{ "metadata": { "title": "AP Pre-Calculus Learning Graph", "description": "A comprehensive learning graph for AP Pre-Calculus covering polynomial, rational, exponential, logarithmic, trigonometric, and polar functions following the College Board curriculum framework.", "creator": "Dan McCreary", "date": "2026-03-16", "version": "1.0", "format": "Learning Graph JSON v1.0", "schema": "https://raw.githubusercontent.com/dmccreary/learning-graphs/refs/heads/main/src/schema/learning-graph-schema.json", "license": "CC BY-NC-SA 4.0 DEED" }, "groups": { "FOUND": { "classifierName": "Foundation Concepts", "color": "LightCoral", "font": { "color": "black" } }, "FUNC": { "classifierName": "Function Fundamentals", "color": "PaleTurquoise", "font": { "color": "black" } }, "RATE": { "classifierName": "Rates of Change", "color": "Thistle", "font": { "color": "black" } }, "LNQD": { "classifierName": "Linear and Quadratic", "color": "MistyRose", "font": { "color": "black" } }, "POLY": { "classifierName": "Polynomial Functions", "color": "Plum", "font": { "color": "black" } }, "RATL": { "classifierName": "Rational Functions", "color": "SteelBlue", "font": { "color": "black" } }, "TMOD": { "classifierName": "Transformations and Modeling", "color": "PeachPuff", "font": { "color": "black" } }, "SEQX": { "classifierName": "Sequences and Exponential", "color": "MintCream", "font": { "color": "black" } }, "LOGR": { "classifierName": "Logarithmic Functions", "color": "Lavender", "font": { "color": "black" } }, "TRIG": { "classifierName": "Trigonometric Functions", "color": "Honeydew", "font": { "color": "black" } }, "POLR": { "classifierName": "Polar and Parametric", "color": "LightYellow", "font": { "color": "black" } }, "VECM": { "classifierName": "Vectors and Matrices", "color": "LavenderBlush", "font": { "color": "black" } } }, "nodes": [ { "id": 1, "label": "Real Number System", "group": "FOUND", "shape": "box" }, { "id": 2, "label": "Number Line", "group": "FOUND" }, { "id": 3, "label": "Order of Operations", "group": "FOUND" }, { "id": 4, "label": "Variables and Expressions", "group": "FOUND" }, { "id": 5, "label": "Coordinate Plane", "group": "FOUND" }, { "id": 6, "label": "Ordered Pairs", "group": "FOUND" }, { "id": 7, "label": "Input and Output", "group": "FOUND" }, { "id": 8, "label": "Function Definition", "group": "FUNC" }, { "id": 9, "label": "Function Notation", "group": "FUNC" }, { "id": 10, "label": "Domain", "group": "FUNC" }, { "id": 11, "label": "Range", "group": "FUNC" }, { "id": 12, "label": "Independent Variable", "group": "FOUND" }, { "id": 13, "label": "Dependent Variable", "group": "FOUND" }, { "id": 14, "label": "Interval Notation", "group": "FOUND" }, { "id": 15, "label": "Set-Builder Notation", "group": "FOUND" }, { "id": 16, "label": "Vertical Line Test", "group": "FUNC" }, { "id": 17, "label": "Function Evaluation", "group": "FUNC" }, { "id": 18, "label": "Piecewise Functions", "group": "FUNC" }, { "id": 19, "label": "Domain Restrictions", "group": "FUNC" }, { "id": 20, "label": "Graphing Functions", "group": "FUNC" }, { "id": 21, "label": "Intercepts", "group": "FUNC" }, { "id": 22, "label": "X-Intercept", "group": "FUNC" }, { "id": 23, "label": "Y-Intercept", "group": "FUNC" }, { "id": 24, "label": "Increasing Functions", "group": "FUNC" }, { "id": 25, "label": "Decreasing Functions", "group": "FUNC" }, { "id": 26, "label": "Constant Functions", "group": "FUNC" }, { "id": 27, "label": "Function Behavior", "group": "FUNC" }, { "id": 28, "label": "Positive and Negative Regions", "group": "FUNC" }, { "id": 29, "label": "Bounded Functions", "group": "FUNC" }, { "id": 30, "label": "Even Functions", "group": "FUNC" }, { "id": 31, "label": "Odd Functions", "group": "FUNC" }, { "id": 32, "label": "Symmetry", "group": "FUNC" }, { "id": 33, "label": "Change in Tandem", "group": "RATE" }, { "id": 34, "label": "Average Rate of Change", "group": "RATE" }, { "id": 35, "label": "Slope", "group": "RATE" }, { "id": 36, "label": "Slope Formula", "group": "RATE" }, { "id": 37, "label": "Rate of Change Units", "group": "RATE" }, { "id": 38, "label": "Secant Line", "group": "RATE" }, { "id": 39, "label": "Linear Rate of Change", "group": "RATE" }, { "id": 40, "label": "Nonlinear Rate of Change", "group": "RATE" }, { "id": 41, "label": "Concavity from Rates", "group": "RATE" }, { "id": 42, "label": "Increasing Rate of Change", "group": "RATE" }, { "id": 43, "label": "Decreasing Rate of Change", "group": "RATE" }, { "id": 44, "label": "Linear