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    "# Receiver Operating Characteristic (ROC)\n",
    "\n",
    "A ROC curve shows the ability of a probabilitic forecast of a binary event (e.g., chance of rainfall) to discriminate between events and non-events. It plots the hit rate or probability of detection (POD) against the false alarm rate or probability of false detection (POFD) using a set of increasing probability thresholds (e.g., 0.1, 0.2, 0.3, ...) that convert the probabilistic forecast into a binary forecast.\n",
    "\n",
    "The area under the ROC curve is often used as a measure of discrimination ability. ROC is insensitive to forecast bias so should be used together with reliablity or some other metric which is measures bias."
   ]
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    "from scores.categorical import probability_of_detection, probability_of_false_detection\n",
    "from scores.probability import roc_curve_data\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import xarray as xr\n",
    "from scipy.stats import beta, binom"
   ]
  },
  {
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   "metadata": {},
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    "Imagine we have a sequence of binary forecasts and a sequence of binary observations, where 1 indicates a forecast or observed event and 0 indicates a forecast or observed non-event."
   ]
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    "fcst = xr.DataArray([1, 0, 1, 0, 1])\n",
    "obs = xr.DataArray([1, 0, 0, 1, 1])"
   ]
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    "We can then use `scores` to calculate the POD ($\\frac{H}{H + M}$) and POFD ($\\frac{F}{C + F}$), where $H, M, F, C$ are the number of hits, misses, false alarms, and correct negatives respectively."
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray &#x27;ctable_probability_of_detection&#x27; ()&gt;\n",
       "array(0.66666667)</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'ctable_probability_of_detection'</div></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-9e970daf-6820-4c52-9cff-e43a59d05983' class='xr-array-in' type='checkbox' checked><label for='section-9e970daf-6820-4c52-9cff-e43a59d05983' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>0.6667</span></div><div class='xr-array-data'><pre>array(0.66666667)</pre></div></div></li><li class='xr-section-item'><input id='section-6fd1b81a-8028-43c3-9a9a-0bf1013f825d' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-6fd1b81a-8028-43c3-9a9a-0bf1013f825d' class='xr-section-summary'  title='Expand/collapse section'>Coordinates: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'></ul></div></li><li class='xr-section-item'><input id='section-f25b9774-39ac-4b3e-8aeb-1c683fa8a816' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-f25b9774-39ac-4b3e-8aeb-1c683fa8a816' class='xr-section-summary'  title='Expand/collapse section'>Indexes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'></ul></div></li><li class='xr-section-item'><input id='section-cc759fb0-ff02-4965-a97e-cb289b1cb1ac' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-cc759fb0-ff02-4965-a97e-cb289b1cb1ac' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray &#x27;ctable_probability_of_false_detection&#x27; ()&gt;\n",
       "array(0.5)</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'>'ctable_probability_of_false_detection'</div></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-c213b1eb-e266-4e17-bbf7-6b3099653fe2' class='xr-array-in' type='checkbox' checked><label for='section-c213b1eb-e266-4e17-bbf7-6b3099653fe2' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>0.5</span></div><div class='xr-array-data'><pre>array(0.5)</pre></div></div></li><li class='xr-section-item'><input id='section-7f8736a0-c5dc-4484-908c-767c385d816c' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-7f8736a0-c5dc-4484-908c-767c385d816c' class='xr-section-summary'  title='Expand/collapse section'>Coordinates: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'></ul></div></li><li class='xr-section-item'><input id='section-bcbdb4f6-3209-41f8-bdc3-596af8bdebd8' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-bcbdb4f6-3209-41f8-bdc3-596af8bdebd8' class='xr-section-summary'  title='Expand/collapse section'>Indexes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'></ul></div></li><li class='xr-section-item'><input id='section-809fc073-c4e5-4888-bed0-936638087321' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-809fc073-c4e5-4888-bed0-936638087321' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
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       "<xarray.DataArray 'ctable_probability_of_false_detection' ()>\n",
       "array(0.5)"
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     },
     "execution_count": 4,
     "metadata": {},
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   "source": [
    "probability_of_false_detection(fcst, obs)"
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  },
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   "source": [
    "Now suppose that we have a forecast that is the probability of rain occuring, and corresponding observations where 1 means it rained, and 0 means that it didn't rain. We generate some synthetic forecasts using a Beta distribution and generate some corresponding observations."
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  {
   "cell_type": "code",
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   "source": [
    "fcst = beta.rvs(2, 1, size=1000)\n",
    "obs = binom.rvs(1, fcst)\n",
    "fcst = xr.DataArray(data=fcst, dims=\"time\", coords={\"time\": np.arange(0, 1000)})\n",
    "obs = xr.DataArray(data=obs, dims=\"time\", coords={\"time\": np.arange(0, 1000)})\n",
    "\n",
    "thresholds = np.arange(0, 1.01, 0.01)"
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   "metadata": {},
   "source": [
    "Now calculate the ROC curve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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       "  grid-column: 2 / -1;\n",
       "}\n",
       "\n",
       ".xr-section-details {\n",
       "  display: none;\n",
       "  grid-column: 1 / -1;\n",
       "  margin-bottom: 5px;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked ~ .xr-section-details {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-array-wrap {\n",
       "  grid-column: 1 / -1;\n",
       "  display: grid;\n",
       "  grid-template-columns: 20px auto;\n",
       "}\n",
       "\n",
       ".xr-array-wrap > label {\n",
       "  grid-column: 1;\n",
       "  vertical-align: top;\n",
       "}\n",
       "\n",
       ".xr-preview {\n",
       "  color: var(--xr-font-color3);\n",
       "}\n",
       "\n",
       ".xr-array-preview,\n",
       ".xr-array-data {\n",
       "  padding: 0 5px !important;\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-array-data,\n",
       ".xr-array-in:checked ~ .xr-array-preview {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-array-in:checked ~ .xr-array-data,\n",
       ".xr-array-preview {\n",
       "  display: inline-block;\n",
