3evHmIi4vDe++9x653iXO6QPf09MTw4cORnZ1tvc9isSA7OxtZWVkXtQyz2Yzc3FxERkbaq0y3YLFYYDKZ2MrsBaPRCEEQGOZ0Vp6ennjyyScxduxYPP300/jtt9/svk4vLy/Mnj0bOTk52LNnj93XR+JxymbXQw89hHnz5mHEiBEYOXIkXn31VXR0dGDBggUAgDvuuAPR0dFYsWIFgD8uajF69GikpKSgtbUV//znP1FWVoa77rpLzM1weT1d7WydXxyj0Qiz2QxPT0+ONaBzUiqV+O///m8EBQXh+eeft1533Z5GjBiByy67DB9++CEyMzPh7e1t1/WROJxyrzN37ly8/PLLWL58OTIzM5GTk4ONGzdaB8qVl5efdgpIS0sLFi1ahLS0NEyfPh06nQ67du3CwIEDxdoEl9fTbezh4SF2KS7BZDLBbDbDw8ODYU4XJJfLsWTJEowbNw7PP/+8Q46p33nnnejs7MSXX35p93WRODiXO6Q9t29fCIIAvV4PpVLJ1vlFMJvNMBqNfL+o10wmE5566ikcOnQIL7zwAtLT0+26vg0bNuDTTz/FSy+9hISEBLuuy1lJeX/PpgSdwWg0sqv9IlksFhiNRigUCr5f1GtKpRL/+Mc/MGbMGDz77LMoLy+36/quvfZaDBgwAF999RUHyEkQA51O0zMRCrvaL8xisUCv10OhULjl+2U0GtHa2or6+nrU1taiuroadXV10Gq1vCZ3L3h6euKBBx6ARqPBE088gZaWFrutS6FQ4MYbb8TBgwexf/9+u62HxMEud0i7C6Y3BEFAd3c3FAoFPD09xS7HqQmCgK6uLshkMskPMOru7kZZWRkqKytRXl6Ozs5OVFVVwWw2w2AwwN/fH+3t7fDw8IDZbIZarUZ3dzd8fHwQEBCA6OhohIWFITo6GtHR0bxw0jnU19fjb3/7G0JDQ/Hyyy9DpVLZbV0rVqxAbW0tXnnlFbfrWZLy/p6BDml/wL1hMBhgNpvh5eXFU64uoLu7G2azGd7e3pIbBCcIAqqqqpCbm4sjR46gu7sbDQ0N8PHxQVRUFOLi4uDr62udabFnVL9MJoMgCOjs7ERnZyfa29vR0tJibcH3TLQTFRWF1NRUpKamIjQ0lL9rf3Ly5EksXboUI0aMwBNPPGG3363Kyko8/PDDuOOOOzB9+nS7rMNZSXl/z0CHtD/gi2WxWNDd3Q1PT0+3+8beW0ajEXq9Hl5eXpJ6r1pbW/H777/jxIkTKCwshLe3NzIyMjBgwAAkJSUhLCysz+FrsVjQ2NiIyspKnDhxAkVFRVAoFAgLC8OgQYOQkZHBlvv/2rNnDz766COMGTMGt99+u93W8+6772L37t1444034OPjY7f1OBsp7++lszeiS2I0GiGXyyUVUPbQc9zcw8NDMu9VeXk5Nm7ciP379yMsLAypqamYMmUKUlNTbbaNcrkcYWFhCAsLw7Bhw2AymVBcXIz8/Hxs2bIF27Ztw7Bhw3DZZZchKCjIJut0VaNHj0ZpaSk++ugj9O/fH6NGjbLLeubMmYPCwkL8/PPPuPHGG+2yDnIsttAh7W9sF8NsNkOv10OlUnG+9vPoOW4OAGq1WuRqLl1lZSU2btyI3bt3IyoqCuPGjcPll1/u8G1rb2/HoUOHkJ+fj87OTgwcOBBjx451q1bjfxIEAU8//TRyc3Pxxhtv2G3Wyy+++AKbNm3CG2+8AV9fX7usw9lIeX/PQIe0P+CL0dXVBblcbtdBOFKg1+thNBqhVqtd+rh5e3s7NmzYgC1btiA+Ph5Tp07FqFGjRN8mo9GIQ4cOYefOnbBYLBg/fjyGDRvmtl8yOzo68Le//Q1RUVH4xz/+YZeBqjqdDn/7298wffp03HTTTTZfvjOS8v6egQ5pf8AX0nM82NVDyt5MJhO6urrg5eXl0qeo7du3D6tXr0ZAQAAmTJiASZMmOd2hg66uLuzatQuFhYXw8fHBNddcg5CQELHLEkVJSQkefPBBTJ8+HYsXL7bLOj799FNkZ2e7zbF0Ke/vuQd3Y4IgwGAwcLrSCxAEAR0dHZDL5S4b5h0dHXjzzTfx2muvYdiwYXj88ccxZcoUpwtzAPD29sakSZMwe/ZsmEwmfPTRRzhw4IBbToSSmJiIBQsWYMOGDTh8+LBd1nHttdfCZDLh559/tsvyyXG4F3djPVcGc9WQcpTu7m4AcNnzzcvKyrBs2TJUVlbi3nvvxV133YWAgACxy7qg8PBwzJs3D0OHDsWhQ4fw008/wWQyiV2Ww11//fXIzMzEv/71L7S1tdl8+QEBAZg8eTJ+/vlndHZ22nz55DgMdDclCAKMRiNb5xfQM2DQy8vLJd+nffv24fnnn0dQUBCWLl2KMWPGiF1SryiVSlx55ZWYOHEiioqKsHbtWrcLHZlMhqVLl8JoNOL111+3S0/FddddB6PRiE2bNtl82eQ4rreHIpvoaZ1zRrjz6+zshEKhcMkBg5s2bcKrr76KtLQ0/P3vf0doaKjYJfVZv379MHfuXOh0Onz99ddobW0VuySHCgoKwn333Yeqqiq7XEM9MDAQV155JX788UfrmRzkehjobujPrXPO0nVuer3eOpWpq/n+++/x3nvvYcaMGbj//vsl8cUtPDwct956Kzw8PLBu3Tq7dD87s7FjxyI+Ph7vvPMOdDqdzZd//fXXIzAwEL/++qvNl02OwUB3Q0ajEQAksZO3l56Z81zx3Px169Zh9erV+Mtf/oK5c+dK6kubn58frrvuOshkMqxbt87tut8XL14Ms9mMDz74wObLDgoKQnJyMn766SdeXMdFMdDdzJ+vdS6lHb2tdXV1QRAEl5uOdMuWLfjxxx9x0003YcaMGWKXYxe+vr644YYbrMd8e76guoPAwEAsXLgQ2dnZOHr0qM2XP336dDQ1NfFKbC6Kge5mDAYDj51fgMlkgl6vh7e3t0t96cnJycEHH3yA0aNHS36SkICAAFx//fVobGzE9u3bxS7HoSZPnozLL78c77zzjs1b0nFxcRg+fDj27dtn0+WSYzDQ3YzBYICnp6dLBZWjdXZ2utzMeTU1NXjxxRcxbNgw3HnnnW7x+YaGhmLixIk4efIkjh07JnY5DiOTyXDTTTehsrLSLqPSx4wZg/3796Ompsbmyyb7YqC7EbbOL8xkMsFgMLjUOecGgwHvvfceAgICcO+997rk6XV9lZKSgiFDhuD3339HY2Oj2OU4TFJSEq688kp89tln6OjosOmyR4wYAV9fX7uMpif7cp+/fILBYIBSqXSrHX5vueJpal988QUOHz6Mxx57zCVH5F+qMWPGIDIyEtu3b4fFYhG7HIe5/fbbYTQa8dVXX9l0uUqlEmPGjMGOHTs4OM7FcM/uJkwmEywWi0sFlaP1tM5dKRSPHz+Or776CnfeeScSExPFLkcUcrkcl19+OVpaWtyq6z0wMBCzZ8/G999/b/Pu8XHjxkGr1dpl4B3ZDwPdTXR3d0OhULjcKViO5Gqtc6PRiHfeeQepqamYPn262OWIKiQkBIMGDcKBAwfQ3t4udjkOM3PmTKSmpmLt2rU2XW58fDzi4+PZ7e5iGOhuwGKxwGQycc728zCZTOju7nap1vn69etRWVmJ++67j4dR8MexXz8/P7dqVXp6emLixInYvn07