Function Definition", "group": "LNQD" }, { "id": 45, "label": "Slope-Intercept Form", "group": "LNQD" }, { "id": 46, "label": "Point-Slope Form", "group": "LNQD" }, { "id": 47, "label": "Standard Form of a Line", "group": "LNQD" }, { "id": 48, "label": "Parallel Lines", "group": "LNQD" }, { "id": 49, "label": "Perpendicular Lines", "group": "LNQD" }, { "id": 50, "label": "Linear Regression", "group": "LNQD" }, { "id": 51, "label": "Residuals", "group": "LNQD" }, { "id": 52, "label": "Correlation", "group": "LNQD" }, { "id": 53, "label": "Quadratic Function Definition", "group": "LNQD" }, { "id": 54, "label": "Standard Form of Quadratic", "group": "LNQD" }, { "id": 55, "label": "Vertex Form", "group": "LNQD" }, { "id": 56, "label": "Factored Form", "group": "LNQD" }, { "id": 57, "label": "Vertex", "group": "LNQD" }, { "id": 58, "label": "Axis of Symmetry", "group": "LNQD" }, { "id": 59, "label": "Parabola", "group": "LNQD" }, { "id": 60, "label": "Completing the Square", "group": "LNQD" }, { "id": 61, "label": "Quadratic Formula", "group": "LNQD" }, { "id": 62, "label": "Discriminant", "group": "LNQD" }, { "id": 63, "label": "Complex Numbers", "group": "LNQD" }, { "id": 64, "label": "Imaginary Unit", "group": "LNQD" }, { "id": 65, "label": "Complex Zeros", "group": "LNQD" }, { "id": 66, "label": "Polynomial Definition", "group": "POLY" }, { "id": 67, "label": "Degree of a Polynomial", "group": "POLY" }, { "id": 68, "label": "Leading Coefficient", "group": "POLY" }, { "id": 69, "label": "Monomial", "group": "POLY" }, { "id": 70, "label": "Binomial", "group": "POLY" }, { "id": 71, "label": "Trinomial", "group": "POLY" }, { "id": 72, "label": "Polynomial Addition", "group": "POLY" }, { "id": 73, "label": "Polynomial Multiplication", "group": "POLY" }, { "id": 74, "label": "Factoring Polynomials", "group": "POLY" }, { "id": 75, "label": "Factor Theorem", "group": "POLY" }, { "id": 76, "label": "Remainder Theorem", "group": "POLY" }, { "id": 77, "label": "Synthetic Division", "group": "POLY" }, { "id": 78, "label": "Long Division of Polynomials", "group": "POLY" }, { "id": 79, "label": "Zeros of Polynomials", "group": "POLY" }, { "id": 80, "label": "Multiplicity of Zeros", "group": "POLY" }, { "id": 81, "label": "Real Zeros", "group": "POLY" }, { "id": 82, "label": "Complex Conjugate Zeros", "group": "POLY" }, { "id": 83, "label": "Fundamental Theorem of Algebra", "group": "POLY" }, { "id": 84, "label": "Polynomial End Behavior", "group": "POLY" }, { "id": 85, "label": "Leading Term Test", "group": "POLY" }, { "id": 86, "label": "Turning Points", "group": "POLY" }, { "id": 87, "label": "Polynomial Graphs", "group": "POLY" }, { "id": 88, "label": "Local Maximum", "group": "POLY" }, { "id": 89, "label": "Local Minimum", "group": "POLY" }, { "id": 90, "label": "Global Maximum", "group": "POLY" }, { "id": 91, "label": "Global Minimum", "group": "POLY" }, { "id": 92, "label": "Intermediate Value Theorem", "group": "POLY" }, { "id": 93, "label": "Rational Function Definition", "group": "RATL" }, { "id": 94, "label": "Rational Expressions", "group": "RATL" }, { "id": 95, "label": "Simplifying Rational Expr", "group": "RATL" }, { "id": 96, "label": "Vertical Asymptotes", "group": "RATL" }, { "id": 97, "label": "Horizontal Asymptotes", "group": "RATL" }, { "id": 98, "label": "Slant Asymptotes", "group": "RATL" }, { "id": 99, "label": "Holes in Graphs", "group": "RATL" }, { "id": 100, "label": "Rational Function Zeros", "group": "RATL" }, { "id": 101, "label": "Rational Function Domain", "group": "RATL" }, { "id": 102, "label": "End Behavior of Rationals", "group": "RATL" }, { "id": 103, "label": "Rational Function Graphs", "group": "RATL" }, { "id": 104, "label": "Rational Inequalities", "group": "RATL" }, { "id": 105, "label": "Parent Functions", "group": "TMOD" }, { "id": 106, "label": "Vertical Translation", "group": "TMOD" }, { "id": 107, "label": "Horizontal Translation", "group": "TMOD" }, { "id": 108, "label": "Vertical Stretch", "group": "TMOD" }, { "id": 109, "label": "Vertical Compression", "group": "TMOD" }, { "id": 110, "label": "Horizontal Stretch", "group": "TMOD" }, { "id": 111, "label": "Horizontal Compression", "group": "TMOD" }, { "id": 112, "label": "Reflection Over X-Axis", "group": "TMOD" }, { "id": 113, "label": "Reflection Over Y-Axis", "group": "TMOD" }, { "id": 114, "label": "Combined Transformations", "group": "TMOD" }, { "id": 115, "label": "Transformation Order", "group": "TMOD" }, { "id": 116, "label": "Writing