3 Twists and Trajectories.ipynb

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   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "try:\n",
    "  # We must install required packages if we are in Google Colab\n",
    "  import google.colab\n",
    "  %pip install roboticstoolbox-python>=1.0.2\n",
    "except:\n",
    "  # We are not in Google Colab\n",
    "  # Apply custon style to notebook\n",
    "  from IPython.core.display import HTML\n",
    "  import pathlib\n",
    "  styles_path = pathlib.Path(pathlib.Path().absolute(), \"style\", \"style.css\")\n",
    "  styles = open(styles_path, \"r\").read()\n",
    "  HTML(f\"<style>{styles}</style>\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\large{\\text{Foundations of Kinematics and Algorithms in Robotics}} \\\\ \\large{\\text{Module 3: Twists and Trajectories}}$\n",
    "\n",
    "$\\text{By Jesse Haviland and Peter Corke}$\n",
    "\n",
    "<br>\n",
    "\n",
    "### Contents\n",
    "\n",
    "[1.0 Twists](#1)  \n",
    "[2.0 Trajectories](#2)  \n",
    "[3.0 Interpolation of Orientation](#3)  \n",
    "[4.0 Interpolation of Pose](#4)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We will do the imports required for this notebook here\n",
    "\n",
    "# numpy provides import array and linear algebra utilities\n",
    "import numpy as np\n",
    "\n",
    "# the robotics toolbox provides robotics specific functionality\n",
    "import roboticstoolbox as rtb\n",
    "\n",
    "# spatial math provides objects for representing transformations\n",
    "import spatialmath as sm\n",
    "import spatialmath.base as smb\n",
    "\n",
    "import spatialgeometry as sg\n",
    "\n",
    "from swift import Swift\n",
    "\n",
    "# The matrix exponential method\n",
    "from scipy.linalg import expm, logm\n",
    "\n",
    "# sympy provides symbolic mathematic operations \n",
    "import sympy as sym\n",
    "\n",
    "# setting up sympy to print nicely\n",
    "from IPython import display as ds\n",
    "from sympy.physics.mechanics import init_vprinting\n",
    "init_vprinting(use_latex='mathjax')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
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   "source": [
    "<br>\n",
    "\n",
    "<a id='1'></a>\n",
    "# 1.0 Twists\n",
    "---"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Earlier, we discussed the concept of Lie groups and we explained how we can get an $\\mathbf{SO}(3)$ matrix from the angle-axis representation:\n",
    "\n",
    "Given the angle-axis representation where\n",
    "$$\n",
    "    \\hat{\\mathbf{\\eta}} = \\begin{pmatrix}\n",
    "        \\hat{\\eta}_0 \\\\\n",
    "        \\hat{\\eta}_1 \\\\\n",
    "        \\hat{\\eta}_2\n",
    "    \\end{pmatrix}\n",
    "$$\n",
    "\n",
    "defines the axis of rotation, and $\\theta$ is the angle of rotation, we can obtain the Euler vector (also known as the exponential coordinates) by\n",
    "\n",
    "\\begin{equation*}\n",
    "    \\bf{\\eta} =\n",
    "    \\hat{\\eta} \\ \\theta \\in \\mathbb{R}^3\n",
    "\\end{equation*}\n",
    "\n",
    "and we can turn the Euler vector into an $\\mathbf{so}(3)$ matrix (the Lie algebra of the $\\mathbf{SO}(3)$ group) through the `skew` operation\n",
    "\n",
    "$$\n",
    "    [\\mathbf{\\eta}]_\\times =\n",
    "    \\begin{pmatrix}\n",
    "        0 & -\\eta_2 & \\eta_1 \\\\\n",
    "        \\eta_2 & 0 & -\\eta_0 \\\\\n",
    "        -\\eta_1 & \\eta_0 & 0\n",
    "    \\end{pmatrix} \\in \\mathbf{so}(3).\n",
    "$$\n",
    "\n",
    "Finally, we can construct the $\\mathbf{SO}(3)$ matrix from the $\\mathbf{so}(3)$ matrix using the matrix exponential\n",
    "\n",
    "$$\n",
    "    \\mathbf{R}(\\mathbf{\\eta}) = e^{[\\mathbf{\\eta}]_\\times} \\in \\mathbf{SO}(3).\n",
    "$$\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Representing Pose as a Twist\n",
    "\n",
    "We can represent pose as a twist\n",
    "\n",
    "$$\n",
    "    \\mathbf{s} =\n",
    "    \\begin{pmatrix}\n",
    "        \\upsilon_0 \\\\\n",
    "        \\upsilon_1 \\\\\n",
    "        \\upsilon_2 \\\\\n",
    "        \\eta_0 \\\\\n",
    "        \\eta_1 \\\\\n",
    "        \\eta_2\n",
    "    \\end{pmatrix}\n",
    "    \\in \\mathbb{R}^6\n",
    "$$\n",
    "\n",
    "where the first three elements $\\mathbf{\\upsilon}$ define the translation and the last three elements $\\mathbf{\\eta}$ define the rotation.\n",
    "\n",
    "_Note that in some textbooks, the $\\upsilon$ and $\\eta$ are swapped in $\\mathbf{s}$._\n",
    "\n",
    "_Note that we are using the Greek letter upsilon $\\upsilon$ (not to be confused with the English letter $v$ or the Greek letter nu $\\nu$) to represent the translation component._\n",
    "\n"
   ]
  },
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   "attachments": {},
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   "source": [
    "We can convert a twist into an augmented skew symmetric matrix (the Lie algebra of the $\\mathbf{SE}(3)$ group) using the `skewa` operation\n",
    "\n",
    "$$\n",
    "    [\\mathbf{s}] =\n",
    "    \\begin{pmatrix}\n",
    "        0 & -\\eta_2 & \\eta_1 & \\upsilon_0 \\\\\n",
    "        \\eta_2 & 0 & -\\eta_0 & \\upsilon_1 \\\\\n",
    "        -\\eta_1 & \\eta_0 & 0 & \\upsilon_2 \\\\\n",
    "        0 & 0 & 0 & 0\n",
    "    \\end{pmatrix} \\in \\mathbf{se}(3).\n",
    "$$\n",
    "\n",
    "and we can convert this matrix into an $\\mathbf{SE}(3)$ matrix using the matrix exponential\n",
    "\n",
    "$$\n",
    "    \\mathbf{T}(\\mathbf{s}) = e^{[\\mathbf{s}]} \\in \\mathbf{SE}(3).\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\mathbf{s} = \\left[\\begin{matrix}\\upsilon_{1}\\\\\\upsilon_{2}\\\\\\upsilon_{3}\\\\\\eta_{1}\\\\\\eta_{2}\\\\\\eta_{3}\\end{matrix}\\right]$"
      ],
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       "<IPython.core.display.Math object>"
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   "source": [
    "# Define the symbolic variables\n",
    "v1, v2, v3, eta1, eta2, eta3 = sym.symbols(['upsilon_1', 'upsilon_2', 'upsilon_3', 'eta_1', 'eta_2', 'eta_3'])\n",
    "\n",
    "# Define the twist\n",
    "s = np.array([v1, v2, v3, eta1, eta2, eta3])\n",
    "\n",
    "# Print the twist\n",
    "ds.display(ds.Math(f\"\\\\mathbf{{s}} = {sym.latex(sym.Matrix(s))}\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle [\\mathbf{s}] = \\left[\\begin{matrix}0 & - \\eta_{3} & \\eta_{2} & \\upsilon_{1}\\\\\\eta_{3} & 0 & - \\eta_{1} & \\upsilon_{2}\\\\- \\eta_{2} & \\eta_{1} & 0 & \\upsilon_{3}\\\\0 & 0 & 0 & 0\\end{matrix}\\right]$"
      ],
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       "<IPython.core.display.Math object>"
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    }
   ],
   "source": [
    "# Turn the twist into an se(3) matrix\n",
    "s_sk = smb.skewa(s)\n",
    "\n",
    "# Print the matrix\n",
    "ds.display(ds.Math(f\"[\\\\mathbf{{s}}] = {sym.latex(sym.Matrix(s_sk))}\"))\n"
   ]
  },
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   "attachments": {},
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   "source": [
    "## The Zero Twist\n",
    "\n",
    "What happens if we make a twist with all zeros?\n",
    "\n",
    "$$\n",
    "    \\mathbf{s} =\n",
    "    \\begin{pmatrix}\n",
    "        0 \\\\\n",
    "        0 \\\\\n",
    "        0 \\\\\n",
    "        0 \\\\\n",
    "        0 \\\\\n",
    "        0\n",
    "    \\end{pmatrix}\n",
    "$$\n",
    "\n",
    "We can convert this into an augmented skew symmetric matrix\n",
    "\n",
    "$$\n",
    "    [\\mathbf{s}] =\n",
    "    \\begin{pmatrix}\n",
    "        0 & 0 & 0 & 0 \\\\\n",
    "        0 & 0 & 0 & 0 \\\\\n",
    "        0 & 0 & 0 & 0 \\\\\n",
    "        0 & 0 & 0 & 0\n",
    "    \\end{pmatrix}\n",
    "$$\n",
    "\n",
    "and we can convert this matrix into an $\\mathbf{SE}(3)$ matrix using the matrix exponential\n",
    "\n",
    "\\begin{align*}\n",
    "    \\mathbf{T}(\\mathbf{s})\n",
    "    &= e^{[\\mathbf{s}]} \\\\\n",
    "    &=\n",
    "    \\begin{pmatrix}\n",
    "        1 & 0 & 0 & 0 \\\\\n",
    "        0 & 1 & 0 & 0 \\\\\n",
    "        0 & 0 & 1 & 0 \\\\\n",
    "        0 & 0 & 0 & 1\n",
    "    \\end{pmatrix} \n",
    "\\end{align*}\n",
    "\n",
    "which gives us the identity matrix. Therefore, the zero twist represents a null or identity transformation.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
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   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\mathbf{s} = \\left[\\begin{matrix}0\\\\0\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right]$"
      ],
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       "<IPython.core.display.Math object>"
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    {
     "data": {
      "text/latex": [
       "$\\displaystyle [\\mathbf{s}] = \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
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     "data": {
      "text/latex": [
       "$\\displaystyle \\mathbf{T} = \\left[\\begin{matrix}1.0 & 0 & 0 & 0\\\\0 & 1.0 & 0 & 0\\\\0 & 0 & 1.0 & 0\\\\0 & 0 & 0 & 1.0\\end{matrix}\\right]$"
      ],
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   "source": [
    "# Do this using code\n",
    "s = np.zeros(6)\n",
    "\n",
    "# Convert to an augmented skew-symmetric matrix\n",
    "s_sk = smb.skewa(s)\n",
    "\n",
    "# Convert to an SE(3) matrix\n",
    "T = expm(s_sk)\n",
    "\n",
    "# Display the results\n",
    "ds.display(ds.Math(f\"\\\\mathbf{{s}} = {sym.latex(sym.Matrix(s))}\"))\n",
    "ds.display(ds.Math(f\"[\\\\mathbf{{s}}] = {sym.latex(sym.Matrix(s_sk))}\"))\n",
    "ds.display(ds.Math(f\"\\\\mathbf{{T}} = {sym.latex(sym.Matrix(T))}\"))\n"
   ]
  },
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   "source": [
    "## Rotation only Twist\n",
    "\n",
    "What happens if we make a twist around the $z$-axis and no translation component?\n",
    "\n",
    "$$\n",
    "    \\mathbf{s}(\\theta) =\n",
    "    \\begin{pmatrix}\n",
    "        0 \\\\\n",
    "        0 \\\\\n",
    "        0 \\\\\n",
    "        0 \\\\\n",
    "        0 \\\\\n",
    "        \\theta\n",
    "    \\end{pmatrix}\n",
    "$$\n",
    "\n",
    "We can convert this into an augmented skew symmetric matrix\n",
    "\n",
    "$$\n",
    "    [\\mathbf{s}(\\theta)] =\n",
    "    \\begin{pmatrix}\n",
    "        0 & -\\theta & 0 & 0 \\\\\n",
    "        \\theta & 0 & 0 & 0 \\\\\n",
    "        0 & 0 & 0 & 0 \\\\\n",
    "        0 & 0 & 0 & 0\n",
    "    \\end{pmatrix}\n",
    "$$\n",
    "\n",
    "and we can convert this matrix into an $\\mathbf{SE}(3)$ matrix using the matrix exponential\n",
    "\n",
    "\\begin{align*}\n",
    "    \\mathbf{T}(\\theta)\n",
    "    &= e^{[\\mathbf{s}(\\theta)]} \\\\\n",
    "    &=\n",
    "    \\begin{pmatrix}\n",
    "        \\cos(\\theta) & -\\sin(\\theta) & 0 & 0 \\\\\n",
    "        \\sin(\\theta) & \\cos(\\theta) & 0 & 0 \\\\\n",
    "        0 & 0 & 1 & 0 \\\\\n",
    "        0 & 0 & 0 & 1\n",
    "    \\end{pmatrix}\n",
    "\\end{align*}\n",
    "\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we can see this is just a rotation matrix around the $z$-axis embedded in an $\\mathbf{SE}(3)$ matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\mathbf{s} = \\left[\\begin{matrix}0\\\\0\\\\0\\\\0\\\\0\\\\\\theta\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
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     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle [\\mathbf{s}] = \\left[\\begin{matrix}0 & - \\theta & 0 & 0\\\\\\theta & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
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    },
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     "data": {
      "text/latex": [
       "$\\displaystyle \\mathbf{T} = \\left[\\begin{matrix}\\cos{\\left(\\theta \\right)} & - \\sin{\\left(\\theta \\right)} & 0 & 0\\\\\\sin{\\left(\\theta \\right)} & \\cos{\\left(\\theta \\right)} & 0 & 0\\\\0 & 0 & 1 & 0\\\\0 & 0 & 0 & 1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
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    }
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   "source": [
    "# Define the symbolic variables\n",
    "theta = sym.symbols('theta')\n",
    "\n",
    "# Do this using code\n",
    "s = np.array([0, 0, 0, 0, 0, theta])\n",
    "\n",
    "# Convert to an augmented skew-symmetric matrix\n",
    "s_sk = smb.skewa(s)\n",
    "\n",
    "# Convert to an SE(3) matrix\n",
    "T = sym.simplify(sym.Matrix(s_sk).exp())\n",
    "\n",
    "# Display the results\n",
    "ds.display(ds.Math(f\"\\\\mathbf{{s}} = {sym.latex(sym.Matrix(s))}\"))\n",
    "ds.display(ds.Math(f\"[\\\\mathbf{{s}}] = {sym.latex(sym.Matrix(s_sk))}\"))\n",
    "ds.display(ds.Math(f\"\\\\mathbf{{T}} = {sym.latex(sym.Matrix(T))}\"))"
   ]
  },
  {
   "attachments": {},
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   "metadata": {},
   "source": [
    "## Translation only Twist\n",
    "\n",
    "What happens if we make a twist with no rotation component and a translation component?\n",
    "\n",
    "$$\n",
    "    \\mathbf{s}(\\upsilon) =\n",
    "    \\begin{pmatrix}\n",
    "        \\upsilon_1 \\\\\n",
    "        \\upsilon_2 \\\\\n",
    "        \\upsilon_3 \\\\\n",
    "        0 \\\\\n",
    "        0 \\\\\n",
    "        0\n",
    "    \\end{pmatrix}\n",
    "$$\n",
    "\n",
    "We can convert this into an augmented skew symmetric matrix\n",
    "\n",
    "$$\n",
    "    [\\mathbf{s}(\\upsilon)] =\n",
    "    \\begin{pmatrix}\n",
    "        0 & 0 & 0 & \\upsilon_1 \\\\\n",
    "        0 & 0 & 0 & \\upsilon_2 \\\\\n",
    "        0 & 0 & 0 & \\upsilon_3 \\\\\n",
    "        0 & 0 & 0 & 0\n",
    "    \\end{pmatrix}\n",
    "$$\n",
    "\n",
    "and we can convert this matrix into an $\\mathbf{SE}(3)$ matrix using the matrix exponential\n",
    "\n",
    "\\begin{align*}\n",
    "    \\mathbf{T}(\\upsilon)\n",
    "    &= e^{[\\mathbf{s}(\\upsilon)]} \\\\\n",
    "    &=\n",
    "    \\begin{pmatrix}\n",
    "        1 & 0 & 0 & \\upsilon_1 \\\\\n",
    "        0 & 1 & 0 & \\upsilon_2 \\\\\n",
    "        0 & 0 & 1 & \\upsilon_3 \\\\\n",
    "        0 & 0 & 0 & 1\n",
    "    \\end{pmatrix}\n",
    "\\end{align*}\n",
    "\n"
   ]
  },
  {
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   "metadata": {},
   "source": [
    "For the case where there is no rotation, the translation component of the twist $\\mathbf{\\upsilon}$ to the translation component $\\mathbf{t}$ of the $\\mathbf{SE}(3)$ matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\mathbf{s} = \\left[\\begin{matrix}x\\\\y\\\\z\\\\0\\\\0\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
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    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle [\\mathbf{s}] = \\left[\\begin{matrix}0 & 0 & 0 & x\\\\0 & 0 & 0 & y\\\\0 & 0 & 0 & z\\\\0 & 0 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\mathbf{T} = \\left[\\begin{matrix}1 & 0 & 0 & x\\\\0 & 1 & 0 & y\\\\0 & 0 & 1 & z\\\\0 & 0 & 0 & 1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
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    }
   ],
   "source": [
    "# Define the symbolic variables\n",
    "x, y, z = sym.symbols(['x', 'y', 'z'])\n",
    "\n",
    "# Do this using code\n",
    "s = np.array([x, y, z, 0, 0, 0])\n",
    "\n",
    "# Convert to an augmented skew-symmetric matrix\n",
    "s_sk = smb.skewa(s)\n",
    "\n",
    "# Convert to an SE(3) matrix\n",
    "T = sym.simplify(sym.Matrix(s_sk).exp())\n",
    "\n",
    "# Display the results\n",
    "ds.display(ds.Math(f\"\\\\mathbf{{s}} = {sym.latex(sym.Matrix(s))}\"))\n",
    "ds.display(ds.Math(f\"[\\\\mathbf{{s}}] = {sym.latex(sym.Matrix(s_sk))}\"))\n",
    "ds.display(ds.Math(f\"\\\\mathbf{{T}} = {sym.latex(sym.Matrix(T))}\"))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Caution is needed at this point. Up to this point, we have looked at rotation only and translation only twists and they behave very simply.\n",
    "\n",
    "* For a rotation only twist, the rotation component of the twist acts exactly the same as the Euler vector in a rotation.\n",
    "* For a translation only twist, the translation component of the twist is equal to the translation in the $\\mathbf{SE}(3)$ matrix.\n",
    "\n",
    "If we have a twist with **both** a non-zero rotation and a translation component, then the translation component of the twist does not act the same as the translation component of the $\\mathbf{SE}(3)$ matrix."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Twists as a Pose"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In 3D, a twist is equivalent to screw or helicoidal motion – motion about and along some line in space as shown below. Rigid-body motion between any two poses can be represented by such screw motion."
   ]
  },
  {
   "attachments": {},
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   "metadata": {},
   "source": [
    "<img src=\"./Figures/3/fig2_24.png\" width=\"400\">"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given a twist\n",
    "\n",
    "$$\n",
    "    \\mathbf{s} =\n",
    "    \\begin{pmatrix}\n",
    "        \\upsilon_1 \\\\\n",
    "        \\upsilon_2 \\\\\n",