ysvLbbrs8ePH4/Dhw3aZxIbsg3sBN2AwGCCTyRjo5+FqI9vb2tqwefNmTJs2zW272v+Tp6cnBg0ahMLCQreaRe7KK69ESEgIvvzyS5suNysrCzKZDDt37rTpcsl+GOhuQK/X81S187BYLNZrwruKr7/+GnV1dZg9e7bYpTiV/v37Q6VSITc3V+xSHEapVGLOnDk4evQoKioqbLZcX19fjBgxAr/++qtbXrrWFTHQJY4XYbmwnsujusqscG1tbTh06BBmzZoFjUYjdjlORalUYvDgwSgpKXGraWEnTpwIb29vfPfddzZd7rhx41BVVYXi4mKbLpfsg4EucT2nqnEw3Ll1dHTA09PTZY5Db926FeXl5Zg5c6bYpTilAQMGwMPDw61CSKlUYtq0adixYwe0Wq3Nljto0CAEBwdjx44dNlsm2Y9r7MGoTywWC4xGI1vn5+FqV1QTBAFr167F2LFj2To/B09PT0RGRqKoqEjsUhzqqquuglwut+nscXK5HBMmTMCBAwdgMplstlyyDwa6hHEw3IV1dXVBqVS6zHt04MAB1NXV4ZprrhG7FKeWlJQErVaL5uZmsUtxGF9fX0ycOBE///yzTS9Yk5mZCQ8PD5w8edJmyyT7YKBLmF6v5zXPz6NnMJwrTfOanZ2NYcOGIS0tTexSnFpUVBT8/PxQWVkpdikOdc0110Cn09m0izw+Ph6CILjV6YCuioEuUSaTCWazmd3t59Hd3Q2z2ewygW40GlFaWophw4bxS9oFyGQyREZGoqqqSuxSHCoqKgojRozA9u3bbTYyXSaTIT093a3OHHBVDHSJ0uv1kMvlUCqVYpfitLq6ulxqMNzRo0eRn5+Pyy67TOxSXEJYWBhaWlpgMBjELsWhpk2bhuPHj+PUqVM2W2Z6ejqqqqrc6hCGK3KNPRn1Ws9lUunsXLG7/dChQwgODkZycrLYpbiEsLAwAEB9fb3IlTjWkCFDEBISgm3bttlsmYMGDYJMJmMr3ckx0CWI555fWM+5564U6Lt378aoUaPY3X6RfH19odFo0NLSInYpDiWXyzFx4kTs27cPer3eJsv08fFBcnIyA93JMdAlyGAwsLv9Arq7u12qu12v16O1tRWDBg0SuxSX4uvra9Pzsl3FFVdcgc7OThw+fNhmy0xPT8fx48d5SVUn5hp7M+qVnqle6ewEQUB3d7fLzAwHACUlJairq0NSUpLYpbgUPz8/t5rXvUdUVBRiY2Oxd+9emy1zyJAh6OrqsumxebItBrrE9Fz33FXOqxZDd3c3LBaLSwV6aWkp/P39Gei95Ofnh46ODreci3z06NE4dOiQzc5Jj4+Ph5+fH7vdnRgDXWI4mcyF9Vwb3pUOSZSWlkKtVrvUlxBnoFaroVQqrWMm3MmoUaPQ3d1ts/PHZTIZBg8ezPPRnZjTBvpbb72FhIQEeHl5YdSoUdi3b995n7927VoMGDAAXl5eSE9Px08//eSgSp0LR7dfWHd3t8tcJrVHdXU1QkNDxS7jDBaLBZ9//rnYZZyTSqWyToHsbqKjoxEdHY09e/bYbJnp6emoqKhAa2urzZZJtuOUgf7ll1/ioYcewpNPPolDhw4hIyMDU6ZMOefpJ7t27cItt9yChQsX4vDhw5g5cyZmzpyJY8eOObhycVksFphMJrbOz6Nn5+5qgd7S0oLAwECxyzjDypUrceutt+KVV14Ru5Sz6umFcdeBXKNGjcLBgwdtNg/74MGDIZPJ3G7f6iqcMtD/9a9/YdGiRViwYAEGDhyIVatWQa1W44MPPjjr81977TVMnToVjzzyCNLS0vDMM89g2LBhePPNNx1cubh6WiFsoZ9bzyQjrhboCoUC4eHhYpdxhvfffx8Azvm3Kbaeqwy6a6CPHj0aHR0dyMvLs8ny/Pz8kJ6ejpKSEpssj2zL6QLdYDDg4MGDmDx5svU+uVyOyZMnY/fu3Wd9ze7du097PgBMmTLlnM+Xqp5LpbrKqVhicNUZ9Do6Opzm+Pmdd96JadOmYdq0aSgoKAAA5OfnW++78847Ra7w/8hkMigUCrccFAcAcXFxSE5OtunpawkJCSgtLbXZ8sh2nG6v1tjYCLPZfEZrJDw83Lrz+E+1tbVnfX5tbe1Zn6/X60+bcEGn011i1c7BFbuSHU2v17vke1RXV+cUl69sb2/H6tWrzwhIQRCwceNGAH+E6Ouvvw5fX18xSjyNxWKBQqGwttTdjUwmQ1JSkk0HskVGRuKnn35CZ2eny1x22F24ZVNuxYoVCAgIsN5iY2PFLumS9Zyuxu72cxMEwWUDXS6XO0W3sa+vL/bt24eAgICzPh4QEIADBw44RZgDPI0T+GMgm0wms9mMeT37S3e7kp0rcLpADwkJgUKhQF1d3Wn319XVISIi4qyviYiI6NXzly1bBq1Wa71VVFTYpngR8XS1C+uZEtcVAz0mJsZpPtsRI0acs/ertrYWw4YNc3BF59YzZsJZ3jsx9O/fH7W1tTabECYyMhJKpRLl5eU2WR7ZjtMFuqenJ4YPH47s7GzrfRaLBdnZ2cjKyjrra7Kysk57PgBs2bLlnM9XqVTw9/c/7ebqeo6f07np9XqXvaSsWq1GV1eX2GVYffLJJ2e9/9NPP3VwJednMBigUChc8jO3lcDAQAQFBdks0OVyOWJiYiTREJIapwt0AHjooYfw7rvv4qOPPkJ+fj6WLFmCjo4OLFiwAABwxx13YNmyZdbn33///di4cSNeeeUVFBQU4P/9v/+HAwcO4L777hNrExzOaDS6dSvkYhiNRiiVSpe8uInBYEBRUZHYZVitWbMGwB/dr7t27UJMTAwA4KOPPhKzrDN0dHTAx8fH7QeKpqSk2PT3JzY2loHuhJyySTd37lw0NDRg+fLlqK2tRWZmJjZu3Ggd+FZeXn7aH+iYMWPw2Wef4YknnsDf//539OvXD+vXr8fgwYPF2gSHMplMEASBgX4BPYHuisLDw3HgwAGxy7C69957MXr0aLzwwguQy+UoKyvD448/juHDh4td2mk4cOsPycnJ+Pbbb2GxWGzy5SYuLg47d+6EyWRy2b8pKXLaT+K+++47Zwt7+/btZ9w3Z84czJkzx85VOaee4+f8wzo/o9HoNKd+9VZCQgLy8/MhCIJT9DDMnTsXc+fOtf4sl8vx0ksviVjR2bW1tTnlDHuOlpycDL1ej8rKSsTFxV3y8mJjY2GxWFBdXW2T5ZFtuHc/lES4cleyI7nyYYnY2Fi0tbWdczAanclkMqGrq+ucI/LdSWJiImQymc263WNiYiCTyTgwzskw0CXAaDS67Xm2F8tsNkMQBJftxUhNTcWJEyc45WYvtLS0QKlUOuWUuY7m5eWF2NhYmw2MU6lUCAsL43F0J8NAd3GCIHD+9ovQMy2uq75PoaGhCA8P56Ure6GpqQmenp48hv6/kpOTbdrDw4FxzoeB7uJ6Zg9z1Zano7h6oAPApEmTuAPthdbWVoSEhIhdhtNITExEUVGRzWYcjIuLQ0VFhdtOq+uMGOgujoF+cXpG47ryOIOBAwdiy5YtvHTlRejo6EB7ezsHxP1JeHg41Go1mpubbbK8mJgY+Pr62mx5dOkY6C7OZDJBoVC4dFA5ghSuh33FFVfAZDJh27ZtYpfi9Orq6qBSqRAUFCR2KU4jODgYHR0dNgvg8PBwNDc3o6GhwSbLo0vHQHdxrjxy25F6vvi4spCQEAwdOhSbN28WuxSnJggCampqEBYW5vKfuS31DA601ZzuQUFB0Gg07DFyIgx0F8eJHS6OrSbUENtNN92E1tZWNDU1iV2K02pqaoLFYkFkZKTYpTgVLy8veHt726yF3nMIi7+LzsP193BuzGKxwGKxMNAvgsVikcRhiYkTJyI3NxdffPGF2KU4rZqaGqjVaklco8HWgoKCbNZCBwB/f3/JXH5aChjoLqxnQBy73C9MEARJtNA1Gg1mzpyJTz75RBLjAmxNp9OhpaUF8fHxYpfilAIDA206iM3f3x9ardZmy6NL4/p7ODdmNBohk8l4nPAiSKXLHQDmz58PmUyGn376SexSnE5paSl8fHx4uto5BAUF2TzQ2UJ3HtLYw7kpKQz0chQpBXq/fv0wduxY/POf/7Re75v+GOyl0+mQkJAgdilOy9Zd7gEBAQx0JyKNPZyb4pSvF09KgQ4AixcvRnV1tdNdrlQsFosFpaWlCAwMRHBwsNjlOK3AwEBotVqYzWabLM/Pzw86nY6TyzgJ6ezh3JDZbOaAuIvkLFcps5WUlBTccssteP3111FfXy92OaKrqqpCd3c3EhMTxS7FqWk0GiiVSpu1qv39/WE0GtHd3W2T5dGlYaC7KEEQYDab2UK/CIIgwGKxiF2GzT344IPIyMjA008/LXYpours7ERNTQ2io6M5b/sFqNVqeHp6oquryybL67mSHbvdnQMD3UWZzWZYLBYG+kXoaZlLrVswJCQEs2bNwrp16/D999+LXY4oLBYLioqK4OXlhZiYGLHLcXpKpRJ6vd5mX3B7Tg1koDsHBrqL6vmDlNJxYXuSaiv9hhtuwHXXXYfHHnsM1dXVYpfjcCUlJdDr9ejfvz//Fi6Crb/cMtCdC/8CXBQDvXfkcrkkA10mk+GFF17AsGHDsHDhQrc6lllbW4vW1lYkJSXBy8tL7HJcQs/+wlaB7uXlhYiICJt14dOlYRq4KAZ678jlcsl1uffQaDR4+OGHcfToUdx3332S/OLyn5qbm1FZWYmIiAhegKUXbN1Cl8lk6OzsREdHh02WR5eGaeCieqYyldLIbXuSagu9R2ZmJt5++22sW7cOL774otjl2JVOp0NZWRlCQkIQHR0tdjkupWd/Ycu/BZVKBb1eb7PlUd8x0F2U1M6rtjepBzoAXHvttXjhhRfwzTff4KWXXpJkj0RPmAcEBHB61z6wxwBRT09PTnDkJHgSs4tioPeOOwQ6ACxatAharRbPPPMMurq6sHz5csn04rS2tqK8vBy+vr5ITEyUzHY5Us8+w5Z/C0FBQTzbxkkw0F0UA713ZDKZ9WI2Uvfwww/D29sbTz/9NBQKBR599FF4enqKXdYlqa+vR21tLQIDAxETE8Mw7yN7tNA7OzvdajCmM2OguygGeu8oFAq32unce++9iIyMxKJFi7B9+3Z88skniIiIELusXrNYLKisrIROp0NERATCwsLELsmlyWQyaDQascsgO2EiuCgGeu8olUq3aaH3mDVrFn788UeUlJRgzJgx+O233wAAW7ZsQVZWFuLj45GVlYUtW7aIXOnZdXZ2oqioCF1dXYiLi2OY24DRaIROp+MllyWKLXQXxUDvHaVSCaPRKLk53S9k9OjR2LVrF55++mksXrwYMpkMBQUF1sfLy8tx9dVXY+HChXjvvfdErPT/WCwWNDY2orm5GV5eXoiOjmYA2Uh3dzfCw8N53r5EMRFcFAO9dzw9PWGxWGA0GsUuxeHCw8Px+uuv46qrrjotzP/s/fffR3Z2toMrO5NOp0NJSQlaW1sRFhaGhIQEhrkNtbW1oaGhwTrDG0nLORNh3rx51i46cj4M9N5RqVQA4Lan1ygUChw4cOC8z3niiSccVM2ZOjo6UF5ejtraWqjVaiQlJXHCGDtobW2FUqmEt7e3zZbpbr1ezuyciaDVajF58mT069cPzz//PKqqqhxZF52HxWKxTixDF8fDwwMymcytJ8C40Fzvjp4L3mKxQKfToaKiArW1tVAoFIiNjUVkZCQvC2wnWq0WGo2G+w6JOmegr1+/HlVVVViyZAm+/PJLJCQkYNq0afj666/dstvSmfSccsI/yosnk8ng4eHhti10AIiKirrg44Ig2HVCGkEQ0NXVhcbGRlRUVKC5uRmenp6IiYlBdHS0TVuOdKbW1lbrJU9Jes7bZxsaGoqHHnoIR44cwd69e5GSkoLbb78dUVFRePDBB3Hy5ElH1Un/wR0mSbE1d5+i8kLXTX/mmWcgCAJMJhMMBgNMJpP1Mr2XwmAwoL29HU1NTaiurkZDQwOMRiM0Gg1iYmIQHh5uPSRC9qXVahnoEnZRB2FramqwZcsWbNmyBQqFAtOnT0dubi4GDhyIlStX2rtG+g9Svb63vXl6erp1oF911VVYuHDhWR9buHAhJk+eDLlcDqVSCYVCYQ13vV5vnTyku7sber0eer0eBoPBetPr9eju7kZnZyfa2trQ2tqKpqYm1NbWorGxEW1tbRAEAf7+/oiMjERkZCQCAgLYte5g9gh0pVLJUfNO4px/TUajEd999x0+/PBDbN68GUOGDMEDDzyAW2+91TpCct26dbjzzjvx4IMPOqxgYqD3lZeXFxobG916QOF7772HW265BU888QSqq6sRFRWFZ599FpMmTbI+RyaTQaFQWKfz7BmzYbFYYDabra32nmvMn62bXqFQwNPTE97e3vDw8IBSqeQhIidgj0Bva2vj1K9O4pyBHhkZCYvFgltuuQX79u1DZmbmGc+ZOHEiZx0SAQO9b7y9vSEIArq7u6FWq8UuRzSTJk06LcAvRC6Xn/MLEMdzuA6DwQAfHx8EBwfbdLl6vZ6HTJzEOQN95cqVmDNnznm7UjQaDUpKSuxSGJ2fTCZjoPdSz+9yZ2enWwe6LTHIXUd9fT0aGxsREhJi0+Uy0J3HOfsdb7/9dh4XcWIM9N6Ty+Xw8vJCR0eH2KUQOVxtbS0A2HRO/57JmpgVzsE9DyRKAAO9b3x9fdHe3i52GUQOV1NTA39/f5v2TnV2dkKj0bDHy0kw0F0UA71vfH19odfrOZcCuZ3q6mokJyfbdJnt7e3Q6XTw9fW16XKpbxjoLoqB3jc+Pj4AwFY6uZ2ysjKbX0JXp9MBAOeGdxJOF+jNzc247bbb4O/vD41Gg4ULF15w5zthwgTIZLLTbvfcc4+DKhYHA71vPDw8oFKpGOjkVlpbW6HVahEfH2/T5TLQnYvTzepw2223WSeyMRqNWLBgARYvXozPPvvsvK9btGjRaTNhSf2YDgO97/z8/NDW1iZ2GUQOU1ZWBgB2CXQvLy9eEc9JOFWg5+fnY+PGjdi/fz9GjBgBAHjjjTcwffp0vPzyy+edi1qtVtu8O8mZMdD7ztfXF/X19TAYDPD09BS7HCK7Ky0tRUBAgM3nDdHpdGydOxGn6nLfvXs3NBqNNcwBWKej3Lt373lf++mnnyIkJASDBw/GsmXL0NnZae9yRcVA77uAgADIZDJotVqxSyFyiNLSUiQkJNh8uQx05+JULfTa2lqEhYWddp9SqURQUJD1HMqzufXWWxEfH4+oqCgcPXoUjz32GAoLC/Htt9+e9fk9c1H36DkO