{
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    "> **This is a saved, working copy.** Sliders here are frozen at their\n",
    "> starting value — there's no marimo runtime in plain Jupyter to drive them.\n",
    "> For the live, drag-the-sliders version of this lab (answers), see\n",
    "> [Week 1 lab (answers) — interactive](https://math4120.pages.dev/wasm/week01_lab_answers.html).\n"
   ]
  },
  {
   "cell_type": "code",
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   "id": "ipython-import",
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   "source": [
    "from IPython.display import Markdown, HTML\n"
   ]
  },
  {
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   "id": "Hbol",
   "metadata": {
    "marimo": {
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    "# Week 1 lab: your first models — Answers\n",
    "\n",
    "**MATH4120 — Mathematical Modelling and Programming** Lancaster University, 2026–27\n",
    "\n",
    "---\n",
    "\n",
    "**This is the answers version.** Every blank below contains the completed solution, for instructors and for checking your own work.\n",
    "\n",
    "---\n",
    "\n",
    "New to Marimo, or not sure how it relates to Jupyter (which you'll use to save and submit your work)? See the [Getting Started guide](https://math4120.pages.dev/getting-started/marimo.html) first — it's a two-minute read and explains how the two fit together.\n",
    "\n",
    "This notebook has two kinds of cell:\n",
    "\n",
    "- **Text cells** (like this one) contain explanations and tasks written in Markdown. Double-click any text cell to edit it; press **Ctrl+Enter** to render.\n",
    "- **Code cells** (grey background) contain Python.  Press **Ctrl+Enter** (or **Shift+Enter**) to run a cell and see its output immediately below.\n",
    "\n",
    "When a code cell has a placeholder value (`0.0` or `np.zeros_like(...)`), replace it with the correct expression and run the cell.  Everything that depends on your result will update automatically.\n",
    "\n",
    "Errors are normal — read the message, fix the line, run again.  Ask a demonstrator if you are stuck for more than a few minutes."
   ]
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "vblA",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
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    }
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   "source": [
    "## Exercise 0 — writing in Markdown\n",
    "\n",
    "Text cells use **Markdown**: a lightweight way to write formatted text and maths. The maths notation is **LaTeX** — the same as in the printed lecture notes.\n",
    "\n",
    "| What you type | What you see |\n",
    "|---|---|\n",
    "| `**bold**` | **bold** |\n",
    "| `*italic*` | *italic* |\n",
    "| `## Heading` | a section heading |\n",
    "| `$N_{n+1}$` | $N_{n+1}$ (subscript) |\n",
    "| `$e^{rt}$` | $e^{rt}$ (superscript) |\n",
    "| `$\\frac{dN}{dt}$` | $\\frac{dN}{dt}$ (fraction) |\n",
    "| `$\\alpha,\\,\\beta,\\,\\theta$` | $\\alpha,\\,\\beta,\\,\\theta$ (Greek letters) |\n",
    "| `$$N_{n+1} = R\\,N_n$$` | a centred display equation on its own line |\n",
    "\n",
    "**Task.** Double-click the cell below and fill in:\n",
    "1. A `##` heading with your name.\n",
    "2. The geometric growth rule $N_{n+1} = R\\,N_n$ as a display equation (`$$...$$`).\n",
    "3. One sentence in **bold** describing what you hope to get out of today.\n",
    "\n",
    "Press **Ctrl+Enter** to render it.\n",
    "\n",
    "(Same syntax works in Jupyter later — there's a quick-reference table in the [Getting Started guide](https://math4120.pages.dev/getting-started/jupyter.html#markdown-basics) if you ever need a reminder.)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bkHC",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
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   "source": [
    "## Example solution\n",
    "\n",
    "$$N_{n+1} = R\\,N_n$$\n",
    "\n",
    "**I hope to see how a simple growth rule can produce very different long-term behaviour depending on the value of $R$.**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "lEQa",
   "metadata": {
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   "source": [
    "## The tools: NumPy and Matplotlib\n",
    "\n",
    "The first code cell imports two libraries:\n",
    "\n",
    "```python\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "```\n",
    "\n",
    "Think of them as toolboxes.  **NumPy** (`np`) provides arrays and mathematical functions; **Matplotlib** (`plt`) produces plots.\n",
    "\n",
    "The key idea in NumPy is that operations work on **whole arrays at once**. If `t` is an array of 200 time values, then `np.exp(r * t)` computes $e^{rt}$ at all 200 points simultaneously — no loop needed.  This is called *vectorisation* and is why scientific Python code rarely has explicit loops over data.\n",
    "\n",
    "Functions you will use today:\n",
    "\n",
    "| Call | What it does |\n",
    "|---|---|\n",
    "| `np.linspace(a, b, n)` | $n$ evenly spaced values from $a$ to $b$ |\n",
    "| `np.arange(n)` | integers $0, 1, \\ldots, n-1$ |\n",
    "| `np.zeros(n)` | array of $n$ zeros (used to pre-allocate before a loop) |\n",
    "| `np.exp(x)` | $e^x$, element-wise if `x` is an array |\n",
    "| `np.log(x)` | natural logarithm, element-wise |\n",
    "\n",
    "**Looking up documentation.**  Run `help(np.linspace)` in any code cell to read the full documentation for a function.  Try replacing `np.linspace` with `np.zeros` or `np.exp` to look those up too."
   ]
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     "text": [
      "Help on _ArrayFunctionDispatcher in module numpy:\n",
      "\n",
      "linspace(\n",
      "    start,\n",
      "    stop,\n",
      "    num=50,\n",
      "    endpoint=True,\n",
      "    retstep=False,\n",
      "    dtype=None,\n",
      "    axis=0,\n",
      "    *,\n",
      "    device=None\n",
      ")\n",
      "    Return evenly spaced numbers over a specified interval.\n",
      "\n",
      "    Returns `num` evenly spaced samples, calculated over the\n",
      "    interval [`start`, `stop`].\n",
      "\n",
      "    The endpoint of the interval can optionally be excluded.\n",
      "\n",
      "    .. versionchanged:: 1.20.0\n",
      "        Values are rounded towards ``-inf`` instead of ``0`` when an\n",
      "        integer ``dtype`` is specified. The old behavior can\n",
      "        still be obtained with ``np.linspace(start, stop, num).astype(np.int_)``\n",
      "\n",
      "    Parameters\n",
      "    ----------\n",
      "    start : array_like\n",
      "        The starting value of the sequence.\n",
      "    stop : array_like\n",
      "        The end value of the sequence, unless `endpoint` is set to False.\n",
      "        In that case, the sequence consists of all but the last of ``num + 1``\n",
      "        evenly spaced samples, so that `stop` is excluded.  Note that the step\n",
      "        size changes when `endpoint` is False.\n",
      "    num : int, optional\n",
      "        Number of samples to generate. Default is 50. Must be non-negative.\n",
      "    endpoint : bool, optional\n",
      "        If True, `stop` is the last sample. Otherwise, it is not included.\n",
      "        Default is True.\n",
      "    retstep : bool, optional\n",
      "        If True, return (`samples`, `step`), where `step` is the spacing\n",
      "        between samples.\n",
      "    dtype : dtype, optional\n",
      "        The type of the output array.  If `dtype` is not given, the data type\n",
      "        is inferred from `start` and `stop`. The inferred dtype will never be\n",
      "        an integer; `float` is chosen even if the arguments would produce an\n",
      "        array of integers.\n",
      "    axis : int, optional\n",
      "        The axis in the result to store the samples.  Relevant only if start\n",
      "        or stop are array-like.  By default (0), the samples will be along a\n",
      "        new axis inserted at the beginning. Use -1 to get an axis at the end.\n",
      "    device : str, optional\n",
      "        The device on which to place the created array. Default: None.\n",
      "        For Array-API interoperability only, so must be ``\"cpu\"`` if passed.\n",
      "\n",
      "        .. versionadded:: 2.0.0\n",
      "\n",
      "    Returns\n",
      "    -------\n",
      "    samples : ndarray\n",
      "        There are `num` equally spaced samples in the closed interval\n",
      "        ``[start, stop]`` or the half-open interval ``[start, stop)``\n",
