{
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   "id": "interactive-link",
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   "source": [
    "> **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 lecture, see\n",
    "> [Week 3 lecture — interactive](https://math4120.pages.dev/wasm/week03_lecture.html).\n"
   ]
  },
  {
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   "execution_count": 1,
   "id": "ipython-import",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-11-13T23:25:39.055773Z"
    }
   },
   "outputs": [],
   "source": [
    "from IPython.display import Markdown, HTML\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Hbol",
   "metadata": {
    "marimo": {
     "config": {
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   "source": [
    "# Week 3: Buckingham Π-theorem and the dimension matrix\n",
    "## Computation lecture\n",
    "\n",
    "**MATH4120 — Mathematical Modelling and Programming** Lancaster University, 2026–27\n",
    "\n",
    "---\n",
    "\n",
    "The key insight of this chapter: finding dimensionless groups is a **linear algebra problem**. The Π-groups live in the null space of the dimension matrix, and SciPy finds that null space in one line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "MJUe",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:39.058111Z",
     "iopub.status.busy": "2026-11-13T23:25:39.057934Z",
     "iopub.status.idle": "2026-11-13T23:25:39.518904Z",
     "shell.execute_reply": "2026-11-13T23:25:39.518315Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.linalg import null_space"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "vblA",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
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     "md_prefix": "r"
    }
   },
   "source": [
    "## 1. The pendulum\n",
    "\n",
    "A simple pendulum of length $l$ swings under gravity $g$.  Newton's second law gives $ml\\ddot{\\theta} = -mg\\sin\\theta$, and the mass $m$ cancels immediately. The period $\\tau$ therefore depends only on $l$ and $g$.\n",
    "\n",
    "Three parameters, two independent dimensions (L and T):\n",
    "\n",
    "$$\\begin{array}{c|ccc}\n",
    " & \\tau & l & g \\\\ \\hline\n",
    "\\mathrm{L} & 0 & 1 & 1 \\\\\n",
    "\\mathrm{T} & 1 & 0 & -2\n",
    "\\end{array}$$\n",
    "\n",
    "Buckingham: $n = 3$, $k = 2$ $\\Rightarrow$ $m = 1$ dimensionless group.\n",
    "\n",
    "The **dimension matrix** is this table.  A dimensionless combination $\\Pi = \\tau^{k_1} l^{k_2} g^{k_3}$ requires $D\\mathbf{k} = \\mathbf{0}$, so the exponent vector $\\mathbf{k}$ lies in the null space of $D$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bkHC",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:39.523315Z",
     "iopub.status.busy": "2026-11-13T23:25:39.523029Z",
     "iopub.status.idle": "2026-11-13T23:25:39.530637Z",
     "shell.execute_reply": "2026-11-13T23:25:39.529914Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1. , -0.5,  0.5])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# rows = [L, T],  columns = [tau, l, g]\n",
    "D_pend = np.array([\n",
    "    [0,  1,  1],   # L exponents\n",
    "    [1,  0, -2],   # T exponents\n",
    "])\n",
    "ns_pend = null_space(D_pend)\n",
    "v_pend  = ns_pend[:, 0]\n",
    "v_pend  = v_pend / v_pend[0]    # normalise so tau exponent = 1\n",
    "np.round(v_pend, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "lEQa",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "The output `[1., -0.5, 0.5]` gives the exponents $[k_\\tau,\\, k_l,\\, k_g]$: $$\\Pi = \\tau^{1} \\cdot l^{-1/2} \\cdot g^{1/2} = \\tau\\sqrt{\\frac{g}{l}}.$$ Rearranging: $$\\tau = \\Pi\\sqrt{\\frac{l}{g}}.$$ Dimensional analysis gives the functional form up to the constant $\\Pi$. Solving the small-angle ODE gives $\\Pi = 2\\pi$; a small correction applies for large amplitudes."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "PKri",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "### Solution collapse across planets\n",
    "\n",
    "On Earth, Moon, and Mars, $g$ takes different values, so the dimensional period $\\tau(l)$ is a different curve on each planet.  But $\\Pi = \\tau\\sqrt{g/l}$ is always $2\\pi$ — the same constant everywhere.  This is the same solution collapse idea as in Week 2, now derived purely from the dimension matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "Xref",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:39.532550Z",
     "iopub.status.busy": "2026-11-13T23:25:39.532375Z",
     "iopub.status.idle": "2026-11-13T23:25:39.946583Z",
     "shell.execute_reply": "2026-11-13T23:25:39.945646Z"
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    },
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    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "l_arr_pend = np.linspace(0.1, 3.0, 300)\n",
    "planets_lec = {\"Earth\": 9.81, \"Moon\": 1.62, \"Mars\": 3.71}\n",
    "colors_planets = [\"#1a5276\", \"tomato\", \"#117a65\"]\n",
    "\n",
    "fig_pend, (ax_dim_p, ax_nd_p) = plt.subplots(1, 2, figsize=(12, 4))\n",
    "\n",
    "for (planet_name, g_planet), col_planet in zip(planets_lec.items(), colors_planets):\n",
    "    tau_pend = 2 * np.pi * np.sqrt(l_arr_pend / g_planet)\n",
    "    pi_pend  = tau_pend * np.sqrt(g_planet / l_arr_pend)\n",
    "    ax_dim_p.plot(l_arr_pend, tau_pend, color=col_planet, linewidth=2.5, label=planet_name)\n",
    "    ax_nd_p.plot(l_arr_pend, pi_pend,  color=col_planet, linewidth=2.5, label=planet_name, alpha=0.85)\n",
    "\n",
    "ax_nd_p.axhline(2 * np.pi, color=\"k\", linestyle=\"--\", linewidth=1.5, label=r\"$2\\pi$\")\n",
    "\n",
    "ax_dim_p.set_xlabel(\"Length $l$ (m)\", fontsize=12)\n",
    "ax_dim_p.set_ylabel(\"Period $\\\\tau$ (s)\", fontsize=12)\n",
    "ax_dim_p.set_title(\"Dimensional: each planet a different curve\", fontsize=12)\n",
    "ax_dim_p.legend(fontsize=11)\n",
    "ax_dim_p.grid(True, alpha=0.3)\n",
    "\n",
    "ax_nd_p.set_xlabel(\"Length $l$ (m)\", fontsize=12)\n",
    "ax_nd_p.set_ylabel(r\"$\\Pi = \\tau\\sqrt{g/l}$\", fontsize=12)\n",
    "ax_nd_p.set_title(r\"Nondimensional: all planets collapse to $2\\pi$\", fontsize=12)\n",
    "ax_nd_p.legend(fontsize=11)\n",
    "ax_nd_p.grid(True, alpha=0.3)\n",
    "\n",
    "fig_pend.tight_layout()\n",
    "fig_pend;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "SFPL",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "### Pendulum animation\n",
    "\n",
    "Drag the slider to move forward in time.  Both pendulums start at the same angle ($30°$) but the Moon's weaker gravity means it swings more slowly — a longer dimensional period $\\tau$. In nondimensional time $s = t/\\tau$ both are at exactly the same phase."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "BYtC",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:39.948749Z",
     "iopub.status.busy": "2026-11-13T23:25:39.948485Z",
     "iopub.status.idle": "2026-11-13T23:25:39.951695Z",
     "shell.execute_reply": "2026-11-13T23:25:39.950856Z"
    }
   },
   "outputs": [],
   "source": [
    "t_pend_slider = type('_W', (), {'value': 0.0})()  # static default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "RGSE",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:39.953175Z",
     "iopub.status.busy": "2026-11-13T23:25:39.953032Z",
     "iopub.status.idle": "2026-11-13T23:25:40.060259Z",
     "shell.execute_reply": "2026-11-13T23:25:40.059474Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_t = t_pend_slider.value\n",
    "_l = 1.0\n",
    "_theta0 = np.pi / 6   # 30°\n",
    "_planets_anim = [(\"Earth\", 9.81, \"#1a5276\"), (\"Moon\", 1.62, \"tomato\")]\n",
    "\n",
    "_fig_sw, _axes_sw = plt.subplots(1, 2, figsize=(8, 5))\n",
    "for _ax_sw, (_name_sw, _g_sw, _col_sw) in zip(_axes_sw, _planets_anim):\n",
    "    _theta_sw = _theta0 * np.cos(np.sqrt(_g_sw / _l) * _t)\n",
    "    _x_sw = _l * np.sin(_theta_sw)\n",
    "    _y_sw = -_l * np.cos(_theta_sw)\n",
    "    _ax_sw.plot([0, _x_sw], [0, _y_sw], color=_col_sw, lw=3)\n",
    "    _ax_sw.plot(_x_sw, _y_sw, \"o\", color=_col_sw, ms=22)\n",
    "    _ax_sw.plot(0, 0, \"k.\", ms=10)\n",
    "    _ax_sw.set_xlim(-1.3, 1.3)\n",
    "    _ax_sw.set_ylim(-1.3, 0.3)\n",
    "    _ax_sw.set_aspect(\"equal\")\n",
    "    _ax_sw.axis(\"off\")\n",
    "    _tau_sw = 2 * np.pi * np.sqrt(_l / _g_sw)\n",
    "    _ax_sw.set_title(rf\"{_name_sw}  ($g = {_g_sw}$,  $\\tau = {_tau_sw:.2f}$ s)\", fontsize=12)\n",
    "_fig_sw.tight_layout()\n",
    "_fig_sw;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Kclp",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## 2. Nuclear explosion — the Sedov–Taylor blast wave\n",