5EoY6H2nUCjg4+MDrVaL0NBQscshsiuTyYTq6mpMmzbN5stua2tjoDsRhwT6448/jhdffPG8z8nPz+/z8hcvXmz9f3p6OiIjIzFp0iQUFRWd9TSNFStW4Kmnnurz+pyBTCaD2WwWuwyXpdFoUFNT49bzupN7KCkpQWdnJ1JSUmy+bJ1Oh+joaJsvl/rGIYG+dOlSzJ8//7zPSUpKQkREBOrr60+732Qyobm5uVfHx0eNGgUAOHXq1FkDfdmyZXjooYesP+t0OsTGxl708p2FO1/b+1JpNBqUl5ejtbUVQUFBYpdDZDf5+fnw8/OzefAKgoCOjg6bTyVLfeeQQA8NDb2ors2srCy0trbi4MGDGD58OABg27ZtsFgs1pC+GDk5OQD+uMDM2ahUKpefe1ipVMJkMoldhsvy8vKCj48PmpubGegkafn5+RgwYIDN593X6XTo6uri348Tcaq+xrS0NEydOhWLFi3Cvn37sHPnTtx33324+eabrSPcq6qqMGDAAOzbtw8AUFRUhGeeeQYHDx5EaWkpvvvuO9xxxx0YN24chgwZIubm2JWHh4f1cpbUN0FBQWhtbeV7SJLV1taGyspKDBgwwObLbmhoAAC20J2IUwU68Mdo9QEDBmDSpEmYPn06xo4di3feecf6uNFoRGFhoXUUu6enJ7Zu3Yqrr74aAwYMwNKlSzF79mx8//33Ym2CQ/Sc98lWet8FBQXBYrGgtbVV7FKI7KKgoAAhISF2C3SZTGbzy7FS3znVKHfgj53s+SaRSUhIOG10d2xsLH799VdHlOZUlMo/Pjqj0ejyhw/EolKp4Ovri8bGRu6USJKOHDkCf39/u4xEb2xsRFBQEBQKhc2XTX3jdC10ujgKhQJyuZwXGblEISEhaGlp4QBDkhy9Xo/8/HxkZmbaZfkNDQ087dPJMNBdmIeHB7vcL1FwcDDkcrn1eCCRVBw/fhwmkwkZGRl2WX5dXd15Z+8kx2OguzClUskW+iVSKBQICQlBfX09J+ohScnNzcXAgQPtMgq9q6sLzc3N5zyTiMTBQHdhHh4eDHQbCAsLg16v5+A4kgytVosjR45g8ODBdll+dXU1ACAmJsYuy6e+YaC7MHa524avry/UarV1J0Xk6vbu3QulUmmdz8PWKisr4eHhwVPWnAwD3YV5eHhAEASGug1ERUVBq9Wio6ND7FKILonFYsGePXswdOhQeHl52WUd1dXViIqK4rTJToafhgv786lrdGmCg4OhUqnYSieXd+LECbS0tGDMmDF2W0dlZSXncHdCDHQX1jO5DAP90slkMkRFRaGxsfG0K/ERuZpdu3YhKirKbtenMBgMaGhoYKA7IQa6C5PJZJzT3YbCwsKgUCjYSieXpdVqkZeXhzFjxth87vYeNTU1EASBge6EGOguTqlUskVpIwqFApGRkaipqeFEM+SSDhw4AJVKZbfBcABQXl6OkJAQhIeH220d1DcMdBfn6enJQLehyMhIyOVyVFRUiF0KUa+YTCbs2LEDw4cPt9tgOOCP66trNBrrGB5yHgx0F6dSqWAwGDgpio0olUrExMSgtraWX5TIpezduxdeXl4YP3683dYhCAJKSkqQlJRkt3VQ3zHQXZyXlxcsFgu6urrELkUyIiMjoVQqUVZWJnYpRBdFr9dj69atSEhIsOu54XV1dejs7GSgOykGuotTqVSQy+UMdBtSKBSIjY1FbW0t2tvbxS6H6IJ27NiBrq4uTJkyxa7rKSkpgUKhQFxcnF3XQ33DQJcAb29v6/XhyTYiIyOhVqtRVFQkdilE59XR0YHt27djzJgxCAwMtOu6iouLERMTYz1llpwLA10C1Go1urq6eBzdhmQyGVJSUqDVanklNnJq27ZtAwBMmjTJrusRBAGNjY3o37+/XddDfcdAlwC1Wg2LxcJBXDam0WgQHByM4uJiWCwWscshOkNLSwt27tyJ8ePHw8fHx67rqqqqQm1tLZKTk+26Huo7BroEeHl5QSaTsdvdDpKSkmA2mzlAjpzS5s2b4e3tjXHjxtl9XQUFBfDy8kJ8fLzd10V9w0CXAJlMxuPoduLt7Y2oqCiUl5dzgBw5lbq6Ohw8eBCTJ0+GSqWy+/ry8/ORmprKC7I4MX4yEtFzHJ1sLy4uDmq1GoWFhRynQE5j06ZNCAoKwujRo+2+Lp1Oh+rqagwYMMDu66K+Y6BLhLe3N8xmM4+j24FcLkdqaira2tpQWVkpdjlEOH78OGpqanDttddCoVDYfX2FhYWQyWQcEOfkGOgS4e3tDZlMxla6nfj7+yM2NhbFxcW8ZjqJqrOzE+vWrUNERAQGDRrkkHUWFBQgPj4earXaIeujvmGgS4RcLoeXlxePo9tRYmIivLy8cOzYMY56J9Fs2LABZrMZs2bNstsV1f7MZDLh5MmT7G53AQx0CVGr1Qx0O5LL5Rg0aBC6urpw6tQpscshN5Sbm4ujR49ixowZ8PPzc8g6T548CT8/P6SlpTlkfdR3DHQJUavVMBgM6O7uFrsUyfL19UVKSgoqKyvR1NQkdjnkRtrb27F+/XoMHjwYQ4YMcdh6jx49CpVKhbCwMIetk/qGgS4harUacrkcbW1tYpciaTExMQgODsbx48c5CJEcQhAErFu3DjKZDDNnznRIVzsAGAwG5OfnO/QLBPUdA11CZDIZfH19eb60A6SlpUEulyM3N5fH08nucnJycPz4cdxwww12nxHuz/Lz82E0GpGRkeGwdVLfMdAlxs/PD11dXTCZTGKXImmenp4YPHgwtFotTp48KXY5JGGtra344YcfkJmZ6bBR7T2OHj2KuLg4u1/0hWyDgS4xvr6+AMBudwcICAhAamoqKioqUFVVJXY5JEFmsxlffvklAgMDcd111zl03Z2dnThx4gS7210IA11iFAoF1Go1WltbxS7FLcTExCAmJgbHjx9Hc3Oz2OWQxPz888+oqqrCjBkzHH4OeF5eHnx8fJCenu7Q9VLfMdAlSKPRoKOjA0ajUexS3EJqaiqCgoKQk5PD8QtkMwcPHkR+fj6mT5+O2NhYh65bEATs378fsbGx1l4/cn4MdAny9/eHXC5nK91BZDIZMjIy4O3tjUOHDvG0QbpkxcXF+O6775CamopRo0Y5fP3V1dWoqanBZZdd5vB1U98x0CVILpfDz8+Pge5ASqUSw4YNAwAcPnyYgxKpz+rr6/H5558jKSkJ1157rcNOUfuzffv2QaPRICUlxeHrpr5joEuURqOBXq9na9GBVCoVhg0bhq6uLhw+fJins1Gvtbe34+OPP0ZAQABuvvlmUS5V2t3djdzcXIwYMYKXSnUx/LQkytfXF0qlkq10B/P19cXQoUOh0+mQk5PDy63SRTMajfj0009hMplw++23O+Qa52eTk5MDs9mM4cOHi7J+6jsGukTJZDIEBASgtbWVoeJggYGBGDJkCBoaGnDkyBG+/3RBJpMJX331FTo7O3H77bcjICBAlDp6BsMNHDiQg+FcEANdwjQaDUwmEy/3KYLQ0FAMHToUDQ0NOHToELvf6ZzMZjO++uorFBcX4/rrr0dUVJRotZSXl6O+vp6D4VwUA13CvL294enpyfOjRRIWFoaMjAw0NDRg//79HChHZzCbzVi7di1OnTqFm2++GcnJyaLWc+DAAcTHxyMxMVHUOqhvGOgSFxgYCK1WyzARSVhYGEaOHAmtVou9e/fCYDCIXRI5CYvFgm+//RYnTpzA3Llz0a9fP1HraW5uRm5uLjIyMkQZWU+XzqkC/bnnnsOYMWOgVquh0Wgu6jWCIGD58uWIjIyEt7c3Jk+ezLm1/yQoKAgymYytdBEFBQVh1KhR6Orqwp49e3jmAcFkMmHt2rUoKyvDnDlzkJqaKnZJ2LVrF9RqNTIzM8UuhfrIqQLdYDBgzpw5WLJkyUW/5qWXXsLrr7+OVatWYe/evfDx8cGUKVO40/xfCoUCGo0GTU1NHJwlooCAAGRlZcFsNmP37t0c1+DG9Ho9PvvsM5w8eRLXXnst0tLSxC4J7e3tOHz4MEaNGgUPDw+xy6E+cqpAf+qpp/Dggw9e9NzBgiDg1VdfxRNPPIEZM2ZgyJAhWLNmDaqrq7F+/Xr7FutCQkJCYDQaodVqxS7Frfn4+CArKwsKhQJ79+5lr4kbam9vx0cffYSqqir85S9/wYABA8QuCQCwd+9eyOVyjBw5UuxS6BI4VaD3VklJCWprazF58mTrfQEBARg1ahR27959ztfp9XrodLrTblLm5eUFX19fNDY2il2K2/Py8kJWVha8vLywZ88elJeXi10SOUhtbS3ef/99CIKA+fPnIyEhQeySAPzRM7pv3z4MHz4c3t7eYpdDl8ClA722thYAEB4eftr94eHh1sfOZsWKFQgICLDeHH3hAzGEhISgs7MTnZ2dYpfi9jw8PDB69GjExsbi8OHD1ok8SLqOHTuGDz74AGq1GrfccgsiIyPFLslq3759UKvVyMrKErsUukR2D/THH38cMpnsvLeCggJ7l3GaZcuWQavVWm8VFRUOXb8Y/Pz84OnpiaamJrFLIfwx3356ejqGDRuGqqoq/Pbbb7xSmwQJgoCtW7fi22+/RVpaGhYsWAB/f3+xy7Lq7u7G77//jpSUFNEmsyHbUdp7BUuXLsX8+fPP+5ykpKQ+LTsiIgIAUFdXd9o33rq6uvOO1FSpVKJNqygWmUyGkJAQ1NTUICIiggNfnERsbCw0Gg3279+PX3/9FRkZGYiJiRG7LLKBrq4ufPvttyguLsbVV1+N0aNHi13SGXbu3Amz2Yxx48aJXQrZgN0DPTQ0FKGhoXZZdmJiIiIiIpCdnW0NcJ1Oh7179/ZqpLy7CAoKQk1NDerr6xEdHS12OfS//Pz8MG7cOBw9ehSHDh1CY2Mj0tPToVAoxC6N+qi+vh5ffvkluru7cdttt/W50WJP7e3t2LNnD0aNGgU/Pz+xyyEbcKpj6OXl5cjJyUF5eTnMZjNycnKQk5NzWlfkgAEDsG7dOgB/tDofeOABPPvss/juu++Qm5uLO+64A1FRUZg5c6ZIW+G85HI5QkND0djYCKPRKHY59Cc9l1/NzMy0dsG3tbWJXRb1QU5ODj799FN4e3vjrrvucsowB4AdO3ZAoVDg8ssvF7sUshG7t9B7Y/ny5fjoo4+sPw8dOhQA8Msvv2DChAkAgMLCwtNOv3r00UfR0dGBxYsXo7W1FWPHjsXGjRvh5eXl0NpdRWhoKBoaGthKd1JxcXEIDAzEoUOHsH37dqSmpiIlJYWXsXQBLS0t+Pnnn1FVVYVBgwbhqquuctpDW62trThw4AAmTJjAke0SIhM42wh0Oh0CAgKg1WqdasCKvdTW1qK+vh4DBw6EUulU3+nof5nNZuTn5+PEiRPw9/dHRkaG3Q5d0aWxWCzYt28ffvvtN/j4+GD69OlOPxf6+vXrcfLkSdx///3w9PQUuxyHkvL+nntzNxQaGor6+nrU1dWxle6kFAoFBg8ejNjYWOTk5GDHjh2IiYlBeno6W1ROpLa2Fj/++CPq6+sxcuRIjBs3zmlb5T16Lus7depUtwtzqWOguyGFQoGwsDDU1NQgNDSUf9ROLCAgAOPGjUN5eTmOHTuGLVu2IC0tDcnJyeyGF5HRaMSOHTuwd+9ehIaGYv78+U51bvn5bN26FTExMRg+fLjYpZCNMdDdVM+x9KqqKqfvHnR3MpkM8fHxiIqKwvHjx3Hs2DGUlpYiMzOT3fAiKCkpwc8//4y2tjaMHz8eo0ePdpkvVydOnMDJkycxZ84cHm6TIH6ibkqhUCAqKgplZWUICwuDj4+P2CXRBXh4eCAjIwMJCQmndcOnpaXxtCMHaGhowM6dO1FRUYHAwEDcfPPNCAoKErusi2YymbBp0yYkJSU5xQVhyPYY6G4sODgYDQ0NqKiocJqLRNCFBQQEYPz48SgvL0dhYSF+/vlnxMbGYsCAAQgMDBS7PMmpr6/Hrl27cOLECYSHh2PSpEkYOHCg2GX12p49e6DVanHLLbeIXQrZCQPdzcXExODEiRNobm52qdYG/XGKW3R0NEpLS1FQUIAtW7YgIiICAwYMQFhYmNjluby6ujrs2rULJ0+ehEajwbRp0zBo0CCX6V7/M51Ohx07dmDkyJEICQkRuxyyEwa6m/P19YVGo0FVVRU0Go1L7qzcmUKhQHJyMpKSklBRUYGCggJs374dwcHBSEtLQ2RkJGQymdhlupTa2lrs2rULp06dQmBgIKZPn46BAwe69N/G5s2bERwcjPHjx4tdCtkRA50QExODvLy8M+bEJ9chk8kQFxeHuLg41NTUID8/H7///jsCAgLQv39/xMfHu3Qg2ZvFYkFxcTEOHz6M0tJSBAYG4pprrkFaWprLv295eXkoKCjAjTfe6HbXsHA3DHSCp6cnwsPDUVdXh+DgYJ7G5uIiIyMRGRmJxsZG5OfnW6dQjouLQ0JCAoKDg8Uu0Wm0tbXh2LFjOHr0KNra2hAZGYnrr78e/fv3l0TPRkdHBzZu3IiBAwdynIwbYKATgD+uId/U1ITq6mokJCSIXQ7ZQEhICK644gq0tbWhqKgIxcXFKCwshK+vL+Lj45GQkOCWl8zU6/U4ceIECgoKUFFRgYCAACQkJCAzMxPh4eFil2dTGzduhEwmw9SpU8UuhRyAgU4ATj+NLTQ0lKexSYifnx8yMzORkZGBuro6lJWV4eTJk8jLy4NGo0F8fDzi4+Ph6+srdql2093djdLSUpw8eRLFxcUwm82Ii4vDlClT0K9fP0n2SuXn5yM/Px+zZs2CWq0WuxxyAM7lDmnP7dsbgiDgxIkTMJvNSEtLk0SXI52dxWJBTU0NSktLUVVVBZlMBm9vb0RFRSEqKgqhoaEufflWQRBQX1+P0tJSlJaWora2FoIgICoqCsnJyUhNTZX0F5jOzk6sWrUKcXFxuPHGG8Uux6lIeX/PFjpZyWQyxMTEID8/H3V1dYiIiBC7JLITuVyO6OhoREdHw2Qyobq6GlVVVSgpKcHx48ehVCqh0WgQGhqKsLAwhIaGOvUVDAVBQHNzM2pqalBbW4vi4mJ0dnbC09MTcXFxmDRpEhISEiQd4n+2adMmCIKAadOmiV0KORADnU7j4+OD8PBw1NTUQKPROPVOnGxDqVRaR8gDf1wGtOeKfCUlJcjLywMA+Pv7Izg4GBqNxnrz9fV1aE+OIAhoa2tDS0sLmpubrbeOjg7odDrIZDJERUVh4MCBSEhIQFRUlMuPUu+twsJC5OXlYebMmTx05mYY6HSGmJgYtLS04NSpUxg0aBC73t1MYGAgAgMDrdODdnR0oL