      "        (depending on whether `endpoint` is True or False).\n",
      "    step : float, optional\n",
      "        Only returned if `retstep` is True\n",
      "\n",
      "        Size of spacing between samples.\n",
      "\n",
      "\n",
      "    See Also\n",
      "    --------\n",
      "    arange : Similar to `linspace`, but uses a step size (instead of the\n",
      "             number of samples).\n",
      "    geomspace : Similar to `linspace`, but with numbers spaced evenly on a log\n",
      "                scale (a geometric progression).\n",
      "    logspace : Similar to `geomspace`, but with the end points specified as\n",
      "               logarithms.\n",
      "    :ref:`how-to-partition`\n",
      "\n",
      "    Examples\n",
      "    --------\n",
      "    >>> import numpy as np\n",
      "    >>> np.linspace(2.0, 3.0, num=5)\n",
      "    array([2.  , 2.25, 2.5 , 2.75, 3.  ])\n",
      "    >>> np.linspace(2.0, 3.0, num=5, endpoint=False)\n",
      "    array([2. ,  2.2,  2.4,  2.6,  2.8])\n",
      "    >>> np.linspace(2.0, 3.0, num=5, retstep=True)\n",
      "    (array([2.  ,  2.25,  2.5 ,  2.75,  3.  ]), 0.25)\n",
      "\n",
      "    Graphical illustration:\n",
      "\n",
      "    >>> import matplotlib.pyplot as plt\n",
      "    >>> N = 8\n",
      "    >>> y = np.zeros(N)\n",
      "    >>> x1 = np.linspace(0, 10, N, endpoint=True)\n",
      "    >>> x2 = np.linspace(0, 10, N, endpoint=False)\n",
      "    >>> plt.plot(x1, y, 'o')\n",
      "    [<matplotlib.lines.Line2D object at 0x...>]\n",
      "    >>> plt.plot(x2, y + 0.5, 'o')\n",
      "    [<matplotlib.lines.Line2D object at 0x...>]\n",
      "    >>> plt.ylim([-0.5, 1])\n",
      "    (-0.5, 1)\n",
      "    >>> plt.show()\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(np.linspace)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Xref",
   "metadata": {
    "marimo": {
     "config": {
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   "source": [
    "## Exercise 1 — plotting an exponential\n",
    "\n",
    "The exponential model $N(t) = N_0\\,e^{rt}$ describes a population growing (or decaying) at a constant per-capita rate $r$.\n",
    "\n",
    "The cell below is already complete — run it first to see what it produces.\n",
    "\n",
    "1. Change $r$ to $-0.3$ and run again.  What changes?\n",
    "2. Change $N_0$ to $500$ and run again.\n",
    "3. What value of $r$ keeps the population exactly constant?"
   ]
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    {
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",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N0 = 100\n",
    "r = 0.3\n",
    "\n",
    "t = np.linspace(0, 10, 200)\n",
    "N = N0 * np.exp(r * t)\n",
    "\n",
    "fig1, ax1 = plt.subplots(figsize=(7, 4))\n",
    "ax1.plot(t, N, color=\"#1a5276\", linewidth=2)\n",
    "ax1.set_xlabel(\"Time $t$\")\n",
    "ax1.set_ylabel(\"Population $N(t)$\")\n",
    "ax1.set_title(\"Exponential model\")\n",
    "ax1.grid(True, alpha=0.3)\n",
    "fig1;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "BYtC",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Exercise 2 — iterating a difference equation\n",
    "\n",
    "Instead of a closed formula, we can build a sequence step by step.  The geometric growth rule is $$N_{n+1} = R\\,N_n.$$\n",
    "\n",
    "The code below sets up an array and fills it in with a `for` loop.  One line is missing.\n",
    "\n",
    "**Task.**\n",
    "1. Replace `0.0` on the marked line with the iteration rule.  Use `R` and `N_d[n]`.\n",
    "2. Run the cell.  The plot below will update automatically.\n",
    "3. Try `R = 0.7`, then `R = 1.0`, then `R = 2.5`.  Describe what you observe each time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "RGSE",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:31.862610Z",
     "iopub.status.busy": "2026-11-13T23:25:31.862355Z",
     "iopub.status.idle": "2026-11-13T23:25:31.867657Z",
     "shell.execute_reply": "2026-11-13T23:25:31.866622Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  100.        ,   135.        ,   182.25      ,   246.0375    ,\n",
       "         332.150625  ,   448.40334375,   605.34451406,   817.21509398,\n",
       "        1103.24037688,  1489.37450879,  2010.65558686,  2714.38504226,\n",
       "        3664.41980706,  4946.96673953,  6678.40509836,  9015.84688278,\n",
       "       12171.39329176, 16431.38094387, 22182.36427423, 29946.19177021,\n",
       "       40427.35888979])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R = 1.35      # try 0.7, 1.0, 2.5\n",
    "N0_d = 100\n",
    "steps = 20\n",
    "\n",
    "N_d = np.zeros(steps + 1)\n",
    "N_d[0] = N0_d\n",
    "for n in range(steps):\n",
    "    N_d[n + 1] = R * N_d[n]\n",
    "N_d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "Kclp",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:31.869313Z",
     "iopub.status.busy": "2026-11-13T23:25:31.869158Z",
     "iopub.status.idle": "2026-11-13T23:25:32.034773Z",
     "shell.execute_reply": "2026-11-13T23:25:32.033747Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_fig2, _ax2 = plt.subplots(figsize=(7, 4))\n",
    "_ax2.stem(np.arange(steps + 1), N_d, linefmt=\"#1a5276\", markerfmt=\"C0o\", basefmt=\"k-\")\n",
    "_ax2.set_xlabel(\"Generation $n$\")\n",
    "_ax2.set_ylabel(\"Population\")\n",
    "_ax2.set_title(f\"Geometric growth  ($R = {R}$)\")\n",
    "_ax2.grid(True, alpha=0.3)\n",
    "_fig2;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "emfo",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Exercise 3 — the logistic map\n",
    "\n",
    "The geometric model grows without bound when $R > 1$.  A carrying capacity $K$ adds a braking factor: $$N_{n+1} = R\\,N_n\\!\\left(1 - \\frac{N_n}{K}\\right).$$\n",
    "\n",
    "When $N_n \\ll K$ this behaves like geometric growth.  When $N_n$ approaches $K$ the factor $(1 - N_n/K)$ suppresses growth.\n",
    "\n",
    "**Task.**\n",
    "1. Replace `0.0` on the marked line with the logistic rule. Use `R_log`, `N_log[n_log]`, and `K`.\n",
    "2. Run for `R_log = 2.0`.  Describe the long-term behaviour.\n",
    "3. Change `R_log` to `3.2`, then `3.8`.  What happens?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "Hstk",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:32.036896Z",
     "iopub.status.busy": "2026-11-13T23:25:32.036680Z",
     "iopub.status.idle": "2026-11-13T23:25:32.043128Z",
     "shell.execute_reply": "2026-11-13T23:25:32.042422Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10.        , 18.        , 29.52      , 41.611392  , 48.59262512,\n",
       "       49.96038592, 49.99996861, 50.        , 50.        , 50.        ,\n",
       "       50.        , 50.        , 50.        , 50.        , 50.        ,\n",
       "       50.        , 50.        , 50.        , 50.        , 50.        ,\n",
       "       50.        , 50.        , 50.        , 50.        , 50.        ,\n",
       "       50.        , 50.        , 50.        , 50.        , 50.        ,\n",
       "       50.        , 50.        , 50.        , 50.        , 50.        ,\n",
       "       50.        , 50.        , 50.        , 50.        , 50.        ,\n",
       "       50.        , 50.        , 50.        , 50.        , 50.        ,\n",
       "       50.        , 50.        , 50.        , 50.        , 50.        ,\n",
       "       50.        , 50.        , 50.        , 50.        , 50.        ,\n",
       "       50.        , 50.        , 50.        , 50.        , 50.        ,\n",
       "       50.        ])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_log = 2.0    # try 3.2, then 3.8\n",
    "K = 100\n",
    "N0_log = 10\n",
    "steps_log = 60\n",
    "\n",
    "N_log = np.zeros(steps_log + 1)\n",
    "N_log[0] = N0_log\n",
    "for n_log in range(steps_log):\n",
    "    N_log[n_log + 1] = R_log * N_log[n_log] * (1 - N_log[n_log] / K)\n",
    "N_log"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "nWHF",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:32.044700Z",
     "iopub.status.busy": "2026-11-13T23:25:32.044557Z",
     "iopub.status.idle": "2026-11-13T23:25:32.204234Z",
     "shell.execute_reply": "2026-11-13T23:25:32.203414Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_fig3, _ax3 = plt.subplots(figsize=(8, 4))\n",
    "_ax3.stem(np.arange(steps_log + 1), N_log, linefmt=\"#1a5276\", markerfmt=\"C0.\", basefmt=\"k-\")\n",
    "_ax3.axhline(K, color=\"grey\", linestyle=\"--\", alpha=0.5, label=f\"$K = {K}$\")\n",
    "_ax3.set_xlabel(\"Year $n$\")\n",
    "_ax3.set_ylabel(\"Population\")\n",
    "_ax3.set_title(f\"Logistic map  ($R = {R_log}$,  $K = {K}$)\")\n",
    "_ax3.legend()\n",
    "_ax3.grid(True, alpha=0.3)\n",
    "_fig3;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "iLit",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "**Your observations** (double-click to edit this cell):\n",
    "\n",
    "- $R = 2.0$: the population rises smoothly and settles at a steady value of $K/2 = 50$ — *not* $K$ itself. For this discrete map the non-trivial fixed point is $N^* = K(1 - 1/R)$, which only approaches $K$ as $R$ grows large; at $R=2$ it sits at exactly $K/2$.\n",
    "- $R = 3.2$: the population settles into a stable oscillation, alternating between two fixed values (a period-2 cycle).\n",
    "- $R = 3.8$: the population becomes chaotic — no repeating pattern, and tiny changes in $N_0$ lead to very different sequences."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ZHCJ",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Extension — Newton's law of cooling\n",
    "\n",
    "A cup of coffee starts at $90°$C in a room at $20°$C.  Newton's law of cooling gives the temperature at time $t$ (minutes): $$T(t) = T_\\infty + (T_0 - T_\\infty)\\,e^{-kt}.$$\n",
    "\n",
    "**Task.**\n",
    "1. Replace `np.zeros_like(t_cool)` with the formula for $T(t)$. Use `T0_cool`, `Tinf_cool`, `k_cool`, `t_cool`, and `np.exp(...)`.\n",
    "2. Run the cell.  At roughly what time does the coffee reach $60°$C?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ROlb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:32.206784Z",
     "iopub.status.busy": "2026-11-13T23:25:32.206574Z",
     "iopub.status.idle": "2026-11-13T23:25:32.209752Z",
     "shell.execute_reply": "2026-11-13T23:25:32.209007Z"
    }
   },
   "outputs": [],
   "source": [
    "T0_cool   = 90.0   # initial temperature (°C)\n",
    "Tinf_cool = 20.0   # room temperature (°C)\n",
    "k_cool    = 0.05   # cooling rate (min⁻¹)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "qnkX",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:32.211257Z",
     "iopub.status.busy": "2026-11-13T23:25:32.211088Z",
     "iopub.status.idle": "2026-11-13T23:25:32.216541Z",
     "shell.execute_reply": "2026-11-13T23:25:32.215639Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([90.        , 89.30117056, 88.60931773, 87.92437185, 87.24626398,\n",
       "       86.57492585, 85.91028988, 85.25228915, 84.60085742, 83.95592912,\n",
       "       83.31743932, 82.68532374, 82.05951874, 81.43996133, 80.82658913,\n",
       "       80.2193404 , 79.618154  , 79.02296941, 78.43372671, 77.85036659,\n",
       "       77.27283031, 76.70105974, 76.13499732, 75.57458605, 75.01976952,\n",
       "       74.47049188, 73.92669783, 73.38833263, 72.85534208, 72.32767252,\n",
       "       71.80527083, 71.28808442, 70.77606123, 70.26914971, 69.76729883,\n",
       "       69.27045806, 68.7785774 , 68.29160731, 67.80949878, 67.33220328,\n",
       "       66.85967275, 66.39185962, 65.9287168 , 65.47019766, 65.01625605,\n",
       "       64.56684627, 64.12192306, 63.68144165, 63.24535769, 62.81362727,\n",
       "       62.38620694, 61.96305366, 61.54412484, 61.12937831, 60.7187723 ,\n",
       "       60.31226549, 59.90981694, 59.51138616, 59.11693302, 58.72641781,\n",
       "       58.33980123, 57.95704434, 57.57810863, 57.20295593, 56.83154849,\n",
       "       56.46384891, 56.09982018, 55.73942565, 55.38262904, 55.02939443,\n",
       "       54.67968625, 54.33346931, 53.99070875, 53.65137007, 53.31541909,\n",
       "       52.98282201, 52.65354534, 52.32755593, 52.00482096, 51.68530794,\n",
       "       51.36898471, 51.05581943, 50.74578056, 50.43883689, 50.13495753,\n",
       "       49.83411188, 49.53626965, 49.24140087, 48.94947584, 48.66046518,\n",
       "       48.3743398 , 48.09107089, 47.81062992, 47.53298868, 47.25811921,\n",
       "       46.98599383, 46.71658516, 46.44986607, 46.18580971, 45.9243895 ,\n",
       "       45.66557912, 45.40935252, 45.15568389, 44.90454772, 44.6559187 ,\n",
       "       44.40977182, 44.16608228, 43.92482557, 43.68597739, 43.4495137 ,\n",
       "       43.2154107 , 42.9836448 , 42.75419269, 42.52703127, 42.30213766,\n",
       "       42.07948922, 41.85906355, 41.64083845, 41.42479195, 41.2109023 ,\n",
       "       40.99914797, 40.78950765, 40.58196022, 40.37648479, 40.17306068,\n",
       "       39.97166742, 39.77228471, 39.5748925 , 39.37947092, 39.18600028,\n",
       "       38.99446111, 38.80483413, 38.61710024, 38.43124056, 38.24723637,\n",
       "       38.06506914, 37.88472054, 37.70617241, 37.52940677, 37.35440583,\n",
       "       37.18115198, 37.00962777, 36.83981593, 36.67169937, 36.50526116,\n",
       "       36.34048456, 36.17735296, 36.01584996, 35.85595928, 35.69766483,\n",
       "       35.54095068, 35.38580106, 35.23220033, 35.08013305, 34.92958389,\n",
       "       34.78053771, 34.63297949, 34.4868944 , 34.34226771, 34.19908486,\n",
       "       34.05733146, 33.91699321, 33.778056  , 33.64050584, 33.50432889,\n",
       "       33.36951142, 33.23603987, 33.10390081, 32.97308093, 32.84356706,\n",
       "       32.71534616, 32.58840533, 32.46273178, 32.33831287, 32.21513607,\n",
       "       32.09318897, 31.97245931, 31.85293492, 31.73460378, 31.61745397,\n",
       "       31.5014737 , 31.3866513 , 31.27297519, 31.16043395, 31.04901624,\n",
       "       30.93871084, 30.82950665, 30.72139268, 30.61435804, 30.50839196,\n",
       "       30.40348376, 30.29962289, 30.1967989 , 30.09500142, 29.99422022,\n",
       "       29.89444514, 29.79566615, 29.69787329, 29.60105673, 29.50520671,\n",
       "       29.4103136 , 29.31636782, 29.22335993, 29.13128057, 29.04012046,\n",
       "       28.94987043, 28.86052138, 28.77206434, 28.68449038, 28.59779071,\n",
       "       28.51195657, 28.42697935, 28.34285047, 28.25956148, 28.17710398,\n",
       "       28.09546968, 28.01465036, 27.93463788, 27.85542418, 27.7770013 ,\n",
       "       27.69936134, 27.62249648, 27.54639898, 27.47106118, 27.3964755 ,\n",
       "       27.32263443, 27.24953054, 27.17715646, 27.10550492, 27.03456869,\n",
       "       26.96434063, 26.89481369, 26.82598085, 26.75783519, 26.69036984,\n",
       "       26.62357802, 26.557453  , 26.49198813, 26.42717681, 26.36301251,\n",
       "       26.29948879, 26.23659925, 26.17433754, 26.11269742, 26.05167266,\n",
       "       25.99125713, 25.93144475, 25.87222949, 25.81360539, 25.75556655,\n",
       "       25.69810713, 25.64122135, 25.58490347, 25.52914783, 25.47394881,\n",
       "       25.41930086, 25.36519847, 25.3116362 , 25.25860867, 25.20611051,\n",
       "       25.15413647, 25.10268129, 25.05173981, 25.00130689, 24.95137745,\n",
       "       24.90194647, 24.85300898, 24.80456004, 24.75659479, 24.70910838,\n",
       "       24.66209604, 24.61555304, 24.5694747 , 24.52385636, 24.47869345,\n",
       "       24.43398141, 24.38971574, 24.34589199, 24.30250574, 24.25955263,\n",
       "       24.21702833, 24.17492857, 24.1332491 , 24.09198572, 24.05113429,\n",
       "       24.01069069, 23.97065086, 23.93101075, 23.89176637, 23.85291379,\n",
       "       23.81444908, 23.77636838, 23.73866784, 23.70134368, 23.66439214,\n",
       "       23.6278095 , 23.59159207, 23.5557362 , 23.5202383 , 23.48509479])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_cool = np.linspace(0, 60, 300)\n",
    "T_cool = Tinf_cool + (T0_cool - Tinf_cool) * np.exp(-k_cool * t_cool)\n",
    "T_cool"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "TqIu",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:32.218442Z",
     "iopub.status.busy": "2026-11-13T23:25:32.218256Z",
     "iopub.status.idle": "2026-11-13T23:25:32.381506Z",