    "        \\upsilon_3 \\\\\n",
    "        \\eta_1 \\\\\n",
    "        \\eta_2 \\\\\n",
    "        \\eta_3\n",
    "    \\end{pmatrix}\n",
    "$$\n",
    "\n",
    "or a pair of vectors\n",
    "\n",
    "$$\n",
    "    \\mathbf{s} =\n",
    "    \\begin{pmatrix}\n",
    "        \\mathbf{\\upsilon} \\\\\n",
    "        \\mathbf{\\eta}\n",
    "    \\end{pmatrix}\n",
    "$$\n",
    "\n",
    "where $\\mathbf{\\upsilon}$ defines a moment and $\\mathbf{\\eta}$ is a vector parallel to the rotation axis. The moment encodes a point lying on the twist axis, as well as the screw pitch which is the ratio of the distance along the screw axis to the rotation about the screw axis.\n",
    "\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To illustrate the underlying screw motion, we will progressively rotate a coordinate frame about a screw. We define a screw parallel to the $z$-axis that passes through the point (2, 3, 2) and has a pitch of 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "axis = [0.0, 0.0, 1.0]\n",
    "point = [2.0, 3.0, 2.0]\n",
    "pitch = 0.5\n",
    "\n",
    "S = sm.Twist3.UnitRevolute(axis, point, pitch)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and the coordinate frame to be rotated is described by an $\\mathbf{SE}(3)$ matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Describe the coordinate frame {x} relative to the world frame\n",
    "Tx = smb.transl(3, 4, 2)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For values of $\\theta$ in the range 0 to 15 rad, we evaluate the twist for each value of $\\theta$, apply it to the frame ${^0\\mathbf{T}}_x$ and plot the result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"600\"\n",
       "            height=\"400\"\n",
       "            src=\"http://localhost:52000/?53000\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            \n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.IFrame at 0x2a545d8a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "env = Swift()\n",
    "env.launch(browser='notebook')\n",
    "\n",
    "# Add the coordinate frame {x} to the environment\n",
    "# This will be the largest coordinate frame\n",
    "Tx_ax = sg.Axes(0.5)\n",
    "Tx_ax.T = Tx\n",
    "env.add(Tx_ax)\n",
    "\n",
    "for theta in np.arange(0, 15, 0.3):\n",
    "    ax = sg.Axes(0.1)\n",
    "    ax.T = S.exp(theta).A @ Tx\n",
    "    env.add(ax)\n",
    "\n",
    "env.set_camera_pose([10.0, 4.0, 12.0], [0, 2.0, 1.0])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Swift environment above clearly shows the screw motion in the successive poses of the frame ${x}$ as it is rotated about the screw axis.\n",
    "\n",
    "We can also convert an arbitrary $\\mathbf{SE}(3)$ matrix into a twist using `spatialmath`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1.1204 1.6446 3.1778; 0.041006 0.4087 0.78907)\n"
     ]
    }
   ],
   "source": [
    "T = smb.transl(1.0, 2.0, 3.0) @ smb.eul2tr(0.3, 0.4, 0.5)\n",
    "S = sm.Twist3(T)\n",
    "print(S)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and we see that the twist vector is the unique elements of the logarithm of the $\\mathbf{SE}(3)$ matrix. The screw in this case is parallel to"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.04100647, 0.40869691, 0.78907378])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S.w"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "passes through the point"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.00113807,  0.84730078, -0.43891444])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S.pole"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and has a pitch of"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 3.22562162893513$"
      ],
      "text/plain": [
       "3.22562162893513"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S.pitch"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and the rigid-body motion requires a rotation about the screw of"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0.889579745611291$"
      ],
      "text/plain": [
       "0.8895797456112915"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S.theta"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "radians, which is about 1/7th of a turn. Adjust the parameters in the Swift environment above to see the effect of changing the screw parameters."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Your Understanding\n",
    "\n",
    "#### Question 1\n",
    "\n",
    "What is the difference between a twist and a unit twist? How may a unit twist be used in practice?\n",
    "\n",
    "#### Question 2\n",
    "\n",
    "How would you compose two twists?\n",
    "\n",
    "#### Question 3\n",
    "\n",
    "What is the inverse of a twist (the twist that causes the opposite transformation)?\n",
    "\n",
    "#### Question 4\n",
    "\n",
    "Is it faster to compose two $\\mathbf{SE}(3)$ matrices or to convert them to twists and compose them?\n",
    "\n",
    "#### Question 5\n",
    "\n",
    "What is an advantage of using twists over $\\mathbf{SE}(3)$ matrices? What is a disadvantage?\n",
    "\n",
    "#### Question 6\n",
    "\n",
    "Following the Rotation only Twist example above, what is the $\\mathbf{SE}(3)$ matrix for the twist\n",
    "\n",
    "$$\n",
    "    \\mathbf{s}(\\theta) =\n",
    "    \\begin{pmatrix}\n",
    "        0 \\\\\n",
    "        0 \\\\\n",
    "        0 \\\\\n",
    "        \\theta_x \\\\\n",
    "        0 \\\\\n",
    "        \\theta_z\n",
    "    \\end{pmatrix}\n",
    "$$\n",
    "\n",
    "What does the result mean?"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "<a id='2'></a>\n",
    "# 2.0 Trajectories\n",
    "---"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We wish to make trajectories with boundary conditions. The boundary conditions are that at time $t=0$ we have a set pose, orientation, or position and at time $t=T$ we have a desired pose, orientation, or position.\n",
    "\n",
    "Additionally, real-world  constraints exist. For example, a drone, car, or manipulator cannot instantly _step_ in velocity, to do so would require infinite acceleration. Therefore we may define another boundary condition that the initial and final velocity is zero."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.1 Smooth One-Dimensional Trajectory"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Polynomial Trajectory"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start our discussion with a scalar function of time that has a\n",
    "specified initial and final value.\n",
    "An obvious candidate for such a smooth function is a polynomial\n",
    "function of time. Polynomials are\n",
    "simple to compute and can easily provide the required smoothness and boundary conditions. A quintic\n",
    "(fifth-order) polynomial is commonly used\n",
    "\n",
    "$$\n",
    "\tq(t)=At^{5}+Bt^{4}+Ct^{3}+Dt^{2}+Et+F\n",
    "$$\n",
    "\n",
    "where time $t\\in [0,T]$. The first- and second-derivatives are also polynomials\n",
    "\n",
    "\\begin{align*}\n",
    "\t\\dot{q}(t)  &= 5At^{4}+4Bt^{3}+3Ct^{2}+2Dt+E \\\\\n",
    "\t\\ddot{q}(t) &= 20At^{3}+12Bt^{2}+6Ct+2D\n",
    "\\end{align*}\n",
    "\n",
    "and therefore smooth. The third-derivative, jerk, will be a quadratic.\n",
    "\n",
    "The trajectory has defined boundary conditions for position ($q_0$, $q_T$), velocity ($\\dot{q}_0$, $\\dot{q}_T$) and\n",
    "acceleration ($\\ddot{q}_0$, $\\ddot{q}_T$).\n",
    "Writing $q(t)$ to $\\ddot{q}(t)$ for the boundary conditions $t=0$ and $t=T$ gives six\n",
    "equations which we can write in matrix form as\n",
    "\n",
    "$$\n",
    "\t\\left(\\begin{array}{c}\n",
    "\t\tq_{0}\\cr\n",
    "\t\tq_{T}\\cr\n",
    "\t\t\\dot{q}_{0}\\cr\n",
    "\t\t\\dot{q}_{T}\\cr\n",
    "\t\t\\ddot{q}_{0}\\cr\n",
    "\t\t\\ddot{q}_{T}\n",
    "\t\\end{array}\\right)%þ\n",
    "\t=\\begin{pmatrix}\n",
    "\t\t0       & 0       & 0      & 0     & 0 & 1\\cr\n",
    "\t\tT^{5}   & T^{4}   & T^{3}  & T^{2} & T & 1\\cr\n",
    "\t\t0       & 0       & 0      & 0     & 1 & 0\\cr\n",
    "\t\t5T^{4}  & 4T^{3}  & 3T^{2} & 2T    & 1 & 0\\cr\n",
    "\t\t0       & 0       & 0      & 2     & 0 & 0\\cr\n",
    "\t\t20T^{3} & 12T^{2} & 6T     & 2     & 0 & 0\n",
    "\t\\end{pmatrix}\n",
    "\t\\left(\\begin{array}{c}\n",
    "\t\tA\\cr\n",
    "\t\tB\\cr\n",
    "\t\tC\\cr\n",
    "\t\tD\\cr\n",
    "\t\tE\\cr\n",
    "\t\tF\n",
    "\t\\end{array}\\right)  \\,\\,.\n",
    "$$\n",
    "\n",
    "The matrix is square and, if $T \\ne 0$, we can invert it to solve for the coefficient vector $(A, B, C, D, E, F)$.\n",
    "\n",
    "_This is the reason for choice of quintic polynomial. It has six coefficients that enable it to meet the six boundary conditions on initial and final position, velocity and acceleration._"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Toolbox provides a function to generate the trajectory described above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The initial position\n",
    "q0 = 0.0\n",
    "\n",
    "# The final position\n",
    "qf = 1.0\n",
    "\n",
    "# The start time\n",
    "t0 = 0.0\n",
    "\n",
    "# The end time\n",
    "tf = 1.0\n",
    "\n",
    "# A vector for time\n",
    "# Steps from t0 to tf in 50 steps\n",
    "t = np.linspace(t0, tf, 50)\n",
    "\n",
    "# Create the trajectory\n",
    "traj = rtb.quintic(q0, qf, t)\n",
    "\n",
    "# Plot the trajectory\n",
    "traj.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"600\"\n",
       "            height=\"400\"\n",
       "            src=\"http://localhost:52001/?53001\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            \n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.IFrame at 0x2a544e5f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Animate the trajectory\n",
    "env = Swift()\n",
    "env.launch(browser='notebook', realtime=True)\n",
    "obj = sg.Sphere(0.03, color=\"#fc0349\")\n",
    "env.add(obj)\n",
    "env.set_camera_pose([0.5, 1.0, 0.5], [0.5, 0.0, 0.0])\n",
    "\n",
    "for q in traj.q:\n",
    "    obj.T = sm.SE3.Tx(q)\n",
    "    env.step(0.02)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see in the above Figure that the initial position, velocity and acceleration are 0, the final position is 1, and the final velocity and acceleration are 0. These are our boundary conditions. Adjust the variables in the code above and see how the trajectory changes."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can access the position, velocity, acceleration vectors using `traj.q`, `traj.qd`, `traj.qdd` respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The position vector, rounded to 3 decimal places, is\n",
      "[-0.     0.     0.001  0.002  0.005  0.009  0.015  0.023  0.034  0.046\n",
      "  0.061  0.078  0.098  0.12   0.145  0.171  0.2    0.23   0.263  0.297\n",
      "  0.332  0.368  0.405  0.443  0.481  0.519  0.557  0.595  0.632  0.668\n",
      "  0.703  0.737  0.77   0.8    0.829  0.855  0.88   0.902  0.922  0.939\n",
      "  0.954  0.966  0.977  0.985  0.991  0.995  0.998  0.999  1.     1.   ]\n"
     ]
    }
   ],
   "source": [
    "print(\"The position vector, rounded to 3 decimal places, is\")\n",
    "print(np.round(traj.q, 3))\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can set the desired initial final velocity by providing extra keyword arguments to the `traj` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The initial position\n",
    "q0 = 0.0\n",
    "\n",
    "# The final position\n",
    "qf = 1.0\n",
    "\n",
    "# The start time\n",
    "t0 = 0.0\n",
    "\n",
    "# The end time\n",
    "tf = 1.0\n",
    "\n",
    "# The initial velocity\n",
    "# we use qd as shorthand for qdot or dq/dt\n",
    "qd0 = 10.0\n",
    "\n",
    "# The final velocity\n",
    "qdf = 0.0\n",
    "\n",
    "# A vector for time\n",
    "# Steps from t0 to tf in 50 steps\n",
    "t = np.linspace(t0, tf, 50)\n",
    "\n",
    "# Create the trajectory\n",
    "traj2 = rtb.quintic(q0, qf, t, qd0, qdf)\n",
    "\n",
    "# Plot the trajectory\n",
    "traj2.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"600\"\n",
       "            height=\"400\"\n",
       "            src=\"http://localhost:52002/?53002\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            \n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.IFrame at 0x2ab984c70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Animate the trajectory\n",
    "env = Swift()\n",
    "env.launch(browser='notebook', realtime=True)\n",
    "obj = sg.Sphere(0.03, color=\"#fc0349\")\n",
    "env.add(obj)\n",
    "env.set_camera_pose([1.1, 1.0, 0.5], [1.1, 0.0, 0.0])\n",
    "\n",
    "for q in traj2.q:\n",
    "    obj.T = sm.SE3.Tx(q)\n",
    "    env.step(0.02)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This illustrates an important problem with polynomials – non zero initial velocity causes the polynomial to overshoot the terminal value, in this example, peaking at over 2 on a trajectory from 0 to 1."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another problem with polynomials, a very practical one, can be seen in the middle graph of our first `traj` plot. The velocity peaks when $t = 0.5$ s which means that, for most of the time, the velocity is far less than the maximum. The mean velocity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0.523102222222221$"
      ],
      "text/plain": [
       "0.523102222222221"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qd = traj.qd\n",
    "\n",
    "qd.mean() / qd.max()\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "is only 52.3% of the peak so we are not using the motor as fully as we could. A real robot joint has a well-defined maximum speed and, for minimum-time motion, we want to be operating at that maximum for as much of the time as possible. We would like the velocity curve to be _flatter_ on top."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Trapezoidal Hybrid Trajectory"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A well known alternative to polynomials is a _trapezoidal_ hybrid trajectory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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N+D/YVftlDWfFRcax6CGqB4sfIiINlZwt8RjO+uzAZ1g3ZR06hHRwm2TL4Swi32DxQ0TUTLwNZQGAxWrB6oOrsfrgapScKfE6nFVaUYoO0R3cHudwFpFv+Kz4qampgRDCdfdkIqJg5jaUJRTM6jcLoUoovjn6DaJCozAiYQSeGvQUbE6b9+GsNilez8vhLKKmu+L7/OzatQubN2/Gnj17cOjQIdTU1G5wZzKZEB8fj27duuH6669Hz549fRqwL/E+P9rj/TP0g7nwndKKUo+CRkDglRGv4ObONyPUEOrWfulPSz2Gs+7odgfzoRN8b+iHJvf5cTgcWLlyJT799FMcP34ckZGR6Ny5M4YOHYrIyEhIKVFZWYmysjKsX78e//vf/xATE4Px48dj1KhRPtuQjIhIS/UNZ52sPolVB1dh2d5lboUPAEhIxEbEehQ+gPfhrCC+/yxRs7usnp+HH34YDocDGRkZGDRoELp06XLJ9oWFhdi0aRPWrVsHo9GIRYsWNTlgX2LPj/b4F5V+MBeNU3c4a2baTBgVIzYf24w2oW1wY9KNuCb6GozJG+MxlPXNHd80esiK+dAP5kI/fNXzc1nFz4oVKzB8+PDLntfjcDiwZs0ajB49+rIDbE4sfrTHi4p+MBcNq28467UbX8PYzmMRoly4Nnobyrqz+52Nfi7mQz+YC/3QZNirbvHyq1/9Cr/97W/Rr1+/Sz+J0ai7woeIqK76hrPKqsqw+uDqeoez2oW3cyt8AK7MItKzJk3CqaqqQlVVVb3HCwsLsXfvXowdO7YpT0NE1OzqDmfNSJsBgzAg/1g+zGFmjEwaib/c8BeM+nAUbzRI5OeUy/2Gn376Cd988w2OHTvWYNvDhw/j7bffvqLAiIhaSmlFqavwAQBVqljw/QJc3fZq/ONn/8BLI15C5lWZ6GbuhueGPAeDMAAAbzRI5Kcuu+dn586dWLZsmevrf//739ixYweSk5ORlJSElJQUREZGAgDKy8sRFhbmu2iJiK5AfcNZRyuPYtXBVVi+b7nX4azosGgYFffLJIeziPzfZRc/kydPxuDBg1FYWIiXX34ZRqMRO3fuxNq1a11toqOj0a5dOxQVFaFXr16NPnd+fj5yc3MhpURmZiZGjhzpdvzJJ5/EqVOnXBOun3nmGYSGhuLMmTN48cUXcfLkSSQlJWH69OkIDfVcTkpEwafucNb0PtNhUAz4vux7xITHYGTSSDw75FmMXD6Sw1lEQeKK5vzExcUhLi4On332GSZMmID+/fujqqoKJSUlKC4uRnFxMU6ePIkRI0Zg0qRJjTqn0+lEbm4unnjiCURERCA7Oxv9+/dHVFSUW7tZs2YhKSnJ7bH//Oc/GDBgAMaOHYvc3FysXr2a84yIyOtw1sJtC/Hm6Ddr5/QoBldb7ptFFDyaNOH5L3/5i+v/ERER6N69O7p3735F5yooKEBCQgLMZjMAIC0tDdu3b8eQIUMa/N78/HzMmzcPADBs2DD885//rLf4sdvtcDgcCA8Ph5SSNxLT2PnXn3nQnj/morSyFAdOH0DnNp0R1+pCoVJaUYpVB1fhw4IPvQ5ntQ5pDUUobj/rHd3uwLCEYSg6XYSUNimIa6XtjQb9MR+BirnQD1/lQDe3XC4vL3cVPgBgNpthsVg82r300ktQFAXDhg3DuHHjANSuOouIiLjk952Xl5eH/Px85OTkoKamBjabzcc/CV0Jq9WqdQh0jr/kYlnBMjz27WNQoUKBggd6PgBFKNhxcgdiw2MxIn4Enrr+Kdz86c1QcaEAUoSCjqaOqK6u9jhntBKN6OhoAPB6XAv+ko9gwFxoz2Qy+eQ8uil+GmP69Okwm82oqqpCTk4O4uLiGrzHUF0TJ07E+PHjAQChoaFQlMte8EY+JKWE1WpFWFgYbx6mMX/KRWllKR777jFXUaNCxeJdi/HW6Lcwd8BcKOLC+zpnaA7mbpjrGs56dsiz6NLu0nen1wN/ykegYy70w1fbZF3WWWbOnIkJEybghhtuaHQAdrsdGzZswMcff4wXX3yx3nbR0dFuPTYWiwWpqalubc73DEVERGDQoEEoKChAv379EBER4er9sVgsrr/cvAkJCXFNmBZC8BdZJ5gL/dBDLupbnXXo7CGsKFmB/+z/j9fhrKjQKLd5PABwV/e7MDxhuN+uztJDPqgWc6E9X73+l1X8DB8+HLm5ufjHP/6B9PR09O7dG507d0ZsbKyrK8pqtaKsrAyFhYX44YcfkJ+fD6PRiFtuueWS505NTcXBgwdhsVgQERGBrVu3uk2WdjqdqKysROvWreFwOLBt2zZkZGQAAPr164d169Zh7NixWLduHdLT0y/3dSAinai7Ouvh3g8DAthxfAfiI+MxKmkU/jrsrxj+7+FcnUVEV+Sy9vYCasfBV69ejbVr16KkpMT1uMFQ+9eW0+l0PZaYmIgRI0ZgxIgRrjk5l7Jlyxa8++67UFUVmZmZGDVqFObNm4esrCxERETgiSeegNPphKqqSE9Px1133QUhBM6cOYP58+fDYrEgMTERjzzySKOWunNvL+1xzxz90EMu6ts7652fvYMRiSPchrOauneW3ukhH1SLudAPTTY2rausrAx79uxBaWkpzp49CwCIiopCfHw8rr76ap8E2JxY/GiPFxX9aIlc1DecVXymGCtLVuLjwo+x5dgWj+9b9vNlGBw32Ov5/HU4qyF8b+gHc6EfmmxsWldsbKzuCxwi0oe6w1kP9X4IUkrsPLkTiVGJGJ00Gi9mvIiMZRkcziKiZtWknp/Zs2cjMTERSUlJSEpKQmJiIjp06ODL+JoVe360x7+o9KM5c1HfcFbu2FyMSBjh9nyBPpzVWHxv6AdzoR+66PlJTEzE/v37sWnTJtdjJpMJ8fHxrmLofGHUtm3bpsZKRDpV33BW4elCrCxZiU8KP/G6OivM4Ll0mHtnEVFza1Lxc8MNN2Dr1q0YPXo0unfvDqvVitLSUqxfvx6FhYVubSMjI13F0H333dekoIlIP+oOZ2VdmwVVqvjR8iNSWqdgdPJoLBy+kMNZRKQbTRr2mjlzJvr06YN7773X7fGamhq8//772LlzJ26//XYcPXoUhw8fxqFDh1BaWoo333yzqXH7BIe9tMfuZP24klzUN5z13tj3kJGQweGsJuB7Qz+YC/3QxbBXWVmZxyajQO2dk6dOnYqcnBzs2bMHd97JCxyRv6lvKEtKif2n92NlyUr898B/vQ5nhRpCOZxFRLrVpOInPj4e27Ztw4033uj1eHp6OpYvX87ih8jP1B3KmnfDPKS0TsHKkpXYU74HV7W5CqOTR2NsylgM/WAoh7OIyK80aWOrzMxMfPvtt1i2bJnX4aPDhw/rZnNAImqc0spSV+EDAKpUkb0hG18d/gp3dLsDS25agqdveBoZCRlIaZ2C54Y8B4Oovcnp+eEsFjhEpGdNnvBcXl6OJUuWYMWKFcjIyEBycjIAYM+ePVi5ciXS0tJ8EigR+calhrP2nd6H9/a95zGUBQAjEkagu7m7x+McziIif9Pk7VHHjRuH3r17Iy8vD1988QVsNpvrWO/evZGVldXUpyAiH6k7nPWXG/6C5KhkrCxZiX2n9qFzZGcM7jQY/9r7r0YPZQEcziIi/9Kk1V51ORwOHDt2DDabDTExMWjdurWvTt0suNpLe1xF0XK8rcwCgOl9p+PW1FtxVZurYLVaER4ejn/t+RdXZmmM7w39YC70QxervTxOZjQiPj7el6ckoka61HDWT+U/4W87/uZ1OGto/FB0je6Ki/8O4lAWEQUynxY/RKSNusNZzwx+BolRiVhZshKFpwvR3dwdwxOG44N9H3BlFhEFPRY/RH6utMJzddbvv/49ZvSdgft63oer2l7lalthr/AYzmKBQ0TBhsUPkc5tLduK745+h/4d+yMt9sLqSSkldll24a2db3kdzhoSP8St8AE4nEVEBLD4IdK1R9Y+gmX7lrm+vjX1VmRelYmVJStRfKYYPdv1xKjEUfj3vn9zOIuIqJF0Vfzk5+cjNzcXUkpkZmZi5MiRrmM2mw3z589HWVkZFEXB6NGjcdNNNwEAPvjgA6xevRpRUVEAgPvuuw/XXHONJj8Dka9sLdvqVvgAwIcFH6JdWDtkXZuFzm06ux5/ruY5DmcRETWSboofp9OJ3NxcPPHEE4iIiEB2djb69+/vKmgAYMKECejRowesVivmzp2LtLQ0dOzY0XVs7NixWoVPdNmO7t+Kkv3fIemq/uh41YXhLFWq2HFiB57b8pzX74uPjHcrfAAOZxERXQ7dFD8FBQVISEiA2WwGAKSlpWH79u0YMmQIAMBkMqFHjx4AgLCwMMTFxaG8vNxV/DSW3W6Hw+FAeHg4pJTw4W2O6Aqcf/2DLQ/Lc2dipnUZVAVQDgA5GybCnDEOK0tWorSyFNe2uxbjOo/DusPrPL43vUO619erU6tO6NSqE4Arez2DNRd6xXzoB3OhH77KgW6Kn/LyclfhAwBmsxkWi8Vr2xMnTqC4uBidO1/46/fTTz/FypUr0a1bN0ydOhVhYWFevzcvLw/5+fnIyclBTU2N2x2pSTtWq1XrEFpM2YHtrsIHAFQFeNSWh0cKzHig9wNIiExwtf3m8Df48MCHrq9v7Xwrukd2b9Y984IpF/6A+dAP5kJ7JpPJJ+fRTfHTWHa7HQsWLHArcMaMGYPJkycDAN577z0sW7YMU6dO9fr9EydOxPjx4wEAoaGhUJQm7e1KTSSlhNVqRVhYWMDcOVUpLYXxwAE4OneGGnfR8JPVCtO336Lgk5eg1tkiSwpgmJqAru27uj3+0siX8Kvjv8KWo1twXcfrkNa++fbKC8Rc+DPmQz+YC/0wGn1Ttuim+ImOjnbr6bFYLEhNTXVrI6XEK6+8grS0NAwcOND1eNu2bV3/HzFiBN566616nyckJAQhISEAACEEf5F1IlByEbF0Kdo8+iiEqkIqCs48+ihkZCRMX38NOJ2oGTAAceN+CWXvt66eHwAwqEDSVdd7fQ36xfZDv9h+LfYzBEouAgXzoR/MhfZ89frrptsjNTUVBw8ehMVigdVqxdatW9GnTx+3NkuWLIHJZMKkSZPcHi8vL3f9f/PmzUhISABRS1NKS12FDwAIVUXrnBzI8HCcWrgQ5W+/jcoHH0TMiEwsCL8NhnMr0w0q8GL4bW6TnomIqPnopufHYDDgnnvuwZ/+9CeoqorMzExERUVh3rx5yMrKgpQSH330ERISEjBnzhwAwN13342+ffvivffeQ1FREYQQ6NSpE3eSp2bhdTjLbkfItm0wbdiAsFWrXIXPeUJKOJOSIFu1cnt80j0LcMP+X+Jg4RYkdrmOhQ8RUQvy6a7u/oa7umvPX3ZLrjucVT1uHITDAVFTg5q+fWEbOhTO2Fh0uOEGtwJIGgw49s037nN/dMpfchEsmA/9YC70Q5e7uhP5o3onKAOAlAj59lu0mTMH4tzfCUJVEf7ppyhbuxbOq9y3jzj93HNok50N4XRCGgw4nZPjF4UPEVEwYfFDQa1uj87pnBzU9O+P0E2bEPrtt1BOnYI0mVyFz3lCVWE4dsyj+Km6805YMzJgLCqCIyWFhQ8RkQ5x2IvDXppqru7kS/bmXNSmw4AB7sNUAKruuAO20aNh698f0mz23s6PhrMai137+sJ86AdzoR++GvbSzWovIl+JWLoUHQYMQMyUKegwYAAili51HRNVVQj9+mtELlyI6Icf9pygDKB60iRYx46FPHfTTTUuDqefew7SYAAADmcREfk59vyw50dTvv6LymsvjaKgasoUGMrKIMPCYO/bFzXXXw9H+/boMGxYo3t0lNLSgB7O4l+3+sJ86AdzoR+c8ExB6VLDWaKyEuH//a9nb46qwjZoEKyTJgF1LlyXM0FZjYtDTQAWPUREwYbFD/mNupOTK6ZPh7NjR4Rs21bbqxMRAUdKCqQQbhOUpcGAmsGDPQofgBOUiYiCEYsf0gWltBQhRUXeJyjX1CD06689lptHLlyIUy+8gLOPPgq1QwdXc2dKymUtN2ePDhFRcGHxQ82qMauuopYtQ+xjj13o0XnoITg7dULojh1Qjh+HDA2FDA/3XG5+7u7JFxc+AHtziIjo0jjhmROem43HPXSeew5Vd95Ze9DphKG4GKEbN6Lt3Lnuw1RC4NSCBbANGwb13MS2YFluriVO6tQX5kM/mAv94IRn0lRDPTreNvlsM2cOTGvXQlRXA4oCR3IypMHgvUcnLs5V+AAXlpvz7slERNRULH7ITWOGqbz26EyeDGNxMYwFBTAWFCB040avm3xWT5wI69ixFx47fBiRb77p0aPjSEnxeF4OZxERkS9w2CtIhr2uuKg5P0wFAKoK47ZtaH/LLe7DVACsw4fD2b07HKmpcKSmQm3VCu1/9rMGh6mklDDm5iL28cfdenTcnpdaBLv29YX50A/mQj98NezF4icIip8GixrUM6dGCFTdfjuUU6cgHA5ACEghEP7llx7PcWLZstrl5HWft84wVd3nPX9RaVVejpDiYvboaIgXeH1hPvSDudAPzvkJYI3ppWlsW69zbx59FBKAUl0Nw6FDMBw+DENpqddhKtsNN8A6fjwQEuI6X9jKlT4fplLj4lATH3/Jn5WIiMgXWPz4QGOLFZ8MPV2i7ZnsbNgHDIBy9CgMZWVQjh1DyA8/eL3jcci+fbBlZMA2bBic8fEQ5eVeV1PVDBzoKnyAy594zHvoEBGR3uhq2Cs/Px+5ubmQUiIzMxMjR450O15QUIBXX30VdrsdGRkZmDx5MgDg6NGjWLBgASorK3Httdfi/vvvb1TX5PFdu2CPjq73uC+LlSseelIUlC9aVHvcYoHh5EkoJ09COXQIYatW4eKfUgqBiocfhqNrV6gdOsDZoQOklIgdPbpRS8QbM0zl9tr4YOIxu5P1g7nQF+ZDP5gL/Qi4YS+n04nc3Fw88cQTiIiIQHZ2Nvr374+oqChXm7feegszZsxAYmIiHn/8cfTv3x9JSUn45z//idtuuw3p6emYP38+vv/+e6Snpzf4nDG//CVO33lnk4oVjyGl7GzYBgyAbN0aorISoqoKhuJij7sTt5kzByH5+RBOJ8SZMxBOJxSLxWsvTeimTbCnp8OZnAx7v35Q27WDYc8ehK9a5d5WStiGD/eYe9PYnprLHqZijw4REfkh3RQ/BQUFSEhIgNlsBgCkpaVh+/btGDJkCADAYrHA6XQiOTkZADB48GDk5+cjMTERe/fuxaxZswAAQ4cORX5+fr3Fj91uh8PhqK3gzxUhxu+/ByIiAKcTUFWIs2cR8eGHrl4Voapo87vfwfSf/wDh4a5zeS1WnE60yc6GMykJMiICslUriBMnvN7LxjZoEGzDh0Nt3RowGqGUlqLjwIEevTRnf/Mbj0JERW2vUN229uRk1O3Mq7zjDlQPG+Ze1NTT4efs1AnOTp3OnbD5OwXPx6qjDsigxVzoC/OhH8yFfvgqB7opfsrLy12FDwCYzWZYLJZLHt+9ezfOnj2LyMhIV1dk3e+rKy8vD/n5+cjJyQFQW4RU9OsHa9++gKIABgNMW7ei1Ycfun2fAGDJykL1wIGuxwxHjiBl+HCPYaojzz57oYA4167V++97tDvdty+c4eGA3V77LzoaZU8/7bbVQ9lTT6EyOhqornb/QS6n7bn2OD/E5+24xqxWq9Yh0DnMhb4wH/rBXGjPZDL55Dy6KX5aysSJEzF+/HjX19JggBw2DCEX96yEh3vtVVG6dUP4RT0/6NIFp3JyardnODekdOrZZxHapYv7kza2HQDHPffg6KhRbr004R6tLr+tXkkpYbVaERYWxrF0jTEX+sJ86AdzoR9Go2/KFt0UP9HR0W49NhaLBampqZc8Hh0djaioKFRUVEBKCSGE6/H6hISEIOTc6qXz819kfLz7xOH4eK/zZOq2A4Dqu+6CbfhwtwLE21ujse3OP7/93LLvht5ml9NWz4QQvKjoBHOhL8yHfjAX2vPV66+b4ic1NRUHDx6ExWJBREQEtm7dikmTJrmOm81mKIqC4uJiJCYmYuPGjcjKyoIQAl27dnVNct6wYQOGDRvWqOc88Y9/1Lvaqzkm/3KSMBERkfZ0tdR9y5YtePfdd6GqKjIzMzFq1CjMmzcPWVlZMJvN2Lt3L15//XXY7XYMHToUU6ZMAQAcOXIECxYsQFVVFXr16oX7778fiqI0+HznJ1GTdqSUsNlsMJlM/ItKY8yFvjAf+sFc6IfBYHCb/3uldFX8tBS73e4a+iIiIiL/0tTP8Ya7RwKQ3W7HwoULUa3DVU/Bprq6GtnZ2cyFDjAX+sJ86AdzoR/V1dVYuHAh7HZ7k84TlMVPSEgIOnXq5LNZ43TljEYj0tPTmQsdYC70hfnQD+ZCP4xGIzp16tTk0ZugHPYiIiKi4BWUPT9EREQUvFj8EBERUVBh8UNERERBhcUPERERBZWAn7qen5+P3NxcSCmRmZmJkSNHuh0vKCjAq6++CrvdjoyMDEyePFmjSAPfpXJhs9kwf/58lJWVQVEUjB49GjfddJOG0Qa2ht4XAKCqKh577DG0a9cOs2fP1iDK4NFQPs6ePYvXXnsNpaWlEEIgOzsbHTt21CjawNZQLjZs2IC8vDwAQGJiIqZNm8b7xjWD559/Hrt370avXr28Xn+a/NktA5jD4ZDTp0+XJ0+elNXV1XL69OnyzJkzbm3mzp0ri4qKpNPplH/4wx9kcXGxRtEGtoZyYbVa5a5du6SUUlZXV8sZM2bII0eOaBVuQGvM+0JKKVesWCH/+te/yhdeeEGDKINHY/KxcOFCuX79eill7Xulurpai1ADXkO5UFVVPvDAA67HXnzxRVdeyLd27twpN2/eXO/1p6mf3QE97FVQUICEhASYzWaEhYUhLS0N27dvdx0/v71FcnIyFEXB4MGDkZ+fr2HEgauhXJhMJvTo0QMAEBYWhri4OJSXl2sVbkBrKBcAUFFRgY0bN2LUqFEaRRk8GspHVVUVCgsLMWTIEAC175WwsDCtwg1ojXlvyHNbXaiqCqvVesmNtOnK9ezZE+Hh4V6P+eKzO6CHvcrLy932ADGbzW47w3s7vnv37haNMVg0lIuLnThxAsXFxejcuXNLhRdUGpOLpUuXum0sTM2noXyUlZUhKioKL730Eg4dOoQePXpg6tSpMBgMWoQb0BrKhRAC9913H2bPno3Q0FD06tULPXv21CLUoOaLz+6A7vkh/2O327FgwQJMnTqVf91q5MCBA6isrORFXSecTicKCgpwyy234Nlnn8WZM2ewZs0arcMKSg6HA6tWrcL8+fOxePFiSCmxbt06rcOiKxDQxU90dLRb1W6xWNyqRW/H2YXZPBrKBVDbnfzKK68gLS0NAwcObOkQg0ZDudi3bx9+/PFHTJs2DQsWLMC2bduwePFiLUINCg3lw2w2IzY2FikpKVAUBddffz2Kioo0iDTwNZSLoqIiKIqCmJgYKIqCAQMGYO/evVqEGtR88dkd0MVPamoqDh48CIvFAqvViq1bt6JPnz6u42azGYqioLi4GKqqYuPGjbjuuus0jDhwNZQLAFiyZAlMJhOHW5pZQ7kYM2YMFi9ejEWLFuGRRx5B3759kZWVpWHEga2hfERHR6NNmzYoKysDAOzatQsJCQlahRvQGvOZUVJSgoqKCgDAjh07EBcXp1W4QcsXn90Bv7fXli1b8O6770JVVWRmZmLUqFGYN28esrKyYDabsXfvXrz++uuw2+0YOnQopkyZonXIAetSuZBS4qGHHkJCQoJrLsPdd9+Nvn37aht0gGrofXHerl278Pnnn3OpezNrKB/79+/HG2+8AYfDgZSUFDz44INcXt1MGsrF559/ji+++AKKoiAxMREPP/wwQkNDtQ474Dz11FMoKiqCzWZDZGQkZs2aheXLl/vsszvgix8iIiKiiwX0sBcRERFRXSx+iIiIKKiw+CEiIqKgwuKHiIiIggqLHyIiIgoqLH6IiIgoqPjF3l4NbW3/5JNP4tSpU677XjzzzDONuu/C+c3RSDvnNwk0mUwQQmgdji7J06cAy3HA3B6iTdtma1c3F409X0vGGKjtvLWt772hZYzBitcp/TAYDB67A1wJvyh+br75ZowYMQJfffVVvW1mzZqFpKSkyzqvw+GAw+FoanjUBOcvKoqi8KLihbr+S8h3FwFSAkJATJ0GZeiYZml3cS7khhWNOl9LxxiI7eprK4aM9nhvaBljMON1Sj98dWtCvxj2utTW9pfLbrejuroaQO2LyH/a/wvWXKiW41B/3A7Vcrze464PptoXCfK9Vz3a+7IdgEafT6sYA6ldQ20vfm9oGWNjfl8D/V+wXqf0+M8X/OYOz5e6zf6TTz6JiooKKIqCYcOGYdy4cfWe54MPPkB+fj5ycnJw8OBB2Gy25gybyCtl02oY338TQkpIIeC4/X6og26sPehwQBwpgbJlA4xrP/P4XmfK1UBk1IUHKs7CUOS5uWKzt9PyuQOlnQ5jtN/xANT+GcC5bWaABn5fiVqQyWRCYmJik8/jF8NeDZk+fTrMZjOqqqqQk5ODuLg49OvXz2vbiRMnYvz48QCA0NBQKIpfdH4FLCklrFYrwsLCgqY7WZafgHz/Tddf3EJKhLz/JlC4B6iqAIxGID4ZSOwMCHHhL3MAUBQYH8qGiI5xP9/cXze53flcmKorgN/f3+D5fPncwdruUm0NDz4KW3ik673RIjEKgZCjJcA7CwGnE4iJBdp1BD78h/vv6wd/g0gb4PGzBKpgvE7pldHom7IlID75z09+ioiIwKBBg1BQUFBv25CQENcQmhCC/3TwL+hyUXbE/QMHAKSE6DsAyvT/g2HaH2GY8AsYhv0MYuo04HyBrigQv3gYirm92/kUc3uftQPQ6PP5+rmDsV1DbS9+b7RIjFOnwXD3wzD85jEo0/8PypiJEDXVnr+vqgpx/Kj276UW/Bd01ykd//MFvx/2cjqdqKysROvWreFwOPDCCy8gIyMDgwYNavCcZWVlnPCsMSklqqurER4e7rNfaj2TNTaoee8BKz9yP6AoUOb9DcLs+Ze0tJwAjh8B2nfyetxX7ermorHna8kYA7Wdt7b1vTdaOkZpOQF17v/z6CESzyyG0r7jJX+mQBFs1yk9MxqNiI2NbfJ5/KL4udTW9hEREXjiiSfgdDqhqirS09Nx1113NeoXlMWP9oLpoiK3fwd1xUdQbvw5ZGUF5HuvAqp64S9zjVfZBFMu/IGe8qGu/9Lt9xUDRwCW41DG3QHRrZemsbUEPeUi2AVV8dNcWPxoLxguKrLsCNTl70B0TIC4+TYIk6n28cvoFWgJwZALf6K3fHj0TFVVQH68FKisgJh0D0TbdlqH2Gz0lotg5qviJyAmPBPpibScAMpKIdvGAN+ugTxcDGXSvRAd4tzaCXMMoIOih6gx6v6+iohIiDvuhzx4AOo7r0B07w0xcjxw5hRQVgrExumiqCfyhj0/7PnRVKD9ReV20zgAYsTNEHdm+cXPFmi58Hf+lA8pJeQ3ayE/WwYcOxxwN030p1wEOl/1/ATEai8iPZCWE+43jQMgv/ocKD+pYVREzU8IAdHt2guFD+C6aaK0nNA2OCIvWPwQ+YC02aB+mOt1STCOH9EmKKKWVFbq9fdfHj2oTTxEl8Dih6gJpJSQ32+E+vKfIa7pU3tTwospCtC+kzbBEbWk2DjP338hID9aCrl7qzYxEdWDxQ/RFZJHD0N9dR7k4RIoM56AcsNIrzeX46RPCgbCHOP1ponKI09C7toG9Y3nIU8e1zZIonM44ZkTnjXlTxMJL6ziagdsXAmUHYWY9EuIOjd609sS9sbyp1wEA3/NR7030Swtqb3lQ5duEGMmAmdP+82qMH/NRSDifX58gMWP9vzlouKximvkeCh33K9xVL7lL7kIFoGYDykl5JYNkB8tuTBHyA9WhQViLvwVV3sRtRCvq7jW/JerWIgukxAC4qpr3CdHc1UYaYDFD9ElSGsV1GV/5youIl+pb1XYkRJt4qGgxOKHyAspJdTv1kF95RmI3tdzFReRr9S3Kuzjf0H+sFmbmCjosPghqkMeLoH6ytPAiWNQZjwJZdAIruIi8pF6V4XN+jNkwY9wvv4s5PGj2gZJAY8TnjnhWVN6mEjoWsXVJhrYsAI4VV67UaO5vWc7P1zF1Vh6yAVdEOj5qHdV2NHDtavCEjtDjL0VqDir+aqwQM+FP+FqLx9g8aM9rS8qHqu4RmdCmfL/WjwOPdA6F+QumPMhpQS2flN713QdrAoL5lzoDVd7ETWR11Vcqz7hqhMijQkhgJSuXBVGzYbFDwUlWVUJ9f2/cRUXkV7VtyrsMFeFUdOx+KGgIqWEumkN1NfmQVx3A1dxEelVfavCPv0X5NZvEMQzNsgHWPxQ0JAHD0B96c/A2dO1q7iuH8pVXEQ6Ve+qsNlPQR4shPraPMhjpdoGSX6LE5454VlTzTWR8PwKLsTGAWFhtbfTr66EuPWXEG3Nnm0DeBVXY3FSp74wH7XqXRV2/CjU5f+A6BAPcfNtQGVFs60KYy70g6u9fIDFj/aa46LitoJLCKBjPJS7H4bo1ssn5w9UvMDrC/PROPKHzVA/+HuzrgpjLvSDq72IvPBYwSUlcKwUqLPzOhEFiITOXBVGl43FDwUUWbKfK7iIgkm9q8KKNAmH/INR6wCIfEGqKuTXKyE3rqod6rr4YsgVXESB6/yqsIvf80JAfvoBVKsV4robOFRFHtjzQ35PFu2DuvBPQE0NlN/9hSu4iIJIvavCfvcMUFYKddEzkEcOahsk6Y5fTHh+/vnnsXv3bvTq1QuzZ8/2OF5QUIBXX30VdrsdGRkZmDx5cqPOywnP2rvciYRuq7hCQyH/8x7gdEJM/AVE62j3dlzBdVk4qVNfmI/LU++qsJPHIT98B2jbDmL87RBhEW7XkcZcH5gL/fDVhGe/GPa6+eabMWLECHz11Vdej7/11luYMWMGEhMT8fjjj6N///5ISkpq4SipubnvwyWATvFQ7vktROo1Hm2FOQZg0UMUNOp7z4t27SHu/x3krq1QF/2ldvHDhhWa7xdG2vKL4qdnz57YtWuX12MWiwVOpxPJyckAgMGDByM/P7/e4sdut8PhcCA8PBxSSt4lVGPnX/+G8iDL6+7DVbuKS5pjPCc70hVpbC6oZTAfPtajLxDTEXgs68Jj51aGqT3TIKLr/2OJudAPX+XAL4qfSykvL4fZfOGmdWazGbt37663fV5eHvLz85GTk4OamhrYbLaWCJMaYLVaL3lc7N2FUC8rOmwHiyDDWjVjZMGnoVxQy2I+fEccPYTQug9exnWEudCeyWTyyXn8vvi5XBMnTsT48eMBAKGhoVAUzvnWkpQSVqsVYWFhXsfSpeoE1n0J+d06r6u4TIkpEOHhLRhx4GooF9SymA/fk4kpkHWvIwBCjx+BuDa93teZudAPo9E3ZYvfFz/R0dGwWCyury0WC6Kjo+ttHxISgpCQEACAEIK/yDrhLRdy/0+QHy+B6DcYypxnIL9eBfneq7X37Tm3iksxt9co4sDF94W+MB++I8ztoU6d5n4duSsLsFZDvvI0xK1TIRI61//9zIXmfPX6+33xYzaboSgKiouLkZiYiI0bNyIrK6vhbyRdkeUngLIjtau4jEbIvHcBgwHK/b+DiGwNABBDx0D27MdVXER0xZR6riOyfwbkh+9AtoqCuOUuiIhWrlVhMrYTwOH1gNKsS91ramoghHD1tFypp556CkVFRbDZbIiMjMSsWbOwfPlyZGVlwWw2Y+/evXj99ddht9sxdOhQTJkypVHn5VJ37UkpYVv9X4S8/+ZFq7gSofxqBkTnrlqHF1S4nFdfmA9tyJ9+gPrZMsDcHti4yrUqzH77/TDd+HPmQmO63Nh0165d2Lx5M/bs2YNDhw6hpqYGQO0Epfj4eHTr1g3XX389evbs6aunbBIWP9pTLcehzv01RJ25PMq8v7Fnp4Xxw1ZfmA/tqMePQv4hC8CF65IUCpRn3+RQu8Z0c58fh8OBlStX4tNPP8Xx48cRGRmJzp07Y+jQoYiMjISUEpWVlSgrK8P69evxv//9DzExMRg/fjxGjRrls8lL5J/kgX3uhQ9wYS8uFj9EpAFxsgwS7tclIdXaoXkWPwGhyZXH9OnT4XA4kJGRgUGDBqFLly6XbF9YWIhNmzYhLy8Pn3zyCRYtWtTUEMgPSacTcs1/ga3fQArh0fPDvbiISDNe9guTAFC8H/LqXhBcJez3mjzstWLFCgwfPvyy5/U4HA6sWbMGo0ePbsrTNwmHvbQh9+6E+un7EAMygIEjULP2fwj54G/uq7h4x9UWx2EWfWE+tKWu/9JtVZh98v9DqJCQu76HMmEqRPJVWocYlHQ55wcAfvWrX+G3v/0t+vXr58vTNgsWP83PbS8uRYH8MBcIj6hdTdEq0nWBD7NWQhw/ylVcGuKHrb4wH9o7v1+YbN8R1rBWCA8PB86egvzwXSAkFGLC3RCtoi57rzC6crqZ81NXVVUVqqqq6j1eWFiIvXv3YuzYsb5+atIZj7244pKg/L+ZEEmeQ6MiOgaCY+lEpCOu/cKkBKqrax9rHQ1x73TIgt1QFz8HtDED367lXmF+xicDlz/99BO++eYbHDt2rMG2hw8fxttvv+2LpyUdkxYve3EdPQicu2cPEZE/E6k9IH75G+CbtReuc+f2CpOWE5rGRg3zSc/Pzp07sWzZMtfX//73v7Fjxw4kJycjKSkJKSkpiIyMBFC7F1dYWJgvnpZ0TO7/yXPDUa7iIqIAIo4f81gVxuucf/BJ8TN58mQMHjwYhYWFePnll2E0GrFz506sXbvW1SY6Ohrt2rVDUVERevXq5YunJR2SDgfkqk8gd+Z73YuLq7iIKGB4WRUGAOr+PVC69oBQDBoFRg3x2ZyfuLg4xMXF4bPPPsOECRPQv39/VFVVoaSkBMXFxSguLsbJkycxYsQITJo0yVdPSzoif9wO9bNlEDeMgjLrKcgNKzz24uJkQCIKFMIcA1F3r7C7HwJUFerCP0PJvAuiSzetwyQvmnV7C73jaq8r57aKC4Bc/g7Qpi3E+DshwiPc211iLy6uaNEP5kJfmA/9aCgX3q5z8uwZyP+8B0gVYuJUiKg2XBXmA7pd6u5PWPxcGY9VXAnJUH79O4j4pMs+Fy/w+sFc6AvzoR9NyYU8sBfqR/+sXezx3TquCmsiXxU/vE0lXRavq7hKS4CLenuIiKiW6Hw1xNRpwLfruCpMR5pc/MycORNfffXVZfWg2O12rFmzBjNnzmzq01MLkwU/1r+Ki4iIPIjjR4H6VoWRJpo84Xn48OHIzc3FP/7xD6Snp6N3797o3LkzYmNjYTKZAABWqxVlZWUoLCzEDz/8gPz8fBiNRtxyyy1N/gGoZUi7HfLLPMg9O7mKi4joctS3KmzvLiipPSAMXBXW0nwy56e6uhqrV6/G2rVrUVJS4nrccC6hTqfT9VhiYiJGjBiBESNGICJC26ESzvlpHLkzH+oXeVAyxgLpN3hdxXWlY9ec16AfzIW+MB/64Ytc1N0rTNz9UO2WP9+tgzL+ToiuPXwcdWDS7YTnsrIy7NmzB6WlpTh79iwAICoqCvHx8bj66qt9ErSvsPjx5LaKS3XW7sUVEwtx8xSIsHD3dpdYxdXo5+MFXjeYC31hPvTDV7nwuiqssgLyo38CNivErfdAtInmqrBL0G3x409Y/LhzX8UFILELlAd+B9Exodmekxd4/WAu9IX50I+WyIUs2Q81793axSNbvuaqsHrodmPT2bNnIzExEUlJSUhKSkJiYiI6dOjg66chH/NcxQXgcBEQyq1IiIiam0i6CuIXD0P+/n7PVWE9+7EHyMd8XvwkJiZi//792LRpk+sxk8mE+Ph4VzF0vjBq27atr5+erpDcu5N7cRERaUgcPwqPwRheh5uFz4ufG264AVu3bsXo0aPRvXt3WK1WlJaWYv369SgsLHRrGxkZ6SqG7rvvPl+HQo0ga2yQny+HPLCXq7iIiLRU36qwH7dDueoaCKPPP7KD1hXN+XE6nVi8eDGEEHjooYfcjs2cORN9+vTBvffe6/Z4TU0N3n//fezcuRO33347jh49isOHD+PQoUMoLS3Fm2++2aQf5EoE85wfKSWw/Tuoqz6BMnIc0GeAT1dxXU4cnNegD8yFvjAf+tGSufBYFfaLhwFjCOTGVVB+PgWie+9mfX6903TOj5QSu3bt8vpLUFZWhqQkz20OQkNDMXXqVOTk5GDPnj248847r+Sp6Qq5reJy1EBdngsRlwTlt49DhNbej0kMHQPZs59PVnEREdHlU+q5Dss+/SE/WQq5YQXEpHshottxVVgTXFHxYzQasWjRIq/H4uPjsW3bNtx4441ej6enp2P58uUsflqQxyqupKugZD0KEes5pCXMMRxbJiLSkLfrsIhoBXH7ryEPF0N9dxEQEgps3cRVYVfI53t7ZWZm4ttvv8WyZcu8DikdPnwY1dXVvn5aqofXVVyHDgDGEO2CIiKiKyLikyF+8dCFwgfgXmFXoFkmPJeXl2PJkiVYsWIFMjIykJycDADYs2cPVq5cibS0tMs6Z35+PnJzcyGlRGZmJkaOHOl2/Mknn8SpU6cQElL7gf7MM88gNDTUNz+Qn5M//cBVXEREAUSUHeGqsCZqlqnj48aNQ+/evZGXl4cvvvgCNpvNdax3797Iyspq9LmcTidyc3PxxBNPICIiAtnZ2ejfvz+ioqLc2s2aNcvrXKNgJW1WyP9+AHm4mKu4iIgCSX2rwnbmQ+nSHSKEPfsNabZ1c0lJSZgxYwYcDgeOHTsGm82GmJgYtG7d+rLOU1BQgISEBJjNZgBAWloatm/fjiFDhlxRXHa7HQ6HA+Hh4ZBSelbPfk5KCXy/EXLt/yDGTIAycarXVVyIbqeLn/18DHqIJdgxF/rCfOiH7nIR3Q5i6jS36zrufggiLBzqS3+C+NlEiJ79tI6yWfgqB81+0wCj0Yj4+Pgr/v7y8nJX4QMAZrMZFovFo91LL70ERVEwbNgwjBs3rt7z5eXlIT8/Hzk5OaipqXHrlfJLp07W3hirfUcImxWGj5dAJl0F5/1zaifEVVcD6UOAq65xtUPbdrWP64jVatU6BDqHudAX5kM/dJULb9d1AOjaC4YvlkOs+xKOW+4CzO3dPidc7fyUyWTyyXkC4o5J06dPh9lsRlVVFXJychAXF4d+/bxXvRMnTsT48eMB1C6/VxSfz/luMXLDCvfJzMmpEA9mQ7Tzcg+E8ASgU/Pt0XWlpJSwWq0ICwvjvUw0xlzoC/OhH7rNhbfreng4cPuvIY8cguHDd2qHx7Z/57YqTAwZrU28PmD00Y0edV/8REdHu/X0WCwWpKamurU53zMUERGBQYMGoaCgoN7iJyQkxDUxWgihr1/ky+B1FdfBQgjF4Jc/kz/nItAwF/rCfOiHP+VCxCVCvSsLcu6vPVaFCT/eK8xXr7/uuz1SU1Nx8OBBWCwWWK1WbN26FX369HEddzqdOHPmDADA4XBg27ZtSExM1CrcFiN3b6t/FRcREQU9UXaEnxP10H3Pj8FgwD333IM//elPUFUVmZmZiIqKwrx585CVlYWIiAg888wzcDqdUFUV6enpGDhwoNZhNxtZXVV7l8/jR7mKi4iI6lffqrBt30HpfLXr7v7B6Ir29goU/rS3l5QS8tuvIDesgHLzZIgeaV73gPG3O3xy/yL9YC70hfnQD3/OhbfPCdEqCurqT6GMzoTo01/rEC+Lr/b2YvGjw+Kn7n4t8lAR1A9zIa7uCTHqFoiL7s4sLSf8ei8uf76oBBrmQl+YD/3w91x4+5yQNhvk/5ZBHjkEZdIvIWI7+cVeYZpubErNx20fLiGA7r0hWreF8ouHvf4yci8uIiK6FK97hZlMEBN+AVlWCnX5PwCHA9ixJWj2CtP9hOdg4rGCS0rgpx8gbv2lbqtwIiLyXyI2DuL2X18ofICg2CuMxY+elJV6zsyXkjPziYio2QTjqjAWPzohqyqgfrPW8wBXcBERUXM6vyqsDjV/I6RNR3e19iEWPxqTqgr161VQX8+BMuhGiHt+U1vwABdm5nPIi4iImokwx0BMneb+2XPPb6D06gf15acg8zfqZ18zH+FqrxZc7eWxiqtkP9S8dyF6pkEM/znEudt2+/sKrsvh76soAglzoS/Mh34ESy68rgqz10B+/iFkyf7aVWEdEy601WBlGFd7+RmPVVxX94JoFwvl3hkQbaLd2nIFFxERtTSvq8JCQiHG3wF5/Cjkh7mQMR0Acwzk0jf8emUYh71agNdVXHt3QmTe7VH4EBER6Y1o3xFK1qNAXBLkksV+vzKMxU9L4CouIiIKACK6neeDfrgyjMVPM5MVZ6B+vdLzAFdxERGRv/G6MkxAtm6rRTRXjMVPM5GqE+q6z6G+8TyUjJu4iouIiPye15Vho8ZDLlkM9duv/GZVGFd7+WC1l8cqrgN7of7nnxB9B0Bk/AxCMVxoFySruBorWFZR+APmQl+YD/1gLjzV/TyTdjvkyo8g9+2GMuleiPikC+18uCqMG5v6gC+KH49VXKk9IDrGQ0ycChHVxkeRBi5eVPSDudAX5kM/mIvGk5bjkMtzgTZtgZgOkP9606erwnxV/HDYqwm8ruIq2A0x7g4WPkREFHSEuT2U+2cDyakXlsMDulsVxuKnKbiKi4iIyIPX27joaFUYi58rJM+cgrruC88DXMVFRETBrr5VYToZFWHxc5mk0wl19adQ33oRyugJXMVFRERUh9dVYWMyIZe+AXXjKs1XhXHC8yUmPHus4irYDfXjpRDXDYEYMhriXFK5iuvKcSKhfjAX+sJ86AdzceU8VoU5HJCrP4X8cTuUiVMhkrpcaNeIVWFc7eUDlyp+PFZxXdUdIiEFYsIvIFpFtXCkgYsXFf1gLvSF+dAP5sL35CkL5IfvAGERQIc4yPf/1qhVYVzt1Yy8ruLa/xPETbex8CEiImoi0dYM5b6ZQLdeF5bDAy22KozFjzdcxUVERNTsvHYotMCqMBY/dchTFqhr/ut5gKu4iIiIfMvrqjBARjbvKAuLn3OkwwH1y/9AfedlKD+/nau4iIiImpnXVWFjJ0G+/1bt3FtVbZ7n9YcJz/n5+cjNzYWUEpmZmRg5cqTb8YKCArz66quw2+3IyMjA5MmTG3XeYwV74YyIhNyzA+qn70MMuhFi0AjXhDau4mp+nEioH8yFvjAf+sFcND+PVWFOJ+RX/4P8YTOUCb+ASOkKADBUVaBD6tVNfj5jk8/QzJxOJ3Jzc/HEE08gIiIC2dnZ6N+/P6KiLnSJvfXWW5gxYwYSExPx+OOPo3///khKSmrw3PLlP8OpSojOV0N5aC5ERKTbcWGOAVj0EBERNau6n7fCYIC4cRzkdUMg896F3LAC6JgAJX8DsPC9Jj+f7oufgoICJCQkwGw2AwDS0tKwfft2DBkyBABgsVjgdDqRnJwMABg8eDDy8/PrLX7sdjscDgfCw8NrJzEf2AtkPQqEt9L8pkvB6Pxrztdee8yFvjAf+sFcaCiqDcQ9v4G69RvgtXnAVd18clrdFz/l5eWuwgcAzGYzLBbLJY/v3r273vPl5eUhPz8fOTk5tQ9ICdvBIsiwVr4PnhrNarVqHQKdw1zoC/OhH8yFdoTBiFAfnk/3xY+vTZw4EePHj7/wgKLAlJgCER6uXVBBTEoJq9WKsLAwjqVrjLnQF+ZDP5gL7cnEFEgfvva6L36io6PdenosFgtSU1MveTw62stusueEhIQgJCSk9otzq7gUc3vfB06XRQjBi4pOMBf6wnzoB3OhHWFuD3XqNGDTKp+cT/dL3VNTU3Hw4EFYLBZYrVZs3boVffr0cR03m81QFAXFxcVQVRUbN27Edddd16hzi988Xu8ttImIiEg/lKFjIH7zuE/OpfueH4PBgHvuuQd/+tOfoKoqMjMzERUVhXnz5iErKwtmsxn33XcfFi5cCLvdjqFDhzZqpRcAhJhjoDidzfwT0KVIKaGqKkJCQvgXlcaYC31hPvSDudAPg49WYPvFfX58zW63Xxj6IiIiIr/S1M9x3Q97NQe73Y6FCxeiurpa61CCXnV1NbKzs5kLHWAu9IX50A/mQj+qq6tdIz1NEZTFT0hICDp16gSjUfejfgHPaDQiPT2dudAB5kJfmA/9YC70w2g0olOnTk0evQnKYS8iIiIKXkHZ80NERETBi8UPERERBRUWP0RERBRUWPwQERFRUAn4qev5+fnIzc2FlBKZmZkYOXKk2/GCggK8+uqrsNvtyMjIwOTJkzWKNPBdKhc2mw3z589HWVkZFEXB6NGjcdNNN2kYbWBr6H0BAKqq4rHHHkO7du0we/ZsDaIMHg3l4+zZs3jttddQWloKIQSys7PRsWNHjaINbA3lYsOGDcjLywMAJCYmYtq0abxvXDN4/vnnsXv3bvTq1cvr9afJn90ygDkcDjl9+nR58uRJWV1dLadPny7PnDnj1mbu3LmyqKhIOp1O+Yc//EEWFxdrFG1gaygXVqtV7tq1S0opZXV1tZwxY4Y8cuSIVuEGtMa8L6SUcsWKFfKvf/2rfOGFFzSIMng0Jh8LFy6U69evl1