       "}\n",
       "\n",
       ".xr-dim-list {\n",
       "  display: inline-block !important;\n",
       "  list-style: none;\n",
       "  padding: 0 !important;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list li {\n",
       "  display: inline-block;\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list:before {\n",
       "  content: '(';\n",
       "}\n",
       "\n",
       ".xr-dim-list:after {\n",
       "  content: ')';\n",
       "}\n",
       "\n",
       ".xr-dim-list li:not(:last-child):after {\n",
       "  content: ',';\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-has-index {\n",
       "  font-weight: bold;\n",
       "}\n",
       "\n",
       ".xr-var-list,\n",
       ".xr-var-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-var-item > div,\n",
       ".xr-var-item label,\n",
       ".xr-var-item > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-even);\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-var-item > .xr-var-name:hover span {\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-var-list > li:nth-child(odd) > div,\n",
       ".xr-var-list > li:nth-child(odd) > label,\n",
       ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-odd);\n",
       "}\n",
       "\n",
       ".xr-var-name {\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-var-dims {\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-var-dtype {\n",
       "  grid-column: 3;\n",
       "  text-align: right;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-preview {\n",
       "  grid-column: 4;\n",
       "}\n",
       "\n",
       ".xr-index-preview {\n",
       "  grid-column: 2 / 5;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-name,\n",
       ".xr-var-dims,\n",
       ".xr-var-dtype,\n",
       ".xr-preview,\n",
       ".xr-attrs dt {\n",
       "  white-space: nowrap;\n",
       "  overflow: hidden;\n",
       "  text-overflow: ellipsis;\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
       "  overflow: visible;\n",
       "  width: auto;\n",
       "  z-index: 1;\n",
       "}\n",
       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data,\n",
       ".xr-index-data {\n",
       "  display: none;\n",
       "  background-color: var(--xr-background-color) !important;\n",
       "  padding-bottom: 5px !important;\n",
       "}\n",
       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data,\n",
       ".xr-index-data-in:checked ~ .xr-index-data {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
       "}\n",
       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-index-name div,\n",
       ".xr-index-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data,\n",
       ".xr-index-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2,\n",
       ".xr-no-icon {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
       "Dimensions:    (threshold: 101)\n",
       "Coordinates:\n",
       "  * threshold  (threshold) float64 0.0 0.01 0.02 0.03 ... 0.97 0.98 0.99 1.0\n",
       "Data variables:\n",
       "    POD        (threshold) float64 1.0 1.0 1.0 1.0 ... 0.1125 0.0875 0.04063 0.0\n",
       "    POFD       (threshold) float64 1.0 1.0 1.0 1.0 1.0 ... 0.0 0.0 0.0 0.0 0.0\n",
       "    AUC        float64 0.8074</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-317a5270-a842-4834-907b-01f781a14611' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-317a5270-a842-4834-907b-01f781a14611' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>threshold</span>: 101</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-ed66b20a-f9c0-4fbf-bd05-3f3a8d75a9f2' class='xr-section-summary-in' type='checkbox'  checked><label for='section-ed66b20a-f9c0-4fbf-bd05-3f3a8d75a9f2' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>threshold</span></div><div class='xr-var-dims'>(threshold)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.0 0.01 0.02 ... 0.98 0.99 1.0</div><input id='attrs-8a5052e7-b221-4cdf-8899-6fc4dcec15dd' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-8a5052e7-b221-4cdf-8899-6fc4dcec15dd' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-5eccaee2-6b06-42fd-88e0-bce00df01f16' class='xr-var-data-in' type='checkbox'><label for='data-5eccaee2-6b06-42fd-88e0-bce00df01f16' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0.  , 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1 , 0.11,\n",
       "       0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2 , 0.21, 0.22, 0.23,\n",
       "       0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3 , 0.31, 0.32, 0.33, 0.34, 0.35,\n",
       "       0.36, 0.37, 0.38, 0.39, 0.4 , 0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47,\n",
       "       0.48, 0.49, 0.5 , 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59,\n",
       "       0.6 , 0.61, 0.62, 0.63, 0.64, 0.65, 0.66, 0.67, 0.68, 0.69, 0.7 , 0.71,\n",
       "       0.72, 0.73, 0.74, 0.75, 0.76, 0.77, 0.78, 0.79, 0.8 , 0.81, 0.82, 0.83,\n",
       "       0.84, 0.85, 0.86, 0.87, 0.88, 0.89, 0.9 , 0.91, 0.92, 0.93, 0.94, 0.95,\n",
       "       0.96, 0.97, 0.98, 0.99, 1.  ])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-592e15d6-31fd-4857-bf95-9d4875a14923' class='xr-section-summary-in' type='checkbox'  checked><label for='section-592e15d6-31fd-4857-bf95-9d4875a14923' class='xr-section-summary' >Data variables: <span>(3)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>POD</span></div><div class='xr-var-dims'>(threshold)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.0 1.0 1.0 ... 0.0875 0.04063 0.0</div><input id='attrs-d6b384d9-b822-45f8-9300-a757ede220b5' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-d6b384d9-b822-45f8-9300-a757ede220b5' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-a941672c-71bf-44f9-b49a-fd2dafaa0c85' class='xr-var-data-in' type='checkbox'><label for='data-a941672c-71bf-44f9-b49a-fd2dafaa0c85' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([1.       , 1.       , 1.       , 1.       , 1.       , 1.       ,\n",
       "       1.       , 1.       , 1.       , 1.       , 1.       , 1.       ,\n",
       "       1.       , 1.       , 0.9984375, 0.9984375, 0.996875 , 0.9953125,\n",
       "       0.9953125, 0.9921875, 0.9921875, 0.9921875, 0.9921875, 0.9921875,\n",
       "       0.990625 , 0.9890625, 0.9875   , 0.9875   , 0.984375 , 0.9828125,\n",
       "       0.9828125, 0.978125 , 0.975    , 0.9734375, 0.9734375, 0.9671875,\n",
       "       0.9625   , 0.95625  , 0.9515625, 0.9484375, 0.9390625, 0.9328125,\n",
       "       0.928125 , 0.925    , 0.9203125, 0.9125   , 0.9015625, 0.89375  ,\n",
       "       0.8890625, 0.8828125, 0.88125  , 0.871875 , 0.8671875, 0.8578125,\n",
       "       0.853125 , 0.8453125, 0.834375 , 0.83125  , 0.815625 , 0.8046875,\n",
       "       0.79375  , 0.778125 , 0.765625 , 0.753125 , 0.7421875, 0.725    ,\n",
       "       0.7140625, 0.7      , 0.690625 , 0.6671875, 0.65625  , 0.6390625,\n",
       "       0.6203125, 0.596875 , 0.58125  , 0.575    , 0.5671875, 0.5546875,\n",
       "       0.5328125, 0.51875  , 0.5      , 0.4890625, 0.465625 , 0.446875 ,\n",
       "       0.43125  , 0.4140625, 0.3921875, 0.3734375, 0.346875 , 0.3328125,\n",