     "shell.execute_reply": "2026-11-13T23:25:32.379972Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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OBAIBW7FihUy/7OxsZmhoWOlCbNy4cUxdXV3uMjs7O9a/f3/24sUL1rZtW2Ztbc38/f3LXF+7du1KDHyX9zN//ny5z//ll19KPRqxaNEi7khxab799tsSRyPefa0AuKO0L168YDt37uSOnhQUFLBVq1YxAGzOnDllvk7Gin+/AGT+2GCMMS8vLyYUCtnZs2dl2vv168ecnZ25x6UVYgDYy5cvZZ47YcIEZmxs/MGY3hUTE8OePn3KDSB//2IFRYiLi2MA2NSpU+UuLyoqYr/99hsbN24cW7x4cZlHb168eFGufcfJyYn5+PjIXceuXbvkfnZ+8803DABzcHBgjBX/QQ6AjRkzpsQ6goKCGAD27bfflhprREQEAyB3P7506RIDwH755ZdSn/+uP//8kwFgW7ZsKVd/KenR4/fPqNRH8q9DJbWSQCDA+vXr4eXlhR07dmDevHkl+ly+fBkqKiowNTXFixcvwIqLbTDG0LRpUwQEBAAoHpfSvXt3XLhwAQBw6dIlqKmpYerUqVi/fj0uXLiAli1b4uLFi3BxcYGBgUGZsT169Ag5OTno1atXiWWenp7w8/NDSEgIHBwcuPauXbvK9JNOzxEZGYkmTZrI3Y6Xlxd27tyJCRMmYOjQoejatSuMjIzKjK00z549w6xZs3Djxg2Ym5tDR0cHAoEAYrEYERERMtvcvXs3Hj16BEdHR1y/fh27d++GsbExLly4gO+//x4XL17k+pYmJiYGb968wahRo0os8/T0xN69e3H//n3069evQq/Dz88PpqamcHFxKbXPrVu3AKDE78fS0hL29vbc8tu3b8vtp6ysDA8PD+zfvx/5+fkVvmS/rN81ANy9exeMMXTr1k2mn4aGBlxcXPD48eMKbU8qOzubGx/zLul4Rw0NDbRr1w5eXl64fPnyB6d0ePDgQaXikFJSUgIAueOcpG1lXfpfnudLpxewt7eXmdZGRUUFK1aswIMHD7Bt2zZ88cUXMDU1/WDM7u7uMo9tbW0hkUhKTElha2uLmzdvfnB9pqamaN68uUybnZ0dEhMTkZubC3V19Q+uAwB2796NI0eOwMzMDDt27MCOHTsQFBRUrueW14fGh33xxRf4+++/sXDhQly7dg1dunTB06dP5e5z9vb2VY5v/Pjx2LVrF2bPno3s7Gy0adMGfn5+2LhxIzQ1Nbn3ZU3sZx+aokJKOl1GecbOvkuaw6qMA64rqBCrYzw9PdGnTx+sWbMGn332WYnl0jmdRo8eLff5jRo14v7v5eWFuXPnIiYmBhcvXkS3bt2gpqYGT09PXLx4ETNmzMDNmzexcOHCD8aVlZUFAHILNmlbZmamTPv7BZT0A7isN97mzZvh6OiII0eOYMyYMSgoKECnTp2wceNGuLm5fTBOqcLCQvTt2xeNGjVCdHQ0zMzMZOJ4dzB5r169IBAIcOHCBaSmpiIvLw+enp4wMjLCjz/+iISEBFy8eBHW1tYlvmDeVZkclUdGRkaJuXjkbVsoFEJPT0/utqOiosoVo0QiQXZ2doULsQ/9rqXblVcIVWW+K0NDQ6SlpYExBoFAwLUHBgaCMQaJRIK8vDzMmzevXNt5/vx5uSaa1NXVhZWVVYl2aeGTnJxcYlliYiKUlJTK/F1+6PlGRkbcl2hpunfvjhMnTiAoKOiDhZimpmaJwkhdXR0ikQhaWlol2svzpSnvD6d394fyFmIrVqzAihUrytW3sgIDAwEA7dq1K7EsOzsbmzdvxqVLl+Du7o6pU6fCwcEBBw8exKRJk0r0L2tet/eZm5vL3Q9UVVVx5coVbNmyBUeOHMGvv/6KZs2a4caNG/D09ETjxo0BFBfjBgYGpe4nAMr83RsZGUEoFFb6+e+S/tFV3tcuJZ3A+kOfbfUBFWJ10Pr169G2bVusXbu2xDJLS0sIBAI8ePDgg1+W0qM3Fy5cwMWLFzF//nwAQO/evTF58mRcuHAB+fn5ZR7lkZJOSClvIkRpW2UmrXyfiooKZs2ahVmzZiE/Px9+fn6YNWsW+vfvj7i4uFInG3zf48ePER0dje+//16mCIuKiipxNZGRkRHatm2LCxcuIC0tDW3atIGxsTG6du0KkUiEixcv4vLlyxg0aFCZ2zQzM4NAICgzR+8WyuVlZWWF8+fPQyKRQCiUfyG0hYUFJBIJoqOjYW1tXWLblpaWXD9pW/v27Uv009DQkFvMVZV0wt7o6OgSR/YqctXm++zs7FBUVIS3b9/K7H/SL1hfX1/MnTsXQ4YMwbVr19C6desy19euXTvk5+d/cLvDhw/H0aNH5T4fAJ48eVJi2dOnT+Hk5FTm+1aamydPnsDT01NmWVBQkNyC4X3SYr+8BU9D9vDhQygrK6Nly5Yllj169AhCoRCdO3cGUHzGolevXrh9+7bcQuzFixflvvLyhx9+wKJFi+QuU1dXx9KlS7F06VKuLSQkBImJiejduzfXVtqR5KdPnwKQX1xKqampwcnJqdT9VCAQlPu1ODk5oVmzZjh58iS2bNlS6md0UVGRzB8R0s/EZs2alWs7dRlNX1EHtWrVChMmTMCWLVtKfElJjxL5+PjIfe67RYaDgwMaNWqErVu3Ijo6miu4PD09kZeXh5UrV0JDQ4P7oAHAzab//q2CnJycYGtriz/++EPmiEFBQQEOHjyINm3acF/2VfFu/CKRCH369MH48eORnJzM/aVWHtKZqN8/ArVt2za5xYyXlxdu3rwJX19fLk9qamro2rUrNmzYgISEhA8WrLq6uujatSuOHj0qc+SAMYa9e/fC1NQUrq6u5X4NUh9//DGys7Pl/s6lU0AMHDgQALBv3z6Z5X5+foiIiOCW9+jRA5qamiX6JSQk4MyZM+jfv3+pxV5VdO3aFdra2jhw4IBMe1hYGO7du1fp9UpPdUpPyUs9fPgQxsbGsLW1xZEjR+Dk5IS+ffsiPDy8zPU5OTmV6+f9YleqUaNG8PDwwF9//cX9boDiwurx48cYN24c11ZYWFhiGo127dqhRYsWOHjwoMx0LxcvXkRcXJzM8+UVjPn5+Th06BAMDQ3LPJVd1+Xl5SEoKEju1BgVERgYCAcHB6ipqZVYlpiYCENDQ5kjrSYmJiWm85FSV1cv9/5T1nCLd/cbqbVr18LS0hLjx4/n2j755BPuaL0UYwx//PEHnJycZAqp8PDwEqdNP/nkEzx9+lSmGCsoKMCRI0fQo0ePCv1hvX79ekRHR+OLL76Quzw4OBhfffWVTNudO3egqqpaZ+6EUiW8jU4j5fLuYP13RUVFMXV1dW6Kg3ctXbqUqaqqsoULF7KLFy+y27dvs/3797NBgwaxVatWyfSdOHEiAyBzpSRjjLVu3ZoBYH379pVpLywsZI0aNWI9evRgt2/fZk+fPuUu/z937hxTVVVlAwYMYBcuXGBnz55lHh4eTEtLi925c4dbh3Rw+ftXskmvrinrCig7Ozv2xRdfsFOnTrH79++zgwcPMktLS9azZ88y8/j+YH2JRMI6d+7MzM3N2ZEjR9iNGzfYokWL2Oeff84MDQ1LXC108eJF7oqmdy+E+OGHHxgAJhAIWGJiYpkxMFY8AFVXV5d17NiRnTx5kl2+fJkNHz6cKSsrs3/++YfrV5HB+hKJhE2YMIGpqKiwr776ivn5+bFz586xmTNnsm+++YbrN3XqVKasrMxWrlzJbt68yfbs2cMMDQ2Zq6urzAzhv/76KxMIBOzzzz9n165dY8eOHWNOTk7MzMyMhYeHc/0qMlj//f03PDycAWA///wz17Zz504GgM2cOZPduHGD/fXXX6xXr15s6NChJfbP8hKLxczS0pK7GEGqZcuWMvt2cnIyc3R0ZHZ2djLTWVSHx48fM21tbTZ48GB28+ZNdurUKda8eXPm4uIiMy2BNEcTJ06Ueb6fnx9TVVVlEydOZHfu3GFHjx5lFhYWzMvLS+Zqz9GjR7MZM2awv//+mwUEBLA///yTubq6MlVVVbkzn79POn3F++bOnctEIlGJ9oULFzIlJSXucVnTV7xP+j4qz3uoPKRXjC5cuLDS60hLS2MCgYBNmDBB7vKTJ0+W+Oz94osv2NChQyu9zfLo1q0b27p1K7tz5w67cOECGzVqFNPX12d3796V6ScWi1nPnj2ZhYUF++uvv9idO3fYxIkTmUgkKnHVrYeHB3u/HMjOzmZt27ZlzZo1YydPnmQ3b95kQ4YMYTo6OjJXZ5fXzz//zFRUVFjfvn3Zn3/+yR48eMAuX77MFi5cyNTU1NjkyZNl+js7O1d7LmsLOjVZyxkbG8s9XWFpaYkVK1bgwIEDJf56WrduHfr06YN9+/bhyy+/hLKyMpo3b45p06aVGAg+ZMgQuQPER48eDbFYjBEjRsi0Kysr49ixY1i/fj2mT5+OwsJCzJgxAzNmzECfPn1w7949bNmyBV9++SUEAgFcXFzw22+/yRxeNjExgZOTU4mxLJqamnBycoKOjk6p+bhz5w527dqFX375BXFxcTAzM8MXX3whd7zcu3R0dODk5MQNABUIBDh16hTWrl2LzZs3Q0VFBYMGDcK6desQEhJS4hRhly5duIk/3x2k3K9fP+zduxfNmjUr10UDrVu3RmBgIDZu3Ig1a9agqKgITk5OuHPnjswRCmVlZTg5OcHY2PiD6xQIBNi3bx8GDBiAw4cP48yZMzA3N8eAAQNk7tX2yy+/oFu3bjh8+DCOHz8OPT09LFmyBLNmzZI5TTV58mQ0b94cO3fuxPz586Gmpob+/ftjwYIFMqdxLSws4OjoKBOLo6OjzF/K+vr6cvdfVVVVODk5yYxFmzJlCszNzfHLL79g3rx5aNOmDXx8fLBgwQK5RyTKQ0lJCVOnTsVPP/2ETZs2QSQSQSwWQ0lJSeY0joGBAc6dO4ePP/4Yixcvxp49ez441qqyWrVqhQcPHuCHH37AvHnzIBKJMHbsWCxcuFDmdUpz9P6RZA8PDwQEBGDDhg2YOXMmtLS0MH/+fMyZM0fmaOW+fftw8OBBHD58GGFhYVBXV4e7uzv279+PFi1afDBOeb9foPg0spOTk9x2Z2dn7rG2tjacnJygqanJtdnY2Mgd5G1kZAQnJ6dyDy34EOnEs/LiL6+wsDA4OjqiR48ecpc3btwYycnJyM7O5l5jREQEbGxsKr3N8jhy5Ah++OEHHDp0CMrKyujSpQuCg4NLjNlSUlLCmTNnsHXrVmzbtg1ZWVlwcnJCQEAAWrVqJdPX1ta2xGS9GhoauH79OjZs2IDvv/8e+fn5aNOmDR4+fIimTZtWOG7p98+ePXvw22+/cfeatLW1xd9//81NCAsUn/YNCgrCTz/9VOHt1EV0029CSK3m6uoKDQ0NXLt2rVLPT0tLQ7NmzbB69WpMmzZNwdGR2mjx4sU4ceIEnj9/rrDi7n2MMTRu3BjLli3D9OnT8fbtWzg6OuLo0aNyrx4n5TdhwgSEhYXB39+f71BqBI0RI4TUCvIub3/69CkePHiAPn36VHq9enp6WLduHY4fP16uKx5J3RcTE4N169ZVWxEGFB+J/uWXX7Bs2TL06NEDbdu2xZAhQ6gIq6K4uDg8efIEGzdu5DuUGkNHxAghtcKVK1ewbds2jB07FpaWlnj69Cm+/vpr6OrqIiAggLvAgpDaJD4+Hvfu3YOFhUW5rlol5H1UiBFCao0TJ07g8OHDeP36NTQ1NdG9e3fMnTu3SnOJEUJIbUaFGCGEEEIIT2iMGCGEEEIIT6gQI4QQQgjhSYOYR0wikSA2Nhba2toysyATQgghhCgaYwyZmZmwsLD44N1IGkQhFhsbK/cGvIQQQggh1SUqKuqDt/drEIWY9LL3qKioMmdtryyJRILExEQYGxtXy334GgrKo+JQLhWD8qgYlEfFoDwqRk3kMSMjA1ZWVuWadqdBFGLS05E6OjrVVojl5eVBR0eH3hxVQHlUHMqlYlAeFYPyqBiUR8WoyTyWZzgU/SYJIYQQQnhChRghhBBCCE+oECOEEEII4UmDGCNGCCF1SVFRkdyboNdVEokEhYWFyMvLo7FNVUB5VAxF5FFFRQVKSkoKiYcKMUIIqSUYY4iLi0NaWhrfoSgUYwwSiQSZmZk0l2MVUB4VQ1F51NPTg5mZWZV/F1SIEUJILSEtwkxMTKChoVFvvmwZYxCLxVBWVq43r4kPlEfFqGoeGWPIyclBQkICAMDc3LxK8fBeiEkkEkRERCAtLQ0ODg5QV1eX2y8qKgrx8fFo3rx5tUxBQQghfCoqKuKKMENDQ77DUSgqIBSD8qgYisijtFZJSEiAiYlJlU5T8nqSOSAgAA4ODujWrRsmTpwICwsLHDlyRKZPXl4ehg8fDnt7e4wfPx5mZmbYunUrTxETQkj1kI4J09DQ4DkSQkh5SN+rVR3PyVshVlhYiKFDh6JLly6IjIzE06dPcfDgQUyYMAGvXr3i+q1cuRIBAQEIDQ1FcHAwDh48iDlz5uDu3bt8hU4IIdWGjnQQUjco6r3KWyH24sULxMbGYtq0adwhvX79+sHS0hI+Pj5cPx8fH0yaNIk7BztkyBA4OzvL9KkNXkQl8B0CIYQQQuoY3saIGRgYAABiYmLg6uoKoPg0ZHJyMh48eACg+Gbd8fHxcHFxkXmum5sbAgMDS113fn4+8vPzuccZGRkAisejSSQShb6Ot8npWLn3FE7fCcKeJePh5eqo0PU3JBKJhLuahVQN5VIxajKP0m1Jf+ob6Wuqj6+tJlEeFUMReZS+V+XVFhX5zOCtEGvUqBFGjBiBOXPmICMjA0ZGRtixYwcEAgFSUlIAgPv3/YGrhoaG3DJ5vL29sXLlyhLtiYmJyMvLU+CrAC7ef4HTd4IAACv2+KKFhR5EKrxfA1EnSSQSpKengzFGc+RUEeVSMWoyj4WFhZBIJBCLxRCLxdW6LUVKSkqChYUF91hXVxctWrTAl19+ib59+wIo/sIqKioCUHtOvXbp0gX9+/fHF198wXco5VbVPPL9mgsLC3HgwAH89ttveP78OYyNjTFs2DCsWLECmpqaXL/MzEwsXLgQx48fh1gshpeXFzZv3gwzM7NS112e55w+fRrz5s1DVlYWFixYgEWLFsnk8caNG9iwYQPu3r2LnJwcNG7cGH379sX8+fPlblssFkMikSA5ORkqKiol4ikvXiuGAwcO4JdffsE///yD3NxcfPzxx9DW1kZMTAwAcC/s/eIpNzcXqqqqpa53+fLlWLBgAfdYehd0Y2NjhV9xOb6fMU7efYE7z8MRk5SOv28FY97IXgrdRkMhkUggEAhgbGxMxUMVUS4VoybzmJeXh8zMTCgrK0NZue78MSeN1dfXFwMHDkRqaipWrVqFESNGIDAwEA4ODlzf97+s+CQQCCAUCutUrqUqm0e+X/OVK1dw584dbN26FU5OTggODsbo0aPx9u1bHDhwgOs3depUPH/+HLdu3YKGhgYmTJiAESNG4Pbt26UWoB96jkQiwbx583Dq1CkYGxujb9++GDx4MBwdi89i7d69GzNmzMCXX36Jn3/+GSYmJggPD8f58+exfft2eHt7l9imsrIyhEIhDA0NoaamJrPs/cdlYrVMs2bN2PTp0xljjGVnZzOhUMh+//13mT5Dhw5lffv2Lfc609PTGQCWnp6u0FilnkfEMqsRS5nFsCWsyegvWGRccrVsp74rKipib9++ZUVFRXyHUudRLhWjJvOYm5vLnj9/znJzc6t9W4qUmJjIALCTJ09ybXl5eUxJSYlt2bKFMcaYRCJhaWlpbOrUqczIyIiJRCLm7u7O7ty5I7Ou7OxsNm3atDL7tG7dmk2bNo0NGDCAGRoaMiMjI7Zq1Sr26tUr1rt3b6aurs6srKxKfG+8a8CAAQyAzE9iYiITi8Vs5cqVzNramqmpqbGWLVuyw4cPK2T7rVu3ZnPnzmWDBg1iBgYGzMTEhK1Zs0amz4e2L5FIWKtWrbj1aGpqshEjRjDGGBs+fDj3WoyNjdnw4cPZmzdvPviaGzVqxHx8fGTi6NWrF1u6dKlM7PPmzSuxzZiYGDZ69Gimp6fH9PT0WJ8+fdizZ89Kzbs8O3fuZCKRiBUWFjLGGAsPD2cA2OnTp7k+jx49YgCYn5+f3HWU5zlFRUXMysqKPX/+nMXHx7N27dqxp0+fcq9DJBKxL774okKxl/WerUjdwWshlpOTI/P40qVLDAC7ffs219alSxc2cuRI7nFWVhbT1tZmGzZsKPd2qrsQKyoqYou3HWYWw5Ywi2FL2Kfee6tlO/UdFQ+KQ7lUjNpSiBUWFpb6IxaLFdq3osoqxH744QfGWHEBMXHiRGZvb88ePXrEkpKS2Ny5c5muri5LTEzknvfZZ599sE/r1q2Zuro6++eff1hWVhb7/fffGQBmZWXFTp48ybKystjOnTuZqqoqi4mJKTXuDh06sNWrV8u0zZ49m7m6urJHjx6x7OxsdubMGaalpcUuXrxY5e23bt2aCQQC9ssvv7D09HR2+vRppq2tzfbt21fu7UsLMRUVFXbgwAGWnZ0t97VFRUWxUaNGMXd39w++5vIWYu9vMycnhzVv3pzNmjWLxcbGsrS0NPbVV18xCwuLCn3XrlmzhhkYGHCPDxw4wACwrKwsmX6GhoZs7dq1ctdR3uf89ddfzNLSkhkYGLC1a9cyiUTCGGNsy5YtXGFaEfWiEPvqq6/YsmXL2Pnz59mWLVuYgYEBW7ZsmUwfPz8/pqKiwpYtW8ZOnDjBPD09WdOmTVlmZma5t1MThdirsAjW5n+ruWLs0v3gatlWfUbFg+JQLhWjthRivr6+pf68f8To9OnTpfa9efOmTN9z586V6FNR7xdiKSkpbN68eUxNTY2FhIQwxhh7+/YtEwqFMkcsxGIxs7Gx4QqDuLg4JhQK2ZkzZ0rtw1hxUTBlyhSZGExNTdmcOXNk2rS0tNjx48dLjfv9oiQhIYEpKyuzwMBAmX6zZ89mo0ePrvL2W7duzfr16yfTZ+nSpax169bl3r60EPvkk09KfV1Sb9++ZQBkisGqFGLvb3PPnj2scePGXDEjZW1tXeIoYmkiIiKYvr6+zLY2bNjANDQ0SvR1cHAokePKPkcikbCCggIu9tmzZ8sUg+WlqEKM18Ej33zzDYyNjbFx40bcunULPj4+Jc7Denh44OrVq4iMjMTmzZvh5OQEf39/aGlp8RS1fFrqInw1vj/3+Os9vsgrqD837SWEkLIMGjQIAoEABgYG2LFjB44fP45mzZoBAF6+fAmJRIIOHTpw/ZWUlODq6ornz5+Xu4+UnZ2dzGM9Pb0Sbbq6ukhNTS13/I8ePYJYLEb79u2hrKwMJSUlCIVCbN26FWFhYQrZfvv27WUeu7q64sWLF5BIJBXavnRc07vu3buH3r17w8jICAKBgJvy6c2bN+XOQVmcnJxkHt+/fx+RkZHcza+FQiGEQiHevHlTIl55kpKS0L9/f7Rp0warVq36YH/GWIUvUCjvcyqzbkXidZSisrIyFixYIDOwXh53d3e4u7vXUFSVN6RLaxy6fA+3n4UhIi4Zv/hex7wRNHCfEFI1/fr1K3XZ+18gvXv3LnffXr0U9/l08uRJDBw4EDExMZg+fToWLlyIrl27QkNDo9QpAt79AixPHyl5X5pV/SKVTjcQExMDU1PTMvtWdvul9ZEOJi/v9t+/WC0nJwf9+vXDpEmT4OPjA1NTU2RlZUFfX79SV+DKm3rh/W1KJBJ07NgRt27dqvD6k5OT4enpCSMjI5w6dUpm3WZmZsjJyUF2drbMlZSJiYml5qUyz3lX8+bNkZycjKSkJBgZGVX49VQVXU6lQAKBAGsmDYbSv1dXbf37CqISSp9mgxBCykN6JaW8n/fvcVfVvlXVqFEj7N+/HwkJCdwZjhYtWkAoFCIgIIDrV1RUhAcPHnBXVZanjyKpqKjIFBytW7eGUCjEuXPnFL4tqXv37pV4bG9vD4FAUKXth4SEIDk5GcuWLUOjRo2grKwsk0ep918zAOjr68scuWOMITQ09IPbbNeuHR49eoS4uLgKxZqSkgJPT0/o6urizJkzJW7p1blzZwCAn58f1/bkyRMkJydzy95Xmee8a/jw4RCJRNi4cWOFXouiUCGmYC2szfB5/+JffF6BGN/6nOI5IkIIqVl6enr4+uuv8dNPPyE2NhampqYYP348Fi5ciCdPniAlJQWLFy9GSkoKpk6dCgAwNTXFxIkTsWDBglL7KJKNjQ3u37+P3NxcAMVHVaZPn47FixfjxIkTyMzMRFhYGDZs2IAtW7YoZJvnzp3Dzp07kZGRgTNnzmDHjh2YP39+lbdvY2MDdXV17Nq1Czk5Obh37x5mzZr1wdcMAF27dsWePXsQERGBlJQULFmypFynM8eOHQsrKyuMHDkST548QXZ2Nh4+fIjPP/8cT58+lfuctLQ0eHp6QkdHB2fOnJE5eiXVuHFjDB8+HEuWLMGLFy/w5s0bzJo1C25ubujWrRvXz9LSEosWLarQc0pjYWGBLVu24IcffsDq1asRHR2N/Px8vHz5Eps3b672edeoEKsGC0d5wURPGwBwLuAZrjx8wXNEhBBSs6ZOnQpzc3N8++23AIBNmzahW7du6NmzJywsLBAQEIALFy7A2NiYe87WrVvh4eFRZh9FWbZsGd6+fQsDAwMIBAIkJSVh8+bNWLhwIRYvXgwjIyP06dMHCQkJGD9+vEK2OXv2bJw6dQqNGzfGxIkTsWjRInz66afc8spuX19fHwcOHMCvv/4KPT09fPLJJ5g3b165XvPq1avRrFkztG7dGu3atYOSkhK6du36wdeioaGB69evw87ODp6enjAxMcHUqVPh4eFRYjyZ1KlTpxAYGIjr169DS0sLAoGA+4mOjub6+fj4oGPHjujYsSMcHR1hbGyM48ePl3n6tzLPedeUKVNw/vx53LlzB61bt4aenh6GDh2KqKgozJkzp1zrqCwBK+3EfD2SkZEBXV1dpKenK3xCV6D4XHlCQgJMTEy4SR+PXQ/E7M2HAQCNzQxxeeN8qKnWnskMayN5eSSVQ7lUjJrMY15eHsLDw2Fra1uxySDrAMYYxGIxlJWVa83M+jWtTZs2GDduHHcUpzIoj4qhqDyW9Z6tSN1Bn9DVZGjXNujoaAsAiIhLxo7jfvwGRAghhJBahwqxaiIQCLB28hAoK0kH7l/F65hEnqMihBBCSG1ChVg1src2w7SPigcKFoiLsGznsSrd6Z0QQkjd9OjRoyqdliT1FxVi1WzeyF6wNjEAANx+Foaj1x7yHBEhhBBCagsqxKqZukgVa6cM4R6v3HsKKRnZ/AVECCGEkFqDCrEa0KOtPT5ybwUASM3MwZrfz/AcESGktqLhC4TUDYp6r1IhVkO+/WwQtDVEAIAjV+7j9rMP34uLENJwqKgUT2+Tk5PDcySEkPKQvlel793K4vVekw2Jqb4Olo/thy9+Ow4AWLbzGC5smAeRCv0KCCHFN7jW09NDQkICgOIJM+vLXFE0/5ViUB4Vo6p5ZIwhJycHCQkJ0NPTK3HrsIqiKqAGje/dAX/5PUDgqyi8jknEjuN+mD/Sk++wCCG1hJmZGQBwxVh9wRiDRCKBUCikAqIKKI+Koag86unpce/ZqqBCrAYJhUJ8P20Y+i3eiiKJBFv/vorB7m3QxKLm7/ZOCKl9BAIBzM3NYWJigsLCQr7DURiJRILk5GQYGhrSnR6qgPKoGIrIo4qKSpWPhElRIVbDnBpbYMqgrvj5xDXkF4qx7NdjOPLNZPrrhhDCUVJSUtiHfG0gkUigoqICNTU1KiCqgPKoGLUtj/xH0AAt+NgTlsb6AICbT0Nx+PI9niMihBBCCB+oEOOBhpoq1k0dyj1ete804lIyeIyIEEIIIXygQownPdraY0T3dgCAjJw8fPHrPzR/ECGEENLAUCHGo28+HQgjXS0AwPl7z3Hy1hOeIyKEEEJITaJCjEcG2pr4bvJg7vFXu04gJZNuf0QIIYQ0FFSI8WxAx5bo18EJAJCckY1vfU7xHBEhhBBCagoVYjwTCAT4bvIQ6GioAQD+vvYQVx6+4DkqQgghhNQEKsRqAVN9HXzz6UDu8dKdx5CZk8djRIQQQgipCVSI1RKjerZH11Z2AIDYpHR4HzjHc0SEEEIIqW5UiNUSAoEA66cNh7qo+C7u+87dxp1nYTxHRQghhJDqRIVYLWJtaoBln/TlHi/Y/heyc/N5jIgQQggh1YkKsVrms36d4dqiMQAgMj4F3/1xlt+ACCGEEFJtqBCrZZSUhNg4a6TMKcobT17zHBUhhBBCqgPvhRhjDGFhYXjw4AESEhJK7RcVFYX79+8jI6P+35PR1twIX47rzz1euP0vuoqSEEIIqYd4LcSePHkCR0dHdO7cGVOmTIGtrS2GDx+O3Nxcrk9eXh6GDx8Oe3t7jB8/HmZmZti6dSuPUdeMiX07orNzUwBATFIaVu6liV4JIYSQ+obXQmz69OmwsbFBdHQ0Hjx4gODgYFy+fBnbt2/n+qxcuRIBAQEIDQ1FcHAwDh48iDlz5uDu3bs8Rl79hEIhfpo5AppqqgCAQ5fv4fIDmuiVEEIIqU94LcQSExPh6uoKZWVlAIC1tTUsLS2RmJjI9fHx8cGkSZNgbm4OABgyZAicnZ3h4+PDS8w1ycrEAF9P/G+i1yW//I20rBweIyKEEEKIIinzufFVq1Zh0aJFaNy4MWxsbHDhwgXk5ORgxowZAIDY2FjEx8fDxcVF5nlubm4IDAwsdb35+fnIz/9v2gfpuDKJRAKJRKLw1yGRSMAYq5Z1j+nVHmfuPMW1x68Ql5KBFbtOYPOcUQrfTm1QnXlsaCiXikF5VAzKo2JQHhWjJvJYkXXzWoj17NkTbm5uWL58OSwtLREWFoZly5bB2toaAJCSkgIAMDQ0lHmeoaEht0web29vrFy5skR7YmIi8vIUP+hdIpEgPT0djDEIhYo/yLh0pAcehLxBVm4+jt14hM4OVujR2k7h2+FbdeexIaFcKgblUTEoj4pBeVSMmshjZmZmufvyVogxxtCvXz9ujJiqqiqioqLg5uYGsViMr776CioqxVM4vF885ebmQlVVtdR1L1++HAsWLOAeZ2RkwMrKCsbGxtDR0VH4a5FIJBAIBDA2Nq6WX6qJiQlWfT4IC7YfBQB4H76CXm6tYKSrpfBt8am689iQUC4Vg/KoGJRHxaA8KkZN5FFNTa3cfXkrxGJjY/Hw4UOsWbOGK6qsrKzw0UcfwdfXF1999RWsrKwgFAoRExMj89yYmBjuqJk8IpEIIpGoRLtQKKy2pAsEgmpd/8c92uNcwHNcuPccyRnZWPLLMfgsmwiBQFAt2+NLdeexIaFcKgblUTEoj4pBeVSM6s5jRdbL22/SwMAAQqEQ0dHRMu1RUVEwNjYGAGhoaKBz587w9fXllmdnZ+PSpUvw8vKq0Xj5VnwvymEw1NEEAFy8H4wDFwN4jooQQgghVcHbETF1dXVMnjwZX3zxBYqKitCkSRNcuHAB586dw+nTp7l+a9asgZeXF5YvX45OnTph69atMDExwZQpU/gKnTfGetr4ccYIfLZuHwDg270n0cm5CZpaGPMcGSGEEEIqg9djm9u3b8f69evh5+eHH374AWlpabh16xb69evH9fHw8MDVq1cRGRmJzZs3w8nJCf7+/tDSql/jo8qrt6sjxvXuAADIzS/EnM2HUSgu4jkqQgghhFQGr1dNKikp4bPPPsNnn31WZj93d3e4u7vXUFS13zcTB+JWUCjCYpPw6HU0Nv51CUvG9OE7LEIIIYRUEI32q4M01FSxbe4YKCsV//q2HruKey8i+A2KEEIIIRVGhVgd1drOEgs+Lr5gQSJhmLP5CN0YnBBCCKljqBCrw2YN7Q7XFo0BAG8SUvD1Ht8y+xNCCCGkdqFCrA5TUhJiy5xR0FIvnjPtz6sPcOr2E56jIoQQQkh5USFWx1mbGmD1/wZzj5f8fAzRCak8RkQIIYSQ8qJCrB4Y2b0dBnVuBQBIz87FzE2HIC6iKS0IIYSQ2o4KsXpAOuu+lYk+AOD+y0hsOHKJ56gIIYQQ8iFUiNUTOprq2D5/DJSE/01p4f/0Nc9REUIIIaQsVIjVIy7NbbD0k+KJXRljmL3pMJLSs3iOihBCCCGloUKsnpk+uBu6tW4GAEhIy8T8rX9CIpHwHBUhhBBC5KFCrJ4RCoXYPHsUjHSL78V5JfAlfjvlz3NUhBBCCJGHCrF6yERfG1vmjOIeex84h8evo3mMiBBCCCHyUCFWT3m0aY7pgz0AAIXiIszYeJBugUQIIYTUMlSI1WNLxvRG22ZWAICIuGQs3HEUjDGeoyKEEEKIFBVi9ZiqijJ2zP8EOhpqAIDTt59iz5lbPEdFCCGEECkqxOo5a1MDbJr9Mfd49f7TeBASyWNEhBBCCJGiQqwB6OPmhGkfdQNQPF5s2oYDSMnM5jkqQgghhFAh1kAsG9sXbg6NAQCxSemYu/kIzS9GCCGE8IwKsQZCRVkJO+Z/AkMdTQDF84ttPebHb1CEEEJIA0eFWANibqiLbfPGQCAQAAB+PHIBN5+G8hwVIYQQ0nBRIdbAdGvdDAs+7gUAkEgYZm46iPjUDJ6jIoQQQhomKsQaoLnDe3H3o0xMy8L0DQdRKC7iOSpCCCGk4aFCrAFSUhJi29zRMDPQAQDcDQ7H6n2neY6KEEIIaXioEGugDHW18OvicVBRVgIA7D5zE0f9HvIcFSGEENKwUCHWgLk0t8Ga/w3mHi/d+TeehsXwGBEhhBDSsFAh1sCN690Bn3i6AgDyCsSYtP53pGTQZK+EEEJITaBCjGDNpCHczcGjE1MxY+NBiIto8D4hhBBS3agQIxCpKOPXxeNgpKsFALjx5DW+P3ie56gIIYSQ+k+Zz43fvn0bRXKOvJiZmcHOzk6mLSoqCvHx8WjevDl0dHRqKsQGw8JQDzsXjsWolb9BXCTBjuPX0KqpJQZ1bsV3aIQQQki9xWsh9s033yAnJ4d7XFBQgHv37mH58uVYu3YtACAvLw9jx47F2bNnYWNjg8jISHz//feYPXs2X2HXWx2dmuDriQPx9R5fAMCC7X/BrpExHGzMeY6MEEIIqZ94PTV54cIF+Pv7cz/z588HAEycOJHrs3LlSgQEBCA0NBTBwcE4ePAg5syZg7t37/IVdr32ef/OGO7RDgCQk1eAz9bto8H7hBBCSDWpVWPEdu/ejW7dusHe3p5r8/HxwaRJk2BuXnxUZsiQIXB2doaPjw9fYdZrAoEA308dhlZNGwEAohJSMeXHP1BQKOY5MkIIIaT+4fXU5LsiIiJw5coV7N+/n2uLjY1FfHw8XFxcZPq6ubkhMDCw1HXl5+cjPz+fe5yRUXwvRYlEAolEouDIi9fLGKuWdfNBpKKEXYvHY+Cy7UhIy8TtZ2H4atcJeE8Zwt0wvDrUtzzyiXKpGJRHxaA8KgblUTFqIo8VWXeFC7GHDx/i8OHDuH79OqKjowEAVlZW6NatG8aMGYM2bdpUdJUAgD179kBPTw8jRozg2lJSUgAAhoaGMn0NDQ25ZfJ4e3tj5cqVJdoTExORl5dXqfjKIpFIkJ6eDsYYhMJadZCx0pQArJ80AFM2/YUCcREOXApAI31NjOreptq2WR/zyBfKpWJQHhWD8qgYlEfFqIk8ZmZmlrtvuQuxwMBAzJ8/H3fu3EHnzp3h4eEBU1NTAEB8fDwCAgKwadMmdO7cGT/99BPatm1b7iAkEgn27t2LcePGQU1NjWtXUVEBgBLFU25uLlRVVUtd3/Lly7FgwQLucUZGBqysrGBsbFwtV1xKJBIIBAIYGxvXqzdHLxMT/DBdgrlb/wQAbPj7Gtq0aIKurew+8MzKqa955APlUjEoj4pBeVQMyqNi1EQe361lPqTchdigQYOwePFi/PPPP9DX15fbJyUlBb///jsGDRrEHS0rjwsXLiAqKgqTJ0+WabeysoJQKERMjOxtd2JiYmBtbV3q+kQiEUQiUYl2oVBYbUkXCATVun6+jOjugpCoBGw/7ociiQTTfzqIU+tmoYmFUbVsr77mkQ+US8WgPCoG5VExKI+KUd15rMh6y90zJCQEc+fOLbUIAwADAwPMnTsXISEh5Q4AAHbt2oUOHTqgZcuWMu0aGhro3LkzfH19ubbs7GxcunQJXl5eFdoGqbyln/SBp4sDACA9OxefrduLjOxcnqMihBBC6r5yF2IaGhrlXmlF+iYlJeHkyZMljoZJrVmzBsePH8fy5cvh6+uLIUOGwMTEBFOmTCn3NkjVKCkJsW3eaNhbFZ+Kfh2TSLdBIoQQQhSgQsfkoqKiMHfu3FKXz507F1FRURUK4NatW+jUqRNGjRold7mHhweuXr2KyMhIbN68GU5OTvD394eWllaFtkOqRltDDT7LJkJfu7jIvhoYghW7fcEY4zkyQgghpO6qUCH2/fffw8HBodTlDg4OWL9+fYUC+Oijj+Dn51dmYeXu7o6DBw/i8uXL2LRpE8zMzCq0DaIYNmaG+G3xeKgoKwEA9p+/g19P3uA5KkIIIaTuqlAhdvHiRXh6epa6vFevXrh48WKVgyK1VyenJvhx+n9TjKzefwZn7wbxGBEhhBBSd1WoEIuMjCzzakVra2tERERUNSZSy43o3g4LPi4uyBljmLXpMB69rtgpaUIIIYRUsBDT1tZGbGxsqctjY2OrZZ4uUvss+NgTw7oVzxWXV1CIT733IjohleeoCCGEkLqlQoWYu7s7du7cWerynTt3okuXLlUOitR+AoEAP84YgQ4OtgCAxLQsTFjrQ9NaEEIIIRVQoUJs6dKl2LBhA2bOnInQ0FDu3o2hoaGYOXMmNm7ciGXLllVXrKSWEakoY9fS8bA1L57c9WVUPKb8+AcKxTStBSGEEFIeFSrEOnXqhP379+P333+HnZ0d1NXVoaamBjs7O/zxxx/4448/4ObmVl2xklrIQFsTv3/5GTetxY0nr7F05zGa1oIQQggphwrf9Hv06NHo06cPTp06hZCQEAgEAjRr1gyDBg2Cnp5eNYRIajtbcyPsWToBo779DQXiIhy5ch9mBjpYMqYP36ERQgghtVqFCzEA0NfXx/jx4xUdC6nD3BxssWXuaEz/6SAYY9h89ArMDHQxoU9HvkMjhBBCaq0K3+3y9u3buHXrVnXEQuq4QZ1bYeVng7jHX+46jnN3n/EYESGEEFK7VagQW7FiBZYsWYJly5bhq6++qq6YSB32vwHumDHEAwAgkTDM3HQQ915E8BsUIYQQUktVqBDbtm0bTpw4gePHj2P79u3VFROp45aP7fvOHGNifOq9FyFR8TxHRQghhNQ+FSrEDA0NERERgbCwMBgYGFRXTKSOEwqF2DBjBDxaNwMApGXlYuya3XibnM5zZIQQQkjtUqFC7JdffsHo0aMxevRo/Pzzz9UVE6kHVFWU8evi8WjZpBEAIDYpHePX7EFaVg7PkRFCCCG1R4UKMU9PT4SEhOD169fo3bt3dcVE6gktdRH2f/EZrE2Kj54Gv4nDxLV7kZNXwHNkhBBCSO1Q4asmCakIE31tHFjxPxjpagEA7r+MxOQffkdBoZjnyAghhBD+lbsQ69GjB27evPnBfjdu3ED37t2rEhOpZ5pYGOHAiv9BR0MNAOD3KASzNx9GUZGE58gIIYQQfpV7QtdPP/0UI0aMgJGREQYNGgQXFxeYmpqCMYa4uDjcu3cPJ0+eRFpaGry9vaszZlIHOdtaYN8Xn2LMqt3IKyjEqdtPoav5D76fNgwCgYDv8AghhBBelLsQmzhxIkaOHIk//vgDhw8fxsaNG5GXlwcAUFNTQ+fOnbFw4UKMHTsW6urq1RYwqbvcHGzx2+Jx+GzdPoiLJDhwKQC6Wur4cnx/vkMjhBBCeFGhWxxpaGhgypQpmDJlCiQSCZKSkiAQCGBoaAihkIabkQ/r2a4FtswdjZkbD4Exhh3Hr0FPSwMzh3bnOzRCCCGkxlXqXpNA8VxRJiYmioyFNBCD3VsjIzsXy3b+AwBY+8dZaGuoYZyXG8+REUIIITWr0oUYIVUxvndHpGflwvvAOQDA8l//gUhFCR6OVjxHRgghhNQcOp9IeDNrWA/MHNKde7xox984d/8FfwERQgghNYwKMcKr5eP64n8D3AEAEsbw9b5zOHMniOeoCCGEkJpBhRjhlUAgwMrPBmF8744AgCIJw8xNh3Dh3nOeIyOEEEKqX6ULsYSEBOzcuRNLly7l2m7evAmxmGZMJxUjEAiwdvJgjOzuAgAQF0kw9cc/cO1RCM+REUIIIdWrUoXYw4cP4eDggO3bt2P9+vVc+4EDB7B3715FxUYaEKFQiB+mDUOf9vYAgAJxET7/fh9uBYXyHBkhhBBSfSpViC1cuBDLli3DkydPZNqnTp2KTZs2KSIu0gApKQmxakJf9O/gDADIKxBjovde3H0eznNkhBBCSPWoVCH24MEDTJs