6+Hg0NDWhsbER5eTmMRiOAP8ZeBAYGQq1Ww8fHBz4+PlCr1fD29oaHh8cZt3MxGo0wGAzQ6/UwGAyn3To6OtDa2orm5ma0tLTAZDIB+GMq3MDAQAQFBaFfv34ICQlBeHi401/tzJ46Ojrw22+/oX///hg8eLDY5ZCDMdDpDDKZDCkpKcjLy0NFRYW15UbuycfHB4mJiaddxKezsxOtra1obW1FW1sbWltbUVlZiY6ODsjlcnR3d5+xHJlMBqVSCbVaDaPRCA8PD7S1tcFgMJx3/YGBgVAoFAgNDUVqaiqCgoIQGBjo8N4BZycIAr7//nt0dnbi1ltvFbscEgEDnc5KrVYjLi4OZWVl8Pf3h0ajEbskciJqtRpqtRpRUVFnPKbX66HX62E0Gq03g8Fg/b/ZbIbJZIJcLodcLoenp+cZN5VKBU9PT7dubffWvn37UFxcjJtvvpld7W6KgU7nFB4eDq1Wi+LiYgwePFiSp/aQ7alUKs5I5mDV1dX45ZdfMHr0aCQlJYldDonEvUaLUK8lJSVBLpejuLgYPMORyPl0dXVh8+bNiIyMxIQJE8Quh0TEQKfzUiqVSEpKgk6nQ01NjdjlENGfWCwWrF+/HlqtFjfccIPbjein0/HTpwvy9/dHVFQUqqqq0N7eLnY5RPS/srOzUVFRgVmzZklukhTqPQY6XZTo6Gj4+PigqKgIZrNZ7HKI3F5OTg4OHjyIq6++GrGxsWKXQ06AgU4XRSaTITk5GSaTCSUlJWKXQ+TWKioqsHnzZgwbNgyZmZlil0NOgoFOF02lUiExMRHNzc1oaGgQuxwit6TVarFu3TrExMRg8uTJYpdDToSBTr0SFBSE0NBQlJWVnXXyECKyH6PRiG+//RYeHh4cBEdn4G8D9Vp8fDxUKhUKCwt5PJ3IgX788Uc0Nzdj9uzZ8Pb2FrsccjIMdOo1uVyOlJQUGAwGFBQUwGKxiF0SkeTt2rULBQUFuO666xAWFiZ2OeSEGOjUJ97e3khNTUVbWxtOnToldjlEknb8+HEcOnQIV1xxBfr37y92OeSkGOjUZ/7+/ujXrx8aGxs58p3ITkpLS/HTTz8hKSkJl19+udjlkBNjoNMlCQ4ORlJSEmpqalBVVSV2OUSSUl1djXXr1iEhIQFTp04Vuxxycrw4C12yiIgIGAwGlJWVwcPDg8f3iGygpqYGX3/9NeLj43HddddxRDtdEAOdbCIuLg5GoxFFRUXw8PBAYGCg2CURuayamhqsXbsWoaGhuPbaa3kZWboo/MpHNpOUlITAwEAUFhaira1N7HKIXFJ1dbU1zGfPns3LFtNFY6CTzchkMvTv3x8+Pj7Iz89HV1eX2CURuZTq6mp8/fXXCAsLY5hTrzHQyabkcjnS0tLg4eGB48ePw2AwiF0SkUuoqqrC2rVrGebUZwx0sjmlUomBAwdCEAQcP34cRqNR7JKInFpVVRW+/vprREREYPbs2TxmTn3CQCe7UKlUGDhwIIxGI/Ly8mAymcQuicgpVVZWWsN81qxZDHPqMwY62Y1arUZaWhq6u7uRm5vLljrRf6isrMQ333yDyMhIhjldMgY62ZWvry/S09NhMBhw7NgxhjrR/yorK7OG+Q033MAwp0vmVIH+3HPPYcyYMVCr1dBoNBf1mvnz50Mmk51244xKzsXHxwfp6ekwmUzIycnh6HdyeydOnMD69euRlJTEMCebcapANxgMmDNnDpYsWdKr102dOhU1NTXW2+eff26nCqmv1Go10tPTAQA5OTk8T53c1r59+/DLL78gJSUF06dPZ5iTzTjVTHFPPfUUAGD16tW9ep1KpUJERIQdKiJb8vLyQmZmJvLy8nDkyBGkpaUhODhY7LKIHMJoNGLTpk04deoURo8ejVGjRkEmk4ldFkmIU7XQ+2r79u0ICwtDamoqlixZgqampvM+X6/XQ6fTnXYjx/Dw8MCQIUMQFBSEvLw81NTUiF0Skd1ptVp88cUXKCsrw3XXXYfRo0czzMnmXD7Qp06dijVr1iA7Oxsvvvgifv31V0ybNg1ms/mcr1mxYgUCAgKst9jYWAdWTD2Tz0RHR+PkyZO89CpJWnl5OT777DOYzWbcfPPNSE5OFrskkiiZIAiCPVfw+OOP48UXXzzvc/Lz8zFgwADrz6tXr8YDDzyA1tbWXq+vuLgYycnJ2Lp1KyZNmnTW5+j1euj1euvPOp0OsbGx0Gq18Pf37/U6qe8qKytRXFxs7WFhq4Wk5ODBg/j9998RHx+PadOmQaVSiV2S29PpdAgICJDk/t7ux9CXLl2K+fPnn/c5SUlJNltfUlISQkJCcOrUqXMGukql4h+Wk4iJiYFKpUJBQQH0ej0GDhzIQULk8kwmE7Zu3YqCggKMGDECl19+Ob+skt3ZPdBDQ0MRGhpq79VYVVZWoqmpCZGRkQ5bJ12a0NBQeHp64vjx4zhw4AAGDRokuW/O5D50Oh1++OEHNDc3Y/r06ejfv7/YJZGbcKpj6OXl5cjJyUF5eTnMZjNycnKQk5OD9vZ263MGDBiAdevWAQDa29vxyCOPYM+ePSgtLUV2djZmzJiBlJQUTJkyRazNoD4ICAjAsGHDoFKpcPjwYVRVVYldElGvVVZW4vPPP0d3dzfmzp3LMCeHcqrT1pYvX46PPvrI+vPQoUMBAL/88gsmTJgAACgsLIRWqwUAKBQKHD16FB999BFaW1sRFRWFq6++Gs888wy71F2QSqVCZmYmioqKcPLkSeh0OvTv3x8KhULs0ogu6MiRI9i+fTtiYmIwffp0eHt7i10SuRm7D4pzBVIeJOGq6uvrUVhYCC8vLwwaNAhqtVrskojOqru7G7/99hsKCwsxZMgQXHHFFZDLnarzk/5Eyvt7p2qhE/UICwuDr68vjh07hoMHD6J///4IDw8Xuyyi05w6dQq//vorLBYLpk2bhpSUFLFLIjfGQCenpVarMXz4cJw4cQLHjh1DU1MT+vfvD6WSv7Ykro6ODvz6668oLi5GUlISJkyYwF4kEh33jOTUFAoF0tLSEBgYiBMnTqC1tdX6M5EYCgoKsGPHDsjlckydOpWtcnIaDHRyCREREdBoNMjPz8fhw4cRGxuL5ORkHqskh2lra8Mvv/yC8vJypKam4oorroCXl5fYZRFZMdDJZfRc3KWyshJFRUVoaGhAamoqL/BCdiUIAvLy8rBz5054enri2muvRUJCgthlEZ2BgU4uRSaTITY2FsHBwdbWelhYGPr378/WEtmcVqvFtm3bUFVVhUGDBuHyyy+Hp6en2GURnRVPW4O0T2OQurq6Opw4cQJGoxGJiYmIj49nNzxdMkEQkJOTg71790KtVuPKK69ETEyM2GWRDUh5f88WOrm08PBwhISEoLi4GMXFxaipqWE3PF2Suro67NmzBxUVFcjIyMDo0aN5fQFyCQx0cnkKhQL9+vVDVFQUCgoK2A1PfdLW1oZ9+/ahsLAQISEhuPHGGxERESF2WUQXjV3ukHYXjDuqra3FyZMnYTKZkJiYiLi4OHbD0zm1t7fj0KFDKCgogL+/P4YMGYK0tDReHU2ipLy/ZwudJCciIgIhISEoKSlBUVERqqqq0K9fP4SFhYldGjmRzs5OHDp0CMePH4enpydGjhyJwYMHc+Iicln8zSVJUiqV6NevHyIjI3Hq1Cnk5ORAo9EgMTERISEhbH25sa6uLhw+fBh5eXlQKpUYMWIE0tPTeZycXB4DnSTN19cXmZmZaGpqQlFREQ4ePAhfX18kJiYiMjKSXfFupLu7G0eOHEFubi7kcjmGDh2KIUOG8DQ0kgwGOrmF4OBgBAcHo6WlBSUlJcjNzcWJEyeQkJCA2NhYdrNKmF6vx9GjR3H06FEIgoAhQ4YgIyODl1gmyeFejNxKYGAgAgMD0d7ejtLSUpw8eRJFRUWIjY1FfHw8R8VLSFtbG44dO4bi4mJ0dXVh0KBByMzM5HXKSbIY6OSWfH19MXjwYPTr1w9lZWUoLy9HaWkpoqKikJiYCF9fX7FLpD6qra3F0aNHUVZWBk9PTwwcOBCDBw9mkJPkMdDJralUKvTv3x9JSUmorKxEaWkpqqqqEBoaisTERAQFBYldIl0EvV6PoqIiFBUVoaamBhqNBmPHjkW/fv14OIXcBs9Dh7TPS6TesVgsqKmpQUlJCdrb26HRaBAbG4uIiAgoFAqxy6M/EQQBVVVVKCwsRFlZGQAgLi4OAwYM4DStdE5S3t8z0CHtD5j6rqGhAeXl5airq4NKpUJQUBCioqIQGhrK0fEi0mq1OHHiBE6dOoWOjg4EBgaif//+SElJYbc6XZCU9/fsiyI6h9DQUISGhqKzsxNVVVWorq5GVVUVlEolwsPDGe4O1NnZidLSUhQVFaGurg6enp5ITk5G//79ERoaKnZ5RE6BLXRI+xsb2VZbWxtqampQU1ODtrY2a7hHRkYiLCyM4W5Dra2t1gGLDQ0NkMlkiIuLQ0JCAuLj43lsnPpEyvt7/kUQ9YKfnx/8/PzQv39/tLe3o7q6GjU1Nae13BnufSMIgvUwR1lZGbRaLZRKJWJiYpCWlobY2FieO050HmyhQ9rf2Mgx/hzuPS33gIAAhIaGIiQkBAEBAZxu9ix0Op21x6O2thadnZ3w8vJCXFwc4uLiEB0dzcGIZFNS3t8z0CHtD5gcr729HXV1dWhoaEBTUxPMZjM8PDwQEhKCoKAgBAYGIiAgwO2Cymw2o6WlBY2Njaivr7cGuFwuR0hICCIjIxEVFYWwsDB++SG7kfL+nl3uRDbm6+sLX19fJCcnw2KxWEOssbEReXl5sFgskMlk8Pf3h0ajsc5e5+fnJ5lueoPBgJaWFjQ3N6OpqQnNzc3QarUQBAEymQwhISFISkqyHp7ghVGILh1b6JD2NzZyLhaLBTqdDi0tLWhtbUVLSwva2togCAIUCgUCAgKgVqvh4+MDX19f67/OegERQRDQ0dEBrVaLlpYWa3i3tbUBABQKBQIDAxEUFGS9BQYGul3vBDkPKe/v2UInciC5XA6NRgONRmO9z2w2o7W1Fa2trdBqtWhra0NdXR30er31OR4eHqcFvJeXF7y9vaFSqeDl5QWVSmWzkDQajdDr9dZbd3f3WX82Go3QarWwWCxQqVQwmUwICgpCTEwMgoKCEBwczLEDRA7EQCcSmUKhsF4N7s9MJhM6OjrQ3t6O9vZ26/+bmprQ3d0Ns9l82jKMRiPkcrn1plAoTvv5XDej0Yiuri5rWFssljNq9PDwgEqlsn6B8Pf3h7e3N1JSUuDv7w8/Pz/4+PgwvIlExEAnclI9I+UDAgLOeEwQhDNazyaTCWazGRaL5aJvMpkMnp6e8PHxOS2we/7f87NUju0TSRkDncgFyWQyeHl58XKvRGTFr91EREQSwEAnIiKSAAY6ERGRBDDQiYiIJICBTkREJAEMdCIiIglgoBMREUkAA52IiEgCGOhEREQS4FSBXlpaioULFyIxMRHe3t5ITk7Gk08+CYPBcN7XdXd3495770VwcDB8fX0xe/Zs1NXVOahqIiIi8TlVoBcUFMBiseDtt99GXl4eVq5ciVWrVuHvf//7eV/34IMP4vvvv8fatWvx66+/orq6GrNmzXJQ1UREROJz+uuh//Of/8T//M//oLi4+KyPa7VahIaG4rPPPsONN94I4I8vBmlpadi9ezdGjx59wXVI+fq4RET0f6S8v3eqFvrZaLVaBAUFnfPxgwcPwmg0YvLkydb7BgwYgLi4OOzevfusr9Hr9dDpdKfdiIiIXJlTB/qpU6fwxhtv4O677z7nc2pra+Hp6QmNRnPa/eHh4aitrT3ra1asWGG9LGVAQABiY2NtWTYREZHDOSTQH3/8cchksvPeCgoKTntNVVUVpk6dijlz5mDRokU2rWfZsmXQarXWW0VFhU2XT0RE5GgOuR760qVLMX/+/PM+Jykpyfr/6upqTJw4EWPGjME777xz3tdFRETAYDCgtbX1tFZ6XV0dIiIizvoalUoFlUp10fUTERE5O4cEemhoKEJDQy/quVVVVZg4cSKGDx+ODz/8EHL5+TsRhg8fDg8PD2RnZ2P27NkAgMLCQpSXlyMrK+uSayciInIFTnUMvaqqChMmTEBcXBxefvllNDQ0oLa29rRj4VVVVRgwYAD27dsHAAgICMDChQvx0EMP4ZdffsHBgwexYMECZGVlXdQIdyIiIilwSAv9Ym3ZsgWnTp3CqVOnEBMTc9pjPWfXGY1GFBYWorOz0/rYypUrIZfLMXv2bOj1ekyZMgX//ve/HVo7ERGRmJz+PHRHkPJ5iURE9H+kvL93qi53IiIi6hsGOhERkQQw0ImIiCSAgU5ERCQBDHQiIiIJYKATERFJAAOdiIhIAhjoREREEsBAJyIikgAGOhERkQQw0ImIiCSAgU5ERCQBDHQiIiIJYKATERFJAAOdiIhIAhjoREREEsBAJyIikgAGOhERkQQw0ImIiCSAgU5ERCQBDHQiIiIJUIpdgDMQBAEAoNPpRK6EiIjsqWc/37PflxIGOoC2tjYAQGxsrMiVEBGRI7S1tSEgIEDsMmxKJkjxa0ovWSwWVFdXw8/PDzKZ7IzHdTodYmNjUVFRAX9/fxEqtA0pbIcUtgHgdjgbKWyHFLYBsP92CIKAtrY2REVFQS6X1lFnttAByOVyxMTEXPB5/v7+Lv2H0kMK2yGFbQC4Hc5GCtshhW0A7LsdUmuZ95DW1xMiIiI3xUAnIiKSAAb6RVCpVHjyySehUqnELuWSSGE7pLANALfD2UhhO6SwDYB0tkMMHBRHREQkAWyhExERSQADnYiISAIY6ERERBLAQCciIpIABvpZlJaWYuHChUhMTIS3tzeSk5Px5JNPwmAwnPd13d3duPfeexEcHAxfX1/Mnj0bdXV1Dqr6TM899xzGjBkDtVoNjUZzUa+ZP38+ZDLZabepU6fat9AL6Mt2CIKA5cuXIzIyEt7e3pg8eTJOnjxp30IvoLm5Gbfddhv8/f2h0WiwcOFCtLe3n/c1EyZMOOPzuOeeexxU8R/eeustJCQkwMvLC6NGjcK+ffvO+/y1a9diwIAB8PLyQnp6On766ScHVXp+vdmO1atXn/G+e3l5ObDaM/3222+47rrrEBUVBZlMhvXr11/wNdu3b8ewYcOgUqmQkpKC1atX273OC+ntdmzfvv2Mz0Imk6G2ttYxBbsQBvpZFBQUwGKx4O2330ZeXh5WrlyJVatW4e9///t5X/fggw/i+++/x9q1a/Hrr7+iuroas2bNclDVZzIYDJgzZw6WLFnSq9dNnToVNTU11tvnn39upwovTl+