{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fitting a model to data with both x and y errors with `Bilby`\n",
    "\n",
    "Usually when we fit a model to data with a Gaussian Likelihood we assume that we know x values exactly. This is almost never the case. Here we show how to fit a model with errors in both x and y."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-03-20T14:26:58.473765Z",
     "iopub.status.busy": "2025-03-20T14:26:58.473608Z",
     "iopub.status.idle": "2025-03-20T14:26:59.553430Z",
     "shell.execute_reply": "2025-03-20T14:26:59.552887Z"
    }
   },
   "outputs": [],
   "source": [
    "import bilby\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from bilby.core.utils.random import seed, rng\n",
    "\n",
    "#sets seed of bilby's generator \"rng\" to \"123\"\n",
    "seed(123)\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulate data\n",
    "\n",
    "First we create the data and plot it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-03-20T14:26:59.555623Z",
     "iopub.status.busy": "2025-03-20T14:26:59.555076Z",
     "iopub.status.idle": "2025-03-20T14:26:59.635625Z",
     "shell.execute_reply": "2025-03-20T14:26:59.635160Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# define our model, a line\n",
    "def model(x, m, c, **kwargs):\n",
    "    y = m * x + c\n",
    "    return y\n",
    "\n",
    "\n",
    "# make a function to create and plot our data\n",
    "def make_data(points, m, c, xerr, yerr, seed):\n",
    "    xtrue = np.linspace(0, 100, points)\n",
    "    ytrue = model(x=xtrue, m=m, c=c)\n",
    "\n",
    "    xerr_vals = xerr * rng.standard_normal(points)\n",
    "    yerr_vals = yerr * rng.standard_normal(points)\n",
    "    xobs = xtrue + xerr_vals\n",
    "    yobs = ytrue + yerr_vals\n",
    "\n",
    "    plt.errorbar(xobs, yobs, xerr=xerr, yerr=yerr, fmt=\"x\")\n",
    "    plt.errorbar(xtrue, ytrue, yerr=yerr, color=\"black\", alpha=0.5)\n",
    "    plt.xlim(0, 100)\n",
    "    plt.show()\n",
    "    plt.close()\n",
    "\n",
    "    data = {\n",
    "        \"xtrue\": xtrue,\n",
    "        \"ytrue\": ytrue,\n",
    "        \"xobs\": xobs,\n",
    "        \"yobs\": yobs,\n",
    "        \"xerr\": xerr,\n",
    "        \"yerr\": yerr,\n",
    "    }\n",
    "\n",
    "    return data\n",
    "\n",
    "\n",
    "data = make_data(points=30, m=5, c=10, xerr=5, yerr=5, seed=123)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define our prior and sampler settings\n",
    "\n",
    "Now lets set up the prior and bilby output directory/sampler settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-03-20T14:26:59.637317Z",
     "iopub.status.busy": "2025-03-20T14:26:59.636973Z",
     "iopub.status.idle": "2025-03-20T14:26:59.639758Z",
     "shell.execute_reply": "2025-03-20T14:26:59.639360Z"
    }
   },
   "outputs": [],
   "source": [
    "# setting up bilby priors\n",
    "priors = dict(\n",
    "    m=bilby.core.prior.Uniform(0, 30, \"m\"), c=bilby.core.prior.Uniform(0, 30, \"c\")\n",
    ")\n",
    "\n",
    "sampler_kwargs = dict(priors=priors, sampler=\"bilby_mcmc\", nsamples=1000, printdt=5, outdir=\"outdir\", verbose=False, clean=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fit with exactly known x-values\n",
    "\n",
    "Our first step is to recover the straight line using a simple Gaussian Likelihood that only takes into account the y errors. Under the assumption we know x exactly. In this case, we pass in xtrue for x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-03-20T14:26:59.641336Z",
     "iopub.status.busy": "2025-03-20T14:26:59.641014Z",
     "iopub.status.idle": "2025-03-20T14:27:16.651742Z",
     "shell.execute_reply": "2025-03-20T14:27:16.651267Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:26 bilby INFO    : Running for label 'known_x', output will be saved to 'outdir'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Analysis priors:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : m=Uniform(minimum=0, maximum=30, name='m', latex_label='m', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : c=Uniform(minimum=0, maximum=30, name='c', latex_label='c', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Analysis likelihood class: <class 'bilby.core.likelihood.GaussianLikelihood'>\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Analysis likelihood noise evidence: nan\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Single likelihood evaluation took 5.887e-05 s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Using sampler Bilby_MCMC with kwargs {'nsamples': 1000, 'nensemble': 1, 'pt_ensemble': False, 'ntemps': 1, 'Tmax': None, 'Tmax_from_SNR': 20, 'initial_betas': None, 'adapt': True, 'adapt_t0': 100, 'adapt_nu': 10, 'pt_rejection_sample': False, 'burn_in_nact': 10, 'thin_by_nact': 1, 'fixed_discard': 0, 'autocorr_c': 5, 'L1steps': 100, 'L2steps': 3, 'printdt': 5, 'check_point_delta_t': 1800, 'min_tau': 1, 'proposal_cycle': 'default', 'stop_after_convergence': False, 'fixed_tau': None, 'tau_window': None, 'evidence_method': 'stepping_stone', 'initial_sample_method': 'prior', 'initial_sample_dict': None}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Global meta data was removed from the result object for compatibility. Use the `BILBY_INCLUDE_GLOBAL_METADATA` environment variable to include it. This behaviour will be removed in a future release. For more details see: https://bilby-dev.github.io/bilby/faq.html#global-meta-data\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Initializing BilbyPTMCMCSampler with:\n",
      "  Convergence settings: ConvergenceInputs(autocorr_c=5, burn_in_nact=10, thin_by_nact=1, fixed_discard=0, target_nsamples=1000, stop_after_convergence=False, L1steps=100, L2steps=3, min_tau=1, fixed_tau=None, tau_window=None)\n",
      "  Parallel-tempering settings: ParallelTemperingInputs(ntemps=1, nensemble=1, Tmax=None, Tmax_from_SNR=20, initial_betas=None, adapt=True, adapt_t0=100, adapt_nu=10, pt_ensemble=False)\n",
      "  proposal_cycle: default\n",
      "  pt_rejection_sample: False\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Setting parallel tempering inputs=ParallelTemperingInputs(ntemps=1, nensemble=1, Tmax=None, Tmax_from_SNR=20, initial_betas=None, adapt=True, adapt_t0=100, adapt_nu=10, pt_ensemble=False)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Initializing BilbyPTMCMCSampler with:ntemps=1, nensemble=1, pt_ensemble=False, initial_betas=[1], initial_sample_method=prior, initial_sample_dict=None\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Using initial sample {'m': 9.290579764179022, 'c': 5.310327080197345}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Using ProposalCycle:\n",
      "  AdaptiveGaussianProposal(acceptance_ratio:nan,n:0,scale:1,)\n",
      "  DifferentialEvolutionProposal(acceptance_ratio:nan,n:0,)\n",
      "  UniformProposal(acceptance_ratio:nan,n:0,)\n",
      "  KDEProposal(acceptance_ratio:nan,n:0,trained:0,)\n",
      "  FisherMatrixProposal(acceptance_ratio:nan,n:0,scale:1,)\n",
      "  GMMProposal(acceptance_ratio:nan,n:0,trained:0,)\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Setting convergence_inputs=ConvergenceInputs(autocorr_c=5, burn_in_nact=10, thin_by_nact=1, fixed_discard=0, target_nsamples=1000, stop_after_convergence=False, L1steps=100, L2steps=3, min_tau=1, fixed_tau=None, tau_window=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Drawing 1000 samples\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Checkpoint every check_point_delta_t=1800s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Print update every printdt=5s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Reached convergence: exiting sampling\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Checkpoint start\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Written checkpoint file outdir/known_x_resume.pickle\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Zero-temperature proposals:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : AdaptiveGaussianProposal(acceptance_ratio:0.23,n:2.3e+04,scale:0.0013,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : DifferentialEvolutionProposal(acceptance_ratio:0.46,n:2.4e+04,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : UniformProposal(acceptance_ratio:1,n:1e+03,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : KDEProposal(acceptance_ratio:0.00013,n:2.3e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : FisherMatrixProposal(acceptance_ratio:0.55,n:2.4e+04,scale:1,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : GMMProposal(acceptance_ratio:4.5e-05,n:2.2e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Current taus={'m': 1, 'c': 1}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Creating diagnostic plots\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Checkpoint finished\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Sampling time: 0:00:10.010002\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Summary of results:\n",