Transformed Eqns", "group": "TMOD" }, { "id": 117, "label": "Function Model Selection", "group": "TMOD" }, { "id": 118, "label": "Data Analysis for Models", "group": "TMOD" }, { "id": 119, "label": "Regression Models", "group": "TMOD" }, { "id": 120, "label": "Model Assumptions", "group": "TMOD" }, { "id": 121, "label": "Model Validation", "group": "TMOD" }, { "id": 122, "label": "Extrapolation", "group": "TMOD" }, { "id": 123, "label": "Interpolation", "group": "TMOD" }, { "id": 124, "label": "Residual Analysis", "group": "TMOD" }, { "id": 125, "label": "Goodness of Fit", "group": "TMOD" }, { "id": 126, "label": "Competing Models", "group": "TMOD" }, { "id": 127, "label": "Sequence Definition", "group": "SEQX" }, { "id": 128, "label": "Arithmetic Sequence", "group": "SEQX" }, { "id": 129, "label": "Common Difference", "group": "SEQX" }, { "id": 130, "label": "Arithmetic Sequence Formula", "group": "SEQX" }, { "id": 131, "label": "Geometric Sequence", "group": "SEQX" }, { "id": 132, "label": "Common Ratio", "group": "SEQX" }, { "id": 133, "label": "Geometric Sequence Formula", "group": "SEQX" }, { "id": 134, "label": "Recursive Formulas", "group": "SEQX" }, { "id": 135, "label": "Explicit Formulas", "group": "SEQX" }, { "id": 136, "label": "Sequence Convergence", "group": "SEQX" }, { "id": 137, "label": "Sequence Divergence", "group": "SEQX" }, { "id": 138, "label": "Exponential Function Def", "group": "SEQX" }, { "id": 139, "label": "Base of Exponential", "group": "SEQX" }, { "id": 140, "label": "Growth Factor", "group": "SEQX" }, { "id": 141, "label": "Decay Factor", "group": "SEQX" }, { "id": 142, "label": "Exponential Growth", "group": "SEQX" }, { "id": 143, "label": "Exponential Decay", "group": "SEQX" }, { "id": 144, "label": "Natural Base e", "group": "SEQX" }, { "id": 145, "label": "Continuous Growth", "group": "SEQX" }, { "id": 146, "label": "Compound Interest", "group": "SEQX" }, { "id": 147, "label": "Exponential Equations", "group": "SEQX" }, { "id": 148, "label": "Exponential Graphs", "group": "SEQX" }, { "id": 149, "label": "Exponential Transformations", "group": "SEQX" }, { "id": 150, "label": "Exponential Modeling", "group": "SEQX" }, { "id": 151, "label": "Half-Life", "group": "SEQX" }, { "id": 152, "label": "Doubling Time", "group": "SEQX" }, { "id": 153, "label": "Percent Rate of Change", "group": "SEQX" }, { "id": 154, "label": "Logarithm Definition", "group": "LOGR" }, { "id": 155, "label": "Common Logarithm", "group": "LOGR" }, { "id": 156, "label": "Natural Logarithm", "group": "LOGR" }, { "id": 157, "label": "Logarithmic Form", "group": "LOGR" }, { "id": 158, "label": "Exponential-Log Conversion", "group": "LOGR" }, { "id": 159, "label": "Properties of Logarithms", "group": "LOGR" }, { "id": 160, "label": "Product Rule for Logs", "group": "LOGR" }, { "id": 161, "label": "Quotient Rule for Logs", "group": "LOGR" }, { "id": 162, "label": "Power Rule for Logs", "group": "LOGR" }, { "id": 163, "label": "Change of Base Formula", "group": "LOGR" }, { "id": 164, "label": "Logarithmic Equations", "group": "LOGR" }, { "id": 165, "label": "Logarithmic Graphs", "group": "LOGR" }, { "id": 166, "label": "Logarithmic Transformations", "group": "LOGR" }, { "id": 167, "label": "Logarithmic Modeling", "group": "LOGR" }, { "id": 168, "label": "Logarithmic Scale", "group": "LOGR" }, { "id": 169, "label": "Semi-Log Plot", "group": "LOGR" }, { "id": 170, "label": "Linearizing Exp Data", "group": "LOGR" }, { "id": 171, "label": "Log-Log Plots", "group": "LOGR" }, { "id": 172, "label": "Exponential Regression", "group": "LOGR" }, { "id": 173, "label": "Power Regression", "group": "LOGR" }, { "id": 174, "label": "Composition of Functions", "group": "FUNC" }, { "id": 175, "label": "Domain of Compositions", "group": "FUNC" }, { "id": 176, "label": "Decomposing Functions", "group": "FUNC" }, { "id": 177, "label": "Inverse Function Definition", "group": "FUNC" }, { "id": 178, "label": "One-to-One Functions", "group": "FUNC" }, { "id": 179, "label": "Horizontal Line Test", "group": "FUNC" }, { "id": 180, "label": "Finding Inverses Algebraically", "group": "FUNC" }, { "id": 181, "label": "Inverse Function Graphs", "group": "FUNC" }, { "id": 182, "label": "Restricting Domains", "group": "FUNC" }, { "id": 183, "label": "Angle Definition", "group": "TRIG", "shape": "box" }, { "id": 184, "label": "Degree Measure", "group": "TRIG" }, { "id": 185, "label": "Radian Measure", "group": "TRIG" }, { "id": 186, "label": "Degree-Radian