    "\n",
    "In July 1945 the Trinity test detonated the first atomic bomb.  The photographs were declassified in 1947.  In 1950, G.\\ I.\\ Taylor published a paper showing that dimensional analysis alone — applied to five frames of film — could determine the bomb's yield to within 3\\%.  It caused a security scandal: the yield was still classified.\n",
    "\n",
    "**Governing parameters:** energy released $E$, ambient air density $\\rho$, time $t$, blast radius $R$.  Their dimension matrix is:\n",
    "\n",
    "$$\\begin{array}{c|cccc}\n",
    " & E & \\rho & t & R \\\\ \\hline\n",
    "\\mathrm{M} &  1 &  1 & 0 & 0 \\\\\n",
    "\\mathrm{L} &  2 & -3 & 0 & 1 \\\\\n",
    "\\mathrm{T} & -2 &  0 & 1 & 0\n",
    "\\end{array}$$\n",
    "\n",
    "$n = 4$, $k = 3$ $\\Rightarrow$ $m = 1$ dimensionless group."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "emfo",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:40.062126Z",
     "iopub.status.busy": "2026-11-13T23:25:40.061974Z",
     "iopub.status.idle": "2026-11-13T23:25:40.066228Z",
     "shell.execute_reply": "2026-11-13T23:25:40.065518Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.2,  0.2, -0.4,  1. ])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# rows = [M, L, T],  columns = [E, rho, t, R]\n",
    "D_sed = np.array([\n",
    "    [ 1,  1,  0,  0],   # M\n",
    "    [ 2, -3,  0,  1],   # L\n",
    "    [-2,  0,  1,  0],   # T\n",
    "])\n",
    "ns_sed = null_space(D_sed)\n",
    "v_sed  = ns_sed[:, 0]\n",
    "v_sed  = v_sed / v_sed[3]    # normalise so R exponent = 1\n",
    "np.round(v_sed, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Hstk",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "The exponents $[k_E,\\, k_\\rho,\\, k_t,\\, k_R]$ are $[-1/5,\\, 1/5,\\, -2/5,\\, 1]$, giving: $$\\Pi = E^{-1/5}\\,\\rho^{1/5}\\,t^{-2/5}\\,R = \\text{const},$$ and therefore $$\\boxed{R = \\Pi\\!\\left(\\frac{E\\,t^{2}}{\\rho}\\right)^{\\!1/5}.}$$\n",
    "\n",
    "This is the **Sedov–Taylor law**: $R \\propto t^{2/5}$, a power law.\n",
    "\n",
    "**A quick note on log-log plots**, since this is the first time we've used one and we'll rely on the trick a lot from here on. If two quantities are related by a power law, $y = Cx^p$, taking logarithms of both sides turns it into a straight line: $\\log y = \\log C + p\\log x$. A **log-log plot** puts both axes on a logarithmic scale, so any power-law relationship shows up as a dead-straight line — and that line's **slope is exactly the exponent $p$**. That's the whole reason to reach for one here: it turns \"how does the blast radius grow with time?\" into \"what's the slope of this line?\", read straight off the plot below rather than guessed from the shape of a curve.\n",
    "\n",
    "Taylor did exactly this: he read the slope of $\\log R$ against $\\log t$ from the declassified photographs, found it to be $2/5$, then inverted the formula to infer $E \\approx 8.4 \\times 10^{13}$ J $\\approx$ 20 kilotons of TNT."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "nWHF",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:40.069296Z",
     "iopub.status.busy": "2026-11-13T23:25:40.069154Z",
     "iopub.status.idle": "2026-11-13T23:25:40.457848Z",
     "shell.execute_reply": "2026-11-13T23:25:40.456906Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KCtra2igtLRXp43X9/PWH69+UkpIisf/V958smxrWR95+wuFwlG6TTUxMDDIyMrB//35s3rwZJSUlSn2raGFhAS6Xi5kzZwrfkzfHnjlz5gAA3NzcsHv3bhQUFOD8+fMIDw/H8uXLFf625HWS/l3V/Zuqra3F33//jSlTpmD06NGwsrICl/vq4w1bfwTE3zNF6pD0Ptb3/srzuqqyDrZ+2pDvG2maaGJBSCNZunSp2MomwKtfcNnZ2TAzMxMeGzRoEK5cucL6dfzrAgMDcfnyZbGvtPft2ycW27dvX9y4cQOPHj0SOb57927h+To+Pj5o27Yt1q1bh61bt6Kqqkrlt0EBrz44v/nLb/Pmzayx77//PpKSkjB//nzk5eXJlE/dNdX9Vb3OxYsXkZGRIXLNijh48KDYxob79u1DixYt4OrqKrWsPNcOAI6Ojhg/fjxiY2NRXV2NCxcuAHg1yePxeMK/jsqi7puIuXPnQkdHBz179hQeT0hIwH///YeOHTvCxsZGoZwNDAwQERGBHTt2ICEhAVevXhV7vwYNGoSamhqxFXjI/9Td8iLpvQ0ODoaLiwt+/fVXrF27FhYWFqy3Qcpar7GxMQICArB//35UVFTIlKOOjg569OiBpUuXIiwsTOR2nPryl2T//v0iPycnJyM3N1fk3yuHwxG7DfLkyZN4/vy5zO2oog5ZyPO6qvK9kUba+0aIPGhiQUgjuXTpEjw9PbFy5Uo8f/4clZWVuHnzJiIiIpCdnY3PPvtMGPv555/Dzc0NAwcORHx8PAoKCpCfn4+kpCRER0djz549AIA5c+bA0NAQI0eOxK1bt1BYWIjff/+d9S9+n3/+OSwtLREeHo6rV6+iuLgY27Ztw8KFCzF48GD07t1bJD4qKgpJSUlYsWIFevToIfa8h7IGDRqE2tpazJ49GwUFBXjy5AkiIyPh4uLCGj9p0iQYGRnhp59+gr6+PsaMGVNvG8OHD4evry8+/vhjxMfHo6SkBMnJyRg/fjxcXFyU3vW7bdu2iI6OxtOnT5GVlYXPPvsM586dEy4dKoms1/7+++/jhx9+QFpaGiorK/H8+XPExcVBV1cXPj4+AF7d2uTu7o6zZ88iPz9fprzbtGkDR0dHHD58GP7+/tDX1wfwamJRVVWFs2fPij1fIe/7Vfet17hx42BgYCD2foWGhmLMmDGIiYnBH3/8gczMTJSVleH69ev4+uuvsXDhQpmu5V3Wrl07AMCBAwdYn6/hcrmYPn268Pa1+p45kqXe1atXIz8/H4MHD8aFCxdQVlaGzMxMHDx4EKGhoUhPT8e9e/cwaNAgHDp0CFlZWaisrMSZM2eQnJyMPn36yJy/JCkpKdizZw9KSkpw/vx5TJ48GW5ubpgyZQqAV30+JCQEGzZsQEJCAkpLS3H06FHMnz8f3bt3l6kNVdQhD1leV0D590YaWd83QuTSYI+FE0KkevnyJfPzzz8zvXr1YmxtbRktLS3G2tqaCQ4OZvbt2ycWX1JSwsyfP59p06YNo6ury1hZWTG9evViNmzYwFRVVQnjbt68yQQFBTH6+vqMtbU18+mnnzK3b99mXXHn0aNHzJgxYxgrKytGW1ubcXV1Zb7++muR+urk5OQwOjo6rKvaKIJtVagtW7YwHh4ejJ6eHtOqVStm7dq1wtV46lapet3777/PAGAmTJggdk7S6kslJSXMp59+yjRv3pzR0tJibG1tmaioKJHVdOpWefr+++9lupbX47dv3864u7szOjo6TNu2bZl//vlHprxkufZnz54xn3/+OePp6cno6ekxtra2zJAhQ5jz58+L1HX27Fmmc+fOwvfr9WVjJYmMjGRdvalTp04MAObIkSNiZeR9vzp06MAAYCZOnMiag0AgYH7//Xeme/fujKGhIWNsbMx07tyZWbJkCZOXl1fvNTQkaatCsZG2KpSkul9/zdjKMwzDzJw5k7GxsWE4HA4DgLl69arI+dzcXEZPT48BwFy/fl3m65NW75MnT5jo6GjGycmJ0dbWZhwdHZlBgwYxhw4dYhjm1fsWHx/PDBw4kLG1tWUMDAyYNm3aMAsWLBBbEra+/F9X93oVFxczEydOZExNTRljY2Nm1KhRzPPnz0Vic3JymAkTJjBWVlaMsbExExoayjx48IDp27cv4+XlJVYnG2XrqBvTampqRI5LWtmpvtdVltdMljok5SvP+0aIrDgM8//LFBBCyFtm7ty5WL58OU6fPo2AgIDGToeQRldeXg5bW1u4u7vj0qVLjZ2OUur+fdPHFELeHnQrFCHkrcQwDHbs2AE3Nzf06tWrsdMhRCMcOnQIJSUlmDp1amOnQghpgrQaOwFCCJFX3Xr9jx8/xsaNGxtslR1C3ia5ublYvnw5HB0dMWHChMZOhxDSBNE3FoSQt8rhw4ehpaWF+fPnY86cOZg0aVJjp0RIo+vXrx/s7OxQXV2NXbt2CR/AJ4QQdaJnLAghhBBCCCFKo28sCCGEEEIIIUqjiQUhhBBCCCFEafTwtpoIBAJkZmbC2NiYHjQlhBBCCCFvBYZhUFJSAnt7e3C50r+ToImFmmRmZsLJyamx0yCEEEIIIURuz549g6Ojo9QYmlg0sNjYWMTGxqK2thYAcOXKFRgZGYnECAQCFBcXw8TEROJMsL4YaedlqV+TqTN/VbelTH3ylpUnnvqcZOrOXZXtqbO/yVOmofubovlrChrjaIxTp6Y6xilSXpVjnCxxmtrnSktL0aVLFxgbG9cbS6tCqUlxcTFMTU1RUFAAExMTkXMCgQA5OTmwtraWOgBKi5F2Xpb6NZk681d1W8rUJ29ZeeKpz0mm7txV2Z46+5s8ZRq6vymav6agMY7GOHVqqmOcIuVVOcbJEqepfa64uBjm5uYoKioS+wz7JvrGQs24XC5rh+BwOBLPyRoj7bws9Wsydeav6raUqU/esvLEU5+TTN25q7I9dfY3eco0dH9TNH9NQWMcjXHq1FTHOEXKq3KMkyVOE/ucPO29ff8aCCGEEEIIIRqHJhaEEEIIIYQQpdHEQgFXr17F4MGD0aVLF3z++eeoqalp7JQIIYQQQghpVPSMhQI+/vhjzJ49GzY2Nvjwww8RGxuLWbNmqax+Pp8vNlkRCASoqalBZWWlxAd+JJ2vr6ymU2f+qm5LmfrkLStPvCyxTbXPqTt3Vbanzv4mTxlV9TeBQCDbxRBCCGkUGjexEAgEyM3NhZWVVYP+Un/58iX4fD7s7e1ZzzMMg+zsbBgbG8PAwEDk3IkTJ8Dj8QAAwcHBqKqqUklODMPgxYsXKCwsZD0nEAhQUlLCusGetPP1ldV06sxf1W0pU5+8ZeWJlyW2qfY5deeuyvbU2d/kKaOq/sbn8wEAdnZ2b12/IoSQpkCjJhY//vgjvvvuO3A4HGhpaWHhwoWYNm2aStvYuXMn1q5di8TERLRt2xbXrl0Tizly5AimTp2KwsJCVFVVYezYsfj999+ho6MDAMJJRWpqKo4dO4ZDhw6pJLeXL1+iqKgINjY2MDAwEPnFyTAMamtroaWlJfGXrqTz9ZXVdOrMX9VtKVOfvGXliZcltqn2OXXnrsr21Nnf5Cmjiv4mEAhQWlqKvLw8cDgc2NnZyXZhhBBC1EZjJhZLly7F999/j3379iEgIAClpaVYsWKFxHg+ny/8gC/rOT6fjx07dmD+/Pk4ePAgTpw4IRbz7NkzDBs2DF9++SXmzp2LJ0+eoGfPnvjyyy9F8klOTsa8efPw77//wszMTP4LfoNAIEBhYSGaNWsGS0tLsfNN9UMeQBMLmlioF00sNHNiwTAMtLW1weVykZOTAxsbG4m/AwghhDQOjZhYFBQUYOnSpVi6dCkCAgIAAEZGRli8eLHEMiNHjoSPjw8+++wzkeMLFizAkydPsGnTJrEyPB4PO3fuBACJ3zJs3LgRRkZGmDt3LrhcLlxcXPDRRx9h+fLlWLZsGbS0tPDvv/9i1apV2LNnDywsLOS6Vrb7hAUCgfArfn19fUjas7DuuCLn6yur6dSZv6rbUqY+ecvKEy9LbFPtc+rOXZXtqbO/yVNGVf3NwMAADMOgqqoKenp6wnMCgUB4O9XbRp25q7otZeqTt6w88bLE1hcj7Tz1t8ZpT9m6GqrPqSpO2vna2lo8yymElZWVTLmrkjyvt0ZMLM6cOYOKigqMGDEClZWVKC0trfeF++STTxASEgItLS18/PHHAICFCxdi9erVOH78uMK5XLp0Cd7e3iLPd/j7+2PevHm4f/8+3NzcMHLkSNjZ2aF79+4AgFGjRmHZsmWs9cXGxiI2NlY4ccjJyUFlZaVITN027XX3ENfW1orV8/r9xfXdf8z212NpZTWdOvNXdVvK1CdvWXniZYltqn1O3bmrsj119jd5yqiyv9XW1kIgECAvLw/a2trC8wKBAEVFRWAY5q1cMEBduau6LWXqk7esPPGyxNYXI+089bfGaU/Zuhqqz6kqju18RVUNDlxIw7bTV1FYWoH4b6Kgp6sjw9WqTklJicyxGjGxePbsGXR1dbF161YsX74cXC4XWlpaWLp0KaZOncpaxt/fHwcOHEBoaCh4PB6KioqwcuVKHDt2DF5eXgrnkpOTgzZt2ogcq5vk5OTkwMPDA3fv3hU5b2pqKrG+mJgYxMTEoLi4GKamprC2thbbDl0gEKC2thalpaXQ0tKClpbkt+X1X6Tynq+vrKZTZ/6qbkuZ+uQtK0+8LLFNtc+pO3dVtqfO/iZPGVX0N+DVLrCWlpZi31hwOBxYW1u/lR/01JW7qttSpj55y8oTL0tsfTHSzlN/a5z2lK2rofqcquJeP/8irxgbD5/DPycuoqjsf3+QPv8gC6P6dK03d1V6faytj0ZMLDgcDqqqqnD+/Hk8f/4choaG2Lx5MyZNmgR3d3f06tWLtVxAQAD+++8/4TcXJ0+eRLdu3ZTKhcvlin1jULf0a939vK1atVKqfknbtNf9r6S/1r0eI8/5+spqOkXzf/78OSIjI3Hx4kW4u7tj3bp1aNeuncT4GzduwN/fH7NmzcKiRYvA4XCQmZmJKVOm4Ny5c3B3d0dcXBw6dOjQ4LkrUlaeeFlim2qfU3fuqmxPnf1NnjIN0d/YxlJJx98G6sxd1W0pU5+8ZeWJlyW2vhhp56m/NU57ytbVUH1OFXEMw+Daw0zs2XIchy+mgc9yC9LmoxcQ0be7TLmrijyvtUb8a3B0dAQAfPbZZzA0NAQATJgwAS4uLjhy5IjUshcvXhTOpK5cuaKSXLKyskSO1f3s4OCgdP1EfT788EM4Ozvjzp07GDZsGCZMmCAxtqamBh999BGCgoJE9hCZOXMmHB0dcefOHYwaNQrjxo1TR+qEEEIIaSKqa2qx+8wVhM2NRfTPOxB/PlVsUmFhbIjokB6ImyP5s4wm0IhvLHr27AltbW0UFRUJj/H5fJSWlsLY2FhiuR9++AHLli3D4cOHUVZWhqFDh0JLS0upJWp79+6NTz/9FKWlpTAyMgIAHD58GC1atEDLli0VrpeoV1lZGQ4cOIDMzExYW1tjzpw5+Omnn5CWloa2bduKxX/zzTeYMGECbt68KTxWWVmJvXv34tmzZ7C1tcWnn36Kn376CTdu3JDrWwtCCCGEkDflFpVi89Hz2HT4PLIL2Z9j8Ghhh6kD/TDItwOKCwtgY27CGqcpNGJiYWlpiVmzZmH27NnQ09ODtbU11qxZg8rKSkRERLCW+eWXX7Bw4UIcOnQIfn5+AIB///0Xw4cPB4/HQ1RUFGu5zMxMVFdXo7i4GNXV1Xjy5AkAoHnz5uByuZg4cSJWrFiBcePG4auvvsLNmzexZs0arF27tkGu/V01adIklJWVAXh1z3SLFi0QGRkJd3d3tbSfkZEBY2NjWFtbA3j1NZ6rqyvS09PFJhZXrlzBlStXsHjxYsycOVN4/Pnz59DX14etrS2AV19f1tWhyMTihx9+gJOTE0aPHq3ElZG7d+/ijz/+QEZGBrp3745PP/20sVNqMAkJCfjll1+wa9cuAEB+fj6mTZuGRYsWwdPTs5GzU5379+9jyZIl+PXXX6U+Y0YIIe+CtCcvsP5QMvYmXENVjfiCPRwOB/27eiB6oD98PF3A4XBeLfTTCLnKSyNuhQKA7777DtHR0Zg7dy7GjRuHsrIyJCcnS/yWoLCwEAcOHEDPnj2Fx4KDg7Fr1y7k5eVJbCc6Ohq9e/fG0aNHUV5ejt69e6N3794oLS0FABgaGuL06dMwNjbG+PHj8eeff+L333/HlClTVHq977LMzExs2rQJrq6uiIiIQEhICM6dO4dOnTrhxo0bKm8vLS0N4eHhYjuWv3mfNpfLFVsyrbq6GjNmzJA4cZSlDlncvHkTixYtgr+/v9xl33VJSUkIDw+X6XUtKytDz549kZ+fjxEjRgj/qPCuSk9Px+7du4U/l5eXY/fu3cjJyWnErFSvdevWuHfvHmJjYxs7FUIIaRB8vgCHL97CtJU7MeCzVdh+MkVsUmGkr4uxfTojYfVsrJ87Cb7tXN+65xQ15k9DXC4Xn376qcx/ffz6669Zj4eGhiI0NFRiuYMHD9Zbd4sWLbBlyxaZ8iDi6p51mTJlivAbitDQUFhbW2PHjh0qv43o6NGjSEpKEtmo0N7eHkVFRSgoKIC5uTkYhsHjx4/h5OQkUjYtLQ3nzp1D69atAUD44P7z58/x+++/o7S0FLm5ucKVwR49eiRWhyy++eYbhIeH03M6LJ49e4bdu3dDIBDU+4BYWloacnJysHjxYoXeB6K5ZsyYIfxPnhVICCFEkxWXVWDbyRRsOJiMp9n5rDEtbS0xJdQP4QGdUVFaDBsb+fZI0yQaM7Eg746rV6/C0NBQ+GEd+N8Skrq6uipt69NPP8XevXtRW1uL8PBwAMCsWbPg7++PoKAgLFmyBEuWLMHGjRthamqK9u3bi5Tv2LGj8JYtAJg9ezYMDAywZMkS6OjoIDQ0FEuWLMG3336LLVu2QF9fH507d5Yrx5cvX2Lv3r2sCxFkZ2dj/fr1uHXrFgwNDTFq1CgEBgYKz69evRppaWn49ddfoaPzat3qe/fuYf78+fjwww8REBCAR48eYc6cOViyZAn+++8/3L59GyYmJoiKihKbxL148QJ//vkn7t69CyMjIwwaNAgDBw4Uns/MzMSMGTOwePFinDp1CleuXIGBgQHGjh0LHx8fkbrKysqwceNGpKSkgMPhIDg4GKNGjRL+daW8vBxRUVGYM2cOUlNTcfHiRXC5XAwbNgxBQUEAgPPnz2PlypUAgNGjR4PD4cDNzY11X5hNmzZh3bp1AIAPPvgAurq6+Pzzz+Hg4IAZM2Zg0aJFOHz4MK5duwYvLy/MmjULAHD69Gns3r0beXl5cHFxQVRUFJydnYX1btu2DefOnUNkZCT+/fdfPH78GC1btsSsWbPA4/Hw22+/4datW2jWrBliYmJEyrL54osv4OrqCmdnZxw8eBD5+fno0aMHoqOjhSvLPXv2DB9//DF+/vln4eIVALBy5UpUV1djzpw5Utuoz40bN/D3338jMzMTzs7OmDhxonA1u8LCQuG3wxcuXMC1a9egpaWF8ePHC/fmAYBbt24J/4CjpaWFFi1aYOjQoWL9AHj1rdOePXuQnZ2N9u3bY/r06SLLaufk5CAuLg63b9+GoaEhwsPD0a9fP5E6hg4divfeew+7du3C+PHjlbp+QghpbI8yc7HhUBK2n0xBWWU1a4x/+1aICvND3y5twOO9uiOiovRtuOFJMo25FYq8O65cuYL27dsL//osEAiwcOFCGBoaYuLEiRLLJSYmol27dmjRogXWr18PAJg3bx5sbW0lrg4WEBCA4uJiBAcHIyIiAhEREcJvSVatWoWzZ8/C0NAQP//8MzZu3Cj80Gtra4srV66Aw+FAT09P+B+PxwOPxxNOhFauXInk5GQYGhpixYoVInXI6vjx4+BwOGIfyG7cuAFPT0/s27cP/v7+sLe3x8CBA/Hnn38KY8LDw3HgwAF88sknAF59WB8xYgRKSkqEtwHm5+dj9+7d6NmzJ+7fv4+ePXvi5cuX6N69O86fPy+s6/Hjx+jQoQNOnTqF3r17w8LCAuHh4fjyyy+FMcXFxdi9ezf69euH27dvw8/PDzU1NfD390dycrIwLicnB127dsXKlSvRqVMndOrUCTNnzhR+mAde3Wa2e/duDBo0CImJifDx8YGhoSGCg4Oxd+9eAICTk5PwdRk9ejQiIiKEk443de7cWTjpGjJkCCIiIuDg4CDMOTAwEA8ePEBwcLCwztWrVyMoKAg6Ojro168frl27hg4dOuDq1avCelNTUxEXF4dRo0bB0tISfn5+2Lx5MwIDA+Hv74/8/Hz069cPaWlp6NGjh8giE2xOnjyJuXPn4uuvv4abmxs6dOiAr776Ch9++KEwpqioCLt37xar6/z58yKvsyIuXbqE7t27o6KiAgMGDICenh7Cw8Nx+/ZtAK8WJdi9ezeCg4ORkJAAX19fCAQC4fLddWxsbIT/poYMGQIOh4OgoCBs3LhRpL2FCxciMDAQ1dXV6Nu3L/Lz89G/f3/h+Vu3bqFdu3bYu3cvfH194ejoiCFDhojdfqinp4fu3bvj8OHDSl0/IYQ0FoZhkHDjASYt24heM37A+oPJYpMKXW0exvTthuM/zcL2hVPRv1tb8Hjvzsdx+sZCgxWXVeDO01dL3TIMwOfXgsfTAtvnWmnn6ytbnzbNbWFiqC9z/NWrVyEQCBAeHo7a2lqkpqbCxcUFycnJaNGiBWuZ2tpazJo1Czt37gQAhIWF4dy5c3j06BGuX78OS0tL1nJ9+vRBXl4eRo8eLfKXd+DVfduXLl1ivcUmPT1d+A3A63744QeRfUxcXV1x8eJFmW7TkeTatWtwcXGBvr7oazht2jTY2Njg7NmzwomMk5MTZs+ejdGjR8PY2Bh2dnb4+++/0b9/f/j7++Pw4cMoLCzEqVOnxPIZMWIEVq9eDS0tLUyZMgWDBg3Cp59+iqSkJADA3Llz0axZMxw/fly4X4uLiws++OADTJo0SeQbpvfeew8LFixAbW0tIiMjce3aNfz111/w9fUF8GrCl5WVhVu3bsHe3h4cDge+vr7w8fHBe++9Bw8PD2Fdw4cPF/kQef/+fWzYsAFDhw6Fg4MDevToIYyT9uBu+/bthc9PDRw4UPhQfXHxq7/uTJgwAT/88IMwPicnB/PmzcOSJUvw+eefAwAiIyPRq1cvzJo1C2fOnBHGVlZW4uDBg2jVqhUYhoGRkREmTJiAn376CR9//LEwPwsLC8THx2Ps2LES8wQAc3NznDx5Uvi+6unp4eOPP0ZsbGyDrxt/+PBheHp6YtWqVcJjn376KaqqqkTifHx8sG3bNgCvXhcOh4PZs2dj6NCh4PF4sLa2Fn4LCABjxoyBra0tFi1ahMmTJwN49W992bJl2LhxIyZNmiSMff0ZkPfeew8WFhY4deoUDAwMwOFw0KJFC8yYMQNjxowRuYWxffv2Mt2uSgghmqSiqgZ7km5iZ8JN3H32kjXG1sIEEwd4o38nF7i7tHgr9z+RBU0sNNidp1kY9uVvjZ0G9iyZju4e0m//qFNQUID09HR8+umn8Pb2Rn5+PtLS0nDv3j2pGws+evQIXl5ewg+k69evR//+/fHs2TPY2NiIbVpY5+rVq2AYBl26dJFYN9s/Xkm3ZEn6YKvMAJCdnQ0LC9H7JXNycnDhwgX89NNPIjsNR0REICoqCufPnxf+5b5Pnz5YvHix8NueM2fOCJ/5eN2oUaNEfh45ciQiIyNRVVUFXV1dnD59GjExMeDxeGAYBsCrD4vTpk1DUlKSyMSib9++InW5ubnh2bNnwp8PHDiA4cOHw8bGRnisW7duaNmyJQ4fPiwysWCr6/jx41JeMcWEhISI/JySkoKysjKMGTNGeIzD4SAiIgKzZs1CbW2t8P12cnIS6Z8uLi4AXr32depWGcvIyKg3l169eom8r25ubqisrERubq7Ia9YQunbtim+//RaLFi3CsGHD4OnpCV1dXbE+z9Zffv/9dzx9+lR4u9fVq1exc+dOZGRkoLy8HNnZ2UhPT0dFRQX09fVx8OBB6Onpid26VLcaW0FBAZKSkrB8+XKRifyoUaMwefJkJCcnizwTZ2FhgezsbJW+HoQQ0lBe5BVh4+Fz2HrsAgpKylljOrd2QnSYP8J82oPH5bzzYxxNLIhK1T24PWnSJOHzDF27doWXlxe2b9+OyMhI1nJGRkYoKCgQ/pydnY3a2lqcO3cOQ4YMkdqera0t7O3tVXgVqqWjo4PqatGvQuuudefOncJvFOrweDw8fvxY5FjXrl1RU1MDFxcXdOzYkbUdc3NzkZ8tLCwgEAiQn58PW1tb5Ofni01wDA0NoaurK7bK0JsPz765GlZ+fj4uXryI0aNHi0y6CgsLxXKvry5VMTU1Ffk5NzcXAMSu2cLCArW1tSgoKBB+AGbLUdJxWXKXVF9DXPebQkJCEB8fj02bNmHgwIEoLS3F6NGj8f333wv35gHY+wvwatLr7OyMv//+G5MnT8a0adMQEBAAExMTXL9+HQkJCSgrK4O+vj6KiopgYWEhceJd18/37NmD8+fPi8Sx9fOqqirWbxIJIUSTXLn3FHEHEhF//iZq+eLjOo/LRZhPO0QP9IeX2//u1FDH74DGRhMLNRMIBGIdSyAQCP+CzDDMa/9f7emxYhgIc6rPlStXoKOjA3d3d2GZzp07w8PDA7t27RLeQvEmOzs7lJSUYNGiRTAyMkJsbCz27duHqVOnIiMjA0OGDIGjo6NYHleuXEGXLl1kzk8Wr78XquDk5ITjx4+L1Gdvbw9tbW14e3uLPXsxevRodOrUSZhDZmYmxo8fjylTpuDo0aN4//33Re5zr6v3wYMHwr0NGIbB/fv3oa+vj2bNmgEAWrZsiXv37olc39OnT1FVVQVnZ+c3+h77a1D3c8uWLeHh4YERI0YIH0iuy73ur91sfbq+uut7zdn/nbC3U5fHvXv3RB64v3fvHoyNjWFlZcVaj7Q65clTWn11E4+KigqR87m5uTAyMpL4PkjL6/W2goKChN94Xb9+HQMGDIClpSW++eYbYbn79++L1PHgwQPh68YwDH7//XdERkZi9erVwpi6v7TVte/s7IwXL14IV197k62tLXR0dNC9e3f4+PiI9ZUOHTqI5JCVlQUnJyep11b3v2+OpXXj6Nv4i1uduau6LWXqk7esPPGyxNYXI+089bfGaU/ZupTpczW1fBy8kIp18Um4ev8Za7yZkT7G9euOiQO8YW9lJqxD1vY1tc/J0yZNLBpYbGwsYmNjwefzAbz6a2BlZaVIjEAgQElJCRiGQW1trfC2n1YOVti5MBrAqw/3AgEfXC5P4jMWks7XV7Y+rRysJN6K9KbLly+jTZs24HA4ImUGDBggXL5V0lKSW7duxerVq5Geno49e/agbdu22LlzJzZt2gQvLy80a9ZM7MHp9PR0tG7dWub86sMwjPC9UsXa0QzDwNvbG0uWLMGzZ89gZ2cH4NWtWOPGjUNKSgq+/PJL4Q7zAoEA27Ztg6mpKWpqalBVVSX8sL569WpcvnwZffv2hZ+fn/Dbn7p8f/jhB/Tp0wcmJibIy8tDbGwsxo4dKzw/btw4rFy5Eu+//z5cXV1RU1ODBQsWwM7ODoGBgSJ9j8/no6amRli2bkCrOz9t2jTExsZi2bJlaNGihfC1OnHiBLS0tETK8vl8kffnzbrqnp/JzMys95unujpfz/X1nF9vp0uXLnB3d8eiRYvwzz//QFtbG8+fP8cff/yBCRMmCGPfzOf1PvB6O6/nL62/1X3ofj3mzfrs7e1haGiIQ4cOoWPHjuDz+bh48SLOnj2L4OBgkWt6/RolXevrbe/ZswedO3cWTqzc3NxgYWGB0tJSkev59ddfERERASsrK5SVleH7779H//79YWpqKrxNLCMjQxj/4sUL/PTTTyLXMXToUMyfPx8ff/wx1q5dC21tbTAMg507d2LUqFHQ1tbGxIkTkZKSgi+++ALm5ubCjZ527NgBExMTkdc9JSUFvXr1knhtdf1SIBAgLy9P5HYzgUCAoqIiMAzz1t27rM7cVd2WMvXJW1aeeFli64uRdp76W+O0p2xdivS5py9eYv2Ri9iVcAPZhaWscc62FhjSwx0jenWGgZ4uIKhmveXpbe1zJSXsu4KzoYlFA4uJiUFMTAyKi4thamoKa2trkWUYgf99UCktLYWWlpbwvm8LEyP4tPvffd81NTUiv0jfJO18fWVV5fr16+jWrZvYswqhoaFYuXIlkpKSMGDAANay5ubmWLBggcgxf39/+Pv7S8w/NDQUX3/9NbKysqCvr49NmzapZA18Vb5WAQEBsLGxwdGjR0V2hF+zZg2mT58OV1dXdOnSBVwuF7dv30afPn0QHh4ObW1tzJ07F7dv38aVK1egr68Pf39/fPfdd5g5cya6d++Ojh07Cv8KbG9vj06dOsHT0xNXrlxB8+bNsWzZMuF7MXfuXNy8eRPdu3eHt7c30tPTUVhYiH/++Uf41+a62NdXxtLW1gaXywWHwxGe/+STT5Cfnw8vLy906tQJRkZGuHPnDlq3bo24uDhoa2sL8+LxeCL94c26/P390aZNGwQFBaFdu3Zwd3dnXW62rq66POvKv57z6+1oaWlhy5YtGD58ONq1a4fWrVvj4sWL6NKlC5YuXSqMfTMfSe28nr+0h8w5HE699WlpaeHHH3/ERx99JFw1LC8vD+3atROp//Vy0q71dbq6uhg0aBAMDAzg6OiI1NRUmJqaYvbs2SLX4+HhgS5duqBDhw5ITU0V/vupe9+//vprDBkyBF26dIG9vT1SUlLg5eWFR48eCeuxs7PDnj17MGnSJLi7u8PT0xP3799HSEiI8AH3VatW4f3334e7uzu8vLzA4/GQlpaGgIAADBs2TJhPZmYmUlNTERsbW+/u21wuF5aWliL/1gUCATgcDqytrd/KD3rqyl3VbSlTn7xl5YmXJba+GGnnqb81TnvK1iVP+bvPXmJdfBL+PXsVVTV81pi+XdwxJdQPfu1ckJubW2+9b2ufk+dzFU0s1IzL5bJ2iLq/+NZ9KHkTwzAiMfKcr6+sKi1btgxubm5i7QQEBGDnzp1wdnaWOwdp+X/++ecYNGgQ7t+/Dy6XK7bykrxU/VoxDANdXV2899572LhxI6Kjo4XnDA0NsXnzZmRmZuL69evQ1dVFu3bthA/31tTUwNvbG5MnTxZZTeuTTz5Bq1atUFVVJdJfli1bBl1dXeGtPt7e3iK3nujp6WH37t24d++ecD8BX19fGBgYCGMcHR2xc+dO4YPMdXV/+OGHqKysFHltli5dilmzZuH69esQCATw8PBA8+bNhddtZGSEHTt2oFu3biKv5YQJExAUFCQ8pq+vjxs3buDixYvIzs6GmZmZxNe+Xbt22LlzJywsLIQxr+f8ZrmuXbviwYMHuHTpEvLy8vDjjz+iXbt2IjFjx45FQECAsCzDMHB1dcWOHTvg6OgoUucff/wBV1fpO6F+++23wr/MS8v7vffeQ1hYGG7evAlLS0t07NgR165dE/7yAP7376buZysrK+zcuRPt2rWTOA6EhYUhLCwMqampyMzMhJOTk8h+JnXlZsyYgfbt2yM1NRU8Hg8+Pj7CsYnD4aBXr154/PgxLl26hNraWnTs2BFaWlo4e/YsTE1NweFwwDAM/Pz88ODBA6SkpKCgoADt2rUT9oO693fDhg1YvHgxbt26BR0dHbRv317sIfa//voLHTp0gK+vr0xjHNtYKun420Cduau6LWXqk7esPPGyxNYXI+089bfGaU/ZuqSVFwgEOHHlLtbFJyLhxgPW8gZ6OhjdpysiQ33ham8tLCdrXm9jn5OnPQ6jypvTiUR131gUFRWxfmPx/PlzlJSUwMXFhXVmWHdrhZaWlsRfupLO11dW06kzf1W3VVdfeXk53N3dsW3bNvTu3VuluaSkpKBbt25IS0tDq1atZMpdlrqbap9Td+6qbE+WurKysmBnZ4djx46JbFKnSB6ylqkvrqysDC4uLti8ebPIpJOtjtraWjx58gTOzs5i31hkZ2fDxsbmrfugp87cVd2WMvXJW1aeeFli64uRdp76W+O0p2xdksqXVlRhx6kUrD+YjMcvclnLOtmYIzLEFxF9u8H0jSX4Zc3rbe1z0j7Dvom+sSBEDUxMTHD48OG38kE/QhpacXExNmzYILK8LyGENLSnL/Ox/mAStp28hJLyKtaYLq0cMH1oHwR393ynNrJrKDSxIERN6lZ6UjVXV1fs3LkTDg4ODVI/ebeYm5tj586dIrdHNTY7OzvY2tqqbBEGQgiRhGEYnLv1CBsOJePIpTQIBOI37uho8TDEvxOmhPrCxlDrrfxmqrHQxIKQt5y5uTnCw8PFViIihI2urq7IjtqEENIUVFbXYG/CNfy+7wzuPc9hjbE2M8KkAT4Y378HrM2MhbcfEdnRxIIQQgghhLyTsgtKsOnIOWw6ch55xWWsMe1dHBAd5o9Bfh2gq00fjZVBrx4hhBBCCHmn3HiYgbj4JPyXdB01teLLxXK5HAR398TUgf7o1qblW7fQiKaiiQUhhBBCCHnr1fL5OHzxFtbFJ+Hi7SesMUb6uhjXrzsiQ33hZGOh3gSbAJpYKODGjRtYuHAhMjIyEBQUhEWLFtW7oZOsaPVfQgiRjMZIQsibCkvL8c/xS9hwKBnPcwtZY1ztrREZ6oMADye0bO5ID2M3EJpYKCAmJgaffvopbGxsMGPGDNjY2GDmzJlK1Vm3kVl5ebnSm7wRQsi7qry8HACEO4QTQpquBxnZWHcwCTtPX0ZFVQ1rTO9ObogK80PvTm4AQA9jNzCNnFgUFRWhpKQENjY20NHRaZA28vLywOfzxXZ/fTPGyMgIurq6IsdPnTol/IYiLCwMFRUVSufD5XJhZmYm7PAGBgYi9/s11c3KgHdjgzxF6pO3rDzxtEGeZO/6BnmqLKuqDfJkiREIBCgtLUVeXh7MzMxEdpUnhDQdDMPg9LV7WH8wCaeu3mON0dPRxsjeXogK80Vrx2bC47SXVMPTuIlFQUEBOnXqhKdPnyIhIQH+/v4qrX/Pnj1Yu3YtTp8+jbZt2+LatWtiMcePH8fUqVORnZ2N2tpaTJw4Eb/++qvwL2R1k4rbt2/jyJEjOHTokEpya9asGTgcDutsmmEYCAQCcLlciR/yJJ2vr6ymU2f+qm5LmfrkLStPvCyxTbXPqTt3Vbanzv4mTxlV9Tc+nw9LS0vY2trKdlGEkHdGeWU1dp6+jD/+O4snL/NZY+wsTTEl1Bdj+naHubGBmjMkgAZOLKKjoxEYGIiNGzdKjePz+RL/YiXpHJ/Px6ZNm/Dpp5+iffv2OHHihFhMRkYGhgwZgs8//xzz58/Ho0ePEBAQgK+++grfffedMO7ChQv47LPPsHv3bpibm8t3kRJwOBzY2dnBxsYGNTWiX+kJBALk5eXB0tJS4jbwks7XV1bTqTN/VbelTH3ylpUnXpbYptrn1J27KttTZ3+Tp4yq+lthYSFsbW3fuskqIURxz3MKsPHwOWw9dhFFZex3iHR1b4GoMD+E9GgHbS36NrMxadTE4tdff0V2djaWLVtW78Ri1KhR8Pf3x8cffyxyfPHixXj06BFreR6Phz179gAAjh07xlrvxo0bYWhoiPnz54PH46F169b46KOPsGLFCixZsgRaWlrYt28ffvrpJ/z777+wsrKS6xoFAoHYV3ECgUD41zrg1QTjzVvABAIBtLS0oKOjI/GXrqTz9ZXVdOrMX9VtKVOfvGXliZcltqn2OXXnrsr21Nnf5Cmjqv7G4XAk3srw5jj6NlFn7qpuS5n65C0rT7wssfXFSDtP/a1h22MYBil307H+YDIOXbgFPktZLR4Xg3w7YEqoLzq1chJpT1W5yBqvqjhN7XPytKkxE4sbN25g8eLFuHDhgthf69nMnDkToaGh4PF4mDFjBgBgyZIl+Omnn3D06FGF87h48SJ69Ogh8o1Hz5498cUXX+D+/ftwc3PD8OHD4eDgILxNa+TIkfjmm29Y64uNjUVsbCz4/FdrKOfk5KCyslIkRiAQoKioCAzDSP2lKy1G2nlZ6tdk6sxf1W0pU5+8ZeWJpz4nmbpzV2V76uxv8pRp6P6maP6agsY4GuPUSZPHuJpaPo5duYd/Tl1F2tOXrDGmBroY0bMjRvXqCGszIwCyP5DdUH1OVXGa2udKSkpkjtWIiUV5eTkiIiLw448/okWLFnjw4EG9ZXr16oX//vsPAwcOhJaWFoqKirBixQocPXoU3bt3VziXnJwctGnTRuRY3bcSOTk58PDwwK1bt0TOm5mZSawvJiYGMTExKC4uhqmpKaytrWFiYiISU/eXOGtra6kDoLQYaedlqV+TqTN/VbelTH3ylpUnnvqcZOrOXZXtqbO/yVOmofubovlrChrjaIxTJ00c43KLSrHl2AVsPnIB2YXsH2I9WtgiMsQHfu4OcLS3Uyj3hupzqorT1D6np6cnc6xGTCw+//xzODk5ISAgABkZGcjKygLw6oN83T23bAIDA7F3717h5OLYsWPw9vZWKhcul4va2lqRY3XfoNR9i/HmxEPe+tk6BIfDkXhO1hhp52WpX5OpM39Vt6VMffKWlSee+pxk6s5dle2ps7/JU6ah+5ui+WsKGuNojFMnTRnjbj3JxLr4JOxNuIaqmlrWcv27eiAqzB++7VzAMAyys7OVyr2h+pyq4jSxz8nTnkZMLLKysnDr1i3hpKDutqH33nsPgwcPRlxcnMSy169fh66uLmpra3Hr1i34+fkplYujo6NwYlPn5ctXX8c5ODgoVTchhBBCSFPG5wtwLOU24uITce7WI9YYI31dRPTthsgQX7S0/d8fl2mDTM2nEROLnTt3ivz84MEDtG7dGv/++6/U5WZXrlyJRYsW4eDBgygrK8Pw4cPB4/EQFRWlcC69evXCnDlzUFZWBkNDQwDA4cOH0bx5c7Ro0ULhegkhhBBCmqqS8krsOH0Z6+OT8TSbfbnYlraWmBLqh1F9vGBsIPvtN0RzaMTEQhGxsbGYP38+4uPj0atXLwDArl27EB4eDi0tLUyaNIm1XHZ2Nqqrq1FaWoqamhpkZGQAePVtBIfDwaRJk7BixQpMmDABCxYswM2bN7FmzRqsWbOGljgkhBBCCJHD4xe5+PXfU9h/Pg1lldWsMX7tXREd5o++XdqAx3v7bi0j/6OREwstLS04ODiI7Xj9uqysLPz333/o3bu38FhYWBh27NiBmzdvSiw3YcIEkYev626/SktLg4mJCYyMjHD69GnMmzcP4eHhsLCwwJo1axAdHa38hRFCCCGEvOMYhkHizYdYF5+I45fvsN7CpKutheG9OiMqzA8eLewaIUvSEDRyYtGyZUvhNwmSSFreddCgQRg0aJDEckeOHKm3fWdnZ2zbtq3eOEIIIYQQ8kpFVQ32JFzFuvgk3HmaxRrTzNwYk4J9MT6oOyxNjdScIWloGjmxIIQQQgghb4cXeUX46/A5bDl2AQUl5awxHV0dMXWQP8K820NHmz5+vqvonSWEEEIIIXK7ev8Z4g4k4sC5G6jli+/OzONyEerdDsN9PNC3R0eRzYfJu4kmFoQQQgghRCY1tXwcvJCKuAOJuHLvKWuMmZE+xgf1wMRgH9hZmCA7O5sWwGkiaGJBCCGEEEKkyi8pw9/HLmLDoWRk5Rezxrg52iAqzB8jAjpDX1cHwKsdo0nTQRMLQgghhBDC6u7TLKyLT8Lus1dRWV3DGhPYpQ2mDvRDzw6t6ZuJJo4mFoQQQgghREggEODk1buIO5CIhBsPWGMM9HQwqrcXIkP90MrBWs0ZEk1FEwtCCCGEEIKyiirsOHUZ6w4m4fGLXNYYR2tzRIb6YkzfbjA11FdzhkTT0cRCAVVVVdi6dSsyMjLQr18/+Pr6NnZKhBBCCCEKefoyHxsOJWPbiUsoLq9kjfFu64yoMH/07+YBLVrdiUhAEwsFBAQEoF27drCxscHAgQOxefNmhIWFNXZahBBCCCEyYRgG5249wrr4RBy5lAaBQHx3bB0tHob4d0J0mB/auTg0QpbkbUMTCwVs2rQJbm5uAAA9PT2cO3eOJhaEEEII0XiV1TX479wt7Eq8iVtPXrDGWJkaYVKwNyb094a1mbGaMyRvM42ZWKSnp2PVqlW4dOkSDAwM0KdPH8TExMDISLXbvRcWFmLTpk3Ytm0bnJycsH37drGY7OxsfPPNN0hJSYGFhQWmTp2KoUOHCs/XTSoqKipw5MgRrF27VqU5EkIIIYSoUnZBCTYdOYfNRy8gt6iUNaadsz2iB/pjsF9H6NLu2EQBGtFrSkpKMHjwYEydOhXDhw9HVlYWvvzySxw/fhzHjh1TWTt8Ph+enp4YPnw47O3tcffuXbGYqqoq9O7dG3Z2dli8eDFSU1MxcuRIbN26FaNGjRLGFRUVISIiAl988QU6dOigshwJIYQQQlTl5qPn+PNAIv5Luo6aWr7YeS6Xg+Bunoge6I/uHi1puViiFI2YWBgaGuLy5cvQ0vpfOgzDYOTIkSguLoaJiYlYmZUrV8LPzw/dunUTOX727FmkpaVh+vTpYmV4PB7u378PAwMDzJ49Gw8eiC+htmXLFjx69AjJyckwMzNDUFAQHj58iC+//FI4scjIyEBERASWLl2KgIAAZS+fEEIIIURlavl8HLmYhrj4RFy8/YQ1xsRAD2P6dUNkiC+cbCzUmyB5Z2nExILL5YLL5Qp/5vP5OHHiBNzd3WFszH5vX3FxMfr374/jx4/Dy8sLAJCYmIiwsDAsWrRIYlsGBgZSczlx4gR8fX1hZmYmPDZw4EDExsbi2bNncHBwgI+PD9zd3bF//37s378fPXr0wMiRI2W6VoFAILYLpUAgAMMwUnenrC9G2nlZ6tdk6sxf1W0pU5+8ZeWJpz4nmbpzV2V76uxv8pRp6P6maP6agsY4GuNUpbC0AttOXsLGQ+fwPLeQNcbFzgoje7bHpLCeMDZ4tVxsQ16HpoxxipRX5RgnS5ym9jl52tSIiUWdxYsXY/fu3Xj+/DmcnZ1x8uRJiV/JLViwADU1NQgKCsLJkydRXl6OkJAQLFiwAJ988onCOTx79gzNmzcXOWZvby885+joiJkzZ4qcNzU1lVhfbGwsYmNjwee/+voxJycHlZWiS7kJBAIUFRWBYRiRCZY8MdLOy1K/JlNn/qpuS5n65C0rTzz1OcnUnbsq21Nnf5OnTEP3N0Xz1xQ0xtEYp6wnL/Ox7fQ17D9/C5XVtawx3h4tMLZPZ/Rwb46SkmKUFRehorSkwXPTlDFOkfKqHONkidPUPldSIns/0aiJRWRkJAYOHIj79+9j4cKFmD59Ovbt2ydxcvHNN9+guroa/fr1Q3V1Nb744gt89tlnSuVQU1MDXV1dkWN1P9fU1IDD4WD27Nky1xcTE4OYmBgUFxfD1NQU1tbWYrd2CQQCcDgcWFtbSx0ApcVIOy9L/ZpMnfmrui1l6pO3rDzx1OckU3fuqmxPnf1NnjIN3d8UzV9T0BhHY5wiGIbBmev3sf5gEk5dvccao6ejjfCAzogM8YWbUzMAr3Ln8bhNboxTpLwqxzhZ4jS1z+np6ckcq1ETCycnJzg5OaFLly5wd3dH586dkZycDD8/P4llhg0bhp9//hna2toqWfLV0tISeXl5Isfqfra0tFS6/jdv+6rD4XAknpM1Rtp5WerXZOrMX9VtKVOfvGXliac+J5m6c1dle+rsb/KUaej+pmj+moLGOBrjZFVeWY1dZ65g/cEk3M/IZo2xszRFZIgvxvbrDnNj8VvAm+oYp0h5VY5xssRpYp+Tpz2Nmli8ztraGgBQUFAgMSYlJQXBwcH48ssvUVRUhH79+uHUqVPw9PRUuF0vLy/ExcWBYRjhNyXnzp2DkZGRcJlZQgghhBB1ep5TgI2Hz+Hv4xdRWFrBGtPVvQWiwvwQ0qMdtLVod2yifhoxsThx4gSqqqoQEhICDoeD8vJyfP311zAzM4O/vz9rmatXr6J///6YOXMmFixYAODV10SBgYE4ffo0PDw8FMpl0qRJWL58OX799VfExMTg5cuXWLNmDSZNmgQdHR2Fr5EQQgghRB4MwyDlbjriDiTi0IVb4LM8RKvF42KwX0dEhfmhUyunRsiSkP/RiIlFmzZt8Mknn2DcuHFo1qwZnj17hk6dOuHw4cMiqzO97quvvsL7778vsgLUzz//DD6fj0WLFmHbtm2s5UaPHo27d+8iMzMTJSUl6NSpEwAgISEBxsbGcHV1xdatWzFt2jR8++23yM3NRXBwMFasWKHqyyaEEEIIEVNdU4sD524i7kAirj/MYI2xMDHEhP49MHGAD2wtxJflJ6QxaMTEwsHBAdu3b0d5eTkyMjJgZ2cncZnZOrt27WJ9mGTVqlViqy69bvHixaioEP8K8fVlaMPDwzF48GA8evQI5ubmaNasmRxXQwghhBAiv7yiUmw+dgGbDp/DywL2lXg8mtsiKswPQ3t2hr6utpozJEQ6jZhY1DEwMJD5OQZpT6hLO+fu7i5T/To6OmjTpo1MsYQQQgghikp78gLr4hOxJ+EaqmrEl4vlcDgI6uqBqDA/+LVzpd2xicbSqIkFIYQQQkhTwOcLcPzybcTFJyE59SFrjJG+LkYHdsWUUD+0tFV+ZUpCGhpNLAghhBBC1KSkvBLbTl7ChoPJSH+ZzxrT0tYSkSG+GB3YFcYGsu8hQEhjo4kFIYQQQkgDe/wiFxsOJmP7qRSUVlSxxvi1d0V0mD/6dmkDHu/t24+FEJpYEEIIIYQ0AIZhkHjzIdbFJ+L45TtgGEYsRldbC8N6dkJUmD/atrRrhCwJUR2lJxYVFRWorq6GqampKvIhhBBCCHmrVVTVYG/CVcTFJ+HO0yzWmGbmxpgU7IvxQd1haWqk5gwJaRhyTyxevnyJTZs24dixY7hw4QKKi4sBANra2vD09ESfPn0wZswYdOvWTeXJEkIIIYRoqqz8Yvx1+Bw2Hz2PgpJy1phOrRwRPdAfYd7toaNNN46Qd4vMPfrZs2eYP38+tm3bhtraWri7uyMkJARWVlbQ0dFBXl4eHj58iLVr1+Lnn39G165dsWzZMgQFBTVk/oQQQgghjerq/WdYF5+I/ck3UMsX3x2bx+Ui1Lsdogf6w8utOS0XS95ZMk0skpOT0a9fP3h6euKXX37BqFGjYGnJvuxZTU0Njh07hs2bNyM0NBSffPIJli9frtKkCSGEEEIaUw2fj/+SbmD9oSRcvvuUNcbMSB/j+vXApBAfOFiZqTdBQhqBTBMLbW1t7Ny5E2FhYTLFhoaGIjQ0FEuWLEFSUpLSSRJCCCGEaIL8kjJsPXoBGw4m4WVhKWtMa0cbRIX5YUSvLjDQ01FzhoQ0HpkmFoo+L+Hq6gpXV1eFyhJCCCGEaIp7z14iLj4Ru89cRWV1DWtMYJc2iA7zQ6+Orel2J9Ik0VNDhBBCCCEsBAIGJ6/cwbqDyTh7/T5rjIGeDkb19kJkqB9aOVirOUNCNIvCE4va2lps374dhw4dQkZGBiorK0XOBwYGYtmyZUonSAghhBCiTmUVVdh+KgVx+xOQnl3AGmNnYYKogf4Y2687TA311ZwhIZpJoYkFwzAICQnB8ePH0bx5czg4OEBPT3TLeW1tbZUkSAghhBCiDk9f5mPDoWRsO3EJxeWVrDE9PJwRFeaLjs2tYG9nCy6XdsgmpI5CE4vz588jKSkJx44dQ79+/VSdEyGEEEKIWjAMg/O3HiEuPhFHLqVBIBDfHVtHi4fB/h0RHeaP9i4OEAgEyM7OboRsCdFsCk0sCgsL4efnR5MKQgghhLyVqmpqsf/8LexMuIlbT16wxlgYG2BSsA8mDvCBjbmxmjMk5O2j0MTCy8sLWVlZYBimSa56UF1djW3btiEjIwP9+vVD9+7dGzslQgghhMggu6AEm4+ex6Yj55FbxL5cbDtne0wJ9YVPazs4OtjT7U6EyEihiYWNjQ0++ugjfPTRR1i2bBlMTExUnZdGCwgIgLu7O2xsbDBgwAD8/fffCAkJaey0CCGEECLBzUfPERefiP8Sr6O6li92nsvlILibJ6LC/NCjrTMYhqHbnQiRk8KrQk2dOhULFiyAra0tXF1dYWpqKnK+T58++Oabb5ROUBNt2LABbdq0AQAYGRkhKSmJJhaEEEKIhqnl83Hswi2si0/ChduPWWNMDPQwpl83RIb4wsnGQnicYcSftSCESKfwxGLSpEnYvHkzHBwcoK+v/DJrKSkpiIuLw507d2BjY4OxY8di6NChStf7puLiYmzZsgXbtm2Dk5MTtm7dKhaTm5uLpUuXIiUlBRYWFpg6dSoGDhwoPF83qaisrMTRo0exZs0aledJCCGEEMUUlVVg0/EU7E68iYycQtYYZztLjOrZAZEDA2BMy8USohIKTSyuXbuGXbt24ciRI+jfv7/SSezfvx9LlizBlClTMGbMGNy4cQPjxo3DggUL8Pnnnytdfx0+n482bdpgyJAhsLKywq1bt8Riqqqq0Lt3b1hZWeGLL75Aamoqhg4dim3btiE8PFwYV1JSgoiICMyZMwedOnVSWY6EEEIIUcyD5zlYfzAJO09dRnlVNWtMr46tER3mj4COrZCbmwtDfV01Z0nIu0uhicWLFy/g5+enkkkFAPTt2xeDBg0S/hwQEIDc3FysXLlS4sRizZo18PX1RZcuXUSOJyUl4fbt24iOjhYrw+PxcO/ePRgZGWH27Nl49OiRWMzWrVtx//59JCQkwNzcHCEhIXj8+DHmz58vnFhkZmYiIiICCxcuRGBgoDKXTgghhBAlMAyDs9fvIy4+CSev3GGN0dPRxoiAzogK9YN7c1sAgEAgUGeahDQJCk0sunTpotJVoQwMDFiP1dbWSiyTnZ2NoKAgnDhxQviNQXJyMkJCQvDVV19JLGdkZCQ1lxMnTsDX1xfm5ubCY4MGDcLatWuRkZEBe3t7eHt7o02bNjh69CiOHj2K7t27Y/jw4fVc5SsCgUBsMBMIBGAYRuogV1+MtPOy1K/J1Jm/qttSpj55y8oTT31OMnXnrsr21Nnf5CnT0P1N0fw1BY1xio1xFVXV2H32KtbHJ+P+c/aHrO0sTTFpgDfG9usGc2NDYT2ytE9jnOa1p2xdDfV7VVVxmtrn5GlToYlFs2bN8Mknn2D27NlYtGhRvR/W5VVQUIA1a9Zg2LBhEmMWL16Mmpoa9OvXDydPnkR5eTlCQkIwb948fPbZZwq3/fTpUzRv3lzkmL29vfCcg4MDPvjgA5Hz0p4xiY2NRWxsLPj8VytQ5OTkoLJSdDdPgUCAoqIiMAwjcUm7+mKknZelfk2mzvxV3ZYy9clbVp546nOSqTt3Vbanzv4mT5mG7m+K5q8paIyTb4x7kV+MXQk3sCfpJorLq1hj2zvbYUh3N4T5tIeOtjZqKsqQXVEmV/s0xmlee8rW1VC/V1UVp6l9rqSkROZYhSYWZ86cwV9//YXHjx/j999/R+vWrcVWhQoICMCiRYvkrruqqgrh4eEwNjbG999/LzX222+/RU1NDfr27Yvq6mrMnj0b8+bNk7vN19XU1EBXV/R+y7qJQ01NDTgcDubOnStzfTExMYiJiUFxcTFMTU1hbW0ttjyvQCAAh8OBtbW11F+60mKknZelfk2mzvxV3ZYy9clbVp546nOSqTt3Vbanzv4mT5mG7m+K5q8paIyrvyzDMLh05wl+25uEk9cegs/yF1QtHhcDfdpjSqgfOro6ICcnh8Y4Fk11jFOkvCrHOFniNLXP6enpyRyr0MRCIBCgsrISdnZ2sLOzAwCxv8LX1NTIXW9VVRWGDx+OjIwMnD59Wmyywmb06NFYtWoVtLW1Zb4dSRpLS0vk5eWJHMvNzRWeUxaXy2XtEBwOR+I5WWOknZelfk2mzvxV3ZYy9clbVp546nOSqTt3Vbanzv4mT5mG7m+K5q8paIxjL1tdU4sD525iXXwirj3IYI0xNzbAhP7emDjAG3aWrz431H0IozGOXVMd4xQpr8oxTpY4Texz8rSn0MSiT58+OH/+vCJFJaqursaIESNw//59nD59WjhhkebKlSvo378/5s2bh8LCQgQGBuL06dPw8PBQOI8uXbpgw4YNIs+PXLhwAUZGRnBzc1O4XkIIIYTIJq+oFJuPXcCmw+fwsoD9NgyP5raICvPD0J6doa+rreYMCSFsFN7HQpVqamoQHh6Oe/fu4fTp08JnGqS5ceMGgoKC8MEHHwhvuRIIBMLJhbu7u0K5TJo0CcuXL8fvv/+O6dOnIycnB2vWrMGECROgo6OjUJ2EEEIIqV/akxdYF5+IPQnXUFUjvoALhwP08/JA9EB/+LVzVckCMoQQ1ZFpYvHs2TMYGRmJrJQkC4FAgFu3bqF9+/ZS4zZv3oz9+/fD2dkZgwcPFjl3+vRp1ofD582bh+joaCxdulR4bPXq1RAIBFiwYAG2b9/O2ta4ceNw9+5dZGRkoLi4GF27dhVpp1WrVti8eTPee+89fPfdd3j58iX69u1b7/MehBBCCJEfny/A8ct38OeBRCSnPmSNMdLXxeg+XhjUzR1e7dzeytuPCGkKZJpYpKSkIDIyEjNmzEBUVBRatGghNb68vBy7d+/GihUr0LZtW4kf8usMGjQIly5dYj0nacWlnTt3si5Tu2bNGrHnPV43f/58lJeXS21n9OjRGDJkCB48eAALCwuZvkEhhBBCiOxKyivx96kr2JlwE09f5rPGtGhmgSmhfhgd2BWGejrIzmZfVpYQohlkmlgMHToUpaWl+OKLL7BkyRL4+PjA19cX7du3h6WlJbS1tZGfn49Hjx7h4sWLOHHiBKqrq/Hhhx9K3VOijrW1NaytreVKnG1SAbx6sEXa8q9t27aVqX49PT20a9dOrpwIIYQQIt2TrDysP5iE7SdTUFrBvlysbztXRIf5oZ+XB3i8V99OvI17RhDS1Mg0seBwOJgwYQJGjRqFXbt2Yf369Vi9ejWqqsQHBA8PD8yZMwdTp06Fra2tyhMmhBBCyNuFYRgkpT7EuvgkHEu5DYZhxGJ0tbUwrGcnRIX5o23L+hdwIYRoHrke3tbV1cW4ceMwbtw4VFZW4saNG8jKykJ1dTWsrKzQtm1b2NjYNFSuhBBCCHmLVFTVYG/CVayLT8Ltp1msMTbmxpgU7IMJQT1gaaraDXcJIeql8KpQenp66N69uypzIYQQQsg7ICu/GH8dPoctxy4gv7iMNaaDqwNG+rfH2AF+0NOlVRcJeRdoxHKzhBBCCHn7Xb3/DOviE7E/+QZq+eLPRPC4XIR6t0NUmB+6tHZCTk4OdLTpowgh7wr610wIIYQQhdXw+fgv6QbWH0rC5btPWWPMjPQxrl8PTAr2hoP1q6Xr6WFsQt49NLEghBBCiNwKSsqx9dgFrI9PxMvCUtaY1o42iArzw4heXWCgR7c7EfKuo4kFIYQQQmR279lLrDuYhF2nr6CyuoY1JrCzO6IH+qNXx9a0OzYhTQhNLAghhBAilUAgwKmr97AuPhFnrt9njdHX1caoPl0xJdQPrRzk25uKEPJuoIkFIYQQQliVVVRh5+nLWHcwCY8yc1lj7CxMMCXMD2P7dYeZEfvmtYSQpkHuiUVycjJSUlJgZWWFQYMGwdjYWCympKQE9+/fR5cuXVSSJCGEEELU51l2PjYcSsY/xy+huLySNaaHhzOmhPqiUwsr2NvZgsvlqjlLQoimkWtisXDhQixatEj4c7NmzXD06FF06NABlZWV2L17N3bs2IGjR48iLCwMu3btUnnChBBCCFE9hmFw8fYTxB1IxOFLtyAQiO+Ora3FwxD/jogO80d7FwcIBAJkZ2c3QraEEE0k88Ti5cuXWLZsGUaNGoWRI0ciLy8Pa9euxdixY/Hdd99hypQpyMnJAY/Hg7+/P8aOHduQeRNCCCFEBapqavFf0nXEHUhE6uNM1hgrUyNMHOCNCf29YWMufqcCIYQAckws0tLS4OLign/++Uf4dWdkZCS6du2KMWPGwN7eHosXL8aIESNgbU0PbRFCCCGaLKewBJuPnsemI+eRI2G5WE9ne0SH+WOIf0fo0kZ2hJB6yDxK5Ofno23btiL3UOro6GDKlClYsWIFrly5AkNDwwZJkhBCCCGqcfvpS3y74zT+S7qB6lq+2Hkul4MB3doiOswfPdo603KxhBCZyTyxYBiG9cEsR0dHdO3alSYVhBBCiIbi8wU4cikNfx5IwMXbT1hjjA10MaZvd0SG+KJ5Mwv1JkgIeSfI9b1mamoqYmNj4enpCU9PT+EtTzo6tJsmIYQQommKyirwz4lL2HAwGRk5BawxznZWiAr1w8g+XjDS11VzhoSQd4nMEwtDQ0M8evQIH374ofCYtbU1zM3NYWRkhOPHj8PLywvm5uYNkighhBBCZPMwMwfr45Ow4/RllFdWs8b06tgaUWF+COzsTkvFEkJUQuaJRUhICIqLi3H9+nVcvnwZKSkpSElJQVpaGvh8PoKCggAArq6u6Nq1K0aOHIkRI0Y0WOKEEEII+R+GYXD2+n3ExSfh5JU7rDF6OtoI7dYGH4zoC48WdmrOkBDyrpPrVig9PT306NEDPXr0EB6rqKjAtWvXkJKSIpxw7Nq1C7W1tTSxIIQQQhpYRVU1dp25gvXxSbiXwb6nhK2FCSJDfDGmb1fUVJTBxsZGzVkSQpoCpdeO09fXh4+PD3x8fITHysvLkZWVpWzVhBBCCJHgeW4h/jp0DluPX0RhaTlrTBe35oge6I/QHu2grcV7taFdRZmaMyWENBUNsii1gYEBXFxcGqJqQgghpMliGAaX7z1F3IFEHDyfCr5AIBajxeNioE8HRIX5oYtb80bIkhDSVNFuN4QQQoiGq66pRfz5m1gXn4Sr95+xxpgbG2B8UA9MCvaBnaWpmjMkhBCaWBBCCCEaK6+oFFuOXcRfh5PxsqCENaZNc1tEh/lhaM/O0NfVVnOGhBDyPzSxIIQQQjTM7fQXWBefhH/PXkVVTa3YeQ6Hg35ebRA90B9+7Vxpd2xCiEagiQUhhBCiAfh8AY5fvoO4+EQk3XzIGmOop4OIwG6IDPWFs52VmjMkhBDpVDqxuHbtGnJychAQEEC7cRNCCCEyKCmvxN+nrmBXwk2kv8xnjWluY4EpYb4Y3acrTAz11ZwhIYTIRuGJxffffw9bW1tMmDABALBs2TLMnz8fAODr64uzZ8+Cx+OpJktCCCHkHfMkKw/rDyZh+8kUlFZUscb4tnNFdJgf+nl5gMej3bEJIZpNoYlFcXExfvnlF9y7dw/Aq30rlixZgnHjxmH48OGYMWMG9u3bh+HDh6s0WUIIIeRtxjAMklMfIS4+EcdSboNhGLEYXW0tDOvZCVPC/ODZ0r4RsiSEEMUoNLG4efMmWrVqBQMDAwBAQkICqqursXr1apibm+PBgwdISEigiQUhhBACoLK6BnsTriEuPgm301+wxtiYGWNSiA8mBPWApamRmjMkhBDlKfyNhZ6envDnM2fOoFOnTjA3NwcA2Nvb4+bNm6rJkBBCCHlLZeUXY9ORc9h89ALyi9l3vO7g6oCR/u0xdoAf9HTp+URCyNtLoYmFs7MzLly4gIKCAhgaGmLnzp0YPHiw8PyTJ0/QsmVLVeVICCGEvFWuPXiGdfFJ+C/pOmr54rtj87hchPTwRPRAf3Rp7YScnBzoaNNCjYSQt5tCo1ibNm3g4eEBd3d3GBgY4NmzZ5g4caLw/PHjx7FkyRKVJUkIIYRoulo+HwfPp2JdfBJS7qazxpgZ6WNsv+6YHOwDB+tX3/ILBOITD0IIeRsp/OeR/fv3Y+nSpXj+/Dl++eUXdOzYEQDw9OlT2Nrawt/fX2VJEkIIIZqqoKQcfx+/iI2Hk5GZW8Qa08rBGlFh/ggP6AIDPbrdiRDyblJ4YmFpaYmffvpJ7Hjz5s2xbds2pZIihBBCNN29Zy+x7mASdp2+gsrqGtaYwM7uiArzQ6+OrcHl0nKxhJB3G93QSQghhMhIIBDg9LV7iDuQiDPX77PG6OtqY2RvL0SF+qGVo42aMySEkMaj0MRiz549GDNmjNSY4cOH4++//1YoKUIIIUSTlFVUYeeZK1gXn4hHmbmsMQ5WZpgS6ouIvt1gZmSg5gwJIaTxKTSxcHFxwfTp00WOVVVV4eHDhzh37hzGjRsHb29vlSSoaXJyclBcXAwXFxdwOJzGTocQQkgDysguwIZDyfj7+EUUl1eyxnT3aInoMH8M6N4WWjyemjMkhBDNodDEomPHjli5ciXruVu3bmH27Nn48ccflclL49TW1uKjjz7C7t27oaurCysrKxw7dgxWVlaNnRohhBAVYhgGF28/QVx8Ig5fvAWBQHx3bG0tHgb7dUR0mB86uDo2QpaEEKJ5VP4kmaenJ/z9/bF27VpVV92oysrK0KlTJ7x8+RLp6elwcHDA7t27GzstQgghKlJVU4udpy8jZM5qDP/qNxw8nyo2qbAyNcLHI/vi4m/zsGrGaJpUEELIaxrk4W0bGxucOXOmIapWyoMHD/Dff/+hefPmCA8PFzvPMAyOHTuGtLQ02NnZYdCgQTAweHWfrKmpKd577z0AAIfDQVVVFTw9PdWaPyGEENXLKSzB5qPnsenIeeQUlrLGeDrbIyrUD0P8O0JPR1vNGRJCyNtB5ROLnJwc/PbbbwgMDFR11QorKirCqFGj8PDhQwCvNvh7c2IhEAgQHh6OCxcuICwsDBs2bMCCBQtw9uxZNGvWTCR29uzZ8Pf3p706CCHkLZb66Dni4pOwL/Eaqmv5Yuc5HA6Cu7dFVJg/vNs603N1hBBSD4UmFklJSfj2229FjjEMg9zcXFy/fh16enrYsWOHShJUBYZh8PHHH2PAgAEYM2YMSkvF/yL1zz//4ODBg0hLS4OLiwsqKirQtWtXfPXVV/jjjz8AADU1NZg6dSratWuH2bNnq/syCCGEKInPF+BoShriDiTifNpj1hhjA12M6dsdkSG+aN7MQs0ZEkLI20uhiUV5eTmePHkicozL5aJZs2b46KOPMGvWLDg4OKgiP5UwMzNDcHCw1JidO3ciMDAQLi4uAAB9fX1MmDABK1aswB9//IHKykoMGjQIrVq1Qu/evZGSkgJ7e3vY29uz1ldVVYWqqirhz8XFxQBefTMiEAhEYgUCARiGETsuT4y087LUr8nUmb+q21KmPnnLyhNPfU4ydeeuyvbU2d/kKdPQ/U2W80VlFdh+MgUbD53Ds5wC1piWtpaICvVFeG8vGOnrCuttaDTG0RinTk11jFOkvCrHOFniNLXPydOmQhOLoKAgpKamKlJUY92+fRuhoaEix9zd3VFQUICsrCwwDIOCggJcunQJly5dAgBMmzYN06ZNY63v22+/xaJFi8SO5+TkoLJSdMlCgUCAoqIiMAwjcWfW+mKknZelfk2mzvxV3ZYy9clbVp546nOSqTt3Vbanzv4mT5mG7m/Szqe/LMD2M9fw37lbqJCwO3aPNs0xpk9n+LV1BpfLQXlJEcpL6rt61aExjsY4dWqqY5wi5VU5xskSp6l9rqRE9gGRdt7+f6WlpTA1NRU5ZmZmJjzXqlUrpKSkyFzfvHnz8Mknnwh/Li4uhpOTE6ytrWFiYiISKxAIwOFwYG1tLXUAlBYj7bws9Wsydeav6raUqU/esvLEU5+TTN25q7I9dfY3eco0dH978zyHw0HCjQdYF5+Ek1fvsranq62FEb06IzLUF22a28p0vQ2Fxjga49SpqY5xipRX5RgnS5ym9jk9PT2ZY2WaWOTl5eH27duwsrJCmzZthD9LUxf7tjA0NBTerlSnqKhIeE5eurq60NXVFTvO5XJZOwSHw5F4TtYYaedlqV+TqTN/VbelTH3ylpUnnvqcZOrOXZXtqbO/yVOmofsbAFTW1OKfEylYfzAJ9zKyWWNsLUwwOcQX4/p1h4WJ/GN7Q6ExjsY4dWqqY5wi5VU5xskSp4l9Tp72ZJpYnDp1CiNHjsSIESOwa9cu4c/S1MW+Ldzc3PDgwQORYw8ePICJiQlsbRv3r1mEEEIky8wrxMaDydhy7AKKyth3x+7i1hzRYX4I9W4PbS3aHZsQQhqCTBOLnj174tChQ8IP2HU/S/O2fRgfNmwYPvroIzx//hwODg6oqanB1q1bMXToUFpikBBCNNDle+mIO5CI+HOp4LM8XKjF42KgTwdEhfmhi1vzRsiQEEKaFpkmFs2aNRNZVenNn98Gq1atQnl5OW7fvo3q6mp899130NHRET4HMWnSJPzzzz/o1asXwsPDkZSUhNzcXCxZsqSRMyeEEFKnuqYWhy7ewrr4JFy9/4w1xtzYAOODemBSsA/sLE1ZYwghhKhek3l4u6ioCGVlZQgJCQEAFBYWijwDoaWlhSNHjmD37t24desWxo8fj9GjR8Pc3LyxUiaEEPL/8ovLsO7wBexOTMXLgmLWGFc7S7w3JADDe3WBvi7tjk0IIeom08Ti9OnT+PLLL+WquE+fPvjmm28USqohfPXVV/XG8Hg8jBo1qkHzEAhoHwt50RrvtMa7OjXVNd4VKavKNd4lxdx5moX1B5Px79mrqKqpFSvH4XDQt4s7IkN84dbMGDY2NuByuW9V36MxjsY4dWqqY5wi5VU5xskSp6l9Tp42lfrGIj09HdnZ2WjZsiUMDAzw5MkTVFZWwsvLS5lq3ymxsbGIjY0Fn88HQPtYKEKd+au6LWXqk7esPPHU5yRTd+6qbE+d/U2eMvL2N4CDxFuP8M+pq7h4l/12JwNdbQzy9kRE705obmMuLA/It4KJJqAxjsY4dWqqY5wi5VU5xskSp6l9TuX7WPTu3RuJiYkixzZs2IDz589j6dKlsLKyAgDw+Xxs2rQJx44dw9dffy1Hyu+umJgYxMTEoLi4GKamprSPhQLUmb+q21KmPnnLyhNPfU4ydeeuyvbU2d/kKSNrfyuvqkH85QfYcOgc0l/ms8Y52ZgjMsQXo/t0hYmhnkh56nPqb4vGOOpv6mxP2boaqs+pKk5T+5zK97F408uXL7F8+XLcunULPN7/lu3j8XiIjIxEWloa1q9fL3FX6qZMmbWJ38a1j1WF1ninNd7Vqamu8d5Y+1ikZ+Vh3cEkbDtxCWWV1azlfTxdEO7XDiMCe0Bbm/1XF/W5xmmLxjjqb+psj/axeAf2sXjT5cuX0bx5c5FJxes8PDxw5swZmlgQQghhxTAMklMfYV18Io6m3P7/W6BE6WjxMKxXZ0SF+cGjuS2ys7PB4719H+IIIaSpUGhiYWJigsuXLyMvLw+WlpZi5w8fPoxmzZopnRwhhJB3S2V1DfYlXsOfB5JwO/0Fa4yNmTEmBntjQn9vWJkaAZDv4UFCCCGNQ6GJhbe3N8zNzdG3b18sXLgQXbt2hYGBAR4+fIg1a9Zg165dSE5OVnWuhBBC3lI5RaX46+Q1bD12EXnFZawxHs1tMH1Ibwz26wgdCbc7EUII0VwKjdxaWlrYt28fhgwZgmHDhomc09PTwx9//