2DQBkbk9jZ2eHkBA6nUQqT1lJiK1zR8GrvQMAICevAOO+24Pbz8J4jowQQghRvEoVYioqKsjIyCjRHhwcDCMjowqvr6ioCEFBQQgLK/3LNioqCvfv35e7XVK/qKooY+eicejZtvg0ZU5eAcZ/twc3n9JpSkIIIfVLpQqxAQMG4JtvvkFRURF3RCwsLAzTpk3DRx99VKF1HTt2DJaWlhg8eDAGDx4MLy8vJCUlccvz8vIwfPhw2NvbY/z48TAzM8PWrVsrEzapQ0Qqyti1dAJ6ubQAAOTmF2LCWh/4P33Nc2SEEEKI4lSqENuwYQPu378PU1NTSCQSODg4oHnz5igqKoK3t3e513P9+nWMHDkS3333HUJDQ/H06VN8+eWXiI+P5/qsXLkSAQEBCA0NRXBwMA4ePIg5c+bg7t27lQmd1CEiFWX8tng8d5oyr6AQE9f64PrjVzxHRgghhCiGgDHGKvNEsViMkydP4v79+5BIJGjXrh2GDBkCFRWVcq+jZ8+eUFFRwfnz50vtY2ZmhunTp+Obb77h2lq2bAl3d3f88ssv5dpORkYGdHV1kZ6eDh0dnXLHV14SiQQJCQkwMTGhm59XQWl5LCgUY9qGAzj/79xiaqrK2LN0IjzaNOcr1FqP9knFoDwqBuVRMSiPilETeaxI3VGpe016eXnh4sWLGDp0KIYOHVqpIPPz8+Hv74+ffvoJmZmZCAkJgYWFBczNzbk+sbGxiI+Ph4uLi8xz3dzcEBgYWOa68/PzucfScWUSiQQSiaRS8ZZFIpGAMVYt625ISsujspIQO+aPwYyNh3D+3nPkFYjx2bp9+G3xOPT4dxwZkUX7pGJQHhWD8qgYlEfFqIk8VmTdlSrE7ty5g+zsbGhqalbm6QCApKQkFBYW4smTJ7C3t4eZmRlev36NTp064eDBgzA0NERKSgoAwNDQUOa57y6Tx9vbGytXrizRnpiYiLy8vErHXBqJRIL09HQwxuivlCr4UB5XjvdEYWEBrjx6jfxCMf63/nd4f94fPVrb8RBt7Ub7pGJQHhWD8qgYlEfFqIk8ZmZmlrtvpQqxvn374siRI/j8888r83QA4E5hXrx4EY8ePYKJiQmSk5PRqVMnLFq0CD4+Plyf94un3NxcqKqqlrru5cuXY8GCBdzjjIwMWFlZwdjYuNpOTQoEAhgbG9ObowrKk8ddSz/F7M2HcfpOEArFRVi66zQ2zhqJoV3b1GywtRztk4pBeVQMyqNiUB4VoybyqKamVu6+lSrE9PX1MXnyZBw7dgyOjo4liqI1a9Z8cB1GRkbQ1NTEsGHDYGJiAqD4SNfIkSNx5MgRAICVlRWEQiFiYmJknhsTEwNra+tS1y0SiSASiUq0C4XCaku6QCCo1vU3FB/Ko0hViB0LPsH8bX/h2PVAFEkkmLv1T+QVFGKsV4cajrZ2o31SMSiPikF5VAzKo2JUdx4rst5KFWIhISHo2rUrsrKyEBAQUJlVQCgUwsvLq0SRFR0dDWNjYwCAhoYGOnfuDF9fX4wbNw4AkJ2djUuXLuHbb7+t1HZJ3aespITNsz+Ghpoq/rhwF4wxLPnlGHLyCzB5YFe+wyOEEELKrVKFmJ+fn0I2vmrVKri7u+Obb76Bu7s77t69i4MHD+LPP//k+qxZswZeXl5Yvnw5OnXqhK1bt8LExARTpkxRSAykbhIKhVg3ZSg01VSx0/cGAOBbn1PIzivA3OE9Ze74QAghhNRWvB7bbNmyJW7duoXo6GisX78e4eHhuHbtmsyVmB4eHrh69SoiIyOxefNmODk5wd/fH1paWjxGTmoDgUCAFRMGYOEoT67th0MXsPaPs6jkrCyEEEJIjarUETHpfSZLU975vQDA2dkZu3fvLrOPu7s73N3dy71O0nAIBAIs+NgLGmoirN53GgCw4/g1pGfnwnvyUCgp0TgKQgghtVelCrF3b0EEFF+B8OrVKwQFBaF///4KCYyQipj2UTdoiFSx/Nd/AAAHLgYgNSMHW+eNhppq+ScZJoQQQmpSpQqxo0ePym3/9ttvkZaWVpV4CKm0CX06QltDhHlb/4S4SIIzd4OQumYP9iydAB1Ndb7DI4QQQkpQ6HmbuXPn4tixY4pcJSEVMrRrW+xb/ik01IqnVLn9LAzDv96JhNTyT65HCCGE1BSFFmKJiYkVmk2WkOrQva09/vx2CvS1NQAAzyPeYsiXOxARl8xzZIQQQoisSp2a3LRpU4m21NRU/PHHHzRGjNQKbZtZ4fia6fhk9W7EJKUhMj4Fg7/YgQNffQ7nJo34Do8QQggBUMlCbNeuXSXa9PX1MWrUKCxfvrzKQRGiCHaWJjixdgbGrt6Nl1HxSErPwvCvd2L30gno0pLuT0kIIYR/lSrEjh8/Djs7+V9kr1+/hra2dpWCIkRRzA11cWzNNHzqvQ/3XkQgKzcf49fswZa5ozGocyu+wyOEENLAVWqMWLNmzSq1jBA+6Glp4NDX/4OniwMAoEBchGkbDuDn49do4ldCCCG8Uuhg/ezsbGhoaChylYQohLpIFbuXjseonu25tjW/n8HyX49DXFTEY2SEEEIasgqdmly0aJHc/wPFk7oGBgaibdu2iomMEAVTVlLChhkjYGWijx8PXwQA/H7hDmISU/HzwrHQUhfxHCEhhJCGpkKFWFBQkNz/A4CKigqcnZ0xf/58xURGSDUQCASYP9IT1iYGWLjjKArFRbgS+BJDv/oZ+7/4DOaGunyHSAghpAGpUCF27tw5AMC4cePwxx9/VEtAhNSE4R7tYGGkh0nr9yMtKxfPI95i4LJt2P/lZ3BqbMF3eIQQQhqISo0RoyKM1AednJrgxHczYG1iAACIS8nA0C9/xtXAlzxHRgghpKGo1PQVAFBUVISXL1/izZs3EIvFMssGDhxY5cAIqQl2liY4uW4mPvXei8BXUcjOK8DEtXvx3eTBGN+7I9/hEUIIqecqVYi9fv0aw4YNw7NnzyCRSKCkpISif688E4lEyMvLU2iQhFQnI10t/LVyCuZsPoIzd4NQJJFg2c5/EBIVj28+HQhlJSW+QySEEFJPVerU5Lx589CpUyfuvpJ5eXm4e/cuWrVqhR9//FGhARJSE9RFqti5aCymftSVa9tz5hbGrdmD1MwcHiMjhBBSn1WqELt9+zZWrVrFzRnGGIObmxv279+PjRs3KjRAQmqKUCjE1xMH4sfpw6GiXHwU7MaT1xi4bBteRcfzHB0hhJD6qFKFWEpKCkxNTQEARkZGiI8v/pKys7NDdHS04qIjhAdjPN3w57eTYaijCQCIiEvGwGXbcfnBC54jI4QQUt9UeWZ9V1dXrF+/HhEREVi3bl2p96AkpC5xc7DFme9nw7GxOQAgKzcfE7330m2RCCGEKFSlCrH//e9/3P+9vb1x7Ngx2NraYuvWrXRqktQblib6OPHdDPTv6Ayg+BT8mt/PYO7WP5FXUMhzdIQQQuqDShViu3bt4v7funVrvHnzBuHh4YiPj0fv3r0VFhwhfNNQU8XOhWOxcJQn1/b3tYcY8fVOvE1O5zEyQggh9UGlCjEvLy/ZlQiFaNy4MUQiulcfqX+EQiEWfOyFnYvGQl2kAgAIfBWFvou34PazMJ6jI4QQUpdVqhC7c+cOsrOzFR0LIbXawE6tcPy7GWhkpAcASErPwqhvf8NO3+s0bowQQkilVKoQ69u3L44cOaLoWAip9ZxtLXDuhzno1roZAKBIIsGqfacx/aeDyM7N5zk6QgghdU2lZtbX19fH5MmTcezYMTg6OkJVVVVm+Zo1axQSHCG1kYGOJv748nP8eOQitvx9BQBw8tYTvHgTh11LJsCukTHPERJCCKkrKlWIhYSEoGvXrsjKykJAQICiYyKk1lNSEmLpJ33QtpkV5mw5jMycfLyKTsCApVuxafbH6NfBme8QCSGE1AGVKsT8/PwUHAYhdVNvV0ec+X4OJv/wO168iUNWbj4mrf8dM4d0x5JPetN9KgkhhJSpyhO6EtLQNbEwwknvmRjSpQ3Xtv24H0Z9+xtNcUEIIaRMlS7Ejh49in79+sHe3p5r8/b2RmJiYrnXERoaCn9/f5mfwMBAuX2joqJw//59ZGRkVDZkQqqNhpoqts0bjVWffwRlpeK31Z3n4ei9aDOuBr7kOTpCCCG1VaUKsT179mDatGlwdXVFSEgI166trQ1vb+9yr+eHH37AkCFDsGzZMu7n/Zn58/LyMHz4cNjb22P8+PEwMzPD1q1bKxM2IdVKIBDgfwPccXTVVJgb6gIAUjKyMW7NHqz9/SwKxUU8R0gIIaS2qVQh9uOPP+Lo0aNYtWqVTPvAgQNx+PDhCq2re/fuMkfE9u/fL7N85cqVCAgIQGhoKIKDg3Hw4EHMmTMHd+/erUzohFQ71xaNcWHDXHi6OHBt24/7YcTXOxGTmMpjZIQQQmqbShViYWFh6NChA4DiowBS+vr6SE5OrtC68vLy8PDhQ4SGhkIikZRY7uPjg0mTJsHcvPjmy0OGDIGzszN8fHwqEzohNcJAWxN7l0/E1xMHcKcq77+MRO9Fm3Hh3nOeoyOEEFJbVOqqSQsLCzx//hwuLi4yhdi5c+fQtGnTCq3r/PnzePPmDeLi4iASibBz5070798fABAbG4v4+Hi4uLjIPMfNza3UsWQAkJ+fj/z8/ybXlI4rk0gkcou9qpJIJGCMVcu6G5L6mMfJA7ugvb0NZm48hKjEVKRl5eKzdfswaYA7lo/tC1WVSr0FP6g+5pIPlEfFoDwqBuVRMWoijxVZd6W+BaZOnYrPP/8cmzdvhkAgwMuXL3Hu3Dl88803WL16dbnX06dPH6xatQomJiYoKirC8uXLMXLkSDx58gRNmzZFSkoKAMDQ0FDmeYaGhtwyeby9vbFy5coS7YmJicjLyyt3fOUlkUiQnp4OxhiEQroQtbLqax4b6Yrw+5LRWHXgIq48eg0A2HX6JvyfvMJ3n/VDY1MDhW+zvuayplEeFYPyqBiUR8WoiTxmZmaWu6+AVeImeYwxfPXVV9i4cSNyc3MBACKRCIsWLcLq1atljpJVRFFREQwNDfHNN99g/vz5ePnyJVq0aIErV66gR48eXL/Zs2fjypUrePbsmdz1yDsiZmVlhdTUVOjo6FQqtrJIJBIkJibC2NiY3hxVUN/zyBjDvnO3sXr/GRT8O3BfTVUFX08cgHFebpV+38hT33NZUyiPikF5VAzKo2LURB4zMjKgr6+P9PT0D9YdlToiJhAI8N133+HLL7/Es2fPIJFI4OjoCG1t7UoFLKWkpARDQ0PExMQAAKysrCAUCrnHUjExMbC2ti51PSKRCCKRqES7UCistqQLBIJqXX9DUd/z+PmALnB1sMXMjYcQGpuIvIJCfPHbcVwNfIkNM0bAUFdLYduq77msKZRHxaA8KgblUTGqO48VWW+VItDQ0ICjoyOcnZ0rXIQxxrijaVKvXr1CZGQknJ2dufV37twZvr6+XJ/s7GxcunQJXl5eVQmdEN60bNII53+cg/G9O3JtF+8Ho9eCjbjy8AWPkRFCCKlplSrEJBIJNm3aBBsbG2hpaUFLSwuNGzfGli1byj1ArbCwEC4uLvjpp59w/vx5/Pbbb+jduzfatWuHMWPGcP3WrFmD48ePY/ny5fD19cWQIUNgYmKCKVOmVCZ0QmoFdZEq1k0dCp9lE2GoowkASEzLwvjvfLBi9wnk5hfyHCEhhJCaUKlCbPny5VizZg2mT5+OS5cu4dKlS5g2bRpWrVqFr776qlzrUFVVxeXLl5GUlIRNmzbh6tWrWLJkCW7evClzWtHDwwNXr15FZGQkNm/eDCcnJ/j7+0NLS3GncAjhS29XR1z6aT56tv3vDhV7ztzCgKVb8SwilsfICCGE1IRKDdY3MDDA33//LTOAHgCuXLmCkSNHVnguseqWkZEBXV3dcg2aqwyJRIKEhASYmJjQefsqaMh5/G8g/2nkFYgBACrKSpg/0hMzh3pU+ObhDTmXikR5VAzKo2JQHhWjJvJYkbqjUhEoKSmhXbt2JdpdXFxo5yCkEgQCAT7t1xln18+BY+PiyYsLxUVYf+g8Plq+AyFR8TxHSAghpDpUqmry8PDArl27SrTv2rUL3bt3r2pMhDRYza1McWrdLMwa1gNCYfF0Fo9Do9Fn0WbsOO6HoiKayJEQQuqTSk1fYWBggEWLFuHvv/+Gq6srGGO4f/8+bt++jcmTJ8uME1uzZo3CgiWkIRCpKGP52L7o6+aEeVuP4HVMIgrERfju97M4e/cZNs76GHaNjPkOkxBCiAJUqhALCQmBh4cHAODx48cAigffe3h4ICQkBCEhIYqLkJAGqm0zK5z7YS5+PHwBO0/eAGMMD0PeoM+iTVj6SV/8r787lJRoKAAhhNRllSrE/Pz8FBwGIUQedZEKVkwcgL4dnDBv65+IiEtGXoEYK/eewtm7Qfhh+gg6OkYIIXUY/TlNSB3g2qIxLv00D//r7861BQRHoPfCTdh89AoKCsU8RkcIIaSyKnVEDCg+PXn79m2kpqaWWDZv3ryqxEQIkUNdpIpV//sI/To6Y+H2vxAZn4L8QjHWHzqPkzcf44cZI9C2mRXfYRJCCKmAShViP//8M2bNmgVzc3Po6emVWE6FGCHVp5NTE1zeOB8/Hr6IX0/dgETCEPwmDh99sR2f93fHktG9oS5S4TtMQggh5VCpQmz16tU4ePAgRo0apeh4CCHloC5SxYqJAzC4S2ss+vlvPAuPhUTCsOuUP87dfQbvKUPgaKHHd5iEEEI+oFJjxNLT0zFw4EBFx0IIqaBWTS1xet0sfDGuH9RUi/+uik5MLb5n5d6zSE7P4jlCQgghZalUIdarVy+cP39e0bEQQipBRVkJM4d2x6Wf5qOzc1Ou/cy9F/CY+xN+v3AHEglNBEsIIbVRpU5Nbtu2DR06dICvry+aNm0KgUAgs7y8N/4mhCiOrbkR/vx2Mo5cuY9V+04hPTsP6dm5WLbzHxy5ch/eU4aiZZNGfIdJCCHkHZUqxLZs2YK4uDjcuXMHL168KLGcCjFC+CEQCDC6lyt6tG2OFb/9g9MBwQCAwFdR6L90Kyb26YTFY3pDV1Od50gJIYQAlSzEdu/eDV9fXwwaNEjR8RBCFMBYTxurJvbFxP5d8NWuEwiJToBEwuBz9hZO3X6CrycOxNCubUoczSaEEFKzKjVGTFlZGT179lR0LIQQBevk1ATnf5yLL8f346a0SEzLwuzNhzHym18REhXPc4SEENKwVaoQ69SpE3x9fRUdCyGkGqiqKGPGkO64tnkh+ndw5tpvPwuD54JN+Hq3L9KycniMkBBCGq5KnZo0MDDAhAkTcPz4cdjZ2ZU4vbFmzRqFBEcIUZxGxvr4bcl4XH7wAit2n0BkfAqKJBLsPnMTx24EYvHo3hjr5QZlJSW+QyWEkAajUoVYREQE3N3dER8fj/h4OrVBSF3Sy6UFOjs3xc6T17Ht2FXk5hciNTMHX/x2HL9fuIuVnw2Ce8umH14RIYSQKqtUIebn56fgMAghNUldpIJ5I3rh4x4u8P7jHI5dDwQABEe+xcff/or+HZ2xYsIAWJsa8BwpIYTUb5UaI0YIqR8sDPWwde5oHP9uOlo3teTaz9wJQve5G7DuwDlk5uTxGCEhhNRvlS7Ejh49in79+sHe3p5r8/b2RmJiokICI4TUHNcWjXFq3Uz8NHMEjPW0AAD5hWJsPXYV7jPXY+/ZWygUF/EcJSGE1D+VKsT27NmDadOmwdXVFSEhIVy7trY2vL29FRYcIaTmCIVCjOrpihtbF2PGEA+oKBcP2k/OyMaXu06g5/yfcO7uMzDGeI6UEELqj0oVYj/++COOHj2KVatWybQPHDgQhw8fVkhghBB+aGuo4cvx/XFt80J85N6Kaw+LTcL/1u/HsBW/4GHIGx4jJISQ+qNShVhYWBg6dOgAADJTV+jr6yM5OVkxkRFCeGVjZoifF4zFqXWz0MHBlmsPCI7AoOXbMW3DAUTE0fudEEKqolKFmIWFBZ4/fw5AthA7d+4cmjaly94JqU/aNrPC36unYs/SCWhqYcy1n7z1BN3nbsAXvx1HfGoGjxESQkjdValCbOrUqfj888/h5+cHgUCAly9fYvPmzZg6dSqmT5+u6BgJITwTCATo4+aEyxvnY+3kITDSLR7QXyguwr5zt9F5xnp89/sZpGRm8xwpIYTULRWaR0xPTw9paWlYsmQJMjIy0L9/fxQVFaFFixYQiURYtGgRZs2aVV2xEkJ4pqKshIl9O2G4Rzv8fPwafj11Azl5BcgrKMSO49fw+4U7mPpRN0we2BVa6iK+wyWEkFpPwCpwCZRAIJC5YionJwfPnj2DRCKBo6MjtLW1qyXIqsrIyICuri7S09Oho6Oj8PVLJBIkJCTAxMQEQiFNzVZZlEfFqalcJqVnYduxq9h//g7yC8Vcu4GOJmYP64EJfTpCTVWl2rZf3WifVAzKo2JQHhWjJvJYkbqjShFoaGjA1dUVHTp0qHIRlp6eDn9/f4SHh8tdHhUVhfv37yMjg8aiEFJbGOlq4dvPBuHGtsUY6+kGpX8/1FIysrFy7yl0mfUD9p67LVOkEUII+U+Fb3F0/PjxD/YZMmRIhdbJGMPYsWNx9uxZzJ49G5s2beKW5eXlcctsbGwQGRmJ77//HrNnz65Y4ISQatPISA/rpw/HtMEe+PHwBZy4+RgA8DY5HV/+dhxb/76CWUN7YIyna50+QkYIIYpW4UJs6NChH