LWvleqq6u1CDXgNZQLVVXlAw884HrsxRdfdOWFfGvnzp1y8+bN9V5/mvrZHdDDXgUFBUhISIDZbEZYWBjS0tKwfft213GLxQKn04nk5GQoioLBgwcjPz9fw4gDV0O5MJlM6NGjBwAgLCwMcXFxKC8v1yrcgNZQLgCgoqICGzduxKhRozSKMng0lI+qqioUFhZiyJAhAGrfK2FhYVqFG9Aa896QUsJms0FVVVit1ktupE1XrmfPnggPD/d6zBef3QE97FVeXg6z2ez62mw2u+0A7+347t27WzTGYNFQLi524sQJFBcXo3Pnzi0VXlBpTC6WLl2KSZMmtXRoQamhfJSVlSEqKgovvfQSDh06hB49emDq1KkwGAxahBvQGsqFEAL33XcfZs+ejdDQUPTq1Qs9e/bUItSg5ovP7oDu+SH/Y7fbsWDBAkydOpV/3WrkwIEDqKys5EVdJ5xOJwoKCnDLLbfg2WefxZkzZ7BmzRqtwwpKDocDq1atwvz587F48WJIKbFu3Tqtw6IrENDFT3R0tFvVbrFY3KpFb8fZhdk8GsoFUNud/MorryAtLQ0DBw5s6RCDRkO52LdvH3788UdMmzYNCxYswLZt27B48WItQg0KDeXDbDYjNjYWKSkpUBQF119/PYqKijSINPA1lIuioiIoioKYmBgoioIBAwZg7969WoQa1Hzx2R3QxU9qaioOHjwIi8UCq9WKrVu3ok+fPq7jZrMZiqKguLgYqqpi48aNuO666zSMOHA1lAsAWLJkCUwmE4dbmllDuRgzZgwWL16MRYsW4ZFHHkHfvn2RlZWlYcSBraF8REdHo02bNigrKwMA7Nq1CwkJCVqFG9Aa85lRUlKCiooKAMCOHTsQFxenVbhByxef3QG/t9eWLVvw7rvvQlVVZGZmYtSoUZg3bx6ysrJgNpuxd+9evP7667Db7Rg6dCimTJmidcgB61K5kFLioYceQkJCgmsuw913342+fftqG3SAauh9cd6uXbvw+eefc6l7M2soH/v378cbb7wBh8OBlJQUPPjgg1xe3UwaysXnn3+OL774AoqiIDExEQ8//DBCQ0O1DjvgPPXUUygqKoLNZkNkZCRmzZqF5cuX++yzO+CLHyIiIqKLBfSwFxEREVFdLH6IiIgoqLD4ISIioqDC4oeIiIiCCosfIiIiCiosfoiIiCioBPTeXg05vzkaaef8JoEmkwlCCK3DCWrMhb4wH/rBXOiHwWDw2B3gSgR18WO3nIAzIrLe49JyAigrBWLjIMwxumvnDzE21O78RUWctkCUHeFrqKHzuVAUhRd4HWA+9IO50A9f3ZowqIsf+fKfoQ4eBWXoGI9j6vovId9dBEgJCAExdZqu2vlDjI1tp2xaDfn+m7W/1HwNiYiomQX1HZ6PTr8b9sK9wM1TICJauR6XVZXAfz8AcNFLI4Ru2vlDjJfTTv73fbj9LRWMr6GiQJn3N017gKSUqK6uRnh4OP+61QHmQz+YC/0wGo2IjY1t+nl8EIt/kxKiVSREUpcLj5UUQkLqt50/xNjIdrJ4PzwuJcH4GqoqcPwIoIPhLyKiQMfiR1Eg0m9w/4u7fSfIZX+vHZLQYzt/iLGR7UT7jlD//TYEX0OgfScQEVHzC6il7jabDQ8//DByc3Mb9w2KAvGLhz0+FIU5BmLqtNoPJB2284cYG90uOgaO2+/na1hPjERE5HsBNedn6dKlOHr0KNq1a4d77rmnwfbHCvY2vNrr+BGgfaeGV+1o0M4fYmyo3fmx9DBrJcTxo0H3GqpvPA9x3yNQYrXv9eG8Bn1hPvSDudAPX835CZji58iRI/jnP/+J6667DiUlJfUWP3a7HQ6HA+Hh4Th27BgcDkcLR0oXk1LCarUiLCwsKC8q6sdLIXr1g+jSTetQgj4XesN86AdzoR9GoxEdOnRo+nl8EIsuvPvuu/jFL36BvXv3XrJdXl4e8vPzkZOTg5qaGthsthaKkC7FarVqHYImlLgkoOBHqJ2StA7FJVhzoVfMh34wF9ozmUw+OU9AFD+bN29Gp06dEBcX12DxM3HiRIwfPx4AEBoaCkUJqGlPfifY/6KSV/eE/PAdKOHhWocS9LnQG+ZDP5gL/TAafVO2BETxs2/fPmzcuBHffPMNrFYrHA4HIiIiMHnyZI+2ISEhCAkJAQAIIfiLrBPBmgvRJhrOM6d19bMHay70ivnQD+ZCe756/QOi+Lnrrrtw1113AQDWrl2LkpISr4UPkS6ZTJDWaogw7Xt/iIiCAcd8iDQmErsAJYVah0FEFDQCoufnYsOHD9c6BKLLIjp3hSwugLi6p9ahEBEFBfb8EGktORUoKtA6CiKioMHih0hjolUUZFWF1mEQEQUNFj9EOiDCI1gAERG1EBY/RHqQkgoU79c6CiKioMDih0gHRHJXyKJ9WodBRBQUWPwQ6UFyF/b8EBG1EBY/RDogwiIgbdw3iIioJbD4IdIJEdka8uxprcMgIgp4LH6I9CKlK+/3Q0TUAlj8EOmESEnlpGciohbA4odILxI7Qx7kHl9ERM2NxQ+RTohQE2CvgZRS61CIiAIaix8iHRHRMcApi9ZhEBEFtIDZ1f3EiRN45ZVXcPr0aRgMBkyaNAmDBg3SOiyiy5OcChTtA6LbaR0JEVHACpjix2Aw4N5770VKSgpOnTqF7OxspKWlISwsTOvQiBpNpHSF/H4TRNpArUMhIgpYAVP8REdHIzo6GgDQtm1btG7dGhUVFR7Fj91uh8PhQHh4OKSUnF+hsfOvP/NQS8YlQn6yVJPXg7nQF+ZDP5gL/fBVDgKm+LlYYWEhVFVFTEyMx7G8vDzk5+cjJycHNTU1sNlsGkRIdVmtvLvxecaaGtiqqgAhNHl+5kJfmA/9YC60ZzKZfHKegCt+Kioq8MorryArK8vr8YkTJ2L8+PEAgNDQUCgK53xrSUoJq9WKsLAwCI0+7PVG7dAJxqqzEDEdWvR5mQt9YT70g7nQD6PRN2VLQBU/drsdzz//PCZMmIBu3bp5bRMSEoKQkBAAgBCCv8g6wVxcIM7d6Vm076jN8zMXusJ86AdzoT1fvf4B0+0hpcSiRYvQs2dPDBs2TOtwiK6YSOkKFPNOz0REzSVgen727NmDTZs2ISkpCZs3bwYA/Pa3v0VSUpLGkRFdpo4JkEcOaR0FEVHACpjip3v37nj//fe1DoOoyYTBAEgJqaoQnJNGRORzvLIS6ZDoEAccK9U6DCKigMTih0iPUrpCct4PEVGzYPFDpEMiORUoKtA6DCKigMTih0iPYjtBlh3ROgoiooDU7MVPTU0N7HZ7cz8NUUARigIIAel0ah0KEVHA8flqr127dmHz5s3Ys2cPDh06hJqaGgC1t6SOj49Ht27dcP3116Nnz56+fmqigCI6JQJHSoCEzlqHQkQUUHxS/DgcDqxcuRKffvopjh8/jsjISHTu3BlDhw5FZGQkpJSorKxEWVkZ1q9fj//973+IiYnB+PHjMWrUKJ/drpookIjOXSGLCiBY/BAR+ZRPqo7p06fD4XAgIyMDgwYNQpcuXS7ZvrCwEJs2bUJeXh4++eQTLFq0yBdhEAWW5FTg8+XAkNFaR0JEFFB8UvxMnDgRw4cPd+2Z1ZAuXbqgS5cuuP3227FmzRpfhEAUeNrFQp48rnUUREQBxycTnkePHu1W+PzqV7/C999/3+D3GY1GjB7Nv2qJvBFCAEYjJBcMEBH5VLOs9qqqqkJVVVW9xwsLC/H55583x1MTBRSRkAIcLtI6DCKigOKz4uenn37CN998g2PHjjXY9vDhw3j77bd99dREAUskp0IW8U7PRES+5LNlVjt37sSyZctcX//73//Gjh07kJycjKSkJKSkpCAyMhIAUF5ejrCwMF89NVHgSkkF/vOt1lEQEQUUnxU/kydPxuDBg1FYWIiXX34ZRqMRO3fuxNq1a11toqOj0a5dOxQVFaFXr16+emqX/Px85ObmQkqJzMxMjBw50ufPQdSSRNt2UE8cg/zpByA2DsIcU29baTkBlJW2eDstnztQ2vlLjESBwqc32ImLi0NcXBw+++wzTJgwAf3790dVVRVKSkpQXFyM4uJinDx5EiNGjMCkSZN8+dRwOp3Izc3FE088gYiICGRnZ6N///6Iiory6fMQtSR1/ZfAnh1Q9+wAhICYOg3K0DFe28l3FwFStmg7LZ87UNrV11Z4ucWBljESBRIhpZRaB+ELe/bswccff4w5c+YAAP7xj38gNTUVQ4YMcWtnt9vhcDgQHh6OY8eOweFwaBEunSOlhNVqRVhYWO3qJnKR5Scg5/669oPpPEUB/rQIIrrdRe1OAv/3cJPbSSlhs9pgqq4AnpjW4Pl8+dzB2u6SbZ98BbbwSJjCTBBCtFiMYt6bENHsAboYr1P6YTQa0aFDh6afxwex6EJ5eTnMZrPra7PZDIvF4tEuLy8P+fn5yMnJQU1NDWw2W0uGSfWwWq1ah6A74mARQuv+baKqcL7zEhDV5sJjZ0/D4KN2RgDOxp7Px88dlO0u1Tb3ZRij2sDZUDsfx2g7WAQZ1grkidcp7ZlMJp+cJ2CKn8aaOHEixo8fDwAIDQ2FonBjey3xL6r6ycQUSCE8/jI33v87t7/M6+shutx253Nhqq4Afn9/g+fz5XMHa7tLtTX8ejZs4ZGu90ZLxWhKTIEIDwddwOuUfvhqOyyffPLPnDkTX3311WUNIdntdqxZswYzZ870RQiIjo526+mxWCxuPUHnhYSEIPzcG1sIwX86+MdceP+nmNtDTJ1WO2QB1A5J/OLh2sebqR2ARp9PqxgDqV1DbS9+bzRbjKLhGPmP1yk9/fMFn8z5+eijj/Dxxx9DVVWkp6ejd+/e6Ny5M2JjY11dVFarFWVlZSgsLMQPP/yA/Px8GI1G3HLLLcjMzGzyD+J0OjFz5kw8+eSTrgnPTz/99CUnPJeVlXHOj8aklKiurkZ4eLjPfqkDjbScAI4fAdp3anjVThPa1c1FY8/XkjEGajtvbet7bzRHjOprz0J5aC5Xe9WD1yn9MBqNiI2NbfJ5fDbhubq6GqtXr8batWtRUlLietxgMACoLU7OS0xMxIgRIzBixAhERET44ukBAFu2bMG7774LVVWRmZmJUaNGXbI9ix/t8aKiH8yFvrRkPtS3F0Lceg9Em+hmfR5/xfeGfuiu+LlYWVkZ9uzZg9LSUpw9exYAEBUVhfj4eFx99dU+CdwXWPxojxcV/WAu9KVFi581/4VoFwvR+/pmfR5/xfeGfviq+GmWCc+xsbG6KXCIiOjSREpXyB1bWPxQ0GhS8aOqKoqKihAXF+e2XcXs2bORmJiIpKQkJCUlITEx0Sfr8omIqBkkpEB+9m+toyBqMU0qfs6cOYPf//73ePzxx922q0hMTMT+/fuxadMm12Mmkwnx8fGuYuh8YdS2bdumhEBERE0kQkIBhx1SSg7rUFBoUvETERGBhx56CAkJCW6P33DDDdi6dStGjx6N7t27w2q1orS0FOvXr0dhYaFb28jISFcxdN999zUlHCIiukLCHAOUnwDOLbEnCmRNKn5CQ0Nx3XXXeazYWrJkCUaMGIF7773X7fE77rgD77//Pnbu3Inbb78dR48exeHDh3Ho0CFs2rSJxQ8RkVaSU4GiAhY/FBSaVPycOnUKWVlZHsNeZWVlSEpK8mgfGhqKqVOnIicnB3v27MGdd97ZlKcnIiIfESldIbdsgOg3SOtQiJpdk+7wHBYWhsmTJ3us7IqPj8e2bdvq/b709HSsW7euKU9NRES+FJcEWVrScDuiANDk4ue2227zKH4yMzPx7bffYtmyZV7vo3P48GFUV1c35amJiMiHhNEIqCqa4dZvRLrTLPf5ueGGG1BeXo4lS5ZgxYoVyMjIQHJyMgBgz549WLlyJdLS0prjqYmI6AqJmA7A8aNAbCetQyFqVs22q/u4cePQu3dv5OXl4YsvvoDNZnMd6927N7KysprrqYmI6EqkdIUs2gfB4ocCXLMVPwCQlJSEGTNmwOFw4NixY7DZbIiJiUHr1q2b82mJiOgKiJRUyK9XAv2HaR0KUbNq1uLH9SRGI+Lj41viqYiI6Ep1jIc8ckjrKIiaXZMmPBMRUeAQigEAIFWnxpEQNa8W6flpTjabDfPnz0dZWRkURcHo0aNx0003aR0WEZFfEh3jgWOlQKdErUMhajZ+X/wAwIQJE9CjRw9YrVbMnTsXaWlp6Nixo9ZhERH5n5SukAf2QbD4oQDm98WPyWRCjx49ANTedyguLg7l5eX1Fj92ux0OhwPh4eGQUvKeFho7//ozD9pjLvRFs3wkp0Ku/gRy0IiWfV4d43tDP3yVA78vfi524sQJFBcXo3PnzvW2ycvLQ35+PnJyclBTU+O2BJ+0Y7VatQ6BzmEu9KXF8xHZBsajpbDxRrQe+N7Qnslk8sl5/Kb4mTNnDlRV9Xj8j3/8I8xmM+x2OxYsWICpU6ciLCys3vNMnDgR48ePB1C715iicM63lqSUsFqtCAsLgxBC63CCGnOhL1rmQzUaYQwJqb3rM/G9oSNGH/1O+s1v9vPPP1/vMSklXnnlFaSlpWHgwIGXPE9ISAhCQkIAAEII/iLrBHOhH8yFvmiRDxGfDHH0EERi/b3owYjvDe356vUPiG6PJUuWwGQyYdKkSVqHQkTk90RKKmTRPq3DIGo2fl/8nDx5Eh999BEKCgowZ84czJkz55I7yhMRUQOSuwJFBVpHQdRs/GbYqz7t2rXDBx98oHUYRESBwxwDaTmudRREzcbve36IiMi3hBCAMQTSXqN1KETNgsUPERF5EIkpwKEircMgahYsfoiIyINI7grJeT8UoFj8EBGRp5RUoJgrvigwsfghIiIPok005JnTWodB1CxY/BARkXehoZA2bulAgYfFDxEReSUSuwAlhVqHQeRzLH6IiMgrkdIVkvN+KACx+CEiIu9SUnmnZwpILH6IiMgr0SoKsrJC6zCIfI7FDxER1UuER0BWVWodBpFPsfghIqL6JacCxRz6osDC4oeIiOpVO+mZxQ8FloApflRVxR/+8AfMnz9f61CIiAJHchegeL/WURD5VMAUP6tXr0b79u21DoOIKKCIsAje6JACjlHrAHyhoqICGzduxMSJE/Hll19esq3dbofD4UB4eDiklJBStlCU5M3515950B5zoS+6ykerSKhnTkFEtdE6Ek3oKhdBzlc5CIjiZ+nSpZg0aVKj2ubl5SE/Px85OTmoqamBzWZr5uioMaxW/mWpF8yFvughH4a4ZKj7dkNe01frUDSlh1wEO5PJ5JPz+E3xM2fOHKiq6vH4/fffj8rKSvTs2RO7du1q8DwTJ07E+PHjAQChoaFQlIAZ+fNLUkpYrVaEhYVBCKF1OEGNudAXPeVDdu0B/PQDRL9BmsahFT3lItgZjb4pW4T08368L7/8EsuXL4fRaERNTQ2sViuGDBmCrKysBr+3rKwMDoejBaKk+kgpUV1djfDwcF5UNMZc6Iue8iFtNqh/fxGGh+ZqGodW9JSLYGc0GhEbG9v08/ggFk2NGTMGY8aMAQDs2rULn3/+eaMKHyIiahxhMgFVFZA//QDExkGYY+ptKy0ngLJS3ba7knPK2E5AWCvd/Sz+9Br6rN2ZUwCLHyIiam7q+i+Bn36A+tMPgBAQU6dBGTrGazv57iJASl22a8o5ldvvB278uW5+Fn98DX3RTtm4Elj4nte4LoffD3s1BYe9tMfuZP1gLvRFL/mQlhNQ5/6/2g+mi6XfAGEKu9DOZgXyv/Y8gU7aNfWcEoBIHwxhCtf8Z/HX19AX7UKu6oaOL/3Ts/1lYs8PERHVr6zUs/ABIAZmQKT2uPDAvt2QXj7EdNOuiecUADBgOERXHfwsfvoaNke7K8Xih4iI6hcbBwjhXgApCkRSKkRk6wuPJadC6rldE88phQIl+Sp9/Cx++hr6pJ2PcJ03ERHVS5hjIKZOA87fFkRRIH7xsMekVL23a+o5Hbf/GiJaHz+Lv76GPm3XRJzzwzk/mtLLvAZiLvRGb/mQlhPA8SNA+04Nr9rRcbsrOads3xHWsFb15kLvP7MeXkNftTNUVaBD6tWXjK0xgrr4sVgscDqdWocR1KSUsNlsMJlMurjABzPmQl+YD/1gLvTDYDDAbDY3+TxBWfzY7XaEhIRoHQYRERFdgaZ+jgflnB+73Y6FCxeiurpa61CCXnV1NbKzs5kLHWAu9IX50A/mQj+qq6uxcOFC2O32Jp0nKIufkJAQdOrUyWd7hNCVMxqNSE9PZy50gLnQF+ZDP5gL/TAajejUqVOTR2+CctiLiIiIgldQ9vwQERFR8GLxQ0REREGFxQ8REREFFRY/REREFFQCfup6fn4+cnNzIaVEZmYmRo4c6Xa8oKAAr776Kux2OzIyMjB58mSNIg18l8qFzWbD/PnzUVZWBkVRMHr0aNx0000aRhvYGnpfAICqqnjsscfQrl07zJ49W4Mog0dD+Th79ixee+01lJaWQgiB7OxsdOzYUaNoA1tDudiwYQPy8vIAAImJiZg2bRrvG9cMnn/+eezevRu9evXyev1p8me3DGAOh0NOnz5dnjx5UlZXV8vp06fLM2fOuLWZO3euLCoqkk6nU/7hD3+QxcXFGkUb2BrKhdVqlbt27ZJSSlldXS1nzJghjxw5olW4Aa0x7wsppVyxYoX861//Kl944QUNogwejcnHwoUL5fr166WUte+V6upqLUINeA3lQlVV+cADD7gee/HFF115Id/auXOn3Lx5c73Xn6Z+dgf0sFdBQQESEhJgNpsRFhaGtLQ0bN++3XX8/PYWycnJUBQFgwcPRn5+voYRB66GcmEymdCjRw8AQFhYGOLi4lBeXq5VuAGtoVwAQEVFBTZu3IhRo0ZpFGXwaCgfVVVVKCwsxJAhQwDUvlfCwsK0CjegNea9Ic9tdaGqKqxWK6KjozWKNrD17NkT4eHhXo/54rM7oIe9ysvL3fYAMZvNsFgslzy+e/fuFo0xWDSUi4udOHECxcXF6Ny5c0uFF1Qak4ulS5di0qRJLR1aUGooH2VlZYiKisJLL72EQ4cOoUePHpg6dSoMBoMW4Qa0hnIhhMB9992H2bNnIzQ0FL169ULPnj21CDWo+eKzO6B7fsj/2O12LFiwAFOnTuVftxo5cOAAKisreVHXCafTiYKCAtxyyy149tlncebMGaxZs0brsIKSw+HAqlWrMH/+fCxevBhSSqxbt07rsOgKBHTxEx0d7Va1WywWt2rR23F2YTaPhnIB1HYnv/LKK0hLS8PAgQNbOsSg0VAu9u3bhx9//BHTpk3DggULsG3bNixevFiLUINCQ/kwm82IjY1FSkoKFEXB9ddfj6KiIg0iDXwN5aKoqAiKoiAmJgaKomDAgAHYu3evFqEGNV98dgd08ZOamoqDBw/CYrHAarVi69at6NOnj+u42WyGoigoLi6GqqrYuHEjrrvuOg0jDlwN5QIAlixZApPJxOGWZtZQLsaMGYPFixdj0aJFeOSRR9C3b19kZWVpGHFgaygf0dHRaNOmDcrKygAAu3btQkJCglbhBrTGfGaUlJSgoqICALBjxw7ExcVpFW7Q8sVnd8Dv7bVlyxa8++67UFUVmZmZGDVqFObNm4esrCyYzWbs3bsXr7/+Oux2O4YOHYopU6ZoHXLAulQupJR46KGHkJCQ4JrLcPfdd6Nv377aBh2gGnpfnLdr1y58/vnnXOrezBrKx/79+/HGG2/A4XAgJSUFDz74IJdXN5OGcvH555/jiy++gKIoSExMxMMPP4zQ0FCtww44Tz31FIqKimCz2RAZGYlZs2Zh+fLlPvvsDvjih4iIiOhiAT3sRURERFQXix8iIiIKKix+iEgz+/fvx9NPP611GA2aNm0afvrpp0u2efnll3mTVCI/weKHiJpFYwqGZcuWYdy4cS0UUfMaP348PvjgA63DIKJGYPFDRJooLy9HYWEhevfurXUoPpGSkoKamhocOHBA61CIqAEBvb0FEWnj9ddfx4kTJ/D0009DCIEHHngAQ4cOdWvzww8/IDU1FYpS+zdYTU0NXn31VddeSomJifjzn/8MACgpKcFbb72FkpISxMbG4oEHHsBVV10FoHb7h7feegv79u2D0WjEhAkTcPPNN6Ompga5ubn49ttvYTQaMXLkSNx6661QFAUffPABjh49CofDgW3btiEhIQGPPPIIYmNjAQBbt27F3//+d1RUVODmm292i3v16tX497//jYqKCkRHR+OBBx5w3Q37mmuuwbZt27g1C5HOsfghIp978MEHsWPHDvz2t79F9+7dvbYpKSlBx44dXV+vXbsWNpsNixcvhsFgcN0512q14plnnsGvfvUr9O/fH1u2bMELL7yAhQsXwmAwYN68eRg0aBBmz54Nh8OBo0ePAgCWL1+OQ4cO4cUXX4TVasVTTz2FmJgYDB8+HADw3XffYe7cuZgxYwZee+01fPDBB/jNb36DM2fO4MUXX8SMGTPQp08f/Otf/8LJkyddsbzzzjt49tln0alTJxw/fhwX3y0kLi4OBQUFzfGSEpEPcdiLiDRRWVnptn+b0WhERUUFjh07BoPBgGuuuQYAkJ+fj8TERAwcOBCKoqB///5o06YN9u3bh3379sFqtWLy5MkIDQ1FREQEunTpAgDYuHEjJk+ejMjISMTExGDcuHH4+uuvXc/Xq1cv9OrVCwaDAYMHD0ZxcTEA4Pvvv0eXLl2Qnp4Oo9GI2267DUIIt9gPHjwIu92O9u3bu3qLACA8PBzV1dXN9poRkW+w54eINBEREQGr1er6etiwYTh+/DheeOEF2O12jB49GhMnTsSJEyewe/du3Hvvva62TqcT5eXlbvss1WWxWBATE+P6un379m77AbVt29b1f5PJ5Irl1KlTaNeunduxqKgoAEBYWBhmzJiBTz75BK+++ip69+6Ne++913VX7OrqaoSHhzfthSGiZsfih4g0kZSUhO+++871tdFoxO23347bb78dhw8fxpNPPomrr74aZrMZffr0QXZ2tsc59uzZgxMnTkBK6dE7YzabceLECdfQ2okTJzw20/Wmbdu22LZtm+vrmpoanD171vV1v3790K9fP1itVrzxxhtYunQppk2bBgAoLS1FUlLSZb0ORNTyOOxFRM3i4s04venduzcKCgqgqioAYOfOnTh48CBUVUV4eDgMBgMURUF6ejqKiorw3Xffwel0oqamBtu2bUNVVRVSU1MRFhaG5cuXo6amBlVVVSgsLAQADBo0CMuXL0dFRQVOnDiBTz/9FIMHD24w7n79+qGwsBDff/89HA4Hli1b5prXc+rUKeTn56OmpgZGoxEmk8mt1+nHH3/kfnREfoA9P0TULDIzM/H222/j73//O379619jyJAhbsfNZjO6dOmCHTt2oE+fPjh16hTeeOMNlJeXIyIiAqNHj3bN+5k7dy7eeecdvPbaazAajejWrRuuvvpqGAwGzJ07F3/729+QlZWFkJAQ3HrrrejSpQsmT56Md955BzNnzoTBYMCNN96IjIyMBuNu3bo1ZsyYgbffftu12uv8MJiUEh9//DFeeuklKIqCq6++Gg8++CAAoKioCKGhoa45R0SkX9zYlIg0s3//fvzrX//CH//4R61DabKXX34ZgwcPRnp6utahEFEDWPwQERFRUOGcHyIiIgoqLH6IiIgoqLD4ISIioqDC4oeIiIiCCosfIiIiCiosfoiIiCiosPghIiKioMLih4iIiIIKix8iIiIKKix+iIiIKKj8fx10A/nE9WYIAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The initial position\n",
    "q0 = 0.0\n",
    "\n",
    "# The final position\n",
    "qf = 1.0\n",
    "\n",
    "# The start time\n",
    "t0 = 0.0\n",
    "\n",
    "# The end time\n",
    "tf = 1.0\n",
    "\n",
    "# A vector for time\n",
    "# Steps from t0 to tf in 50 steps\n",
    "t = np.linspace(t0, tf, 50)\n",
    "\n",
    "# Create the trajectory\n",
    "traj3 = rtb.trapezoidal(q0, qf, t)\n",
    "\n",
    "# Plot the trajectory\n",
    "traj3.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"600\"\n",
       "            height=\"400\"\n",
       "            src=\"http://localhost:52003/?53003\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            \n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.IFrame at 0x2aed7ec80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Animate the trajectory\n",
    "env = Swift()\n",
    "env.launch(browser='notebook', realtime=True)\n",
    "obj0 = sg.Sphere(0.03, color=\"#008cff\")\n",
    "obj1 = sg.Sphere(0.03, color=\"#fc0349\")\n",
    "env.add(obj0)\n",
    "env.add(obj1)\n",
    "env.set_camera_pose([0.5, 1.0, 0.5], [0.5, 0.0, 0.0])\n",
    "\n",
    "for q_0, q_1 in zip(traj.q, traj3.q):\n",
    "    obj0.T = sm.SE3.Tx(q_0)\n",
    "    obj1.T = sm.SE3.Tx(q_1)\n",
    "    env.step(0.02)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The animation above shows a comparison of the polynomial and trapezoidal profiles. The red sphere is trapezoidal and the blue sphere is polynomial."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The velocity trajectory has a trapezoidal shape, hence the name, comprising three linear segments. The corresponding segments of the position trajectory are a straight line (constant velocity segment) with parabolic blends. The term blend refers to a trajectory segment that smoothly joins linear segments. This type of trajectory is commonly used in industrial motor drives. It is continuous in position and velocity, but not in acceleration.\n",
    "\n",
    "The function `trapezoidal` has chosen the velocity of the linear segment to be"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1.5$"
      ],
      "text/plain": [
       "1.5"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "traj3.qd.max()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "but this can be overridden by specifying an additional argument"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set the maximum velocity to 1.2\n",
    "v_max = 1.2\n",
    "\n",
    "traj4 = rtb.trapezoidal(q0, qf, t, V=v_max)\n",
    "traj4.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set the maximum velocity to 1.9\n",
    "v_max = 1.9\n",
    "\n",
    "traj5 = rtb.trapezoidal(q0, qf, t, V=v_max)\n",
    "traj5.plot()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that as the velocity of the linear segment increases, its duration decreases and ultimately its duration would be zero. In fact, the velocity cannot be chosen arbitrarily – too high or too low a value for the maximum velocity will result in an infeasible trajectory and the function will return an error"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interpolate Simple Translations and Rotations"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From what we have learned so far, we start to interpolate single parameter positions and orientations.\n",
    "\n",
    "For a 2D orientation, we can describe the rotation angle using a single number $\\theta(t)$. We can interpolate the rotation angle using a polynomial or trapezoidal trajectory.\n",
    "\n",