246WXXsLrr7+OVatWYe/evfDx8cGUKVPQ3d1tx0rP77bbbkNeXh62bNmCH374Ab/99hsWL158wdctWrTotM/jpZdeckC1f/jyyy/x0EMP4cknn8ShQ4eQkZGBKVOmoL6+/qzP37VrF2655RYsXLgQhw8fxsyZMzFz5kwcO3bMYTWfTW+3A/hjprI/v+9lZWUOrPhMHR0dyMjIwFtvvXVRzy8pKcE111yDiRMnIicnBw888ADuuusubNq0yc6Vnl9vt6NHYWHhaZ9HWFiYnSp0YQJdlJdeeklITEw85+Otra2Ch4eHsHbtWut9+fn5AgBh9+7djijxnD788EMhICDgop47b948YcaMGXatp68udjssFosQEREh/POf/7Te19raKqhUKuHzzz+3Y4Xndvz4cQGAsH//fut9P//8syCTyYSqqqpzvm78+PHC/fff74AKz27kyJHCvffea/3ZbDYLUVFRwooVK876/Jtuukm45pprTrtv1KhRwt13323XOi+kt9vRm78ZMQAQ1q1bd97nPProo8KgQYNOu2/u3LnClClT7FhZ71zMdvzyyy8CAKGlpcUhNbkyttAvklarRVBQ0DkfP3jwIIxGIyZPnmy9b8CAAYiLi8Pu3bsdUaLNbN++HWFhYUhNTcWSJUvQ1NQkdkm9UlJSgtra2tM+i4CAAIwaNUq0z2L37t3QaDQYMWKE9b7JkydDLpdj7969533tp59+ipCQEAwePBjLli1DZ2envcsF8EfPyMGDB097H+VyOSZPnnzO93H37t2nPR8ApkyZIurfQF+2AwDa29sRHx+P2NhYzJgxA3l5eY4o12ac8bO4FJmZmYiMjMRVV12FnTt3il2OU+LFWS7CqVOn8MYbb+Dll18+53Nqa2vh6el5xjHe8PBwlzrWM3XqVMyaNQuJiYkoKirC3//+d0ybNg27d++GQqEQu7yL0vN+h4eHn3a/mJ9FbW3tGV2ESqUSQUFB563p1ltvRXx8PKKionD06FE89thjKCwsxLfffmvvktHY2Aiz2XzW97GgoOCsr6mtrXWq9x3o23akpqbigw8+wJAhQ6DVavHyyy9jzJgxyMvLu6gLOTmDc30WOp0OXV1d8Pb2Fqmy3omMjMSqVaswYsQI6PV6vPfee5gwYQL27t2LYcOGiV2eU3GrFvrjjz9+1sEVf7795x94VVUVpk6dijlz5mDRokUiVf5/+rINvXHzzTfj+uuvR3p6OmbOnIkffvgB+/fvx/bt2223EbD/djiKvbdj8eLFmDJlCtLT03HbbbdhzZo1WLduHYqKimy4FfSfsrKycMcddyAzMxPjx4/Ht99+i9DQULz99ttil+Z2UlNTcffdd2P48OEYM2YMPvjgA4wZMwYrV64UuzSn41Yt9KVLl2L+/PnnfU5SUpL1/9XV1Zg4cSLGjBmDd95557yvi4iIgMFgQGtr62mt9Lq6OkRERFxK2afp7TZcqqSkJISEhODUqVOYNGmSzZZrz+3oeb/r6uoQGRlpvb+urg6ZmZl9Wua5XOx2REREnDEAy2Qyobm5uVe/H6NGjQLwR69RcnJyr+vtjZCQECgUijPO1Djf73RERESvnu8IfdmO/+Th4YGhQ4fi1KlT9ijRLs71Wfj7+7tM6/xcRo4cid9//13sMpyOWwV6aGgoQkNDL+q5VVVVmDhxIoYPH44PP/wQcvn5OzOGDx8ODw8PZGdnY/bs2QD+GJVZXl6OrKysS669R2+2wRYqKyvR1NR0WjDagj23IzExEREREcjOzrYGuE6nw969e3s94v9CLnY7srKy0NraioMHD2L48OEAgG3btsFisVhD+mLk5OQAgM0/j7Px9PTE8OHDkZ2djZkzZwIALBYLsrOzcd999531NVlZWcjOzsYDDzxgvW/Lli02/Rvorb5sx38ym83Izc3F9OnT7VipbWVlZZ1xyqDYn4Wt5OTkOORvwOWIPSrPGVVWVgopKSnCpEmThMrKSqGmpsZ6+/NzUlNThb1791rvu+eee4S4uDhh27ZtwoEDB4SsrCwhKytLjE0QBEEQysrKhMOHDwtPPfWU4OvrKxw+fFg4fPiw0NbWZn1Oamqq8O233wqCIAhtbW3Cww8/LOzevVsoKSkRtm7dKgwbNkzo16+f0N3dLdZm9Ho7BEEQXnjhBUGj0QgbNmwQjh49KsyYMUNITEwUurq6xNgEQRAEYerUqcLQoUOFvXv3Cr///rvQr18/4ZZbbrE+/p+/U6dOnRKefvpp4cCBA0JJSYmwYcMGISkpSRg3bpzDav7iiy8ElUolrF69Wjh+/LiwePFiQaPRCLW1tYIgCMLtt98uPP7449bn79y5U1AqlcLLL78s5OfnC08++aTg4eEh5ObmOqzms+ntdjz11FPCpk2bhKKiIuHgwYPCzTffLHh5eQl5eXlibYLQ1tZm/d0HIPzrX/8SDh8+LJSVlQmCIAiPP/64cPvtt1ufX1xcLKjVauGRRx4R8vPzhbfeektQKBTCxo0bxdoEQRB6vx0rV64U1q9fL5w8eVLIzc0V7r//fkEulwtbt24VaxOcFgP9LD788EMBwFlvPUpKSgQAwi+//GK9r6urS/jrX/8qBAYGCmq1WrjhhhtO+xLgaPPmzTvrNvy5ZgDChx9+KAiCIHR2dgpXX321EBoaKnh4eAjx8fHCokWLrDs9sfR2OwThj1PX/vGPfwjh4eGCSqUSJk2aJBQWFjq++D9pamoSbrnlFsHX11fw9/cXFixYcNqXkv/8nSovLxfGjRsnBAUFCSqVSkhJSREeeeQRQavVOrTuN954Q4iLixM8PT2FkSNHCnv27LE+Nn78eGHevHmnPf+rr74S+vfvL3h6egqDBg0SfvzxR4fWey692Y4HHnjA+tzw8HBh+vTpwqFDh0So+v/0nL71n7eeuufNmyeMHz/+jNdkZmYKnp6eQlJS0ml/I2Lp7Xa8+OKLQnJysuDl5SUEBQUJEyZMELZt2yZO8U6Ol08lIiKSALca5U5ERCRVDHQiIiIJYKATERFJAAOdiIhIAhjoREREEsBAJyIikgAGOhERkQQw0ImIiCSAgU5ERCQBDHQiIiIJYKATuZmGhgZERETg+eeft963a9cueHp6Ijs7W8TKiOhScC53Ijf0008/YebMmdi1axdSU1ORmZmJGTNm4F//+pfYpRFRHzHQidzUvffei61bt2LEiBHIzc3F/v37oVKpxC6LiPqIgU7kprq6ujB48GBUVFTg4MGDSE9PF7skIroEPIZO5KaKiopQXV0Ni8WC0tJSscshokvEFjqRGzIYDBg5ciQyMzORmpqKV199Fbm5uQgLCxO7NCLqIwY6kRt65JFH8PXXX+PIkSPw9fXF+PHjERAQgB9++EHs0oioj9jlTuRmtm/fjldffRUff/wx/P39IZfL8fHHH2PHjh34n//5H7HLI6I+YgudiIhIAthCJyIikgAGOhERkQQw0ImIiCSAgU5ERCQBDHQiIiIJYKATERFJAAOdiIhIAhjoREREEsBAJyIikgAGOhERkQQw0ImIiCSAgU5ERCQBDHQiIiIJYKATERFJwP8HPjhKLWn6RAoAAAAASUVORK5CYII=",
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