gtsam/python/gtsam/examples/RangeSLAMExample_plaza2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Range SLAM with Batch Optimization\n",
    "\n",
    "A 2D Range SLAM example using batch optimization (Levenberg-Marquardt) on the Plaza2 dataset.\n",
    "\n",
    "This notebook mirrors the functionality of the MATLAB batch SLAM script, adapted using Python and GTSAM, drawing structural elements from the iSAM example.\n",
    "\n",
    "Author: Frank Dellaert (adapted for batch by AI)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"https://colab.research.google.com/github/borglab/gtsam/blob/develop/python/gtsam/examples/RangeSLAMExample_plaza2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "source": [
    "GTSAM Copyright 2010-2022, Georgia Tech Research Corporation,\n",
    "Atlanta, Georgia 30332-0415\n",
    "All Rights Reserved\n",
    "\n",
    "Authors: Frank Dellaert, et al. (see THANKS for the full author list)\n",
    "\n",
    "See LICENSE for the license information"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Data is second UWB ranging dataset, B2 or \"plaza 2\", from\n",
    "\n",
    "> \"Navigating with Ranging Radios: Five Data Sets with Ground Truth\", by Joseph Djugash, Bradley Hamner, and Stephan Roth, available at https://www.ri.cmu.edu/pub_files/2009/9/Final_5datasetsRangingRadios.pdf\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "tags": [
     "remove-cell"
    ],
    "vscode": {
     "languageId": "markdown"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[31mERROR: Could not find a version that satisfies the requirement gtsam-develop (from versions: none)\u001b[0m\u001b[31m\n",
      "\u001b[0m\u001b[31mERROR: No matching distribution found for gtsam-develop\u001b[0m\u001b[31m\n",
      "\u001b[0mNote: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "%pip install --quiet gtsam-develop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pylint: disable=invalid-name, E1101\n",
    "\n",
    "import gtsam\n",
    "from gtsam import Point2, Pose2, symbol\n",
    "import numpy as np\n",
    "import math\n",
    "import time \n",
    "import plotly.express as px\n",
    "\n",
    "from gtsam.utils import plot # Needs matplotlib\n",
    "from numpy.random import default_rng\n",
    "\n",
    "rng = default_rng()\n",
    "\n",
    "NM = gtsam.noiseModel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Read 4090 odometry entries.\n"
     ]
    }
   ],
   "source": [
    "# load the odometry\n",
    "# DR: Odometry Input (delta distance traveled and delta heading change)\n",
    "#    Time (sec)  Delta Distance Traveled (m) Delta Heading (rad)\n",
    "odometry_data = {}\n",
    "data_file_dr = gtsam.findExampleDataFile(\"Plaza2_DR.txt\")\n",
    "odo_times_list = []\n",
    "for row in np.loadtxt(data_file_dr):\n",
    "    t, distance_traveled, delta_heading = row\n",
    "    odometry_data[t] = Pose2(distance_traveled, 0, delta_heading)\n",
    "    odo_times_list.append(t)\n",
    "\n",
    "odo_times_list.sort() # Ensure times are sorted\n",
    "M = len(odometry_data)\n",
    "print(f\"Read {M} odometry entries.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Read 1816 range triples for 4 unique landmarks.\n"
     ]
    }
   ],
   "source": [
    "# load the ranges from TD\n",
    "#    Time (sec)  Sender / Antenna ID Receiver Node ID  Range (m)\n",
    "triples = []\n",
    "landmark_ids = set()\n",
    "data_file_td = gtsam.findExampleDataFile(\"Plaza2_TD.txt\")\n",
    "for row in np.loadtxt(data_file_td):\n",
    "    t, sender, receiver, _range = row\n",
    "    landmark_id = int(receiver)\n",
    "    triples.append((t, landmark_id, _range))\n",
    "    landmark_ids.add(landmark_id)\n",
    "\n",
    "K = len(triples)\n",
    "sorted_landmark_ids = sorted(list(landmark_ids))\n",
    "print(f\"Read {K} range triples for {len(landmark_ids)} unique landmarks.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Set Parameters and Noise Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "# parameters\n",
    "sigmaR = 50        # range standard deviation (matches MATLAB)\n",
    "sigmaInitialLandmark = 1.0 # Stddev for random landmark init (matches MATLAB)\n",
    "robust = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set Noise parameters (mirrors MATLAB script)\n",
    "priorSigmas = gtsam.Point3(1, 1, math.pi)  # Prior on Pose 0\n",
    "pointPriorSigmas = gtsam.Point2(1, 1) # Loose prior on landmarks\n",
    "odoSigmas = gtsam.Point3(0.05, 0.01, 0.2) # Odometry noise\n",
    "\n",