Conversion", "group": "TRIG" }, { "id": 187, "label": "Arc Length", "group": "TRIG" }, { "id": 188, "label": "Sector Area", "group": "TRIG" }, { "id": 189, "label": "Standard Position", "group": "TRIG" }, { "id": 190, "label": "Terminal Side", "group": "TRIG" }, { "id": 191, "label": "Reference Angle", "group": "TRIG" }, { "id": 192, "label": "Coterminal Angles", "group": "TRIG" }, { "id": 193, "label": "Unit Circle Definition", "group": "TRIG" }, { "id": 194, "label": "Unit Circle Coordinates", "group": "TRIG" }, { "id": 195, "label": "Special Angles", "group": "TRIG" }, { "id": 196, "label": "Quadrantal Angles", "group": "TRIG" }, { "id": 197, "label": "Signs by Quadrant", "group": "TRIG" }, { "id": 198, "label": "Sine Function", "group": "TRIG" }, { "id": 199, "label": "Cosine Function", "group": "TRIG" }, { "id": 200, "label": "Tangent Function", "group": "TRIG" }, { "id": 201, "label": "Reciprocal Trig Functions", "group": "TRIG" }, { "id": 202, "label": "Secant Function", "group": "TRIG" }, { "id": 203, "label": "Cosecant Function", "group": "TRIG" }, { "id": 204, "label": "Cotangent Function", "group": "TRIG" }, { "id": 205, "label": "Trig Function Evaluation", "group": "TRIG" }, { "id": 206, "label": "Exact Trig Values", "group": "TRIG" }, { "id": 207, "label": "Right Triangle Trig", "group": "TRIG" }, { "id": 208, "label": "SOH-CAH-TOA", "group": "TRIG" }, { "id": 209, "label": "Sine Graph", "group": "TRIG" }, { "id": 210, "label": "Cosine Graph", "group": "TRIG" }, { "id": 211, "label": "Amplitude", "group": "TRIG" }, { "id": 212, "label": "Period", "group": "TRIG" }, { "id": 213, "label": "Midline", "group": "TRIG" }, { "id": 214, "label": "Frequency", "group": "TRIG" }, { "id": 215, "label": "Phase Shift", "group": "TRIG" }, { "id": 216, "label": "Vertical Shift of Trig", "group": "TRIG" }, { "id": 217, "label": "Sinusoidal Functions", "group": "TRIG" }, { "id": 218, "label": "Tangent Graph", "group": "TRIG" }, { "id": 219, "label": "Period of Tangent", "group": "TRIG" }, { "id": 220, "label": "Asymptotes of Tangent", "group": "TRIG" }, { "id": 221, "label": "Secant Graph", "group": "TRIG" }, { "id": 222, "label": "Cosecant Graph", "group": "TRIG" }, { "id": 223, "label": "Cotangent Graph", "group": "TRIG" }, { "id": 224, "label": "Graphing Trig Transformations", "group": "TRIG" }, { "id": 225, "label": "Sinusoidal Modeling", "group": "TRIG" }, { "id": 226, "label": "Periodic Data Analysis", "group": "TRIG" }, { "id": 227, "label": "Tidal Models", "group": "TRIG" }, { "id": 228, "label": "Temperature Models", "group": "TRIG" }, { "id": 229, "label": "Daylight Hour Models", "group": "TRIG" }, { "id": 230, "label": "Sinusoidal Regression", "group": "TRIG" }, { "id": 231, "label": "Period from Data", "group": "TRIG" }, { "id": 232, "label": "Amplitude from Data", "group": "TRIG" }, { "id": 233, "label": "Pythagorean Identity", "group": "TRIG" }, { "id": 234, "label": "Reciprocal Identities", "group": "TRIG" }, { "id": 235, "label": "Quotient Identities", "group": "TRIG" }, { "id": 236, "label": "Cofunction Identities", "group": "TRIG" }, { "id": 237, "label": "Even-Odd Identities", "group": "TRIG" }, { "id": 238, "label": "Sum and Difference Formulas", "group": "TRIG" }, { "id": 239, "label": "Double Angle Formulas", "group": "TRIG" }, { "id": 240, "label": "Verifying Identities", "group": "TRIG" }, { "id": 241, "label": "Simplifying Trig Expr", "group": "TRIG" }, { "id": 242, "label": "Arcsine", "group": "TRIG" }, { "id": 243, "label": "Arccosine", "group": "TRIG" }, { "id": 244, "label": "Arctangent", "group": "TRIG" }, { "id": 245, "label": "Inverse Trig Domains", "group": "TRIG" }, { "id": 246, "label": "Inverse Trig Ranges", "group": "TRIG" }, { "id": 247, "label": "Inverse Trig Graphs", "group": "TRIG" }, { "id": 248, "label": "Composing Trig Inverses", "group": "TRIG" }, { "id": 249, "label": "Solving Trig Equations", "group": "TRIG" }, { "id": 250, "label": "General Solutions", "group": "TRIG" }, { "id": 251, "label": "Solutions in an Interval", "group": "TRIG" }, { "id": 252, "label": "Trig Inequalities", "group": "TRIG" }, { "id": 253, "label": "Multiple Angle Equations", "group": "TRIG" }, { "id": 254, "label": "Polar Coordinate System", "group": "POLR" }, { "id": 255, "label": "Polar Point Plotting", "group": "POLR" }, { "id": 256, "label": "Rectangular to Polar", "group": "POLR" }, { "id": 257, "label": "Polar to Rectangular", "group": "POLR" }, { "id": 258, "label": "Multiple Polar