    "In the following example we will interpolate between a starting angle $\\theta(0) = 15^\\circ$ and a final angle $\\theta(1.0) = 120^\\circ$, where we wish the final angle to occur at time $t = 1$ s."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2Pm3lxHQhQl/Qznb4/vvv+eqrrzh8+HCdbffv389rr70WrKcWQoizoisr0ZuyMV+b61/LozXqyKGAj1POFO/KLkl8hAhJQRv52bx5M++88071v//+97+zadMmOnbsSGZmJp06dSIxMRGAoqIi4uLigvXUQghRK79anv170Gs+8S5Pz+qPmvhz9P/9l9TyCBEhgpb8TJo0iWHDhpGbm8tzzz1HdHQ0mzdv5rPPPqtuk5SURHJyMnl5efTu3TtYTy2EEDXyqeVBQfsMVI/zUcMuQU28tXqVVsBjJmRkR4iwFNSan7S0NNLS0vjwww+57rrrGDRoEKWlpezZs4fdu3eze/dujh49yujRo5k4cWIwn1oIIfyYRw751vKg4fA+1IOP+iU2UssjRORo8uMt7Ew2ObSebB5mH6EYi0DHTADovT+gV3+C3rkFdu/ye5zxX4/7nbFlJ6EYi3Am8bAPW21yKIQQzc3vmIkbbgcFelM2Ki0TNfQS1Njr/HdklloeISJe0FZ7CSFEcwm0NF2//SeIi8e4/3cYk+9AZXbxrsqaMs2b8IDU8gghgCCN/Dz00ENcd911XHTRRfU+p8vtdrNq1SreffddnnnmmWB0QwgRAbTW6E1rAxwzAapNe1S0707zUssjhDhTUJKfiy++mIULF/KXv/yFgQMH0qdPn+qDTR0OBwAul4v8/Hxyc3PZuHEj2dnZREdHc+211wajC0KIMBKolkcXF6K//hy95Tto065Bx0zIGVtCiNMFreC5rKyMTz/9lM8++4w9e/ZU3x4VFQVAZWVl9W0ZGRmMHj2a0aNHk5CQEIynPytS8Gw9KSS0D7vEwu+YiRGXw/FiVIwDNWQU9OqPiorytjtjabox4jLL+h1MdomF8JJ42EewCp6bZLVXfn4+27dv58CBAxw/fhyAli1b0qFDB7p16xaUjgeDJD/Wkw8V+7BDLHRhgX+BslKoR57F6NAxYPtwnM6yQyzEKRIP+7D1aq/U1FTbJDhCiNCgj+Zjvvtm4GMmSo4FfIxMZwkhzkaTJD8zZ84kIyODzMxMMjMzycjIoG3btmd9vTlz5rB161Z69+7NzJkz/e7PycnhhRdewO12M2rUKCZNmtSY7gshmojfMROuUnT2avR3a1CJrVBZ/dFrPpWl6UKIJtUkyU9GRga7du1izZo11bc5HA46dOhQnQxVJUatW7eu83pXXXUVo0eP5vPPPw94/5/+9CceeOABMjIy+N3vfsegQYPIzMwM1o8jhAgCv1qezt2g5TmogRdh3PVLlMN73p9Z7pJjJoQQTapJkp+LLrqIdevWMXbsWHr06IHL5eLAgQOsXLmS3Nxcn7aJiYnVydDtt98e8HpZWVls2bIl4H2FhYVUVlbSsaO3HmDYsGFkZ2fXmPy43W48Hg/x8fHeJbORu8G1LVS9/hIH6zVlLHSR/748/LAT9eQrqKQUn+dVw8dCVn/IPwip7VFJKRH3+yHvC3uReNhHsGLQJMnP4sWLGT16NLfeeqvP7T/5yU9466232Lx5M5MnT+bQoUPs37+fffv2sWbNmhqTn9oUFRXhdDqr/+10Otm6dWuN7ZcuXUp2djazZ8+moqKC8vLyBj+nCD6Xy2V1F8RJDY5F8VHUkUPoNu2gdbLvfT8WEpW9GuO71Rh+tTwm5Xvz0HEt/K8Z1wIyu3r/u6ysYf0JI/K+sBeJh/Wqts9prCZJfvLz8wOOvMTGxjJlyhRmz57N9u3buemmm5ri6Ws1YcIExo0bV90fw5BNrq2ktcblchEXFyerKCx2NrHQq5b5HjExZRpcMBzWfYX+bg3ExaEuHIkeNBJ+O9WvlseR0QkVH99EP1HokveFvUg87KO+GynXeZ2gXOUMHTp0YP369VxyySUB7x84cCBLliwJSvKTlJREYWFh9b8LCwtJSkqqsX1MTAwxMd4dYJVS8otsExIL+6hvLAIeMbHweVi7CjV4JMYvHkLFn9rHy5wyzX9fHmebpvoxwoK8L+xF4mG9YL3+TZL8jB8/nmeffZZ33nmHCRMm+GVq+/fvpyxIQ9lOpxPDMNi9ezcZGRmsXr2aqVOnBuXaQoia6cP7Ax4xYVx9Q8AT0+WYCSGEXTRZwXNRURGLFy9m2bJljBo1qrogefv27Sxfvpz+/fvX+3qPPfYYeXl5lJeXc/fddzNjxgyWLFnC1KlTcTqd3H777cybNw+3282IESNkpZcQQRDoiAkAffiA95iJbev9H1THsnTZl0cIYQdNssNzlT179lQXGJ9eWNynTx/uu+8+zjnnnKZ66nqRHZ6tJzun2sfpsfCr5Zl0GxgGenM2KjkVNWgUnNcL/eXysD1iwkryvrAXiYd92Pp4izN5PB4OHz5MeXk5KSkptGrVqqmfsl4k+bGefKjYR1Us4lwn0A/f4TelpX5+P2rwxagY31PTw/WICSvJ+8JeJB72YevjLfyeJDqaDh06NMdTCSEao9yF/uLjgLU8qk07v8QHZCpLCBF6miX5EULYh98RE+4K2Pwd5reriC49Ad16e3dgliMmhBBhSpIfISKI3xETXXpAQgtU1gDUpNvwOOKJiY9HJ7aUIyaEEGFLkh8hIoR55JD/ERO52zGefNU7AqR19W7KsixdCBHOJPkRIkwEWpquPW7YthGd/SV6/27/Wh5tehOcAMmN1PIIIcKVJD9ChIEzp7PU6KvBVYY+Vozq2Qd1zWSUEYX58C+klkcIEfEk+REixAU8ZmLFB6iH/x9RXbr7tFUBjpiQKS0hRKSR5EcIm6txp+UTx9Eb1qK/XBZgOkuj3BV+15JaHiGEkORHCFvzm866/ucQG4veuh4VEwt9LkT99G7076fXezpLanmEEJHOsLoDQojAAk5nLfkLxMZi3PlLjKn/jTF0NEaHjqgp07wJD8h0lhBC1EFGfoSwSI3TWW437NiM+fm/a9hpuT3K4fC5TaazhBCi/iT5EcICftNZN9wGCYmw+Tt0RTmqW2/UJePQ67+W6SwhhAgySX6EaGYBp7Pe/jPcdBfGz+7BaNGyuq0pq7OEECLoJPkRIshqnM46/iN663r06k8CTmcZHTqiTkt8QKazhBCiKUjyI0QQ+U1nXX49GFHoPTnexKZXP9SEW9DbNsh0lhBCWESSHyGCxCw84j+d9fE/UNN+gzH+JpQRdaqtTGcJIYRlJPkRop4Cnp1VfBT9/Ubv+VkHAp2dpVFx8T6JD8h0lhBCWCkkkp/s7GwWLlyI1prx48dz6aWX+tz/6KOPUlxcTExMDACPP/44sbGxVnRVhKkzp7Po1huio1GtndCjD2rCz1CmbtDZWTKdJYQQ1rB98lNZWcnChQt55JFHSEhIYNasWQwaNIiWLX0LQ2fMmEFmZqZFvRShqqbi5Or7jxWh132FfuPF027UsGML6slXMJxtfNrL2VlCCGF/tk9+cnJySE9Px+l0AtC/f382bNjA8OHDz+p6brcbj8dDfHw8Wmt0gFU3ovlUvf5WxEGvWuY7mvOze1Hdz4edW9A7t8KPRXBOa0hsFeDBJuQfRCf5JjZq+FjI6g/5ByG1PSopJWR+x6yMhfAlsbAXiYd9BCsGtk9+ioqKqhMfAKfTSWFhoV+7Z599FsMwGDlyJNdcc02N11u6dCnZ2dnMnj2biooKysvLm6TfomFcLldwL1h8FHXkELpNO2idHPD+2EXzUacXJy+aT+WgkZg9+2FePhFaO0+1XfavU20BrQzKWyVBWZn/teNaQGZX738Hut/mgh4LcdYkFvYi8bCe44zd7c+W7ZOf+pg+fTpOp5PS0lJmz55NWloaAwYMCNh2woQJjBs3DoDY2FgMQ443s5LWGpfLRVxcHEqp4FzzjBEdNWUaXDQGjuZD7nb0Dztg13a/4mQFRI+4zDv6c7r4dPQZ01nGz+4lvn16UPprF00RC3F2JBb2IvGwj+jo4KQttk9+kpKSfEZ6CgsL6dq1q0+bqpGhhIQEhg4dSk5OTo3JT0xMTHVhtFJKfpFtor6xqLNGJ9DuyQufh68/R7VPh87dMEZdiR47Hv2rO/2Kk1VqWsB+qAhanSXvC/uQWNiLxMN6wXr9bZ/8dO3alb1791JYWEhCQgLr1q1j4sSJ1fdXVlZy4sQJWrVqhcfjYf369YwaNcrCHoum4reB4JRp3hqbHwthdy567y701g1+IzoAxrif+IzoKBq+146szhJCiPBg++QnKiqKW265hd///veYpsn48eNp2bIlTzzxBFOnTiUhIYHHH3+cyspKTNNk4MCBDBkyxOpuiwbSRQUni4QbNqKjv/kC1aYdZHRB9ewHF4xA/8+99VpuLnvtCCFEZFI6gsvX8/Pz8Xg8VncjrNU5TaU15Z9+QMxbr5wa0fnZvagefeDAbvT+PXBgD/rIIfhhh9/jjf963K9Gx1z5H78RHWPEZU32M4YLrTVlZWXEx8fL0L7FJBb2IvGwj+joaFJTUxt/nSD0RYiAAk1TnZ6E6PJyzJytRFclPlC96koPuxR1bndU994w+iqUy1XvDQRlREcIIURtJPkRZ+WsCo8Xzady+yYoK/XeHhsLUdE+S8irGMMu8R3RSUhs0AaCUp8jhBCiJpL8RIi6kpWGtPMb0bn2p6iOXdFH873LyY/me/870DlX/YagBg6rHjo2C49grl3pmwDJiI4QQogmJMmPDQUzUYG6p59qbDfpNu/oS3Eh+sdC7//nH4CvPz+tExr9r8Xo627GyOgM52VBchtU6YmA01SqS3efOXOVlIJn8p3EvP2qjOgIIYRoFhGd/OhjxZCQWPP9QU5CzmpUpb6JSg3tapp+Mk3T+++SY3D8R/TRI7D+q9MeqNHv/Bl96bWo9uneAzw7ngtHDqNPT368jTG69vSdpoqLr/c0lTn0ElT/wagjh2RERwghRJOL7OTnuf/FHDamUclFMNsFTlRewOyQiYpLgPJyqChHH80PsOx7PpXbN6PMSnTFaUd2lBwLOP2kjxzG6NYLMjp7z646uBd9evJzktF/sG9S07I1WqmgFx6rpBTUGYeECiGEEE0hopOf6qRh7w+o+ITqL3RdVgqffejfLm8nyhEHGtAm2lUGXy4/o93zVG7ORkXHettUVoKrFLau92+3dpW36LdKwETFRP/7H9CuAzgcEOtAFx4NsJGfRvUbjDp/ICrWUT21pAsLAk4/GZdc7ZuMRMfUK6lRzhQpPBZCCBHSIjv5AUCjMrugOp3n/adS8MMO/NcfaVTXnqjO3cFQgPKeE3V68nOSGnqpd4m2EYWKMtA7t6BPT35OMq6+wWdUpcZE5aa7fJILXViA+el7getpHHG+falnstKQpEYKj4UQQoQySX4MA9Wrv+8XeHyLgKMgqnufeo2WqMwu3pGkKm3Tgzqq0tDRl/omKw2appIRHSGEECEqspOfRiYXVo6qNHT0pb7JiiQ1Qgghwl1EH29xOGcHlXWt9qpHchHsdpFEto23D4mFfUgs7EXiYR/BOt4iopOfwsJCKisrre5GRNNaU15ejsPhkA8Vi0ks7ENiYS8SD/uIiorC6XQ2+joRmfy43W5iYmKs7oYQQgghzkJjv8eNIPYlZLjdbubNm0dZWZnVXYl4ZWVlzJo1S2JhAxIL+5BY2IvEwz7KysqYN28ebre7UdeJyOQnJiaG9u3bEx0d2fXedhAdHc3AgQMlFjYgsbAPiYW9SDzsIzo6mvbt2zd69iYip72EEEIIEbkicuRHCCGEEJFLkh8hhBBCRBRJfoQQQggRUST5EUIIIURECfvS9ezsbBYuXIjWmvHjx3PppZf63J+Tk8MLL7yA2+1m1KhRTJo0yaKehr/aYlFeXs7TTz9Nfn4+hmEwduxYrrzySgt7G97qel8AmKbJb3/7W5KTk5k5c6YFvYwMdcXi+PHjvPjiixw4cAClFLNmzaJdu3YW9Tb81RWPVatWsXTpUgAyMjKYNm2a7BvXBObMmcPWrVvp3bt3wM+fRn936zDm8Xj09OnT9dGjR3VZWZmePn26PnbsmE+bhx9+WOfl5enKykr961//Wu/evdui3oa3umLhcrn0li1btNZal5WV6QceeEAfPHjQqu6Gtfq8L7TWetmyZfqPf/yjfuqppyzoZWSoTyzmzZunV65cqbX2vk/Kysqs6GpEqCsepmnqu+66q/q2Z555pjo2Irg2b96s165dW+PnT2O/u8N62isnJ4f09HScTidxcXH079+fDRs2VN9fdbxFx44dMQyDYcOGkZ2dbWGPw1ddsXA4HPTq1QuAuLg40tLSKCoqsqq7Ya2uWACUlJSwevVqxowZY1EvI0NdsSgtLSU3N5fhw4cD3vdJXFycVd0Ne/V5b+iTR12YponL5SIpKcmi3oa3rKws4uPjA94XjO/usJ72Kioq8jkDxOl0UlhYWOv9W7dubdY+Roq6YnG6goICdu/eTefOnZurexGlPrF48803mThxYnN3LeLUFYv8/HxatmzJs88+y759++jVqxdTpkwhKirKiu6GvbrioZTi9ttvZ+bMmcTGxtK7d2+ysrKs6GpEC8Z3d1iP/IjQ43a7mTt3LlOmTJG/cC3yww8/cOLECflQt4HKykpycnK49tprefLJJzl27BgrVqywulsRy+Px8Mknn/D000+zYMECtNZ88cUXVndLnIWwTn6SkpJ8svbCwkKfbDHQ/TKE2TTqigV4h5Off/55+vfvz5AhQ5q7ixGjrljs3LmTbdu2MW3aNObOncv69etZsGCBFV0Ne3XFwul0kpqaSqdOnTAMgwsvvJC8vDwLehoZ6opHXl4ehmGQkpKCYRgMHjyYHTt2WNHViBaM7+6wTn66du3K3r17KSwsxOVysW7dOvr27Vt9v9PpxDAMdu/ejWmarF69mgsuuMDCHoevumIBsHjxYhwOh0y3NLG6YnHZZZexYMEC5s+fz4MPPki/fv2YOnWqhT0OX3XFIikpiXPOOYf8/HwAtmzZQnp6ulXdDXv1+c7Ys2cPJSUlAGzatIm0tDSruhuxgvHdHfZne3377bcsWrQI0zQZP348Y8aM4YknnmDq1Kk4nU527NjBSy+9hNvtZsSIEdx4441Wdzls1RYLrTX33HMP6enp1fUMN998M/369bO202GqrvdFlS1btvDRRx/JUvcmVFcsdu3axcsvv4zH46FTp07cfffdsrS6CdUVj48++oiPP/4YwzDIyMjg3nvvJTY21upuh53HHnuMvLw8ysvLSUxMZMaMGSxZsiRo391hn/wIIYQQQpwurKe9hBBCCCHOJMmPEEIIISKKJD9CCCGEiCiS/AghhBAiokjyI4QQQoiIIsmPEEIIISJKWJ/tVZeqw9GEdaoOCXQ4HCilrO5ORAvFWOgfi6HwCDjboM5p3eh2dhGKsQhnEg/7iIqK8jsd4GxEdPLj8XjweDxWdyOiVX2oGIYhHyoWs1MsdGEB5B+A1DSUMyVgG3Plf9CL5oPWoBRqyjSMEZeddbv6Pm9zsFMshMTDToK1NWFEJz9CiOYVrKRGFxacagOgNfqNF9BZA3yuW9929X3ehvwcQgj7kuRHCNEs6pNcmIVH/JOVRfOpPLQfpU0oPYEuLYFjxafaVD/YxHz5/0Fiq1O3lRwL3O5Pf0S1TYOERGiR6P1r8p9vBD1JEkLYkyQ/QohGqc8oSMARmEXzqSwsQJWWeK9hVgZOVrRGtWmL6tEXWiSi4lvAsWLMh3/h29YwMO76b7+Rn0Dt1M/vR8U6oOwEnCiBHZv9h9NNE3PBbFRSCqSkQkpbcMTXeySpvq+NEKL5SfIjhDhrtY2CaNOE/APoPbnodV8HTmri4lFDR6OcbVDR0TUnK30G+SYPzhTUlGnoN14A0/S2+dm9fgmGqqGdkdre26D1ycJJZxv06SM/J5/XmDoLWrSEo4eh4DDm5nUBR5L0mk9h6CWQlFxdEyIjRELYV0QfbJqfny8FzxbTWlNWVkZ8fLwUElqsobEImKgoBUNGe0dwlEKltoeMLtA6CT33Uf/k4olXA08rnZms1FZ7c+QgtGlf68hKfdrV53lr/JmvuxlVkI8uOgpRUZCUDJ9/VK+fN2B/5X1hKxIP+4iOjiY1NbXx1wlCX4QQYai2KRvtdqOzvww8mtOrH2rQSJThu42YWY+RGgBjxGXorAH1SmqUMwXqkUzUp119nrfGkaTTkiTt8aDXfBpwGk1vzobhY/1eG5keE6J5SfIjhPDjN2Vz892otI7o7ZvQP+zwjna06+D9/zOnqLr19vtyh6ZJaoItGEmSio6GrAHoM18bpdB7dqGfW4NyxMN5WajuvdG5273J1GnTY2r42Kb48YQQJ8m0l0x7WUqGk+2jKhZxrhPoh+/wH9UZex1Gv8HQuRsqJgZo2BRVpKnttdGlJ2DnVswNX8PK//g+0DBQT7yCK66FvC9sQj6n7EOmvYQQZ6WmKRZtVqJ2bUN/ucw/8QGMvheiumX53taA0ZxIU9troxJaQN8LMRwOzDOTH9NEv/smauQV6E5d/b5sZYpMiMaT5EeICOI3nfXTqaikFPS6r9BFBRgdz4MRl8N3a/yms2jTPuA1rZqiCgV1vjapaQGnDsnqj7H6E/Q/F2FmdEH1HwxduqO//ERWkAkRBDLtJdNelpLh5OYTcKUSwLU/xRh2CTjbVMdCr1om01nNJND0mBo+1jsFGReH2peHXv8Vevsm2LHF98ENWEEmzp58TtmHTHud4cSJEzz22GNUVlZimiZXXnklY8aMsbpbQtiCrqxEf/VZ4Omsblmo5FSf1UkyndV8Ar3WVbFQSqEyu6Ayu6C/34j59G99H2ya6PwDEh8hGihskp/4+Hh+//vf43A4cLlczJw5k8GDB9OyZUuruyZEswhUC6L3/uBddr1/N3TqFniKRaazLFev1zrQFBkK/a+/Yv6wAzX4Yr/draU2SIjAwib5MQwDh8MBUD2VFWhGz+124/F4vEP7WgfthFhxdqpef4lD4+hVy3xqQRgwDEpPQIdM7w7K6Z1RSqFTUv2mWEhK9nkvSCysFzAWSckB9xhi2CWwbSPmPxdBaSlqwFC0qxT+9oosnw8SeW/YR7BiEFY1PydOnODRRx/l4MGD/OxnP+OKK67wa/P222+TnZ3N7Nmz2bt3L+Xl5Rb0VIggKj5K7KP3oU57K2ulqPjdPEgOMDdefBR15BC6TTtondyMHRVBUVv8XGUYX31K9NJFnF6ZopVBxaPPSbxFyHM4HGRkZDT6OmEz8gPQokUL5syZQ3FxMU8//TRDhgyhdevWPm0mTJjAuHHjAIiNjcUIsBmbaD5aa1wul7ewUwoJG0z/WIT+eIlfLY/SmrgTx1DpHf0fFJ8O7dP9ryWxsI1aY1FD/Lz3xaM7d+PMv2iVNnEcPYxR0+NEreS9YR/R0cFJW8Iq+anSunVrOnbsyPfff8+QIUN87ouJiSHm5AZtSin5RbYJiUXNzqzd0FpDzjb05/+GykpUv8HoNSv8d1pOTTur11RiYR9nFYu2HQLuLs3H/0BvXY+6+CpU27Tqu6Q2qP7kvWG9YL3+YZP8FBcX43A4iI+Pp7S0lG3btnHZZbI0V4S2M/flYfAoOFaM6nQeasItqOQ23nYV5fU6N0uEv9rOH9O7c9AfLcEsOYZx0Rj0sWK/ozVkSwMRCcKm5icnJ4cFCxYA3iHKyy+/nLFjay/wk31+rCf7Z9SsphPE1R8WYKS2C9i+MUvTJRb2EYxY1Pb7oEuOYS57Fz582/dBsm9QQPLesA/Z5+cMXbt2Zc6cOVZ3Q4ig0ZvWBj41vegIBEh+ZGm6OF1tvw8qsRVGzz6YZyY/pulNmOT3SIS5sEl+hAgHWmvYth7z0w+gRcsG7csjRIME3DcIzM8+xGh5Diot06KOCdH0JPkRwiKnF5rSOgmdvRq9ahnq3B4YP5+OatkKs2tPqeURTaKm2iB1Xi/0f/6JWVqCMeZaVNdegBRGi/ASNjU/Z0NqfqwXqXPpPoXMKGjXAXXxlajhY1GOOJ+2ja3lqa9IjYUdNWcsavr90sVH0cvfRe/fg0pth17xYcQWRst7wz6k5keIEKULC05LfAA05B9A9R/ql/iA1PKIplXT75dqnYyadBvmgd3oR6ZD1e5BWqPfeAGdNUBGgETIkh3+hGhGutyF+cFb/oXMVYWmQtiMOvYjnLltommiD++3pD9CBIOM/AjRDHRFOfrzj9CbvkUNvMh/EzopZBZ2FagwWin0u4vRpSeg/xCU7JQvQoz8xgoRZLqwAP39Ru//uyswP3kP87nHoLUT48HfY4y6AjVlmjfhASlkFrZWVRjt8/s6ZRrGg79HFxzCnPsIet1Xpw7/PO33Xwi7koJnKXi2VLgVEgYsZL5mMurC4SgjyqdtcxUy11e4xSKU2TEWNRZGu0rRn36A3r4J1S4dveKDsCuMtmM8IpUUPAthMzUWMp+X5Zf4gBQyi9BSY2F0XALqqhsw+w1BPzLt1B1SGC1sTKa9hAgCrTX6y+VSyCwiljpW5H+j/P4Lm5LkR4hG0jlbMZ/9X3R5mbcw9HRSyCwiRVVh9BnMT95HHzlkQYeEqJlMewlRT2fucKsP7kW/+yack4Rx+0PeHZnbdpAdmUVEqnHH6HN7oJe8jm7tRF09GdWyFSA7RgtrScGzFDxbKlQKCX0KmZWCrr1Qyamoa29CtfE9ZNRuhcz1FSqxiAShHIsaC6N3bsX88G3vcRkJieg3F4RMYXQoxyPcBKvgWZIfSX4sFQofKrqwAPPhX/jtc2I8+aeQSm7qEgqxiBThGgutNbrqD4nTGQbGE6/a9v0UrvEIRcFKfqTmR4g66EP7/AuZtZZCTiEaSCmFSg1QAyeF0aKZSfIjRC30tg3o994EpJBZiKCooTA6YqcghCUk+REiAH34AJUvPYne8h3G/f+DukV2ZBYiGALuGH39LfDFx5hvvYo+UWJtB0VEkJofqfmxlNVz6X4ruEpL0B+8DYUFqAk/Q6Wm+bYNwULm+rI6FuKUSIhFoPeT3r7ZWxTdbwhq5OWoqChbrAqLhHiEirApeK6oqEApRUxMTLM/tyQ/1rPyQ8VvBdfgUfBjEcaVk1A9+zZrX+xAPuDtI5Jjoc1K9JefoNeuRKV3RC9/z/JVYZEcD7sJ2eMttmzZwtq1a9m+fTv79u2joqICAIfDQYcOHejevTsXXnghWVlZzd01EUH8jqLQGr7+HPXEy6jkttZ2TogIpowo1IjLMM/tKcdliCbTLMmPx+Nh+fLlvP/++xw5coTExEQ6d+7MiBEjSExMRGvNiRMnyM/PZ+XKlfz73/8mJSWFcePGMWbMGKKja+9mQUEBzz//PD/++CNRUVFMnDiRoUOHNsePJkJV/oGAK7hUQT5I8iOE5dSxIv8i6KpVYZL8iEZqluRn+vTpeDweRo0axdChQ+nSpUut7XNzc1mzZg1Lly7lvffeY/78+bW2j4qK4tZbb6VTp04UFxcza9Ys+vfvT1xcXDB/DBEmtLsCc1O2/x2ygksI+6haFXbGHynm/t0Y3XrL9JNolGZJfiZMmMDFF19c77qeLl260KVLFyZPnsyKFSvqbJ+UlERSUhIArVu3plWrVpSUlARMftxuNx6Ph/j4eO+GW5Fb720LVa9/c8VBb/gGvfxd1MVXoadMg7++6LMVP0nJEfs70dyxEDWTWABJyX7HZXDTVFRZKeZzj6EmTEGld2qWrkg87CNYMbCk4Pm2227j/vvvZ8CAAUG/dm5uLvPnz+fpp58OeP/bb79NdnY2s2fPZu/evZSXlwe9D8IGio+ijhxCt2kHrZNR+QeJeu9NdLsOVI69DmIdAdsJIWwm0Hu0uJDo999Ex7eg8sobIKGFvJcjhMPhICMjo9HXseRg09LSUkpLS2u8Pzc3lx07dnDFFVc06LolJSU8//zzTJ06tcY2EyZMYNy4cQDExsZiGLLVkZW01rhcLuLi4oI2jK1XLfNdxZU1AGIdqBtv999dNj4d2qcH5XlDXVPEQpwdicVpAr1H4zvAnf+F3r6Z6NfneWuA1qzwWRWmho8NWhckHvZRVw1wva8TlKvUw/fff09xcTGdO3eus+3+/ft57bXXGpT8uN1u5syZw3XXXUf37t1rbBcTE1M9/aaUkl9kmwhWLAKu4tryXdidw9WU5H1hHxKL2qke52OmpKJ/dRfVe0SfXBWmmmBVmMTDesF6/Zst+dm8eTPvvPNO9b///ve/s2nTJjp27EhmZiadOnUiMTERgKKiogYVK2utmT9/PllZWYwcOTLofRchpIZVXLJCRIjwpAoOo89cFyarwkQdmi35mTRpEsOGDSM3N5fnnnuO6OhoNm/ezGeffVbdJikpieTkZPLy8ujdu3e9r719+3bWrFlDZmYma9euBeD+++8nMzMz2D+GsDFdXo657iv/O2QVlxDhq6ZVYXt2yaowUSNLCp5//etfc9111zFo0CBKS0vZs2cPu3fvZvfu3Rw9epQ2bdowceLE6hVcTUV2eLZesHZO1RvWYi77J8aYa9HHf/RZIaJ+dq8lu8KGGtnF1j4kFg1jrvyP73v+p3dDRTl62waMiT9HdejYqOtLPOwjbI63sJIkP9Zr6IeK31lcR/PR77wGbdNQV92IcjhOtQvjc7iagnzA24fEouECnhVWdBS95C9wThJq3E9QcQmn2jbgvDCJh31I8hMEkvxYryEfKn5ncfUbDKaJMelWVDtZsdVY8gFvHxKL4NJb12P+++8Yo65Al5X6fI7U57wwiYd9BCv5kXXeIiQEXMW1/mvUT6dK4iOEqJXq1Q9j+iOYeTvRC5/3+RzRb7zgHQkSEaVZkp+HHnqIzz//vEGjLG63mxUrVvDQQw81Yc9EyKjpLK4jh6zpjxAipKiYGIzeA/3vqFoZJiJKs6z2uvjii1m4cCF/+ctfGDhwIH369KFz586kpqbiOFmj4XK5yM/PJzc3l40bN5KdnU10dDTXXnttc3RR2Jg2KzFztvrfIau4hBANEWhlmFLyORKBmq3mp6ysjE8//ZTPPvuMPXv2VN8eFRUFQGVlZfVtGRkZjB49mtGjR5OQkNBkfZKaH+vVNZeu83ZiLn0DNXCY999nnMUlq7iCR+oa7ENi0XTOXBlGz36oFi1Rk25FJQU+FkPiYR8hXfCcn5/P9u3bOXDgAMePHwegZcuWdOjQgW7dugXlB6tvPyT5sVZNHyq6tAT9z79CRTlq4s9RLc/x3i6ruJqMfMDbh8SiaZ35OaL378Zc8jqqV1/U6GtQJ/8or24v8bCNkE5+7EKSH+tVfajEuU6g8g+iU9vDzq3oL5djXDMZ1a3+m12KxpEPePuQWDQ/bZroNZ+iv/4cY/zNqHN7VC+J16ntccW1kHjYQEgnPzNnziQjI4PMzEwyMzPJyMigbdu2zd0NSX5sQGtN+acfEPPWK6fm4QcMw7hzJio6xtrORRj5wrUPiYV1dMkx9NJF6EP7YeeW6iXx7sl34rjkaomHxYKV/FhyqntGRga7du1izZo11bc5HA46dOhQnQxVJUatW7e2oouimeiiAqJPT3wA1n8Fx36Uc3mEEM1OJbaCqyejH/6Fz5L46LdeRfcfjHK2sbaDIigsSX4uuugi1q1bx9ixY+nRowcul4sDBw6wcuVKcnNzfdomJiZWJ0O33367Fd0VTUh/9RnqzMFHOZRQCGGlAFtrKG1C/kGQ5CcsNFnyU1lZyYIFC1BKcc899/jct3jxYkaPHs2tt97qc/tPfvIT3nrrLTZv3szkyZM5dOgQ+/fvZ9++faxZs0aSnzCijx7xbjvfoiVaKd8ESJawCyGsFGBJvAZYuwrd6TxUXLxlXRPB0WTJj9aaLVu2BJwfzc/PD3jiemxsLFOmTGH27Nls376dm266qam6JyyiPR708n+hd26tPpaivF06MW+/6rOEXVZyCSGsopwpqCnTfJbEe268g9i27THnP44x+mroP0Tqf0KYJQXP//3f/027du2YMWNGwPuXL1/OkiVLePHFF5u0H1Lw3PROP0CQgkOY77+FumgMatBIlFK+q72OHJIl7BaSIlv7kFjYQ9WSeN2mXfVqLzxu9Ef/QO/7AWPSbag27Rp8UKo4eyFd8Dx+/HieffZZ3nnnHSZMmEB0tG839u/fT1lZmRVdE0HkcxApQPfzMe79FSoh0a+tSkqRQkIhhK0oZ4q39lBrOPmdpGJiUeN+gs4/gPn2nwENG75p0EGpwnqWFTwXFRWxePFili1bxqhRo+jYsSMA27dvZ/ny5fTv39+Krokg8TuIFLzLRl0uCJD8CCFEKFGpaaib7kQ/fIf/QalZA2QEyOYsSX4ArrnmGvr06cPSpUv5+OOPKS8vr76vT58+TJ061aquiSDQ67/yP4hUVnEJIcKIyj+IX+WIfM6FBMuSH4DMzEweeOABPB4Phw8fpry8nJSUFFq1amVlt0Qj6GNF6H8sQld6/A8QlFVcQohwEuigVMDc+C1Gl+6omFiLOibqYljdAfAWMHXo0IEuXbpI4hOidGUl5ifvYf55Lmr0VUT9YgZqyjRvwgOyiksIEXaqVoX5fM7dch9Gl26Y836P3vSttR0UNQqbs73mzJnD1q1b6d27NzNnzqzXY2S119kLuIpr0EjUsEtRhuHbrpaDSGVVi31ILOxDYmEvdcUj0OecLnehP3gbnX8AY+KtsiosSEJ6tVdTuOqqqxg9ejSff/651V0JewFXcd3zK1SLAKu4qlZLCCFEmAr0Oacccajrb0Ef2o/5zp/BrISN38qqMJsIm+QnKyuLLVu21NnO7Xbj8XiIj49Ha+1frCZqpYsCr+LS5WWQ0KLh1zt5HYmD9SQW9iGxsJdGxaNtGky+A351p9+qMDOrPypJ/jhsiGC9J8Im+amvpUuXkp2dzezZs6moqPBZZSbqoDVRn39MdIDVDeV789BxDU9+qrhcrkZ2TgSLxMI+JBb2crbxUPt2E9sEn5uRyOFwBOU6EZf8TJgwgXHjxgHe4zQMwxY137an9+9G//MNSGkbcBWXI6MTKr7h591orXG5XMTFxUltg8UkFvYhsbCXxsZDZ3RCB1gVFrv2C1SnrqhWrYPU0/B35qbIZ32doFwlhMTExBATEwOAUko+WOqgjx9Dv7sYXGUYN01FJbfB7NDR58wb9bN7MRq5O7PEwj4kFvYhsbCXs42HcrbBPOOsMPWze1FpmZivzYVe/VCXXIOKjgl+p8NMsN4PEZf8iNpVrUbQyamw4Wv0pu8wxv0E1bVndRtjxGXorAG1ruISQghxSk2fm8b0R9DffIE591GMseOhz4VQdFRWhTWxsFnq/thjj5GXl0d5eTmJiYnMmDGDbt261foYWeruy28V10VjMG65z2fperDJkl77kFjYh8TCXpojHrrc5T0wdcPXsC9PVoXVIFhL3cMm+TkbkvycogsLMB/+hV8tj/HEq036l4d8yNuHxMI+JBb20lzxsOpzOJQEK/mRal+BLjiM+fpzNZ/FJYQQounlHwj4Oaz3/WBNf8KY1PxEMH38GPrDt6HoKOry69Hb1stZXEIIYZVAZ4Uphf733zHzD6JGXYmKkaLoYJCRnwihCwvQ32/0/n+5C/ODtzH//AxqwDCMu2dh9OorZ3EJIYSFAp4VNmUaxi+fgMRWmPMexfzqM7RpAr6f66JhpOYnAmp+fAuZFbTrgDHxFug72G/+uq6zuIJNahvsQ2JhHxILe2nueNT0OazdbvTn/0ZvXItK64j+9L2IK4yWs71EvejCM4+j0N555cyuAd/EchaXEEJYq6bPYRUTgxpzLWavfuhH7jt1x8njMnTWABmtryeZ9gpj2qzEXPmxFDILIUQYUceK/W+Uz/UGkZGfMKQrK9FrV6K/XA7n9Qp4HIUUMgshRIgKVBiNwvzgHQxloLplWda1UCEjPyHszGI3XVmJufoTzLmPQGkJxv2/I+ran0ohsxBChJGAhdG3TMO4YwZ641oqn3vM+91QdRq9FEb7kYLnEC149iliVgqGjobCAtTAi1AXjfFbDtnchcz1JYWd9iGxsA+Jhb3YNR41FkYfP4Ze/i/03h9Q7dLQy8OnMFp2eA6CUE1+Au4CqhTq8QUYbdpZ17GzYNcPlUgksbAPiYW9hGo8zP156Een+94Y4jtGyw7PEUzv2uZfxKw1qvCINR0SQghhO+r4Mf8bTRO9X3aMloJnG6o6Wf30E3211pC7Hb3iA7SrTIqYhRBC1K6mHaM//ifm1o2oS65GnTZbEOi7J1xJ8mMzZ9byqJvvBkc8+qsVqPROqAlTMJJTve3eeMG7vFGKmIUQQpyhqjD6zO8KY8Rl6B92ot97E11Rgbr4SvSRQ77fPSFeG1QXqfmxUc1PwFoegAlTMC4dh3LE+bW3YxFzQ4TqXHo4kljYh8TCXkI9HrV9V+jiQsyPlsAn7/k+yKa1QVLzE4b0wT3+iQ9gnNvDL/GBk1l99/Nt98sphBDCPmr7rlCtnRj9Bvs/yDTR+QeaoXfWkGmvZlRrLc9XK9AH9gAKkFoeIYQQzaSGTRP1v/6KuWMzasjFqNQ0n4eEen2QJD/NxK+W57qfgceNztmG6twNdck1GO0zpJZHCCFEs6qpNkhdNAZytqI/+gdm0VFUnwtRFwxHr/8q5OuDpOanGWp+aqrlUXfPQvUfijIMv/ahXstTX6E+lx5OJBb2IbGwl0iJR621Qe4K2LgW88vlsCnb94HNWB8kp7rbSE3Df7qiHHZuDXy4KKASW/klPiAnqwshhGh+tX33qJhYGHgRRouWmGcmP6aJ3vgNjLwcZUT53GXX6TFJfhrJbzpr3E0QF4/esQXQqPN6oUZegf5ujezLI4QQIrTVtHfQgX3o5x5DJSRCr36oXv3Rm7NtOz0WNtNe2dnZLFy4EK0148eP59JLL63zMYdzdlCZkFjj/XVlrOah/ej/udevSEzd/iBqwDCUw3GqbYBaHrv8ElgpUoaTQ4HEwj4kFvYi8fBV2/eZPn4MvW09et0a+PZL3wfWMj1W3xGiqNIS2nbt1uifISxGfiorK1m4cCGPPPIICQkJzJo1i0GDBtGyZctaH6ef+1/MYWMCJiF+Izrjf4pql47et9u7KstdAeVlAaaztLd47LTEB/BuKpU1IGJqeYQQQoSn2r7PVMtWqEEj0a1aY56Z/Jgm5ktPolLbQ4dOqPRO0KEjest39RohMlf+B2P1cpj3RqN/hrBIfnJyckhPT8fpdALQv39/NmzYwPDhw/3aut1uPB4P8fHxoDV60XwqDcM7T1l6AspOeDPQlR+fepDW6H8uRk+6FdXnAtTl16McDnRRAfrhO/yms3SbdgFrfEhK9v6Pk0vcRfXrIK+H9SQW9iGxsBeJRwB1fJ/p1PYBj2FSd8+CWAfs34Pel4f+6jP45vPTHqjRC+dTmX8AlZwK8S0gIRHtccOi+dCl8aM+ECbJT1FRUXXiA+B0OiksLAzYdunSpWRnZzN79mzvDVrj2Z2D7ngeOikZ0jJRifuJ8XukpqJdOrptuneor6wM4lpgTL6T6LdeRWkTrQw8N96BGdfCe7+oN5fLZXUXxEkSC/uQWNiLxKMBavt+BMjoAhldUCltiT09+QFA427RClqcA2UnoLgIY28uUUFMPsMi+WmICRMmMG7cuFM3GAYxV0xEJZ22Sqtte/Ri/4zVkdEJFR/ve8FLrkb3Hwz5B1Gp7XEkyXRWQ2itcblcxMXFyVy6xSQW9iGxsBeJx1mqx/ejzuiEDjBCFDtohO/3clEB2i9JOnthkfwkJSX5jPQUFhbStWvXgG1jYmKIiTk5rlNVqOVs49NGOdtgBjoM7ox2p7enhvtE/Sil5EPFJiQW9iGxsBeJR8PV9f1Y3+/bqnas+SQo/QqL5Kdr167s3buXwsJCEhISWLduHRMnTqzzceq+32HUsNpLCpSFEEKIplff71tjxGWogcOC8pxhs9T922+/ZdGiRZimyfjx4xkzZkydjyksLKSysrIZeidqorWmvLwch8Mhf1FZTGJhHxILe5F42EdUVJRPje/ZCpvkpyHcbvepqS8hhBBChJTGfo/7n60QAdxuN/PmzaNMVmRZrqysjFmzZkksbEBiYR8SC3uReNhHWVkZ8+bNw+12N+o6EZn8xMTE0L59e6Kjw6LkKaRFR0czcOBAiYUNSCzsQ2JhLxIP+4iOjqZ9+/aNnr2JyGkvIYQQQkSuiBz5EUIIIUTkkuRHCCGEEBFFkh8hhBBCRBRJfoQQQggRUcK+dD07O5uFCxeitWb8+PFceumlPvfn5OTwwgsv4Ha7GTVqFJMmTbKop+GvtliUl5fz9NNPk5+fj2EYjB07liuvvNLC3oa3ut4XAKZp8tvf/pbk5GRmzpxpQS8jQ12xOH78OC+++CIHDhxAKcWsWbNo166dRb0Nf3XFY9WqVSxduhSAjIwMpk2bJvvGNYE5c+awdetWevfuHfDzp9Hf3TqMeTwePX36dH306FFdVlamp0+fro8dO+bT5uGHH9Z5eXm6srJS//rXv9a7d++2qLfhra5YuFwuvWXLFq211mVlZfqBBx7QBw8etKq7Ya0+7wuttV62bJn+4x//qJ966ikLehkZ6hOLefPm6ZUrV2qtve+TsrIyK7oaEeqKh2ma+q677qq+7ZlnnqmOjQiuzZs367Vr19b4+dPY7+6wnvbKyckhPT0dp9NJXFwc/fv3Z8OGDdX3Vx1v0bFjRwzDYNiwYWRnZ1vY4/BVVywcDge9evUCIC4ujrS0NIqKiqzqblirKxYAJSUlrF69ul7HxIizV1csSktLyc3NZfjw4YD3fRIXF2dVd8Nefd4b+uRRF6Zp4nK5SEpKsqi34S0rK4v4+PiA9wXjuzusp72Kiop8zgBxOp0+p78Hun/r1q3N2sdIUVcsTldQUMDu3bvp3Llzc3UvotQnFm+++Wa9DgcWjVNXLPLz82nZsiXPPvss+/bto1evXkyZMoWoqCgruhv26oqHUorbb7+dmTNnEhsbS+/evcnKyrKiqxEtGN/dYT3yI0KP2+1m7ty5TJkyRf7CtcgPP/zAiRMn5EPdBiorK8nJyeHaa6/lySef5NixY6xYscLqbkUsj8fDJ598wtNPP82CBQvQWvPFF19Y3S1xFsI6+UlKSvLJ2gsLC32yxUD3yxBm06grFuAdTn7++efp378/Q4YMae4uRoy6YrFz5062bdvGtGnTmDt3LuvXr2fBggVWdDXs1RULp9NJamoqnTp1wjAMLrzwQvLy8izoaWSoKx55eXkYhkFKSgqGYTB48GB27NhhRVcjWjC+u8M6+enatSt79+6lsLAQl8vFunXr6Nu3b/X9TqcTwzDYvXs3pmmyevVqLrjgAgt7HL7qigXA4sWLcTgcMt3SxOqKxWWXXcaCBQuYP38+Dz74IP369WPq1KkW9jh81RWLpKQkzjnnHPLz8wHYsmUL6enpVnU37NXnO2PPnj2UlJQAsGnTJtLS0qzqbsQKxnd32J/t9e2337Jo0SJM02T8+PGMGTOGJ554gqlTp+J0OtmxYwcvvfQSbrebESNGcOONN1rd5bBVWyy01txzzz2kp6dX1zPcfPPN9OvXz9pOh6m63hdVtmzZwkcffSRL3ZtQXbHYtWsXL7/8Mh6Ph06dOnH33XfL0uomVFc8PvroIz7++GMMwyAjI4N7772X2NhYq7sddh577DHy8vIoLy8nMTGRGTNmsGTJkqB9d4d98iOEEEIIcbqwnvYSQgghhDiTJD9CCCGEiCiS/AghhBAiokjyI4QQQoiIIsmPEEIIISKKJD9CCCGEiChhfbZXXaoORxPWqTok0OFwoJSyujsRTWJhHxILe5F42EdUVJTf6QBnI6KTH4/Hg8fjsbobEa3qQ0X9WIjKPwipaShnSs3tCwsg/0Cd7UTDVcXCMAz5gLeYxMJeJB72EaytCSM6+RFNrz7JirHmU/Rbr3h/qZVCTZmGMeIyv3bmyv+gF82HOtrV93mFEEJEJkl+xFmpT3IRKFlRQ0dD6QkoLYHSE5iHDhD91iveNgBaoxfNp/JYMSqxFRgGKIUuOwHvvHZGuxcwO52H6pCJMqJqfV5JkoQQQlQJueRnzpw5bN26ld69e1efN5STk8MLL7yA2+1m1KhRTJo0yeJehreakgvt8UDBYcg/gJm3E97726kHaY1e+Dz6u9Woc5zQIhHiW8DxH1FnDmNqjTKiUK2TQZtgmlB4xH+4U5vof7yOjo7xtgGoqIDvN/g+76L53iQpvZPPkHVDkiQhhBDhI+SSn6uuuorRo0fz+eefV9/2pz/9iQceeICMjAx+97vfMWjQIDIzMy3sZeiqayREFxacShigOqmp/GYlxMWjUlK9j3XEEWhm1rhiIqr7+dX/NguPYK74wDcBMgzU4FG+z9/pPPT7b5163pPtjCn3+bTT32/EPD35qerj3/+Cjo72JlbxLdCtzoFP3vP9Od54AZ01oMYRIBklEkKI8BByyU9WVhZbtmyp/nfViq2OHTsCMGzYMLKzs2tMftxuNx6Ph/j4eLTWQSueCgd61TL/aarhY9HFhbBrGzpnG+za7puAnKSuvsEnqdFFBbDkdb9kRbdp53tb62Q8k+8k5u1XvaM3hoH62b2QlOwbm6Rk1JRp6DdeqLWdTm0PSvk9r/r5fagkb8KiS0vgm5X+P4dpYn7wNurCEdCxCyouoc7XJpxUvY7ynrCexMJeJB72IQXPJxUVFfkse3M6nWzdurXG9kuXLiU7O5vZs2dTUVFBeXl5c3TT/oqPErto/qkRGK0xFz6PufpTSE7F7NwNPfhi9IjLif39/T4jNVoZlLdKgrKyU9eLa4Ex+U6i33oVpU20MvDceAdmXAvfdgBDL6G8Z1/UkUPe5Kh1sn8bgIHD4dyetberz/OqKOh+PrFK+f0c7s7dMHZsRn36HpSXQ4tEdHJboj5e4vvaLHqBinN7evsQZlwul9VdECdJLOxF4mE9h8MRlOuEfPLTUBMmTGDcuHEAxMbGYhiyz6N2u9Hrv/IbCVFA9Pif+ozoAOgzRmCMn91LfPt0/wtfcjW6/2DIP4hKbY8jKcA0mta4XC7i2nVABbrGmeLToa529Xhe4tMD/hxxF13q27/jP6JXLfd/bbSJo/AIRoC+6KICOHwA2qZVjzaFgupYxMXJcl6LSSzsReJhH9HRwUlbQj75SUpKorCwsPrfhYWFJCUl1dg+JiaGmJgYAJRSEfOLfGa9inaVwZbv0Ou+QpeegE5dA08Xpab5vUZqxGXorAFw5CC0aV9r/YtytgFnmzr7F+xY1Od56/NzqFat0UMuxvznIt/XRilY9k/Mzz5Ede6G6tkXOnZFr/7EZ3qMECyijqT3hd1JLOxF4mG9YL3+IZ/8OJ1ODMNg9+7dZGRksHr1aqZOnWp1t2zlzFVNZJ7rraHpPRB1w+0Y53iTRTMpxa+mpqbERjlTIAyKfuvzcyhnSsB6I2PEZWi3G37Yjt6cjV66CL7feOqB9SiiFkII0fyUDrEKrscee4y8vDzKy8tJTExkxowZALz00ku43W5GjBjBjTfeWK9r5efnh/0Oz+bRw+hf3XXGqIWB8eSrNa7mqs+ITrBorSkrKyM+Pt72f1HV9dro7zdiPv1bv9vVTVNRF1+JOmOK1W6rx0IpFuFOYmEvEg/7iI6OJjU1tdHXCbnkJ5jCOfnRx39Er/wP+tsvYW+u3/3Gfz3uV8tjhXD6UNGFBZgP/8J/euySa+DgPlRyG1TfwdCzD/rrz223x1A4xSLUSSzsReJhH8FKfkJ+2iuS+dXxaA2529Gff4SucGEMHwuDR6F/dadfLQ9t2lvX8TBV2/QYgD5yCL3hG/Qn78G29aceKNNjQgjRrCT5CVF+dTxDRsOPRaiMzqhxP8Fo0w7wrtgyA3why5ds0zBqKaJWbdqhxlyLTu+EeXryA2Ca6P17JC5CCNEMJPkJQYF2WearFag/vISR6j+iU9sXsgi+OouoU9P8V9Yphf7PPzDXfoEaNBJ69kVFec8rs1ttkBBChDpJfkKQ3pPjvzux1qiiAgiQ/ED4rM4KB7WuHis8gl67Er3sX6i2aRAXj/5oia1qg4QQItRJ8hNCdFkpetm/0Ds2BdyTR+p4QkdNo3HK2QZ1+fVw+fWY2zag//i7Uw+S2iAhhAgK2d7YhnRhAfr7jd7pDkCXl2N+/A/Ml55EdT4PY+bjqCnTvAkPSB1PiFLOFFT382veSynQqhLT9J4z5nE3ce+EECJ8yciPzfgVMl84Ao7/iDHqStQDj1bvFdOQXZZFiApYG2Sgowz0c4+h0juhho9Ftc8ApDZICCHqS5IfGwlYyLx2JeqJl1HJbf3aSx1PeKu1NugqDXt2oT95D/PoEWjVGtZ8KrVBQghRD5L82En+gcCFzAX5ECD5EeGvxtogpaBjV1THrpiH9qP/516fpFlqg4QQomZS82MT2lWGuXal/x1SyBzx6qwNKj7qnzSbJnrNJ2izshl6KIQQoUWSHxvQG9ZiPv8HjP5DUbfcJ4XMomGqaoNOpwy02435zCOYHy1BlxyrvuvMgnohhIg0Mu3VjPyOoyg6in7nz5DSFuP+/0E5HCiQQmbRILXWBpmVsOk7zNefQyW2gtbJ6A/ektogIUREk4NNm+lgU79VXBeMgLITGJNuQ3XIbJY+2JEcGBg8dZ06b27fhH7qN743GgbGE69Wnw0nsbAHiYW9SDzsQw42DSEBV3F9uxL1xCuo5MYHUQioe/Wf0hq/v3RME70/T0YYhRARJaySn2nTplVn5omJiTzyyCNWd8mrxlVch0GSH9FcajpT7KMlmDnbYPTVEBtnXf+EEKKZhFXyA/CHP/yBuDh7fYDruHj/G2UVl2hmNdUGqeFjYecWzDdfJtoRh758AqpDR9k0UQgRtsIu+amL2+3G4/EQHx+P1pqmLnnSm75FL/sXXHszvP+mz5cOSclN/vx2V/XzR/rr0FzU8LGQ1R/yD0Jqe1TSyaTmvCxU115U5u0iavm7VO7ZBXt/8CmMVsPHWtv5CCLvC3uReNhHsGIQVgXP06ZNIzExEcMwuOqqqxgxYoRfm7fffpvs7Gxmz57N3r17KS8vb5rOeDxEvf8myuPBM/5miImF4qOoI4fQbdpB6+SmeV4hGqv4KLGP3oc67aNBK4OKR5+T31shhKUcDgcZGRmNvk5YJT+FhYU4nU6Kiop47LHHeOCBB+jYsaNPm9NHfg4fPtwkq710/kH04pdQo65A9R8a9OuHE601LpeLuLg4WUVhsapYOHbvhNNPk69yxUTUtT9FRUfcgHGzk/eFvUg87CM6Opq2bRt/4kFYfYo5nU4AkpKS6N+/Pz/88INf8hMTE0NMTAzgPSIgGL/Ip9dG6Jyt6DUrMG65T1ZyNUCwYiEaT7VNQ59ZGG0YEN8C/ezvYcAw1EWXomIdgByo2pTkfWEvEg/rBev1D5vkx+VyobUmPj4el8vF5s2bGTq06UddfPbvATj/Aoz7fouKimry5xaiKaikFKhp08TLJ6DXrsR8/g+onv3A4UD/7RXZNFEIEVLCJvn58ccfeeqppwAwTZNLL72Url27Nulz+u3fA7DlO/ixSE5bFyGtxgNVo6JQQy5GDxqJXr0c/frzpx4kB6oKIUJE2CQ/bdu2Zc6cOc37pIH27zFN7xeGfPiLEFfbponKMCClXcBNE+X3Xwhhd3KwaSOYeTn+N8r+PSJSBDpQFTC/+hz9Y5EFHRJCiPqR5OcsaNPE/PtfUKXHUVOmySnsIiJVbZro8/t/y30YF12K+caLmH97BV181OcxcqK8EMIOwmbaq7no8nL0689Cr34YJzd9070HyinsIiLVVBsU1bUnetf3mIsXoFono66YiN7ync/hvlIcLYSwSljt89NQDT3VXRcXYr42D+PKiagefZqwZ5FDTku2j6aKhf5hJ+a7i2Fztu8dp50oL3zJ+8JeJB72EaxT3WXaqxanD9HrfT9gvvo0xk/ulMRHiAZQnc/DuHyC/x1VxdFCCNHMgjbtVVFRgVKqegPBUOezf49S0D4T478eR7VsZXXXhAg9gU6UR6Ed8cjf0UKI5nbWyc+WLVtYu3Yt27dvZ9++fVRUVADeczc6dOhA9+7dufDCC8nKygpaZ5uL3/49WsOhveCusLZjQoSogCfKXzER/cHbmCltUVdej2qVVN1edo0WQjSlBiU/Ho+H5cuX8/7773PkyBESExPp3LkzI0aMIDExEa01J06cID8/n5UrV/Lvf/+blJQUxo0bx5gxY4gOlTOBZP8eIYKupuJonbMNc+F8VLsOqMuvR6//WgqjhRBNqkHZyPTp0/F4PIwaNYqhQ4fSpUuXWtvn5uayZs0ali5dynvvvcf8+fMb1dnmolMD7NMj+/cI0WiBNk5UXXsSdd9v0Ts2Y778FHy/4dSdsmu0EKIJNCj5mTBhAhdffHG963q6dOlCly5dmDx5MitWrDirDjY3bZrw77/D4FGwdqXP2Uby4StE01HdeqOuqkSfnvyAjLoKIYKuQcnP2LFjff592223cf/99zNgwIDanyQ62u+xdqTNSvQbL0LnbkSNuAx9/c9l/x4hmpFq28H/RHml0K2SpDBaCBE0jVrqXlpaSmlpaY335+bm8tFHHzXmKZqNrqz0HtLYtVd1fYFypqC6ny+JjxDNJOCu0RdfiX5zAeayf6Eryi3tnxAiPDS4Avn777+nuLiYzp0719l2//79vPbaa1xxxRVn1bnmoj0e767N51+AMWik1d0RIqIFKozWponO/hLzucdQA4ahRoxFRcfIqjAhxFlpcPKzefNm3nnnnep///3vf2fTpk107NiRzMxMOnXqRGJiIgBFRUXExcUFr7dNQHvc6D/PRQ28CDVwmNXdEULgXxitDAN14Qj0gGHorz/HnPd77/1rVsiqMCFEg53V8RYHDhwgNzeX5557joyMDMrKyigoOHVQYVJSEsnJyeTl5dG7d29+9atfBbXTgWRnZ7Nw4UK01owfP55LL720zscc+n4r7r++hDHsElTfQU3eR+FPto23j1CKhXnkEPrXU4HTPr7C6LiMUIpFJJB42EdUaQltu3Zr9HXOauOdtLQ00tLS+PDDD7nuuusYNGgQpaWl7Nmzh927d7N7926OHj3K6NGjmThxYqM7WZfKykoWLlzII488QkJCArNmzWLQoEG0bNmy9ge+8DiqUzdJfIQIMepoPhr/vbh0/oGwSH6EEP7Mlf/BWL0c5r3R6Gs1atfB//u//6v+74SEBHr06EGPHj0a3amGysnJIT09HafTCUD//v3ZsGEDw4cP92vrdrvxeDzEx8cDoFd8gHnZdagk+cC0QtXAYwSfr2sboRQLndre/7gMpdDvLsZ0uyGrf0j/hR5KsYgEEg/r6aKTJy90afyoDwTxbC8rFRUVVSc+AE6nk8LCwoBtly5dSnZ2NrNnz/beYJqU781Dx7Vojq6KGrhcLqu7IE4KiVjEtcCYfCfRb72K0iZaGXgm34HZdzBRn32IWv4ulZdei+7a09u++CjqyCF0m3bQOtnSrjdESMQigkg8rKP25hEbxOQzLJKfhpgwYQLjxo07dYNh4MjohDo5EiSal9Yal8tFXFxcSP+lHg5CLhaXXI3uPxjyD6JS2+OoGr2deAv6+DGiPv4HfPERdMj0blx6WmG0Gm7vfcdCLhZhTuJhPTOlTVCv16Dk56GHHuK6667joosuqvc5XW63m1WrVvHuu+/yzDPPnFUn65KUlOQz0lNYWEjXrl0Dto2JiTm1Q/XJnZsNZ3BfVNFwSin5ULGJUIqFcraBAO9f1eocuOE2zLwc9OMzTt1x8rgMFSLHZYRSLCKBxMMa+sRxePvPqKtuhJ2bgnLNBiU/F198MQsXLuQvf/kLAwcOpE+fPnTu3JnU1FQcDgfgHRbMz88nNzeXjRs3kp2dTXR0NNdee21QOhxI165d2bt3L4WFhSQkJLBu3bp6FVqr+36HkZDYZP0SQlhLuUrPLIuW4zKECCH6+DHMV+ZgTLoNldkFVVoSlOs2KPkZP348l112GZ9++imfffYZK1eurL4vKioK8K68qpKRkcGNN97I6NGjSUhICEqHA4mKiuKWW27h97//PaZpMn78+LpXegGqVWvweJqsX0IIi6Wm+RdGA+ZnH2I426DatLOoY0KIuuhjRZiv/hFj8h2oDh2Bk9/bQXBW+/xUyc/PZ/v27Rw4cIDjx48D0LJlSzp06EC3bt1ITU0NSiebSn5+Ph5Jfiwl+2fYR7jGwlz5H/QbL/geUtylB/qDtyChBeqqG6unwOyyY3S4xiJUSTyany4+ivmnZzB+ejeqfXr17dHR0UHJLRqV/IQ6SX6sJx8q9hHOsdCFBQEPKda7d2F++A4qKRmcbdB/f80WO0aHcyxCkcSjeenCI5h/nosxZRqqbZrPfc2a/JimSV5eHmlpaT7HVcycOZOMjAwyMzPJzMwkIyODtm3bNrpTzUWSH+vJh4p9RHIszHVfoV/4P98bLdwxOpJjYUcSj6ZXNeqqo2PQ/3wD4+f3B5yWDlbyU6+an2PHjvGrX/2K3/3ud/Tu3bv69oyMDHbt2sWaNWuqb3M4HHTo0KE6GapKjFq3bt3ozgohRFNQ8QlSGC2ERcyV//FuYHhyLEZNvLXJ6/HqlfwkJCRwzz33kJ6e7nP7RRddxLp16xg7diw9evTA5XJx4MABVq5cSW5urk/bxMTE6mTo9ttvD95PIIQQjVVTYfT6bzAyuqASZBNUIZqCLizwSXwA9NKF6EEjm3TUtV7JT2xsLBdccIHfiq3FixczevRobr31Vp/bf/KTn/DWW2+xefNmJk+ezKFDh9i/fz/79u1jzZo1kvwIIWxFOVNQU6b5F0YnJWO+/P9Q52WhLr0GFef9DLRLYbQQIS//gN8fHc0x6lqv5Ke4uJipU6f6TXvl5+eTmZnp1z42NpYpU6Ywe/Zstm/fzk033RS8HgshRBMwRlyGzhrgVxhtZA2Ajd9ivvgkqkdfiItDv/myLQqjhQh15t4f/G80DGjTvkmf16hPo7i4OCZNmuRXZNShQwfWr19f4+MGDhzIF1980agOCiFEc1HOFFT3831Gc5RSqL4XYjz4e0hsiV684NRfqid3jNaFBRb1WIjQpLXG/NdfUUUFqCnTvAkPnBp1beIR1XqN/MTFxXHDDTf43T5+/HieffZZ3nnnHSZMmOB35MX+/fspKysLTk+FEMJCSilo004Ko4VoJO2uQC98Hs7tiXHxld7beg8MuB1FU2nUwaYXXXQRRUVFLF68mGXLljFq1Cg6dvTuwrh9+3aWL19O//79g9JRIYSwXE2F0VvWYXTsioqTA5KFqI0+Voz52lyMMeNRWafyA+VMadY/IIKyyeGePXtYunQp2dnZlJeXV9/ep08f7rvvPs4555zGPkWTkH1+rCf7Z9iHxKJ+/HaMvvkeVGIrzM8+RPXog7rk6kYXRkss7EXiERz6wB7MxQswbpqK6uBfL1wfttzh2ePxcPjwYcrLy0lJSaFVq1bBunSTkOTHevKhYh8Si/oLtGO01ho2fIO54kPUeb0gvgX6rVfOqjBaYmEvEo+zV7154Y+F6DUrMG5/ENUq6ayv16ybHNb7YtHRdOjQIZiXFEII2wk0RK+Ugn6DMfoOQq/5FP3avFN3VhVGZw2QpfEiYvhtXnjz3Y1KfIKpXqu9hBBC1I9SCuVs439HVWG0EBEg4OaFb75sm5WRkvwIIUSwVRVGn8Fc/Sn66BELOiRE89I7Nte8eaENSPIjhBBBVrVjtM/eJbfchzH6KvSSv2D+5Vn0oX3V7XVhAfr7jbb5q1iIxtDfrkKv/Nj/D4Bm2LywvoJa82OVRx99lOLiYmJiYgB4/PHHiY2NtbhXQohIVtOO0equX6IP7EH/ewna44bU9ugP3vYpjFbDx1rceyEaTleUo9/+E8S3wHjoMW/t25lHxtik5i0skh+AGTNmBDxqQwghrFLT3iUqLRN12wOYu7ahn5x16o6ThdFk9Yc4OUxVhA59YA/m317BuGwCqvcAAFQNfwDYQdgkP/XldrvxeDzEx8ejtSaIK/3FWah6/SUO1pNYWKCiwv820/ROiXXqLrGwCXlv+NNFBXD4ADq1PWrLOvTGtajbHoTWTt/XKSnZ+z+C8/oFKwZhk/w8++yzGIbByJEjueaaa2psV7UZ4+zZs6moqPDZlFFYx+VyWd0FcZLEohmd4yRWKdTpK2KUQi/9K8bAYbgGXwyOOOv6J3zIe8PLWPMp0W+9gtIaDVSefyGe2x/y1vQ08ZFWDocjKNcJ6iaHTemXv/wlpmn63f6b3/wGAKfTSWlpKbNnz2b8+PEMGDAg4HVOH/k5fPiwbHJoMa01LpeLuLg42TzMYhILa+hVy/zqIvSQ0bi//pyYtV9Ap/NQo69GnePdH6XqL27apqGS7DONEM7kvXGKLipAP3yH70ouw0A98Uqz/D5GR0fTtm3bxl8nCH1pFnPmzKmzTUJCAkOHDiUnJ6fG5CcmJqa6MFopFfG/yHYhsbAPiUXzClQXobXGHDAMNewS1M6tmG++DC0SISkF/d6b1cXRNGDXaNF48t4AvX93wCXs6sihwPtbBVmwXv+QX+peWVnJsWPHAO/xGuvXrycjI8PiXgkhRP0pZwqq+/l+BaFKKVT33kTd8zAMGol+d/GpL56qXaNlebxoJnrjWvT7b9t6CXt9hczIT03cbjePP/44lZWVmKbJwIEDGTJkiNXdEkKIoFKAX42CaaL3/WCrVTQi/Ojio+h3XgNnG4wZj6G/+dy2S9jrK2RqfpqCHGxqPTkw0D4kFvYRKBa6sADz4V/4TjkoBd3PR7VPR42+BtU+/dQ1zvJEeeEvUt8b2qxEf/4ReuNajIm3otI7nbovwOG+zcGWB5sKIYRoGlW7Rp/5F7cx4jL03h/Qy/6JefxHjOFj0T8WedudxYnyInKdnjBTcgxzyeuoAUMx7v8flOFbJVPTHlahQkZ+ZOTHUpH6F5UdSSzso7ZY1PYXtz5xHPM//4QP3/G9oGFgPPGqjACdpUh4b5x5AjtdumPc++vqVYZ2EayRn5AveBZCiEhSU3E0gGrREqNnX/8HmSb68P5m6J0IRYFOYCdvJ1RWWtepJibJjxBChJNAJ8orhf7XXzHff8tvdZgcqhrZtGlirvzY1iewNwWp+RFCiDBSU22QumgMbN+E/sfrmO4KjCGj0ceK0X99UWqDIpDWGjZ8g/np+9ClhzdhPmPjwlBbvt4QkvwIIUSYqelEeXr2RfXsiy45hvnpB/Dem6ceVLVvUNYAqQ0KMz6FzEnJsG095n/+iTovC+PeX6HiEjCT24T88vWGkORHCCHCUG2rcVRiK4xuWfgdGGSa6F3bUM4RTd4/0Tx8CpmVgg4dUX0GYdz5S1SLxOp2NSbMYUqSHyGEiERVtUFn7Bukv11F5ZoVqL6DUBdchGrREpB9g0KRXyGz1rB/D+r+//FJfKqE+vL1hpDkRwghIlCt+waVl6M3rsVcNN+7rXSLlrDqP1IbFEJ06QnMj/7hX8isTxYyR0iSUxNJfoQQIkLVNNWhHA7UhcPhwuGY+/PQjz5A9eEaWqMXSW2QHQQajdP78tCffYguLkSdPxAdYYXM9SXJjxBCRLC6pjrU8WPoM08V0ybmy/8PdeEIVL/BqORTm87J9Fjz8KvlGX4ZFB9FpaSiRl+D0SHT286IiqhC5vqS5EcIIUTNAtUGGQbqtgdRh/ahP3gb8+gRVJfu3lGhD9+W6bEmFrCWZ9V/UL9/HqN9hk/bSCtkri9JfoQQQtSoxtqgtmnQNg3Vd5D3AMz136BffOLUA+uYHpMRoprV9NporWH/bu8RJn61PBp1rBjOSH4gsgqZ60uSHyGEELWqa/RAGVGQ0OLMyTHv9NiL/4c6tyeqRx/o1huV0MJvykZGiE7xe21+di8qvRP6uzXoPbtQHTqh+g1Gf7VCankaIaSSn1dffZWvv/6a5ORknnzyyerbDx06xNy5czlx4gTnn38+d955Z9gePieEEFaoc/Sgpumxe36FKnehv98IC5/HLPkRtm8+1aaOzRUjaYQo0HSWXjQfPfoajIsuRU38efV3mxloF+8wf32CKaSSn+HDh3PJJZfw8ssv+9z+17/+lRtuuIGBAwfy9NNP89133zFw4ECLeimEEJGnxukxZxvv/e0zYPTVmNvWo09PfgBME3PZPzEGj4IOnVAxMd6bw2yEqMbprNITkLsd8+vP/KezAGPgUFTHc31vk1qeRgmp5KdHjx7k5+f73Ka1ZseOHcyYMQOAESNGkJ2dXWPy43a78Xg8xMfHo7X2zqEKy1S9/hIH60ks7CNUY6GGj4Ws/pB/EFLbo5JS/H+Gth0CbK5oQFom5vqv4f23weOGlq3g6899R0HeeAEzqz8qKcAIUVEBHD7grUMKcH9j1BWP+jy3XrXMd3XWRWMgKhoKDkN8PKpzd7hguO/PDGAY6DbtAiZFJCV7/1dL38JNsH7OkEp+Ajl+/DiJiYnVQ4FOp5PCwsIa2y9dupTs7Gxmz55NRUUF5eXlzdVVUQuXy2V1F8RJEgv7CMlYxLWAzK7e/y4rC3i/MflOot96FaVNtDLwTL4Dc+DwU220RmV/SexXn/k+1jTxLH4Fs1sWuk07dJv20NqJ8fVnRL/1CkprtFJ4Jt+JOfSSmvtYfBR15JA3qWidXO92geJhrPk08HObJvxYiDpyCLV7F9Hvv0l1MYbW6C+XUzH9UejczZsMVV3vzNfmxjsw41oEfi0jkMPhCMp1bJf8/PKXv8Q0/U6c4Te/+Q1Op7PR158wYQLjxo0DIDY2FsMwGn1Ncfa01rhcLuLi4qROy2ISC/sI+1hccjW6/2DIP4hKbY8j0EhO7/4BN+iLuvQaosvLIP8geks2HD4I32+obqK0JuatVyAuDtUuHRJbQctzIC4epZTfCIyaMs07YnXm85/Rzj35TmJHX+W9hlkJZaXog/vgrVeq+6i0JuZvL8P6ryDWAUnJqNQ0dJT/94zSmrjoKFRCQoNfm0gWHR2ctMV2yc+cOXMa1L5ly5aUlJSgtUYpRWFhIUlJSTW2j4mJIebkfLJSKjw/WEKQxMI+JBb2Ec6xUM42cLIeqKb7AxX1Gj37+LTT32/EPC358d6oYd9uKDoKJcfg+DG0qxRdUeGTKKE1euHz6G9XgSPO+xxGFNpdAeu/9mkX/beX0eu/RsfGetvFJ4DLFbhG55rJqO7nn3p4YQHmu4v9i8FT0wLGt67XJpIF6/1gu+SnoZRSnHfeedVFzqtWrWLkyJFWd0sIIUQj1auot4ZVZsbY8X7tAyZKgLpiIuq8LO+5V6aG7RvRpyc/gALU1Tdg9DiVfOnCAsz1X9W55LymYnApUrZOSCU/8+fPZ8OGDRw/fpy7776bn//85wwdOpSbb76ZuXPn8pe//IXevXszYMAAq7sqhBAiCOo8fqMhiUVNy/HbdkCdPp2S3tlvyk0rA5V69kmNrM6yF6UjpUQ8gPz8fDwej9XdiGhaa8rKyoiPjw/b4f1QIbGwD4lFw+nCgnolFubK/wQ8yb6udu4b78BxydUB41Hf5xaNFx0dTWpqat0N6yDJjyQ/lpIPefuQWNiHxKJp1TdZqWqn27TDFddC4mEDkvwEQWFhIZWVlVZ3I6JprSkvL8fhcMiHisUkFvYhsbAXiYd9REVFBWXld0QmP263u3rFlxBCCCFCS2O/xyNykxu32828efMok02jLFdWVsasWbMkFjYgsbAPiYW9SDzso6ysjHnz5uF2uxt1nYhMfmJiYmjfvn3QNksSZy86OpqBAwdKLGxAYmEfEgt7kXjYR3R0NO3bt2/07E1ETnsJIYQQInJF5MiPEEIIISKXJD9CCCGEiCiS/AghhBAiokjyI4QQQoiIEval69nZ2SxcuBCtNePHj+fSSy/1uT8nJ4cXXngBt9vNqFGjmDRpkkU9DX+1xaK8vJynn36a/Px8DMNg7NixXHnllRb2NrzV9b4AME2T3/72tyQnJzNz5kwLehkZ6orF8ePHefHFFzlw4ABKKWbNmkW7du0s6m34qyseq1atYunSpQBkZGQwbdo02TeuCcyZM4etW7fSu3fvgJ8/jf7u1mHM4/Ho6dOn66NHj+qysjI9ffp0fezYMZ82Dz/8sM7Ly9OVlZX617/+td69e7dFvQ1vdcXC5XLpLVu2aK21Lisr0w888IA+ePCgVd0Na/V5X2it9bJly/Qf//hH/dRTT1nQy8hQn1jMmzdPr1y5UmvtfZ+UlZVZ0dWIUFc8TNPUd911V/VtzzzzTHVsRHBt3rxZr127tsbPn8Z+d4f1tFdOTg7p6ek4nU7i4uLo378/GzZsqL6/6niLjh07YhgGw4YNIzs728Ieh6+6YuFwOOjVqxcAcXFxpKWlUVRUZFV3w1pdsQAoKSlh9erVjBkzxqJeRoa6YlFaWkpubi7Dhw8HvO+TuLg4q7ob9urz3tAnj7owTROXy0VSUpJFvQ1vWVlZxMfHB7wvGN/dYT3tVVRU5HMGiNPppLCwsNb7t27d2qx9jBR1xeJ0BQUF7N69m86dOzdX9yJKfWLx5ptvMnHixObuWsSpKxb5+fm0bNmSZ599ln379tGrVy+mTJlCVFSUFd0Ne3XFQynF7bffzsyZM4mNjaV3795kZWVZ0dWIFozv7rAe+RGhx+12M3fuXKZMmSJ/4Vrkhx9+4MSJE/KhbgOVlZXk5ORw7bXX8uSTT3Ls2DFWrFhhdbcilsfj4ZNPPuHpp59mwYIFaK354osvrO6WOAthnfwkJSX5ZO2FhYU+2WKg+2UIs2nUFQvwDic///zz9O/fnyFDhjR3FyNGXbHYuXMn27ZtY9q0acydO5f169ezYMECK7oa9uqKhdPpJDU1lU6dOmEYBhdeeCF5eXkW9DQy1BWPvLw8DMMgJSUFwzAYPHgwO3bssKKrES0Y391hnfx07dqVvXv3UlhYiMvlYt26dfTt27f6fqfTiWEY7N69G9M0Wb16NRdccIGFPQ5fdcUCYPHixTgcDpluaWJ1xeKyyy5jwYIFzJ8/nwcffJB+/foxdepUC3scvuqKRVJSEueccw75+fkAbNmyhfT0dKu6G/bq852xZ88eSkpKANi0aRNpaWlWdTdiBeO7O+zP9vr2229ZtGgRpmkyfvx4xowZwxNPPMHUqVNxOp3s2LGDl156CbfbzYgRI7jxxhut7nLYqi0WWmvuuece0tPTq+sZbr75Zvr162dtp8NUXe+LKlu2bOGjjz6Spe5NqK5Y7Nq1i5dffhmPx0OnTp24++67ZWl1E6orHh999BEff/wxhmGQkZHBvffeS2xsrNXdDjuPPfYYeXl5lJeXk5iYyIwZM1iyZEnQvrvDPvkRQgghhDhdWE97CSGEEEKcSZIfIYQQQkQUSX6EEJbZtWsXf/jDH6zuRp2mTZvG999/X2ub5557TjZJFSJESPIjhGgS9UkY3nnnHa655ppm6lHTGjduHG+//bbV3RBC1IMkP0IISxQVFZGbm0ufPn2s7kpQdOrUiYqKCn744QeruyKEqENYH28hhLDGSy+9REFBAX/4wx9QSnHXXXcxYsQInzYbN26ka9euGIb3b7CKigpeeOGF6rOUMjIy+N///V8A9uzZw5/+9Cf27NlDamoqd911F+eeey7gPQLiT3/6Ezt37iQ6OprrrruOq666ioqKChYuXMjXX39NdHQ0l156Kddffz2GYfD2229z6NAhPB4P69evJz09nQcffJDU1FQA1q1bx5///GdKSkq46qqrfPr96aef8ve//52SkhKSkpK46667qnfD7tmzJ+vXr5ejWYSwOUl+hBBBd/fdd7Np0ybuv/9+evToEbDNnj17aNeuXfW/P/vsM8rLy1mwYAFRUVHVO+e6XC4ef/xxbrvtNgYNGsS3337LU089xbx584iKiuKJJ55g6NChzJw5E4/Hw6FDhwBYsmQJ+/bt45lnnsHlcvHYY4+RkpLCxRdfDMA333zDww8/zAMPPMCLL77I22+/zX333cexY8d45plneOCBB+jbty9/+9vfOHr0aHVfXn/9dZ588knat2/PkSNHOH23kLS0NHJycpriJRVCBJFMewkhLHHixAmf89uio6MpKSnh8OHDREVF0bNnTwCys7PJyMhgyJAhGIbBoEGDOOecc9i5cyc7d+7E5XIxadIkYmNjSUhIoEuXLgCsXr2aSZMmkZiYSEpKCtdccw1ffvll9fP17t2b3r17ExUVxbBhw9i9ezcA3333HV26dGHgwIFER0dzww03oJTy6fvevXtxu920adOmerQIID4+nrKysiZ7zYQQwSEjP0IISyQkJOByuar/PXLkSI4cOcJTTz2F2+1m7NixTJgwgYKCArZu3cqtt95a3bayspKioiKfc5bOVFhYSEpKSvW/27Rp43MeUOvWrav/2+FwVPeluLiY5ORkn/tatmwJQFxcHA888ADvvfceL7zwAn369OHWW2+t3hW7rKyM+Pj4xr0wQogmJ8mPEMISmZmZfPPNN9X/jo6OZvLkyUyePJn9+/fz6KOP0q1bN5xOJ3379mXWrFl+19i+fTsFBQVorf1GZ5xOJwUFBdVTawUFBX6H6QbSunVr1q9fX/3viooKjh8/Xv3vAQMGMGDAAFwuFy+//DJvvvkm06ZNA+DAgQNkZmY26HUQQjQ/mfYSQjSJ0w/kDKRPnz7k5ORgmiYAmzdvZu/evZimSXx8PFFRURiGwcCBA8nLy+Obb76hsrKSiooK1q9fT2lpKV27diUuLo4lS5ZQUVFBaWkpubm5AAwdOpQlS5ZQUlJCQUEB77//PsOGDauz3wMGDCA3N5fvvvsOj8fDO++8U13XU1xcTHZ2NhUVFURHR+NwOHxGnbZt2ybn0QkRAmTkRwjRJMaPH89rr73Gn//8Z+644w6GDx/uc7/T6aRLly5s2rSJvn37UlxczMsvv0xRUREJCQmMHTu2uu7n4Ycf5vXXX+fFF18kOjqa7t27061bN6Kionj44Yd59dVXmTp1KjExMVx//fV06dKFSZMm8frrr/PQQw8RFRXFJZdcwqhRo+rsd6tWrXjggQd47bXXqld7VU2Daa159913efbZZzEMg27dunH33XcDkJeXR2xsbHXNkRDCvuRgUyGEZXbt2sXf/vY3fvOb31jdlUZ77rnnGDZsGAMHDrS6K0KIOkjyI4QQQoiIIjU/QgghhIgokvwIIYQQIqJI8iOEEEKIiCLJjxBCCCEiiiQ/QgghhIgokvwIIYQQIqJI8iOEEEKIiCLJjxBCCCEiiiQ/QgghhIgokvwIIYQQIqL8fyUiaUrD7J+vAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Our inital and final angles in radians\n",
    "theta0 = np.deg2rad(15)\n",
    "thetaf = np.deg2rad(120)\n",
    "\n",
    "# The start and finish time\n",
    "t0 = 0.0\n",
    "tf = 1.0\n",
    "\n",
    "# A vector for time\n",
    "# Steps from t0 to tf in 50 steps\n",
    "t = np.linspace(t0, tf, 50)\n",
    "\n",
    "# Create the trajectory/interpolate between the two angles\n",
    "traj6 = rtb.quintic(theta0, thetaf, t)\n",
    "\n",
    "# Plot the trajectory\n",
    "traj6.plot()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"600\"\n",
       "            height=\"400\"\n",
       "            src=\"http://localhost:52004/?53004\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            \n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.IFrame at 0x2b202bee0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Animate the trajectory\n",
    "env = Swift()\n",
    "env.launch(browser='notebook', realtime=True)\n",
    "obj = sg.Arrow(0.2, 0.005, 0.2, 0.2, color=\"#fc0349\")\n",
    "env.add(obj)\n",
    "\n",
    "env.set_camera_pose([0.0, 0.0, 0.5], [0.0, 0.0, 0.0])\n",
    "\n",
    "for q in traj6.q:\n",
    "    # Note that the sm.SE3.Rx(np.pi / 2) * sm.SE3.Ry(np.pi / 2) below is to\n",
    "    # get the arrow in the xy plane\n",
    "    obj.T = sm.SE3.Rx(np.pi / 2) * sm.SE3.Ry(np.pi / 2) * sm.SE3.Ry(q)\n",
    "    env.step(0.02)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test your Understanding\n",