AFvb2+VJEgIIeTtdf1BBv48kID9yTdQyxf/1oHL5SC0RztMCfVFc3N9NGvW7K28Z50QQogSy816enri9u3bOHjwIK5evYrq6mo4Oztj0KBBsLW1VWWOhBBC3iK1fD4OXbiFuAOJSLmbzhpjaqiPcUHdMTnYBw7Wr5aLzc7OVnOmhBBCVEmp75q1tbUxZMgQDBkyRFX5vPMEAtogT160eRRtHqVOTXXzKEXKvlmmoKQc205ewsZD55CZV8RappWDNaaE+mFEr84w0NMR1qNMf1M0f01BYxyNcerUVMc4RcrLGq+qOE3tc/K0qfRNrDk5OcjMzBRb0cPMzAwtW7ZUtvq3Hm2Qpzx15q/qtpSpT96y8sRTn5NM3bmrsj119rfXyzx6kYftZ67jwIU01t2xAaBbaweM79cVvm2dweVyUFpciNJi2dtX9rwmozGOxjh1aqpjnCLlZY1XVZym9jmVb5DH5ubNmxg/fjxu3LjBen7EiBHYtWuXotW/M2iDPOWpM39Vt6VMffKWlSee+pxk6s5dle2pu7+dunoXv+87g3O32W930tfVRnhAF0wO9oGpDhqsvymSvyahMY7GOHVqqmOcIuVljVdVnKb2uQbfIE8gEGDo0KFwdXXF+++/jytXrmDSpElITU3Fjh07MGPGDAQGBipS9TtPmU1P3sZNVVSFNo+izaPUqaluHiVL2bKKKuw8cwXr45PwMDOHNcbBygyRIb4Y068bzIwMIBC8en6iIfubrPlrKhrjaIxTp6Y6xilSnjbIU8MGeVevXkVxcTH279+P/fv3Izs7G++//z4A4IsvvsDQoUMxefJkRaomhBCigTKyC7DhUDL+OXEJRWUVrDHdPVoiKswPwd09oSVhA1VCCCHvLoUmFhkZGfDy8oKuri64XC6qq6uF5xwcHDB+/Hj8+eefWLx4scoSJYQQol4Mw+DSnSf480AiDl+8BYFAfHdsLR4XQ/w6InqgPzq4OjZCloQQQjSFQhOLmpoaGBm92g3VzMwM6emi99caGRkhJSVF+ewIIYSoXVVNLf5Luo518Um4+eg5a4yliSHGB/VAiJcrPFu7vJW3gxBCCFEtpVeF6tixI9LS0nDw4EGEhoaioKAAv//+O/r376+K/AghhKhJfkk5/j5zApuOnkdOYSlrTNuWdogO88cQ/47Q0eLR3hOEEEKEFJpYcLlc8P7//llLS0tER0cjLCwMNjY2KCoqgq6uLq0IRQghb4nUx5mIO5CIvYnXUFPLFzvP4XAwoFtbRA/0h3dbZ3A4HADyrW1OCCHk3afQxGL48OEYPny48OfVq1ejY8eOSExMhJ2dHaZPn47mzZurLMl3Sd1GUG8eo418JKPNo2jzKHVqKptH8fkCHE25jfUHk3A+7TFrjLG+LkYHdsXkEF+0aGYB4NVzF3X7Fqly8yhl+ps8uWgiGuNojFOnpjLGqaK8Ksc4WeI0tc/J06ZCE4sHDx7gwIEDGDhwIFq1agUtLS1Mnz4d06dPV6S6dxptkKc8deav6raUqU/esvLEU5+TTN25q7I9WeoqqajCvuRUbD9zDZl5xawxTtZmiOjdCYO8PWGopwOglvWWJ1lzb+j+Jk8umojGOBrj1OldH+NUWV6VY5wscZra5xp8g7zbt2/j77//xqxZsxQp3qTQBnnKU2f+qm5LmfrkLStPPPU5ydSduyrbk1bX4xe5WH8wGTtOXUZ5VTVr+e7uzTF9SAD6erVRaZ9r6P4mTy6aiMY4GuPU6V0d4xqivCrHOFniNLXPNfgGeZ6enqipqVGkaJOnzKYnb+OmKqpCm0fR5lHq9K5sHsUwDBJuPEBcfCJOXL7DGq+no4URvbpgcogPLPS4sLGxkSsPVW4eRRvk0Rinynga4yR7V8Y4dZSnDfLUsEGei4sL/P398dtvv9HtT4QQomEqqqqxN/HVcrF3n71kjbG1MMHkEF+M69cdFiaGEAgEtMITIYQQpSg0sUhNTYWhoSF++OEHxMbGolu3brC2thauFAIA7du3x7hx41SWKCGEEOle5BVh7b5E7ElORWEp++7YnVs7YepAf4R6t4e2Fu2OTQghRHUUmljcuXMHy5cvF/6cmpoqFjNixIh3dmKxY8cO3LhxAwDwxRdfwMDAoJEzIoQ0ZZfvpSPuQCLiz6WCz7J6hxaPizDv9oga6AcvtxaNkCEhhJCmQKGJRXh4uHC5waZIW1sbenp6+P777zFr1iyaWBBC1K6mlo/4czcRF5+Iq/efscaYGRlgfP8emBTsDXtLM/UmSAghpMlReuftpmjYsGEYNmwYfvvtt8ZOhRDSxOQXl2HLsQv46/A5ZOWzLxfr5tQM0WF+GN6rM/R1ddScISGEkKZKoyYW9+7dwy+//ILbt2/Dzc0NX3zxhco32istLcXff/+Nbdu2wdHREZs2bRKLyc/Px7fffouUlBRYWFhg6tSpCA4OVmkehBAijztPs7AuPhH/nr2Kyupa1ph+Xm0w3LctBvbsCh6Pnp8ghBCiXhozsUhISEBwcDAmTpyIL7/8EpmZmZgwYQLOnDmjsjb4fD7c3NwQFhYGExMT4XMSr6uurkbv3r1hZmaGzz77DKmpqRg4cCB27tyJYcOGqSwXQgipj0AgwPHLd7AuPgmJNx+wxhjq6WB0YFdEhvihpa0FsrOzRRbSIIQQQtRFIyYWfD4fkydPxqhRo7B27Vrh8fDwcIll1q5dCx8fH3Tq1Enk+Llz53D37l1MnjxZrAyPx8OdO3dgYmKC2bNn48mTJ2IxW7duxd27d/HixQtYWFhg0KBBSE9PxxdffEETC0KIWpRWVGH7yRSsP5iEJ1l5rDFONuaYEuqHiMCuMDHUB/BqIkIIIYQ0Fo2YWCQnJ+PRo0fYtm2byHFpO/1lZGSgX79+OHnyJDp06AAAuHDhAoKDgzF37lyJ5d7c9fpNJ06cgK+vLywsLITHhgwZgt9//x3Pnz+Hg4MDjh8/jtOnT6O4uBjffvstvLy8MHbsWFkuFQKBQOyXv0AgAMMwUj8U1Bcj7bws9Wsydeav6raUqU/esvLEU5+TTN25v95e+st8bDiUjB0nU1BSUcUa793WGVFhfgjy8gCPxxXWoWzuipSVtUxD9zdF89cUNMbRGKdOjTnGNXZdDdXnVBWnqX1OnjY1YmKRlpYGHo8HHo+HiIgI5Obmom3btpg9e7bEZyyWLl2K6upq9OvXD6dOnUJ5eTkGDBiA2bNnY968eQrnkp6eLtamvb298JyDg4NwVag5c+YAeLVKlCSxsbGIjY0Fn88HAOTk5KCyslIkRiAQoKioCAzDSNzdsL4YaedlqV+TqTN/VbelTH3ylpUnnvqcZOrOnc/n4+y1u9h/6T+cTX0EtgX3tLV4CO7qjjG9O8PdyQYAkJeXKxanzv4mT5mG7m+K5q8paIyjMU6d1J27KttTtq6G6nOqitPUPldSUiJzrEITi0OHDmH//v349ddfFTr/psrKSnA4HIwbNw7z58+HjY0NfvvtN3Tu3Bk3btyAg4MDa7nvv/8eNTU1CAwMRHV1NWbOnImvvvpKkUsSqqmpga6ursgxfX194TkACAgIQEBAgEz1xcTEICYmBsXFxTA1NYW1tbXYtyYCgQAcDgfW1tZSB0BpMdLOy1K/JlNn/qpuS5n65C0rTzz1OcnUlXtldQ32JV3H+vgkpKVnscbYmBljQv8eGBfUHdZmxvXWqc7+Jk+Zhu5viuavKWiMozFOndSduyrbU7auhupzqorT1D4n7Q6iNyk0sSgrK0N2drbE86WlpcjJyZG5PgsLC9TW1mLJkiUYMWIEAKB3796wt7fH1q1bhd8MsJkwYQJ+/fVXaGtrIyIiQvaLkJJLfn6+yLG8vFf3OFtaWipdP5fLZe0QHA5H4jlZY6Sdl6V+TabO/FXdljL1yVtWnnjqc5I1ZO4vC4qx6fB5bD56HnnFZawxHVwdEBXqj0F+HaCrLd8wrc7+Jk+Zhu5viuavKWiMozFOndSduyrbU7auhupzqorTxD4nT3sNcivU48ePYWxc/1/X6nTt2hXA/245AgAdHR1YWFigoKBAYrlr166hf//++Oyzz1BYWIjAwECcPn0a7u7uCufepUsX/PXXX2AYRriyyoULF2BoaIjWrVsrXC8hpGm7/iADcfGJ2J98AzW1fLHzXA4HId7tMHWgP7q6t6CVnQghhLx1ZJ5YJCYmYsmSJQCAly9f4sWLF6x7OxQVFSElJUXm26AAwMPDAz179sRvv/2G7t27g8fj4ciRI3j48CH69u3LWiY1NRVBQUGIjo7G0qVLwTAMGIYRTi4UnQRMnDgRy5cvx7p16xAdHY28vDysWbMG48ePF7tFihBCpKnl83Howi2si0/CpTtPWGNMDfUwxMcT7w/vi+bNlP9WlBBCCGksMk8sKisrkZX16j7goqIikZ/rcDgcWFpaYunSpYiMjJQrka1bt2L48OFwdHSEubk5MjIy8P3336Nfv36s8XPmzBFOAurarntI+ssvv8T27dtZy02cOBH37t3D06dPUVRUBG9vbwDA8ePHYWRkBDc3N2zcuBHvv/8+vvvuO7x48QI9e/bE999/L9f1EEKarsLScvx9/CI2HEpGZm4Ra4yrvTWiwvwwoldnlBYXwsbaXM1ZEkIIIaol88SiX79+uHbtGgDgv//+w+7du/HXX3+pLBEnJydcunQJDx8+RGVlJVxdXaU+LLJz504YGhqKHONwOPjtt99QUVEhsdxnn32GsjLx+5rrHtAGgHHjxmHYsGG4d+8eLCwsVL77NyHk3XQ/4yXWxSdj15nLqKiqYY3p3ckN0QP9EdCxNbhcLgQCAUqL1ZwoIYQQ0gAUesZi8ODBGDx4sKpzAQC4urrKFPfmpKIOh8OBgYGBxHLt27eXqX4DAwOxzfcIIeRNAoEAZ67fR9yBRJy+do81Rl9XGyN7e2FKqC9aOzZTc4aEEEKIeij88HZKSgrKysqEy65euHAB7733HnJycjBv3jx8+OGHKkuSEEI0TXllNXaevox18Ul4mMm+Cp69lSmmhPhhTL9uMDOS/AcPQggh5F2g0MSCz+cjKipK+BwDwzCYOHEiSktL4eXlhZkzZyIwMBBt27ZVabKEENLYMrILsPHwOfx9/CKKythvu+zWpiWiwvwQ0sMTWjyemjMkhBBCGodCE4vbt2+Dw+GgTZs2AICbN2/i3r17uHLlCjp37owPPvgA27Ztw+LFi1WaLCGENAaGYXDpzhPExSfh0IVUCATi22Nra/EwyLcDosP80bGVYyNkSQghhDQuhSYW6enpcHJyEv585swZODk5oXPnzgAAHx8fnDhxQjUZEkJII6muqcV/STew7mAibjx8zhpjaWKICf29MTHYG83MTdScISGEEKI5FJpYWFhY4MGDB8Kf4+Pj4e/vL/y5sLAQJib0C5aNQCCAQCAQO8YwjNhxeWKknZelfk2mzvxV3ZYy9clbVp546nOSCQQC5BWXYevp49hy7CKyC0tY49q2sMOUMF8M8esIPR1tYVlF2lPVa6XO/iZPmYbub4rmrylojKMxTp3UnbumjHGKlFflGCdLnKb2OXnaVGhi0alTJ+Tm5iI6Oho2NjY4evQotm7dKjx/7do19OrVS5Gq3zmxsbHC/TUAICcnB5WVlSIxAoEARUVFYBhG4rbp9cVIOy9L/ZpMnfmrui1l6pO3rDzx1OfY3X2Wjb9PXcGRlLuo4YsPpBwOENDBFWN6d4ZXa0dwOBwUFxZAmdViVflaqbO/yVOmofubovlrChrjaIxTJ3XnriljnCLlVTnGyRKnqX2upIT9D2xsFJpY6OvrY/369YiMjER+fj6GDx+O0aNHAwDy8/Nx/PhxrFmzRpGq3zkxMTGIiYlBcXExTE1NYW1tLfZtjkAgAIfDgbW1tdQBUFqMtPOy1K/J1Jm/qttSpj55y8oTT33uf/h8AY5dvo118Uk4n/aYNcZIXxcRgV0xOcQXLZpZqLR9Vb5W6uxv8pRp6P6maP6agsY4GuPUSd25a8oYp0h5VY5xssRpap+Ttq/cmxRebnbQoEHIyclBRUWFyL4Rurq6SEpKEtlwjvwPl8tl7RAcDkfiOVljpJ2XpX5Nps78Vd2WMvXJW1ae+Kbe54rLKrDtZAo2HEzG0+x81piWtpaICvPDqD5dYaSv22C5qPK1Umd/k6dMQ/c3RfPXFDTG0RinTurOXVPGOEXKq3KMkyVOE/ucPO0pPLEA2DejMzQ0lLh5HSGENLZHmbnYcCgJ20+moKyymjWmu7sT3h/WB/28PN7KDw2EEEJIY1BqYpGcnIwTJ04gMzMTDCO6/GKXLl0wbdo0pZIjhBBVYBgGCTceYF18Ek5cuSM2XgGAno4WhvfqjMnBvrDU58LGxoYmFYQQQogcFJ5YfPvtt5g/fz60tF5VIRAIwOfzoaWlBUNDQ1RUVNDEghDSqCqqavDv2StYF5+Eu89essbYWphgUrAPxgf1gIWJIQQCAbKzs9WcKSGEEPL2U2hiUVBQgIULF2LLli3Q1tbG9u3bsW3bNty+fRvff/89PDw8MG/ePFXnSgghMsnMK8Rfh89j67ELKCgpZ43p3NoJ0WH+CPNpD20t2h2bEEIIUZZCE4srV66gTZs2GDt2LHbt2gWGYaClpYX27dtj06ZNGDFiBA4fPozg4GBV50sIIRJdufcUcQcSEX/+JmpZlovlcbkY6NMeUQP94OXWohEyJIQQQt5dCk0sioqK4OzsDADQ0dERW9926NCh2LdvH00sCCENrqaWj4Pnb+LPA4m4ev8Za4yZkQHG9++BScHesLc0U2+ChBBCSBOh0MRCIBAIn61wcHDAjRs3UFtbKzz2+PFjVFezr7ZCCCGqkF9Shq3HLmLjoWRk5bNvUefmaIPogf4Y3qsz9HV11JwhIYQQ0rQotSoU8GoXbi6Xi1GjRmHChAl4/Pgxvv/+e6xcuVIF6WmmXbt2ITU1FQAwZ84csSV3CSEN587TLKyPT8Lus1dQWV3LGtPXqw2iw/zRs0MrcDgcNWdICCGENE0KTSxatWqFkJAQAACPx8O6deswevRo7NmzBwAwYsQITJ48WWVJaqqffvoJH374IU0sCGlgAoEAJ67cRdyBRCTefMAaY6Cng9F9uiIy1Beu9tZqzpAQQgghCk0sOnXqhE6dOgl/DgkJQUZGBm7cuAE7Ozu4urqqKj+NFB4ejvDwcMTFxTV2KoS800orqrDjVArWxSfhSVYea4yTjTkiQ3wR0bcbTA311ZwhIYQQQuoofStUHRMTE/j7+6ukrunTpyM1NRVr165F+/btVVJnnfLycmzbtg3btm2Dg4MDNmzYIBZTUFCAFStWICUlBRYWFoiOjkZQUJBK8yCESPb0ZT7WH0zCtpOXUFJexRrj4+mCqDA/9O/aFjwebWRHCCGENDaZJhYFBQV4+PChXBVbWFjAxcVF7oRWrVqFhIQEpKWloaioSO7y0vD5fLRu3Rr9+/eHvr4+rl69KhZTU1ODPn36wNDQELNnz0ZqaipCQkKwe/duDBkyRKX5EEL+h2EYnE97jLgDiTiakgaBQHx3bB0tHob27ISoMH+0c7ZvhCwJIYQQIolME4sTJ05g5MiRclU8YsQI7Nq1S64y165dw4oVK/DPP/+gV69eUmP//PNP9OjRAx06dBA5fvHiRdy9excTJkwQK8Pj8XDr1i2YmZlh9uzZSE9PF4v5+++/kZaWhszMTFhZWWHYsGHIyMjAvHnzaGJBSAOorK7BvsRriItPQtqTF6wx1mZGmDTAB+P794C1mbGaMySEEEKILGSaWPj6+gofzJaVg4ODXPFlZWWIiIjAmjVrYGdnV2/8gwcPMH/+fJw6dQqenp4AgJSUFPTv3x+zZ8+WWM7MzExqvceOHYOvry+srKyEx4YMGYI//vgDz58/h4ODA06ePImzZ8+iuLgYK1asQJcuXRARESHTdQoEAggEArFjDMOIHZcnRtp5WerXZOrMX9VtKVOfvGXlideEPveyoBibj1zAlmMXkFdcxhrT3tkeUWF+GOjbAbraWsK6G5K6/72osj119jd5yjR0f1M0f01BY9y7OcZpqqY6xilSXpVjnCxxmtrn5GlTpomFvb09hg4dqmg+Mvnggw8QEBCAoUOH4sED9lVfXrd8+XJUV1cjMDAQp0+fRnl5OYKCgjBz5kx8+eWXCueRnp6O5s2bixyrmyQ9ffpUZML0ySef1FtfbGwsYmNjwefzAQA5OTmorKwUiREIBCgqKgLDMOBy2e8Vry9G2nlZ6tdk6sxf1W0pU5+8ZeWJb8w+d/vpS/xz6iqOXL7Lujs2l8NBn46uGNOnCzq52oPD4aCoIL++y1cZdf97UWV76uxv8pRp6P6maP6agsa4d2uM03RNdYxTpLwqxzhZ4jS1z725EbY0Knt4WyAQoKSkBKampnKX3bJlC86fP48rV67IVe7nn39GTU0NAgMDUVVVhQ8++ACLFi2Su/3X1dTUQE9PT+SYvv6rlWbqNv0LDAxEYGCgTPXFxMQgJiYGxcXFMDU1hbW1NUxMTERiBAIBOBwOrK2tpQ6A0mKknZelfk2mzvxV3ZYy9clbVp54dfe5Wj4fRy6mYd3BZFy684S1PVNDPUQEdsPkEB84WpvXe70NRd3/XlTZnjr7mzxlGrq/KZq/pqAx7u0f494mTXWMU6S8Ksc4WeI0tc+9+blYGrkmFgzDYNu2bbh8+TJcXFwwefJk6Orq4rPPPsNvv