       "       0.3140625, 0.2828125, 0.259375 , 0.2296875, 0.2046875, 0.1734375,\n",
       "       0.1375   , 0.1125   , 0.0875   , 0.040625 , 0.       ])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>POFD</span></div><div class='xr-var-dims'>(threshold)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.0 1.0 1.0 1.0 ... 0.0 0.0 0.0 0.0</div><input id='attrs-0d41d2d4-9cfc-404c-9764-a128b9c4159e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-0d41d2d4-9cfc-404c-9764-a128b9c4159e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-1da63ead-2bf1-429e-9324-10bbf2c17215' class='xr-var-data-in' type='checkbox'><label for='data-1da63ead-2bf1-429e-9324-10bbf2c17215' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([1.        , 1.        , 1.        , 1.        , 1.        ,\n",
       "       0.99722222, 0.99444444, 0.98888889, 0.98611111, 0.98055556,\n",
       "       0.97777778, 0.97777778, 0.96944444, 0.95555556, 0.95277778,\n",
       "       0.94444444, 0.93611111, 0.93055556, 0.92222222, 0.91388889,\n",
       "       0.90277778, 0.89722222, 0.88611111, 0.86666667, 0.85555556,\n",
       "       0.84444444, 0.84166667, 0.82777778, 0.81111111, 0.8       ,\n",
       "       0.79444444, 0.78055556, 0.77222222, 0.75277778, 0.74722222,\n",
       "       0.74166667, 0.725     , 0.70555556, 0.68611111, 0.66944444,\n",
       "       0.64444444, 0.63055556, 0.61666667, 0.6       , 0.57777778,\n",
       "       0.56388889, 0.54722222, 0.53333333, 0.51944444, 0.5       ,\n",
       "       0.49166667, 0.46666667, 0.46111111, 0.45      , 0.42222222,\n",
       "       0.40277778, 0.39722222, 0.38611111, 0.37222222, 0.35555556,\n",
       "       0.33055556, 0.325     , 0.31111111, 0.29444444, 0.28333333,\n",
       "       0.27222222, 0.25833333, 0.24722222, 0.24166667, 0.21666667,\n",
       "       0.20555556, 0.19722222, 0.18611111, 0.18333333, 0.16666667,\n",
       "       0.15833333, 0.14444444, 0.13888889, 0.13611111, 0.12222222,\n",
       "       0.11666667, 0.11111111, 0.09722222, 0.07222222, 0.06388889,\n",
       "       0.06111111, 0.05555556, 0.05555556, 0.04722222, 0.03888889,\n",
       "       0.03611111, 0.03055556, 0.02777778, 0.01944444, 0.01111111,\n",
       "       0.00277778, 0.        , 0.        , 0.        , 0.        ,\n",
       "       0.        ])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>AUC</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.8074</div><input id='attrs-879a1ca8-6c58-4044-9270-b8afac977c91' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-879a1ca8-6c58-4044-9270-b8afac977c91' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-28a60a5a-791e-43cf-98c9-f1cc35f4a735' class='xr-var-data-in' type='checkbox'><label for='data-28a60a5a-791e-43cf-98c9-f1cc35f4a735' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(0.80740451)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-6557a37c-2e39-4272-9e42-278e365e8c47' class='xr-section-summary-in' type='checkbox'  ><label for='section-6557a37c-2e39-4272-9e42-278e365e8c47' class='xr-section-summary' >Indexes: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>threshold</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-2f5eb842-dcf2-4c3e-a66a-6c00bf6ac4ac' class='xr-index-data-in' type='checkbox'/><label for='index-2f5eb842-dcf2-4c3e-a66a-6c00bf6ac4ac' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Float64Index([               0.0,               0.01,               0.02,\n",
       "                            0.03,               0.04,               0.05,\n",
       "                            0.06,               0.07,               0.08,\n",
       "                            0.09,\n",
       "              ...\n",
       "                            0.91,               0.92,               0.93,\n",
       "              0.9400000000000001, 0.9500000000000001,               0.96,\n",
       "                            0.97,               0.98,               0.99,\n",
       "                             1.0],\n",
       "             dtype=&#x27;float64&#x27;, name=&#x27;threshold&#x27;, length=101))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-347868c9-88a8-4b71-bb0d-7f7979ad5bd1' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-347868c9-88a8-4b71-bb0d-7f7979ad5bd1' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.Dataset>\n",
       "Dimensions:    (threshold: 101)\n",
       "Coordinates:\n",
       "  * threshold  (threshold) float64 0.0 0.01 0.02 0.03 ... 0.97 0.98 0.99 1.0\n",
       "Data variables:\n",
       "    POD        (threshold) float64 1.0 1.0 1.0 1.0 ... 0.1125 0.0875 0.04063 0.0\n",
       "    POFD       (threshold) float64 1.0 1.0 1.0 1.0 1.0 ... 0.0 0.0 0.0 0.0 0.0\n",
       "    AUC        float64 0.8074"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "roc = roc_curve_data(fcst, obs, thresholds)\n",
    "roc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The output that we have calculated the POD and POFD for each threshold. We also calculated the AUC which is the area under the ROC curve, which we will discuss shortly. Let's now plot the ROC curve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NDw+PLF+OZ8+ezfHoqH+2muSFdu3a8dVXX/Hdd99ldukBOR4hl5Onn36a2bNnM3To0GyHz4PZ9bh8+XLuu+++XNWVm/flao/h5uaWJXQnJSXxf//3f1n269ChA66ursycOZNWrVpd8fGu9P536dKFL7/8ErvdTsuWLa+5vtwoUaIEPXv25PTp04wcOZLjx49Tv379zOkXruXnolOnTixYsIC5c+eqe0yyURCSIqtkyZKMGzeOZ555hvnz5/PQQw/x0Ucf0alTJzp27MiAAQOoWLEiFy5cYP/+/ezYsYNFixYBMGHCBL777jtuvfVWnn/+eRo1asSlS5dYvXo1o0aNom7duowcOZIlS5Zw66238vTTT9O4cWMcDgcRERF8//33jB49+l//+D/66KMMHjyYM2fO0Lp162yha8KECaxdu5bWrVszYsQI6tSpQ3JyMsePH2fVqlV8+OGH191t8fnnn3PnnXfSoUOHHCdUrFu3bo6HiAcFBXH77bfz0ksvZR41duDAgSwBIS/qzjiUeujQofTs2ZOTJ0/y2muvUb58+Wwzhjdq1Iiff/6Zb775hvLly+Pv73/FAHut+vfvz3vvvcdDDz3ExIkTqVmzJt999x1r1qwB+NeWg5CQkMzWvqZNm2ZOqAjmhH6zZ8/GMIxcB6HcvC9Xcs899zB58mT69u3LE088QUxMDO+88062uZuqVavG888/z2uvvUZSUhIPPvgggYGB7Nu3j+jo6MzD2xs1asTSpUuZOXMmYWFhuLi40Lx5c/r06cO8efPo3LkzTz31FC1atMDd3Z1Tp06xbt06unXrluvXD9C1a9fMecPKlCnDiRMneP/996latWrmkZKNGjUC4IMPPqB///64u7tTp06dbK1QYI77mjNnDkOGDOHgwYO0b98eh8PB77//Tr169ejTp0+ua5RixNqx2iL/LuOosX8evWUYhpGUlGRUqVLFqFWrlpGenm4YhmHs2rXL6NWrl1G2bFnD3d3dKFeunHH77bcbH374YZb7njx50nj00UeNcuXKGe7u7kaFChWMXr16GefOncvc5/Lly8aLL75o1KlTx/Dw8DACAwONRo0aGU8//XSWI6v+edRLhtjYWMPb2/uqR6ycP3/eGDFihBESEmK4u7sbpUqVMsLCwowXXnjBuHz5smEYfx199fbbb+fqvbt8+bLx+uuvG02bNjV8fHwMHx8fo3HjxsbEiRMzH/vvAGPYsGHGjBkzjBo1ahju7u5G3bp1jXnz5uVL3W+88YZRrVo1w9PT06hXr57xySefGC+//LLxzz9NO3fuNNq0aWP4+PgYQOYRQVc6aszX1zfbc+X0uBEREUaPHj0MPz8/w9/f37j//vuNVatWGYDx9ddfX/W9zXDkyBFj6NChRs2aNQ1PT0/D29vbqF+/vjFq1KgsRzS1a9fOaNCgQbb79+/fP9sRWdf6vmR8XjmZPXu2UadOHcPT09OoXr26MWnSJGPWrFk5Hmn1+eefGzfddJPh5eVl+Pn5GaGhoVmOmrtw4YLRs2dPo0SJEobNZstSR1pamvHOO+8YTZo0ybx/3bp1jcGDBxt//vln5n5Vq1Y17rnnnhxr/efvz7vvvmu0bt3aCAoKMjw8PIwqVaoYgwYNMo4fP57lfuPGjTMqVKhguLi4ZPk5+OdRY4Zh/q0YP368UatWLcPDw8MoXbq0cfvttxubNm3KsSZxHlpiQ0Qy2Ww2hg0bxrRp06wuxTKvv/46L774IhEREdfdGiciRYe6xkTEaWUEvrp165KWlsZPP/3ElClTeOihhxSCRJyEgpCIOC0fHx/ee+89jh8/TkpKClWqVOHZZ5/lxRdftLo0ESkg6hoTERERp2XphAq//vorXbt2pUKFCthstmxzXOTkl19+ISwsDC8vL6pXr86HH36Y/4WKiIhIsWRpEEpISKBJkybXPDDz2LFjdO7cmbZt2xIeHs7zzz/PiBEjWLJkST5XKiIiIsVRoekas9lsLFu27KqrZT/77LOsWLEiy3o7Q4YMYdeuXWzevLkAqhQREZHipEgNlt68eXPm+jkZOnbsyKxZs0hLS8txUceUlJQsU9M7HA4uXLhA6dKlr3m6dxEREbGWYRjEx8fn+bpxRSoInT17NtuCiMHBwaSnpxMdHZ3jgn6TJk3KnB1VREREiraTJ0/m6fQWRSoIQfZF+zJ69q7UujNu3DhGjRqVeT02NpYqVapw8uRJAgIC8q9QERGRPGAYkJ9rEScnw+bN8OOP8MMPcOzYtd3P3x+qV4d/fpXWrAl9+kCJEjde267IaKqV8CfQ25PLl+O4447KOS6jciOKVBAqV65ctpWho6KicHNzy1wV+588PT2zra8DEBAQoCAkIiKWSk2FyEg4ffqv05kzWa+fPg15vObwVbm5QdmyWbcFB0OLFnDTTdCggRl2SpeG/BphkmZ38O73h/hw8xHa1gris4EtuHzZvC2vh7UUqSDUqlUrvvnmmyzbvv/+e5o3b57j+CAREZGC5HCYwebwYYiLy3mflBRYsgR++gmiogq2viupXh3uvhs6doT27c3WHqucuZTEkwvC2X7iIgDVSvuS7si/47osDUKXL1/m8OHDmdePHTvGzp07KVWqFFWqVGHcuHGcPn2azz//HDCPEJs2bRqjRo3i8ccfZ/PmzcyaNYsFCxZY9RJERMTJJCebrTZHj5qBJ+N05Ih5ym3rjYcHVKgAFSv+dfrn9aAgyMPxwVnYbODnlz+PnVs/7j/H6EW7uJSYhr+nG2/c35h7Gpvjf5Pz6TktDULbtm2jffv2mdczxvL079+fuXPnEhkZSURERObtISEhrFq1iqeffprp06dToUIFpkyZwv3331/gtYuISPFz8iT8/DOEh4Pdbm5LTMzaTRUTc/XHcHWFatWgVKkrdx01aQIDBkDt2vnbxVRUpNkdvLX6AJ+sNwcoNaoYyLS+oVQt7Zvvz11o5hEqKHFxcQQGBhIbG6sxQiIiTu7UKTP4ZJyOHLm2+3l5QUiIOVamRg3zPONy1aqg0Rq5czklnS5T1nM8JpGBbarxXKe6eLq5Ztknv76/i9QYIRERkRsRHw/r1sGaNfD992aX1t+5uEDz5tC6Nfj+rzHC0zN7V1XJkmrFyUt+nm5M69uM05eS6NigXIE+t4KQiIgUOenpfw00NgxISIBLlyA21jxlXP77thMnYNMmSEv763FcXKBZM3OA8G23wS23ZD8cXPJeSrqdSasOULW0DwPbhADQsGIgDSsGFngtCkIiIlKkhIdDjx5w/Pj13T8kBDp1Mo+QatcOAgv+u9epnYhJYPj8cHafjsXDzYXOjcoTHOBlWT0KQiIiUmQsWwYPPWQOYHZx+etIKl9fM9AEBpoT+WVc/vv1oCBo29Ycy6NuLWt8+0ckzy35g/iUdEr6uPNuryaWhiBQEBIRkUIsIQF27ICtW83ZjxcvNrd36AALF+bN7MWS/5LT7Ez8dh9f/GYeCd68akmm9g2lfKC3xZUpCImISCGRlgZ79pihZ8sW83zPHnOSwr8bPhzee8+cAVkKv3S7g94fbWbXqVgAht5Wg1F31cbNNZ8mRsol/RiJiIglEhPh999h/Xr49VezxScxMft+FSqYyzu0aAG33gpt2hR8rXL93Fxd6NSoPKcuJjG5d1Pa1S5jdUlZKAiJiEiBuHgRNm40g8/69bBtW9YjuMAcy9O8+V/B56abzMPVpWhJSrUTfTmFyqV8AHiibXV6hlUiyC/72p9WUxASEZE8FxMDf/zx12nbNti92zzU/e8qVjQHMGecGjTIv6UkpGAcjopn2Lxw7IbBiuFt8PFww8XFVihDECgIiYjIDUhNhYMHs4aeP/4w1+LKSa1aZvdWRvAJCdERXMXJ4u2neGn5HpLS7AT5eXIiJpF65Qv3xEwKQiIiclXJyXDsWPYFRg8fNufyyViT65+qV4fGjc1TkybmbM3lCnbSYCkgianpvLR8L0t2nAKgTc3SvNe7KWX9rT00/looCImISBZRUebyE6tXm2N5Tp7M3qX1dwEBfwWejFPDhuDvX3A1i3UOno1n2PwdHI66jIsNRt5Zm2Hta+LqUjSa+hSEREScXFqaecTW6tXmGlw7dmTfx9//r4VF/77QaI0a5jgfdW85rze+28/hqMsEB3jyQZ9Qbq5e2uqSckVBSETECR07ZoaeNWvgxx/NxUj/LjTUXILirrvM1p0yZRR2JGdv3t+Y11ft56Uu9SldSAdEX42CkIiIE0hLM1dd//Zbs+Xn0KGstwcFmcGnY0dz1ubgYGvqlMJv75lYfj54nmHtawJQNsCL9/uEWlzV9VMQEhEpptLTzfCzaBEsXWoe0p7B1RVatYK77zZPoaE6bF2uzjAMvvg9gtdW7iM13UHNsn50bFD0R78rCImIFCPp6fDLL/DVV2b4iY7+67YyZaBbN3Pl9Tvu0Krrcu3iktMYt2Q33+6OBOCOumVpUa2UxVXlDQUhEZEizG6H8HD4+Wez9Wf9+qzjfYKCoEcP6NUL2rXT+lySe3+cusTw+eFEXEjEzcXGc53qMuiWEGzFZNCYfiVERIoIux1OnTLn8Nm50ww+v/4KcXFZ9ytd+q/wc9ttCj9y/RZsiWD813tIsxtULOHNtL6hhFYpaXVZeUq/HiIihYjdDidOmIOZ/z5x4eHDcPSoOZPzPwUEmLM1t29vBp8mTcwxQCI3qpSvB2l2gw71g3m7ZxMCfdytLinPKQiJiFggIcEMOwcOwP795vmBA+a2lJQr38/d3ZyxuU4dc4mK9u2haVMFH8k7ianp+HiY8aBjg3J8+cTNtAwpVWy6wv5JQUhEJJ+lpMCyZfDbb38Fn4iIK+/v6WmuyfX3CQwzJi+sXFmhR/KHYRh8uv4Yn6w/ytfD21A+0BugyE2QmFsKQiIi+SQiAj76CD75BM6fz357UBDUrQv16pnnGZerVFHYkYJ1MSGVMYt28eOBKAAWbTvFiDtqWVxVwVAQEhHJQ4YBP/0E06bBihXgcJjbK1aEBx6ABg3+Cj1BQdbWKgKw7fgFnlwQTmRsMh5uLrzUpT4PtaxidVkFRkFIRCQPJCfDnDkwZYrZ/ZWhfXsYNsycv0dHb0lh4nAYfPjrEd79/hB2h0FIkC/T+obSoIJzTTClX0sRkRuQmGh2fb31Fpw5Y27z84NHHoGhQ80WIJHCaO6m47y1+iAA3ZpW4L/3NcLP0/ligfO9YhGRPHD5MsycCe+8A1HmsAoqVYKxY2HAAPOQdpHC7MEWVfh652n6tqxCr+aVi+1RYf9GQUhEJBdiY83xP++999faXdWqwbhx0L+/ecSXSGFkdxis2HWabk0q4uJiw9vDlWVD2+Di4pwBKIOCkIjINYiMhA8/NMcAXbpkbqtVC55/Hvr1M+f3ESmsouKTeXrhTjYejiEyNpmht5krxzt7CAIFIRGRKzIM2LjRbAFassRc0BTMQ9xffNFcwkIDoKWw23g4mqe+3En05RS83V0pF+BldUmFin6FRUT+ISEB5s2D6dPhjz/+2t66NYwcCfffDy4ulpUnck3sDoMPfjjE1HWHMQyoE+zP9H6h1Czrb3VphYqCkIgIEB0Nv/wCP/4I8+ebY4EAvL3Nrq9hw8ylLESKgnNxyYxYEM7vxy4A0OemyrzctQHeHpqp858UhETEKcXEmCu3r1sHP/8Mu3dnvb1GDfPw94EDoWTxWmxbnMD5+BTCIy7h6+HK6z0a0a1pRatLKrQUhETEKZw5A+vX/3XavdscA/R3DRuaq7d36QJ33aXuLym6GlYMZHLvJtQvH0D1Mn5Wl1OoKQiJSLFjGHD4cNbgc+RI9v3q1zeDT/v2cOutULZsgZcqkifOXEpizKJdPNepLo0rlQCgS+MK1hZVRCgIiUiRFhNjhp7Dh82ws2ePGXzOns26n81mjvFp2/avU3CwJSWL5KmfDpxj1Fe7uJSYxrilu1n55C1OOzni9VAQEpEi5fJlc1zPmjWwenXOLT0AHh5w001mS0/btuYRX4HOtYSSFHNpdgdvrT7AJ+uPAdCoYiDT+oYqBOWSgpCIFGqGYR7CnhF8NmyAtLSs+1SsCDVrmqdataBVKzMEeXtbU7NIfjt5IZEnF4Sz8+QlAAa0rsa4znXxdNNRYbmlICQihU5MDKxdawaf7783Z3X+u2rV4O67zVP79lrXS5zL0fOX6T59I3HJ6QR4ufFWzybc3bCc1WUVWQpCIlIoJCXBBx/AsmWwdWvWI7q8vc3Ac/fd0LGj2eqj1n9xVtVK+9KsakkuJqYx7cFQKpfysbqkIk1BSEQst3YtDBkCR4/+ta1hw7+Czy23gJdWBRAnFhGTSJC/Bz4ebri42PigTyje7q54uGmOhxulICQilomKglGjzOUswBzr89JLcM89UKmStbWJFBbf/hHJc0v+4O6G5Xj7gSYABHprld+8oiAkIgXOMGDOHBg7Fi5cMLu5nnwSJk4Efy2DJAJAcpqdid/u44vfIgA4Gp1AUqpdy2TkMQUhESlQBw/C4MHmul5gzu3z8cfmUV4iYjoWncCweTvYFxkHwH9uq8Gou2rj7qqusLymICQi+cpuN5e3OH7cHAv05puQmgo+PvDqq+Zq7m76SySS6eudp3l+6W4SUu2U8vVgcq8m3FZH057nF/35EZEb4nCYh7cfPw7Hjpnnfz9FRGSf96dTJ5gxwzwMXkT+EpecxoRv9pGQaqdFSCmm9AmlXKCOFMhPCkIics2Sk81Znb/7Dvbv/yvopKZe/X5ublC1KoSEwOOPwwMP6PB3kZwEeLkzuXdTth2/wFN31MJNXWH5TkFIRK7q7Fn49lv45huzaysxMfs+rq5QpYrZwhMSYp7//VShgrmPiGS3ZPspfD3dMidFbFe7DO1ql7G4KuehICQiWRgG7NwJK1ea4Wfr1qy3V6oEXbpAy5Zm6AkJMYOOxvmI5E5iajrjv97L4u2n8Pdyo0nlQMoHal2YgqY/XSKS6eOPYcIEOH066/abboKuXc1Tkybq1hK5UQfPxjNs/g4OR13GxQaPt61OWX+NBbKCgpCIAOZipkOGmC1CPj5w111m8LnnHiinZYxE8oRhGHy17STjv95LSrqDsv6eTHkwlJurl7a6NKelICQiXL4M/fubIeihh+CTT7SkhUheszsMRn+1k+U7zwBwa+0yTO7VhCA/T4src24KQiLCM8+Y63xVqQLTpikEieQHVxcbJXw8cHWxMbpDbYbcWgMXF/UzW01BSMQJGQacPAlbtphdYjNnmttnz4bAQGtrEylODMMgMdWOr6f5dTuuc13uC61Ik8olrC1MMikIiTgJhwM++ghWrTKPBDt3Luvtw4fDHXdYU5tIcRSXnMa4pbs5H5/C/Mda4ubqgqebq0JQIaMgJOIEEhLg4Ydh2bK/trm5QePG5hFhbdtCnz7W1SdS3Ow+FcvwBTs4EZOIm4uN8JOXuKlaKavLkhwoCIkUc6dOwb33Qng4eHjA+PFw++3mYqfemrJEJE8ZhsFnm47z+qoDpNodVCzhzdS+oTSrUtLq0uQKFIREirGtW80QdPYslCkDy5dD69ZWVyVSPMUmpvHMkl2s2Wv2O3eoH8zbPZsQ6ONucWVyNQpCIsXUV1+Zh8QnJ0PDhuYs0VrkVCT/PP3VTn46EIW7q43nO9djQOtq2DT7aKGnICRSzBiGOTv0K6+Y1++5BxYsAH9/S8sSKfae61SX0xeTePuBxjSuVMLqcuQaaVlbkWJk/364776/QtCoUfD11wpBIvnhUmIqq/dEZl6vHezPd0+1VQgqYtQiJFIM7N4NEyfCokVmi5Cbmzk30GOPWV2ZSPG0/cQFnpwfzrn4FBY+4Unz/x0RpgkSix4FIZEibMcOeO01cxB0hu7d4eWXzaPCRCRvORwGH/16lHe+P4jdYRAS5Iu3h6vVZckNsLxrbMaMGYSEhODl5UVYWBjr16+/6v7z5s2jSZMm+Pj4UL58eQYOHEhMTEwBVStSOPz+O3TpAmFhZgiy2aBXL9i1y5wrSCFIJO/FXE7h0c+28ubqA9gdBvc2qcA3T95Cgwqajr0oszQILVy4kJEjR/LCCy8QHh5O27Zt6dSpExERETnuv2HDBh555BEGDRrE3r17WbRoEVu3buUxtf+LE7hwAebMgTvvhJtvhm+/BRcX6NcP9u6FhQvNCRJFJO/9fjSGzlPW8/PB83i6ufBGj0Z80Kcpfp7qWCnqLP0EJ0+ezKBBgzKDzPvvv8+aNWuYOXMmkyZNyrb/b7/9RrVq1RgxYgQAISEhDB48mLfeeqtA6xYpKFFRZovP4sWwbh2kp5vb3dzMmaLHjYNatSwtUcQp7I+M41xcCjXK+DK9XzPqlguwuiTJI5YFodTUVLZv385zzz2XZXuHDh3YtGlTjvdp3bo1L7zwAqtWraJTp05ERUWxePFi7rnnnis+T0pKCikpKZnX4+Li8uYFiOSTM2dg6VJYsgR+/dVcIyxD48bQs6cZgjQnkEj+Mgwjcx6g/v+bE6hnWKXMBVSleLDs04yOjsZutxMcHJxle3BwMGfPns3xPq1bt2bevHn07t2b5ORk0tPTuffee5k6deoVn2fSpEm8+uqreVq7SF47ccIMPkuWwD//D2je3Aw/998PNWtaU5+Is9l0OJr3fjjE7AE34e/ljs1mo3/ralaXJfnA8sHS/5x18+8J/J/27dvHiBEjGD9+PNu3b2f16tUcO3aMIUOGXPHxx40bR2xsbObp5MmTeVq/yI3YsgVatDBbd0aP/isEtW4N774Lx46Zy2Q8+6xCkEhBsDsMJq89RL9Zv7P1+EWm/XTY6pIkn1nWIhQUFISrq2u21p+oqKhsrUQZJk2aRJs2bRg7diwAjRs3xtfXl7Zt2zJx4kTKly+f7T6enp54enrm/QsQuUHp6dC3Lxw5Yg56vvVWs9XnvvugYkWrqxNxPufiknnqy3B+O3oBgN7NKzPyztoWVyX5zbIg5OHhQVhYGGvXruW+++7L3L527Vq6deuW430SExNxc8tasqurOX+DYRj5V6xIPli0yAxBpUubEyLmkONFpID8eug8Ty/cSUxCKj4errx+XyO6h+o/Emdg6YivUaNG8fDDD9O8eXNatWrFxx9/TERERGZX17hx4zh9+jSff/45AF