    "\n",
    "#### Question 1\n",
    "\n",
    "Convert the trajectory calculated in `traj6` above to a list of $\\mathbf{SO}(2)$ objects using the `spatialmath` class `SO2`.\n",
    "\n",
    "#### Question 2\n",
    "\n",
    "Plot the interpolated coordinate frames from Question 1 using `SO2` plot methods.\n",
    "\n",
    "#### Question 3\n",
    "\n",
    "For interpolating orientations, would you prefer to use a polynomial or trapezoidal trajectory? Why?\n",
    "\n",
    "#### Question 4\n",
    "\n",
    "What are some other robotics applications for trajectories?"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 Multi-Axis Trajectory"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Most useful robots have more than one axis of motion and it is quite straightforward to extend the smooth scalar trajectory to the vector case. In terms\n",
    "of configuration space, these axes of motion correspond to the dimensions of the robot's configuration space -- to its degrees of\n",
    "freedom. We represent the robot's configuration as a vector $\\mathbf{q}\\in\t{\\mathbb{R}}^{n}$ where $n$ is the number of degrees of freedom. The configuration of a 3-joint\n",
    "robot would be its joint coordinates $\\mathbf{q}=(q_{0}, q_{1}, q_{2})$. The configuration vector of wheeled mobile robot might be its position $\\mathbf{q}=(x, \\ y$) or its position and heading angle $\\mathbf{q}=(x,y,\\theta)$. For a 3-dimensional body that had an orientation in $\\mathbf{SO}(3)$ we\n",
    "would use roll-pitch-yaw angles $\\mathbf{q}=(\\alpha, \\beta, \\gamma)$, or for a pose in $\\mathbf{SE}(3)$ we would use\n",
    "$\\mathbf{q}=(x,y,z, \\alpha, \\beta, \\gamma)$. \n",
    "\n",
    "_For orientation, any 3-parameter representation could be used: roll-pitch-yaw angles, Euler angles or exponential coordinates._\n",
    "\n",
    "In all these cases, we would require smooth multi-dimensional motion from an initial configuration vector to a final configuration vector.\n",
    "\n",
    "Consider a 2-axis $xy$-type robot moving from configuration $(0,2)$ to $(1, -1)$ in 50 steps with a trapezoidal profile. \n",
    "\n",
    "Using the Toolbox, this is achieved using the function `mtraj` and we write"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
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tYpI4BcmmTZvIy8tj6dKlNDU10djYGO4miYvYbLZwN6FLmpwRxfDvZ1BS66B3nJHkaCMNDQ2e61Oj4LJkE29ddDuXgg17S7huYDxZ8SavKb3yBgfFtQ76xDlIjpbDkJ7I5yQEKsvRzhajUvtAYrLfEMMXH2Pc+CqRSqE0jcZbFuCacE2Lcdq5OEcLcVSWE7luJVpzYqwUrnWraMoaALFx0NSI1tQE5SWYfOJW4igrRTNFgr0JHHaoriJ656c0XH8ztrQM0DRUcZH7vi5cW8npRGuo92mOqqyEiIhzsRq4nGh1tb5x9fUoU6TnPjW7Ha3K6hPnamyCKLP7D02DJhuG8rO+cXYnREWhNdqIqirHYWvA6LOmeevkiBUk8+bNY86cOQBERkZiaM6QRdgppbDZbJjNZr+LpYm2ZUVDlqXl6/ulGNEo9ZnSuzwjns9ONVJYVU1WQiTfy4yjuLaJV3aWeqb07ruyN7MGJnbuExBtks9JywIe0QkgLpDRHFVRhtr46rnRGNCUwvTG72HoSDRzDNjqwdaAOlsMF8f96VUoOOr+ANps0HTuR3xttSeumaZcRL3535DSG6KiIDIKqiv9xClM0dFo/YZAZCSYIlGFx+HLj4n9+/94xy5+Fm3o+S1OVEUZ6vG7ve/TYEBb8qrXa9SuuN/8IrC4ZY+3ETfUHffun2mPLp84NTU1oWkaJlN4C1FNJpOnDZqmyYFHh6RfOk9qbKTfs/Sm9U9kWn/3l/KpaveU3l++Of9rUQEv7yhhXEacFJPrRE/6nARSx+Pa+oFXosP8+zFMubZdccrhgIZ61JnC8zEASqHWrUSdPokGUF+HstX7TV5wueCNP0CfDDBHQ1S0/zgU2mWXow0f446JdJ/AoaxluB6/yyeRMNz5iNdzV9YyXF984hs3fpp3XGw8Lk3zTUzSMrzeP5olFdf8+1Gvr3I/B4MB7Wf3+Uw9hjuOLz4iUF0ucfrmm2/YuXMn3333HadOnaKpqQmAqKgoMjMzGTp0KN/73vcYMWJEmFsqRM/S1ll62b2iGNMn1itxAveU3v/sP8ucoRb6JkbJWXqiwy4lIdL8JETKWuYn0VmFKyEJLSICVVcD9bWoslL4YNMFN1SotStw7tjqHqExRKDFxKJsDb6JjlJoGTlow0ZDdCxadDRUV/lPcu540DfJ+eT/fJOXwSPQEhK9HkazpKD5SSQufn2CHQdgmHItasQ4OHsGUtNb7JNwxhlyJ/m9zh9NdYFKQIfDwYcffsjf//53zp49S1xcHP379yctLY24uDiUUtTV1VFaWsrx48epra0lJSWFOXPmMHPmTIzGS88Pn3nmGU6cOEFjYyNxcXEsWrSIIUNaLyIrLS3F4fC/Q7QIPaUUDQ0NREdH95hf0nrV0kafiyelc7jMxsnKRtLjIxmfFUdJrZ1XdspZeqHSFT4nwUqIXOWlqCcWeCccmgbfvxFNOaG2GlVX6x7ROfad74NMnIHWdyDExqPFxqHOlqA2rPYJM/zLf3hPW7U06rPk9z7Px7X1A9/RkpZGugKIu7ANbSUSnRGndyaTidQAlyPoEonTfffdh8PhYNq0aUyYMIEBAwa0Gn/s2DG++OILPvvsM4xGIytXrgxRS90kcdKXrvCF0JNszq/0mdK7MCE6Xd3Ep8er2Hig3Ot2Bg1evWGgjDx1knB9TgI97b21hEgp5Z7mKjyOeuHffEd1Rl1x/swscNf7HD3k8xjajxegXXa5+8ywmDioqggo0emMhAjcZ9U1Fp4gKrtf62fVdZPkJZy6XeK0efNmrr76ak8NkVIqoA+2w+Hgk08+8exXEyqSOOmLJE76c7auiZNltfRNiSM1NtLn+v3FdTz1UaHP5TMGJDB7qIX+STKlF2zB/px0dHSoORmiusKdEP3+ed+EaPjl7qkwQIuOda8ptGubz+NoD/0Sw8hxXm0L58hPwKM5cuwKmW6XOF3stdde4/bbbw93M1okiZO+yMFHf9rqk5am9B6dnMGRchvHKhrpHWtifFYcZ+tkSi8YAv2cdDghcjqhuhJVeAy14tnWk6GYWEhIQjU2wJZ3fR4nFFNhnucchmkrOXaFTnsSpy5XHA7w/vvvk52dzTXX+Fmr4pxDhw4xbNiwELZKCBEsLe2lNzEngYk57gX2ztS4p/T+5+vzU3qyl96lUxVlaIUnUNn90FqYFmo1IXI4zo8OXVxQ3VwoHRUFmgEtIdE9OuTnd7vhBz/ySobgXEL06Xs+CRGp6V5xnVGw3Hy/BJAIBRonurYumTjdeeedrFmzhvT0dIYPH+5z/Xvvvce6detYv359GFonhAiG1s7SA0iPj+SytBjAuxbKpeD1vWeZPdTCAEsUhh4+pdeeEaLmxRZdXgmRHarOjRC1lBBFRkJEhDshsreQEM2+2Xd06IuP20yGIPwJkRAX6pKJ08yZMzl58iTPPfccS5YsIS0tDXDXNL366qts2bKFa69t+awCIUTXcKl76V2VHccXhTW8vu8sqbFGrsiMw1rv6FZTeh2eMrPb3SNEBQEkRL2SUE1NQU2I2pMMgSREQj+6ZI0TgMvl4tlnn6Wqqopnn32WhoYGnnvuOQoKCrj77ru5+uqrw9Y2qXHSF6kT0J9g9klbZ+mV1Dax5Xg1G/aXed1Or2fpBSUhqrK6p8xeXuKb7Awb406IjEa0hCSUvQk+/9DnMfRWP9QTybErdLpdcfg777xDdnY2OTk59Op1fmfj2tpannjiCRITEykpKcFkMrF48eI2lyvobJI46YscfPQn2H1SVm9vcUoPWj5L7+p+CfxgaBKDks2dPqXX8YSoCSrPJUSrf91KQmQ6N0LUKAlRFyfHrtDpdsXhr732muffCQkJZGVlkZOTQ3Z2NnPnzuUPf/gDw4cP5+GHHyY+Pj6MLRVChMOlTulN7BvPztO1bNhfRnLM+Sm9V3cFNqUXlDWILkyI/E2Z7dx2foSol8WdEAU6Zbb9I90XVAvR1XSJESebzUZhYSEFBQVe/9XWnt9JOTU1lX79+pGTk+NJqjIzM8PSXhlx0hf51aY/4eiTtqb0ztbZ2XK8itf3BTal19YK1aqpEaoq2h4hMpnQEpPd8Vs/8Gl3qEaIAl1sUYSOHLtCp9uNOJnNZgYPHszgwYO9Lq+srOTkyZNeydTevXux2+0AbNy4MRzNFULo0KxBiVwe3ciZolLSM9JIzUz0uj411sTQlGif27kUvLbnLD8YksTgZDMGexOq4Chq3UrKIhM4E51CekMZKRcWVIN3QhToCNG2zeEbIUpKQZnP7ZUmhGhRl0icWpKYmEhiYiJjxozxXOZyuSguLqagoCCMLRNChFKg9UOWdSuxnBshcl08QtRoo0/5CTSlobTz23MYlIvJu/+XvG/T+J+IZJK0JnKbzlCZfhVrBs9FaQY05eLn373JrB/MxTBstE/bwpoQyZSZEEHVJabquhqZqtMXGe7Wn1CtUg2gbA2ok0dRz//Cz3TZaIiMAkCLMqOcTj4ssrN66I24NAMG5eLe795k1k/PJ0Tl9XY++eYM676rc28Me45Bufjd9GRSM3v7b6POi6rlc6I/0ieh0+2m6oQQ3UtHV6kGULZ6d0Lkdw2iz3wSIn/TZdoPbvYaIVLWMmY+fheXVxymODqZPg3lpNhr0NJ+7olJjjExJDsZDtd7t1cz8NpxB9eb6hmWEk2E4YKkasq1nB0whjNFZ0nPSPWbXHnaJCNEQuhal0icHnnkEW644QYmTZqE0RhYk+12O9u2bePtt9/mN7/5TSe3UAgBQVilWiloHiFqbVFGQDNHo5yOFuqHbvGtH9rzhc90mZaW4XW75umylNdXkdJY1eJ0WUtn6V3Tvxdfl9TzlwPlJJgjuCIjjnEZsWwvqGHlVxUojGiHK7j/yqguvfimED1Zl0icrr76atauXcsf//hHcnNzGT16NP379yctLY2oKPevSpvNRmlpKceOHWP//v3k5eVhNBr54Q9/GObWC9H1BWWn+4ATohiUq6WEyE9B9W7fhKiz64da2ktvXGYc4zLjALA2OMg7XcsLnxexq6jufJuR/fSE6Mq6TI1TQ0MDH3/8MVu2bPEq/I6IiADA6XR6LsvOzmb69OlMnz6dmJiYkLdVapz0ReoEWhaUhKihzr1txwtPtXzKPc0JkRN2bfN5jK66KGNbC29Cy4tv3jUujR8MTfKa0mu+z3DspyefE/2RPgmdbrdy+MVKS0v57rvvKCoqoqamBoD4+HgyMzMZMmSIZ++6cLZPEif96GkHn6AsyqgU1Ne5T7v/zb+3nhBFx7hriLpRQhRMZfV27t501GtaTwNuGJ5EQVUTcZER5GbEMi4jji8La1j5VXFY9tPraZ+TrkD6JHS6feKkd5I46Ut3OfgE5QwzpaC+1j1ltvzp1hOimFiUwwm7tvo8jiRE7dPa4puVDQ7yimrZXlDjNaUHod1Pr7t8TroT6ZPQ6fZn1S1evNizd13zKuG9e7d8looQehaUhMjlRJ064ad+aCXO3V+4637O0WLjUI521BDlbQt6DZFrxNiAVqnuLmeYzRqUyNiMWL/TeonRRmYMTCQ11uSTOLkUfH6ymh8MtWDUyZSeED1dl0ycsrOzOXr0KF988YXnsqioKDIzMz2JVHNSlZiYGL6Gim4p0KmwDtcPuVzu0aHW9jAznfvCNBjA7yn3Cm3mHAwjxvm0zbUr+AmRrFLdskvZT0/ToNLm5D8/PUWMyUBuRhy5mXF8FcYpPSF6ui6ZOE2aNIk9e/Ywa9Yshg0bhs1mo6ioiK1bt3Ls2DGv2Li4OE8ideedd4apxaIrCMbIT2tx2uRZ0GiDmiqorUYVFbZ+hpmmocXEoex2/2sQXX8jhuHnV81vabpMS8/xva2sUq07LZ2p15wQVdsc7Cqq46UvithxWs7SEyJcumTitGHDBqZPn84dd9zhdfmPf/xjNm7cyIEDB7jlllsoLi7m9OnTnDp1ii+++EISp24m4JGfICy22Px4PonOulW4klPRNAPU1aBqq1FnS+CDTRfc0J0QqZ3b0OLiIb4XxCegams7NF2m9fbexLo9yRBIQqRHrU3pJZiNXDOgFykxRq/ECdxTeltPVDN7qAVThEzpCdGZumTiVFpaSk6O76/oyMhI5s+fz9KlS/nuu+/4yU9+EobWCX+COb0F7R/58bfYIriLL1XxKT8J0UqcZSVoygV1tai6Gqgo9010lAu1/WPoOwhi49GS09y399Nmww9+5JsQffy3sE2XNd+3JET6cilTegYNapuc/PqzU5jPTemNy4hl56lamdITIsi6ZOKUmZnJ3r17ueaaa/xen5uby5tvvimJkx/BTmA6e3rLX1yLIz9JyWimSPe6Qg0NqPIS+N8NF9zwgtqg5h3swT195pMQKbT4XmjDx0BsHFpMHNTW+D9z7B9v937u1jLU//wufPVDkgx1a21N6dU0OskrqmXVV8V8darWczuZ0hMiOLpk4jR37lx++9vf8uc//5l58+b5bMNy+vRpGhoagvZ4eXl5rF27FqUUc+fOZcaMGa3Gq+pKiIlrPaYbJDAdmt7KzEEzx7iTFlsDqrzU/xlh332NphTqwuSmrsb/yM9Xn0F2P4iORYuOAWNk4CM//mqDxk30fi0tUQElOpIQic7W2pRefFQEV/fvhSXa6JU4gXtK77PjVcweZiEywuB1XVm9nRNlNvqlGEmNjUQI4V+XTJwmTZpERUUFGzZsYPPmzUybNo2+ffsC8N133/Hhhx8yduzYoDyW0+lk7dq1PP3008TExPDYY48xfvx44uPjW7yNeun/4Zo4s8W1aXSTwLy+Cteg4WhxCWC3g8PuP4FZtxKnvQktMsodZ290J4fv+9bx+Izm1Fb7T3LefQv6ZEKUGcxmd+Ln74ywsVehjRiLFmlGO3dKfYtrBs2b7zvy89ZrYRn5kYRIdLZLndKzORT/tfU0kREGxmXEkpsRx67TF07plcqUnhCt6JKJE8Ds2bMZPXo0mzZt4v3336exsdFz3ejRo1m4cGFQHic/P5+srCwsFgsAY8eOZd++fUyePNkrzm6343A4iI6OPp9slBahRce6v7jPfXmrhno/hcMrcRYchaho9xe3ckF9HWz/6KK4FTj37wKjEVxOcLrcIzaH9vnGXbD3F+A/gXG5UBteQVlS3ae1G01QVel32oqqSug7AExRYIqEopP+X7Drb/Tebb6iDPX43b6jOT9ZgJZ0QbJQUYb68G3fJKf/EPfrwrnFGwGSkv0mOiQl47Wea6Bx4D7jbcRYKD0Daenu0+VbWhs2Kdn934Vt6khcD9T8esjr0nmSo43cd2VvXt5R4pnS+/n43swamAi4a6L2FNWxekcxX/qZ0rs8PUam9MJMPieh057XuMsmTgA5OTk89NBDOBwOSkpKaGxsJCUlhYSEhKA9RkVFhSdpArBYLFitVp+4TZs2kZeXx9KlS90XKIU9NgGV3R/Q3AuyAFrhcXwPRQp7el9Uv8GgaSiDAe1kPpEXJk7nNI2fiho8AgwR7kTg6LdEXpg4NcfN/KE7rlllOZG//Ge0C94cSjPQ9JOFkJjsHZe3zTfuymnecQmJRGqab1wvC1w4TWqOxXDLAowbf4+mXCjNgOPmu3GZYy8trlnuZBg4HO1sMSq1j7ttHYk71wZyBrn/HcSpXtEym80W7iZ0a5Mzohj+/QxKah30jjOSHG30lDFEAFf0NhFtiPFKnMA9pbf5cDn/MCjeZ0qvvMFBca2DPufuT3Q++Zx0PpfLFXBst3jXG41GMjMz2w7sRPPmzWPOnDnnLzAYiBw/xXtUBVB9MlBv/rfPyErk5d/zilXx8ShN84mLGjgUrVfi+bjsfv7jsvt5Ly4YnYW6aPTF8LP7iE7P8n4iwY4DuOYHqLFXQukZtLR0opJamJYKNO6CNuDv8S6izJnYEpMxm82ybYFOKKWw2WzSJyGQFQ1Zlpav75diRKPUZ0pPMxhZmVdJhAHGpsdyRUYceWdqWfVViecsvfuuPD+CJYJPPiehYzIFPrraLRKnzpSUlOQ1wmS1Whk0aJBPnMlkOv/CN++/5WfNIM2SisvP9NHFscGOA9ACrLsJdlxzO2lla432xl0KTdPk4KMz0ifhlxob2epZenVNTvaeqePVvBK+KPSe0nt5RwnjMuJkSq+Tyeek87Xn9ZXEqQ2DBg2isLAQq9VKTEwMe/bs4cYbb2z1Nto/P4WhlbPqgl1g3BmFyMGOE0Lo16xBiVyeHsPJslr6psR5nVUXGxnBpL4JxEdFeCVO4J7S+/hYFXOHWYgy+p6lJwtviu5IEqc2REREcNttt/GrX/0Kl8vF3LlzWz2jDkBLSASHo/UYSWCEEDqSEmMiNtVMdLT/JKels/RcSvH850VoGlzeJ5bvZcWxp6hOFt4U3ZampFw/6EpLS3G0kTiJ0FFK0dDQQHR0tAx364T0if4E0ieb8ytbnNKrtzvZd6aerSer+bygxut2Bg1evWGgjDy1k3xOQsdkMpGaGliZiIw4CSGECEhrC2/GmCKYkBNPbKTBJ3FyKfjwqHtKL9okU3qia5PESQghRMAudeHNCA2Wf1GEUjCmTyxXZMayv7hepvRElyOJkxBCiKBpay89m8PF/uI61u8r49MT1Z7byV56oquQxEkIIURQtTalZzYaGJ8Vj9lo8EqcwD2l9/dDVuYMs5DsJ3mSaT2hB5I4CSGECLpLndJLjY3k9X1nsTY4GZAURW5GHMNSo/nkWJVM6wldkMRJCCFEyLU+pZeESylOVDSSV1TLxq/Psr/k/DZIMq0nwkkSJyGEEGHR2pSeQdMYYDEzwGJmaEo0+0sKvW7rUrD5SCU/GGYhISrC6zqZ0hOdSRInIYQQYdPWlB60PK1nNhp4dVcJtY1O+iVFMaaPOwl7ZWeJTOmJTiOJkxBCCF1r60w9l1KcrGxke0E1bxw4v7doW1N6MjIlLoUkTkIIIXSvrWm9/klmahqdXokTuKf0/mvracamxzKydwxDkqOJMhrYnF8pxebikkjiJIQQoku41DP1Fk/KoNLm5EBJPX87VEGD3dmuYnMZmRIXksRJCCFEt9DSlF7vuEh6x8HQlGgA9p6p81ts/v6RSq4dlEhq7PnkSEamxMUkcRJCCNFttDal1yyrl/+RqViTgTcOlFFW5yAuMoLMXib+tL/cEyfLIAiQxEkIIUQ309aUXlvF5gC1jU7eO1LhlVyBe2Tq29IGJvc1omma13UypdczSOIkhBCix2lrZCouKoKrB/Ti9X1lXsmTBuw8Xcsnx6swRWgMTDIzKNnM6eom1uSVypReDyCJkxBCiB6poyNTjQ4Xxysa2Xumlv/5utxzOwWs/KqYwclm+iWZfe5XRqa6NkmchBBCiBa0NjIVZTQwLDWaJqcLKPe6nQL+sLsUo0EjMkKjX6KZ/pYoTlc1sXbv2YBGpsrq7Zwos9EvxUhqbGRnPUXRTpI4CSGEEK241GUQHpyQTkqMiUaHi5OVjewvqWPd3jJPTPPIVC9zBKP7xGI2GjzXeZ/NVypTfzoiiZMQQgjRAS1N6TUnW1FGA0NSorE5XD63VcAXhTVsOV5No8OFKULDEm3kncOVAZ/NJ1N/oSWJkxBCCNFBgSyD0NLI1E/HpHrim5wuPjlW5fdsvj/uLmVseixZvaLITIgkLjKi3etMSZLVcZI4CSGEEEFwqcXmF94mMsJAbmYcGiU+CdbMgYnU2Z3sO1PHO99VUGGzs6/YewX0lTuKGZEWTUZClM/jtyfJkgSrZZI4CSGEECESyMhUSwnW5emxXnH7i+vYV+y9ArpS7rqpaJMBpSDBbCQ93kSsKYJXd5UENP0nq6W3ThInIYQQIoTaGpkCd4J1eXoMJ8tq6ZsS5/esupam/h6ZlEFKjAmlFNWNTopr7ew4VeN3+m/1V8UMS40hJdZIWqyJCIPmSZogePVV3WkESxInIYQQQodSYkzEppqJjvafaLQ19adpGr3MRnqZjSTHGHnzG6tPknXz6BScLsXZOgffnm3g0Nl6vwnWn/aXcVlaDJZoo+e/7YXVrPqqpM2Rqc6YIgxnIiaJUyt+//vf89VXX5GcnMyvf/3rcDdHCCGE8BLI1B+0nGQNSXZvfDw81R1XVp/Azk1HfRKsKzJicQKFVY3sK66jqKaJLwtrPTEKWPFVMflWG+nxJhKijPSKisCFCngEK9AEqzMSsUqbg9QWr/UmiVMrJk+ezDXXXMPvfve7cDdFCCGE8CuQqT/oWH3VVTkJXnH7i+u8EqdmQ5LNpMWZqLY5Kamzc6Sswe8I1n9tPU0vsxGz0UCsyYBBw2cJhpVfFWOJNtInPhKzUcNsNFDb5OyUROzD47Wsuz29zdcQJHFq1bBhwygtLQ0o1m6343A4iI6ORimFUhe/VUS4NPeF9Il+SJ/oj/SJ/nRGnyRHG0mONrZ6vzMH9uLy9BjO1NhJjzd56qUulB5v8ltfNbpPjFcC873MWD45Xu0T9+jkDJKjjdgcitomJ3vP1PkkWArYeqKaBHMENocLm0NRUtvUYiKWEBXhuczuVOwtrve6rxVfFXOgpJ6YSAMGTcMA2BwuPjhaxdC0uNZeNi+SOAXJpk2byMvLY+nSpTQ1NdHY2BjuJomL2Gy2cDdBXET6RH+kT/QnHH0Sq8GgBA1w0NDg8Hv9grEWfr/X6hmZuvtyC7Gad3xrcTabOy7OAMMtEX4TsRuHxXkSPYDyBgcPvFfkE/fAFRavuK9LG7wSp2ajU00MSorChTtxPFze/u/qHp84Pfroo7hcvqu5/uIXv8BisQR8P/PmzWPOnDkAREZGYjAY2riFCBWlFDabDbPZjKZp4W6OQPpEj6RP9EfvffIPw6MZ3zfRa2TqUuOyouG+K3vz8o4ST4L18/G9ybLEX1LcgFQjGmd9R8Qye3k9fnysHW23tV3Pu8cnTsuWLQvK/ZhMJkym82cy6PFN3tNJv+iP9In+SJ/oj577JDU2MqANiAOJu3ZQEuMy4tosdA8kLjU20m+t1sVtaI776IRvvVZLenziJIQQQgh9CLTQPdC1sAI543DWoEQm9k8KuI2akkrAFq1cuZJ9+/ZRU1NDr169uP3225kwYUKbt7NarTidzhC0UARCKUVjYyNRUVG6/dXW00if6I/0if5In4SO0WgkKSmw5EkSpyCy2+2e6TohhBBCdD9SwRxEdrudF198kYaGhraDRcg0NDTw2GOPSb/oiPSJ/kif6I/0iT5J4hREJpOJ9PR0jEYpHdMTo9FIbm6u9IuOSJ/oj/SJ/kif6JNM1QkhhBBCBEhGnIQQQgghAiSJkxBCCCFEgCRxEkIIIYQIkCROQgghhBABklL9IMrLy2Pt2rUopZg7dy4zZswId5N6pGXLlnHw4EFGjhzJ4sWLAcjPz2fVqlXY7XamTZvGTTfdFOZW9hxlZWWsWLGCqqoqIiIiuPHGG5kwYQLFxcUsX76curo6Ro0axYIFC2SRvxCqq6vjmWeewel04nK5uP7665k5c6Z8VnSgsbGRRx55hKuuuorbbrtN+kRvlAgKh8OhHnzwQVVeXq4aGhrUgw8+qKqrq8PdrB7pwIEDaufOneq5557zXPb444+rEydOKKfTqZ588kl18uTJMLawZ7Farer48eNKKaUqKirUPffcoxoaGtRzzz2ndu3apZRSXv8WoeF0OpXNZlNKKdXQ0KDuu+8+VV1dLZ8VHdiwYYN64YUX1GuvvaaUkuOX3shUXZDk5+eTlZWFxWLBbDYzduxY9u3bF+5m9UgjRowgOjra83fzFjh9+/bFYDAwceJE8vLywtjCniUpKYl+/foBkJiYSEJCArW1tRw+fJhx48YBMGXKFOmTEDMYDERFRQHgcDgA90iHfFbC68yZM5w+fZqxY8cCcvzSI0mcgqSiogKLxeL522KxYLVaw9gi0Uz6Rj+OHTuGy+UiMjKSuLg4z9Sc9El41NXV8eijj3LvvfcyZ84cqqqq5LMSZuvWrePWW2/1/C3HL/2RxEkIERK1tbWsWLGCe+65J9xNEefExsaybNkyVqxYweeff47L5Qp3k3q0nTt3kp6eTkZGRribIlohxeFBkpSU5PUrwGq1MmjQoDC2SDTz1zeB7oItgsNut7Ns2TJuuOEGhg4dilKK2tpalFJomiZ9EmaJiYn07duXoqIi+ayE0ZEjR9i+fTtffvklNpsNh8NBTEyM9InOyIhTkAwaNIjCwkKsVis2m409e/YwZsyYcDdL4B7aNhgMnDx5EpfLxfbt27niiivC3aweQynFypUrGTFiBFOnTgVA0zQGDx7M7t27Adi2bRu5ubnhbGaPU1lZ6dk8tr6+nm+//Zb+/fvLZyWMbr31Vl5++WVWrlzJ/PnzmTFjBjfddJP0ic7IXnVBtGvXLtatW4fL5WLu3LnMnDkz3E3qkZ555hlOnDhBY2MjcXFxLFq0CIDVq1djt9uZMmUKN998c5hb2XMcOnSIp59+mpycHM9lDzzwACaTieXLl1NfX8/IkSNZsGABBoP8lguV/Px8XnnlFcCd3H7/+99n1qxZHD58WD4rOrBlyxYKCgq47bbbpE90RhInIYQQQogAyc87IYQQQogASeIkhBBCCBEgSZyEEEIIIQIkiZMQQgghRIAkcRJCCCGECJAkTkIIIYQQAZKVwztB86aMQh+UUjQ2NhIVFeXZG024qapKsJ4FSypar8SQxbmqKmgqKSKydwaGXi2vghyu9gU7riu0MVx9Ilomx67QMRqNAa/ILolTJ3A4HJ7dxkX4NR98DAZDjzj4KGsZlBZBWgaaJaXFONfWD1DrVoJSoGlo8+/HMOXakMY1helxQxnXFdoYrj6BwN+vPVFPO3Z1FTJVJ0QXoaxlqEP73V80LXBt/QDX43fhev7f3P/f+kHL99X8xQagFOr1VT73LXEdi+sKbQznaxPo+9Xrvtv4DAjR2WTl8E5QWloqI046opSioaGB6OjoLvurLZBf8K7yUtQTC85/YQFoGky5Fg0NbA2oRvfeZNRWw9FDvg80cBjEJZz/W+I6FtcV2hjKuPhENLMZoswogE/f847RDGi/fhWDJdXn5u0ZxeouusOxq6swmUykpvq+7/yRqTohwqytqQq/v+DXrcTZaEOrrYaSIlSjDepqvJOmc7HaoOFow8eAORot0oxmMKCsZbgev8s73mDAcM+/erVB4joW1xXaGMo4EpPAZgNbA3y7D3Vx4qRcqNVLccYloMXEQu9M6J0B0bH+R7FGjGvxMyPTf6KzyFSdEJ2kI1Nryt6EOl2A2r0d19//5Dchoq4GbdwEtNsfIOLBf8ew8DH3CNOFDAa0oaPREpPRzDFo5zbR1SwpaPPvh+ZNdQ0GtJ/d5/MlI3Edi+sKbQxlnGaIQIuJdf97+Bi/71fDvY8T8eC/o926EG3kOHA5UTs+9f0MuFyoLz5BFZ9GXTDC357pP5n6E5dCpuo6gUzV6Us4hrsveWoNYNhoiIlFS013/9qOjUet/rXvL/glv/f50nJt/QD1+ipwuTxfWK1NZyhrGZw9A6nprf4yD3acy3qWxsITRGX38zstE+72BTuuK7QxHH0S6PvV7yiWpsENP0OrqUaVFYPT6f7v4B7vG7f2WdH51J9M1YVOe6bqJHHqBJI46UuwDz6BTK35PcjfdAdabTWq5AzYm9xTa8e+87m94V/+A23oKK/L2pMQtefLPFzkC0F/wtUnASd2AXwGXN/sRi3/pe+N+w9BS+nt/iHSO9M99bfy2YB+jHjaGIapP/mchI7UOAnRSVr6laoaG+FsERSfxnVgt/9aI5sNbfw0tNR0tKioFmtBSE33eVzDlGtRI8YF9AWjWVJApwmTEBcL9P0ayGdAS89BaZpvQnTv4xAT464HLD6Nyvu8ham/j2DcREjpg2YyuS/uAiNTIrQkcRLinLZ+VbrKS3wLVNeuwLnjM4iNQ0vLgD6ZaGPGo7Z/5HPw1ibP8rrf5lqQi39Ft5QUSUIkerq2PgNtfqb6DkLrOwg1eASuLz/xGRVWBiNs+xB19ox72s9hh4N7z8dIUbpAEifRA6iKMrTCE6jsfmgt1G74/Kq8dp57WL+kyH0Qtduhvtb3VypgmH2L79RagAlRe0aShBBtC2hkqoUEy2fq7+Be1IWJE4DLheuVpe5jSVoG9M5A65OJOn4YtfH3AY1MSYLVtUmNUyeQGif9aHFqzdYApUWokiLUiSPwwV+9b6hp7mRn4HBI64Nmimz5NOvW6iIkIfJLajf0pyf2SVuf0dY+88TGuX9YlRShThxu4Rjy83PHkHQ0UyTQzlXVe2CfhIvUOIkeoc2ptbPFLU6taXEJnkJRLaU3Pr8elELrnYGWmeO5SKbWhOheOjz1lzMALWcAKj4B18WJk1Ko0jNwtsT9f3sTOBzw7V7vmNam/gIYLRehJ4mT0JVL3mft2hsgLd39C7C0GJyOgKfWlLUM9T+/C3qRthCi6wvoM5+W4T5z9uKRqWvmeMW7vt2LujBxAvfU3+pfQ1IKWu9094+53hmo4/moP68hUimUpuGSqT/dkMRJ6EZrQ9iqvs49tVZ8GnUiHz56+/wNlUJ98Fe02/4ZbfK1aKm90YymgM9ak5EkIURrOjwy1RzXO6vls/7i4qH0DJQU4dq3A95763zMud0CXE4n2sBh7qm/KDMgZ/2FgyROIiQuaVuR5jPWTJFo0THnp9bSM/1PraX2QUvP8lzUnoRIRpKEEB3RkaJ0T2xWP8jqhyE2DteFiRO4j4nlpVBR5k6umhrdJ60c2ucd08rUH8joVDBI4iQ6JJAPoc8von+8Ha3vQFTJaffUWlkJVFX4nVbTfnAzhmGjfR5TaasDnlpzjRgb0IrIMpIkhOiIQI4hHZr6m/6Di6b+9qEuTJzggqm/ZLTUPuem/jKhTwZq387AC9MlwWqRJE7ikrU+tVbrXgzy2Hew8ffnb6QU6s0/omb/GEP/wXDZ5WjJvaGqwu+0mpaW4fO47Z5aS0pBmWPRoqOD+vyFEOJSBG/qL7Plqb/4Xu7krKQIdewQass7sHPr+bjm6b/EZLTBl6GZzx8fZfqvdbIcQSfoDssRXNK2IuDeZy0y6tzO5hkopxP+vtHn9h3dVsTTxkD2zJJTenVH+kR/pE/0J5D9AwPe7+/QflzP/5vvHVw1Hc3pcC/RAhATC199BrRj2ZVuMDIlyxGIFl3a1NptaNkDzk+tlZdCdWVAU2vKWobr/97olDPWZGpNCNGdBTJaHvBxs6Xpv3nzPbdRSqF2fY766lPv27pcuH63DG3AEPfUX59M9w/jr/N65NSfJE49SIuLQSoFtTVQcm5q7c9/OH8jpVBvvob64U8w9B8Co65AS06FysCm1uSMNSGE6FyBHDcDORZrmgYDh/md/tPuegTN6XD/eD6Rj/rsfdjx2fmY5qm/hCT31F9MrOeq7jb1J1N1nSAcU3UdmlozRZ5fENLpQP3tTz637+jUWjhX0ZYpCP2RPtEf6RP96Yw+CeRYHMixvcWpvwnXuKf+Gurdf5ujYec29D71J1N13cglTa3Nm4+W1f/81FpFWYtTa34Xg/z7xqBPrclIkhBChF+nn/l3w8+8p/52f4G6sCgdzk/99RvkPfV3YLc7YdP51J8kTjrW6tRaTZV7LY+jh+DNP56/kVKot9ahbrjVPbU29iq0pBSotMpikEIIIQISjDP/NE2D/kP8T/3dvQjN5XT/uD99ArX9I/hyy/mY5qm/+F5og0egxcZ5rgr31J9M1XWCQKbqOjy1lpAIvTPBYUe9vcHn9l15ai3YZApCf6RP9Ef6RH+6Qp90+tTfpJnuqb+6WvffUVGwazvBnvqTqTo/8vLyWLt2LUop5s6dy4wZM7yuz8/PZ9WqVdjtdqZNm8ZNN90EQHFxMcuXL6euro5Ro0axYMGCNt/AFWfLiU/q1eL1Ptny3J+hZfdDFV8wtVZbHfjU2t/+R6bWhBBChFynT/398Fbvqb89X6B2fe59W5cL1+/+Cy1nIPQ5t+Bn7wzUwb0BT/1VlJYHnDgZAorq4pxOJ2vXruXpp5/mv/7rv3j77bepqanxilmzZg0PPfQQL774Inv27KGgoACA9evX86Mf/YiXXnqJmpoadu/e3ebjPburmg/ePd+xSilUZTnqu69xvvsX1NoV3luL/PV1XKeOo2X3