    "priorNoise = NM.Diagonal.Sigmas(priorSigmas) # prior on pose 0\n",
    "pointPriorNoise = NM.Diagonal.Sigmas(pointPriorSigmas) # loose LM prior\n",
    "odoNoise = NM.Diagonal.Sigmas(odoSigmas)     # odometry\n",
    "\n",
    "# Range noise\n",
    "gaussian = NM.Isotropic.Sigma(1, sigmaR)     # non-robust\n",
    "base = NM.mEstimator.Tukey(15) # Tukey M-estimator like MATLAB\n",
    "tukey = NM.Robust.Create(base, gaussian)  # robust\n",
    "rangeNoise = tukey if robust else gaussian"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Build Factor Graph and Initial Estimate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initializing Landmarks...\n",
      "Initialized 4 landmarks.\n"
     ]
    }
   ],
   "source": [
    "# Initialize Factor Graph and Initial Values\n",
    "graph = gtsam.NonlinearFactorGraph()\n",
    "initial = gtsam.Values()\n",
    "\n",
    "# Add prior on first pose\n",
    "# Estimate pose0 from the first odometry time's neighborhood or use a fixed reasonable guess.\n",
    "# Using the same value as the iSAM example for consistency.\n",
    "pose0 = Pose2(-34.2086489999201, 45.3007639991120, math.pi - 2.021089)\n",
    "graph.add(gtsam.PriorFactorPose2(0, pose0, priorNoise))\n",
    "initial.insert(0, pose0)\n",
    "\n",
    "# Initialize Landmarks (similar to MATLAB approach)\n",
    "print(\"Initializing Landmarks...\")\n",
    "for j in sorted_landmark_ids:\n",
    "    landmark_key = symbol('L', j)\n",
    "    # Initialize randomly around origin (adjust scale if needed)\n",
    "    initial_point = Point2(sigmaInitialLandmark * rng.normal(), sigmaInitialLandmark * rng.normal())\n",
    "    initial.insert(landmark_key, initial_point)\n",
    "    # Optional: Add a loose prior to help localization if landmarks are poorly constrained\n",
    "    # graph.add(gtsam.PriorFactorPoint2(landmark_key, Point2(0,0), pointPriorNoise))\n",
    "print(f\"Initialized {len(sorted_landmark_ids)} landmarks.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Building Pose Chain and Odometry Factors...\n",
      "Added 4090 odometry factors and initial pose estimates.\n"
     ]
    }
   ],
   "source": [
    "print(\"\\nBuilding Pose Chain and Odometry Factors...\")\n",
    "lastPose = pose0\n",
    "pose_times = [odo_times_list[0]] # Approximate time for pose 0\n",
    "# Loop over odometry measurements\n",
    "for i, t in enumerate(odo_times_list, 1):\n",
    "    # get odometry measurement for this time step\n",
    "    odometry = odometry_data[t]\n",
    "\n",
    "    # add odometry factor\n",
    "    graph.add(gtsam.BetweenFactorPose2(i - 1, i, odometry, odoNoise))\n",
    "\n",
    "    # predict pose and add as initial estimate\n",
    "    predictedPose = lastPose.compose(odometry)\n",
    "    lastPose = predictedPose\n",
    "    initial.insert(i, predictedPose)\n",
    "    pose_times.append(t)\n",
    "\n",
    "print(f\"Added {M} odometry factors and initial pose estimates.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Adding Range Factors...\n",
      "Added 1816 range factors.\n"
     ]
    }
   ],
   "source": [
    "print(\"\\nAdding Range Factors...\")\n",
    "# Convert pose_times to numpy array for efficient search\n",
    "pose_times_np = np.array(pose_times)\n",
    "\n",
    "# Add range factors\n",
    "range_factors_added = 0\n",
    "for t_range, landmark_id, measured_range in triples:\n",
    "    # Find the pose index active at the time of the range measurement\n",
    "    # Get the index of the *last* pose time that is <= t_range\n",
    "    pose_index = np.searchsorted(pose_times_np, t_range, side='right') - 1\n",
    "    \n",
    "    # Ensure pose_index is valid (it might be -1 if t_range is before the first odometry time)\n",
    "    if pose_index < 0:\n",
    "        # print(f\"Warning: Range measurement at time {t_range} is before the first pose time {pose_times_np[0]}. Skipping.\")\n",
    "        pose_index = 0 # Or skip the measurement\n",
    "\n",
    "    landmark_key = symbol('L', landmark_id)\n",
    "    graph.add(gtsam.RangeFactor2D(pose_index, landmark_key, measured_range, rangeNoise))\n",
    "    range_factors_added += 1\n",
    "\n",
    "print(f\"Added {range_factors_added} range factors.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimize the Factor Graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Optimizing the factor graph...\n",
      "Initial error: 2.9e+02, values: 4095\n",
      "iter      cost      cost_change    lambda  success iter_time\n",