27duXxxx9n5syZdOzYkcjISEaOHEmLFi2oUKGClS9FJFccDnj9dfPyyJEKQSJWWrrjFKO+2gVAvfIBTO8bSvUyfhZXJQXF0iDUu3dvYmJimDBhApGRkTRs2JBVq1ZRtWpVACIjI7PMKTRgwADi4+OZNm0ao0ePpkSJEtx+++28+eabVr0Ekevy7bewZ4+5BtiwYVZXI+Lc2tUuQ3CAJ3fWC+alLvXxctdM0c7EZjhZn1JcXByBgYHExsYSEKB5IKTgGQa0amXODv3ss/DGG1ZXJOJ89kfGUa/8X98BFxNSKenrYWFF8m/y6/vb8qPGRJyJYcD06WYI8vKCp5+2uiIR55Jmd/D6qv10+mA9y8JPZW5XCHJemhVKpICcOmWuBr9mjXl92DC4wgGSIpIPTl1M5MkF4YRHXALg4NnL1hYkhYKCkEg+MwyYO9ccFB0XB56e8N//mtdFpGB8v/csYxbtIi45HX8vN97u2Zi7G+ooBVEQEslXp0/DE0/AqlXm9ZYtzVBUt66lZYk4jdR0B5O+28+cjccBaFIpkGl9m1G5lI+1hUmhoTFCIvnAMODzz6FhQzMEeXrCm2/Cxo0KQSIFaUfExcwQ9NgtISwa0lohSLJQi5BIHvvtt6zLZdx0k9kKVL++pWWJOKWbq5dmbMc61An25876GpQn2alFSCSPHD8OffqYh8Zv2gQ+PuakiZs2KQSJFJTkNDv//XYfJy8kZm4b1r6mQpBckVqERG7QpUtm4PngA0hNBZsNBgyA117TmmEiBelYdALD5+9g75k4tp24yJIhrXFxyXkRb5EMCkIi1yktDT76CF55BWJizG133AHvvANNm1pZmYjz+XrnaZ5fupuEVDulfD146o5aCkFyTRSERK7Dr7+aR4MdPGher1vXDECdO5stQiJSMJLT7Lz6zV4WbDkJQIuQUkzpE0q5QC+LK5OiQkFIJBfsdrPL67XXzIVTg4Lg1Vfh8cfB3d3q6kScS2RsEgPnbOXA2XhsNhjeviZP3VELN1cNf5VrpyAkco1OnYJ+/czWIDDHAb3/PgQGWlmViPMq6eOBq4uNID8P3u8dyi21gqwuSYogBSGRa/DNN2bwuXAB/Pzgww/NUCQiBSsp1Y6HmwuuLja83F358KEwPN1cKBugrjC5Pmo/FLkKh8OcE+jee80QFBYG4eEKQSJWOHQunnunbeCDH//M3Fa5lI9CkNwQBSGRq3jxRZg82bw8apQ5J1DNmtbWJOJsDMPgq60nuXfaBv6MusxXW09yOSXd6rKkmFDXmMgVfPIJTJpkXp49GwYOtLYeEWeUkJLOC8t2s3znGQDa1grivd5N8fPU15fkDf0kieRg9Wr4z3/My6+8ohAkYoV9Z+IYPn8HR6MTcLHB6A51+E+7GpofSPKUgpDIP+zaBQ88YB4q/8gjMH681RWJOJ+ElHT6fvoblxLTKBfgxZQHQ2kRUsrqsqQYUhAS+ZtTp+Cee+DyZWjf3uwe0wSJIgXP19ON5zvV47s9kbzbqymlfD2sLkmKKQUhkf+JizND0OnT5iKpS5eCh/72ihSYPadjSXcYNK1cAoAHmlfigeaVsOm/EclHOmpMnJ5hmKGncWP44w8IDoZvv4USJayuTMQ5GIbBZ5uO02PGJoZ+sZ1LiakA2Gw2hSDJd2oREqe2dy889RT8+KN5vVIlWL4cqlWzsioR5xGblMazi/9g9d6zADSoGIgNhR8pOApC4pQuXTLXCJs61RwU7ekJY8fCc8+Br6/V1Yk4h50nLzF8/g5OXUzC3dXGuE71GNimmlqBpEApCIlTcThgzhwYNw7Onze3de8O774L1atbWpqI0zAMg1kbjvHm6gOk2Q0ql/Jm2oPNaPK/sUEiBUlBSJxGWpq5Xtj8+eb1OnVgyhTo0MHSskSc0pZjF0izG3RqWI437m9MoLe71SWJk1IQEqeQnAy9epmLp7q5mTNGjxiho8JECpJhGJkDoN/u2YQ79kbSq3lldYWJpRSEpNi7fBm6dYOffgIvL1i82DxMXkQKhsNh8PH6oxw6G8+7vZpgs9kI9HGn901VrC5NREFIireLF6FzZ/jtN/Dzg5UroV07q6sScR4xl1MYvWgXPx80B+Xd16wibWuVsbgqkb8oCEmxde6cOf7njz+gVCn47jto0cLqqkScx5ZjF3hywQ7OxaXg6ebCy10bcEvNIKvLEslCQUiKpdhYuO02OHAAypWDtWuhYUOrqxJxDg6HwYyfDzN57SEcBlQv48v0vs2oVz7A6tJEslEQkmLH4YCHHjJDUKVKsG4d1KxpdVUizmPM4l0s3XEagB6hFXmte0N8PfV1I4WTltiQYmfCBHMskKenOUu0QpBIwXogrDK+Hq683bMxk3s3VQiSQk0/nVKsLFpkzhgN8NFHEBZmbT0izsDuMDh0Lj6z66tVjdJsfO52Svhofgop/NQiJMVCYiI8+aQ5VxDA8OHQv7+1NYk4g6i4ZPp9+hs9Z27i6PnLmdsVgqSoUIuQFHnbt/81JgjMEDR5srU1iTiDXw+d5+mFO4lJSMXHw5Vj0QlUL+NndVkiuaIgJEWW3Q5vvAGvvALp6VC+vLmOWMeOVlcmUryl2x2898MhZvx8BMOAuuX8mda3GTXLKgRJ0aMgJEXS0aPw8MOwaZN5/f77zTFBpUtbW5dIcRcZm8RTC3ay5fgFAPq2rML4LvXxcne1uDKR66MgJEWKYZitPk89ZS6d4e8PU6fCI4+AlisSyX8Ltpxky/EL+Hm68XqPRtzbpILVJYncEAUhKTLOn4cnnjAPiQe45Rb4v/+DatWsrErEuTx5e03Oxycz+NYaVAvytbockRumo8akSFi1Cho1MkOQu7s5NujnnxWCRPLb6UtJvLR8D2l2BwDuri5M6tFYIUiKDbUISaGWkABjxsCHH5rX69eHL76A0FBr6xJxBmv3nWPMol3EJqUR6O3OmI51rC5JJM8pCEmhFR4OffrAoUPm9ZEj4fXXwdvb0rJEir3UdAdvfHeA2RuPAdCkUiC9b6pscVUi+UNBSAodwzAHQI8dC6mpUKECfPYZ3Hmn1ZWJFH8nLyQyfP4Odp2KBWDQLSE8e3ddPNw0kkKKJwUhKVRiYmDgQPjmG/N6t24wa5YOixcpCOv/PM/QeTuIT04n0Nuddx5owl31g60uSyRfKQhJofHrr9C3L5w+DR4e8O67MGyYDosXKSiVSvrgcBg0q1KCqX2bUbGE+qGl+FMQkkJh1izz0HiHA2rXhoULoWlTq6sSKf7iktMI8HIHICTIl4WDW1GnnD/uruoKE+egn3Sx3OHD5vpgDoc5W/T27QpBIgVhxa4z3PLGT2w6Ep25rWHFQIUgcSpqERJLORzw2GOQnAx33GEOilZXmEj+Sk6z8+o3+1iwJQKAeb9F0LpGkMVViVhDQUgs9ckn8Msv4ONjXlYIEslfR85fZti8HRw4G4/NBsNuq8nIO2tZXZaIZRSExDInT5qHyIM5P1BIiLX1iBR3y8JP8cKyPSSm2int68H7fZrStlYZq8sSsZSCkFjCMOA//4H4eGjVyhwjJCL557ejMTy9cBcAraqX5oM+TSkb4GVxVSLWUxASS8yfD99+ax4m/+mn4OpqdUUixVvLkFL0CK1I5VI+jLijFq4u6ocWAQUhscDBgzB0qHn5pZfM9cNEJG8ZhsGKXWdoV7sMJXw8sNlsvNurCTYNxBPJQsdISoGKj4f77oO4OGjbFp591uqKRIqfhJR0Rn+1i6e+3MnYxX9gGAaAQpBIDtQiJAXG4YD+/WH/fnP9sK++And3q6sSKV72R8YxbP4Ojp5PwMUGTSuXwDB0RKbIlSgISYF54w1YtswcF7RkCZQrZ3VFIsWHYRgs2HKSV7/ZS0q6g3IBXkx5MJQWIaWsLk2kUFMQkgKxejW8+KJ5edo0uPlma+sRKU7ik9N4ftkevtl1BoDb6pRhcq+mlPL1sLgykcJPQUjy3ZEj8OCD5iHzTzwBjz9udUUixYvdYbDjxEVcXWw807EOj7etjouOChO5JgpCkq+SkszB0Zcuma1AU6ZYXZFI8fD3AdAlfDyY3q8ZdodBWNWSFlcmUrToqDHJVytWwO7dULYsLF4Mnp5WVyRS9MUmpTF03g4Wbj2Zua1p5RIKQSLXQS1Ckq/27DHPu3WDihWtrUWkONh18hLDF+zg5IUkNvwZTadG5Qn01uGXItdLQUjy1f795nm9etbWIVLUGYbB7I3HeeO7/aTZDSqV9GZa32YKQSI3SEFI8lVGEKpb19o6RIqyS4mpjFn0Bz/sPwfA3Q3K8WbPxgpBInnA8jFCM2bMICQkBC8vL8LCwli/fv1V909JSeGFF16gatWqeHp6UqNGDWbPnl1A1UpupKfDn3+al9UiJHJ9klLtdJ22gR/2n8PD1YUJ3Row8yG1BInkFUtbhBYuXMjIkSOZMWMGbdq04aOPPqJTp07s27ePKlWq5HifXr16ce7cOWbNmkXNmjWJiooiPT29gCuXa3H0KKSlgY8PXOHjFJF/4e3hSo/QSizfeZrpfZvRsGKg1SWJFCs2I+MYTAu0bNmSZs2aMXPmzMxt9erVo3v37kyaNCnb/qtXr6ZPnz4cPXqUUqWub7bUuLg4AgMDiY2NJSAg4Lprl3/39dfQvTuEhsKOHVZXI1J0XEhIJSElncqlfABznqCkNDt+nhrNIM4rv76/LesaS01NZfv27XTo0CHL9g4dOrBp06Yc77NixQqaN2/OW2+9RcWKFalduzZjxowhKSnpis+TkpJCXFxclpMUjAMHzHN1i4lcuy3HLtD5g/UM/r/tJKfZAXB1sSkEieQTy36zoqOjsdvtBAcHZ9keHBzM2bNnc7zP0aNH2bBhA15eXixbtozo6GiGDh3KhQsXrjhOaNKkSbz66qt5Xr9cXWIifP+9eVkDpUX+ncNhMPOXI0xeewi7w8DHw5Xz8SmZrUIikj8sHyxt+8eSyIZhZNuWweFwYLPZmDdvHi1atKBz585MnjyZuXPnXrFVaNy4ccTGxmaeTp48meN+kne2b4ewMPjpJ/P6Pxr9ROQfoi+n0H/OFt5ecxC7w+C+0Ip88+QtCkEiBcCyFqGgoCBcXV2ztf5ERUVlayXKUL58eSpWrEhg4F+DBevVq4dhGJw6dYpatWplu4+npyeems64QKSnw5tvwiuvmJfLl4c5c6BlS6srEym8Nh2J5qkvd3I+PgUvdxcmdGvIA2GVrvgPoYjkLctahDw8PAgLC2Pt2rVZtq9du5bWrVvneJ82bdpw5swZLl++nLnt0KFDuLi4UKlSpXytV67u6FFo185cYT49He6/31xao2NHqysTKbwMw2Dy94c4H59CrbJ+rBh+C72aV1YIEilAlnaNjRo1ik8//ZTZs2ezf/9+nn76aSIiIhgyZAhgdms98sgjmfv37duX0qVLM3DgQPbt28evv/7K2LFjefTRR/H29rbqZTg1w4DZs6FJE9i0Cfz94bPPYNEiKF3a6upECjebzcb7fZrSv1VVvh7ehtrB/laXJOJ0LD0MoXfv3sTExDBhwgQiIyNp2LAhq1atomrVqgBERkYSERGRub+fnx9r167lySefpHnz5pQuXZpevXoxceJEq16CUzt/Hp54ApYvN6+3bQuffw7VqllZlUjhtuHPaHadusSw9jUBqFTSh1e7NbS4KhHnZek8QlbQPEI3Li0NPvzQHAt04QK4u8PEiTB6NLi6Wl2dSOGUbnfw/g9/Mv3nwxgGzHusJW1qBlldlkiRkV/f35qYQq6ZYcCKFfDMM3DokLmtUSOzFahpU0tLEynUzsYmM+LLcLYcuwBA35ZVCKta0uKqRAQUhOQapKWZs0S//z5s3GhuK1sWJkyAQYPATT9FIle07mAUo7/axYWEVPw83Xi9RyPubVLB6rJE5H/0FSZXdPYsfPwxfPQRnDljbvPygqefhueeA/UsilzdBz/8yXs/mM2nDSoEMK1vM0KCfC2uSkT+TkFIsjAMs9Vn+nRYssRsDQKzBejxx2HIENBMBSLXplqQOSHiI62q8nzneni5axCdSGGjICSZ7Hbo2hW+++6vba1awfDh5rxAmpdS5N/FJqUR6O0OQLemFQkJ8qVxpRLWFiUiV2T5EhtSeHz0kRmCPD3NsT87dphzA/XtqxAk8m9S0x28tnIfHd77hejLKZnbFYJECje1CAlgzgn0wgvm5XffhWHDrK1HpCg5eSGR4QvC2XXyEgA/7DtHnxZVrC1KRK6JgpAA8PzzcOmSeRj8/yb2FpFrsHpPJGMX/0F8cjqB3u6880AT7qqf83qJIlL4KAgJW7bArFnm5WnTNCmiyLVISbfz+rf7+WzzCQBCq5Rg6oOhVCqpFeNFihIFIeG118yjxR55BNq0sboakaJh2k+HM0PQ4FurM6ZjHdxdNexSpKhREBK2bTPPhw61tg6RouSJW6uz4XA0T95ek9vrqitMpKjSvy9OLibGnDgRoEEDa2sRKcyS0+zM+/0EGcsz+nu5s/Q/rRWCRIo4tQg5ub17zfNq1cDPz9JSRAqtI+cvM2zeDg6cjSc13cHANiEA2Gw2iysTkRulIOTk9uwxz9UaJJKz5eGneX7ZbhJT7QT5eVCzrP5jEClOFIScXEaLUMOG1tYhUtgkpdp5ZcVeFm47CUCr6qX5oE9TygZ4WVyZiOQlBSEnl9EipCAk8pc/z8UzbP4ODp27jM0GI26vxYg7auHqoq4wkeJGQciJGYa6xkRyEpecxpHzCZTx9+SD3k1pXTPI6pJEJJ8oCDkpwzCX0rhwAVxcoG5dqysSsZZhGJmDn8OqlmJKn1BahJSijL8W2hMpzq778Pno6Gi2bdvG9u3biYmJycuaJJ9dvAjdu8PYseb1YcPA29vSkkQsdeBsHF2nbeDg2fjMbfc0Lq8QJOIEch2E9u7dy6233kpwcDAtW7akRYsWlC1blttvv52DBw/mR42Sh7ZsgdBQWLECPDxgxgz44AOrqxKxhmEYLNgSQbdpG9lzOo7XVu6zuiQRKWC56ho7e/Ys7dq1o0yZMkyePJm6detiGAb79u3jk08+oW3btuzZs4eyZcvmV71ynQwDpk6FMWMgLQ2qV4dFi6BZM6srE7FGfHIazy/bwze7zgBwW50yTO7V1NqiRKTA2YyMaVKvwbPPPssPP/zAxo0b8fLKeghpUlISt9xyCx06dGDSpEl5XmheiYuLIzAwkNjYWAICAqwup0DExsKgQbBkiXm9Rw+YPRsCA62tS8Qqe07HMnz+Do7HJOLqYmNsxzo80bY6LjoqTKTQyq/v71x1ja1du5Znn302WwgC8Pb2ZuzYsaxZsybPipMbl54Ot95qhiB3d7MbbPFihSBxXjtPXqLHjE0cj0mkQqAXXw2+mSHtaigEiTipXHWNHT16lGZX6Utp3rw5R48eveGiJO989x388QeUKAFr1kCLFlZXJGKtRhUDCa1SAn8vN955oAklfDysLklELJSrIBQfH3/V5ih/f38uX758w0VJ3vn4Y/N80CCFIHFe+87EUb2ML17urri62Pi0f3P8PN20VpiI5H4eofj4+By7xsDsv8vFkCPJZ6dOwapV5uXHH7e2FhErGIbBnI3HmfTdfh5sUYUJ3cwp1P293C2uTEQKi1wFIcMwqF279lVv139Yhcfs2eBwQLt2UKeO1dWIFKzYxDTGLt7F9/vOAXA+PoV0uwM31+uePk1EiqFcBaF169blVx2Sx+x2+PRT87Jag8TZ7Ii4yJPzwzl9KQkPVxde7FKPh2+uqn/URCSbXAWhdu3a5VcdksfWrIGTJ6FkSbj/fqurESkYDofBpxuO8tbqg6Q7DKqW9mF632Y0rKjDJEUkZ9e11tjp06dZsmQJhw4dwmazUbt2bXr06EHFihXzuj65DoYB771nXu7fH64wpEuk2Dl/OYVpPx0m3WHQpXF5JvVopPFAInJVuZpQEWDGjBmMGjWK1NRUAgMDMQyDuLg4PDw8mDx5MkOHDs2vWvOEM0yoOGsWPPYYeHrC7t1Qq5bVFYkUnO/3nuX85RT6tqiirjCRYqRQTKj47bffMmLECIYPH87p06e5ePEily5d4vTp0wwdOpSnnnqKVRmHKYkljh+HkSPNyxMnKgRJ8eZwGExfd5h1B6Myt3VoUI5+LTUeSESuTa5ahNq1a0fbtm2ZOHFijre/+OKLrF+/nl9++SXPCsxrxblFyOGAO+6An3+GW24xz11dra5KJH9EX07h6YU7Wf9nNCV93Plp9G2U9NXkiCLFVaFoEQoPD+fhhx++4u0PP/wwO3bsuOGi5PpMnmyGH19fmDtXIUiKr81HYuj8wXrW/xmNl7sL4zrVo4SPxgKJSO7larC0w+HA3f3Kf2zc3d01oaJFfvoJnn3WvDx5MtSoYW09IvnB7jCY9tNhPvjxEA4DapX1Y3q/ZtQO9re6NBEponLVItSgQQO+/vrrK96+fPlyGjRocMNFSe6cOAG9epldYwMGaN4gKZ6S0+w8POt33vvBDEEPhFXi6+FtFIJE5IbkqkVo6NCh/Oc//8HT05MnnngCNzfz7unp6Xz00Ue8+OKLzJgxI18KlZwlJcF990FMDISFwcyZoDGiUhx5ubtSqaQ3Ph6uTOzekB7NKlldkogUA7k+fH7MmDFMnjwZf39/avyv/+XIkSNcvnyZESNG8F7GBDaFVHEaLG0YZgvQ559DUBBs3w5VqlhdlUjeSbc7SEyzE/C/uYCSUu1ExiZRvYyfxZWJSEHLr+/vXAchgN9//50FCxZw6NAhAGrXrk2fPn24+eab86yw/FKcgtDUqTBihDkoeu1aaN/e6opE8s7Z2GRGfBmOl7srcwfchIuLmjpFnFl+fX/nqmssMTGRsWPHsnz5ctLS0rjjjjuYOnUqQUFBeVaQXJtffoGnnzYvv/22QpAULz8fjGLUV7u4kJCKr4crh89f1lggEckXuRos/fLLLzN37lzuueceHnzwQX744Qf+85//5FdtcgWnTpmDo+126Nv3rwkURYq6NLuDN747wIA5W7mQkEqDCgGsHNFWIUhE8k2uWoSWLl3KrFmz6NOnDwD9+vWjTZs22O12XDVpTYG4fNlcRDUqCpo0gU8+0eBoKR7OXEriyQXhbD9xEYBHWlXl+c718HLX3xYRyT+5ahE6efIkbdu2zbzeokUL3NzcOHPmTJ4XJlnZ7TB7NtSuDVu2mKvKL10KPj5WVyZy4wzDYOi8HWw/cRF/Tzdm9GvGhG4NFYJEJN/lKgjZ7XY8PLJOYe/m5kZ6enqeFiVZ/fADNGsGgwZBZCRUrw4rVpjnIsWBzWZjYveG3FStJN+OaEvnRuWtLklEnESuusYMw2DAgAF4enpmbktOTmbIkCH4+vpmblu6dGneVejE9u2DsWMhYx3bEiXgxRdh+HBzZXmRouzkhUR2n47NDD0NKwby1eBWWixVRApUroJQ//79s2176KGH8qwYMUVFwcsvm+N/7HZwc4OhQ2H8eChd2urqRG7c6j1neWbxLpLTHFQu6UOjSoEACkEiUuByFYTmzJmTX3UI5izR778PkyZBfLy5rXt3ePNNc2yQSFGXkm5n0qoDzN10HIDQKiUo6avFUkXEOrkKQpI/HA748ksYNw4iIsxtYWHw7rvQrp21tYnklRMxCQyfH87u07EADL61OmM61sHdNVdDFUVE8pSCkMXCw2HwYNi61bxeqZLZItS3L7jo+0GKiW//iOS5JX8Qn5JOSR933u3VhNvrBltdloiIgpCVzpyBu+4yF0z18zNbhJ5+Gry9ra5MJG+duJBAfEo6N1UryZQHQykfqB9yESkcFIQs4nBA//5mCGraFFavhmD9gyzFiGEYmYOfh9xagyA/T3qEVsRNXWEiUojoL5JF3nvPnB/I2xsWLFAIkuJlefhp7puxicRUc44xFxcbvZpXVggSkUJHf5UsEB5udoOBeZRY3bqWliOSZ5JS7Ty7+A9GLtzJzpOX+L/NJ6wuSUTkqtQ1VsASE82B0GlpcN998PjjVlckkjcOR8UzbF44B8/FY7PBiNtr8VhbTX8uIoWbglABGzMGDhyAChW0YKoUH4u3n+Kl5XtISrNTxt+TD3o3pXXNIKvLEhH5VwpCBSgpCT791Lz82WeaJVqKh49/PcLrqw4AcEvNIN7r3ZQy/loDRkSKBo0RKkA7dphdYuXKwR13WF2NSN64t0lFyvh7MqZDbT57tIVCkIgUKWoRKkC//26e33yzusSk6DIMgx0RlwirWhKAcoFerBtzG36e+nMiIkWPWoQK0G+/mectW1pbh8j1upySzsiFO7l/5iZW74nM3K4QJCJFlf56FaCMIHTzzdbWIXI99p6JZfj8cI5FJ+DqYuNsbLLVJYmI3DAFoQJy5gycPGmuH9a8udXViFw7wzD44vcIXlu5j9R0BxUCvZjaN5SwqqWsLk1E5IYpCBWQDRvM8wYNzHXFRIqCuOQ0xi3Zzbe7zW6wO+uV5e2eTSjp62FxZSIieUNBqIAsWmSed+pkbR0iubHl6AW+3R2Jm4uN5zrVZdAtIZnrh4mIFAeWD5aeMWMGISEheHl5ERYWxvr166/pfhs3bsTNzY2mTZvmb4F5ID4evv3WvNy7t7W1iOTGnfWDGdOhNov/05rH2lZXCBKRYsfSILRw4UJGjhzJCy+8QHh4OG3btqVTp05ERERc9X6xsbE88sgj3FFEJuP55htzMsWaNSE01OpqRK4sNjGNZxbvyjIQevjttWhauYR1RYmI5CNLg9DkyZMZNGgQjz32GPXq1eP999+ncuXKzJw586r3Gzx4MH379qVVq1YFVOmNWbjQPO/TR/MHSeEVHnGRzlPW89W2U4xdvMvqckRECoRlQSg1NZXt27fToUOHLNs7dOjApk2brni/OXPmcOTIEV5++eVrep6UlBTi4uKynArSpUuwerV5Wd1iUhgZhsEnvx7lgQ83c/pSElVL+/BMx7pWlyUiUiAsGywdHR2N3W4nODg4y/bg4GDOnj2b433+/PNPnnvuOdavX4+b27WVPmnSJF599dUbrvd6ff01pKZC/frQsKFlZYjk6GJCKmMW7eLHA1EA3NO4PJN6NCLAy93iykRECoblg6X/OfjSMIwcB2Ta7Xb69u3Lq6++Su3ata/58ceNG0dsbGzm6eTJkzdcc25kdIupNUgKm8NR8XSesp4fD0Th4ebCf+9ryLQHQxWCRMSpWNYiFBQUhKura7bWn6ioqGytRADx8fFs27aN8PBwhg8fDoDD4cAwDNzc3Pj++++5/fbbs93P09MTT09rFoFMTIS1a83LCkJS2FQo4Y2fpxvVg3yZ1rcZ9SsEWF2SiEiBsywIeXh4EBYWxtq1a7nvvvsyt69du5Zu3bpl2z8gIIDdu3dn2TZjxgx++uknFi9eTEhISL7XnFsJCZCebl6uU8faWkQALiWmEuDljouLDR8PN2YPuImSvh5aK0xEnJalf/1GjRrFww8/TPPmzWnVqhUff/wxERERDBkyBDC7tU6fPs3nn3+Oi4sLDf8xyKZs2bJ4eXll2y4i2f12NIYRC8J59JYQhrSrAUDlUj4WVyUiYi1Lg1Dv3r2JiYlhwoQJREZG0rBhQ1atWkXVqlUBiIyM/Nc5hUTk6uwOg+nrDvP+D4dwGLA8/DSDbgnB3dXyIYIiIpazGYZhWF1EQYqLiyMwMJDY2FgCAvJ3TMT581C2rHnZud5lKSyi4pN5euFONh6OAaBnWCUmdGuAj4e6wkSkaMmv72/9NRQppjYejuapL3cSfTkFb3dXJnZvyP1hlawuS0SkUFEQEimGzsen8OjcraSkO6gT7M/0fs2oWdbP6rJERAodBaF8FBtrnmtZDSloZfw9GdepLgfPxfNy1wZ4ubtaXZKISKGkIJSPPvvMPL/1VmvrEOfwy6HzlPb1oGHFQAD6t66m1eJFRP6FDhvJJykp8PHH5uX/zf8oki/S7Q7eXH2A/rO3MGz+DuKT04Dss7aLiEh2ahHKJ0uWQFQUVKgAOcwPKZInzlxKYsSCcLaduAjArbXK6LB4EZFcUBDKJ9OmmedDhoC7lm6SfPDTgXOM+moXlxLT8Pd04437G3NP4/JWlyUiUqQoCOWD7dth82YzAD3+uNXVSHGTbnfw1pqDfPzrUQAaVwpk2oPNqFJas0SLiOSWglA+mD7dPH/gAShXztpapPhxsdk4cDYegIFtqvFcp7p4uumoMBGR66EglMdiYmDBAvOyBklLXnI4DFxcbLi42Jjcqwk7Iy5xZ/1gq8sSESnSNKoyj82eDcnJEBoKN99sdTVSHKSk23llxV7GLd2duS3Iz1MhSEQkD6hFKA/Z7TBjhnl5+HBNpCg37kRMAsPnh7P7tDk758OtqmbOEyQiIjdOQSgP/fe/cPw4lCwJDz5odTVS1H37RyTPLfmD+JR0Svi4M7lXE4UgEZE8piCUR1auhJdfNi+/9x54e1tbjxRdyWl2Jn67jy9+iwCgedWSTHkwlAol9EMlIpLXFITywKFD0K+feXnYMOjf39p6pGh7/PNtrP8zGoCht9Vg1F21cdMkiSIi+UJB6AbFx0P37hAXB7fcApMnW12RFHWP3hLC/sg43u3VlHa1y1hdjohIsaYgdAMMAwYMgP37zaU0Fi0CDw+rq5KiJinVzp9R8TSuVAKA9nXK8usz7fHx0K+niEh+U3v7DVi1CpYuNWeQXrJEkydK7h2Oiqf79I089OnvnLyQmLldIUhEpGAoCN2ADRvM8/79NWeQ5N7i7afoOnUjB8/F4+HmSlR8itUliYg4Hf3beQO2bzfPb7rJ2jqkaElMTeel5XtZsuMUAG1qlua93k0p6+9lcWUiIs5HQeg6GcZfQSgszNpapOg4eDaeYfN3cDjqMi42ePrO2gxtXxNXF82+KSJiBQWh63TiBFy4YI4PatjQ6mqkqPhyawSHoy4THODJB31Cubl6aatLEhFxagpC1ymjNahRI/D0tLYWKTqevbsuAMPb16S0n35wRESspsHS10ndYnIt9p6J5ZnFu7A7DAC83F15uWsDhSARkUJCLULXads287xZM2vrkMLJMAy++D2C11buIzXdQfUyfgxpV8PqskRE5B8UhK5Dejps3mxebt3a2lqk8IlLTmPc0t18+0ckAHfULUvv5pUtrkpERHKiIHQddu6Ey5ehRAkNlJasdp+KZdj8HURcSMTNxcZzneoy6JYQbDYdFSYiUhgpCF2H9evN8zZtwEWjrOR/vt55mrGL/iDV7qBiCW+m9Q0ltEpJq8sSEZGrUBC6DhlBqG1ba+uQwqVuuQBcXKBj3WDeur8JgT7uVpckIiL/QkEolwzjr6U1FIQk+nIKQf87AqxOOX++GX4LNcv6qStMRKSIUMdOLh08COfPg5cXNG9udTViFYfD4JNfj3LLmz+x/cTFzO21gv0VgkREihC1COVSRrdYy5bg4WFtLWKNiwmpjF60i58ORAGw8o8zhFXVWCARkaJIQSiXfv3VPFe3mHPadvwCTy4IJzI2GQ83F8Z3qU+/llWsLktERK6TglAuaaC0c3I4DD789Qjvfn8Iu8MgJMiXaX1DaVAh0OrSRETkBigI5cLJk+Ziqy4u0KqV1dVIQfp+31neWn0QgG5NK/Df+xrh56lfHxGRok5/yXMhozUoNBT8/a2tRQpWxwbl6Na0Aq2ql6b3TZU1IFpEpJhQEMqFjIVW1RpU/NkdBp9vPk7PsEr4e7ljs9n4oE+o1WWJiEgeUxDKhQMHzPMGDaytQ/JXVHwyTy/cycbDMeyIuMSUPk3VAiQiUkwpCOXC/v3meb161tYh+Wfj4Wie+nIn0ZdT8HZ3pV3tMgpBIiLFmILQNUpKguPHzct161paiuQDu8Pggx//ZOpPf2IYUCfYn2l9Q6kVrMFgIiLFmYLQNTp0yFxeo2RJKFvW6mokL0XFJ/Pk/HB+P3YBgD43Veblrg3w9nC1uDIREclvCkLX6O/dYuopKV5cbDaORSfg6+HK6z0a0a1pRatLEhGRAqIgdI00Pqh4cTgMXFzMRBvk58nMh8Io6eNO9TJ+FlcmIiIFSYuuXqOMI8Y0PqjoO3MpiV4fbebrnaczt4VVLakQJCLihNQidI3++MM8V4tQ0fbj/nOMXrSLS4lpnLqYxN0Ny+HpprFAIiLOSkHoGvzxh9ki5O4ON99sdTVyPVLTHby95gCfrD8GQKOKgUzrG6oQJCLi5BSErsHcueZ5165QurSlpch1OHkhkScXhLPz5CUABrSuxrjOdRWCREREQejfpKXBF1+YlwcOtLYWyb2LCal0nbaBS4lpBHi58VbPJtzdsJzVZYmISCGhIPQvVq2C8+chOBjuvtvqaiS3Svp60Lt5ZX47doFpD4ZSuZSP1SWJiEghoiD0LzK6xR5+GNz0bhUJETGJuLraqFjCG4AxHetgGODhpoMkRUQkK30zXEVUFKxcaV4eMMDSUuQardodyT1T1jN8/g7S7A4A3F1dFIJERCRHauO4ivnzIT0dbrpJK84XdslpdiZ+u48vfosAzNmi45PTKeXrYXFlIiJSmCkIXYFhwJw55mW1BhVux6ITGDZvB/si4wD4z201GHVXbdxd1QokIiJXpyB0BTt3mvMHeXhAnz5WVyNX8vXO0zy/dDcJqXZK+XowuVcTbqujVXFFROTaKAhdQUZrUPfuUKqUpaXIFaTbHXz0y1ESUu20CCnFlD6hlAv0srosEREpQhSEcpCUBPPmmZfVLVZ4ubm6ML1fM77eeZrh7Wvipq4wERHJJX1z5OD//g8uXICqVeGuu6yuRv5uyfZTzPz5SOb1kCBfRt5ZWyFIRESui1qE/sHhgPfeMy8/9ZTmDiosElPTGf/1XhZvP4XNBq1rlKZJ5RJWlyUiIkWcvub/4bvvzAVWAwJg0CCrqxGAg2fjGTZ/B4ejLuNig5F31qZhxUCryxIRkWJAQegf3n3XPH/8cTMMiXUMw+CrbSd5ecVektMclPX35IM+obSqoZVvRUQkbygI/U14OKxbB66uMGKE1dXI88t2s2DLSQBurV2Gyb2aEOTnaXFVIiJSnGiE6d9MnmyeP/AAVKlibS0CTSqVwNXFxjN312HugJsUgkREJM+pReh/Tp+GL780L48ebW0tzsowDKIvp1LG3ww8vW+qTPNqpahZ1s/iykREpLiyvEVoxowZhISE4OXlRVhYGOvXr7/ivkuXLuWuu+6iTJkyBAQE0KpVK9asWZMndUydaq4r1rYtNG+eJw8puRCfnMbwBeF0n76R2MQ0AGw2m0KQiIjkK0uD0MKFCxk5ciQvvPAC4eHhtG3blk6dOhEREZHj/r/++it33XUXq1atYvv27bRv356uXbsSHh5+Q3UkJMBHH5mX1RpU8HafiqXL1A18+0ck5+KS2XL8gtUliYiIk7AZhmFY9eQtW7akWbNmzJw5M3NbvXr16N69O5MmTbqmx2jQoAG9e/dm/Pjx17R/XFwcgYGBxMbGEvC/w8Lmz4d+/aBaNTh82BwsLfnPMAw+23Sc11cdINXuoGIJb6b2DaVZlZJWlyYiIoVMTt/fecGyMUKpqals376d5557Lsv2Dh06sGnTpmt6DIfDQXx8PKWushhYSkoKKSkpmdfj4uKy7ZOxnMbDDysEFZTYxDSeWbKLNXvPAdChfjBv92xCoI+7xZWJiIgzsaxrLDo6GrvdTnBwcJbtwcHBnD179poe49133yUhIYFevXpdcZ9JkyYRGBiYeapcuXKW26OiIGOYUb9+uXsNcv3eWnOANXvP4e5q4+Wu9fno4TCFIBERKXCWD5a22WxZrhuGkW1bThYsWMArr7zCwoULKVu27BX3GzduHLGxsZmnkydPZrn9q6/AbjcHSNepc32vQXJvbMc6tKpemiX/ac3ANiHX9JmLiIjkNcu6xoKCgnB1dc3W+hMVFZWtleifFi5cyKBBg1i0aBF33nnnVff19PTE0/PK88988YV5/tBD11a3XJ9Liaks2XGaR9tUw2azUcLHgwVP3Gx1WSIi4uQsaxHy8PAgLCyMtWvXZtm+du1aWrdufcX7LViwgAEDBjB//nzuueeeG6rhzz/h99/BxQV6976hh5Kr2H7iAp0/WM9rK/excOvJf7+DiIhIAbF0QsVRo0bx8MMP07x5c1q1asXHH39MREQEQ4YMAcxurdOnT/P5558DZgh65JFH+OCDD7j55pszW5O8vb0JDMz9Ipzz55vnd90F5crlzWuSvzgcBh/9epR3vj+I3WEQEuRLo0paLFVERAoPS4NQ7969iYmJYcKECURGRtKwYUNWrVpF1apVAYiMjMwyp9BHH31Eeno6w4YNY9iwYZnb+/fvz9y5c3P13IahbrH8FHM5hdGLdvHzwfMA3NukAq/3aISfpyYzFxGRwsPSeYSskDEPwY8/xnLHHQH4+MC5c+CnCYzzzNbjFxg+fwfn4lLwdHPh1Xsb0PumyhoQLSIi163YzSNkta++Ms+7d1cIymtpdgdR8SnUKOPL9H7NqFsu735gRURE8pLTBqHFi81zzR2UN+wOA1cXs8WndY0gPnwojFtqBuGrrjARESnELJ9HyCoxMRAUZA6Ulhuz8XA0d07+hWPRCZnbOjYopxAkIiKFntMGIYDGjcFdkxlfN7vDYPLaQzw063eORSfw3tpDVpckIiKSK079L3vFilZXUHSdi0vmqS/D+e2ouVJ87+aVeeXeBhZXJSIikjsKQpJrvxw6z6iFO4lJSMXHw5XX72tE91C9mSIiUvQ4dRCqUMHqCoqedQejGDhnKwD1ygcwvW8o1cvosDsRESmanDoIqUUo926pGURolRLULx/AS13q4+XuanVJIiIi182pg5BahK7Nb0djCKtaEndXF9xdXVjw+M0KQCIiUiw49VFjahG6ujS7g0mr9tPn49945/uDmdsVgkREpLhw6hYhLbR6ZacuJvLkgnDCIy4BkJruwDAMLZMhIiLFitMGoTJlNIfQlazZe5axi3YRl5yOv5cbb/dszN0Ny1tdloiISJ5z2iBUXt/r2aSmO5j03X7mbDwOQJPKJZj2YCiVS/lYW5iIiEg+URCSTJGxSSzcehKAx24J4Zm76+Lh5tTDyEREpJhz2iCkI8ayq1ral7d7NsHTzYU76wdbXY6IiEi+c9ogpIHSkJxmZ9Kq/dzdsDytapQG4J7GaioTERHn4bT9Hn5OPhnysegE7p+5ic82n2DkwnCS0+xWlyQiIlLgnLZFyJmt2HWGcUv+ICHVTilfD964v7HmBhIREaekIOREktPsvPrNPhZsiQCgRbVSTHkwlHKBXhZXJiIiYg0FIScRm5RG7482c+BsPDYbDG9fk6fuqIWbq9P2joqIiCgIOYsALzdqBfsTfTmF93o3pW2tMlaXJCIiYjkFoWIsMTWddIdBgJc7NpuN1+9rSFKqnbIB6goTEREBJz5qrLg7dC6ebtM2MuarXRiGAYC/l7tCkIiIyN+oRaiYMQyDRdtOMX7FHpLTHMQmpREZm0yFEt5WlyYiIlLoKAgVIwkp6bywbDfLd54BoG2tIN7r3ZQgP0+LKxMRESmcFISKiX1n4hg+fwdHoxNwdbEx6q7a/KddDVxcbFaXJiIiUmgpCBUDdoeRGYLKBXgxtW8oN1UrZXVZIiIihZ4GSxcDri423n6gMXfVD2bVU20VgkRERK6RWoSKqD2nYzkRk5i5SGpY1VJ88ogCkIiISG4oCBUxhmHw+eYT/Pfb/bi4QK1gP2oH+1tdloiISJGkIFSExCal8eziP1i99ywAd9YOpqy/jggTERG5XgpCRcTOk5cYPn8Hpy4m4e5qY1ynegxsUw2bTUeFiYiIXC8FoSJg9oZjTPpuP2l2g8qlvJn2YDOaVC5hdVkiIiJFnoJQEXApKY00u0GnhuV44/7GBHq7W12SiIhIsaAgVEil2x24uZqzGzx1Ry3qlvOnU8Ny6goTkWLLMAzS09Ox2+1WlyIWcXd3x9XVtUCfU0GokHE4DD5ef5TVe86ycPDNeLq54upio3Oj8laXJiKSb1JTU4mMjCQxMdHqUsRCNpuNSpUq4efnV2DPqSBUiMRcTmH0ol38fPA8ACt2nuGB5pUtrkpEJH85HA6OHTuGq6srFSpUwMPDQ63fTsgwDM6fP8+pU6eoVatWgbUMKQgVEr8fjWHEl+Gci0vB082FV+5tQM+wSlaXJSKS71JTU3E4HFSuXBkfHx+ryxELlSlThuPHj5OWlqYg5CwcDoMZPx9m8tpDOAyoXsaX6X2bUa98gNWliYgUKBcXrfrk7KxoCVQQstik7/bzyfpjAPQIrchr3Rvi66mPRUREpCDoG9dij7SqxopdZxjdoQ4PhFVSv7iIiEgBUjtkAbM7DDb8GZ15vXIpH34Z255ezSsrBImIFFGbNm3C1dWVu+++O9ttP//8MzabjUuXLmW7rWnTprzyyitZtoWHh/PAAw8QHByMl5cXtWvX5vHHH+fQoUP5VL1pxowZhISE4OXlRVhYGOvXr//X+8ybN48mTZrg4+ND+fLlGThwIDExMZm37927l/vvv59q1cyVEN5///18fAXXR0GoAEXFJfPQp7/z0KzfWXcwKnO7l3vBzpkgIiJ5a/bs2Tz55JNs2LCBiIiI636clStXcvPNN5OSksK8efPYv38///d//0dgYCAvvfRSHlac1cKFCxk5ciQvvPAC4eHhtG3blk6dOl31tWzYsIFHHnmEQYMGsXfvXhYtWsTWrVt57LHHMvdJTEykevXqvPHGG5QrVy7f6r8R6horIOv/PM/TC3cSfTkVHw9XElLSrS5JRETyQEJCAl999RVbt27l7NmzzJ07l/Hjx+f6cRITExk4cCCdO3dm2bJlmdtDQkJo2bJlji1KeWXy5MkMGjQoM8S8//77rFmzhpkzZzJp0qQc7/Pbb79RrVo1RowYkVnn4MGDeeuttzL3uemmm7jpppsAeO655/Kt/huhFqF8lm538M6agzwyewvRl1OpW86fFcNvoUvjClaXJiJSaBkGJCRYczKM3NW6cOFC6tSpQ506dXjooYeYM2cORm4fBFizZg3R0dE888wzOd5eokSJK953yJAh+Pn5XfV0pdad1NRUtm/fTocOHbJs79ChA5s2bbric7Zu3ZpTp06xatUqDMPg3LlzLF68mHvuueffX2whohahfBQZm8RTC3ay5fgFAPq2rML4LvXVFSYi8i8SE6EAJxfO4vJl8PW99v1nzZrFQw89BMDdd9/N5cuX+fHHH7nzzjtz9bx//vknAHXr1s3V/QAmTJjAmDFjrrpPhQo5/wMeHR2N3W4nODg4y/bg4GDOnj17xcdr3bo18+bNo3fv3iQnJ5Oens69997L1KlTc12/lRSE8tGWYxfYcvwCfp5uTOrRiK5N1AokIlKcHDx4kC1btrB06VIA3Nzc6N27N7Nnz851ELqeVqQMZcuWpWzZstd9f8g+h49hGFc9iGffvn2MGDGC8ePH07FjRyIjIxk7dixDhgxh1qxZN1RLQVIQykfdmlbk1MUk7mlUnmpBufj3QkTEyfn4mC0zVj33tZo1axbp6elUrFgxc5thGLi7u3Px4kVKlixJQIA5QW5sbGy27q1Lly4RGBgIQO3atQE4cOAArVq1ylXNQ4YM4YsvvrjqPvv27aNKlSrZtgcFBeHq6pqt9ScqKipbK9HfTZo0iTZt2jB27FgAGjdujK+vL23btmXixImUL1801shUEMpDpy8l8do3+/jvfQ0p7ecJwLD2NS2uSkSk6LHZctc9ZYX09HQ+//xz3n333Wzja+6//37mzZvH8OHDqVWrFi4uLmzdupWqVatm7hMZGcnp06epU6cOYI7JCQoK4q233soyWDrDpUuXrjhO6Ea6xjw8PAgLC2Pt2rXcd999mdvXrl1Lt27drvh4iYmJuLlljREZy2LcSOtWQVMQyiNr951jzKJdxCal4epqY3rfZlaXJCIi+WjlypVcvHiRQYMGZbbqZOjZsyezZs1i+PDh+Pv7M3jwYEaPHo2bmxtNmjThzJkzvPDCC9SrVy8zRPn6+vLpp5/ywAMPcO+99zJixAhq1qxJdHQ0X331FREREXz55Zc51nKjXWOjRo3i4Ycfpnnz5rRq1YqPP/6YiIgIhgwZkrnPuHHjOH36NJ9//jkAXbt25fHHH2fmzJmZXWMjR46kRYsWmaErNTWVffv2ZV4+ffo0O3fuxM/Pj5o1C0lDgeFkYmNjDcD4739j8+TxUtLsxqsr9hpVn11pVH12pXHv1PVGRExCnjy2iIgzSEpKMvbt22ckJSVZXUqudOnSxejcuXOOt23fvt0AjO3btxuGYRjJycnGhAkTjHr16hne3t5G1apVjQEDBhiRkZHZ7rt161ajR48eRpkyZQxPT0+jZs2axhNPPGH8+eef+fp6pk+fblStWtXw8PAwmjVrZvzyyy9Zbu/fv7/Rrl27LNumTJli1K9f3/D29jbKly9v9OvXzzh16lTm7ceOHTOAbKd/Pk6Gq/0sZHx/x8bmzfd3BpthFKH2qzwQFxdHYGAg//1vLM8/f2MLm568kMjw+TvYdSoWgEG3hPDs3XXxcNOsBCIi1yo5OZljx45lzmoszutqPwsZ39+xsbGZ467ygrrGrtP2ExcZMGcL8cnpBHq7884DTbir/pUHlYmIiEjhoyB0nWoH+1HK14NaZf2Y8mAolUrm4jADERERKRQUhHLhbGwywQGe2Gw2/L3cmfdYS4IDvHB3VVeYiIhIUaRv8Gv0za4z3Dn5Fz7ffCJzW6WSPgpBIiIiRZi+xf9FcpqdcUt38+SCcC6npLN237kiNT+CiIiIXJm6xq7iyPnLDJu3gwNn47HZYNhtNRl5Z62rTjkuIiLXR/9kihU/AwpCV7As/BQvLNtDYqqdID8P3uvdlLa1ylhdlohIsePu7g6YMxV7e3tbXI1YKTU1FfhrhuqCoCCUg2PRCYxZ9Ad2h0Gr6qX5oE9TygZobgsRkfzg6upKiRIliIqKAsDHx0ct707I4XBw/vx5fHx8si3dkZ8UhHIQEuTLMx3rkJRm58nba+Hqol9IEZH8VK5cOYDMMCTOycXFhSpVqhRoEFYQwuyTXLz9FE0ql6B2sD8Ag9vVsLgqERHnYbPZKF++PGXLliUtLc3qcsQiHh4euLgU7HFclgehGTNm8PbbbxMZGUmDBg14//33adu27RX3/+WXXxg1ahR79+6lQoUKPPPMM1kWhcuthJR0Xlq+h6Xhp6lV1o8Vw2/B26Pg+iZFROQvrq6uBTo+RMTSw+cXLlzIyJEjeeGFFwgPD6dt27Z06tSJiIiIHPc/duwYnTt3pm3btoSHh/P8888zYsQIlixZcl3Pvz8yjq7TNrA0/DQuNugeWhFPrRMmIiLiNCxddLVly5Y0a9aMmTNnZm6rV68e3bt3Z9KkSdn2f/bZZ1mxYgX79+/P3DZkyBB27drF5s2br+k5MxZt6/fiHrYYEaSmOygX4MWUB0NpEVLqxl+UiIiI5Ln8WnTVsuaP1NRUtm/fTocOHbJs79ChA5s2bcrxPps3b862f8eOHdm2bVuu+5R/vbyP1HQHt9Upw6qn2ioEiYiIOCHLxghFR0djt9sJDs66YntwcDBnz57N8T5nz57Ncf/09HSio6MpX758tvukpKSQkpKSeT02NhYAIyWJkXfVYkDrEFzsycTFJd/oSxIREZF8EhcXB+T9pIuWD5b+5yFyhmFc9bC5nPbPaXuGSZMm8eqrr2bbfmpmf56eCU/ntmARERGxTExMDIGBgXn2eJYFoaCgIFxdXbO1/kRFRWVr9clQrly5HPd3c3OjdOnSOd5n3LhxjBo1KvP6pUuXqFq1KhEREXn6Rsr1iYuLo3Llypw8eTJP+3wl9/RZFB76LAoPfRaFR2xsLFWqVKFUqbwdymJZEPLw8CAsLIy1a9dy3333ZW5fu3Yt3bp1y/E+rVq14ptvvsmy7fvvv6d58+aZU7T/k6enJ56entm2BwYG6oe6EAkICNDnUUjosyg89FkUHvosCo+8nmfI0mPFR40axaeffsrs2bPZv38/Tz/9NBEREZnzAo0bN45HHnkkc/8hQ4Zw4sQJRo0axf79+5k9ezazZs1izJgxVr0EERERKcIsHSPUu3dvYmJimDBhApGRkTRs2JBVq1ZRtWpVACIjI7PMKRQSEsKqVat4+umnmT59OhUqVGDKlCncf//9Vr0EERERKcIsHyw9dOhQhg4dmuNtc+fOzbatXbt27Nix47qfz9PTk5dffjnH7jIpePo8Cg99FoWHPovCQ59F4ZFfn4WlEyqKiIiIWEnrSYiIiIjTUhASERERp6UgJCIiIk5LQUhEREScVrEMQjNmzCAkJAQvLy/CwsJYv379Vff/5ZdfCAsLw8vLi+rVq/Phhx8WUKXFX24+i6VLl3LXXXdRpkwZAgICaNWqFWvWrCnAaou/3P5uZNi4cSNubm40bdo0fwt0Irn9LFJSUnjhhReoWrUqnp6e1KhRg9mzZxdQtcVbbj+LefPm0aRJE3x8fChfvjwDBw4kJiamgKotvn799Ve6du1KhQoVsNlsLF++/F/vkyff30Yx8+WXXxru7u7GJ598Yuzbt8946qmnDF9fX+PEiRM57n/06FHDx8fHeOqpp4x9+/YZn3zyieHu7m4sXry4gCsvfnL7WTz11FPGm2++aWzZssU4dOiQMW7cOMPd3d3YsWNHAVdePOX288hw6dIlo3r16kaHDh2MJk2aFEyxxdz1fBb33nuv0bJlS2Pt2rXGsWPHjN9//93YuHFjAVZdPOX2s1i/fr3h4uJifPDBB8bRo0eN9evXGw0aNDC6d+9ewJUXP6tWrTJeeOEFY8mSJQZgLFu27Kr759X3d7ELQi1atDCGDBmSZVvdunWN5557Lsf9n3nmGaNu3bpZtg0ePNi4+eab861GZ5HbzyIn9evXN1599dW8Ls0pXe/n0bt3b+PFF180Xn75ZQWhPJLbz+K7774zAgMDjZiYmIIoz6nk9rN4++23jerVq2fZNmXKFKNSpUr5VqMzupYglFff38Wqayw1NZXt27fToUOHLNs7dOjApk2bcrzP5s2bs+3fsWNHtm3bRlpaWr7VWtxdz2fxTw6Hg/j4+DxfYM8ZXe/nMWfOHI4cOcLLL7+c3yU6jev5LFasWEHz5s156623qFixIrVr12bMmDEkJSUVRMnF1vV8Fq1bt+bUqVOsWrUKwzA4d+4cixcv5p577imIkuVv8ur72/KZpfNSdHQ0drs92+r1wcHB2Vatz3D27Nkc909PTyc6Opry5cvnW73F2fV8Fv/07rvvkpCQQK9evfKjRKdyPZ/Hn3/+yXPPPcf69etxcytWfyosdT2fxdGjR9mwYQNeXl4sW7aM6Ohohg4dyoULFzRO6AZcz2fRunVr5s2bR+/evUlOTiY9PZ17772XqVOnFkTJ8jd59f1drFqEMthstizXDcPItu3f9s9pu+Rebj+LDAsWLOCVV15h4cKFlC1bNr/KczrX+nnY7Xb69u3Lq6++Su3atQuqPKeSm98Nh8OBzWZj3rx5tGjRgs6dOzN58mTmzp2rVqE8kJvPYt++fYwYMYLx48ezfft2Vq9ezbFjxzIXC5eClRff38Xq37ygoCBcXV2zJfmoqKhsqTFDuXLlctzfzc2N0qVL51utxd31fBYZFi5cyKBBg1i0aBF33nlnfpbpNHL7ecTHx7Nt2zbCw8MZPnw4YH4ZG4aBm5sb33//PbfffnuB1F7cXM/vRvny5alYsSKBgYGZ2+rVq4dhGJw6dYpatWrla83F1fV8FpMmTaJNmzaMHTsWgMaNG+Pr60vbtm2ZOHGiehEKUF59fxerFiEPDw/CwsJYu3Ztlu1r166ldevWOd6nVatW2fb//vvvad68Oe7u7vlWa3F3PZ8FmC1BAwYMYP78+epzz0O5/TwCAgLYvXs3O3fuzDwNGTKEOnXqsHPnTlq2bFlQpRc71/O70aZNG86cOcPly5cztx06dAgXFxcqVaqUr/UWZ9fzWSQmJuLikvWr09XVFfirNUIKRp59f+dqaHURkHEo5KxZs4x9+/YZI0eONHx9fY3jx48bhmEYzz33nPHwww9n7p9x+N3TTz9t7Nu3z5g1a5YOn88juf0s5s+fb7i5uRnTp083IiMjM0+XLl2y6iUUK7n9PP5JR43lndx+FvHx8UalSpWMnj17Gnv37jV++eUXo1atWsZjjz1m1UsoNnL7WcyZM8dwc3MzZsyYYRw5csTYsGGD0bx5c6NFixZWvYRiIz4+3ggPDzfCw8MNwJg8ebIRHh6eOZVBfn1/F7sgZBiGMX36dKNq1aqGh4eH0axZM+OXX37JvK1///5Gu3btsuz/888/G6GhoYaHh4dRrVo1Y+bMmQVccfGVm8+iXbt2BpDt1L9//4IvvJjK7e/G3ykI5a3cfhb79+837rzzTsPb29uoVKmSMWrUKCMxMbGAqy6ecvtZTJkyxahfv77h7e1tlC9f3ujXr59x6tSpAq66+Fm3bt1VvwPy6/vbZhhqyxMRERHnVKzGCImIiIjkhoKQiIiIOC0FIREREXFaCkIiIiLitBSERERExGkpCImIiIjTUhASERERp6UgJCIiIk5LQUhECo0BAwZgs9mw2Wy4u7tTvXp1xowZQ0JCQuY+n332GS1atMDX1xd/f39uvfVWVq5cmeVxfv7558zH+fvpxRdfzHa7i4sLgYGBhIaG8swzzxAZGVmgr1lErKUgJCKFyt13301kZCRHjx5l4sSJzJgxgzFjxgAwZswYBg8eTK9evdi1axdbtmyhbdu2dOvWjWnTpmV7rIMHDxIZGZl5eu6557LdfubMGbZu3cqzzz7LDz/8QMOGDdm9e3eBvFYRsZ6W2BCRQmPAgAFcunSJ5cuXZ257/PHHWblyJcuWLaNVq1ZMmTKFJ598Msv9Ro8ezdSpUzly5AiVK1fm559/pn379ly8eJESJUpke54r3Z6UlERoaChBQUFs2LAhn16liBQmahESkULN29ubtLQ0FixYgJ+fH4MHD862z+jRo0lLS2PJkiU3/FxDhgxh48aNREVF3dBjiUjRoCAkIoXWli1bmD9/PnfccQeHDh2iRo0aeHh4ZNuvQoUKBAYGcujQoSzbK1WqhJ+fX+YpJibmX5+zbt26ABw/fjxPXoOIFG5uVhcgIvJ3K1euxM/Pj/T0dNLS0ujWrRtTp06lf//+V72fYRjYbLYs29avX4+/v3/m9ZIlS/7r82eMFvjnY4lI8aQgJCKFSvv27Zk5cybu7u5UqFABd3d3AGrXrs2GDRtITU3N1ip05swZ4uLiqFWrVpbtISEhOY4Rupr9+/cDUK1atet+DSJSdKhrTEQKFV9fX2rWrEnVqlUzQxBAnz59uHz5Mh999FG2+7zzzju4u7tz//3339BzJyUl8fHHH3PrrbdSpkyZG3osESka1CIkIkVCq1ateOqppxg7diypqal0796dtLQ0vvjiCz744APef/99KleunKvHjIqKIjk5mfj4eLZv385bb71FdHQ0S5cuzadXISKFjYKQiBQZ77//Po0bN2bmzJm89NJL2Gw2mjVrxvLly+natWuuH69OnTrYbDb8/PyoXr06HTp0YNSoUZQrVy4fqheRwkjzCImIiIjT0hghERERcVoKQiIiIuK0FIRERETEaSkIiYiIiNNSEBIRERGnpSAkIiIiTktBSERERJyWgpCIiIg4LQUhERERcVoKQiIiIuK0FIRERETEaSkIiYiIiNP6fzK55zCHzq83AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Receiver Operating Characteristic')\n",
    "plt.plot(roc.POFD, roc.POD, 'b', label = 'AUC = %0.2f' % roc.AUC.item())\n",
    "plt.legend(loc = 'lower right')\n",
    "plt.plot([0, 1], [0, 1],'--')\n",
    "plt.xlim([0, 1])\n",
    "plt.ylim([0, 1])\n",
    "plt.ylabel('POD')\n",
    "plt.xlabel('POFD')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- A perfect ROC curve would go from the lower left corner, up to the top left corner, and across to the top right corner.\n",
    "- If the curve follows the dotted line, it means the forecast has no discrimination ability. This synthetic forecast clearly does have discrimination ability.\n",
    "- The AUC is the area under the curve. 1 is the maximum value that can be achieved. If we picked a random forecast value from our dataset where the event occurred, and a random forecast value when the event did not occur, the AUC tells us the probability that the former forecast value will be greater than the latter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cautionary notes\n",
    "- ROC or AUC is not a suitable overall performance measure for a probabilistic classifier as it is not a proper scoring rule and is ignorant of calibration (Hand 2009; Hand and Anagnostopoulos 2013, 2023). It is however, a useful tool for understanding potential predictive performance subject to recalibration.\n",
    "- Non-concave ROC curves like the synthetic example above have several problems (Pesce et al. 2010; Geniting and Vogel 2022). To get around these problems, you can apply isotonic regression to the forecast data before you calculate the ROC curves (Fawcett and Niculescu-Mizil 2007).\n",
    "- Results may be misleading if two ROC curves cross (Hand 2009)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References\n",
    "Fawcett, T. and Niculescu-Mizil, A., 2007. PAV and the ROC convex hull. Machine Learning, 68, pp.97-106.\n",
    "\n",
    "Gneiting, T. and Vogel, P., 2022. Receiver operating characteristic (ROC) curves: equivalences, beta model, and minimum distance estimation. Machine learning, 111(6), pp.2147-2159.\n",
    "\n",
    "Hand, D.J., 2009. Measuring classifier performance: a coherent alternative to the area under the ROC curve. Machine learning, 77(1), pp.103-123.\n",
    "\n",
    "Hand, D.J. and Anagnostopoulos, C., 2013. When is the area under the receiver operating characteristic curve an appropriate measure of classifier performance?. Pattern Recognition Letters, 34(5), pp.492-495.\n",
    "\n",
    "Hand, D.J. and Anagnostopoulos, C., 2023. Notes on the H-measure of classifier performance. Advances in Data Analysis and Classification, 17(1), pp.109-124.\n",
    "\n",
    "Pesce, L.L., Metz, C.E. and Berbaum, K.S., 2010. On the convexity of ROC curves estimated from radiological test results. Academic radiology, 17(8), pp.960-968."
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