      "nsamples: 1004\n",
      "ln_noise_evidence:    nan\n",
      "ln_evidence:    nan +/-    nan\n",
      "ln_bayes_factor:    nan +/-    nan\n",
      "\n"
     ]
    }
   ],
   "source": [
    "known_x = bilby.core.likelihood.GaussianLikelihood(\n",
    "    x=data[\"xtrue\"], y=data[\"yobs\"], func=model, sigma=data[\"yerr\"]\n",
    ")\n",
    "result_known_x = bilby.run_sampler(\n",
    "    likelihood=known_x,\n",
    "    label=\"known_x\",\n",
    "    **sampler_kwargs,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-03-20T14:27:16.653456Z",
     "iopub.status.busy": "2025-03-20T14:27:16.653131Z",
     "iopub.status.idle": "2025-03-20T14:27:18.038968Z",
     "shell.execute_reply": "2025-03-20T14:27:18.038420Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 550x550 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = result_known_x.plot_corner(truth=dict(m=5, c=10), titles=True, save=False)\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fit with unmodeled uncertainty in the x-values\n",
    "\n",
    "As expected this is easy to recover and the sampler does a good job. However this was made too easy - by passing in the 'true' values of x. Lets see what happens when we pass in the observed values of x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-03-20T14:27:18.040862Z",
     "iopub.status.busy": "2025-03-20T14:27:18.040470Z",
     "iopub.status.idle": "2025-03-20T14:27:44.306864Z",
     "shell.execute_reply": "2025-03-20T14:27:44.306339Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Running for label 'incorrect_x', output will be saved to 'outdir'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Analysis priors:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : m=Uniform(minimum=0, maximum=30, name='m', latex_label='m', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : c=Uniform(minimum=0, maximum=30, name='c', latex_label='c', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Analysis likelihood class: <class 'bilby.core.likelihood.GaussianLikelihood'>\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Analysis likelihood noise evidence: nan\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Single likelihood evaluation took 5.738e-05 s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Using sampler Bilby_MCMC with kwargs {'nsamples': 1000, 'nensemble': 1, 'pt_ensemble': False, 'ntemps': 1, 'Tmax': None, 'Tmax_from_SNR': 20, 'initial_betas': None, 'adapt': True, 'adapt_t0': 100, 'adapt_nu': 10, 'pt_rejection_sample': False, 'burn_in_nact': 10, 'thin_by_nact': 1, 'fixed_discard': 0, 'autocorr_c': 5, 'L1steps': 100, 'L2steps': 3, 'printdt': 5, 'check_point_delta_t': 1800, 'min_tau': 1, 'proposal_cycle': 'default', 'stop_after_convergence': False, 'fixed_tau': None, 'tau_window': None, 'evidence_method': 'stepping_stone', 'initial_sample_method': 'prior', 'initial_sample_dict': None}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Global meta data was removed from the result object for compatibility. Use the `BILBY_INCLUDE_GLOBAL_METADATA` environment variable to include it. This behaviour will be removed in a future release. For more details see: https://bilby-dev.github.io/bilby/faq.html#global-meta-data\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Initializing BilbyPTMCMCSampler with:\n",
      "  Convergence settings: ConvergenceInputs(autocorr_c=5, burn_in_nact=10, thin_by_nact=1, fixed_discard=0, target_nsamples=1000, stop_after_convergence=False, L1steps=100, L2steps=3, min_tau=1, fixed_tau=None, tau_window=None)\n",
      "  Parallel-tempering settings: ParallelTemperingInputs(ntemps=1, nensemble=1, Tmax=None, Tmax_from_SNR=20, initial_betas=None, adapt=True, adapt_t0=100, adapt_nu=10, pt_ensemble=False)\n",
      "  proposal_cycle: default\n",
      "  pt_rejection_sample: False\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Setting parallel tempering inputs=ParallelTemperingInputs(ntemps=1, nensemble=1, Tmax=None, Tmax_from_SNR=20, initial_betas=None, adapt=True, adapt_t0=100, adapt_nu=10, pt_ensemble=False)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Initializing BilbyPTMCMCSampler with:ntemps=1, nensemble=1, pt_ensemble=False, initial_betas=[1], initial_sample_method=prior, initial_sample_dict=None\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Using initial sample {'m': 9.358110061085181, 'c': 20.036744978532123}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Using ProposalCycle:\n",
      "  AdaptiveGaussianProposal(acceptance_ratio:nan,n:0,scale:1,)\n",
      "  DifferentialEvolutionProposal(acceptance_ratio:nan,n:0,)\n",
      "  UniformProposal(acceptance_ratio:nan,n:0,)\n",
      "  KDEProposal(acceptance_ratio:nan,n:0,trained:0,)\n",
      "  FisherMatrixProposal(acceptance_ratio:nan,n:0,scale:1,)\n",
      "  GMMProposal(acceptance_ratio:nan,n:0,trained:0,)\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Setting convergence_inputs=ConvergenceInputs(autocorr_c=5, burn_in_nact=10, thin_by_nact=1, fixed_discard=0, target_nsamples=1000, stop_after_convergence=False, L1steps=100, L2steps=3, min_tau=1, fixed_tau=None, tau_window=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Drawing 1000 samples\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Checkpoint every check_point_delta_t=1800s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Print update every printdt=5s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Reached convergence: exiting sampling\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Checkpoint start\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Written checkpoint file outdir/incorrect_x_resume.pickle\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Zero-temperature proposals:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : AdaptiveGaussianProposal(acceptance_ratio:0.23,n:5.2e+04,scale:0.0038,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : DifferentialEvolutionProposal(acceptance_ratio:0.43,n:4.4e+04,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : UniformProposal(acceptance_ratio:1,n:9.8e+02,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : KDEProposal(acceptance_ratio:0,n:5e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : FisherMatrixProposal(acceptance_ratio:0.33,n:4.6e+04,scale:1,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : GMMProposal(acceptance_ratio:3.8e-05,n:5.3e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Current taus={'m': 1, 'c': 1.0}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Creating diagnostic plots\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Checkpoint finished\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Sampling time: 0:00:20.016086\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Summary of results:\n",
      "nsamples: 1599\n",
      "ln_noise_evidence:    nan\n",
      "ln_evidence:    nan +/-    nan\n",
      "ln_bayes_factor:    nan +/-    nan\n",
      "\n"
     ]
    }
   ],
   "source": [
    "incorrect_x = bilby.core.likelihood.GaussianLikelihood(\n",
    "    x=data[\"xobs\"], y=data[\"yobs\"], func=model, sigma=data[\"yerr\"]\n",
    ")\n",
    "result_incorrect_x = bilby.run_sampler(\n",
    "    likelihood=incorrect_x,\n",
    "    label=\"incorrect_x\",\n",
    "    **sampler_kwargs,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-03-20T14:27:44.308891Z",
     "iopub.status.busy": "2025-03-20T14:27:44.308488Z",
     "iopub.status.idle": "2025-03-20T14:27:44.453672Z",