      "   0      1.4e+05     -1.4e+05      1e-05      1       0.03\n",
      "iter      cost      cost_change    lambda  success iter_time\n",
      "   0      9.1e+03     -8.8e+03     0.0001      1       0.03\n",
      "iter      cost      cost_change    lambda  success iter_time\n",
      "   0      1.9e+02        1e+02      0.001      1       0.03\n",
      "   1      2.7e+03     -2.5e+03     0.0001      1       0.03\n",
      "   1      1.1e+02           86      0.001      1       0.02\n",
      "   2      1.7e+03     -1.6e+03     0.0001      1       0.02\n",
      "   2           85           22      0.001      1       0.03\n",
      "   3      6.3e+02     -5.5e+02     0.0001      1       0.03\n",
      "   3           76          8.4      0.001      1       0.02\n",
      "   4      3.1e+02     -2.3e+02     0.0001      1       0.02\n",
      "   4           68          8.6      0.001      1       0.03\n",
      "   5      1.9e+02     -1.2e+02     0.0001      1       0.03\n",
      "   5           55           13      0.001      1       0.03\n",
      "   6      2.6e+02       -2e+02     0.0001      1       0.02\n",
      "   6           39           16      0.001      1       0.02\n",
      "   7      1.4e+02          -99     0.0001      1       0.04\n",
      "   7           26           13      0.001      1       0.03\n",
      "   8           94          -68     0.0001      1       0.03\n",
      "   8           21          5.5      0.001      1       0.03\n",
      "   9           63          -43     0.0001      1       0.02\n",
      "   9           19          2.1      0.001      1       0.02\n",
      "  10           46          -27     0.0001      1       0.02\n",
      "  10           17          1.8      0.001      1       0.03\n",
      "  11           35          -18     0.0001      1       0.03\n",
      "  11           15          1.5      0.001      1       0.03\n",
      "  12           27          -12     0.0001      1       0.03\n",
      "  12           14          1.3      0.001      1       0.02\n",
      "  13           22         -7.9     0.0001      1       0.02\n",
      "  13           13          1.2      0.001      1       0.03\n",
      "  14           18         -5.2     0.0001      1       0.03\n",
      "  14           12            1      0.001      1       0.03\n",
      "  15           15         -3.3     0.0001      1       0.03\n",
      "  15           11          0.9      0.001      1       0.02\n",
      "  16           13           -2     0.0001      1       0.02\n",
      "  16           10         0.79      0.001      1       0.04\n",
      "  17           11         -1.1     0.0001      1       0.03\n",
      "  17          9.3          0.7      0.001      1       0.03\n",
      "  18          9.8        -0.44     0.0001      1       0.03\n",
      "  18          8.7         0.62      0.001      1       0.02\n",
      "  19          8.7        0.023     0.0001      1       0.02\n",
      "  20           67          -58      1e-05      1       0.02\n",
      "  20            5          3.7     0.0001      1       0.03\n",
      "  21           23          -18      1e-05      1       0.03\n",
      "  21          3.5          1.4     0.0001      1       0.03\n",
      "  22          9.4         -5.9      1e-05      1       0.03\n",
      "  22            3         0.57     0.0001      1       0.03\n",
      "  23            5           -2      1e-05      1       0.03\n",
      "  23          2.6         0.34     0.0001      1       0.02\n",
      "  24          3.3        -0.71      1e-05      1       0.02\n",
      "  24          2.4         0.26     0.0001      1       0.03\n",
      "  25          2.6        -0.19      1e-05      1       0.03\n",
      "  25          2.2         0.21     0.0001      1       0.03\n",
      "  26          2.1        0.034      1e-05      1       0.03\n",
      "  27          3.7         -1.5      1e-06      1       0.03\n",
      "  27          1.1            1      1e-05      1       0.02\n",
      "  28          1.4        -0.24      1e-06      1       0.04\n",
      "  28         0.93          0.2      1e-05      1       0.03\n",
      "  29         0.96       -0.031      1e-06      1       0.04\n",
      "  29         0.88        0.048      1e-05      1       0.09\n",
      "  30         0.88      0.00063      1e-06      1       0.03\n",
      "Optimization complete in 1.93 seconds.\n",
      "Initial Error: 294.2927831483431\n",
      "Final Error: 0.8771120075818397\n"
     ]
    }
   ],