+xT0QkfN27ciKKiIjg7O5dYtnLlSgQEBCA0NBTm5uY4fvw4hg4dCjc3N24KDUJI7dDEwgg7FnyCmcO6Y/3BC7j0IBgAEJeSga92n8C2f65ixpDu+MTTDeoiKsgIIaTCpyYTExM/+FMRDx48wE8//QQfHx+ZqTCkfHx8MGnSJJibmwMoPtrm7OwMHx+fioZOCKkhTo0tsO+LT3Hm+9nwau/AtcelZODrPb5wn/k9fjt1A7n5hTxGSQgh/KvwETEjIyOFbTwzMxOjR4/G9u3bYWZmVmJ5bGws4uPj4eLiItPu5uaGwMDAUtebn5+P/Px87rF0XJlEIoFEIlFQ9P+RSCRgjFXLuhsSyqPi1JZctmxigT1LJ+BpWAw2Hb2CC/eK5x+MT83Etz6nsP2YH6YN7obxvTtAXaTKa6zy1JY81nWUR8WgPCpGTeSxIuuucCGmSNOnT0evXr0wePBguctTUlIAAIaGhjLthoaG3DJ5vL29sXLlyhLtiYmJyMvLq0LE8kkkEqSnp4MxRleyVAHlUXFqWy5NtVTg/WkffNqrLX47exdXH78GACSmZ2H1/jPY/o8fxvRoi5FdW0FbQ43naP9T2/JYV1EeFYPyqBg1kcfMzMxy961QITZgwIAKB1MaX19fnDp1Cn/++Sf8/f0BANnZ2YiNjYW/vz+6dOkCFZXiMSTvF0+5ublQVS39r+fly5djwYIF3OOMjAxYWVnB2Ni42qavEAgEMDY2pjdHFVAeFae25tLExARdXZwRHPkWm49ewek7QQCAlMwcbPe9iX0X72OcVwf8b4A7zAwU/16tqNqax7qG8qgYlEfFqIk8qqmV/w/KChVip06dqnAwpRGLxXB2dpa5cfjbt2+Rk5OD2NhYXLt2DVZWVhAKhYiJiZF5bkxMDKytrUtdt0gkgkhUcjJJoVBYbUkXCATVuv6GgvKoOLU5l062jfDr4vF48SYOm49exqnbTyGRMGTl5uMX3+vYc+Ymhnu0w7TBHrBrZPzhFVaj2pzHuoTyqBiUR8Wo7jxWZL28/SaHDRsGf39/mR87OzuMHDkS/v7+UFJSgoaGBjp37gxfX1/uednZ2bh06RK8vLz4Cp0QoiAtrM3w84KxuL5lEcb17gCRSvHfhgXiIhy6fA/d527A5PW/I/BVFM+REkJI9aj1JfWaNWtw/PhxLF++HL6+vhgyZAhMTEwwZcoUvkMjhCiIrbkRvp86DHd+XoZZQ7tDW6P4iDZjDGfuBmHgsm0Y+c2v8At8WeHpcQghpDarVYVY27Zt0aRJE5k2Dw8PXL16FZGRkdi8eTOcnJzg7+8PLS0tnqIkhFQXE31tLB/XDwG/LMeX4/vBRO+/O3bcCgrF2DV70HPeTzhw8S5NfUEIqRcqdK/JuoruNVk3UB4Vp77kMq+gEH9fe4ifT1xH+NskmWUGOpoY37sDJvbtBFP96hnYX1/yyDfKo2JQHhWjXt1rkhBCqpOaqgrGenXAtc0L8euicXBt0ZhblpKRjc1Hr6DDtHWYs+UInobFlL4iQgippXidR4wQQspDSUmIAZ1aYkCnlnj0Ogq7Tvnj5K0nEBdJUCguwt/XHuLvaw/R0dEWkwd2hVd7Bygp0d+ZhJDajwoxQkid0sbOCtvmjcGX4/tj77nb+OPCXaRl5QAA7jwPx53n4bA2McD4Ph0wuqcrDHQ0eY6YEEJKR38yEkLqJHNDXSwf2xf3f12OdVOHysw39iYhBd/9fhbtp6zFnC1H8CAkkq62JITUSnREjBBSp6mLVDG+d0eM9XTDtcevsOuUP/wehQAA8gvF3GlLZ1sLTOzbCUO6tIGGWu27ryUhpGGiQowQUi8IhUL0aGuPHm3tEf42Cb9fuIMjV+4jLSsXABAUHovFP/+N1ftOY2QPF0zo04n3WfsJIYROTRJC6h1bcyN8PXEg7v/6JX6aORJt7Cy5ZRk5edh9+iY85vyIkd/8in9uBCKvgOYkI4Twg46IEULqLXWRCkb1bI9RPdvj0eso7D9/Byf8HyGvQAygeJLYW0Gh0NNSx7BubTGmlxscG5vzHDUhpCGhQowQ0iC0sbNCGzsrrJgwAH9evY/fL9zlJolNy8rFnjO3sOfMLbSxs8ToXq4Y0qUNNGksGSGkmlEhRghpUPS1NTD1o26YMqgr7j4Px8HL93D69hPuKNmj19F49DoaK/eewsBOrdC3XVN4GdNYMkJI9aBCjBDSIAkEAnR0aoKOTk2w+n8f4fiNRzh0+R43Q39ufiH+8nuAv/weoIn5FYzo7oLh3drC0kSf58gJIfUJFWKEkAZPV1MdE/t2wsS+nRAUFoNDl+/h2PVAZOTkAQDC3iZh/aHzWH/oPDo5NcEIj3YY0KkltDXUeI6cEFLXUSFGCCHvcG7SCN81aYSvJgzA6dtPsP/cLTx4Fc0tv/0sDLefheHLXcfR180ZI7q3Q9dWdlBWUuIxakJIXUWFGCGEyKEuUsGwbm3RpUUjFAhUcNz/MY76PURobCIAIK9AjOP+j3Dc/xFM9LQxtFsbDOvaFk62FhAIBDxHTwipK6gQI4SQD7A01sec4T0xe1gPPHodjaN+D3Dc/zF3j8uEtEzs9L2Bnb430NTCGIO7tMbgLm1owlhCyAdRIUYIIeUkEAjQtpkV2jazwjefDsSVhy/x97WHuPggGIXiIgBAaGwifvrzEn768xKcbC0w2L01Bru3pkH+hBC5qBAjhJBKUFVRRt8OTujbwQkpmdk4despfG8+xp3n4dwNxp+Fx+JZeCzW/nEWLvbWGNKlDQZ2agUTfW2eoyeE1BZUiBFCSBUZaGtiQp+OmNCnI94mp+PkrSfwvfkYga+iuD4PXr7Bg5dv8I3PSXRwsEX/js7o18EZ5oa6PEZOCOEbFWKEEKJA5oa6mDKoK6YM6oqIuGT43nyME/6P8eJNHABAImHclZcrdvuiXXNrDOjojP4dW8La1IDn6AkhNY0KMUIIqSaNzQwxZ3hPzBneEy/exOGE/2OcvPWEu7USADwMeYOHIW+wev8ZONtaoF9HZwzo6IxmlqY8Rk4IqSlUiBFCSA1oYW2GFp+YYcmY3njxJg5n7gThzJ0g7kgZAASFxyIoPBY/HLqAZpYm6N/RGf07ONOUGITUY1SIEUJIDRIIBHCwMYeDjTkWjvJCaGwizv5blD0O/W/i2FfRCdh89Ao2H70CCyNdeLo4oLerIzo5NYGaqgqPr4AQokhUiBFCCI+aWhhj1rAemDWsB6ITUnHmbnFRdv9lJHf1ZWxSOvafv4P95+9AQ00VHq2bwau9A3q5OMBIV4vnV0AIqQoqxAghpJawNNHnBvrHp2bg3N1nuHj/OW4+DUXBv/OU5eQV4OzdZzh79xkEAgHaNbeCV3tHeLV3gL2VKZ3CJKSOoUKMEEJqIVN9He5G5Fm5+bj++BUu3n+OSw9eICUjGwDAGOOmxVh34BysTQzQs509ure1h7tzU2ioqfL8KgghH0KFGCGE1HJa6qLigfsdnVFUJMHDV29w6X4wLt4PxsuoeK7fm4QU7D13G3vP3YaqshLcHGzRo21zdG9rT0fLCKmlqBAjhJA6RElJCNcWjeHaojGWj+uHyLhkXPy3KLvzPAziIgkAoEBcBP+nr+H/9DVW7z8DMwMd9Ghrjx5t7dGllR10NdV5fiWEEIAKMUIIqdNszAwxaWAXTBrYBZk5ebgVFIqrgSG4GvgS0YmpXL+4lAwcunwPhy7fg5JQCBd7a3i0aY4uLe3Qxs4SykpKPL4KQhquWlGIhYeHIysrC7a2ttDSkn8FUFRUFOLj49G8eXPo6OjUcISEEFL7aWuooY+bE/q4OYExhtDYJPgFvoTfo5e4/SwMeQViAECRRIKA4AgEBEfgh0MXoKUuQkfHJujSqim6tmpGpzEJqUG8FmK+vr5YunQpJBIJlJWVERERgYULF2LVqlVcn7y8PIwdOxZnz56FjY0NIiMj8f3332P27Nk8Rk4IIbWbQCCAXSNj2DUyxqSBXZCbX4i7z8Nw9VEI/AJf4nVMItc3Kzcflx4E49KDYACAsZ4W3J3t0KVlU3RpZQcrE7r1EiHVhddCLC4uDufPn4e1tTUA4MqVK+jVqxe6desGT09PAMDKlSsREBCA0NBQmJub4/jx4xg6dCjc3NzQoUMHPsMnhJA6Q12kgu5ti6+oxGeDEJWQghtPXsP/yWvcDApFUnoW1zcxLQvH/R/huP8jAICNqQG6tLRDZ+em6OBoSzcqJ0SBeC3EpkyZIvO4a9euUFZWRkxMDNfm4+OD6dOnw9zcHAAwZMgQODs7w8fHhwoxQgipJCsTA3zi6YZPPN3AGMOLN3Hwf/oaN568xp1nYcjOK+D6RsanIDI+AAcuBQAovodmB0dbdHCwRUdHW1ibGtCpTEIqifcxYmlpaQgKCkJGRgb27NmD1q1bY/jw4QCA2NhYxMfHw8XFReY5bm5uCAwMLHWd+fn5yM/P5x5nZGQAACQSCSQSicJfg0QiAWOsWtbdkFAeFYdyqRgNKY/2VqawtzLF//q7o1BchMeh0fB/+ho3n4biwcs3KCwq4vpGxCUjIi4ZR67cBwCYG+qig0Njrjiza2QsU5g1pDxWJ8qjYtREHiuybt4LsZcvX2LZsmVISkpCQkICfvzxR27AfkpKCgDA0NBQ5jmGhobcMnm8vb2xcuXKEu2JiYnIy8tTYPTFJBIJ0tPTwRiDUChU+PobCsqj4lAuFaMh59FaXx2fdGuJT7q1RG5BIR6HxuLh62g8fBWDoMg4FIr/K8zeJqfjuP9jHPd/DADQ11JHO7tGaGtnibZ2jdDEzADZWZkNMo+K1JD3R0WqiTxmZmaWuy/vhViHDh3g7+8PAPDz80OfPn2gqamJUaNGQUWl+Ma27xdPubm5UFUtfcbo5cuXY8GCBdzjjIwMWFlZwdjYuFquuJRIJBAIBDA2NqY3RxVQHhWHcqkYlMf/2Fg2wkcergCAvIJCPHodjTvPwxDwPAL3QyKRm1/I9U3NysXlR69x+dFrAICGSBWONibo4NQUrvaN0a65FfS1NXl5HXUZ7Y+KURN5VFNTK3df3guxd3Xv3h1ubm44e/YsRo0aBSsrKwiFQpkxYwAQExPDDfCXRyQSQSQSlWgXCoXVlnSBQFCt628oKI+KQ7lUDMpjSRpqInR2borOzk0BAIXiIjwJi8bd5+G48zwc94IjkJHz3x/QOfkFuB8Sjfsh0QCuASi+2bmLvTVcmtugfQsbNLc0oRyXA+2PilHdeazIenkrxCQSCQoKCmSqxsLCQrx58wZubm4AAA0NDXTu3Bm+vr4YN24cACA7OxuXLl3Ct99+y0fYhBBC3qOirASX5jZwaW6DGUO6o6hIguA3cbjzLAz3X0biwctIxCanyzwnNDYRobGJ+PPqAwCAtoYI7ZpZw8XeBi7NrdHKzhIGdNSMNAC8FWL5+flwdXXFpEmT4OjoiLS0NPz666/IycnBrFmzuH5r1qyBl5cXli9fjk6dOmHr1q0wMTEpccUlIYSQ2kFJSQhnWws421pg0sAukEgkePoyFJEpOXgQ8gYPXkYiKDxWZpxZZk4+rj1+hWuPX3FtNqYGaG1nidZ2VmjT1BItmzSCpnrJsx2E1GW8FWLq6uq4cOECtm3bhvPnz0NTUxM9evTAkSNHZAbne3h44OrVq9i+fTsCAgLQsmVL/P7776XOwE8IIaT2MdXXRkv7pvjIvTWA4nFmT8NicP9FJB6EROL+y0gkpmXJPKd42owU+N58AgAQCgVo1sgEre0s0cbOCm3srOBgYwZVlVo1yoaQChEwxhjfQVS3jIwM6OrqIj09vdoG6yckJMDEhMY4VAXlUXEol4pBeVSM8uSRMYaohFTcfxmJR6+i8Cg0Cs/CY7nbMpVGVVkJjo3N0drOijsKZ29tBlE9LM5of1SMmshjReqO+renEkIIqXMEAgGsTQ1gbWqAYd3aAii+COBlVDwev47C49fReBQajReRcSh6Z46mAnERHr2OxqPX0VybspIQzSxNucLM2dYCTrYW0NYo/5VshNQUKsQIIYTUSirKSlwhNdar+E4qufmFeBYRW1yYvY7Co9dRCItNknmeuEiC4Mi3CI58i7/8HnDtjc0M4djYHM62jYrX28QCJnradFcAwisqxAghhNQZ6iIVtLe3QXt7G64tPTsXz8JjEfTvz7PwWLyKTpA5cgb8d0eAM3eCuDYDHU20sDaDg7UZWtiYoYW1GeytTOmiAFJjqBAjhBBSp+lqqsvMawYUHzl7GRWHoLB/i7OIWDyPeIu8gkKZ56ZkZONWUChuBYXKtNuYGhQXZf8WaA7WZmhiYQRlJaUaeU2k4aBCjBBCSL2jLlLhrqyUKiqSIOxtYvGRs7Di4uzFm7gSV2sC/12xef7ec65NVVkJdpYmxUfQbMxg18gEzSxNYG1iACUlGjxPKocKMUIIIQ2C0r+D+JtZmmJo17Zce3J6FoLfxOFFZBxevCn+eRkVj5y8ApnnF4iL8DziLZ5HvJVpF6koo4mFMZpZGqOZpQlXoDWxMK6XV28SxaI9hBBCSINmqKuFLi3t0KWlHdcmkUjwJiEVLyLjEPzmLVekhb1NgkQiO+tTfqGYuzjgXUKhANYmBmhmaSJToNk1MoaOpnqNvDZS+1EhRgghhLxHKBSisZkhGpsZom8HJ649r6AQr6MT8DIqHq+iE/A6JgGvohMQEZcMcZHsxQESCeMuELh4P1hmmZGuFppYGMHWvPinibn0/4ZQF6nWyGsktQMVYoQQQkg5qamqwLlJIzg3aSTTXlAoRmR8Ml5FJ8oUaK9jEpCbX1hiPUnpWUhKz0JAcESJZWYGOmhiYQxbc0M0sTD+t0gzhKWxfnW9LMIjKsQIIYSQKlJVUebGn71LIpEgNikdr6SFWXQCQmMTEf42CfGpmXLXFZeSgbiUjBJXcgoFApgbaKOppSkamxnCxtQA1qaGxRPhmujT6c46igoxQgghpJoIhUJYmujD0kQfPdrayyzLys1HxNskhP37E/7vT1hsElIzc0qsS8IYYpIzEJOcgevv3BxdSk9L49/izID718qk+P8WRnpQUaapN2ojKsQIIYQQHmipi+Se5gSAtKwchL9NRti/R8/C3yYjNDYRYbGJyH7vas53n5OWlYPHodEllikJhWhkpPfvbaT0YWViAEtjfTQy0oOlsR5MDXRojjSeUCFGCCGE1DJ6Whpo20wDbZv9Nw+aRCJBfHw8lNQ0EZ2Yhjf/znX2Jj4ZkfEpiEpIRWxyWomrOgGgSCLBm4QUvElIAZ6W3J5QKICZgQ5XnDWS/vtvodbIWB9adLeBakGFGCGEEFJHCAQCGOlqwURfB+2aW5dYXlAoRkzSf0VaVIK0WCv+Sc/OlbteiYQhNikdsUnppW5bT0sdFlxxVlyoWRjrwdxAB+aGujDV14EqzZtWYZQxQgghpJ5QVVHmpsSQJy0rB2/iUxCdmIboxFTEJKUhhvs3DckZ2aWuOy0rF2lZuSUmtH2XoY4mzAx1YfZvcWZmoANzg+J/pe26mup0o/V3UCFGCCGENBB6WhrQ09JAq6aWcpfn5hcgJikdsUmpiE4sLs6ik1IRk5iG2KQ0xCano1BcVOr6kzOykZyRjWfhsaX2URepwMxAtlgzM9CFib42TPW1YaynDRM97QZz43UqxAghhBACAFAXqcKukTHsGhnLXV5UJEFiehZ3NC02MQ1vU9L/nXIjHXHJGYhPzSgxue27cvMLuStEy6KhpgoTPW2Y/FucvVukcY/1tWGoo1mnLzSgQowQQggh5aKkJPz3CJYO2tvbyO0jkUiQlJ5dXJilZOBt8rv//le0Zebkl7mtnLwC7s4EZREIBDDU0YSJ/n9FmomeNgx1NWGspw0jXU0Y6mrBSFcLBtqaUBLWrtOiVIgRQgghRGGEQmFxUaSvjVZNS++XlZuPuOR0vP23MEtKy0J8agYS07KQkJaJhH//X9oFBlKMMe5OBc9R+vg1KX1tDehpqqFpIxPs++Kzir48haNCjBBCCCE1TktdBDtLE9hZmpTZL6+gsLhIS8tAYup/RVpCWiYS07KQmJbJFXBljV+TSs3MQWpmDhhqx5ExKsQIIYQQUmupqapwdycoC2MMaVm5/xZpWUjJyEJSejYS0zKR/O//pUfOElMzYayrVUOvoGxUiBFCCCGkzhMIBNDX1oC+tgbsS06xxpFIJEhISICevkHNBVcGId8BEEIIIYTUtNoy+SwVYoQQQgghPKFCjBBCCCGEJ1SIEUIIIYTwhAoxQgghhBCeUCFGCCGEEMIT3guxoqIiBAcH49WrVxCLxaX2i4qKwv3795GRkVGD0RFCCCGEVB9eC7HvvvsOjRo1wvDhw9G7d280btwYp06dkumTl5eH4cOHw97eHuPHj4eZmRm2bt3KU8SEEEIIIYrDWyFWVFSE3NxcPH/+HM+fP0d4eDgmTZqEUaNGIS4ujuu3cuVKBAQEIDQ0FMHBwTh48CDmzJmDu3fv8hU6IYQQQohC8DabmZKSEtasWSPTNn36dKxcuRIPHz5E//79AQA+Pj6YPn06zM3NAQBDhgyBs7MzfHx80KFDhwptUywWyz39KRAIoKSkJNOvNPL6SiQSFBUVQSwWQygUltq3qKgIjLFyrVdRfQFAWVmZ975KSkoQCIrv6yWRSCCRSEr0kebx3fWU1rci660PfRljKCoq/R5qQqGQ2/cYYxCLxXL3SXl9K7Le+tS3PO976T5ZVFQkk8eKfkaUt299