/2GiooKuLq64vfff0ffvn1lrnfdunWorq7GgAEDAED4F/0PPvgAAwcOxLJlyySWjYqKwh9//AFtbW1MnDhRnsthZWFhgbw80WUt6362sLBQun4ul8vaITgcjsRzssZIOy9L/ZpMnfmrui1l6pO3rDzx6uhzxeVV2H4yBRsOJeN5biFrHa721pgS5oeRAV1gqK9bb97qoO5/L6psT539TZ4yDd3fFM1fU9AY93aOcdTf1N+esnU1VJ9TVZwm9jl52pNrYvH555/j+++/F/4cHx8PX19frFq1Cj169ICRkRFSUlIwfPhwpKen1/s8Q51Vq1aJrAD1/PlzRERE4P3330fv3r0llrt58yaCgoLw8ccfo6ioSHhbVOvWreW5LBGdO3fG5s2bRY5dvHgRBgYGcHNzU7heQpqSB8+zEbv7BOIv3kZFVQ1rTO9Oboge6I+Ajq3fyl/MhBBCCBEl88SisLAQa9aswaJFizB27FjcvXsXU6ZMQUpKCk6cOIGAgAAAQH5+Pvz9/bFp0ybMmDFDprrf3Kui7hmL9u3bw8PDg7VMWloa+vbti0mTJmH58uXCB1rqJheKbtI3ceJErFixAhs2bEBkZCQKCgoQGxuLcePGQVdXM/6aSogmEggEOHP9PtbFJ+LU1XusMXo62hjZ2wtRYb5o7dhMzRkSQgghpCHJPLG4desWXFxcsGDBAgBAq1at8OGHHyI+Pl44qQBe3S40depU3LvH/sFCVT799FOMHTsWP/74I4BXXw/9/vvviI6Oxrx587Bjxw7WcpGRkbh//z6ePHmCwsJC4aZ+hw8fhpGREdzd3bFu3TrExMRg+fLleP78OXr06IEffvihQa+HkLdVeWU1dp+9ivUHk/DgeQ5rjL2VKSJDfDGmb3eYGxuoOUNCCCGEqIPME4vs7GyxW4xat27Nuqyso6MjkpOTFU7K0dERCQkJYntUvG7Hjh0wNhZdz57D4eDPP/9ERUWFxHIzZ85EaWmp2PG6B7SBV99aDB8+HHfu3FF4oz9C3nXPcwrx656z2HfuForKKlljurq3QPRAf4T08IQWj6fmDAkhhBCiTjJPLPh8PnhvfDDQ0tICh8MRi+VwOGAY8V1zZaWnpyf8JkGSNycVdbhcLgwNDSWW69Spk0w5GBkZoWvXrjLFEtJUMAyDlLvp+PNAIg5fuAU+y9rW2lo8DPJpj2E+HujdrQM9P0EIIYQ0ESpbbpYQ8u6qrqnF/uQbiItPxI2Hz1ljLEwMMbG/NyYGe8Pa1AjZ2dlqzpIQQgghjUmuicW///4LLa3/FWEYBgzDiByrOz5s2DDVZEgIaTT5JeX4++wJbD5yAdmF7BvkeLSwxdSB/hji3wl6OtoAGn53bEIIIYRoHpknFg4ODhg8eLDMFXfv3l2hhAghje/Wk0zEHUjE3oRrqK7li53ncDgI6uqB4b5tEerXRew2SUIIIYQ0PTJPLHx8fLB3794GTIUQ0pj4fAGOpdxGXHwizt16xBpjpK+LiL7dEBnii+Y25sjOzmZ9zooQQgghTQ89Y0FIE1dcVoFtJ1Ow4WAynmbns8a0tLXElFA/jOrjBWMDPQB0uxMhhBBCRNHEgpAm6ml2AdYcOI8dpy6jrLKaNaa7uxOmD+2Dfl4e4PFodSdCCCGESEYTCwWkp6ejoKAAwKvdwen+cvK2YBgGiTcfIu5AAk5cuQO2VaF1tbUwIqAzJgf7wlKfCxsbG1oylhBCCCH1oomFAtauXYvDhw8jLS0NmZmZsLKyauyUCJGqoqoGexKuYl18Eu48zWKNsbUwwcQBPhgf1B2WpkYQCAS0ZCwhhBBCZEYTCwV89913+O677+Do6NjYqRAi1Yu8Ivx1+By2HLuAgpJy1pjOrZ0QHeaPUO920NGmIYEQQgghitGoTxFXr17FpUuXYGBggJ49e6JFixYN0k5WVhb+/fdfGBkZYeLEiawx58+fx+XLl2FhYYGwsDCYmJg0SC6ENIQr955iXXwSDpy7gVq++EPWPC4XfTu3QszwvujapqX6EySEEELIO0cjJhZVVVUICwtDaWkpOnfujKysLEydOhVLly7FJ598orJ2GIZBREQEkpOTYWxsDB0dHdaJxcyZM7Fp0yYMHjwYd+7cwWeffYbTp0+jVatWKsuFEFWrqeXjSMpd7ErchSv3n7HGmBkZYHxQd0zo3wNagmrY2NioOUtCCCGEvKs0YmLBMAyWLFkCb29v4bGffvoJX3zxBWJiYqCrqytW5s6dO2jevDkMDAxEjhcXFyM7O5t1EsAwDIYPH44tW7Zg3rx5OH78uFhMQkICVq1ahaSkJPj6+oLP5yMwMBCzZs3CgQMHVHC1hKhWfkkZth67iI2HkpGVX8wa4+Zog6gwf4wI6Ax9XR16foIQQgghKqcREws9PT2RSQUAmJqaSl2J5tNPP0VFRQXi4+Ohr68P4NWkYsCAAWjRogW2bdsmVobL5WL06NFSc9mxYwfatWsHX19fAACPx0N0dDQiIyNRXFwMExMTZGVlISsrCzU1NUhNTUWLFi3g7Ows07UKBAKx9f8FAgEYhpG6L0B9MdLOy1K/JlNn/qpuS5n66it799lLrI9Pwu6zV1FVU8sa07eLO6aE+qFnh1bCjezq+iD1OXbqzl2V7TVkf1OmTEP3N0Xz1xQ0xslWVp54GuMka6pjnCLlVTnGyRKnqX1OnjY1YmJR5+jRo7h+/TqePn2KY8eOYePGjazfVgDA1q1b0bdvXwwePBj79+9HTU0NQkJCwOPxEBcXp3AOt2/fhru7u8ixNm3agM/n4/79+/Dy8sLu3bvx559/ws7ODrNmzUKfPn3w888/s9YXGxuL2NhY8Pl8AEBOTg4qKytFYgQCAYqKisAwjMTJVH0x0s7LUr8mU2f+qm5LmfrYygoEDJLSHuOfU1dx4c5T1nL6OtoY7OOJ0QGd0KKZOYBX/U7evJpqn1N37qpsT9X9TVVlGrq/KZq/pqAxTray8sTTGCdZUx3jFCmvyjFOljhN7XMlJSUyx2rUxKKoqAgvXrzAkydPUF5ejqqqKomxZmZmOHbsGAIDAzF06FCUlpaCYRgcPnwYRkZGCudQUlKCli1birVVdw4AYmJiEBMTI1N9dbHFxcUwNTWFtbW12IPgAoEAHA4H1tbWUgdAaTHSzstSvyZTZ/6qbkuZ+l4vW15Vg12nL2P9oWQ8fpHHGu9obY5w//aYMqgXzI0Nlc6rqfY5deeuyvZU1d/kmVjIUqah+5ui+WsKGuNkKytPPI1xkjXVMU6R8qoc42SJ09Q+p6enJ3OsRk0sRo4ciZEjRwIANm/ejClTpsDf31/ibUYWFhbYu3cv3NzcoK2tjcePH8PY2FipHAwMDFBcLHqfelFREQDA0FD6hzVZcLlc1g7B4XAknpM1Rtp5WerXZOrMX9VtKVNfZl4xfj+cgm0nL6GknH2i7d3WGdED/dGvSxvk5eX+X3t3HtXklf4B/BsWIyAGZVMQx5GKQFFxRVlUdCwDWKWoVVqtCy61HrVq7VS7Tdsz0+mp9lg7tlPrgktrnWpxVwRBZFVQ1KKVWhUpoAIqEAQMIe/vj/7MmCYsISEJ8P2c4znl3ue+9wm955rHd0M3W5tmzcU11zBD567P+XQ5VkvGNndMa6+3luZvKjrqHqftWG3iucc1rKPucS0Zr889rjlxprjmtJnPpAqLp4WGhkIul+Py5csNFhbV1dWYM2cOBg8ejOrqasydOxexsbHo1KlTi+ft378/srKyVNpu3LgBkUjEp0KRQQiCgMyrt7DlSCpOZl2FQsPrsTtZmGNyoC/mhwfAp68rAO2ugSQiIiLSN5MoLPLz8+Hk5KTyhKdTp04BADw8PDSOqampwaRJk1BVVYWEhATIZDIEBwdj6tSp2L9/PywtLVuUy+TJk7F582bk5ubCx8cHALBjxw6MGTMG3bp1a9ExiZqjVlaHg6mXsOVoKq7m39EY42jXBa+EjMSs50bC0U63s3NERERE+mQShUVBQQEmTpyIoKAguLq6Ii8vDz/++CPeeecdeHl5aRwzc+ZMPHjwAKdOnVLeA5GYmIjg4GAsWLAAMTExGsft3LkTJSUlyM7ORmlpKdatWwcAWLp0KcRiMUJDQ/Hiiy8iJCQEs2bNQm5uLtLT05GcnNwaH50IJQ+l2BmXgZ1xmbhf+UhjjM+fXTB/YiAmBQyCmG/HJiIiIhNkEt9QRo8ejeTkZBw4cAC3b9/GqFGj8P777zd66dHq1avh4eGhchbB2dkZiYmJKCoqanDc/fv3cffuXQwbNgzDhg3D3bt3Afx++ckTe/bswcGDB5GdnY1x48bh66+/hqurqx4+KdH/XL5RiC1H03Ao7RLq5PVq/WYiEYIHuWNx5DiM9O6rfFwsERERkSkyicICAOzt7REdHd3s+D++9+KJHj16oEePHg2OW7FiRZPHFolEiIiIQERERLPzIWoOeX094s5dxZajqTj3c77GmK7WnfHSX0bglZCREKMOTk5OLCqIiIjI5JlMYUHUnpVX1WBvYja2H09HUVm5xpi+Lg6IDg/EtDFDYGMlhkLBt2MTERFR28HCgqgV/VpUgk37T+HouZ9R87hOY8yYQf0wf2Igxvp6tMnHFhIREREBLCyI9E4QBCRf/AVbjqYiKecXjTGdO1li6tghiA4LgIebs4EzJCIiItI/FhZEelJdK8O+5AvYdiwN1ws1X8LU016CuaH+eOkvI9DN1lpjDBEREVFbxMKCSEdFpQ8RcyID3yWcQ3lVjcaYYf3/hOjwAIT6+cDSwtzAGRIRERG1PhYWRC0gCAKy825jy5FUHD97BfUa3nptYW6G5/0H4oVRXggePpD3TxAREVG7xsKCSAuyOjkOp1/G1qNpuHSjUGNM9642mPWcH14JGQUnuy58shMRERF1CCwsiJqhrKIKu05mYueJTJSUSzXGePXugfkTAzE50BdWYksAgELDmQwiIiKi9oiFBVEjruQXY+vRNBxIuYjHdXK1fpFIhAnDvDA/PBD+Pnw7NhEREXVcLCyI/qBeoUBc1lVsPZqGjCs3NcZ0sRJjxvjhmBvqjz497A2cIREREZHpYWFB9P+k1bXYc+octhxJRVFZhcaYPj3sMS8sAC8GD4WtdWcDZ0hERERkulhYUId3604Zth9Lx/eJWXhUK9MYEzDAHfPDAzF+iCfMzfl0JyIiIqI/YmFBHZIgCEj96Qa2Hk1FwvlrEARBLUZsaYHI0YMxLywA3n16GiFLIiIioraDhQV1KDWP6xCbkoOtR9NwreCuxhgHiQ3mhgZg1nN+sJd0MXCGRERERG0TCwvqEO7cr8COExnYHX8WD6XVGmN8n+mFeWEBGOHuDFeXnnyhHREREZEWWFi0QGFhIcrLywEAXl5eMDc3N25C1KCc679hy5FUHMm4DHm9+jslzM3MED7KB9HhgRjq0RuCIPCFdkREREQtwMKiBT7//HMcP34ceXl5uHPnDhwcHIydEj2lTl6PY2dzseVIKi78UqAxxq6LFWZO8MMrfx0FVwc7Zbumey2IiIiIqGksLFrg008/xaeffopevXoZOxV6ygPpI3wXfw7bj6fj7oNKjTH9ejkhOjwAU8cMgZW4k4EzJCIiImq/TKawUCgUSE9Px7Vr1+Dk5ITx48fDxsamVeYqLS1FbGwsbGxs8PLLL2uMyc7Oxvnz59G9e3eEhoaiSxfexGuq8gruYuuxNOxPzkGtrE5jzLghnlgwMQBBA/vx7dhERERErcAkCouffvoJUVFR6NatGzw9PXH58mUsXLgQhw4dwogRI/Q2jyAImDlzJpKTk2FrawuxWKyxsFi1ahW2bt2K8PBwXLt2DatWrcLp06fRt29fveVCulEoFEjMycPWo2k4c+m6xhjrzp3w4tihmBsWgGdcHQ2cIREREVHHYhKFhbm5Ofbt2wdPT09l27Rp07Bo0SLk5ORoHPPLL7/Azc0NVlZWKu1SqRSlpaUaiwBBEBAWFoZt27bh7bffRkJCglpMamoqPvvsM6SkpCAwMBByuRzBwcFYvnw5Dh8+rOMnJV09qnmM/yadx9Zjabh1p0xjTC/Hbpgb5o+o8cMhsbHSGENERERE+mUShYW3t7daW3BwMI4ePdrgmNdffx11dXU4fPgwOnfuDACoqqpCaGgoXF1dsXfvXrUxZmZmDV769MR///tfPPvsswgMDAQAWFhYYMGCBZg3bx6kUilsbW1RUlKCkpISyOVyXLt2Db1790bv3r2b9VkVCgUUCoVamyAIau3axDTW35zjmzKFQoHC0nJ8dewc/pt0HpXVtRrj/Lz+jOhwf0wY5gWL/39Sl7afWd+/K12Op+1YbeK55hpm6Nz1OZ8h15s2Y1p7vbU0f1NhyNy5xzU/hnuc6c2n67Faa83pK85U15w2c5pEYaHJgQMHMGzYsAb7d+/ejfHjxyMiIgIHDx6EXC5HaGgoFAoFtmzZ0uJ5r169qnLmBAA8PT1RX1+PX375BUOHDsXevXvx9ddfw8HBAa+++irGjx+Pzz//XOPxNm3ahE2bNqG+vh7A7/d31NaqfjFWKBSoqKiAIAgNvjuhqZjG+ptzfFMkCAJyfi3Ct4kXcOanm1BoeGKTpYU5Qob2R1TwYHi6OQEAHty/3+I59f270uV42o7VJp5rrmGGzl2f8xlyvWkzprXXW0vzNxWGzJ17XPNjuMeZ3ny6Hqu11py+4kx1zUml0mbHmmRhsW7dOiQnJyMlJaXBmO7duyM+Ph7BwcGIjIxEVVUVZDIZ4uPjYWtr2+K5pVIp+vTpo9LWrVs3ZR8ALF26FEuXLm3W8ZYsWYIlS5agsrISEokEjo6O6Nq1q0qMQqGASCSCo6NjoxtgYzGN9Tfn+KbkcZ0ch9IuYevRNFzJv6MxxkHSBa+E+GHmBD842rX8//cf6ft3pcvxtB2rTTzXXMMMnbs+5zPketNmTGuvt5bmbyoMmTv3uObHcI8zvfl0PVZrrTl9xZnqmntyZVBzmFxhsXXrVqxduxbff/99kzduOzg44NChQ+jfvz8sLS1x69YttS/t2rK2tlarzCorK5V9ujIzM9O4IEQiUYN9zY1prL85xze2kodS7DqZiZ1xmSirqNIY4/NnF8yfGIhJAYMgtmyd5avv35Uux9N2rDbxXHMNM3Tu+pzPkOtNmzGtvd5amr+pMGTu3OOaH8M9zvTm0/VYrbXm9BVnimtOm/lMqrDYtm0bXnvtNXz77beIjIxsMr6mpgbz58/HwIEDUV1djfnz52P//v2wtLRscQ4eHh44f/68StuNGzcgEonwzDPPtPi41LCfbhZhy9FUHEy9hDp5vVq/mUiEsYPc8VrkOIz07svHxRIRERGZIJMpLHbs2IHFixdj165dmDZtWpPxtbW1iIiIwMOHD3Hq1CnIZDKMHTsWL774In744QdYWLTso02ePBnffPMNrl69qrypfNeuXQgKCkL37t1bdExSJ6+vR9y5q9hyNBXnfs7XGNPVujOi/jIcs0NGQYw6ODk5saggIiIiMlEmUVicOnUK8+bNQ3BwMIqLi7FhwwZl3+LFiyEWi9XGzJo1C/fu3cOpU6eU90AkJiYiODgYCxcuxLZt2zTO9e2336K0tBQXLlxAaWmpcq4n84SFhSEyMhIhISGYPXs2cnNzkZycjOTkZL1/7o6o4lEN9iScw/bjGSgsfagxpq+LA6LDAjBt7FDYWImhUChQUlJi4EyJiIiISBsmUVhYWVkpb4bOz89X6WvoEVevv/46+vfvD3t7e2Vbz549kZiYiKKiogbnKi4uRlFREQYOHIiBAwcq53t6nh9++AH79+9HdnY2/P398cUXX8DNza2Fn44A4NeiUmw7loYfTp9Hda1MY8yYQf0QHR6I4MEebfKaVSIiIqKOzCQKC39/f/j7+2s1JiAgQGO7i4sLXFxcGhy3evXqJo8tEokwdepUTJ06VaucSJUgCDhz6Tq2HElFYk6expjOnSwxdewQRIcFwMPN2cAZEhEREZG+mERhQe1Lda0M+5IvYNuxNFwv1HwJU097CeaG+uOlv4xAN1vdn7ZFRERERMbFwoL0pqj0IWJOZOC7hHMor6rRGDO0f2/MDw9EqJ8PLC3MDZwhEREREbUWFhakE0EQkJ13G1uOpOL42Suo13BPjIW5GZ73H4jo8EAM7sd7VYiIiIjaIxYW1CKyOjmOZPyELUdScelGocaY7l1tMHOCH2b/dRR6dNftxYVEREREZNpYWJBW7ldUYVf8Wew8kYF7D6UaY7x690B0eAAiggbDStzylxUSERERUdvBwoKa5Wr+HWw9morYlIt4XCdX6xeJRJgwzAvR4QEI8HHni+yIiIiIOhgWFtSg+noFEs7/jC1H05Cee0NjTBcrMaaPG4Z5YQHo08NeYwwRERERtX8sLEiNtLoW3ydmYfuxdNy+90BjzJ+cu2NeWACmjxsGW+vOBs6QiIiIiEwNCwtSunWnDNuPpWNvUjaqah5rjPH3cceCiYEYP8QT5uZ8OzYRERER/Y6FRQcnCALScm9gy5FUJJy/BkEQ1GLElhZ4IcgX0eGB8O7T0whZEhEREZGpY2HRQdU8rsOBlBxsPZqGnwvuaoxx7maL2X/1x8wJI2Av6WLgDImIiIioLWFh0cHcfVCJHScysOtkJh5KqzXGDHLvhQXPByJ85AB0suQSISIiIqKm8VtjB5GbfxexexJxJOMnyOvV345tbmaGsJE+iA4PwLD+f+LjYomIiIhIKyws2rljmbn4z8FknP+lQGO/XRcrvPwXP8wOHQVXBzvDJkdERERE7QYLi3YuLuuKxqKiXy8nRIcHYMroIbDu3MkImRERERFRe8LCop2bHx6IfacvKH8eN8QT88MDMHpQP17uRERERER6w8KinRvQ1xXBgz3gaGuF1yLHo5+bs7FTIiIiIqJ2iIVFB7BjzRyUlpbCycnR2KkQERERUTvFVyd3ALzkiYiIiIhaGwsLIiIiIiLSGQsLIiIiIiLSGQsLIiIiIiLSGQsLIiIiIiLSGQsLIiIiIiLSGQsLIiIiIiLSGQsLIiIiIiLSGQsLIiIiIiLSGd+8bSCCIAAAKisr1foUCgWkUik6d+4MMzPNtV5TMY31N+f4psyQ+et7Ll2Op+1YbeK55hpm6Nz1OZ8h15s2Y1p7vbU0f1PBPY57nCF11D2uJeP1ucc1J85U19yT765Pvss2hoWFgUilUgCAm5ubkTMhIiIiItKOVCqFRCJpNEYkNKf8IJ0pFAoUFxfD1tYWIpFIrX/48OHIyspq9BhNxTTUX1lZCTc3N/z222/o2rWr9smbgOb8fkx1Ll2Op+1YbeK55hpmyPWm7/kMud60GdOa6w3gmjPmXNzjuN4MOZ+ux2qtNaevOFNcc4IgQCqVwsXFpcmzJTxjYSBmZmbo1atXg/3m5uZNLpSmYprq79q1a5vcAIHm/X5MdS5djqftWG3iueYaZsj1pu/5DLnetBljiPUGcM0ZYy7ucVxvhpxP12O11prTV5yprrmmzlQ80bYuDGzHlixZonNMc47RVhnys+l7Ll2Op+1YbeK55hpm6M+lz/kMud60GcP11jjucfqP55prWEfd41oyXp97XHPi2vqa46VQHUBlZSUkEgkqKira5L+sUNvDNUeGxjVHhsT1RobWVtYcz1h0AGKxGO+//z7EYrGxU6EOgmuODI1rjgyJ640Mra2sOZ6xICIiIiIinfGMBRERERER6YyFBRERERER6YyFBRERERER6YyFBakoLy+Hr68vfH198dZbbxk7HWqHFAoFNm7ciHnz5iEmJsbY6VA7J5VKlXva6tWrjZ0OdQC1tbVYv3495syZg3//+9+QyWTGTonaucLCQrzxxhtYtGgREhMTjZoLCwtSYWtri5iYGMyePRv5+fnGTofaoTVr1uDAgQMICAjAF198ga+++srYKVE7Zm1tjZiYGERHR+PWrVvGToc6gJdeegl37tzB2LFjsX37drz//vvGTonaMYVCgcjISPTq1Qs+Pj6IiopCTk6O0fLhm7fboLq6OlRUVMDOzg4WFpr/F8rlcshkMlhbW2t1bHNzc/j6+iI/Px9nz57VR7pEKrZt24aLFy/C1dUVAwYMwOLFi7F48WJjp0UmTBAE3L9/H7a2tg0+alGhUKC6uhpdunRRaX+ypxUWFiI5OdkQ6VIHt3nzZjg4OAAA7OzssGvXLiNnRO2ZSCRCfHy88s3Yp0+fxs2bNzF48GCj5MMzFm1IQUEB1q5di969e8PR0RGZmZlqMdXV1XjllVdgY2MDOzs7DB06FBcvXlT2Z2dnKy8L+OMfoqbk5eVh5cqVcHFxQVBQkMaY69evY9KkSejZsye8vb3x2WefKfuqq6tRW1sLV1dXAIC3tzfPjFGDHjx4gE8//RQeHh5wdHTU+AVNEAS89dZbkEgk6N69O9zd3XHixAkjZEvtQXFxMT788EP07dsXPXr00BhTUlKCV155Ba6urnB3d8fatWtRV1en7H9SVMhkMvznP//B0qVLDZI7tU1JSUl48cUX0b17d7z77rsaYw4fPgw/Pz84OzsjICAAp06dUvaJRCJIJBJMnz4do0ePhrm5OZ5//nlDpa+GhUUbsnv3btjY2CA2NrbBmGXLliEjIwN5eXkoLy/H4MGDERoaiqqqKgCAp6cnYmJiNP4hakx9fT0mT54MV1dXhIaGQiqVqsVIpVKMGzcONjY2OHPmDD7++GO899572LBhAwCgU6dOkMvlyvjHjx+jc+fOhvoI1MYcPXoUJSUlOH78eINnKtavX4/NmzcjMTERjx49wvz58xEREYEbN24YOFtqD6KiolBXV4dZs2ahvLxcrV+hUGDixIm4ffs24uLiEBMTgx07dmDFihUqcVVVVZgyZQoWLFiAsWPHGiZ5anPi4+Px4YcfIjIyEi4uLqipqVGLSU1NRWRkJGbMmIHMzEyEhIQgLCwMly5dUombPn06oqKi8PPPPyM9Pd1QH0GdQG3OrVu3BABCSkqKSnt5eblgaWkpbN++Xdn24MEDwdLSUti2bZtWc8TGxgrTp0/XR7rUjigUCkEQBGHVqlXCoEGD1Po3bdokWFtbC48ePVK2vfPOO0KPHj2E+vp6QRAEwcfHR0hKShIEQRB2794thIWFtXre1PaJxWLhm2++UWvv3bu38Le//U35s0KhENzc3IQ333xTJe7w4cPClClTWj1Patue7HHffPONIBaL1frj4uIEAML169eVbTExMYKFhYVw//59QRAEobi4WAgKChLi4uIMkzS1WU/WmyAIwqBBg4RVq1apxTz//PNCSEiIStuwYcOEWbNmCYIgCDdu3BBu3Lih7FuzZo3w3nvvtVLGTeMZi3bkwoULqKurQ2BgoLKtW7duGDBggFb3SwQFBWHFihWIi4uDr68v77UgJZFI1Gh/SkoKRo4cqXJvz4QJE3D37l38+uuvAICPPvoI06ZNw3PPPYeVK1c2eOqXqCl37txBQUGByp4nEokQFBSksm8FBwdj2bJlSEhIgK+vr3H/NY9MWnP2uN69e+OZZ55Rtk2YMAFyuVx5efILL7yA0tJSbN68GVOnTsXatWtbNWdqu5pab8Dva278+PEqbRMmTEBqaioAwMrKCjNmzMCECRMQFBSEnTt34qWXXmqVfJuDN2+3I6WlpQAAR0dHlXZHR0dlX3N8+eWXqK+vV/789AZK1JiioiL06tVLpc3JyQnA79cue3h4ICIiAkOHDsXPP/+MQYMGwdnZ2RipUjvQ2J739L1lX3zxhcoleO7u7gbJj9qfoqIitT3LyckJIpEIxcXFAIAPP/wQlZWVyn57e3uD5kjtR3V1NcrLyzWuuSfrrWfPnkhJSUF6ejrMzc0xYsQIo15izMKiHXlS+T5dFAC/PyHKzKz5J6cGDBig17yoY/njWnvy5DJBEJRtbm5ucHNzM2he1P40d8/z8fExaF7Uvv1xjzMzM4NIJFLucc8995wx0qJ2TNPfq0//nSoWixEcHGzotDTipVDtiIuLCwDg3r17Ku337t1Dz549jZESdTBOTk4oKytTaSspKVH2EekT9zwyNE17XFlZGRQKBfc40jtra2vY2Nho/HvVVNcbC4t2ZMiQIbCxsUFCQoKyrbi4GFeuXGnw0aBE+uTn54fMzEyVRy8mJyfDzs4OHh4eRsyM2iN7e3t4e3ur7HlyuRxJSUnc86hV+Pn54ebNm8rLUIDf9ziRSIThw4cbMTNqr/z8/JCSkqLSlpycDD8/PyNl1DgWFm3I48ePUVZWhocPHwIAKioqUFZWpnw8mZWVFVauXIkPPvgAcXFxyM3NxezZs+Ht7Y2IiAgjZk4dxezZsyESibBmzRrU1NTg8uXL2LBhA1577TVYWloaOz1qY+RyOcrKypT/WldVVYWysjLl47MB4O2338aWLVuwa9cu5OXlYeHChQCARYsWGSVnat/Cw8Ph7u6O5cuXo7KyEr/99hv+/ve/Y9q0acozaET6tHz5chw+fBixsbGQy+XYuXMn0tLSTPf9KEZ7HhVpbdeuXYK9vb3an/Xr1ytj6uvrhX/84x+Cp6en0KtXLyEqKkooLCw0YtbUngQGBgoSiUQQi8WCmZmZIJFIBIlEIpSXlytj0tPTBR8fH8Hc3FywtrYWli5dKtTV1Rkxa2qrMjMzNe55r776qkrctm3bBF9fX8HFxUUIDQ0VLl++bKSMqa2bN2+eIJFIBCsrKwGAco/LyspSxuTl5QmBgYGChYWFYGlpKcyYMUOoqKgwYtbUVt2/f1+5xszMzASxWCxIJBJh7NixKnGbNm0SHB0dBXNzc8HFxUXYsWOHkTJumkgQnrr7g4ioEVKpVO1GWQCQSCRqj82rra2FWCxu1uP0iIhMQXV1NWQymVq7ra0tzM3NVdpkMhnMzc3V2omaSxAEVFRUqLVbWFigS5cuau01NTWwsrIyRGotxsKCiIiIiIh0xnssiIiIiIhIZywsiIiIiIhIZywsiIiIiIhIZywsiIiIiIhIZywsiIiIiIhIZywsiIiIiIhIZywsiIhIK5WVldi3bx8KCwuNnYrOMjMzcfbsWYPOee7cOWRkZBh0TiIiQ7AwdgJERGRcgiBg//79zYodMGAA6urqMG3aNOzZswczZsxo5eya7969e0hJScGYMWPg6OjYZPydO3cwYcIE7NixwwDZqc778ssvIy8vD66urgadm4ioNbGwICLq4ARBwPfff6/Slp2djdu3b2PSpEmwtLRUtltYWGDo0KGYMmUK3NzcDJ1qow4dOoSFCxfi+vXrzSos3n//ffTt2xcvvPCCAbL7n8mTJ6Nfv3549913sW3bNoPOTUTUmvjmbSIiUjNnzhzs2LEDDx8+hJ2dnbHTaZbly5dj8+bNePToEczMGr/S98GDB3B1dcUnn3yCZcuWGSjD/9m4cSNWr16NwsLCZhVBRERtAe+xICIirWi6x+L8+fM4fPgwAEAqlSI+Ph7p6el4+t+upFIpEhISkJSUBJlMpvHYcrkcWVlZOHToEDIzMyGXy5vMp66uDvv27UNqaiocHBzw448/Yt++fUhMTGxwzLfffova2lpMnz5dpT0vLw/79u1DXV0dZDIZkpKS1PKVyWRITk7GyZMn8ejRI43Hz83NxbFjx3D27FmNMdOnT4dMJsPu3bub/HxERG0FL4UiIiKtFBQUqN1j8dVXX+HAgQPYv38/lixZAhcXF2RnZ2PAgAE4fvw4MjIysGzZMri6uuL8+fPo0aMHzpw5A3t7e+Vxjx07hkWLFkEQBPj4+CAvLw8AsHfvXowYMaLBfIqKirBnzx5cuHABnp6eysu6Ro0ahXHjxmkck5CQAHd3dzg7O6u0x8bGYs2aNcjIyMBrr70GBwcH5ObmomvXrjh9+jTKysowc+ZMODk54cqVKxAEAadPn4aHhwcAoLCwEBMnTkRxcTGGDh0KqVSKgoICvPPOO1i4cKFyHmdnZzzzzDOIj4/HihUrWvB/gYjI9LCwICIivXj8+DFiYmKQnZ2Nzp074+bNm/Dy8sKaNWtw584dZGVlwdraGvn5+fDy8sK6devw8ccfAwCysrIQERGBOXPmYNOmTbC0tIRcLsecOXMwceJE5OXloVu3bhrn7dOnDz755BP8+OOPeOONNxAdHd1krllZWfDz82uwf926dYiPj4e9vT0ePnwIHx8frFy5ErW1tYiPj4ejoyPKy8sxYMAAvP322/jhhx8AAGvXroVUKkV+fj6sra0B/H6G59ixY2pzDBo0CElJSU3mSkTUVvBSKCIi0ouqqiqsXLkSnTt3BgD07dsXY8eOxcaNG7FmzRrlF+0+ffpg3LhxOH78uHLsP//5T9ja2mLjxo3Km8UtLCywfv16lJaW4rvvvmt07pycHADA4MGDm8xTEASUlJTAwcGhwZiXX35ZeTalW7duiIiIwJ49exAVFaW8J8LOzg6RkZEqn6OoqAhdu3ZV/g4AoGvXrhqfnuXg4IAHDx40eFkYEVFbwzMWRESkF506dYKPj49Km6urKywsLDBw4EC19qffH5GRkQFXV1ecOHECwO9f/p/86dKlCy5fvtzo3Dk5ObC0tMSzzz7bZJ5yuRz19fUqT7v6oyFDhqjl21D7o0ePUF5eDjs7O8ycORPz5s3DwIEDMXXqVIwZMwb+/v4Qi8Vqc3Tq1AnA7/eIPPlvIqK2jIUFERHpha2tLUQikUpbp06dYGNjA3Nzc7X22tpa5c81NTV4+PChxpuZQ0JCmiwYcnJy4OXlpfEL/B9ZWlpCIpHgwYMHDcZIJBK1fBtrf/JZ5s6dCy8vL3z33XeIjY3FRx99BFtbW3zyySdYtGiRytj79+/DysoKNjY2TeZMRNQWsLAgIiKjc3d3BwDs27evReMvXryIkJCQZsd7e3vj5s2bLZqrKSNHjsTIkSMB/P7SvujoaCxevBhhYWEq7/64ceMGvL29WyUHIiJj4D0WRERkdAsWLEBOTo7K/QpPVFdX4/79+w2Orampwd27d9G3b99mzzdmzBhcunQJjx8/blG+DSkoKFD52dnZGZMmTYIgCCgrK1O2P378GDk5OQgODtbr/ERExsQzFkREZHSvvvoqfvrpJ0yePBlz5szBiBEjIJfLcfXqVRw8eBB79+5VeTTt06ysrODh4YG9e/eiT58+sLa2hr+/P1xcXBqcLyoqCv/6178QFxeHSZMm6e1zREdHw8LCAmPGjIGbmxsKCgqwYcMGhISEwNfXVxkXFxcHmUyGqKgovc1NRGRsLCyIiEjN8OHDUVVVpfGmYolEgilTpqhc1jNs2DAoFAq12CFDhqCmpkatffDgwaioqFD+LBKJ8OWXX2LOnDk4cOAAkpKSYGdnh2effRYffPBBg4+afeLkyZP4+uuvceLECchkMgwfPrzR+IEDByIoKAg7duxQKSw8PT0xZcoUtc/dv39/TJkyRe0ejn79+mHKlCnKp0DFx8cjISEBp06dQm5uLhwdHbF161aEhYWp3H+ya9cu+Pn5qd0MTkTUlomEp1+LSkRE1EGcOXMG48aNQ25uLjw9PQ027/Xr1+Hl5YWTJ082+AI/IqK2iPdYEBFRhzR69Gi89dZbSEtLM+i8aWlpePPNN1lUEFG7wzMWRERERESkM56xICIiIiIinbGwICIiIiIinbGwICIiIiIinbGwICIiIiIinbGwICIiIiIinbGwICIiIiIinbGwICIiIiIinbGwICIiIiIinbGwICIiIiIinbGwICIiIiIinbGwICIiIiIinf0fiyzt7Uh9+aUAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t_blast   = np.logspace(-4, 0, 300)    # seconds\n",
    "E_trinity = 8.4e13                     # Joules\n",
    "rho_air   = 1.2                        # kg/m³\n",
    "t_exp_sed = -v_sed[2]                  # t exponent in R(t), ≈ 2/5\n",
    "\n",
    "R_blast = (E_trinity * t_blast**2 / rho_air) ** 0.2\n",
    "\n",
    "fig_sed, ax_sed = plt.subplots(figsize=(8, 4))\n",
    "ax_sed.loglog(t_blast * 1000, R_blast, color=\"#1a5276\", linewidth=2.5,\n",
    "              label=rf\"$R \\propto t^{{{t_exp_sed:.2f}}}$  (exponent from null space)\")\n",
    "ax_sed.set_xlabel(\"Time $t$ (ms)\", fontsize=12)\n",
    "ax_sed.set_ylabel(\"Blast radius $R$ (m)\", fontsize=12)\n",
    "ax_sed.set_title(\"Sedov–Taylor blast wave — Trinity test parameters\", fontsize=12)\n",
    "ax_sed.legend(fontsize=11)\n",
    "ax_sed.grid(True, alpha=0.3, which=\"both\")\n",
    "fig_sed.tight_layout()\n",
    "fig_sed;"
   ]
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    "## Summary\n",
    "\n",
    "- The **dimension matrix** has one row per base dimension and one column per parameter\n",
    "- The **null space** of $D$ gives the exponent vectors of all dimensionless combinations\n",
    "- `scipy.linalg.null_space(D)` computes this in one call; normalise to read off exponents\n",
    "- The number of Π-groups equals $n - \\mathrm{rank}(D)$\n",
    "- Dimensional analysis determines the functional form up to a dimensionless constant — that constant requires experiment or a full solution\n",
    "- On a **log–log plot**, $R \\propto t^\\alpha$ is a straight line with slope $\\alpha$"
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