Represent", "group": "POLR" }, { "id": 259, "label": "Polar Function Definition", "group": "POLR" }, { "id": 260, "label": "Polar Graphs", "group": "POLR" }, { "id": 261, "label": "Circles in Polar Form", "group": "POLR" }, { "id": 262, "label": "Cardioids", "group": "POLR" }, { "id": 263, "label": "Lima\u00e7ons", "group": "POLR" }, { "id": 264, "label": "Rose Curves", "group": "POLR" }, { "id": 265, "label": "Petal Count of Roses", "group": "POLR" }, { "id": 266, "label": "Symmetry of Polar Graphs", "group": "POLR" }, { "id": 267, "label": "Polar Rate of Change", "group": "POLR" }, { "id": 268, "label": "Polar Graph Intersections", "group": "POLR" }, { "id": 269, "label": "Parametric Equations", "group": "POLR" }, { "id": 270, "label": "Parameter", "group": "POLR" }, { "id": 271, "label": "Parametric Graphs", "group": "POLR" }, { "id": 272, "label": "Eliminating the Parameter", "group": "POLR" }, { "id": 273, "label": "Parametric Motion", "group": "POLR" }, { "id": 274, "label": "Position Functions", "group": "POLR" }, { "id": 275, "label": "Velocity from Parametrics", "group": "POLR" }, { "id": 276, "label": "Direction of Motion", "group": "POLR" }, { "id": 277, "label": "Parametric Modeling", "group": "POLR" }, { "id": 278, "label": "Projectile Motion Model", "group": "POLR" }, { "id": 279, "label": "Vector Definition", "group": "VECM", "shape": "box" }, { "id": 280, "label": "Vector Notation", "group": "VECM" }, { "id": 281, "label": "Magnitude of a Vector", "group": "VECM" }, { "id": 282, "label": "Direction of a Vector", "group": "VECM" }, { "id": 283, "label": "Component Form", "group": "VECM" }, { "id": 284, "label": "Unit Vectors", "group": "VECM" }, { "id": 285, "label": "Vector Addition", "group": "VECM" }, { "id": 286, "label": "Vector Subtraction", "group": "VECM" }, { "id": 287, "label": "Scalar Multiplication", "group": "VECM" }, { "id": 288, "label": "Dot Product", "group": "VECM" }, { "id": 289, "label": "Vector Applications", "group": "VECM" }, { "id": 290, "label": "Matrix Definition", "group": "VECM", "shape": "box" }, { "id": 291, "label": "Matrix Dimensions", "group": "VECM" }, { "id": 292, "label": "Matrix Addition", "group": "VECM" }, { "id": 293, "label": "Matrix Subtraction", "group": "VECM" }, { "id": 294, "label": "Scalar Mult of Matrices", "group": "VECM" }, { "id": 295, "label": "Matrix Multiplication", "group": "VECM" }, { "id": 296, "label": "Identity Matrix", "group": "VECM" }, { "id": 297, "label": "Determinant", "group": "VECM" }, { "id": 298, "label": "Inverse of a Matrix", "group": "VECM" }, { "id": 299, "label": "Linear Transformations", "group": "VECM" }, { "id": 300, "label": "Rotation Matrix", "group": "VECM" }, { "id": 301, "label": "Reflection Matrix", "group": "VECM" }, { "id": 302, "label": "Matrix Applications", "group": "VECM" }, { "id": 303, "label": "Calculator Strategies", "group": "VECM" }, { "id": 304, "label": "Free Response Strategy", "group": "VECM" }, { "id": 305, "label": "Multiple Choice Strategy", "group": "VECM" }, { "id": 306, "label": "Time Management on Exams", "group": "VECM" }, { "id": 307, "label": "Showing Work on Free Resp", "group": "VECM" } ], "edges": [ { "from": 2, "to": 1 }, { "from": 3, "to": 1 }, { "from": 4, "to": 1 }, { "from": 4, "to": 3 }, { "from": 5, "to": 2 }, { "from": 6, "to": 5 }, { "from": 7, "to": 4 }, { "from": 8, "to": 7 }, { "from": 9, "to": 8 }, { "from": 10, "to": 8 }, { "from": 11, "to": 8 }, { "from": 12, "to": 7 }, { "from": 13, "to": 7 }, { "from": 13, "to": 12 }, { "from": 14, "to": 2 }, { "from": 15, "to": 4 }, { "from": 16, "to": 8 }, { "from": 16, "to": 5 }, { "from": 17, "to": 9 }, { "from": 18, "to": 8 }, { "from": 18, "to": 10 }, { "from": 18, "to": 14 }, { "from": 19, "to": 10 }, { "from": 20, "to": 5 }, { "from": 20, "to": 9 }, { "from": 21, "to": 20 }, { "from": 22, "to": 21 }, { "from": 23, "to": 21 }, { "from": 24, "to": 20 }, { "from": 24, "to": 27 }, { "from": 25, "to": 20 }, { "from": 25, "to": 27 }, { "from": 26, "to": 8 }, { "from": 27, "to": 20 }, { "from": 28, "to": 20 }, { "from": 28, "to": 22 }, { "from": 29, "to": 11 }, { "from": 29, "to": 20 }, { "from": 30, "to": 20 }, { "from": 30, "to": 32 }, { "from": 31, "to": 20 }, { "from": 31, "to": 32 }, { "from": 32, "to": 20 }, { "from": 33, "to": 7 }, { "from": 33, "to": 12 }, { "from": 33, "to": 13 }, { "from": 34, "to": 33 }, { "from": 34, "to": 9 }, { "from": 35, "to": 34 }, { "from": 36, "to": 35 }, { "from": 36, "to": 6 }, { "from": 37, "to": 34 }, { "from": 38, "to": 36 }, { "from": 38, "to": 20 }, { "from": 39, "to": 35 }, { "from": 40, "to": 34 }, { "from": 40, "to": 39 }, { "from": 41, "to": 40 }, { "from": 42, "to": 40 }, { "from": 42, "to": 24 }, { "from": 43, "to": 40 }, { "from": 43, "to": 25 }, { "from": 44, "to": 8 }, { "from": 44, "to": 35 }, { "from": 45, "to": 44 }, { "from": 45, "to": 23 }, { "from": 46, "to": 44 }, { "from": 46, "to": 36 }, { "from": 47, "to": 44 }, { "from": 48, "to": 35 }, { "from": 48, "to": 44 }, { "from": 49, "to": 35 }, { "from": 49, "to": 44 }, { "from": 50, "to": 44 }, { "from": 50, "to": 6 }, { "from": 51, "to": 50 }, { "from": 52, "to": 50 }, { "from": 53, "to": 8 }, { "from": 53, "to": 66 }, { "from": 54, "to": 53 }, { "from": 55, "to": 53 }, { "from": 55, "to": 60 }, { "from": 56, "to": 53 }, { "from": 57, "to": 55 }, { "from": 58, "to": 57 }, { "from": 58, "to": 32 }, { "from": 59, "to": 53 }, { "from": 59, "to": 20 }, { "from": 60, "to": 54 }, { "from": 61, "to": 54 }, { "from": 61, "to": 60 }, { "from": 62, "to": 61 }, { "from": 63, "to": 1 }, { "from": 64, "to": 63 }, { "from": 65, "to": 62 }, { "from": 65, "to": 64 }, { "from": 66, "to": 4 }, { "from": 67, "to": 66 }, { "from": 68, "to": 66 }, { "from": 69, "to": 66 }, { "from": 70, "to": 66 }, { "from": 71, "to": 66 }, { "from": 72, "to": 66 }, { "from": 73, "to": 66 }, { "from": 73, "to": 72 }, { "from": 74, "to": 66 }, { "from": 74, "to": 73 }, { "from": 75, "to": 74 }, { "from": 75, "to": 79 }, { "from": 76, "to": 75 }, { "from": 76, "to": 77 }, { "from": 77, "to": 66 }, { "from": 78, "to": 66 }, { "from": 79, "to": 66 }, { "from": 79, "to": 22 }, { "from": 80, "to": 79 }, { "from": 81, "to": 79 }, { "from": 82, "to": 79 }, { "from": 82, "to": 65 }, { "from": 83, "to": 67 }, { "from": 83, "to": 79 }, { "from": 83, "to": 63 }, { "from": 84, "to": 67 }, { "from": 84, "to": 68 }, { "from": 85, "to": 84 }, { "from": 86, "to": 87 }, { "from": 87, "to": 79 }, { "from": 87, "to": 80 }, { "from": 87, "to": 84 }, { "from": 87, "to": 20 }, { "from": 88, "to": 86 }, { "from": 89, "to": 86 }, { "from": 90, "to": 88 }, { "from": 91, "to": 89 }, { "from": 92, "to": 87 }, { "from": 92, "to": 10 }, { "from": 93, "to": 66 }, { "from": 93, "to": 8 }, { "from": 94, "to": 93 }, { "from": 95, "to": 94 }, { "from": 95, "to": 74 }, { "from": 96, "to": 93 }, { "from": 96, "to": 19 }, { "from": 97, "to": 93 }, { "from": 97, "to": 84 }, { "from": 98, "to": 97 }, { "from": 98, "to": 78 }, { "from": 99, "to": 95 }, { "from": 99, "to": 96 }, { "from": 100, "to": 93 }, { "from": 100, "to": 79 }, { "from": 101, "to": 93 }, { "from": 101, "to": 19 }, { "from": 102, "to": 97 }, { "from": 102, "to": 98 }, { "from": 103, "to": 96 }, { "from": 103, "to": 97 }, { "from": 103, "to": 99 }, { "from": 103, "to": 100 }, { "from": 103, "to": 20 }, { "from": 104, "to": 103 }, { "from": 104, "to": 28 }, { "from": 105, "to": 20 }, { "from": 105, "to": 44 }, { "from": 105, "to": 53 }, { "from": 105, "to": 93 }, { "from": 106, "to": 105 }, { "from": 107, "to": 105 }, { "from": 108, "to": 105 }, { "from": 109, "to": 108 }, { "from": 110, "to": 105 }, { "from": 111, "to": 110 }, { "from": 112, "to": 105 }, { "from": 113, "to": 105 }, { "from": 114, "to": 106 }, { "from": 114, "to": 107 }, { "from": 114, "to": 108 }, { "from": 114, "to": 110 }, { "from": 114, "to": 112 }, { "from": 114, "to": 113 }, { "from": 115, "to": 114 }, { "from": 116, "to": 114 }, { "from": 116, "to": 9 }, { "from": 117, "to": 105 }, { "from": 117, "to": 34 }, { "from": 118, "to": 117 }, { "from": 118, "to": 6 }, { "from": 119, "to": 50 }, { "from": 119, "to": 118 }, { "from": 120, "to": 117 }, { "from": 121, "to": 119 }, { "from": 121, "to": 51 }, { "from": 122, "to": 119 }, { "from": 123, "to": 119 }, { "from": 124, "to": 51 }, { "from": 124, "to": 121 }, { "from": 125, "to": 124 }, { "from": 125, "to": 52 }, { "from": 126, "to": 125 }, { "from": 127, "to": 8 }, { "from": 128, "to": 127 }, { "from": 128, "to": 35 }, { "from": 129, "to": 128 }, { "from": 130, "to": 128 }, { "from": 130, "to": 129 }, { "from": 131, "to": 127 }, { "from": 132, "to": 131 }, { "from": 133, "to": 131 }, { "from": 133, "to": 132 }, { "from": 134, "to": 127 }, { "from": 135, "to": 127 }, { "from": 135, "to": 130 }, { "from": 135, "to": 133 }, { "from": 136, "to": 131 }, { "from": 136, "to": 11 }, { "from": 137, "to": 131 }, { "from": 137, "to": 136 }, { "from": 138, "to": 8 }, { "from": 138, "to": 131 }, { "from": 139, "to": 138 }, { "from": 140, "to": 138 }, { "from": 140, "to": 132 }, { "from": 141, "to": 138 }, { "from": 141, "to": 132 }, { "from": 142, "to": 138 }, { "from": 142, "to": 140 }, { "from": 143, "to": 138 }, { "from": 143, "to": 141 }, { "from": 144, "to": 138 }, { "from": 145, "to": 144 }, { "from": 145, "to": 142 }, { "from": 146, "to": 142 }, { "from": 146, "to": 145 }, { "from": 147, "to": 138 }, { "from": 147, "to": 3 }, { "from": 148, "to": 138 }, { "from": 148, "to": 20 }, { "from": 149, "to": 148 }, { "from": 149, "to": 114 }, { "from": 150, "to": 142 }, { "from": 150, "to": 143 }, { "from": 150, "to": 118 }, { "from": 151, "to": 143 }, { "from": 152, "to": 142 }, { "from": 153, "to": 140 }, { "from": 153, "to": 141 }, { "from": 154, "to": 138 }, { "from": 155, "to": 154 }, { "from": 156, "to": 154 }, { "from": 156, "to": 144 }, { "from": 157, "to": 154 }, { "from": 158, "to": 154 }, { "from": 158, "to": 147 }, { "from": 159, "to": 154 }, { "from": 160, "to": 159 }, { "from": 161, "to": 159 }, { "from": 162, "to": 159 }, { "from": 163, "to": 159 }, { "from": 163, "to": 155 }, { "from": 163, "to": 156 }, { "from": 164, "to": 158 }, { "from": 164, "to": 159 }, { "from": 165, "to": 154 }, { "from": 165, "to": 20 }, { "from": 166, "to": 165 }, { "from": 166, "to": 114 }, { "from": 167, "to": 165 }, { "from": 167, "to": 150 }, { "from": 168, "to": 154 }, { "from": 168, "to": 2 }, { "from": 169, "to": 168 }, { "from": 169, "to": 148 }, { "from": 170, "to": 169 }, { "from": 170, "to": 50 }, { "from": 171, "to": 169 }, { "from": 172, "to": 170 }, { "from": 172, "to": 119 }, { "from": 173, "to": 171 }, { "from": 173, "to": 119 }, { "from": 174, "to": 8 }, { "from": 174, "to": 9 }, { "from": 174, "to": 17 }, { "from": 175, "to": 174 }, { "from": 175, "to": 10 }, { "from": 175, "to": 19 }, { "from": 176, "to": 174 }, { "from": 177, "to": 8 }, { "from": 177, "to": 174 }, { "from": 178, "to": 177 }, { "from": 179, "to": 178 }, { "from": 179, "to": 16 }, { "from": 180, "to": 177 }, { "from": 180, "to": 9 }, { "from": 181, "to": 177 }, { "from": 181, "to": 20 }, { "from": 181, "to": 113 }, { "from": 182, "to": 178 }, { "from": 182, "to": 10 }, { "from": 184, "to": 183 }, { "from": 185, "to": 183 }, { "from": 185, "to": 144 }, { "from": 186, "to": 184 }, { "from": 186, "to": 185 }, { "from": 187, "to": 185 }, { "from": 188, "to": 185 }, { "from": 188, "to": 187 }, { "from": 189, "to": 183 }, { "from": 189, "to": 5 }, { "from": 190, "to": 189 }, { "from": 191, "to": 190 }, { "from": 191, "to": 184 }, { "from": 192, "to": 190 }, { "from": 192, "to": 184 }, { "from": 193, "to": 5 }, { "from": 193, "to": 185 }, { "from": 194, "to": 193 }, { "from": 194, "to": 6 }, { "from": 195, "to": 194 }, { "from": 195, "to": 191 }, { "from": 196, "to": 194 }, { "from": 197, "to": 194 }, { "from": 198, "to": 193 }, { "from": 198, "to": 194 }, { "from": 199, "to": 193 }, { "from": 199, "to": 194 }, { "from": 200, "to": 198 }, { "from": 200, "to": 199 }, { "from": 201, "to": 198 }, { "from": 201, "to": 199 }, { "from": 201, "to": 200 }, { "from": 202, "to": 201 }, { "from": 202, "to": 199 }, { "from": 203, "to": 201 }, { "from": 203, "to": 198 }, { "from": 204, "to": 201 }, { "from": 204, "to": 200 }, { "from": 205, "to": 198 }, { "from": 205, "to": 199 }, { "from": 205, "to": 200 }, { "from": 205, "to": 195 }, { "from": 206, "to": 205 }, { "from": 206, "to": 195 }, { "from": 207, "to": 183 }, { "from": 207, "to": 198 }, { "from": 207, "to": 199 }, { "from": 207, "to": 200 }, { "from": 208, "to": 207 }, { "from": 209, "to": 198 }, { "from": 209, "to": 20 }, { "from": 210, "to": 199 }, { "from": 210, "to": 20 }, { "from": 211, "to": 209 }, { "from": 211, "to": 210 }, { "from": 212, "to": 209 }, { "from": 212, "to": 210 }, { "from": 212, "to": 185 }, { "from": 213, "to": 209 }, { "from": 213, "to": 210 }, { "from": 214, "to": 212 }, { "from": 215, "to": 209 }, { "from": 215, "to": 210 }, { "from": 215, "to": 107 }, { "from": 216, "to": 209 }, { "from": 216, "to": 210 }, { "from": 216, "to": 106 }, { "from": 217, "to": 211 }, { "from": 217, "to": 212 }, { "from": 217, "to": 213 }, { "from": 217, "to": 215 }, { "from": 217, "to": 216 }, { "from": 218, "to": 200 }, { "from": 218, "to": 20 }, { "from": 219, "to": 218 }, { "from": 219, "to": 212 }, { "from": 220, "to": 218 }, { "from": 220, "to": 96 }, { "from": 221, "to": 202 }, { "from": 221, "to": 20 }, { "from": 222, "to": 203 }, { "from": 222, "to": 20 }, { "from": 223, "to": 204 }, { "from": 223, "to": 20 }, { "from": 224, "to": 217 }, { "from": 224, "to": 114 }, { "from": 