     "shell.execute_reply": "2025-03-20T14:27:44.453104Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DyKxkUgFLbogwPrZnjlRXIrJPDALIrOROErw0LtLaxegQjlRXIrJP7A4gIiJyUGwJILPS60Wk5BkS7cQFKK1cGsu6sq4Spg0mok6GQQCZVZVGj55vHgZg22mD6zIC1s8M2FpX1pVpg4mos2EQQA6lqYyAfq4yK5aKiMg6GASQQ7kyIyDAtQGIyHExCCCHw4yAREQGnB1ARETkoBgEEBEROSgGAURERA6KYwLIrGRSAQuvDTM+tmeOVFcisk8MAsis5E4SvDkx2trF6BCOVFcisk/sDiAiInJQbAmgdssorjbOu9eLInJUNQCAIA85UvOqrFk0i9LrRWSUqAEAEV4Kpg0mok6HQQC1S0ZxNeJWHEJljb7Jbew1I1+VRo+oVw8AYNpgIuqcGARQuxRUaFBZo8faWd0RF6hElUaHa94/DgDY/UhvuMikzMhHRGSjGASQWcQFKtE/zB0Vap3xub4h7rw7JiKyYRwYSERE5KAYBBARETkoBgFEREQOikEAERGRg+LAQDIrJ6mAh4YFGx/bM0eqKxHZJwYBZFYKJwk+mBZr7WJ0CEeqKxHZJ3YHEBEROSi2BJBZiaJoTCHs5yqDINhvM7kj1ZWI7BODADKryho9ApbsB2D/qXQdqa5EZJ/YHUBEROSgGAQQERE5KAYBREREDopjAojMLKO42jhgEABXUSQim8UggMiMMoqrEbfiECpr9MbnlHIJUp5KZCBARDaHQQCRGRVUaFBZo8faWd0RF6hESm4lZq9LRUGFhkEAEdkcBgFkVk5SAXMSA42P7VlzdY0LVKJ/mLs1ikVEZDIGAWRWCicJPr+9u7WLYXYpuZXGx3V9/PZaVyJyHAwCiJrh5yqDUi7B7HWpxufYx09E9oJBAJmVKIrGQXFKuaTTp9KN8HZGylOJxtH+9fv4w70UdlVXInI8DALIrCpr9HBbvAeA/aTSjfB2bvSu3x7rSkSOhcmCiIiIHBSDACIiIgfFIICIiMhBMQggIiJyUAwCiIiIHBSDACIiIgfFKYJkVlKJgOm9/YyP7VVKbiXUWj2ui/WCwkmw67oSkf1iEEBm5SyTYP2ceGsXw2KayiCYV17DDIJE1OkwCCBqheYyCDIIIKLOhkEAUSs1lUGQiKiz4cBAMqsKtQ7Ck39BePIvVKh11i6ORVWodRjw7lEAQJXGvutKRPaJQQAREZGDYncAkRmczquCi0yKlNxKaxeFiMhkDAKIzODeb88aHyvlEvi5yqxYGiIi0zAIoFbLKK5uMDqegN2P9IaLzLCUsJ+rjAMHiahTYBBArZJRXI24FYdQWaM3Psc7X6BviDtcFVJrF4OIqFUYBFCrFFRoUFmjx9pZ3REXqATAO18ios6KQQC1SVygEv3D3K96XioRMD7Ox/jYnjlSXYnIPjEIILNylkmw9d6e1i5Gh3CkuhKRfWKeACIiIgfFIICIiMhBMQggs6pQ6+D67G64PrvbIdIGO0pdicg+cUwAmV396YP2zpHqSkT2hy0BREREDootAdQiZggkIrJPDAKoWcwQSERkvxgEULOYIdA86reg8PwRka1gEEAmaSpDIDXPz1UGpVyC2etSjc8p5RKkPJXIQICIrI5BAJmVRAKM6uppfGzPTKlrhLczUp5KbDCmYva6VBRUaBgEEJHVMQggs3KRSbHzoT7WLkaHMLWuEd7OvOATkU2y83s1IiIiagqDACIiIgfFIIDMqkKtg/+L++D/4j67T6XrSHUlIvvEMQFkdnWD4ByBI9WViOwPWwKIiIgcFIMAIiIiB8UggIiIyEExCCAiInJQDAKIiIgcFGcHkFlJJEBiuJvxsT1zpLoSkX1iEEBXySiubpDrvjVcZFIcfLy/JYplcxyprkRknxgEUAMZxdWIW3EIlTV643NKuQR+rjIrloqIiCyBQQA1UFChQWWNHmtndUdcoBKAYTlcLoBjXvVbWHh+ichaGARQo+IClegf5t7q/SprdIhfcQgAkPxUIpRyqbmLZjPaUlc/VxmUcglmr0s1PqeUS5DyVCIDASLqcAwCyKxEEbhYrDY+tmdtqWuEtzNSnkpsMOZi9rpUFFRoGAQQUYdjEEDUwSK8nXnBJyKbwIlNREREDopBABERkYNidwCRDeBsASKyBgYBRFbE2QJEZE0MAsisBAGIr80vIAhWLoyFmaOunC1ARNbEIIDMSimX4tRTidYuRocwV105W4CIrIVBgAOqvzYAwD5oIiJHxSDAwTS1NgD7oImIHA+DAAdz5doA5u6DrqzRYeC/jgIADj7ez+7TBjtKXYnIPjEIcFBtXRugJaIIJNdOd3OEtMGOUlcisk9MFkREROSgGAQQERE5KHYHENkgZhAkoo7AIIDIhjCDIBF1JAYBBOCfO8/6d6DU8ZhBkIg6EoMAB9fUnaefq6xNxxMEoIu3wvjYnlmqrswgSEQdhUGAg7vyzhNoXx+0Ui5F+vODzVU8m+ZIdSUi+8QggHjnSUTkoBgEOID6awWwz5+IiOowCLBzTa0V0NY+/5ZUaXQY+UESAOCvh/vARWa/qXQdqa5EZJ8YBNi5K9cKACw771yvBw5llhsf2zNHqisR2ScGAQ7CUmsFEBFR58UggKgTYAZBIrIEBgFENowZBInIkhgEENmwpjII7jpfirhAw3NsGSCitmIQQGTj6udxYMsAEZkTgwA7ZO28AJaafmiLOrquXFuAiMyJQYCd6ei8AFdyVUiR/8rQDnkva7NWXZnhkYjMhUGAnenovABERNR5MQiwU8wLQERELZFYuwBkX6o0Olz7YRKu/TAJVRqdtYtjUY5UVyJrSk9Px+TJk+Hu7g5vb2/ceeedKCgoaHG/nTt3QhCEq/4lJiYCAK699tpGXxcEAa+//rqlq2UT2BJAZqXXA3+eKzU+tmeOVFciaykvL8fo0aPh6+uLr7/+GlVVVXjmmWdw8803Y9++fZBIWr6X/eSTT5CQkGD8283NDQDw4YcfQqVSNdj2yy+/xIcffojx48ebtyI2ikEAkR1gRkHqjNLT0xEVFYULFy4gMjKy0W1WrVqF7Oxs7N27F8HBwQCAyMhIDBo0CJs3b8aUKVNafJ+EhAQMGTLkqufj4+Oveu7RRx9Fr1690Lt379ZVppNiEEDUiTFvANm7LVu2YPTo0cYAAAAGDhyIbt264ccffzQpCDDV2bNncfDgQbzxxhtmO6at45gAok6sLm/A4QX9cHhBP6yd1R2VNXpjHgGyTaIoYvfu3Vi0aBGGDBkCLy8vyOVyhISEYNq0adixY0eT++bk5GDBggWIjY2Fs7Mz/Pz8cOONN+Lnn3/ukDK0p+xtkZyc3KApv05CQgJSUlJMOsbkyZMhlUoRFBSE+++/H8XFxY1ut3btWkgkEsyaNatdZe5UROpQpaWlIgCxtLTUIsc/nKkS8cSf4uFMlUWO35Lyaq2IJ/4U8cSfYnm11ipl6Ci2WFdr//9vL0t/P2zFb7/9JgIQAYgSiUTs1q2b2K9fP9HNzc34/PPPP3/VfsePHxcDAwNFAKJCoRAHDBggxsTEGPdZvny5xcvQ1v1EURT1er2o0WiM/9LS0kQAYlpaWoPn9Xq9cR+ZTCYuXbr0qmPNmzdP7NatW7N1PHLkiLhw4ULxxx9/FHfs2CG+9tproru7u9i3b1+xpqbmqu1jYmLE0aNHt3Tq7ApbAuxARnE1jlwqw5FLZVbJEEi2JyW30viZyCiutnZx6AqiKCImJgYffvghCgoKkJqaiiNHjqCwsBDPPvssAGDZsmXYsmWLcR+tVovp06cjNzcX1157LTIzM3Ho0CGcPXsWv//+O9zd3bF48WL89ddfFitDe/YDgDVr1kAmkxn/xcTEAABiYmIaPL9mzZoG+wmC0Gj5W9KvXz+8+eabmDBhAq699lo8++yz+Oqrr3Ds2DFs2LChwbb79+9HWloaZs+e3eJx7QnHBHRy1s4Q2Bil3HFiS1urK8cIdA6DBg1CSkoKnJwa/gTL5XK89tprOHbsGH766Sd8/PHHmDBhAgBg69atOHPmDBQKBT7//HP4+/sb9xszZgyee+45PPPMM3j55Zfx+++/W6QM7dkPACZOnIiDBw8a/87OzsakSZPwww8/NOjzj4qKMj729vZutPm+uLgYPj4+LdbzShMmTICrqysOHTqE22+/3fj82rVr4ezsjOnTp7f6mJ0Zg4BO6Mq1AWwpQ6CrQoqK5ddY5b07mi3W1ZS1Bep/fgDOJrAGDw+PZl8fO3YsfvrpJ5w5c8b43J49ewAYBsV16dLlqn2mTZuGZ555Bjt37kReXh4CAgLMXob27AcAvr6+8PX1Nf6dnp4OAOjVq1eTswMSEhKQnJx81fPJyckYNmxYs2VpTv3WBa1Wi2+//RYTJ05ssX72hkFAJ9PUnf+IaE/+kBOA5tcWaOrzw5YC21JdbejCcXFxMT5XdzccGhra6D51z+v1ehw8eBA333yz2ctgyf2aMmHCBDz33HPIyclBUFAQAODw4cNITU3F8uXLW328H374ARUVFRg4cKDxuZ9//hn5+fkO1xUAMAiwmmOXy+CmMkSirbkT49oA1BZ1Y0WubDliS4HtEUUR69evBwAMHz7c+LynpycA4PLly43uV//51NTUdgUBTZXBUvs1Z/78+XjvvfcwadIkLFmyBNXV1Xj66acxaNAgTJ482bjdF198gXvuuQe///47Ro0aBQCYPXs2oqOj0b9/f7i5uWHfvn1YsWIFEhMTMW3aNOO+a9euha+vL2666SazlLkzYRBgJaM+OA4oXAG07U7MVtcGqNboMW2NoenuuznxcJbZVp+5OXWGujY1RqCpliO2FFjfxx9/jKNHj0Iul+Pxxx83Pl9353ro0CFkZmYiPDy8wX4bN240Pm5qClx7y2Cp/Zrj7u6OP/74A4899hhuu+02ODk5YcKECXj33XcbZAvU6/XQ6XQNBgwmJCRg3bp1+Ne//oXq6mqEhYXh/vvvx4svvmgc01BeXo4ffvgBc+bMgUzmOMugG1lvYoJjqpsC9dHOs+LhTJW49lBOq6Z02foUMFucNmcpnaWuF4uqxMOZKuO/i0VVxteu/DzV/b32UE6bPp/t5ShTBJty+PBh0dnZWQQgrlixosFrVVVVYkhIiAhAvOaaa8SsrCzja1u2bBE9PDyMU/SefPJJi5TBEvuRdbElwEq6B7jY5J082Z/mxgg0xVZbmuzZhQsXMGHCBFRXV2PWrFlYuHBhg9ednZ3xzTffYPz48di9ezciIiLQvXt3FBcXIysrCxEREejbty/++usvY258c5fB3PuR9TEIsEFX9snWxzwAZG3NfT4BjiFoi5ycHIwdOxbZ2dm4+eab8fnnnzc6N/6aa67BkSNHsHz5cvzyyy84c+YM/P398cADD+CVV14xptCtG0BniTKYaz+yDQwCbExjfbJXsnYeAHJcpn4+OYbAdEVFRRg7dizOnTuHUaNGYf369c32TcfExODTTz+96nmtVoukpCQAwIABAyxahvbu1xqXLl3CG2+8gQMHDiApKQlqtdqkREF10tPT8dhjj+GPP/5oMJ7Az8+vwXbr1q3DO++8g1OnTkGpVKJ///74+uuvr9rO3jAIsDGNjf6/Eu+0yNzqzx5o6fXmPp91sw12nS9FXGDr1y8oLytr9T6dWXl5OcaPH4+TJ09i4MCB+PHHH9s8te7nn39GeXk5QkJC0L9/f4uXwZxlb05aWhrWr1+PgQMHYvDgwSZnRKwroynLEL/xxht48cUXsWjRIrz55puoqKjAzp07oVarzV4fW8MgwEaxT5Y6QlOzB+pamlo7u6Cx7VtFXdG2/TohtVqNyZMn4++//0ZCQgK2b98Od/e2fedramrw4osvAgAefPBBSKVSi5bBnGVvyciRI5GTkwMAeP3111sVBJiyDPGZM2fw/PPP44MPPsB9991n3PfKbIf2ikFAB6trxqooL4NKpTLc+agrcPhcLsrLVEjNqwLUFSgvU0GlMr3Jy1ZUqHXGH3KVSgWdwrQfo87IHurqJQUOPNANhZX/3LX7KmXwktZApapp8XVTjtcaxy7k4bEPTMsL35npdDrMnDkTf/zxB7p27Ypff/3VpBS427Ztg6+vLwYPHmx8LjMzE/fffz+OHDmC+Ph4LFq06Kr9Fi5ciA0bNmD69Ol466232lWGtu7XVvWnAbaWKcsQr169Gs7Ozpg7d64ZStv5MAjoYGW1zZ3jB8U1eP6+DxpuN+qKvzujEDuog6kcqa4doayszJgcxx59++232LRpEwDDRe7WW29tdLvg4GBj8h0A+OWXX7By5Up4e3sjMjIS1dXVOH36NERRRHx8PH755RcoFIqrjlNQUICLFy+ioKCg3WVo637WkJycjDvvvPOq5+svQ7xv3z50794da9aswbJly3D58mX06tULr7/+OsaNG9fRRe5wDAI6WEhICDIzM+Hu7t7oCFqVSoXw8HBkZmY6XA7rtuD5Ml1nOFeiKKKsrAwhISHWLopF1e9rPnv2LM6ePdvodleuEXDLLbcgOzsbBw4cQEpKChQKBQYOHIjbbrsNDz/8cKMBgLnL0Nb9rKG4uBheXl5XPe/j44NTp04BMMxuuHz5MpYsWYI33ngDAQEBePfddzFx4kScOHEC3bt37+BSdyxBtPd2t05GpVLB09MTpaWlNvtDbUt4vkzHc0XWVlZW1mTa4/qCg4MbbQl6/fXX8eyzz5rcXSSXy7FkyRI899xzDZ6fN28edu/ejdTUVMTGxiItLQ1bt27F+PHjAQBVVVWIiorCxIkT8fHHH5v0Xp0VWwKIiKhDbN26tcHyvU1ZvXq1WfroTVmGuO6/o0ePNr7u4uKCIUOGNLp6ob2xvWTnRERkl2bOnAlRFFv8Z65Bes0tQxwXF2fcprGuWVEUjSsi2jMGATZGoVBgyZIlrerbc2Q8X6bjuSJHM2HCBOzYscM4xRD4ZxniiRMnGrcRRRG///67cZvKykrs27ev1UmXOiOOCSAiIpu2YcMGAMCmTZvw1VdfGWcdxMfHIz4+HkDjSwmXlZWhd+/e8Pf3b7AMsa+vrzFZkF6vx9ChQ3Hx4kW8/vrrxoGBe/fuxZEjR+x+YCDHBBARkU27chpi3d9LlizBSy+9BKDxpYRNWYZYIpFg69atWLhwIZ544glUVVVh8ODB2LFjh90HAABbAoiIiBwWWwI6mF6vR1ZWVpN5AogcWf08Ac1liuP3iKhppn6PAAYBHS4rKwvh4eHWLgaRTcvMzERYWFiTr/N7RNSylr5HAIOADle3yMa3f52E0s20BTfu/fYscspqMLa7FwaEulmyePjPvmyUVuks+h7WJncS8MTIUJO2fW93Fipq9HhrYhR6BDS+qqM5VWv1mL7GkM407dmB8HeXW/w9bUldVsOWFqOpe92Wsx+S9en0IvZeKAUADIvyhFRiH61GLdXL1O8RwCCgw9U1XSrd3OHqbtqPV+/IAOScKcbvFzWQOQOJ4W4WawLtEqjG8ezGl5O1FzUAyuBsXCmvOUF+3jhXWI21Jyvw9qRASCzc9KwURYQHeCOztAbP/ZGP/90Z1/JOdqilz3fd6x4eHgwCqFk397PPNShMqZcp1wnmCegEnhgVipHRntCLwLbTxfj+RCFqtHqLvNeEeB908zf/muC25mSOaYHO+DhvOEkEHMuqwIakgpZ3aCdBEPDMdRGQSoBvjuVj80nLvycROS4GAZ2AwkmCl26IwINDgyEAOJFTiY//zkF+eduWa22OTCrBbX380DvY8k3f1nQqp8Kk/OM+Shlu7OENAPjvvmysPZwHvYUn1MQHKnFbH38AwP99fw7lavvuniGyFI1Ojw92Z+GD3VnQ6Cxz42QN5qwXg4BOQhAEzOjrj5W3dIWv0gkFFVqs2peNXedLodOb96IkkQiY3NMXPYPsNxAoqNCioEJr0rb9Q10xIMwNIoBPD+Tgxe0XUVFj2QvznQMCEeQuQ2aJGm/vvGTR9yKyVzVaEY98n4ZHvk9DjdZ+ZsObs14MAjqZXsGu+OjWWAwMd4NOBP5IK8XH+3NwuVTd8s6tIBEETOnpix4B9ts1oKo2LQgQBAET4n0wMd4HEgHYk67CwxvTcKnEvOe8PmeZBNN6G1oDkrLLLfY+ROTYGAR0Qj5KGd64OQqLrwuHwklAbrkGn/ydi59OF6FKY74mL4lEwOQEX3g6S812TFvS2pHC/cPccM+gQLgrpLhYrMbd36Ti84M5Zj3n9bnJDV9PSx2fiIhBQCclCALGdvPGN7PjMLabFwDgQEY5Vv51GQcyyszWReAsk2BKL1+zHMvWtGW6UKinAvOHBKGLtwJaPbDmUB7uXHca21KKzN4to3AyfD2rGQQQkYUwCLAhoigiObcS/959GVM/T8ZD36W1uI+nixMWXxeBtyZGIdJbAbVOxE+ni/HFoTyzXZS6eDsjMdyy+Qmsoa1zht0VUsxJDMD03n7wcpGisFKLN3dewv99fw7nC6vMVj651FA+tgQQkaUwT4ANKFfrsOlkIbanFuFyaY3xeV0rRqEPCHPHJzO6YWtKEd7fk4WMEjV+OVOMm3r4mKWMY2I8cSjTvvqm/ZRt//gLgoCEICW6B7jgQEYZfj1TgpS8Ssz79ix6BikxKcEXo6I9IXdqe5ydVzv7w6cd5SQiag5/XayopEqL9Un52HSyEJW1d3vOTgLcnZ2QX67B4AjTMgrWkUoETErwhb+rDIt/SseBjHJE+zijuxky3bnIpJjd3x9rj+S3+1i24IGhQe26QNdxkggYFumBLt4K7Lmgwum8KpzMqcTJnEqs2peNewcH4Ybu3m1KMnQq15DLYEgXJsMhIstgEGAlL/96EccLAXXt9I6eQUosvDYM03r7Y9DKo8gv12BoG3/8h0Z6YHpvP2w4XoDvTxbikeEKuCnaP7ivq58Lhkd5YM8FVbuPZS1uCinuGhAAf7eWswW2RqinAjP6+qOsWoujWRU4nFmOwkot3thxCZtOFuLh4SHoFezaqmOm1AYBbf0cEDk6hZMEW+YlGB/bC3PWi0GAlRzMKAcUrhgY7o7nrg/HxHhfSCQCDmSokJJbCakEGBjeupaA+uYPCcLRy+U4V1iN386W4Jae5hncN7qrJzKKq5FZUtPyxjbGQyHFnIEB8FGaNwCoz93ZCSOjPTEs0gN/XyzDn+dKkZpfhUc3ncPgCHcsuaELXGQtf2lLq7TIUhnO8aBWtggRkYGTVMDN8fY3sNmc9bKf0KiTGRDuhiU3RGD/o30xuacfJBIBGcXVuGV1MgDgmijPdt29y6USjInxAgBUmDHjnFQiYFovP7MdryNN7+Nn0QCgPieJgOFRHnh0RAj6hxpaAP7OKMPy3zNMyjgolQhwqh24mGnBfARE5NgYBFjJ4cxyvPxLBrouP4Blv15Eck4Fbv7kJLJVNYjyccbCUc0v/2iKfRcNzfaxZl4LwNPFCYuuDcWwyM51h1o32r4juSmkmJjgizmJAZAIwK4LKny8P8ek/YZ0MZzfNYdyLV1MIruk0enx+YEcfH4gx+7SBpurXgwCrGRAuBtc5RKkF6nxwvaLSHjzME7mVMJX6YTXb45sdx9+UaXGuEiOJbL+KeVSjO3mjSdGhWJQROeYPqjRWS9taKSPs7FL5n/H8rElubDFfcZ1N6xZ8OXhXGitWHaizqpGK+Lub87g7m/O2F3aYHPVi0GAlbx8QxdsuCsez4wJR6/aHP0uMgmWj49CgFv715Dfk25oBQjxkMPD2XJDP9wVUtzUwwePDA9GqGf7y21J1p5v3yvYFaO6Gpb/fOfPyzib33xOgcER7vB0liK3TIPHN59DaZVpaY6JyHEcyyrDkUtlyCiubtP+HBhoRc4yCcZ198a47t7IUqkhk0jMNmr997MlAIC4wI5ZBMjXVYZ7Bgbit7Ml2HexrEPes7X2pKsQ4+ds0hrbljIq2gM5qhqk5ldh86lCLLy26W4fmVSC2/r646P9OfhgTxZ+OFWI7fN7Ij6odbMMiMi+ZJb8c8G/5v3jAAClXIKNc+Lh7yZDeZnpv8FsCbARIR4KswUAZWotkrIqAAC9OnBJYIlEwOgYT6v0vZviYrHamIDHWgRBwODavv5fzhSjsoXVCG/vF4DXx0cixEOOzBI1hvz7GPald94pmkTUfoWV//yO7X6kN7bP7wkAuPHjkxjw7lGM+uC4ycdiEGCHzhUYokQvZyk8LdgV0BiZVII4MyQnspTk2rn31hTprYCv0gkanYjNp1oeGzC4iwc+nBaD+EAlytQ6jP5PEraaMKaAiOxf3xB3jOvhg5SnEnF4QT8cXtAPH90aa/L+DALs0LlCQxDg6WKd3p6eHdj60FopuebL7d9WgiDgmihDAqD1SQUmrfHg6eyEtyZGY3CEO9RaEZM+O8UWASIyivB2Rv8wd/QPc0f3VgwGZxDQSZRWa1FabdrAMF9Xw8X/YrEaG44XIKu0Y+eZu5shO6GlVGrMlzOhPerGahRXaVFj4hQfF5kEy26MxLAu7tCLwKp92ZYsIhE5AA4MtHFanYhvk/Kx5lAuFE4SrLylK6J8nJvdZ0SUJ0bHeGJHWilO5VTiVE4lungr0C/UDSEecvi6OrUpl72p6i+CZGtsJUCpm64oAHBuRdpPJ6mA2/oGYO/FMnx/sgDvVXeFewd3+RB1FgonCb69K8742F7IpIa6vH5zJNMG27OU3Eq89eclnK9t3q/R6fDs1gv4YGoMfF2bHkQolQh4cWwXzOpXhW+T8vHb2RJcLFbjYrGhRUAmERDoLkP3ACWGRbqbPSC43MEtD63hJreNIECtNdz9K+WSVs9W6BmsRLinHJmlNXj3r8t48YYuligiUafnJBVwax9/axfD7OqyiY7t5g2ndg7Etp/QyI7o9CJW7rqMhzem4XxhNTycpfjv9Bh083dBbrkGT2+9gOLKlrsGYvxcsPi6CHwzuwfu6B+AhEAlnJ0EaPQiLpXW4PezJdiQVGD2TFp1Oe9tkTkWUjKHQ5cMyzK7tiEokQgC5g4KAgC88Ucmys2YFpqIHAtbAmzQx/uzsemkYfT37AEBeGdSNPzd5Lg+1hsD/3UU5wqr8eimNLw5IRpBHi0n6PF3k+PewYaLhk4v4lKpGn9fLMOq/dlIyatC+eE8zOzrD6WZ7pJNWSDHWryV1v/IH8wsw/7aXAq9W7myYJ26OwH7yYFGZH5anYjvTxYAAKb09Gv3XbOt0NYOJv71TDF6B7u1q162+2vtoH5MLsQ3SYYP7ZezuuPLWT3gX5tBsKufC/5+rB+6eCtwqbQGj28+B5WJgwXrSCUCung7Y0Zff7w9KRpyqYDMkhp8diDXpNYFUwy24VXvQkwImizpdF4lfkopBgDM6uePZ8aEt/oYoiji84OG9QSeHBVmM60bRLZGrdVjxhcpmPFFirELzh7Utd4+szW93fViEGBDDl8qw7/+ugwAeHlcF8weEHjVNrH+Ltjzf30R4+eM3HIN3vnrMkQTVqVrTN8QN6yaHotANxkKK7X4cG82fkktRlkrA4srdfN3QaiVL7ZNsWYQkFmixoakAogAbo7zwb2DgyCVtD6CP1dYjQtF1VA4CXhiVKj5C0pEDoNBgI3IVtVgyc8XoRcNXQAvjI1octtQTwW+nh0HqQT481wpVh/MNWl52sZE+jjj/akxiAtQQqsXse9iGd7dlYV1R/KQklvZpgBDEARMSPBpU3ksJdxLjlt6+pqty6O1NDo91h3Jg040tJQsGBna5vTFv9WmhL6hmze8TVwaec+FUuy5UNqm9yMi+8UgwAZodSJe/T0DFTV6DO3igU9mdGvxApEY7o7l46MAAF8ezsML2y+2eYCYn6sMH0ztitfGR6JXkBKiCJwtqMa3SQX45lgBytpw3CB3OcbEeLapPOYS5aPAxHgfPDYiBHoR2H2hFGdaWLTHkuriqSgf5za1AADAvnQVvj2WDwC4K/HqlqLGfLQvG9e8n4Rr3k/Cp38ztwAR/cP6o6QIH/+djVM5lXCVS7Budg+T530uGh0OX6UMD2w4i73pKsz79gxu6emL8XE+rU4XLAgChnbxwNAuHrhYXI3tp4vxbVI+UvOrcGF3Fm7q4Y0+Ia6tunsdEe2JGD8X7Luowonshul6BQHwVEgR4ilHsIccIR4KeLs4QS4V4CQV4CQRcLm0BieyK3Aqt7LVKwBO7+2L+EAlBEHAX+dLjbkLvj6aj7gAF4zr4d2hKZVlUgkm9/TFt0kF+N+xfCSGu2FAWOvGTmQUV2PZbxkQATw4LBjTTZj69OGeLDy8Mc34973fngUAzBsc3Kr3JiL7xCDAyv46X4pvawcCfnF7D0S2kAjoSvcMDkKvYFdMW5OMzBI1Ptqfg88P5uL6WC9M6umLbn4urW527uLtjPuHBmNsNy+s2HGpdsW7IqQVVGNab99WHS/YQ46pvfxwQzcdytU6OMskcJFJIJcKLR4nwluBCG8FbuzhjXOF1TibX4VzhdUobmZJ3V5BStzYw9vY7F+m1mFHWsNm8JS8KqTkVeHarp7oG+raYcFAXKAS/cPccORSOZb/nolPZ3QzObVzuVqH539KR6VGj5HRnvjX5K4t7vPvXZfx2KZzAIAZffyg0Yv4/kQhAwEiMmIQYEU7z5VgxY5LAAyjvKf29mvTcQZGuCP1mUR8fSQf7+2+jGNZFdh2uhjbThdjem8/PDw8pE3HjfZ1wQdTY/DNsXx8/HcOTuVWIrHYrdWBCmCYn9/WUexSiYBu/i7o5m/Ih11UqcH5wmqUq3WQSgRIBAFSiaEL4sqy7bnQdH79nedKsfNcKQaEueH6WC84d8DUxhu7eyGjuBoFFVq8tycLz1/f9NiP+j7Ym4XM0hqEeymw/q44yFtoLfr5dJExALi9nz/m104RFQBsrA0EegQoMTyqbV02e2vHFwxr4/5EZBsYBFjJgh/O4azKcFEcE+OF5TdHtut4LjIp7hkchLsHBWJvugo3fHQClTX6dveBSyUCZvUPwKVSNX46XYzTeVVtCgLMyUcpg4+JA+KqTFgr4PClcpzJr8LEeB/E+pu+8EZbyKQSTIz3xeqDudh9oRSl1VqTWiLq2kyKKjW4VKpGgHvzsxzqD+c098zoT//ONrYmfDIjli0KZLPkTgJW39bN+NheOEkMNwFLbohod704MNBKzuZXQyIAz18fge339TTmgm4vQRAwPMoTS2+MBAD4uZonzhvSxbDqXVqB9Vfha40Ib9MCljK1DuuO5pstV0Jzwr3kCHCTQa0V8ZGJiwA9ek0oege7oqJGjzH/OY7knIpmt7+xh4+xy2Dd0Xys2p+DD/ZkY+MJQxKqT2bEtqkVoH4AABjGGHCwIdkqmVSCuYOCMHdQkNl+Y22BrDY50KQE33bXy37OSiezemZ3nFg4AEtvirTIh7Muf79fM2sMtEb/UDcIAlBYqe2QC6W5RHorWrX9Xx0wjU4QBNwcZ5hCue10MZKyylvcx1kmwWvjI9Hd3wWl1Tpcv+oEzrUQkD02MhTvTTEEAt8cy8d3JwxjTz6+tW137/UDgKm9fDG1ly8ABgJEnRmDACuZ2tsP8UFtSxlriqza0fDmWjXPTSFFr9rypuZXtrC17fBROrXqHBy7XNGmKZGt5a6QGltp/mtia4CrXIo3JkQhyscZ2aoaXPff48gorm52n0euCcW7k6KNf390ayzuHdL6AGDvhdIGAcAjw0PwyPCQBoHAXuYhIBuj1YnYmlyIrcmF0OrsJ8l2XdrgXedL210vBgF2qkeAYb36744XoKBCY5ZjXls7739PehlqOkkKTkEQ0CekdcGWpb4UOr2I5NxKrD2ch3/vzkJBhaFFpTVBiqezE96aGIVwTzkuFqsxdtUJ5JY1v2DT46PC8OdDvfHnQ70xvw0BAFFnpdbqMeHTU5jw6Sm7TBv8+ObzTBtMjXt6TDj6hriipFqHV3/LgE7f/ij45jgfBLvLUa7WYV/tAjidwXWxXnhwWBBu7O6N+EAl3ORNf+xn9/eHqwVy8R/KLMO7f13G+qQCnKtdGjox3A1Lb+xiTPpkKh+lDG9Nikagmwxn8qsw7qMTKGlm2iQAjOzqhZFdvdpafAyL8sQnM2IBGGYXvL8nC+/vyWowxoAzBYg6H84OsFPOMgm+uSsOfd8+gmNZFfjycC7mDgxq1zHlUgnmDwnCK79mYPcFFQaEuXWaxWsC3OQIcJNjcBd3iKKIkiodVNVaaPQianQiNDo9Qj0VZhtDUV9RpQZbaxcN8lE64aYePhgf540Qj9aNV6gvwE2OtyZG49FN55CUVYGbPzmJX+7rZZEApk7dOIJ7vz1rvPgDnCFA1JmxJcCOdfNX4pMZhukxXxzKwzfH8tu8xkCda7t6GtcZ+Ol0cZsXL7ImQRDgrXRCFx9nxPi5ID5QiT4hbhYJAAAgJdcwgK9PiCu+mR2HewcHtSsAqBPmpcCbE6PgJpdib7oKC3441+5jtmTe4GBjiwDAAICos2MQYOdm9Q/AQ8OCIcIwAO3JH84jp4U+5OYIgoCHhwdDEIDk3EoczGx5ZLujK68xDDTsEaA0+3rmXX1d8NBww0X42OXmpw2ay7zBwdjzSB/seaQPAwCiTo5BgAN4f2oMVk2PhbOTBMeyKnDvt2fwc2rb7+ITglzx0FDDj//PqcXIUbU9qHAEitoLf1WNZWYdaGpHBwd34DLJw6I8OQaAyA4wCHAAgiDgvqHBOLFoAIZ28UBFjR6v/5GJZb9ltnnA4LTefhjWxR16EdhwvKDTzBawhroFoSoaWQRJqzPMGPjmWD5+P1vcpuMX1s7+6MgggIgsK6O4GkculRn/tTQduK04MNCBxPi54K+H+2DFjky8+HM6/kgrQc9gJab0bP2aBYIg4Kkx4Zj/7VnkV2iw+VQhpvX2g6SVixU5grog4PezJZAKAkqrtSip0qKwUouiSg3qx2G7zqswb3AQwr1MHzNQWJu8KbiFVMJEjkbuJOD9KTHGx51FRnE14lYcQmXNPzcOSrkEKU8lIsLb2Zg2+OnRYe2uF4MAB+MkFbD4+ggIArB4Wzr2pqvaFAQAhjnrL4yNwOObzyE5twrOyUUYH+cDqaTzfNk6Qv079F/OXH237+wkgcJJQGm1Dn+eL8Vf50sxPs4HcxID4e/W8mDFunnC7s6dY6YGUUeRSSV4+Jq2LaBmTQUVGlTW6LF2VnfEBSqRkluJ2etSUVChQYS3szFt8Iy+/u3OOMsgwEGN6+6NxdvScTq3CnpRbPMdfK9gVzx3fQSW/pqBI5crkFOmwdRevvC10Ej7zijYQ45bevoit6wGSrkUrnIJlDIJ3BRSeDo7wVUugSAIyCmrwR9nS3C2oBpbU4rwS2oxFl8fjmtbmN9f9//OHLkgiMh2GJYfd7foezAIcFC9gl3hIpOgvEaHSyVqkxfaacyYGC/IJAKW/ZaBLFUN/rsvGzf18EG/UFcI7B4AgNqshc1nLgxyl2NW/wBkFFfjl9QSXFbV4OVfMnC8ZwUeGBYMeRMRf23LIIMAoivo9CJ2nTeksx4R7Wk3rZR13/VDmWXoE+LWrnpxYKCDkkklGBDmBgA4ltX+qWUjoj2xdlZ39At1g1YP/JhchK+P5iOtoApl1dpOmU/AWiK8nXH3oEAMjzSs3Pj9yUIs+zWjye2ldS0BPMVEDVRr9Bj9n+MY/Z/jqG5kYG5nVVObNvj+DWntrhdbAhzYzXE+2H1BhXVH8nBDN284y9oXE/q7yfHWxCh8cywfH+3PwdmCapwtMIxoVcokiPFzxrju3lDK2XfdEqlEwPXdvODpIsW2lGKkFzU9Mti1Ng1yoZnWiCAix8GWAAf22MhQdPFWILdcg3VH88xyTIkg4PZ+AXhlXBeMjvFEF28FBACVGj2OZ1fiP/tycL7QMlNd7FHdzILmshkG1Q48vNBMoEBE1Bi2BDgwF5kUb0+KxvQ1KfjfsXzc1MPHbHPNR0R7YkS0IZmMWqtHSm4l3v3rMjJK1PjycB6GRbpjTIyX3fTRWUpZtSHBkF8zswSCaqcGNtdaQETUGLYEOLipvfxwXawXNDoRr/2egbxy82f/UzhJ0DfUDaumx2JivA8AYG96GT7+OweVFsqiZy9UakMOgOZaAuryAyTnVuJSibpDykVE9oFBgIMTBAH/vqUrnJ0EnMypxJyvz2B9Ur5FRpo7yyR4YlQYnrsuHACQW6bBmzsv46N92fj1TDHOF1ZDyxHuDdSlBFbKmh5HEeoph5+rDDU6EQP/dRQHMlQdVTwi6uQYBBDig1xxaEF/DI/0QLVWjw/3ZuPB787iz3MlOJZVjjP5hjtMjc48o2uv7+aNB4cFI8rHMC0xu0yDvell+PJwHlbsuISvj+bjUGYZytVsJajT3ExLmVSC927piigfZ+SU1WDE+0n4+oh5xngQkX3jmAACYFgU6K+H++CzAzl44ofzOFtQjZd+aTgtLcBNhtfHRyHK1/ScAuVqHX5MLsT3JwqhF0WM6+6NifG+mNHHHzP6+KOwQoMjl8tx+FI5DmaWoahSizP5VTiTX4VfzpTgrgEBCGtFCl171dIMyyAPOd6f0hWv/paBvRfLMOur0ziZU4GXx0WafeVCos5CJhWwYkKU8bG9cKodS/XYiJB214tBABlJJALuHRKMSQm+WPLzRRy+VI4ytRZlah2KKrXIK9dgwQ/n8PXsOLiYMJ2wXK3DbV+moLLePNZ1R/Px9dF8vD0pGv1C3eDrKsPYbt4Y280boigiraAaf2eU4fezxUgvVuOLw3l47JoQuCocc1rhPxf/lrtJlHIpXrkxEp/8nYP/HcvHa79nIjm3EhvnxjNpEzkkuZMEi0aHW7sYjcoorkZBvWm9fq6yFpO2peRWAgDSaqde35UYCLkT0waTmQW4y/Gf6bENniuq1CD61QMorTZkGIz1dzHpWNW1ee0HhrvBR+mEn1NLIAKoaGRAoCAIiPV3Qay/C6b19sUDG9KQUaLG2YIq9A11a3e9OhutXkRaQRUAINTTtNYQqUTA/UODEePnjDd2XMKmk4V4f3cW/m9EqCWLSkSt0NICQVfyc5VBKZdg9rrUBts3N2DYVAwCyCQ+ShncFFKUVpveT++mkOLWPv745lg+Lharoardt3ewK4bVZsNriotMimuiPLDuqGFfRwwCTmRXoLxGD39XGUZEebZq3+tivaFS6/DvXVl48sfzuDbGC72Cm09bTGRvdHoRRy6VAwD6h7Uvva45tbRA0JUivJ2R8lSiseVApxeRU1aD3DINQj0VTBtMtmtWP3/IpQLyyjVIza+CIACPjww1acGiPiGGC3+6hdbRtmWiKGL/xTIAwNRevm3q178lwRdDurhDoxMxa20KqjQcaEmOpVqjx6CVRzFo5VGbTBtct0BQXKCyxW0jvJ3RP8wd/cPcER/oikmfJZulXgwCqNVEE/qn63g4O+HugYHGv2f29TfOCmhJzyAlBAAlVTqUVmtbW8xOq1qjx+ZTRcgr18BJImBCvG+bjiMIAp66NhzeLk44mVOJ13/PNGk/URTxxaFcfHkol2s+ENk5dgeQyeqanFo7U3BKLz/8kVYKQMSdAwJb3L6OUi5FgJsMueUalKt18HS274+rKIo4mVOJn1OLUVHbVzgnMRBu7RgU6eEshbeLE4qrtCblYKhQ63DPN2fwbVI+AODQpTK8O6krJDbSjEpE5mXfv6pkVorapWw1rVyuTuEkwUe3xra8YSPqeg3s/Ya0qFKDrSnFxnUVwr0UeGxECAa0cy3xX84U43xRNdzkUjwxKqzZbdOLqnHL6lNIyqqAVGII9v69KwtFlVp8dls3yJpYypiIOi8GAWSyulUGNfqO61sTYP93oCVVWqzal4ManQiJYLj7n9nPH/J2XnSrNHp8diAHAPDSuC7wbWYk8Y60Etyy+hRU1Tp4uzjh5XFdkFNWg9f/yMTaw3kortTi27viuAIkURvVnxJYN9XPFjAIIJMpnAwX5I7M5FfXElDTytaHzkIURWw+WYganYhYP2e8OLaL2ZIj/XCqEAUVWkT6KPDINSFNbvfz6SJM/OwUNDoR3f1dsPTGLvB3k6NXsCvcFFK89PNFbE0pwgMbzuKLWT3MUjYiR9LUlMArp/jVBQcdGSQwCCCT9Q91w6HMcqw9kofhkZ4dkokuxs8FWaoa7EgrQaRPoEmzCjqT03lVSC9WQyoY7tZDPMyXHTE13/BD8uDQEOOSxFfaeLwAt32ZAq1exLBID7w4NqLBtkO7eOCZMeF45dcM7L7ANQmI2uLKKYFAw+RAlswD0BIGAWSypTdG4n9H85FWUI31x/Nxe78Ai7/nQ8OCsS9dhUulNfj9bAkGhLnB28XJLjLg6fQifjtbAgCY2S/ArAEA8M8yxE0tD/3FoVzc/b9U6EVgVFdPPHddeKP9/oG1yxi3ZlYIkS2QSQUsuSHC+Nja6qYEXunKPABA8xkEzVkvBgFksgB3OVbe0hV3f3MGnx/MxchozxYz2YmiiIIKLTJKqqHWinCTS+GmkMBNYRi13tJgs0B3ORaMCsWKHZewN70Me9PL4CQR4OfqBKVMihqdHjU6ETU6PYLc5Rgf5wP3TpJi+PClchRVauHlLMXt/fzNfvy6xE5XjgWorNHhvd1ZeGbrBQDATT288eSosKYTjtQGXPY+OJPsj9xJgpfGRVq7GCaJ8HZuMW1wHXPWi0EAtcqcgYFYeyQPv58twZKfL+KJUWGIbyTRhU4vYue5Eqw7mm8c8X4lbxcnLLkhwpgUqCk3dvdGYYUWO8+VIKNEDY1ORE6ZBoCmwXYlVVXIUeXgoeHBNj+SXa8X8ee5UgDAXQMD4WqBAXdlakNuhWe3XsD200UAgAMZZTiWVQ611nBFn9bLDw8ND262m6XuFcYARPaHQQC1iiAIWDU9Fn3ePoxzhdV4eGMaRkR5YN7gIIR6KJCUXY5d51XYk16KggrDRUgiGPr2PZylKK3SoaRai/xyDYqrtFj44wU8NToMY7t5N/ueswcEYPaAAOj0IrJVNUgvrkaVRg8XmQQuMglEEXjt90wUV2mRXmT62gbWUqMTjQsr3di96bq3R0KQK3LKSnA8uwLHsysavBbiIcetffwwOcG3xa6VulkhZa1IGU1kC/R6ESl5hrExcQFKu8l3Yc56MQigVuvq54LkpxLx0s8XseZQLnZdUGFPugouMokxyQ1g6NN6bEQIHh4eAm/l1U3Sd32diu+OF+C13zNxuVSNOYmBLV6QpBIBYV6KRkfQD4v0wNaUIpwvqrb5IKBupgWA2mDG/C0Bz10XjrsHBuJ0XiVO5xkWIuoR4IIeAUqEeMhNHlfh42L4mSiu0qJGq2/3qmVEHaVKo0fPNw8DAMpfG243q5Gas14MAqhNIryd8dnM7lh4bRie356O708UoqJGjwA3GSYl+GJKLz+MifEy3kVeSSmX4ts74/DstgtYseMS1hzKQ265Bk9dG9bmQX/9w9ywNaUIF5rofrAlgiDA2UlAtVZEuVoHH6X5RwELgoBQTwVCPRW4LrbtrQ3uzlJIBEAvAnnlGrNNYSQi62MQQO0SH+SKjXMTkJxTgTK1Donh7iavaCWRCHhjQjRi/Fxw3/qz2H66GJMTfNEjoOXFNBrTv3alwbo0w+1Jt9sRnJ0kqNbqUNaBeRfaQiII8FE6oaBCi5yyGgYBRHaE7XpkFvFBrhjcxaNNS1rOHxKMnkGGC39hhaaFrZvm5eKEbrXdAKfzbCcjV2NE8Z8xAUoLdAUQEZmCQQDZhLxyw8U/0L3xOe2murarJwDgVI5tBwFFlVrU6ETIpQIivG37zloviiiqNAzyrMsZQET2gUEAWV2FWmcMAvzbeZEZ3dULAHCxWN2h6Y1bK6esBgAQ7evcptaTjlSm1qFuAcKAdgZpRGRbGASQ1R3MLAMAeDpL271ccJCHHHEBSogAfk8rgWijGW4yStQADFMnbV1JlaEVwNvFqcn0w0TUOXFgIFld3YW/TK1DcaUW3sr2fSyn9vLFq79X4tjlCoR7KtA/rPlkRB0traAKhzLLAQCDwtu3VHBHqNYaxi64yhkAUOcikwpYeG2Y8bG9MGe9GASQ1fULc8PgCHf8nVGG7alF7V6T4Ppu3sgpq8GnB3KxLaUIoZ7ydo81MJfMEjW+OZYPvQiMifHCNVEe1i5Si6S1Uzb1ttmoQtQkuZMEb06MtnYxzM6c9WJobwK9Xt/yRtQuDwwNBgD8eKoIejM04c/qH4CB4W7QicCG4wWo0Zr+/7C0Wou/M8pw+FJ5k/tpdHpoW7m8cV5ZDdYezoNWb2gBeGZM23MidKS6IupstGuFiNqOLQHNOHHiBLRaLfr162ftoti9GX39seCH88guq8GhzHIMimhfM7lEELD4ugjMX38GBRVa/HCqCNN6N50it7JGh5M5lTiVU2nsrweAX88Uo0+IKxLD3OEikyA1vwqpeZU4V1gNJ4mA+UOCTFrus6xai7VH8lGjE5EQqMRL47rY/PoGdQpr0z/rGAtTJ6PXi8bvc4SXwq7SBpurXp3jV8gKjh8/jj59+uDHH39s13HUajVUKlWDf3Q1pVyKOYmBAIAtyYVmOaaXixOevz4CggCcyq3ET6eLGx0omK2qwb93Z+Gn08XGL1bvYFeEecqh1oo4kFGOD/dm4+0/L2NLchHOFlRDLxry/29NLmpx8GFplRZfH81HmVqHLt4KvDY+Ei5NZFK0hqJKDb4+mof1SfmorGk4o+LY5XK8/MtFAMDwSNvvuiCqr0qjR9SrBxD16gFUaewnijVnvdgS0Ihjx45h2LBhWLRoEV588cV2HWv58uV4+eWXzVQy+zZ/SBBW7rqMPekqFFZorloCty36hLhh8ZhwvPp7Jg5mlqOiRodbevoa78KzStVYcygPNToREV4KTIj3wbVdveDvJoNeFHEosxw/JhdizwUVRBhy718T5YlYPxcs/ukC0ovVOJlTiV7Bro2+f3JuJTafLESNToRCKuDVmyLh0c4ZEOZyoaga65Py8duZEmhqO/y/PpqPuQMDcXOcD/7OKMNLv1yERifi2q6e+GJWdyuXmIjMzTZ+jWxIWloaBgwYgKVLl2Lx4sXQaDT47rvvcPr0aXTt2hVxcXFITEw0+XjPPvssnnjiCePfKpUK4eHhlih6p5cQ5IrhkR7Yk67C9tRi3NG/fQME61zfzRs6EVixIxPJuVUorsrDzL5+UFXr8MXhPGh0IhKClHjj5qgGS/pKBAGDItwxKMIdJVVa6EWxQY7/uYlB+PRADn5OLUasn0uDdRI0Oj22p5bgyCXDLIAeAS54/voIhHpaPzGQKIp4+8/L2JpSZHxuSBd3FFRokFZQjXf/uoxvjuUjp6wGehGYlOCLb+6Ma3IdCCLqvBgE1KPT6bB9+3aIooiQkBAAwE033YSCggJoNBqoVCpERETgoYcewh133GHSMRUKBRQK6//wdxbzBgdhT7oKP50uMlsQAADjunsj2F2Op7aeR7aqBu/+lWV8rVeQEq/fHAWlvOn0vV4uV39VZvT1wy9nipFZosaPyUWY2svXmPjn66P5uFBk6Fq4vZ8/7h4YaDNjAM4XVRsDgKm9/PDkqFAMi/JEjVaPVfuy8fIvF5GlMiQzunNAAD67rTucWpiG9Ne5EgDAyNpkTUTUOdjGr5KNkEqlmDZtGpYvX47HHnsMgYGB8PT0xIYNG3Dq1Cls3boVERER+Oyzz5Cbm2vt4todURSxJdlwcXK2QFKa3iGu+Oy2boisl6a3b4gr3pjQfADQFLlUgidGhkKAodl/fVKBcXxAXT/d9N5+uG9IsM0EAADgKjesCggAE+J9MCzKkGpZ7iTB/40IxbnFg7Dspki8NTEan89sOQD4cE8WRn14HKM+PI6P9mVbuvhEZEa288tkI4KDg3HPPffg6aefRv/+/fHiiy8iJiYGANC7d2/cc8892LFjBzIyMqxcUvuz5mAuNp4ogJNEwFOjwyzyHiEeCvx3eizmDw7CfUOC8OaEaLi0YwGfvqFueHV8JKQCkJpfhdN5VQCAgbVJgHadL4XOxibYB7nLMXegYRDmAxvOIimrvMHrni5OeO76CDx5bViLo47f330ZD29MM/59/4az+Hg/AwGijOJqHLlUhiOXypCSa7trmbA7oBH+/v6YN28ebrjhBsTHxwMw5AqQSCRwd3dHXFwcfH19rVxK+3K+sAoP1V5M7h4YiG7+bVtO2BQKJwlmmbGrYWgXD8zsF4CvjuRhR1opuge4oHewK/5IK0FuuQZ/nivFmFgvs72fOdzRPwCncirxd0YZpq9JxqHH+8OzkS6P5qz86zIe33wOAHBbHz9jTob71p+FAODeIcEWKDmR7csorkbcikOorPln5L5SLjFpOnFHc+ggoO7C3pjAwEAEBAQY55XXbbdp0yZ4eHjAy8uro4rZKe25UAoAGF7b1NySRzamoUqjR+9gV9zW19+SRbOI2/r64dukfORXaJCSW4WEICUGhrtj57lSbDheYHNBgEQQ8Ox14bh//VmkFVTj8c3nsHqm6aP/fz5dZAwAZvXzx72DgwAAogh8d6IA89efRVyg0uT//0SW4CQV8NCwYOPjjlJQoUFljR5rZ3VHXKDhhsbPVYYIb2ezHN+c9XLY7oALFy7gk08+gU6nazIjYP3EMqdPn8aiRYvw3//+F6tWrYKPj09HFbXT+fTvbFzzfhKueT/J5KbhY1kVAAzTBFtaVe9icTVe+uUint5yAb+eKYa6FdkALcVd4YRpvfwAAGcLDF0C/UMN0wZT8iqvmn9vCzydDc3+APDV4TzjQkGtJTZ4/M9f9pGWhTozhZMEH0yLxQfTYq2y+FVcoBL9w9zRP8zdbAEAYN56OWRLwPHjxzF48GD4+Phg3rx5kEgkEEWxyWxyqampeOWVV5CSkoKdO3eid+/eHVzizuPTv7Nx77dnjX/ft/4sRBG4b2jzTcN1way8mai2SqPDF4fysP54vjF73YHMMqzcdRlju3nj+lgv9AhQWm1p3n6hbvjfsXxkFBtmBbg7O8HDWQpVtQ5nC6rQJ8S2FjICgJ5BSkR6K5BerMZ3x/Mxb7BpTfjjevjg37d0xaObzuHro/nQ6kXo9CI2njAkevpkRqxxwCER2S6HawlISkrC0KFDMX36dLi6uuKNN94A0PCu/8qWge7du2PRokXYtm0b+vbt25HF7VTqBwBTe/liem/DnfH9G87iv3uzmtvVOACtqeR7+y+qcNfXZ/C/Y4YAYFKCL166oQu6eCtQUaPHppOFeOT7c5j02Sk8u+0Cvk3Kx+VSdeMHs5D42ma/4iotytSGO/8QD8PCRan5VR1aFlMJgoDru3kDAL46kteqff9vRCg+mGoYNLs+qaBBAGBqMEFkSaIoIr+8BvnlNTa7rHhbmLNeDhUEJCUlYfjw4ViwYAG+/PJLDBgwADt37oRW27AZtK7//91338WKFSsAAP369UNwMH/YmrL3QmmDAOCR4SF4aFgwZvQxBAIPfpeGHWklTe4vMS5Sc/VrFTU6vPTLRRRUaBDt64wt8xKw+Z4ELBnXBecXD8Iv9/XCzL7+8HJxQqVGj/0Xy/CfvdmY+78z2HiioMO+/G4KKWL8DE1+BzPKUFSpMU4VPGOjQQAAXFc7XmFnWimyVa0LnB4aHoJV02ONfzMAIFtSWaNHwJL9CFiyv8Egvc7OnPVymO6A8+fPo1+/fli8eDGWLVsGAHj44YcxcuRI/PDDD5g6dWqD7VUqFbZt2watVov58+fD29vbGsXu9Ey9/ArN9CAXVWqh1hqOdHLRgAZT+iQSAWO7e2Nsd2/o9CKSssqxI60Um08VYNd5Fd7bnYXTeZV4YmRYh2S8G9vNG2kF2dh1QYVdF/5ZJyLCy3YTRhVVaAAYVguUtmFVw/uGBiMhyNAKwoGARJ2LwwQB0dHR+OyzzzB37lwAhuyAgwcPxi233IJ169Zh7NixcHf/Z+U6Dw8PfPHFF9DpdAwATDAsyhOfzIjFvd+eNTYLSwQBG44XAAD+My0Go2O8mtxfbCZc0NbOs/dzlTU7p18qEYyDcJ4YFYp//XUZC388j1/PlOBCUTWWjotEUG3zvKXc2tsPMomA9/ZkQRQNSwbP6u+P3k2sLWALvjhs6AaYOzAQAe5tOz+8+BN1Tg4RBGi1Wjg5ORkDAMCQHVAqlWLs2LF49tlnkZWVhe7duxunDer1ejb/t1JdM3D9QAAA/n1LVzwwLKTZfeta7Bu7D9XW9hE0N2jwSoIgYMGoMPQNdcPU1aeQVlCN+zacxROjQnGtBVPbCoKAKb38kBjuDp1eRKSP+UYEW0JqniFXgEQAFl8XYe3iEFEHs+sxARUVFSgrK0Nl5dXZmur6iR988EH06NEDL730EkRRNI4HaCp/ADVv3uBgfDLjnz7ij2+Nxf+NCDV5/7zymquey6rtp5a1YT7s6BgvHF84AIMi3FGm1uHlXzLw2YGcVh+ntcK9FDYfAJRUabFyl2HA5uwBAejq52LlEhFRR2vXle6HH35AdHQ03n777Wa3e/vttxEdHY1t27a15+1aJTk5GVOnTsWoUaMQFxeHr776CsA/F/+62QCiKGLChAk4efIksrKaH8FOppk3OBi7H+mDPY/0MTlr3DW1zcnL/8jEvov/9KXvTVfhtd8zAQAjo9vW5Bzu7Yzdj/TB4usMqzd+eTgPP5wqbGEv+yWKIk7mVOCBDWeRklcJF5kEz1/fxdrFIiIraFcQ8MUXX+DixYuYMmVKs9tNnjwZ6enp+OKLL9rzdiZLTk7GyJEjkZCQgEWLFmHmzJm4++67cezYsatyAQiCgEceeQSnTp3C6tWrO6R8jmB4lGer5ol/dGssbo7zgVor4vmf0vHrmWL8nFqMF7ano0YnYmK8D1bdGtvygZogk0rw6vgovDzOcLFbuesy9qarWtjLfuj0hgv/f/dl466vU/F/359DbrkGsX4uOPR4P8T6sxWAyBG1a0zA0aNHERAQgOjo6Ga3i4mJQWBgIA4dOtSetzNJUVERFixYgDvuuAPvvPMOAOD222/H0aNHsXr1aqxcubJBYiCdTgcvLy8sX74ckydPtnj5qHFKuRTf3x2Pe745g7WH84x3/wBwV2IAPpnRzSwr8b0wNgIZxWp8eiAHr/x6EStujkbvENsdtNdWoijiYrEaR7PKcfRSOZKyK6Cq/idroUwiYEZff3wwNabVawYQdRZOUgFzEgONj+2FOevVrm9/VlaWydnzwsPDcerUqfa8nUk0Gg1KSkowffp0AP+sDxAdHY3CQkMTcP3WAKnUMNr8ySefhJMTfwytSSaVYM3M7vBzleFff10GADw+MhRvT4xucTU7UwmCgP9Mj0FOWQ22phTh2W0XsHpmNwS4WXbWQEc6drkcH+7NNqYvruPpLMXNcT64pZcfbuzuDXdnft7JvimcJPj8dtPXxOgszFmvdv0KuLq6Ij8/36RtCwoKoFBYfq50YGAg1q5di9hYQ9OxTqeDRCJBaGgoLly40GDb8vJyuLkZUrkyALANEomAdyZFY1DtUrwz+/k3mc65rWRSCdbPicOoD47jYGYZNhwvwEMtzF7oDC6VqLFqfzZ21+YnkEkFjIr2xLUxXhjd1RMDI9zN0ppCRPajXVe+Xr164a+//sKhQ4eQmJjY5HaHDh1Ceno6rrnmmva8ncnqAgC9Xg+ZzLB0o06nQ25urnGb5cuXQ6FQ4NFHH2UAYGMEQcDtZlzqtzEuMileGtcFN39yEluTi3DXgEC4KZrOQWBNpdVaPLXlAjKKq+GjlMFH6QRfpQwuMokhZ78oQq3R40BmObR6ERIBeGBoMF4a1wX+dtTCQdRaoigaM+op5RKz31BYiznr1a6r36xZs/Dnn3/ijjvuwE8//dTo2IALFy7gjjvugCAImDVrVnvertXqLwwkCIKx6f/FF1/EsmXLcPToUQYADuzG7t6IC1QiJbcS21KKMMMGlzBWa/V47qd0Y9rhLFUNslRXT6Osc1MPb7w1MRrxQfY3zoGotSpr9HBbvAcAUP7acLjaaKDfWuasV7uugPfccw/WrFmDvXv3omfPnpg6dSoGDx4MLy8vlJSUYP/+/di0aROqqqowbNgwzJ8/vz1v1yZ1QYBUKkV4eDjeeustrFixAocOHUKfPn06vDxkOyQSAU+MDMX89Wex/ngBJib4wqUDUgu3xsf7c3AqpxJucil+nJcAJ4mA7LIaZKtqUKXRQyYV4CQx/OsZpMTINiRCKq7UYOaXp5FbXoPxcT6YGO+LQRHuVluNkYg6TruCAKlUii1btuDuu+/G5s2bsW7dOnz99dfG1+vm5E+ZMgWffvqp8U68I9Ul/ZHJZPj444/h4eGB3bt3o3///h1eFrI9swcEYulvGcgoVuPjv7Px6DWmJzbqCPra75CnixQ9g1zhIpNAmV+JGq0elRo9vF2cDP+UTujur2z18YsrNRi76gQOXyoHACRlVWD575nwd5Ph7oGBePWmKLsaVU1EDbW7LdzLywvff/89Dh06hM2bNyMlJQUqlQru7u5ISEjALbfcYhMX3HHjxuGFF17A3r17ER8fb+3ikI1wlknw8a2xGPfRSXx/ohADQt1sKg/+vMFBOJRZhszSGkS/dsC4RHFjPJ2l2HxPAkaZ2BpQPwDwdJZi7sBAHM+uwIGMMuSXa7BixyVcKlHji1k92CpAdIWM4moU1C6+BRjWNonwtu0soY0xW4d4YmJis4MDrS0xMRFlZWVwdWVfKTV0Q3cfPDYiFCt3XcbyPzKxarozQj1tY9U/V7lhAOPDG9OMAYCnsxRdvJ3hKpegTK1DuVqHokotSqt1uO6/x/HfabEtZmq8MgB4Z1I0on1dcEtPP2h1Iv5IK8GKnZlYd9Qw+4eBANE/MoqrEbfiUINlfJVyCVKeSux0gYBDjYpjAEBNWTEhCgczy7A3XYVntl7Akhu6IKaRXPqiKOJMfhX+PF8KP1cZpvbys3jZon1d8Olt3VBYoUWEl6LR5D5qrR4rdmTij7RSzF9/FhklarxyY2STx7zty5SrAoA6TlIBN3T3hotMgpd/vYh1R/MR7uWM1ydEWaJ6RJ1OQYUGlTV6rJ3V3Ti4ePa6VBRUaBgEEHVGcicJ1t8Vh8Erj+JSaQ0e+i4NExJ8EOAqg4ezEzycpTibX4Xf00pwufSf0flB7nIMi/SwePlCPBQI8Wi6dULhJMHz10cgwjsPnx/MxdJfMyCTCnhhbONrAuSWGZox7xkU1CAAqG9EtCcWXRuO1//IxGcHc/Dq+Ei2BhDVExeoRP8w95Y3tGEMAohqhXgqcOSJ/rj327P44VQhvj/R+CJDCicB3f2VOJ5dgX/vvox+oW42MatAEAypRF2cJPjPvmy8uP0i+gS7YVJP36u2HdfdG8ezK3AypwKTEq5+vc51MV54b/dl5JdrcCCjDEM7IOAhMhepRMD03n7Gx/bCnPViEEBUj7+bHJvujsc3x/Kx76IKRZVaFFZoUFipRaCbDLf19cekBF9IBAHxbx5CRrEaXx7OxX0mrpbYEWb09Ud+hQYbjhfgznWnceqpRIR5NWxFuDneB2/uvIQDGWXQ6cUmf0icpAIGR7jjj7RS/JhcyCCAOhVnmQTr59jfQHBz1otBANEVBEHAzH4BmNmv+ayF70+JwaTPTuHbpHxc29UT3dowRc9S7hsShOPZFTiTX4WHN6Zh8z0JDV4fFukBT2cpSqt12HdRZVzKuTEDwgxBwJbkIrw23jzjAnaklUCvF3FdN2+zHI+I2sb6bZhEndTEBF9M7eUHnR545dcMVNY0PX2vo8mkEjxcux7CkUtljb4+e4BhFbJXf8tEck5Fo8cpU2vxv2OGGQL+rjKzlG3VviyM+c9xXL/qBB7fdA4anb7lnYjIIhgEELXDxzNiEe6lwOXSGrz952VjgixboJQbvt66Jor09qRo3NDNG9VaPZ7emo5zhQ1XHdTo9Fiy/SIyS9QI91Jg7R3tX7Xso33ZeGBDmvHvlbsu44ZVJ5Bf3nQqZKK2qlDrIDz5F4Qn/0JFMzk2Ohtz1otBAFE7+Chl+Hp2D0gE4I+0EnxxOM/aRTKq6+bX6RuPAhROEmycG49hkR4or9HhwQ1peGbrBWxNKUJJlRbv/HUZR7Mq4CKTYMu8BAQ3MzvBFB/ty8b9G84CAKb39sPL47rARSbBznOlGPDuUWw8XoAdacXteg8iah2OCSBqp+FRnnh/agwe+i4Nnx/MhSiKuHNAoNVHI2tqL/5NBQEA4KqQYuu9PTHx05PYfUGFvzPK8HdGGd6qfV0iABvmxKN3iFu7yrL7fGmDAOChYcEQBAERXgos2HwOmSVqTFuTDKgb75Ygsrb6GQJTciutXBrzYRBAZAYPDgvB5VI1Xv0tE2sO5eFkTiUWXxcOH6V5+tFbSxRFrD5gWDq7d0jzSbK8XJyw65G+SMmtxMYTBfjmWD5OZBsuxitv6YrxcT6WK6fFjkxkPk1lCPQz0zgZa2IQQGQmy26KQnd/Je5bfwaHL5XjznWpGBPrhfE9fNAjwKVD1zLfnlqMvzPKIJMIeH9KjEn7xAUq8VxgBBZfF45P/86BIBiSCZnDNdGe+OjWWNy3/iw2HC8AAPQKdsXrf2SiSqNHhLcC707qCqm2Ard8YJa3JDKbKzMEAo2vFVDXQtCZWgoYBBCZ0Z2JgRgQ5obb157G8ewKbEkuwpbkIkT7OGNyT1+M7+Fj8VX5clQ1+GBPFgBg2U2RiA+6uiUgvagaWr3YaGpkQRBaXHugLeYPCYYoAvdvMAQCdcHAtV098e1dcfB3k0Olkpv9fYnMpakMgX6uMijlEsxel2p8rrO0FDAIILuw90IpAGCYDawAGB/kiqNP9Mef50vx6d85WJ+Uj/NF1Xj3r8vYmVaCtydFW6xVIKesBs9vT0dFjR5Du3jgyWvDGrx+sagaz29Px9raAYyjYzzxyPBQTErwbTI4ySyuxqItF6BwErBqejc4tyM74n1DgyFCNM4QeHxkKN6cEM3liqlTi/B2RspTiZ1yVUEGAdTpffp3Nu791jDo7JMZsZg32PrZ+yQSAaNjvDA6xgvvTemKLw7l4fHN53A0qwJJWRXoG9q+gXaNOZRZhqW/ZUBVrYOHsxRf3dHdODixpEqL137LwL92XYam3pzBHWml2JFWinAvBe4bEoS7EgONP1yiKOLLw3l46LuzqKjtC62s0eN/d8a1a9Dj/UND0M1fyWRBZHFSiWAc02LpgboR3s4ddtE3Z70YBFCnVj8AAGB8bAuBQB1vpQyPjQzF6bxK/HdfNjadLDRrEKDTi/j6aB4+O5ALEcCAMDdsmBOPSB/DD1JhhQYD3j2Ci8VqAEDfEFc8MDQY3konbD5ZiK0pRcgsUeOF7RfxwvaLGB3jiTv6B2BLchE2nTSsnxDj54z0IjU2HC/A45vO4d9TurarNWN0jFd7q03UImeZBFvv7WntYpidOevFIIA6rfoBwNRehkVwNp4otMlAAAAeHh6C/+7Lxq4Lpcgvr4G/W/v7v3PKarD890wcrx3NP29QEN6fGtOgyf6h79JwsViNQHcZHhsRiiER7sYL+PwhwZiTGIg/0krwc2oxjmVVGFsHAMBJImDuwEDM7OuPP8+XYumvGXh/TxZCPeV45rqIdpefiKyLQQB1SnsvlDYIAB4ZHmJ8rS4QiAtQ2sQYgTo9g10xqqsn/jxXip9TSzB7QPNrE7QkKascz/1k6P93kUnwwdQY3H3FaP6fTxfh26R8SATg5Ru6oHvA1esbyJ0kuLGHD27s4YOcshr8dqYEv50thlImxZPXhqJr7VLDY2K8UFSpxQd7svDstnQMjfTAqK5e7aoDEVkXgwCiDiKKIspqU3xK25mrc99FFV76+SJqdCIGR7jjqzt6oGsjI/3r5vtfE+XZaABwpSB3OWb09cPhS2Uor9GhuFIL+P5T/gKm96VOpEKtQ8BL+wAAeS8NhatC2uS29ZMBAbY9sK819WoJgwDqlIZFeeKTGbG499uz2Hii0Ph83eNPZsTaVCsAAPx6phhHLpXD2UnA+B5tT8Dz65livLEjEzo9MDHeB9/cFQcXWeM/Ak0935xNJwtxLMsQPCzacgGjunri4WHB+P5kIb5JMkzr++/0GLYCUKdQP8FPU5pKBpTyVKLNBgKm1MsUDAKo06rr878yELCVGQJXeu33TADAhHhfeLq07av33fECvF+bA2D2gAB8dls3yJppVnCpHRtQY+JKfapqrXH64HWxXtiRVoI/z5Vi7wWVMQ3x+1NicP/QkOYOQ9SpXJkMKCW3ErPXpaKgQmOzQYC5cAEh6tTmDQ7GJzNijX/bYgBQWaPDuFUn8Oe5UjhJBMzo49em42w/XWQMAB4bEYo1M7s3GwAAMA4QLKtueaUxnV7Eyl1ZKFPr0DNIiZ/v64UjT/THsEgPYwDw71u64uFrGACQfapLBlSXFdARsCWAOr15g4MRV9vfbWtdAFqdiNvXnsYvZwyr4905IKBNswJEUcS3tU3xi64NwxsTokyaotc3xBUCgFO5lTiQUYZBEVdnOwMMLQXLfs3ArgsqSATgX5O7QioR0CfEDbse7oNNJwuhcBJwc7xvq8tORLaLLQFkF4ZFedpcACCKIh7eeBY/nCqEXCpgxYQo3JUY2KZjncmvwoWiasilAhZfH2HyHP34IFc8OiIUALBiRyZO5Vy9Sl9eeQ2e2XIBuy6oIJMI2DAnvkESH4lEwNTefgwAiOwQgwAiC3n1twx8tD8HAoDnr4/AwPDG78JN8dNpQ0vCtN5+8GrleIJlN0WiR4ALCiu1eHTTOaw9nAudXoReFPHDqULc/b8zOJpVAWcnCbbN74kpvdrWXUFEnQ+7A4gsYGdaCV7YfhEA8H8jQjAiumErhapai5IqLUI8FC3mzb9YXG3sTrh7YOtX9XNTSLH/0X548Luz+PpoPj49kIuCCi3kTgLW13YxDO3igU9v6+ZQfaFk/yQSYFRXT+Nje2HOejEIILKwXFUNRFGEIAjQ6UV8d7wAnx3MgVorQiIAoR5yhHsp0CfEDZMSfBtk+zuVU4HF29JRpdGjb4grxsR6takMni5O+OqOHhgZ7YkHv0vDL2eKUZdy/NWbIvH0mHCL51Yn6mguMil2PtTH2sUwO3PWy45iIyLbcW2MF/4zLQYA8E1SAVbty8aFomr83/fn8J992VBrRSicBOhFILO0BnsvluE/+7Ixe91p/JhcCJ1exL6LKjz543mo1DoMjnDHbw/0bteFWhAEzB8SDA9nKao0elTU6OEql2DR6DAGAEQOii0BRBbywLAQiDDk7v8mqQDrjxdALwKucglW3tIVdw8MQnZZDU7nVuJETgVW7rqM9CI13vnzMv53NB85ZTXQi8BNPbyx/q74dmUFqyOVCBge6WEcY3BNlGeL0wyJyH4xCCCyoAeHhUAUgYc3pkEvAhPiffDf6bEI9VQAAEI9FQj1VOC6bt54cFgIVu3LxtJfM5ClMqTnvXNAAD5tISFQaw2KcDcGAYObmDJIZA8q1DpEvnoAAJD+3CCzBNK2wJz1YhBAZGEPDQ9BrJ8LNHoRN/XwbnJ6n8JJgkdHhGLuwED8Z282XGQSPDI8BBIzNtVnq9RYtS/H+PdH+3PwwLBgBHsozPYeRLak/noA9sRc9WIQQNQBxnb3bnmjWh7OTnh6TLjZy1Cj1ePWNSnIKatBkLsMgGEp4lvXpOCPB3tD7sRuASJHw289kYN48ofz2JOugqtcgjcnROPNCdFwlUuwJ12FhT+et3bxiGxOSm4ljlwqQ0pupbWLYjFsCSByAL+dKTauO7D4ugiEeSmMj5/7KR3v7c7C5ATfBpkCiRyVn6sMSrkEs9elGp9TyiXwc5VZsVSWwSCAyAHUnwJ49HI5hnZxNz6uY86xB0SdWYS3M1KeSmzQ7+7nKrPLFQUZBBA5gNExXvjv9Bg8sCENG44XGJ+ve7xqeixGx3hZqXRE5pdRXI3Mkmrj35kl1egR6Gry/hHeznZ50b8SgwAiB3H/0BAIEHD/hrMNAoFV02Nx31DbWn6ZqD0yiqsRt+IQKmv0xuf6v3sEp58eaBcXdokESAx3Mz5uDwYBRA6k7mJ//4azAICPbo3F/CEMAMi+FFRoUFmjx9pZ3REXqERKbiVmr0tFQYXGLoIAF5kUBx/vb5ZjMQggcjD3DQ1GfO1CQddE29byy0TmFBeoRP8wJsRqDoMAIgdk6Yv/2fwqHM8uhygCehHQiyJ6BrmiZ7DpfbJEZHkMAojIbLQ6Ea/9noGXf7kIvdjwNQHAA8OCsXx8FDxd+NND5pVRXG0czV83r79Ko0fksr9RoxMbPA907tH+lTU6xK84BABIfioRSjnTBhORlYmiiCmfn8KW5CIAQKyfM1xkUgiCITg4lVuJ/+zNxo+nCrF+TjyGdPGwconJXjQ2EFApl8BX6YSLxWoAgItMuGref8pTiZ0yEBBFGOslii1s3AIGAURkFqv2ZWNLchHkUgGLrg3D9VckHjp6uRxv/3kJl0prMOL9JDx/fQRGx3iib6gbPJz5U0Rtd+VAQMBwp++r/Ce5z5EF/VGpMQQJ9jZQsD34zSOidjtfWIUFmw2ph+cPCb4qAACAfqFuWDU9Fm/8kYldF1R46ZeLeOkXw2tdfZ0R4a2ArqqiI4tNdubKgYAVap3xcbiX81Wr7dV1D9hzWuCWMAggonbR60Xc880ZVGv16B3siqm9fJvc1lUuxcvjumBbShH2Z5ThbH4Vcss1OFdYjXOF1YCaQQBZniOlBW4JgwAiapfPD+biz3OlcHYS8NToMEiaWCq5jiAIuDneFzfHG4KF0iotzhZUQVWtg7qyDCs+6IhSkyNzpLTALWEQQETt8t992QCAuxIDEeqpaPX+ni5OSAw3NOFWlEmwwqylI2qco6QFbgmDACJqs9S8ShzMLINEAG7s7mPt4hA1IAgwJsZqoYGqUzFnvRgEEFGbfXk4FwAwKMId3kr+nJBtUcqlOPVUorWLYXbmrBe/tUQOYO+FUgDAsKj2Zwqs1ujx4Hdn8XNqMXLLagAAYxuZDUBEto9BAJGd+/TvbNz7rWHBoE9mxGLe4LYvGKTTi7hz3ekGqxBGeCkwPNKQ+KeyRodLpWpcKqlBpUYHiSBAIgBSiQBvFyfE+rkwWyCRDeG3kciO1Q8AABgftyUQEEURj286hw3HCyCTCHju+gj0DFLCW+mED/Zk4c9zpSis1LZ4nAA3GWL9XDC0izvGx/lAsKfOWrIplTU6DPzXUQDAwcf7tSu9ri0xZ70YBBDZqfoBQN3c/Y0nCtscCLzxRybe35MFAcCz14VjVFdD14KqWouNJwqN2/m7ydDNzwW+rjLo9CJ0ogitTsTFYjXOFlQhr1yDvHIN9qSr8HdGGZ4eEw5XO/lxJtsiikBybSKg9qbXtSXmrBeDACI7tPdCaYMA4JHhIcbX6gKBuAClyWME/jxXgme3pQMAHhoegtExXsbX6n6MPJyluPj8YHg109yvqtYiKasCf5wtwbLfMrDrggrnN5zFk6PC0C/UrZW1JKL2YhBARC2q32CfW1YDURQhCAL+Ol+KZb9lAADGdfduNgAAAA9nJ4yI9sSIaE/c2MMb09ck41JpDZ744TwSgpSQahw3fSuRNTAIILJDw6I88cmMWNz77dkGTfV1jz+ZEduqmQIju3ph1fRY3L/hrHFQYLCHHO/vzoIIYHKCLz6f2b1VZRzcxQMnFyVi8bYL+M/ebJzKqWTaYKIOxiCgGXq9HqIoQir9p7+y7g6IyNbV9flfGQi0dYbAfUMN+9QPBADgwWHBeG9KDKSS1n8vPF2c8MG0WDw4LAQncypQWV6GeUwbTNRhGAQ0ISUlBStXrkRaWhqGDh2KxMRETJ48GYIgtCoQUKvVUKvVxr9VKpWlikx0lfqBAND+KYL1AwEAePWmSDx7XXi7A+Oewa7oGewKlcoZ89p1JCJqDQYBjTh9+jSGDRuGm2++GVFRUdizZw+++uorHDp0CEuXLm1VILB8+XK8/PLLHVBqosbNGxyMuABDilFzJAu6b2gwegS4QAQwqqtXu49HZIqM4upWL/gjCEAXb4Xxsb0wZ70YBFxBFEV89NFHuOGGG7B27VoAwKVLl7BhwwYsXrwYarUaK1asMPnO59lnn8UTTzxh/FulUiE8PNwiZSdqijku/vWN5MWfOlBGcTXiVhxCZY3e+JxSLkHKU4nNBgJKuRTpzw/uiCJ2KHPWi0HAFQRBQFpaGmSyf9aVDgsLw7x58yCXy/HCCy8gODgYCxYsMOl4CoUCCkXrV1YjIiKDggoNKmv0WDurO+IClUjJrcTsdanYdb4UcYEapORyVklbMQhoxMiRI/H999/jzJkz6NatGwDA3d0dM2bMQHp6OjZt2oTbb78dQUFBVi4pEZHjiAtUon+YO/xcZVDKJZi9LtX4mlIugZ+rrJm9qTESaxfAFg0YMABZWVn46quvUFRUZHzez88PkydPxv79+3HhwgUrlpCIyHFFeDsj5alEHF7Qz/ivsa6BKo0OA/91BAP/dQRVGp2VSmt+5qwXWwIaMXr0aDz55JN4/PHHoVAoMHfuXISEGDKuxcbGIi4uzsolJCJybBHezi0ODNTrgUOZ5cbH9sKc9XL4IECv10Mi+adBpG7U/yOPPIKamhq89NJLuHjxIiZNmoSePXvi/fffR0FBASIjI61XaCIiIjNw2CAgNzcXgYGBDQIAwDAwsC4weOKJJxAQEIA1a9ZgxowZiIyMREVFBX788UcEB7d9rjURETWv/pRADvyzHIcMApKSknDjjTfiq6++wpgxY656XSKRQKfTQSqVYvbs2Rg3bhxyc3Oh0WgQEhKCwMBAK5SaiMh+1b/o55drMHVN8lVTAjnwz/wcLghISkrCkCFD8Oijj14VANR1Bej1+gapgv39/eHv79/RRSUicghN5QHYPr8n/N0MF35TkgNR6zlUEJCcnIwhQ4bgmWeewZIlSyCKIjIzM5Gbm4u+ffvCyclwOuq6CN59913odDosXLjQmsUmIrJrV+YBAHjR7ygOEwSUlpZi/vz58Pf3x5IlSwAAM2fORHJyMtLS0hAeHo6nn34a06dPh6enJ0pLS7Ft2zZotVrMmzcP3t7eVq4BEZF9q8sDYE722oVgrno5TBDg6emJKVOm4KeffsKcOXNw6tQpBAcH45VXXkFCQgJee+01vP766/D09DQGAl988QV0Oh0DACKiTshVIUX+K0OtXQyzM2e9HCIIqBvtv3DhQsjlcqxatQoRERH46KOPjKP8P//8c9x4441YuXIlpk+fDr1ezxkARERk1+w6CKioqIBer4coivDw8AAAPProo/D29oaPj48x7a9Wq4WTkxP69euH3bt3A8BVUweJiMh0bVn1jzqe3QYBycnJWLBgAfLz85Gbm4sVK1Zg5syZkEqluPPOO6HRaIwrAdYNCLx8+TISEhKg1+shCEK710gnInJETY323zgn3jjavz5L5QGo0uhw08cnAQA/ze8JF5m0hT06B3PWyy6DgOTkZIwcORJ33XUXBg4ciEOHDuHuu+9GQkIC+vbtCwANVgmsrq7GsmXLsH37duzatYutAERE7XDlaP+6ef831l64GmOJPAB6PfDnuVLjY3thznrZXRBQVFSEBQsW4I477sA777wDALj99ttx9OhRrF69GitXrjTmAwCAbdu24Z133sHp06fx888/o3v37tYsPhGR3ag/2j/lqcQG3QNXYneBddhdEKDRaFBSUoLp06cD+GdQYHR0NAoLCwGgQTP/tddei6NHj+KDDz5gAEBEZCGmLPhDHc/ugoDAwECsXbsWsbGxAACdTgeJRILQ0NCrlv9VqVTw8PDAc889Z42iEhERWZVddn7XBQB6vd7Y96/T6ZCbm2vcZvny5fjkk0+g1WqtUkYiIiJrs7uWgPokEomx/18QBON6AC+++CKWLVuGo0ePGmcGEBERORq7vwLWBQFSqRTh4eF46623sGLFChw6dAh9+vSxdvGIiOyCrS79q5TbZYO32epl90FA3XQ/mUyGjz/+GB4eHti9ezf69+9v5ZIREdmHpvICWDtvv6tCiorl11i1DJZgznrZfRBQZ9y4cXjhhRewd+9exMfHW7s4RER2g6sAdl4OEwQkJiairKwMrq6u1i4KEZHNMUeaX0usAkiW5TBBAAAGAEQWoqo2zLLxcHaonxS70VRzfspTiZ36br5ao8e0NckAgO/mxMNZZh/jA8xZL35jiajN1Fo93v3zEl75NQMA8OLYCCwYFQaFk3382HZmLd3ZXzmQr35zfkpuJWavS0VBhca4T2dcEEinF7Etpcj42F6Ys14MAoio1URRxI+nivDED+dwrrDa+Pyz29Lxyd85eHdyV0yI9+EiXFbS0p19U6+PiPZs9MJury0FxCCAiFpJqxNx25cp2HiiAADgo3TC/MGGZbk//jsH5wqrMemzU5jayw/f3BkHJykDgY525UC9ujv7XedLEReouerOH2j8zr5uql9TLQX1j0edE4MAImqV137PwMYTBZBJBEzv44fZ/QOglBsScY2M9sTaI3nYkFSAjScKsPyPDLwwtouVS9wxWtP83tjr5n4/4J+Ben6uMijlEsxel2p8rbk7/5a2b+p1a08JpNZjEEBEJjubX4WXf7kIAFg0Ogxju3k3eF0pl+K+IcGI8nHGa79n4qWfL2Jm3wDE+rtYo7gdpq3N721tTm/t8SK8na9axa+5IKSl7Vt7PLJdDAKIyGSnciqgF4EYP+erAoD6ro/1wrdJ+UgrqMapnAqLBQHHLpfBTWXobrDmRai1ze+NDby7UnN3+qa835Vau4pfS9tzVUD7wCCgg4miYSSnSqWyckmIWq+yvAxQV8BJq0dFWfOfYSdtJaCuQmV5GVQquUnHr/te1H1PmlL3+qh39wNyQ5+2i1yCtbO6W6VJOjWvClBXIFypRYyHCIVOgItYhdmrjxi3cZFL0NdPQLiHiPIyLaCuwOFzuShv5DwWVGgwe10qqurd6devn6nvp9BVQaWyn1HxrVWh1gHqCgCGz5ZOIbVyicyjpXpVlJcBaPl7BACCaMpWZDaXLl1CeHi4tYtBZNMyMzMRFhbW5Ov8HhG1rKXvEcAgoMPp9XpkZWXB3d290elTKpUK4eHhyMzMhIeHhxVK2LnwfJmuM5wrURRRVlaGkJAQ47ofjWnpe9RROsM57Sx4Ls3H1O8RwO6ADieRSFqMzADAw8ODX4RW4Pkyna2fK09Pzxa3MfV71FFs/Zx2JjyX5mHK9wgAmNaLiIjIQTEIICIiclAMAmyMQqHAkiVLoFAorF2UToHny3Q8V+bHc2o+PJfWwYGBREREDootAURERA6KQQAREZGDYhBARETkoBgEEBEROSgGAURERA6KQQDZJb1e3/JGRNQp8PtsOQwCOgG9Xg+dTtfgOc7sbNyJEydw9OjRFvNlEz9XlsLzaj78Plsez6yNS0lJwUMPPYRx48bhhRdewObNmwEAgiDwh+UKx48fR58+ffDjjz9auyg2j58ry+B5NR9+nzsGgwAbdvr0aQwbNgzl5eWIiorCnj17sGDBArzwwgsA+MNS37FjxzBkyBAsWrQIL774orWLY9P4ubIMnlfz4fe543AVQRsliiI++ugj3HDDDVi7di0AwxrqGzZswOLFi6FWq7FixQqrLqNqK9LS0jBgwAAsXboUixcvhkajwXfffYfTp0+ja9euiIuLQ2JiorWLaRP4ubIMnlfz4fe5YzEIsFGCICAtLQ0ymcz4XFhYGObNmwe5XI4XXngBwcHBWLBggRVLaX06nQ7bt2+HKIoICQkBANx0000oKCiARqOBSqVCREQEHnroIdxxxx1WLq318XNlGTyv5sHvc8djd4ANGzlyJHJycnDmzBnjc+7u7pgxYwbmzZuHTZs2IScnx4oltD6pVIopU6Zg+fLleOyxxxAYGAhPT09s2LABp06dwtatWxEREYHPPvsMubm51i6uTeDnyjJ4XttPKpVi2rRp/D53IAYBNiQ7OxsHDhww/j1gwABkZWXhq6++QlFRkfF5Pz8/TJ48Gfv378eFCxesUVSry87Oxt9//w0ACA0NxT333IOnn34a/fv3x4svvoiYmBgAQO/evXHPPfdgx44dyMjIsGaRrSY1NRULFy40/t2/f39+riyA31fzCA4O5ve5I4lkE5KSksSYmBhxxYoVYkZGhvH5f//736JUKhVfffVV8fLly8bnc3NzxT59+oh79+61RnGtqqlzlZWVJR48eFCsqakRRVEUdTqdKIqiuG/fPjE+Pl48d+6cVcprTUlJSaKvr6+oVCrF48ePG59/7733+LmyAJ5X88nJyeH3uQNwTIANOHfuHK6//nrMnj0bTzzxBKRSqfG1//u//0NVVRWWLVuGixcvYtKkSejZsyfef/99FBQUIDIy0noFt4LmzlVwcDD8/PyM/bJ1c4s3bdoEDw8PeHl5WaPIVpOUlIQhQ4bg7rvvxtatW/HNN9+gV69eAIBHHnkENTU1eOmll/i5agO9Xt9g7rooihAEgee1la48j/UFBgYiICDAOJjS0b/PFmPtKIREcenSpeK0adNEUTREux9++KH48ssvi6+88oox+l2zZo14/fXXi0qlUoyPjxe7dOkiHjlyxJrFtoqmztWrr74qarXaBtumpKSICxcuFD09PcWkpCRrFNdqjhw5Irq4uIjPPPOMKIqiuHz5cjE6Olo8efJkg+2+/PJLfq5aIScnp8nX6r6rosjzaorz58+Lq1atErVabYNz1xRH/j5bkiCKnLhqbffffz98fHywfPlyDB48GM7OzlCr1cjJyYFUKsWOHTsQERGBnJwc4yjZkJAQBAYGWrvoHa65cyWXy/Hrr7+iS5cuSElJwdKlS5GSkoLVq1ejb9++1i56h7l8+TKGDBmCWbNm4Y033gAA7Nq1CzNnzsRrr72GOXPmoKamBnK5HABQUFCAnJwch/5cmSIpKQk33ngjvvrqK4wZM6bRbXQ6nbF1Kj8/H7m5uTyvjTh+/DgGDx4MHx8fZGRkQCqVGltTGpOamoqXX37ZIb/PlsYgwAbcd999uHTpEubMmYPPP/8c33zzDZycnFBWVoapU6eiqqoKR44csXYxbUJL50qtVuPQoUMADD80/v7+CA4OtnKpO1ZOTg4OHjyIiRMnNnj+3nvvxc6dO5GUlARXV9dmm2KpobqulUcffdQYWNWpu3jxfJomKSkJw4YNw9SpU/H3339j7ty5WLx4cYNtGjuXR48eRVBQkMN9ny2Nn1grqou/Zs+ejdLSUqxcuRLh4eHw8PCAs7MzAgMD8e6776KgoMB4YXNUpp6rvLw84wyL3r17O9wPhiiKCAoKahAA1C2+Mnv2bADA9u3brVK2zio5ORlDhgzBM888gzfeeAOiKCIjIwMHDx6ERqMxbld30Xr33Xfx1ltvWau4Ni0pKQnDhw/HggUL8OWXX2LAgAHYuXMntFptg+3qn8sVK1YAAPr16+dw3+eOwCDAiuqavuLj4xEbG4tDhw7h4sWLAP75Eri4uMDNzQ1KpdJq5bQFrTlXbm5uViuntTXWnFp3fkaNGgU/Pz98/vnnDZ6nppWWlmL+/Pnw9/fHkiVLAAAzZ87EzTffjJEjRyIhIQGfffYZSktLjdtv27YNW7duRXFxsTWLbnPOnz+Pfv364fHHH8eyZcsAAA8//DB+++03/PDDD1dtr1KpsG3bNvz00088l5ZkrcEIjkyv11/1OD09XZwyZYro7OwsPvDAA6IoimJhYaH4yiuviP369RPz8vKsUlZr47kyXf1zdaW6QZM//fSTGBwcLG7ZsqWjitXpvfnmm+KYMWPEu+66SxwwYIA4YcIEcePGjWJqaqo4Z84cMSYmRly/fr1x+6ysLDEzM9OKJbZdq1evNj7WarViTU2NOGXKFHHatGmiSqW6anueS8tjENBBsrKyxFOnTjX6Wt3I2MzMTHHRokVicHCw6OXlJfbv318MDAx0uFHFPFema+5cNebSpUtiWFiY+PTTT5s0ItuR1T8/K1euFOPj48Ubb7xRzMrKarDduHHjxGuuueaqfegfGo2mydc+/PBD0dPTUzx9+rQoiv+cQ57LjsGBgR3g8uXL6NOnD0aOHInFixc3uvhF3UCYyspKY5NiSEgI4uPj0aVLFyuU2jp4rkxnyrlqzJo1a5CYmIiEhAQLl7BzqqiogF6vhyiK8PDwMD7/5ZdfwsfHB+PHj4cgCNBqtXBycsKzzz6L3bt3Y9euXVYstW1q6lwCaDAbYMiQIYiKisK6deu4yFIHY6dgBzhz5gxKS0tRWlqK9957r8FIf71eD41GY+yfVSqVCA4Oxrx583DTTTc51EUN4LlqDVPOVX11g6/mzJnDAKAJycnJmDp1KkaNGoW4uDh89dVX0Ol0AIA777wTN9xwg/Ei5eRkyLV2+fJlJCQkGC92ZNDYuQT+GeRbdx5FUcSECRNw8uRJZGVlWa28jopBQAfo06cPxo8fj9tuuw0nT57EO++8g1OnThlfr8twt3r1amRmZlqrmDaB58p0rT1XdRctalxycrJxsN+iRYswc+ZM3H333Thx4oRxm/qrBFZXV+P555/H9u3bsWDBAkgkEt7F1mrqXB47duyqc1SXafHUqVNYvXq1lUrswKzXE+EYtFqtmJeXJ3br1k28dOmSuHHjRnHgwIHi/PnzxWHDhhmz3/31119ibGysOHv27Ksy3zkKnivT8VyZV2FhoXjDDTeIjz76aIPnR48ebXyu/sDLrVu3itddd50YGhrqcONQWtLac1n3uXz99dfFlJSUjisoiaLItQMsTiKRwN/fHwMHDsTJkycxZcoUKBQKzJkzB2q1GvPnzwcAjBgxAgsXLsTYsWMb5MN3JDxXpuO5Mi+NRoOSkhJMnz4dwD/jTqKjo1FYWAig4fTLa6+9FkePHsUHH3yA7t27W6XMtqq157Luc/nkk0+ytcoK2B1gYXUfdqlUip07dwIANm7cCJ1Oh/DwcOzatQt79+4FYMiGFxUVZa2iWh3Plel4rswrMDAQa9euxYgRIwDAOA4gNDT0qnwKKpUKSqUSzz33HAOARrTmXJaXlxsfMwCwDp51CxNrR8COGTMG58+fx0MPPYRt27bh8OHDOHbsGBYtWgS5XI7+/ftDoVA4dJ8iz5XpeK7MLzY2FoDhzrWu71+n0yE3N9e4zfLly6FQKPDoo4/yotUMnsvOg2fewup+fKOionD33XcjMDAQW7ZsQVRUFKKioiAIAvr06QNnZ2crl9T6eK5Mx3NlORKJxBhkCYJgbK5+8cUXsWzZMhw9epQXLRPxXNo+5gnoIBqNBl9++SUSExPRu3fvZlfMcnQ8V6bjubKMun7sl156CdnZ2YiNjcXzzz+PvXv3on///tYuXqfCc2nbGIJ1EJlMhrlz5xr7xPhD3TSeK9PxXFlG3fmUyWT4+OOP4eHhgd27d/Oi1QY8l7aNAwM7EBdsMR3Plel4rixn3LhxAIC9e/eanJGRGsdzaZvYHUBE1IyKigq4urpauxh2gefS9jAIICIiclBsRyQiInJQDAKIiIgcFIMAIiIiB8UggIiIyEExCCAiInJQDAKIiIgcFIMAIiIiB8UggIiIyEExCCAiInJQDAKIiIgcFIMAIiIiB8UggIiIyEExCCAiInJQDAKIiIgcFIMAIiIiB8UggIiIyEExCCAiInJQDAKIiIgcFIMAIiIiB8UggIiIyEExCCAiInJQDAKIiIgcFIMAIiIiB8UggIiIyEExCCC7JggCBEEAAHz//fcYNmwY3NzcEBgYiDlz5iAnJ8e47erVqzFgwAC4uroiICAADzzwAEpLS61VdCKbp9Vq8fHHH2P06NHw9fWFs7MzoqOjMW3aNGzevNnaxSMTCKIoitYuBJGl1AUA//73v/Hoo48iLCwMvr6+OH36NNRqNeLj43H48GE8/fTT+Pe//43o6Gi4uLggNTUVWq0Wo0aNwo4dO4zHISKD4uJiTJw4EXv27AEAdOnSBf7+/sjIyEBeXh66dOmC9PR06xaSWsSWAHIIzz77LNatW4fMzEwcO3YMaWlpiImJQXJyMm6//XasWbMGv/32G86dO4eTJ0/iyJEj8PHxwZ9//ont27dbu/hENueee+7Bnj170LVrV+zfvx/p6ek4ePAgcnNzcfbsWTz88MPWLiKZgEEAOYR7770Xt99+u/HvsLAwLFq0CACwadMmvPTSS7juuuuMr/fq1Qv33XcfADAIILrCwYMHsWnTJigUCvz0008YPHhwg9djYmKM3y+ybQwCyCHMmzfvquf69u1rfHzPPfdc9Xq/fv0AAOfPn7dYuYg6o7r+/ilTpiA2NtbKpaH2YBBADqFr165XPefv72/8r4eHR5Ovl5eXW7ZwRJ1MSkoKAGDIkCFWLgm1F4MAcghKpfKq5+oG+zX2Wv3XOXaWqCGVSgUA8PLysm5BqN0YBBARUau4u7sDAEpKSqxbEGo3BgFERNQqCQkJAID9+/dbuSTUXgwCiIioVW655RYAhpk1586ds25hqF0YBBARUasMGDAAU6ZMQXV1NW666SYcPHiwwetpaWl46623rFQ6ag0naxeAiIg6n08//RQ5OTnYt28fBg0ahMjISPj5+SEzMxO5ubno0qULFi5caO1iUgvYEkBERK3m7e2NP//8Ex988AGGDx+O4uJinDx5EkqlEtOnT8f7779v7SKSCbh2ABERkYNiSwAREZGDYhBARETkoBgEEBEROSgGAURERA6KQQAREZGDYhBARETkoBgEEBEROSgGAURERA6KQQAREZGDYhBARETkoBgEEBEROSgGAURERA6KQQAREZGD+n/J0y/sEh0nngAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 550x550 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = result_incorrect_x.plot_corner(truth=dict(m=5, c=10), titles=True, save=False)\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fit with modeled uncertainty in x-values\n",
    "\n",
    "This is not good as there is unmodelled uncertainty in our `x` values.\n",
    "Getting around this requires marginalisation of the true x values or sampling over them. \n",
    "See discussion in section 7 of https://arxiv.org/pdf/1008.4686.pdf.\n",
    "\n",
    "For this, we will have to define a new likelihood class.\n",
    "By subclassing the base `bilby.core.likelihood.Likelihood` class we can do this fairly simply."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-03-20T14:27:44.455697Z",