/4yQtz9K1bb3XG3s+/53TVU+IxpyXynpZ2VpqloblFftmFb2X/fu3QMANG1afLv22NhYxMfHw8XFRaafm5sbAgMDS11Pfn4+8vPzucfScWUXL16EhoZGif7GxsZwc3PjHl+4cKHUX6SBgQE6derEPb58+TLy8/ORm5sLdXV17k0BALq6uujSpQv3+OrVq8jNlX8XeS0tLXh4eHCPr1+/jqysLLl91dXV0bNnT+7xzZs3kZ6eLrevqqoqvLy8uMd37txBSkqK3L5KSkro27cv9/jevXtITEyU2xcABgwYwP3/4cOHMkcy39enTx/uQ/nx48eIjo4u0YcxhtzcXAwcOBDq6uoAgKCgIERGRpa63h49enC/0+DgYISFhZXat1u3btDW1gYAhISE4NWrV6X2dXd3h56eHgAgNDQUL168KLVvx44dYWhoCACIiIjAs2fPSu3bvn17mJqaAige9/jkyZNS+7Zr1477A+Tt27d4+PBhqX1btWoFKysrAEB8fDzu3bsnd58EACcnJzRu3BgAkJycjDt37pS63hYtWnDvx7S0NNy8ebPUvs2aNUPz5s0BAJmZmbh+/XqpfZs0aQIHBwcAQE5ODq5evVpqXxsbGzg7OwMofm9funSp1L6WlpZo3bo1gOIPwvPnz5fa18zMTOaz5ezZsyX6SPdJa2trmT/8KvoZUVBQILdvQ/mMkEgkePHiBR48eFBif5Qqz2eElKenJ0QiEYCG9Rkh3R+l7+uqfEbcv3+/1L71/TOiZcuWYIyhsLAQFy9eLLVveT4jpN6vI65cuVJq3/fVmkIsKSkJs2fPxscffwx7e3sA4D4MpDuwlKGhYakfFADg7e2NlStXlmjPzc2V+yGQlZWFhIQE7nFOTk6pf7HI61tQUMB90L67fiUlJZm+2dnZMgXiuwQCQYm+pX0gS++T9W5MpfUVi8Xl7isUCsvdF4BM38zMzDL7JiYmcn8tZGRkyO3LGENBQQESExOhpqZWZl+ppKQkrm96evoH+0qXp6Wlldk3OTmZ+52Wp6/0S/lDfVNSUrh9JDU19YN9pTlLSUkps29qair3xSTtK2+flMYo/d19KN53+37od/xu37L2X6D4dyXtm5eXV2bfjIwMrm9BQUG5+0qHP5QmMzNTZh8ua598v29FPyMKCwvl9m0onxESiQS5ubmlfgYD5fuMeLevqqpqufrWp88I6f4IFO8PVf2MKE1D+IxIT0+HWCyu8meElLz3fXkJWFnHlWtIeno6evXqBRUVFVy4cIH7i+Tly5do0aIFrly5gh49enD9Z8+ejStXrpT6V4W8I2JWVlZITEyEjo5Oif6KODWZlJQEIyMjOjVZivKemkxKSoKpqSn3+mrj6QE++lb00HxhYaHcfVJe37pwKoHPU5NJSUkwNjaGiopKmX0rst7S+tbXzwiJRIL4+HgYGhrSqckqnpp8931NpyYr1xcoLuaNjIzK3H+r8l5OSUmBsbEx0tPT5dYd7+L9iFhGRgZ69+4NJSUlnDt3jivCAMDKygpCoRAxMTEyz4mJiYG1dem3VheJRFzl/y5VVVXur6iylKfPu30lEgmUlZWhqqpa6ocMgDKXUV9weVRSUuL61OZ4a7IvAJk3+YcIBIJy7ZMVXW997ivvfS/dJ1VUVGTyWNHPiPKqDftadfVVUlIq1/5YnTHU9b4f+q6pDe+jutBXIpFwhVNFfh/V9r4vd89qIC3CgOIxF7q6ujLLNTQ00LlzZ/j6+nJt2dnZuHTpksyYBkIIIYSQuoi3I2KFhYXo168fwsPDsWfPHjx9+pRb1qxZM26w4po1a+Dl5YXly5ejU6dO2Lp1K0xMTDBlyhS+QieEEEIIUQjeCrGcnBwIBAI0a9YM3t7eMsuWLVuGgQMHAgA8PDxw9epVbN++HQEBAWjZsiV+//13aGlp8RE2IYQQQojC8FaI6erqwt/fv1x93d3d4e7uXs0REUIIIYTULN7vNUkIIYQQ0lBRIUYIIYQQwhMqxAghhBBCeEKFGCGEEEIIT6gQI4QQQgjhCRVihBBCCCE84f0WRzVBei+pjIyMalm/RCJBZmYm1NTUKnzbGvIfyqPiUC4Vg/KoGJRHxaA8KkZN5FFab5Tndt4NohDLzMwEUHzvSkIIIYSQmpCZmVni9o3vE7DylGt1nEQiQWxsLLS1tbk71StSRkYGrKysEBUV9cG7rJPSUR4Vh3KpGJRHxaA8KgblUTFqIo+MMWRmZsLCwuKDR90axBExoVAIS0vLat+Ojo4OvTkUgPKoOJRLxaA8KgblUTEoj4pR3Xn80JEwKTrJTAghhBDCEyrECCGEEEJ4QoWYAohEInzzzTcQiUR8h1KnUR4Vh3KpGJRHxaA8KgblUTFqWx4bxGB9QgghhJDaiI6IEUIIIYTwhAoxQgghhBCeUCFGCCGEEMKTBjGPWHULDQ1FWloaHBwcoKGhwXc4dUZgYCAAoG3btnKXi8ViBAUFQVVVFQ4ODtUyGW9dl5eXh5cvX8LAwACWlpal5ujFixfIzc2Fk5MTVFVVazjK2o8xhvDwcGRnZ6NJkybQ1NSU2y8yMhKJiYmwt7eHtrZ2DUdZdxQWFuLu3bvQ09ODs7NzieWJiYmIiIiAjY0NTExMeIiw9srMzMTjx49LtLdp0wZaWloybVlZWXjx4gWMjIzQuHHjGoqw7klOTkZkZCSaN29eIodA8f767NkziEQitGjRoua/axiptJSUFObh4cG0tbVZs2bNmI6ODjt8+DDfYdV6GzduZPb29kxPT485OTnJ7ePv78/Mzc2ZtbU1MzY2Zo6Ojuz169c1HGntlZKSwqZNm8b09PRYq1atmJGREWvXrh179uyZTL83b96w1q1bM0NDQ2Zra8uMjY3ZpUuXeIq6dvrrr79Ys2bNmL29PXNwcGBaWlps9erVMn2ys7PZwIEDmYaGBmvRogXT0NBgO3fu5Cni2m/x4sVMKBSyXr16lVi2aNEiJhKJmKOjIxOJRGz27NlMIpHwEGXtdPv2bQaAderUibm7u3M/L168kOnn4+PDNDU1mb29PdPU1GR9+vRhmZmZPEVdO2VnZ7Px48czDQ0N5uLiwqysrNiOHTtk+ly7do2ZmZkxGxsbZmRkxJydnVlYWFiNxkmFWBWMGzeOOTs7s/T0dMYYY1u3bmWqqqosPDyc38Bqublz57Lnz5+zpUuXyi3EsrKymJmZGZszZw5jjDGxWMz69OnDXF1dazrUWuvZs2fs559/Zvn5+YwxxvLy8thHH33EHBwcZPp1796dde/eneu3dOlSpq+vz1JTU2s65Fprx44dLDo6mnt8+vRpBoDduHGDa5s3bx5r3Lgxi4+PZ4wxdujQISYQCFhgYGBNh1vrnTt3jtnb27MhQ4aUKMT++OMPpq6uzh48eMAYY+zx48dMQ0OD7d69m49QayVpIVZWUfXs2TOmpKTE9u/fzxhjLCkpiTVt2pRNnz69psKsE0aMGMFatGjBYmJiGGPFn5O//fYbtzwzM5MZGxuzBQsWMMYYKywsZJ6enqxTp041GicVYpWUmZnJVFVV2a5du7g2sVjMjIyMSvw1TeQrrRD7888/mVAo5L70GGPMz8+PAWBPnz6tyRDrlOPHjzMALDk5mTHGWFhYGAPAzp07x/VJTU1lKioqzMfHh6coa7/s7GwmEAi4o9tFRUVMX1+frVu3TqZfs2bN2Ny5c3mIsPZ6+/Yta9SoEbt37x4bO3ZsiUKsZ8+ebMSIETJto0ePZu7u7jUZZq0mLcQePnzIAgMDWVZWVok+S5YsYY0bN5Zp+/HHH5mWlhYrKCioqVBrtcePHzMA7MyZM6X2OXjwIFNSUmJJSUlc26VLlxgAFhwcXBNhMsYYo8H6lfT8+XMUFBTAxcWFa1NSUkK7du24sU+kcgIDA2FlZSUzdsTNzY1bRuS7d+8eDAwMoK+vD+C/XL27j+rp6aFZs2aUx/ekpKTA398fp0+fxpgxY9ChQwd89NFHAICIiAikpqbK5BEAXF1dKY/vYIxh/PjxmDFjBtq3by+3T2BgYIk8urm5UR7lGDx4MEaPHg0DAwMsWLAARUVF3LLS8piVlYXXr1/XdKi10uXLl6GmpgZPT0+EhobiyZMnyM3NlekTGBiIxo0bw9DQkGvj47uGButXUkpKCgDI/AKlj9++fctHSPVGSkpKibyqq6tDXV2dyzuRdf/+fWzYsAFr167lBppKc2VgYCDT19DQkPL4nmfPnmH58uVITExEcnIyNm3aBHV1dQBlv9efPHlS47HWVuvWrUN+fj6WLVsmdzljDGlpaXLzmJOTg/z8/Foz0zmfDAwMcOXKFfTo0QMAcOfOHXh6esLY2BjLly8HULxP2trayjxPmld6bxeLjY2FsbExxo4di3v37kFdXR1RUVFYv349pk+fDkD+d422tjZUVFRqNI90RKySVFRUABRftfau3NxcuiqtilRUVErklTGGgoICyq0cwcHBGDBgAMaNG4d58+Zx7dJ9ND8/X6Y/7aMlde3aFf7+/nj58iUOHTqEzz77DCdOnABA7/XyCAkJwcqVKzF16lTcunUL/v7+SExMRHp6Ovz9/ZGdnQ2BQABlZWW5eQT+y3ND17x5c64IA4COHTvi008/xeHDh7k2eZ+R0jzSPllMRUUFUVFRaN68OcLDw/H8+XPs2LEDs2bN4o52ycujWCyGWCyu0TxSIVZJNjY2AICYmBiZ9piYGFhbW/MRUr1hY2ODt2/fgr1z9623b9+iqKiIcvueFy9eoGfPnhgwYAB+/fVXmcuuS9tHY2NjKY9l8PLyQps2bXD27FkA9F4vj+zsbLRv3x4///wzli1bhmXLliEwMBCvXr3CsmXLuLME1tbWcvNoaWkJoZC+jkpjamoqkzcbGxu5eQRA++S/pNN5TJ06lWsbP3481NXVcfPmTQDFeYyNjZX5rpE+rsk80p5fSXZ2drC1tYWvry/XFh0djQcPHsDLy4vHyOo+Ly8vpKam4saNG1zbiRMnoKamhq5du/IYWe3y8uVL9OjRA3379sWuXbtKzH3ToUMHaGtry+yj9+7dQ2xsLO2j/xKLxSWOGObl5SE6Opo7ZaGnp4f27dvL5DE9PR1+fn6Ux3+1bdsW/v7+Mj+9e/dG+/bt4e/vDzs7OwDF7+1Tp05xX3yMMfj6+lIe35GdnV2i7eLFizLzsXl5ecHf3x+pqalc24kTJ9CyZUuYmprWSJy1nZeXFwQCgUzBmpycjNzcXBgbG3N9kpKScPv2ba7PiRMnoKGhAXd395oLtsYuC6iHDh8+zJSVlZm3tzc7duwYa9++PXN1dWVisZjv0Gq1R48esRs3brCxY8cyW1tbduPGDXbjxg1WWFjI9RkzZgxr3LgxO3jwIPv111+ZtrY2W7VqFY9R1y5v3rxhFhYWrH379uzatWtcDm/cuMGys7O5fhs2bGAaGhps+/bt7MiRI6xZs2bso48+4jHy2iUtLY21bNmSbd68mZ0/f54dOnSIeXh4MDMzMxYVFcX1u3DhAlNWVmYrVqxgx48fZx4eHsze3p7l5OTwGH3tJu+qyfDwcKavr8/Gjh3LfH192cSJE5mOjg579eoVT1HWPjNmzGAzZ85kf//9N/vnn3/YsGHDmLq6OvP39+f65OXlMWdnZ9alSxf2zz//sG+//ZYpKSmxkydP8hh57TN79mzWokULdvjwYXbixAnWtWtX5uDgIPMZOXLkSNakSRN26NAh9ssvvzAtLS22du3aGo1TwNg7x+RIhZ09exa7d+9GWloaOnTogCVLlkBXV5fvsGq1SZMm4cWLFyXaT58+zeWuoKAAW7duxYULF6Cqqorhw4fj008/reFIa69bt25hyZIlcpf9/vvvMgN5Dx06hMOHDyM3Nxc9evTA/PnzoaamVlOh1nrR0dHYtm0bHj16BG1tbbi4uGDq1Knc1adS165dw88//4zExES0adMGy5Yt4/6yJiWtXr0aKSkp2Lhxo0x7SEgIfvjhB4SGhsLW1haLFi2Cg4MDT1HWPkVFRdi3bx/OnTuH3NxcODg4YPbs2bCyspLpl5KSgnXr1uHBgwcwNDTE1KlT0atXL56irp0kEgl27drFHc1u37495s+fL/MdXVBQgM2bN+PSpUsQiUQYOXIkxo8fX6NxUiFGCCGEEMITGiNGCCGEkP+3dz8hUa1xGMefiTOlQ0ZaC8soWjSNJP5NyTSMXIRYLto1EANGSBsDaSlRKzdR0KJFC5mIJHdp0SYkIySGJpu0EibGP5gbm6YiMrGpcxf33uGOOtV1ytep72d3zrzn/H7vWT3nnTNnYAhBDAAAwBCCGAAAgCEEMQAAAEMIYgAAAIYQxAAAAAwhiAEAABhCEAOQMYaGhtTf32+0hwcPHigSiaR1jqXMIxAIaGRkJK26AFYey3QDADAyMqKnT59+c0xDQ4O6uroUDAa1f//+5WlsnvHxcR05ckTDw8NpnWcp83j37p18Pp+Gh4fldDrTqg9g5SCIATDu5cuXunnzZmL7zp072rx5s0pLSxP7amtrVVJSopycnOVv8B9nz56V1+tVfn5+WudZyjwOHjwol8slv9+vEydOpFUfwMrBXxwBWHE8Ho8OHTqk8+fPJ+0fGhpSLBZLrCQNDg5qZmZG5eXlCoVCisViqq2t1fr16/Xx40cNDAzI4XCopqZGLpdrQZ0XL14oHA6roKBAZWVlsqzU96Zv3rxRQUGBHj58qLKysrTqp5pHRUWFQqGQ3r9/r8rKSm3YsCGph4sXL+rq1asKhUJLuKoAViJWxABkjPlf6XV2dqqvr0+zs7PyeDyamJjQ9PS0Lly4oHPnzsntdmt0dFSS9OjRI61bt06S9OnTJ3m9XgUCAe3evVuRSESWZenWrVvaunXrorXv3r0rl8uVtEq31PqLzaO/v1+2bWvLli2KRqMaHx9XX19fUr0DBw6ora1Nk5OTC/4EGkBmIogByGiRSETBYFDFxcWKx+MqKipSS0uLnjx5Io/Ho7m5Oe3YsUN+v1+tra2SpPb2dr19+1ajo6PKysqSbdvy+XxqbW1N+or0vwYHB1VYWCiHw5F2/cWEw2EFAoHEaltTU5M6OjrU3d2dGLNr1y45HA4Fg0GCGPCbIIgByGjV1dUqLi6WJFmWpcrKSm3btk0ej0eStHr1apWXlyscDkuSbNuW3++X1+vV7du3Zdu2bNvWpk2b1NPTk7JONBpVbm5u2vVT2bNnTyKESVJdXZ2uXbuWNMayLOXk5CgajX7vsgDIEAQxABltfjhas2bNovtmZ2clSR8+fFAsFtOzZ8/0+vXrpHENDQ36/Pnzor9KXLt2rcbGxtKun0peXt4PHTMzM2P0BwsAfi6CGIA/SnZ2tizL0rFjx9Tc3PzDx7ndbvX29v7Czr5vcnJS8XhcO3fuNNoHgJ+HF7oC+KM4nU7V19frypUr+vr1a9JnU1NTKY+rr6/XxMSEXr169atbTGlgYEAbN25USUmJsR4A/FysiAH441y6dEl1dXXat2+fjh49qi9fvujevXvKy8tTZ2fnoscUFhaqpqZGN27c0OnTp5e54791d3erublZq1ZxDw38LghiAFacxsbGpAfX/zX/RagVFRXavn170piqqqoFz1bt3btXWVlZiW23263nz5/L7/fr8ePHys3N1fHjx3X48OFv9nXmzBmdPHlSp06dktPpXHL9H5mH2+1WY2NjYntsbEz379/X5cuXv9kjgMzCC10B4H9ob29XU1OTqqqqlrXu9evXFY/H5fP5lrUugF+LIAYAAGAIDxoAAAAYQhADAAAwhCAGAABgCEEMAADAEIIYAACAIQQxAAAAQwhiAAAAhhDEAAAADCGIAQAAGEIQAwAAMIQgBgAAYMhfOObBQlWAUy8AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_fig4, _ax4 = plt.subplots(figsize=(7, 4))\n",
    "_ax4.plot(t_cool, T_cool, color=\"#1a5276\", linewidth=2)\n",
    "_ax4.axhline(Tinf_cool, color=\"grey\", linestyle=\"--\", alpha=0.6,\n",
    "             label=f\"Room temperature {Tinf_cool}°C\")\n",
    "_ax4.set_xlabel(\"Time (min)\")\n",
    "_ax4.set_ylabel(\"Temperature (°C)\")\n",
    "_ax4.set_title(f\"Newton's law of cooling  ($k = {k_cool}$ min⁻¹,  $T_0 = {T0_cool}$°C)\")\n",
    "_ax4.legend()\n",
    "_ax4.grid(True, alpha=0.3)\n",
    "_fig4;"
   ]
  }
 ],
 "metadata": {
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.3"
  },
  "marimo": {
   "app_config": {
    "app_title": "Week 1 Lab (Answers) — Your first models",
    "width": "medium"
   },
   "marimo_version": "0.25.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}