225, "to": 217 }, { "from": 225, "to": 118 }, { "from": 226, "to": 225 }, { "from": 227, "to": 225 }, { "from": 228, "to": 225 }, { "from": 229, "to": 225 }, { "from": 230, "to": 225 }, { "from": 230, "to": 119 }, { "from": 231, "to": 226 }, { "from": 231, "to": 212 }, { "from": 232, "to": 226 }, { "from": 232, "to": 211 }, { "from": 233, "to": 198 }, { "from": 233, "to": 199 }, { "from": 234, "to": 201 }, { "from": 235, "to": 200 }, { "from": 235, "to": 198 }, { "from": 235, "to": 199 }, { "from": 236, "to": 198 }, { "from": 236, "to": 199 }, { "from": 236, "to": 191 }, { "from": 237, "to": 198 }, { "from": 237, "to": 199 }, { "from": 237, "to": 30 }, { "from": 237, "to": 31 }, { "from": 238, "to": 233 }, { "from": 238, "to": 198 }, { "from": 238, "to": 199 }, { "from": 239, "to": 238 }, { "from": 240, "to": 233 }, { "from": 240, "to": 234 }, { "from": 240, "to": 235 }, { "from": 240, "to": 236 }, { "from": 241, "to": 240 }, { "from": 242, "to": 198 }, { "from": 242, "to": 177 }, { "from": 242, "to": 182 }, { "from": 243, "to": 199 }, { "from": 243, "to": 177 }, { "from": 243, "to": 182 }, { "from": 244, "to": 200 }, { "from": 244, "to": 177 }, { "from": 244, "to": 182 }, { "from": 245, "to": 242 }, { "from": 245, "to": 243 }, { "from": 245, "to": 244 }, { "from": 245, "to": 10 }, { "from": 246, "to": 242 }, { "from": 246, "to": 243 }, { "from": 246, "to": 244 }, { "from": 246, "to": 11 }, { "from": 247, "to": 242 }, { "from": 247, "to": 243 }, { "from": 247, "to": 244 }, { "from": 247, "to": 181 }, { "from": 248, "to": 242 }, { "from": 248, "to": 243 }, { "from": 248, "to": 244 }, { "from": 248, "to": 174 }, { "from": 249, "to": 205 }, { "from": 249, "to": 242 }, { "from": 249, "to": 243 }, { "from": 249, "to": 244 }, { "from": 250, "to": 249 }, { "from": 250, "to": 192 }, { "from": 251, "to": 249 }, { "from": 251, "to": 14 }, { "from": 252, "to": 249 }, { "from": 252, "to": 28 }, { "from": 253, "to": 249 }, { "from": 253, "to": 239 }, { "from": 254, "to": 5 }, { "from": 254, "to": 185 }, { "from": 255, "to": 254 }, { "from": 256, "to": 254 }, { "from": 256, "to": 198 }, { "from": 256, "to": 199 }, { "from": 257, "to": 254 }, { "from": 257, "to": 198 }, { "from": 257, "to": 199 }, { "from": 258, "to": 254 }, { "from": 258, "to": 192 }, { "from": 259, "to": 254 }, { "from": 259, "to": 8 }, { "from": 260, "to": 259 }, { "from": 260, "to": 255 }, { "from": 261, "to": 260 }, { "from": 262, "to": 260 }, { "from": 263, "to": 260 }, { "from": 264, "to": 260 }, { "from": 265, "to": 264 }, { "from": 266, "to": 260 }, { "from": 266, "to": 32 }, { "from": 267, "to": 260 }, { "from": 267, "to": 34 }, { "from": 268, "to": 260 }, { "from": 269, "to": 5 }, { "from": 269, "to": 8 }, { "from": 270, "to": 269 }, { "from": 271, "to": 269 }, { "from": 271, "to": 20 }, { "from": 272, "to": 269 }, { "from": 272, "to": 9 }, { "from": 273, "to": 271 }, { "from": 273, "to": 270 }, { "from": 274, "to": 273 }, { "from": 275, "to": 273 }, { "from": 275, "to": 34 }, { "from": 276, "to": 275 }, { "from": 277, "to": 273 }, { "from": 277, "to": 118 }, { "from": 278, "to": 277 }, { "from": 278, "to": 53 }, { "from": 280, "to": 279 }, { "from": 281, "to": 279 }, { "from": 281, "to": 1 }, { "from": 282, "to": 279 }, { "from": 282, "to": 183 }, { "from": 283, "to": 279 }, { "from": 283, "to": 5 }, { "from": 284, "to": 281 }, { "from": 284, "to": 283 }, { "from": 285, "to": 283 }, { "from": 286, "to": 283 }, { "from": 286, "to": 285 }, { "from": 287, "to": 279 }, { "from": 287, "to": 283 }, { "from": 288, "to": 283 }, { "from": 288, "to": 285 }, { "from": 289, "to": 285 }, { "from": 289, "to": 286 }, { "from": 289, "to": 287 }, { "from": 291, "to": 290 }, { "from": 292, "to": 290 }, { "from": 292, "to": 291 }, { "from": 293, "to": 290 }, { "from": 293, "to": 292 }, { "from": 294, "to": 290 }, { "from": 295, "to": 290 }, { "from": 295, "to": 291 }, { "from": 296, "to": 290 }, { "from": 296, "to": 295 }, { "from": 297, "to": 290 }, { "from": 297, "to": 295 }, { "from": 298, "to": 296 }, { "from": 298, "to": 297 }, { "from": 299, "to": 295 }, { "from": 299, "to": 283 }, { "from": 300, "to": 299 }, { "from": 300, "to": 185 }, { "from": 301, "to": 299 }, { "from": 302, "to": 295 }, { "from": 302, "to": 298 }, { "from": 302, "to": 299 }, { "from": 303, "to": 17 }, { "from": 303, "to": 147 }, { "from": 303, "to": 164 }, { "from": 303, "to": 249 }, { "from": 304, "to": 303 }, { "from": 305, "to": 303 }, { "from": 306, "to": 303 }, { "from": 307, "to": 304 } ] }