   "source": [
    "# Graph built, optimize!\n",
    "print(\"\\nOptimizing the factor graph...\")\n",
    "start_time = time.time()\n",
    "\n",
    "params = gtsam.LevenbergMarquardtParams()\n",
    "params.setRelativeErrorTol(1e-3) # Convergence tolerance\n",
    "params.setVerbosityLM(\"SUMMARY\") # Print LM progress\n",
    "optimizer = gtsam.LevenbergMarquardtOptimizer(graph, initial, params)\n",
    "result = optimizer.optimize()\n",
    "\n",
    "end_time = time.time()\n",
    "print(f\"Optimization complete in {end_time - start_time:.2f} seconds.\")\n",
    "\n",
    "print(f\"Initial Error: {graph.error(initial)}\")\n",
    "print(f\"Final Error: {graph.error(result)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Print and Visualize Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Optimized Landmark Locations:\n",
      "  L0: [-48.11741249  31.92467992]\n",
      "  L1: [-80.92811295  53.95372591]\n",
      "  L5: [-47.60339748 -19.97294509]\n",
      "  L6: [-17.70157972  66.35356579]\n"
     ]
    }
   ],
   "source": [
    "# Print optimized landmarks:\n",
    "print(\"\\nOptimized Landmark Locations:\")\n",
    "for j in [0, 1, 5, 6]: # Print specific landmarks like MATLAB example\n",
    "    if j in sorted_landmark_ids:\n",
    "        landmark_key = gtsam.symbol('L', j)\n",
    "        try:\n",
    "            p = result.atPoint2(landmark_key)\n",
    "            print(f\"  L{j}: {p}\")\n",
    "        except Exception as e:\n",
    "            print(f\"  L{j}: Not found in result ({e})\")\n",
    "    else:\n",
    "        print(f\"  L{j}: Not present in TD data.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Extracted 4091 final poses and 4 landmarks.\n"
     ]
    }
   ],
   "source": [
    "# Extract poses and landmarks for plotting\n",
    "poses_result = gtsam.utilities.allPose2s(result)\n",
    "landmarks_result = gtsam.utilities.extractPoint2(result)\n",
    "positions_result = np.array([poses_result.atPose2(key).translation() \n",
    "                             for key in range(M + 1)]) # Poses 0 to M\n",
    "\n",
    "# Also extract initial estimate poses (dead reckoning)\n",
    "poses_initial = gtsam.utilities.allPose2s(initial)\n",
    "positions_initial = np.array([poses_initial.atPose2(key).translation() \n",
    "                              for key in range(M + 1)])\n",
    "\n",
    "print(f\"\\nExtracted {positions_result.shape[0]} final poses and {landmarks_result.shape[0]} landmarks.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
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           "sequential": [
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           "sequentialminus": [
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           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "zaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        },
        "title": {
         "text": "Plaza2 Batch SLAM Result"
        },
        "xaxis": {
         "anchor": "y",
         "domain": [
          0,
          1
         ],
         "title": {
          "text": "X (m)"
         }
        },
        "yaxis": {
         "anchor": "x",
         "domain": [
          0,
          1
         ],
         "scaleanchor": "x",
         "scaleratio": 1,
         "title": {
          "text": "Y (m)"
         }
        }
       }
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot using Plotly (similar to iSAM example)\n",
    "fig = px.line(x=positions_initial[:,0], y=positions_initial[:,1], title='Plaza2 Batch SLAM Result')\n",
    "fig.data[0].name = 'Initial (Odometry)'\n",
    "fig.data[0].showlegend = True\n",
    "fig.data[0].line.color = 'orange'\n",
    "fig.data[0].line.dash = 'dash'\n",
    "\n",
    "fig.add_scatter(x=positions_result[:,0], y=positions_result[:,1], mode='lines', \n",
    "                line=dict(color='black'), name='Optimized Path')\n",
    "\n",
    "fig.add_scatter(x=landmarks_result[:,0], y=landmarks_result[:,1], mode='markers', \n",
    "                marker=dict(color='red', symbol='star', size=8), name='Landmarks')\n",
    "\n",
    "# Configure layout\n",
    "fig.update_layout(margin=dict(l=20, r=20, t=40, b=20), \n",
    "                  legend=dict(yanchor=\"top\", y=0.99, xanchor=\"left\", x=0.01),\n",
    "                  xaxis_title=\"X (m)\", yaxis_title=\"Y (m)\")\n",
    "fig.update_yaxes(scaleanchor=\"x\", scaleratio=1) # Ensure aspect ratio is 1:1\n",
    "fig.show()"
   ]
  }
 ],
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