     "iopub.status.busy": "2025-03-20T14:27:44.455317Z",
     "iopub.status.idle": "2025-03-20T14:27:44.459844Z",
     "shell.execute_reply": "2025-03-20T14:27:44.459347Z"
    }
   },
   "outputs": [],
   "source": [
    "class GaussianLikelihoodUncertainX(bilby.core.likelihood.Likelihood):\n",
    "    def __init__(self, xobs, yobs, xerr, yerr, function):\n",
    "        \"\"\"\n",
    "\n",
    "        Parameters\n",
    "        ----------\n",
    "        xobs, yobs: array_like\n",
    "            The data to analyse\n",
    "        xerr, yerr: array_like\n",
    "            The standard deviation of the noise\n",
    "        function:\n",
    "            The python function to fit to the data\n",
    "        \"\"\"\n",
    "        super(GaussianLikelihoodUncertainX, self).__init__(dict())\n",
    "        self.xobs = xobs\n",
    "        self.yobs = yobs\n",
    "        self.yerr = yerr\n",
    "        self.xerr = xerr\n",
    "        self.function = function\n",
    "\n",
    "    def log_likelihood(self):\n",
    "        variance = (self.xerr * self.parameters[\"m\"]) ** 2 + self.yerr**2\n",
    "        model_y = self.function(self.xobs, **self.parameters)\n",
    "        residual = self.yobs - model_y\n",
    "\n",
    "        ll = -0.5 * np.sum(residual**2 / variance + np.log(variance))\n",
    "\n",
    "        return -0.5 * np.sum(residual**2 / variance + np.log(variance))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-03-20T14:27:44.461287Z",
     "iopub.status.busy": "2025-03-20T14:27:44.461112Z",
     "iopub.status.idle": "2025-03-20T14:28:05.862070Z",
     "shell.execute_reply": "2025-03-20T14:28:05.861600Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Running for label 'unknown_x', output will be saved to 'outdir'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Analysis priors:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : m=Uniform(minimum=0, maximum=30, name='m', latex_label='m', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : c=Uniform(minimum=0, maximum=30, name='c', latex_label='c', unit=None, boundary=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Analysis likelihood class: <class '__main__.GaussianLikelihoodUncertainX'>\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Analysis likelihood noise evidence: nan\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Single likelihood evaluation took 5.549e-05 s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Using sampler Bilby_MCMC with kwargs {'nsamples': 1000, 'nensemble': 1, 'pt_ensemble': False, 'ntemps': 1, 'Tmax': None, 'Tmax_from_SNR': 20, 'initial_betas': None, 'adapt': True, 'adapt_t0': 100, 'adapt_nu': 10, 'pt_rejection_sample': False, 'burn_in_nact': 10, 'thin_by_nact': 1, 'fixed_discard': 0, 'autocorr_c': 5, 'L1steps': 100, 'L2steps': 3, 'printdt': 5, 'check_point_delta_t': 1800, 'min_tau': 1, 'proposal_cycle': 'default', 'stop_after_convergence': False, 'fixed_tau': None, 'tau_window': None, 'evidence_method': 'stepping_stone', 'initial_sample_method': 'prior', 'initial_sample_dict': None}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Global meta data was removed from the result object for compatibility. Use the `BILBY_INCLUDE_GLOBAL_METADATA` environment variable to include it. This behaviour will be removed in a future release. For more details see: https://bilby-dev.github.io/bilby/faq.html#global-meta-data\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Initializing BilbyPTMCMCSampler with:\n",
      "  Convergence settings: ConvergenceInputs(autocorr_c=5, burn_in_nact=10, thin_by_nact=1, fixed_discard=0, target_nsamples=1000, stop_after_convergence=False, L1steps=100, L2steps=3, min_tau=1, fixed_tau=None, tau_window=None)\n",
      "  Parallel-tempering settings: ParallelTemperingInputs(ntemps=1, nensemble=1, Tmax=None, Tmax_from_SNR=20, initial_betas=None, adapt=True, adapt_t0=100, adapt_nu=10, pt_ensemble=False)\n",
      "  proposal_cycle: default\n",
      "  pt_rejection_sample: False\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Setting parallel tempering inputs=ParallelTemperingInputs(ntemps=1, nensemble=1, Tmax=None, Tmax_from_SNR=20, initial_betas=None, adapt=True, adapt_t0=100, adapt_nu=10, pt_ensemble=False)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Initializing BilbyPTMCMCSampler with:ntemps=1, nensemble=1, pt_ensemble=False, initial_betas=[1], initial_sample_method=prior, initial_sample_dict=None\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Using initial sample {'m': 13.99404210792243, 'c': 24.321136444900056}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Using ProposalCycle:\n",
      "  AdaptiveGaussianProposal(acceptance_ratio:nan,n:0,scale:1,)\n",
      "  DifferentialEvolutionProposal(acceptance_ratio:nan,n:0,)\n",
      "  UniformProposal(acceptance_ratio:nan,n:0,)\n",
      "  KDEProposal(acceptance_ratio:nan,n:0,trained:0,)\n",
      "  FisherMatrixProposal(acceptance_ratio:nan,n:0,scale:1,)\n",
      "  GMMProposal(acceptance_ratio:nan,n:0,trained:0,)\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Setting convergence_inputs=ConvergenceInputs(autocorr_c=5, burn_in_nact=10, thin_by_nact=1, fixed_discard=0, target_nsamples=1000, stop_after_convergence=False, L1steps=100, L2steps=3, min_tau=1, fixed_tau=None, tau_window=None)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Drawing 1000 samples\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Checkpoint every check_point_delta_t=1800s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:27 bilby INFO    : Print update every printdt=5s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:28 bilby INFO    : Reached convergence: exiting sampling\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:28 bilby INFO    : Checkpoint start\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:28 bilby INFO    : Written checkpoint file outdir/unknown_x_resume.pickle\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:28 bilby INFO    : Zero-temperature proposals:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:28 bilby INFO    : AdaptiveGaussianProposal(acceptance_ratio:0.23,n:4.2e+04,scale:0.019,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:28 bilby INFO    : DifferentialEvolutionProposal(acceptance_ratio:0.44,n:3.3e+04,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:28 bilby INFO    : UniformProposal(acceptance_ratio:1,n:2.7e+03,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:28 bilby INFO    : KDEProposal(acceptance_ratio:0.00054,n:3.7e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:28 bilby INFO    : FisherMatrixProposal(acceptance_ratio:0.39,n:3.4e+04,scale:1,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:28 bilby INFO    : GMMProposal(acceptance_ratio:0.00067,n:3.4e+04,trained:0,)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:28 bilby INFO    : Current taus={'m': 1.1, 'c': 1.1}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:28 bilby INFO    : Creating diagnostic plots\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:28 bilby INFO    : Checkpoint finished\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:28 bilby INFO    : Sampling time: 0:00:15.012779\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "14:28 bilby INFO    : Summary of results:\n",
      "nsamples: 1708\n",
      "ln_noise_evidence:    nan\n",
      "ln_evidence:    nan +/-    nan\n",
      "ln_bayes_factor:    nan +/-    nan\n",
      "\n"
     ]
    }
   ],
   "source": [
    "gaussian_unknown_x = GaussianLikelihoodUncertainX(\n",
    "    xobs=data[\"xobs\"],\n",
    "    yobs=data[\"yobs\"],\n",
    "    xerr=data[\"xerr\"],\n",
    "    yerr=data[\"yerr\"],\n",
    "    function=model,\n",
    ")\n",
    "result_unknown_x = bilby.run_sampler(\n",
    "    likelihood=gaussian_unknown_x,\n",
    "    label=\"unknown_x\",\n",
    "    **sampler_kwargs,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-03-20T14:28:05.863635Z",
     "iopub.status.busy": "2025-03-20T14:28:05.863475Z",
     "iopub.status.idle": "2025-03-20T14:28:06.013689Z",
     "shell.execute_reply": "2025-03-20T14:28:06.013152Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 550x550 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = result_unknown_x.plot_corner(truth=dict(m=5, c=10), titles=True, save=False)\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Success! The inferred posterior is consistent with the true values."
   ]
  }
 ],
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