d5/O/8//5l7A7OIErZWpNQwGT0xbU2va0FFdfhRJCCFE19HWd08g32WapqH1G+L3u1FbsBht1ly0tHRU8Slcb2/w3cZr3Upcu79A1VRz4WTbB+9+zjO7qgJ+Lj1ixCk/P5+srCwsFgsAY8eOZd++fUyePBkAq9WK0+mkb9++AEycOJG8vDyys7M5fPgwixYtAmDKlCnk5eWRm5vr8xh2ux2Hw0F0dDQKjZfLkxiz8nlSnHXugF5J7gI4p78pPIU2YBhcOLWWlOx3/pikZC6eXdUmz4IRY90bRKalu9f+kBlYj+bXQl4T/ZA+0R/pE/3paX0S0HdZC9+NmiXNfX1Kb7QR4+DQftQXn3jfVinU17tQe79yz+oAZZHxrIr7PkN6Bz4V2iMSp4qKCk/SBGCxWLBara1ef/DgQWpqaoiLi/NMzV18uwtt2rSJvLw8li5dCoBLM1AwYjLx473rjKgsJ/Lt/0G74M2gNAONCUnQ0OAdmzsZBg5HO1uMSu0Dicm+Mc3MsZAzyP3vlmJ6OJvNFu4miItIn+iP9In+9Kg+CeS7LJDvxl4WIjXN57u2adYN7vhzTny5F3WmfZNvPSJxCoV58+YxZ84cz9+aUvylLpny041c3S+BKOO5jonOQl2ULRt+dh/R6Vn+7zg6C1q6TgREKYXNZsNsNuu2wLKnkT7RH+kT/ZE+aUVb341tfNfWNjn5IL+SHQ2paKp96y72iMQpKSnJa6TIarUyaNCgVq9PSkoiPj6e2tpalFJomua53B+TyYTJZALAgOK+ZCvTr53I1pPVLPnsNMNSo7l+SBKJZiPalGs5O2AMZ4rOkp6RSmpm70565uJCmqbJwUdnpE/0R/pEf6RPLo2/79qS2ibePlRBSW0T1w5KZN4/DOLD97bzMXFt3+E5YUmcmhORUBk0aBCFhYVYrVZiYmLYs2cPN954o+d6i8WCwWDg5MmTZGdns337dhYuXIimaQwePJjdu3eTm5vLtm3bmDp1apuP94srEohPmgTANQN6Mb1/AvtL6lm9o5j4qAhSYkz8z/4KFEa0wxXcf2UUswYldtbTF0IIIXqczfmVrPzq/HftIEsDmb0imT00icHJ5/f/u/b6SUysqA74fsOyjtNrr73G7bffHtLH3LVrF+vWrcPlcjF37lxmzpzJkiVLWLhwIRaLhcOHD7N69WrsdjtTpkzh5ptvBuDMmTMsX76c+vp6Ro4cyYIFCzAYWp8PbW0dp33Fdfz7R4Velxk0ePWGgaTEmILzZIWXrrAWSk8jfaI/0if6I31y6crq7dy96eiFqz21+l3bnnWcwpI43Xrrrdx9991cc801LcYcOnSIYcOGhbBVwdNa4rS/uI6nLkqcAH45PZuxGbF+biE6Sg4++iN9oj/SJ/ojfXJpGuwu1u0t5f8OV/pc9+zMbEb19v2ubU/iFJZ1nO68807WrFnDt99+6/f69957j2eeeSbErQqNjIRILn77a8Cfvj7LX74pp7bR6XVdWb2d/cV1lNXbQ9ZGIYQQQs/8fTeW19tZu6eUpVtPk5UQ5fNda9AgPT6yw48dlhqnmTNncvLkSZ577jmWLFlCWpp7/QWHw8Grr77Kli1buPba0O07E0opMSbuv7IPq3YU41LujrxvfB9mDOxF3uk6ln9RRFqsiTnDLBwoqWflV8Uo3MnV/Vf2kVooIYQQPZq7dun8d+PNI5M5W2+n0aGYPTSJ+ZenomkapgjN57s2GCUxYdurzuVy8eyzz1JVVcWzzz5LQ0MDzz33HAUFBdx9991cffXV4WhWUASyV11ZvZ0zNU2kx0f6dORRq403DpTxZWGt1+VSC3VpZLhbf6RP9Ef6RH+kT3z5q10C+M+ZOYzoHeM3vqXv2gvpbq+6d955h+zsbHJycujVy72Hm8FgYNGiRTzxxBP853/+JyUlJZhMJv7f//t/DBgwIBTNCquUGFOLnTjQYuYHQ5J8EieXgjM1TZI4CSGE6JEKKht9kiYAl99LW/+uvVQhSZxee+01z78TEhLIysoiJyeH7Oxs5s6dyx/+8AeGDx/Oww8/THx8fCiapHvNtVAXvxW+KalnoMVMjCkiHM0SQgghQq7K5uDdw5XsLa71+W4MVu1SoEIyVWez2SgsLKSgoMDrv9ra8yMqqamp9OvXj5ycHE9SlZmZ2dlN6xSBTNUFYnN+pdf87L3f601cZASbj1bRLzGK2cOSPJl0Wb2douomMhJaH47siWS4W3+kT/RH+kR/emKfXPxddqqqkbcPVVBpc/APQ5IY0yeGD49W+dQudbT+V/fLETSrrKzk5MmTXsnU6dOnsdvdVfIbN24MV9M6JFiJE7Q8P/vt2Xr+/l0FJoNGWqyJNw6USxF5C3riwUfvpE/0R/pEf3pan1xc9N0/KYqBFjNzhlnomxjlFRto7VKgukzi5I/L5aK4uJiCggKuuuqqcDfnkgQzcWrLwdJ6nthc4HWZFJF762kHn65A+kR/pE/0pyf1SXsXrAw23RWHb9iwwTMFl5mZSUREy/U5BoOBjIwMMjIyQtG0Ls/h8s17XcpdQCeJkxBCCL2rbXKycX+ZT02vXk+ICkni9O6779LU1ARAREQE6enpnjqm5oSqeS0n0T7+isg14M8HyjhU1sA/nNtYuJnUQgkhhAg1f989JbVN/O1QBcW1TVyVHc/mo1VhLfoOVEgSp3Xr1lFaWsqpU6coLCyksLCQI0eOsH37dk+M2Wz2SqSys7MZMWJEKJrXpbW0oObMgb28Nhb+4TALh842yIKaQgghQuri2qUbR1gorXVgMOC14a5SdMqClcEWlhqn/Px8li5dypVXXslll12Gy+UiPz+frVu3ep1pJ8XhgWutUK6gqpE/HyjjsxM1Xpf3lFqonlQn0FVIn+iP9In+dIc+8Ve7pAFLv9+XoSnRfuODWfQdKN3VOF1szZo1TJgwgTvvvNNz2eTJk/nJT37Cm2++ySeffMIdd9wRjqZ1Wa0t8pXTK4pZAxN9Eie9zh8LIYToHk5U+C5YqYAmp8tvfGcsWBlsYdnkt6CggL59+/pcHhUVxa233srQoUPJy8sLQ8u6L3+bCwPsLqrz2VhYCCGE6IjmDXffOljeaZvthktYEqfMzEz27t3b4vWXX345+/fvD12DeoDmWijDuXewQYP7r+zNZakxLP+iiN/tKuFMTZMn3t/O00IIIcSFLv6uOGa18eIXRazJK+WKzDj+Y2aOz3ePXmuXAhWWqbobbriBF198kY0bNzJv3jwiI70zzxMnToS8RqgnmDUokbEZsT7zx9/LiuOo1cafvi7D4VL0jjXx1kGrFJELIYRo0cVF330ToxieGs2PRqSQkXD+e72l756uKiyJ08SJE7Faraxfv57NmzczdepUz8a+Bw4cYMuWLeTm5oajad1eS/PHAy1mHpmYwXdlDfzr+yc9lyvcZzmMzYjt8m92IYQQwVFWb/ckTeD+riioauSp6Vl+vyu6Qu1SoMKSOAHMnj2bkSNH8tZbb7F582bPOk8Ao0eP5p577glX03q0RodvwZ5LwYkKW7d50wshhLh0VTYH6/ee7TILVgZbyBKnt99+m9zcXK+Ne/v168eiRYtwOBwUFxfT1NRESkoKCQkJoWqWuEhLC2q+ddDKgZIGr42FQRbUFEKI7sjfsf3CDXcn5cTzyfHqLrFgZbCFNHFav349qampjBs3jnHjxjFixAhMJhNGo5GsrKxQNUW0oqUFNWcNSuTbs/X89+5STAaNHw6zcNRqkwU1hRCim7m4dmnu8CRKah3ERRq8NtxtcqousWBlsIVsAUylFEeOHGHv3r3s3r2b48ePExkZyYgRIzyJVEpKSiia0unCsQBmsLW2CNmZmibeOFDOx8eqvC7X64Ka3WERue5G+kR/pE/0Jxx90tKClc9f14+ByWa/8d2h6FuXC2BqmsaQIUMYMmQIN998M5WVlezevZu9e/eyYcMG1qxZQ1ZWFuPGjSM3N5chQ4ZgMIRltQRB64V86fGRTO+f4JM49ZT5bSGE6K6OWm1+F6ysd/hf7687FX0HKmzF4YmJiVxzzTVcc801OJ1Ovv32W/bs2UNeXh5vv/02MTExjBkzhh/84AcMHjw4XM0ULfBXCwWw41QN2b2ivDYWFkIIoW/NG+4WVNl8ju09pXYpUGHZq64tpaWl7N69mz179jBixAh++MMfhrtJ7dIdpuoCsTm/0mt+++fje9M7LpJ3D1d4NhbO7uWeCw9nEblMQeiP9In+SJ/oT2f0ycXH4u/KGvj7oQqvDXcvPrY317l2Z+2ZqtNl4tTV9ZTECVqe3y6oauRvh6zUNDpJizPx9rcVYSsily8E/ZE+0R/pE/0Jdp9cXPSd0yuSsRlxzB6aRGqs9w/a7lK7FCjdJ06LFy8mOzubnJwccnJyyM7Opnfv3qFuRqfpSYlTW46V23jkvRNel4W6iFy+EPRH+kR/pE/0J5h94q/oW68n9ISDLovDL5Sdnc3Ro0f54osvPJdFRUWRmZnpSaSak6rExMRwNFEESa3dt6DQpdwJlXxYhRCi85XX2/nj7tIeu2BlsIUlcZo0aRJ79uxh1qxZDBs2DJvNRlFREVu3buXYsWNesXFxcZ5E6s477wxHc0UHtLSg5t8PW9lbUs8PhybR54KiQ1lQUwgh2qel4+bxChtvH7LS6FBM6RvPtpM1UvQdBGGZqnvkkUcYM2YMd9xxh9flTU1NbNy4kQMHDnDLLbdQXFzM6dOnOXXqFEVFRbz66quhbuolkak6by0VGh612vjbISt2l2L20CROVTV1yoKaMgWhP9In+iN9oj+B9MnFdUv3XdkbS7SJ945UkhprZM5Qi2fD3Z5Y9B0o3dc4/fSnP+Wuu+7immuu8Xv90qVLycnJ4Sc/+UmIWxYckjj5aq3Q8Gydnb8cKOe9/Eqvy4M1/y5fCPojfaI/0if601af+KtbApg3PIl/HJFCQlSE39v0pKLvQLUncQrLCpOZmZns3bu3xetzc3P57LPPQtcg0elSYkyM6h3r94OaGmtiUt94n8ub59+FEEL4Kqpu8kmaAHIz4/wmTdD6sVgEJiw1TnPnzuW3v/0tf/7zn5k3bx5Go3czTp8+TUNDQ1AeKz8/n1WrVmG325k2bRo33XSTT0xxcTHLly+nrq6OUaNGsWDBAjRN44033uDjjz8mPt79pX7nnXcyfPjwoLRLeGtpQc1tJ2rkl5EQQlzkVFUjHx6t8rlc6pY6X9iKwysqKtiwYQObN29m2rRp9O3bF4DvvvuODz/8kLFjxwblsdasWcNDDz1EdnY2Tz31FOPHjycnJ8crZv369fzoRz8iNzeX559/nt27d5ObmwvADTfcwHXXXReUtoiW+dtc+Ofje5PdK8prY+EBlvN7JUkhuRCiOyurt3OizEa/FCOpsZEopfi6pJ53DlcSG2ngxhHJjOod0yM32g2nsO2LMXv2bEaPHs2mTZt4//33aWxs9Fw3evRoFi5c2OHHsFqtOJ1OT1I2ceJE8vLyvBInpRSHDx9m0aJFAEyZMoW8vDxP4iRCZ9agRMZmxPrMvw9PjeFMTRN/+66C0v1lXDc4EWuDnVVflYRtUU0hhOhM3kXfpcwc2IuzdXaGpESz8Hu9SYp2f333TYzye9wUnSckidOGDRs86zJlZmYSEeGee83JyeGhhx7C4XBQUlJCY2MjKSkpJCQkBOVxKyoqsFgsnr8tFgsHDx70iqmpqSEuLs5TeGexWLBarZ7r//73v/Phhx8ydOhQ5s+fj9nsuzs0gN1ux+FwEB0djVIKWZD90iRHG0k+d0C48DXsE2diQW4atU1O3vqmnLe+rfBcp4BVO4q5PD3G70Gj+X6kT/RD+kR/pE/0o6ze7kmawH2M+/BoFStn9yMjwb2N1YX91NJxUwSuPa9bSBKnd999l6Ymd5FvREQE6enpXgtd9u3bl8zMzEu+/0cffRSXy+Vz+V133XXJ9wlw7bXXemqiXn/9df785z8zf/58v7GbNm0iLy+PpUuX0tTU5DWCJoInArgs2cRbF13uUnCyrJbYVP+JLYDNZuvUton2kz7RH+mT8Nt7qs6n3lMBZyrrSTL5fteJjvOXQ7QkJInTunXrKC0t5dSpUxQWFlJYWMiRI0fYvn27J8ZsNvtswzJixIiA7n/ZsmV+L7darV6jR1arlaSkJK+Y+Ph4amtrUUqhaZpXzIWrlk+fPp01a9a02IZ58+YxZ84cACIjIzEYwnLCYo/QL8WIhu8quFsKG0jrFePZWLiZUgqbzYbZbJbTrHVC+kR/pE/C77uyBv7+XQV2p/I5WcagQd+UOKKjZSquM5hMgb+uIatxSktLIy0tjXHjxpGfn8++ffuYNWsWl112GS6Xi/z8fLZu3cqRI0c8t9m4cWOHHtNisWAwGDh58iTZ2dls377dp3ZK0zQGDx7sKQjftm0bU6dOBdxTfc1J1M6dO8nKymrxsUwmk+eF1zRNDjydKDU20qeQ/L7xfRiaGu3ZWPgfhiQxqncMmqb5FFgK/ZDPiv5In3S+C09sSTIb2XGqls1HK8nuFcXtY9NIjTX5XaxSjl+dpz3v+bAsgPnEE08wePBgny1UGhsbefPNN/nkk0+44447mDRpUocf6/Dhw6xevRq73c6UKVO4+eabAVi9ejWzZs1i4MCBnDlzhuXLl1NfX8/IkSNZsGABBoOBl156iRMnTqBpGunp6SxcuJC4uLg2H1MWwAyNlhZyq2xw8M6RCr4720BKjImPjlVJEbnOyGKL+iN9EhoXr/SdmRDJtYMSmTWoFzEm77WXztY1cbKslr4pcZI0dbIusXL4nXfeyYwZM/xe/9xzzxEZGcmDDz4Y4pYFhyRO+lBU3ch9fzsuu4HrkHxJ64/0Sefzt9J3a8ck6ZPQ6fIrh19++eXs378/dA0S3VJZvcPvbuDflNSHpT1CiJ7reIWNFV8W+z0myQ4JXUtYEqcbbriBHTt2sHHjRs/Zdhc6ceKEjNiIDmtejfxCGvBFYQ3PbTvNobPeq9OX1dvZX1xHWb09ZG0UQnQfFx9DlFLkna7lPz49xQf5lfxoRLLPMUlW+u56wrIA5sSJE7Faraxfv57NmzczdepUBgwYAMCBAwfYsmWLLEApOszfauTNu4GfrbPzf99VsPHrMmYO6kVto5OXd8iCmkKIS3Nx7dLV/RMob3AwuncMD1yV7tk7zt8xSUoHupaw1Dg1O3HiBG+99RZ79uzxGnkaPXo0//zP/0yvXr3C1bQOkRonfWmtwLLe7uR/v7Xyp6/LvS6XWqjOJbUb+iN9cun81S5pwOof9qdPfJTf+EBW+pY+CZ321DiFbcsVgH79+rFo0SIcDgfFxcU0NTUFdeVwIcA98hSbava7/kmMKYIRaTGAd+LUXHcgiZMQoi37i/0vWHm23uE3cUqJMcmxpQsLa+LUzGg0trpGkhCdqbkW6uID3zuHK4g1RXhtLCyEEOAeDTpQ6t5w16Dhd8FKqV3qnnSROAkRTi3VQo3sHcPfDlkp3e/gusGJjMuIxXBuQc3mxevkV6MQ3d+Fn/lEs5FtJ6v55Hg1Q5LN3HOFe8Pdy/v4Llgpx4fuKaw1Tt2V1DjpS6B1Ai3VHdQ2Onkvv5J9xXVYoo18erxaisg7SGo39Ef6xD9/C1bOHprENQN6EWX0PjE90NqlQEmfhE6XqXESQk9aqjuIi4rgphHJTM6J5963j3ntWL5qRzFjM2Lll6UQ3VBZvd2TNIH7M19U08T3suJ8kiaQ2qWeQnaiFSJApXV2v4vX7TtTF5b2CCE6z3dlDby4/YwsWCl8SOIkRID8Lqipwd7iOn792Sn3mTUXzHzLgppC6NvFn1GnS/FFQQ3/75NCthfU8LPLU2XBSuFDpuqECFBrC2o2byz85jflXN2/F40OF6t3yoKaQujVxbVLk/vGU2VzckVmHP8yOcOz4a4sWCkuJsXhnUCKw/Ul2AWWrRWANjpc/O07K+v2lnldLgtqepOiV/3pSX3S0oKVr8wdQO8439GkYBd9B6on9Um4SXG4EJ2otQLQKKOBIcnRPpfLgppC6Mfuolq/C1aW1tn9Jk5S9C0uJImTEEHW0oKab39rxWQwMCzVN7ESQnQupRS7i+p4L7+SWJNBFqwUl0wSJyGCrKVaqMvTY702Fr4qK54IgyyoKUSwXfiZSoiKYMvxaraerPbacHdEWozULolLIjVOnUBqnPQlXHUCLdVF1NudfHi0ip2naulljmDbyZoeV0QutRv601365MKib4CshEj+8TILU/slYIro3AUrg6279ElXIDVOQuhAS3URMaYIfjjMwpVZcSz8X1lQU4hguXjBSnAvWDkmPdYnaQKpXRKXRtZxEiJMSmr9L6i5+3RtWNojRFellOLrkjqe31YkC1aKTieJkxBh4m9BTYMG355t4Nktp9h1uhaXLKgphMfFnwGHS7HleBW//OQU+4vruTu3tyxYKTqdTNUJESatLahZ0+jk/fxK/veQlSl9E3C6FK/IgpqiB7t4wcoJOXHUNrmYmB3Pk1MzPXvHyYKVorNJcXgnkOJwfdF7gWVrBap2p+KdwxX8YXep1+VdfUFNvfdJT6TnPmlpwcrf3TCAtFj9LFgZbHruk+5GisOF6EJaK1A1RWj0T4ryuVwW1BQ9yVeF/hesLKm1+02cpOhbdCZJnITQuZYW1Hzrm3KUglG9Y+TXqOh2nC7FjlO1bD5aSUqMSRasFLohiZMQOtdSLdT3MuO8Nhae3DcBU4QsqCm6lovfrw12Fx8fq+LLwhqvDXcHJ5uldknogtQ4dQKpcdKX7lIn0FLdRqPDxSfHq/i8oIZYk4Evz01rBFJEHmiSFey4s3VNnCirpV9KHKl+plrC3b5gx3WFNoajTy4u+B6bHosCZgzoxcQc98r6F99nd6hdClR3OXZ1Be2pcZLEqRNI4qQvPeXgU1rXxD1/PeZTQPvra3MYkhKN4aLnfvGXVktJlsR1LK4rtDHUcQ6X4ruzDfziwwKf9+urNwxoNXHrSXrKsUsPpDhciB6ouMZ3QU0FvHWwHJfSUEphijCQEW8iISqCP+4567Nq+eBkM8kX/JIvv2glZolrX1xXaGMo4lZ+VcyRchuVNgdOlyLCoGHQfOv2FFBca5fESeiaJE5CdBP+isgNGtzzvfO1II0OF2dqmtheWON3heU/7iklKfr8YaGiwSFxHYjrCm0MRZwChqWYmdKvF6YI98hJWb3dM63cTAq+RVcgiZMQ3URLReQX1oJEGQ30SzITFxXBG1+X+3xp/fNV6V7x/tbPkbjA47pCG0MVNzo91pM0QWDvVyH0SLZcEaIbmTUokVdvGMizM7N59YaBLdbcNH9pNdfetvSlJXEdi+sKbQznaxPo+1UIPZHi8E4gxeH6IgWWLQv0LKVgx52ta+JkWS19AziDKxztC3ZcV2hjuPpEtEyOXaEjZ9WFmdVqxel0hrsZ4hylFI2NjURFRcnBRyekT/RH+kR/pE9Cx2g0kpSUFFCsJE5BZLfbMZnkl5UQQgjRXUmNUxDZ7XZefPFFGhoawt0UcYGGhgYee+wx6RcdkT7RH+kT/ZE+0SdJnILIZDKRnp6O0SgnK+qJ0WgkNzdX+kVHpE/0R/pEf6RP9Emm6oQQQgghAiQjTkIIIYQQAZLESQghhBAiQJI4CSGEEEIESBInIYQQQogASal+EOXl5bF27VqUUsydO5cZM2aEu0k90rJlyzh48CAjR45k8eLFAOTn57Nq1SrsdjvTpk3jpptuCnMre46ysjJWrFhBVVUVERER3HjjjUyYMIHi4mKWL19OXV0do0aNYsGCBbLIXwjV1dXxzDPP4HQ6cblcXH/99cycOVM+KzrQ2NjII488wlVXXcVtt90mfaI3SgSFw+FQDz74oCovL1cNDQ3qwQcfVNXV1eFuVo904MABtXPnTvXcc895Lnv88cfViRMnlNPpVE8++aQ6efJkGFvYs1itVnX8+HGllFIVFRXqnnvuUQ0NDeq5555Tu3btUkopr3+L0HA6ncpmsymllGpoaFD33Xefqq6uls+KDmzYsEG98MIL6rXXXlNKyfFLb2SqLkjy8/PJysrCYrFgNpsZO3Ys+/btC3ezeqQRI0YQHR3t+bt5C5y+fftiMBiYOHEieXl5YWxhz5KUlES/fv0ASExMJCEhgdraWg4fPsy4ceMAmDJlivRJiBkMBqKiogA8e2s2NjbKZyXMzpw5w+nTpxk7diwgxy89ksQpSCoqKrBYLJ6/LRYLVqs1jC0SzaRv9OPYsWO4XC4iIyOJi4vzTM1Jn4RHXV0djz76KPfeey9z5syhqqpKPithtm7dOm699VbP33L80h9JnIQQIVFbW8uKFSu45557wt0UcU5sbCzLli1jxYoVfP7557hcrnA3qUfbuXMn6enpZGRkhLspohVSHB4kSUlJXr8CrFYrgwYNCmOLRDN/fRPoLtgiOOx2O8uWLeOGG25g6NChKKWora1FKYWmadInYZaYmEjfvn0pKiqSz0oYHTlyhO3bt/Pll19is9lwOBzExMRIn+iMjDgFyaBBgygsLMRqtWKz2dizZw9jxowJd7ME7qFtg8HAyZMncblcbN++nSuuuCLczeoxlFKsXLmSESNGMHXqVAA0TWPw4MHs3r0bgG3btpGbmxvOZvY4lZWVns1j6+vr+fbbb+nfv798VsLo1ltv5eWXX2blypXMnz+fGTNmcNNNN0mf6IzsVRdEu3btYt26dbhcLubOncvMmTPD3aQe6ZlnnuHEiRM0NjYSFxfHokWLAFi9ejV2u50pU6Zw8803h7mVPcehQ4d4+umnycnJ8Vz2wAMPYDKZWL58OfX19YwcOZIFCxZgMMhvuVDJz8/nlVdeAdzJ7fe//31mzZrF4cOH5bOiA1u2bKGgoIDbbrtN+kRnJHESQgghhAiQ/LwTQgghhAiQJE5CCCGEEAGSxEkIIYQQIkCSOAkhhBBCBEgSJyGEEEKIAEniJIQQQggRIFk5vBM0b8oo9EEpRWNjI1FRUZ690UR4SZ/oj/SJ/kifhI7RaAx4RXZJnDqBw+Hw7DYuwq/54GMwGOTgoxPSJ/oTrj4pq7dTVN1ERkIkKTGmoMR2l7izdU2cKKulX0ocqbGRHb6/cD4XvcdV2hwEupONJE5CCCHCYnN+JSu/KkYBGnD/lX2YNSixQ7HdM660w/enn+eiz7gPj9ey7vZ0n+v8kZXDO0FpaamMOOmIUoqGhgaio6NldEMnpE/0J9R9UlZv5+5NR7nwC0gDbh6ZTGxkhFdsXZOTNw6UtxkrcfIaXmrckLQ4Xr99PIGQESchhBAhV1TdxMW/2hUQG2lggCXK6/JjVltAsRInr2Ew4toiiZMQQoiQy0iIRAOvLy2DBpP6JvjUoqTHR/Lfu8+2GStx8hpealx7dMnlCPLy8njooYd48MEH+eijj3yuz8/PZ9GiRTzwwAP85S9/8VxeXFzM448/zgMPPMDvfvc7mmcp33jjDe69914effRRHn30Ub799lvAPXT9u9/9jgceeIDHH3+c4uLi0DxBIYTo5lJiTNx/ZR+aJwUNGtw3vo/fAt7mWIPWeqzEyWvY0bhAdLkaJ6fTyaJFi3j66aeJiYnhscce49lnnyU+Pt4T88QTT3DvvfeSnZ3NU089xcKFC8nJyeH555/n6quvJjc31+vfb7zxBgkJCVx33XVej5WXl8eWLVtYvHix17/bIjVO+iL1NPojfaI/4eqTpVtPM6VvPENSogM6I+xMTRPp8W2fSdUd4s7WNXGyrJa+AZxVF8j9hfO56D2uzqkxODuw4vAuN1WXn59PVlYWFosFgLFjx7Jv3z4mT54MnF9DqW/fvgBMnDiRvLw8srOzOXz4MIsWLQJgypQp5OXlkZub2+Jj7dq1i6lTpwIwbtw4zyiVv4OK3W7H4XAQHR2NUooulo92a819IX2iH9In+hOuPrHZXUzIjg/osZOjjSRHG9uM7U5xsalmzGZjUO6vs9rYHeJ6RQWeDnW5xKmiosKTNAFYLBasVmur1x88eJCamhri4uI8Sc/Ft/v73//Ohx9+yNChQ5k/fz5ms9nrvjRNIzY2lpqaGhISEnzatWnTJvLy8li6dClNTU00NjYG/bmLjrHZbOFugriI9In+hLJPbA4XJs1FQ0NDyB6zK5LPSedzuVwBx3a5xKkzXHvttdx0000AvP766/z5z39m/vz57bqPefPmMWfOHAAiIyMxGLpk+Vi3pJTCZrNhNptlWkgnpE/0Jxx9cry0nkGpsURHR4fk8boa+ZyEjsnU+hTnhbpc4pSUlOQ1UmS1Whk0aFCr1yclJREfH09tba1nqq35coDExERP/PTp01mzZo3XfQ0cOBClFHV1dV61VBcymUyeF17TNHmT65D0i/5In+hPKPsk39rIkGSpc2uLfE46X3te3y43LDJo0CAKCwuxWq3YbDb27NnDmDFjPNdbLBYMBgMnT57E5XKxfft2rrjiCjRNY/DgwezevRuAbdu2eeqbKioqPLffuXMnWVlZAOTm5vLZZ58BsHv3bgYPHixvXiGECJJ8q42BFnO4myFEu3S5EaeIiAhuu+02fvWrX+FyuZg7dy7x8fEsWbKEhQsXYrFYuPPOO3nxxRex2+1MmTKFnJwcAH7605+yfPly/vjHPzJy5EjGjRsHuKfnTpw4gaZppKens3DhQsBdEJ6Xl8cDDzxATEwMDz/8cLiethBCdDt1TU7ioyLaDhRCR7rccgRdgSxHoC9y6rv+SJ/oT6j7pLbJyeodxfzL5MxOf6yuSj4noWMymUhNTQ0otstN1QkhhOj6jsk0neiiJHESQggRckfKbQxOlrPpRNcjiZMQQoiQO2q1+WxEK0RXIImTEEKIkLM5XMSYpDBcdD2SOAkhhAipKptDzqYTXZYkTkIIIUIqv9zG4GQpDBddkyROQgghQirfamOQRQrDRdckiZMQQoiQOl5ho3+SFIaLrqldiVNjYyPHjx/3u5P1oUOHgtYoIYQQ3VeTUxFllN/tomsKeMuVw4cPs3TpUoxGI3V1dcybN48bb7zRc/2SJUt47bXXOqWRQgghuofyejtJ0V1uty8hPAJ+965du5a77rqLiRMncubMGVasWMGZM2e4//770TQN2blFCCFEW6QwXHR1AY+Vnjp1iokTJwKQnp7O008/TW1tLcuWLZN92YQQQgRECsNFVxdw4hQTE4PVavX8HRkZyaOPPkpkZCT/8R//ISNOQggh2nSyspG+iVIYLrqugKfqRo0axSeffOJV1xQREcFDDz3EK6+8wsGDBzulgf7k5eWxdu1alFLMnTuXGTNmeF2fn5/PqlWrsNvtTJs2jZtuugmA4uJili9fTl1dHaNGjWLBggVomsbatWvJy8vDaDQycOBAFi5cSEREBN988w3Lli3z7Jg8bdo0Zs+eHbLnKYQQ3YlSCodLYYrQwt0UIS5ZwInTggULcDqdPpdrmsa9997rSU46m9PpZO3atTz99NPExMTw2GOPMX78eOLj4z0xa9as4aGHHiI7O5unnnqK8ePHk5OTw/r16/nRj35Ebm4uzz//PLt37yY3N5fLL7+cn/70pxgMBl566SU+/fRTrrnmGsCdMC5evDgkz00IIbqz0jo7abGmcDdDiA4JOHEyGo0Yjb7hSik0TSMlJSWoDWtJfn4+WVlZWCwWAMaOHcu+ffuYPHkyAFarFafTSd++fQGYOHEieXl5ZGdnc/jwYRYtWgTAlClTyMvLIzc3l9GjR3vuf8CAAV5TkoGy2+04HA6io6NRSsnUpY4094X0iX5In+hPKPrkSLmNQRaz9HuA5HMSOu15jTt8TujatWu5/fbbO3o3AauoqPAkTQAWi8Ur0fF3/cGDB6mpqSEuLg5N0/zeDtyjWZ9//jl33nmn57KDBw/y6KOPkpKSwu23306fPn38tmvTpk3k5eWxdOlSmpqaaGxsDMrzFcFjs9nC3QRxEekT/enMPjlUUsOUnFi/awGKlsnnpPO5XK6AYzucOL3//vtkZ2d7prb8OXToEMOGDevoQ3W6devWMXjwYAYPHgxA//79WblyJWazmR07dvDiiy+yZMkSv7edN28ec+bMAdyF8waDLO6mF0opbDYbZrPZkziL8JI+0Z9Q9MmZunIGpiYQYZA+D4R8TkLHZAp8CrnDidOdd97JmjVrSE9PZ/jw4T7Xv/fee6xbt47169d39KEASEpK8hopslqtDBo0qNXrk5KSiI+Pp7a21jO12Hx5s/fff5/Tp0/z+OOPey6LiYnx/Hv8+PG8+uqruFwuv0mRyWTyvPCapsmbXIekX/RH+kR/OqtPXEqhAGOE/KhsL/mcdL72vL4dfgfPnDmTa665hueee47S0lLP5Q6Hg5dffpn//u//bnU0qr0GDRpEYWEhVqsVm83Gnj17GDNmjOd6i8WCwWDg5MmTuFwutm/fzhVXXIGmaQwePJjdu3cDsG3bNnJzcwHYvXs3H3/8MY888ggRERGe+6qsrPT8+9ChQyQkJAQ0kqSqK9uOsZahDu1HWcsk7hLi2nWfFWVoR75BVejzuYTzNRQiVIpqmshIiAx3M4ToME0FoerM5XLx7LPPUlVVxbPPPktDQwPPPfccBQUF3H333Vx99dVBaOp5u3btYt26dbhcLubOncvMmTNZsmQJCxcuxGKxcPjwYVavXo3dbmfKlCncfPPNAJw5c4bly5dTX1/PyJEjWbBgAQaDgQceeACn00lsbCwAEyZM4B//8R9599132bx5MxEREZjNZu6880769+/fZvuKH/oZjokzMUy51u/1rq0foNatBKVA09Dm3+83VuL8x3WFNuo9LtyUUjQ0NBAdHS2/pHWis/tky/EqAK7u3yvo991dyeckdEwmk2fpoba0O3F65513yM7OJicnh169zn8AamtreeKJJ0hMTKSkpASTycTixYsZMGBA+1rfDRQ/+FPsxw7DNXPQomO8rlMN9fDR29430DSfWInzH9cV2qirOIMBw5Lfo1lCc9ZroOQLQX86u09+n1fC9YOTyJRRp4DJ5yR02pM4tbvG6cKNfBMSEsjKyiInJ4fs7Gzmzp3LH/7wB4YPH87DDz/stbZSj6MUWkY2Wr9B3pefOIJPpuovVuLkNQxGnMsFZ8+AzhIn0fOcqW4iPV7WcBJd3yUlToWFhRQUFHj+27ZtG7W1tZ6YkpISXnnlFXJycjxJVWZmZlAbrnsGA9rIXN9f+nG9UJrmnkppLVbi5DUMUhyp6QgRTk6X+6Qcg4yaiG6g3cXhZrOZwYMHM2PGDP7pn/6Jp59+mjVr1vDKK6/w5JNP8rOf/Yzhw4dz9uxZ3n77bX7zm994Fp3sMQwGtJ/d53d6RLOkoM2/3/2F1kqsxMlr2OE4TYPcSbqbphM9T2FVI9m9ZIpOdA9BKQ5vicvlori4mIKCAq666qrOehjdKck/jDMmrtUYZS1zT6Gkprf6xSZxLQs01mU9S2PhCaKy+2GwtDyHrffn3N44ldIb9frLGG7/Z7TE5Bbjw0FqN/SnM/vkw6OVRJsMTMpJCOr9dnfyOQmdTi0O37Bhg2cKLjMz0+v0feFWWlqKw+EIdzPEOT354KNOnUC9+yaGBfrab7En94ledWafrN5RzLzLLPSOk1Gn9pDPSeh0anH4u+++S1NTEwARERGkp6d76piaE6q0tLT23q0QohNoWf1QiRbUgd1oI8eFuzmih5LNfUV30u7Ead26dZSWlnLq1CkKCwspLCzkyJEjbN++3RNjNpu9Eqns7GxGjBgR1IYLIQKjzfkxrhXPYhgyAi0yKtzNET2M3akwGmTla9F9XNKWK2lpaaSlpTFu3Djy8/PZt28fs2bN4rLLLsPlcpGfn8/WrVs5cuSI5zYbN24MWqOFEIHTzNEYZsxBvfsXtLk/DXdzRA9zsrKRvomSsIvuo8N71a1Zs4YJEyZw5513ei6bPHkyP/nJT3jzzTf55JNPuOOOOzr6MEKIjrj8StRXW1DFp9H69LClQURY5VsbGJRsDnczhAiaDu9VV1BQQN++fX0uj4qK4tZbb2Xo0KHk5eV19GGEEB2gaRqGm/4J11/+m048kVYIH0fKbQyySOIkuo8OJ06ZmZns3bu3xesvv/xy9u/f39GHEUJ0kJbSG23gMNSOz8LdFNGDVDQ4SI6RwnDRfXQ4cbrhhhvYsWMHGzdu9Jxtd6ETJ07IqflC6IQ2ay5q22ZUfW3bwUJ0UKPDRWREh79mhNCVDtc4TZw4EavVyvr169m8eTNTp071bOx74MABtmzZQm5ubocbKoToOM1owjDnx6i/vo52673hbo7o5o5XNDIgSQrDRffS4cQJYPbs2YwcOZK33nqLzZs3e408jR49mnvuuScYD+ORl5fH2rVrUUoxd+5cZsyY4XV9fn4+q1atwm63M23aNG666SYAiouLWb58OXV1dYwaNYoFCxagaRrV1dX85je/oby8nJycHB588EEiIyNpamrit7/9LQUFBSQnJ/PII4+QkCAr34quTRsyErX9Y9TxI5RFJnCmqJT0jDRSM3u3eJuzp0uCG1dUQsGJInL6ZZCW2Sd0jxumuK7Qxs7ok0+/KWNIeq8WY4Toii5py5W3336b3Nxcvxv3OhwOiouLaWpqIiUlJeiJhtPpZNGiRTz99NPExMTw2GOP8eyzzxIfH++JeeKJJ7j33nvJzs7mqaeeYuHCheTk5PD8889z9dVXk5ub6/XvtWvXkpaWxnXXXef17/fee4/S0lJuu+02r3+3RVYO1xdZfdeXqqnig9+9zsu9p6M0A5pycV9yBddeP8kn9oN3P2dVeZLEXWJcV2hjOF8b0TI5doVOp64cDu7Eaf369aSmpjJu3DjGjRvHiBEjMJlMGI1GsrKyLuVuA5Kfn09WVhYWiwWAsWPHsm/fPiZPngyA1WrF6XR6zvSbOHEieXl5ZGdnc/jwYc+Gw1OmTCEvL4/c3Fzy8vJYsmQJAFOnTmX9+vVcd9117Nq1i5/97Gee+CeffLLFxMlut+NwOIiOjkYpJWcu6UhzX0ifnHe2usGTNAEozcDL5UkMP1pASvr5ffDKzpR5vgAlrv1xXaGNoYq7/HQxqRmtj8oJb3LsCp32vMaXlDi9+uqrHDlyhL1797J7927ef/99IiMjGTFihCeRSknpnB3ZKyoqPEkTgMViwWq1tnr9wYMHqampIS4uzpO1X3i7+vp6YmJifC6/8L5iY2Opr69vsV2bNm0iLy+PpUuX0tTURGNjY5CesQgWm80W7iboRsGJIpQW43WZSzOwastRehkOey6rckWgzOkSd4lxXaGNoYorOFFEXJKUOlwKOXZ1PpfLFXDsJSVOmqYxZMgQhgwZws0330xlZSW7d+9m7969bNiwgTVr1pCVlcW4cePIzc1lyJAhGAzd+8yKefPmMWfOHAAiIyO7/fPtSpRS2Gw2zGazDHefk9MvA+241TMqAGBQLh65brjXqMDZohLu+UTiLjWuK7QxVHE5/TKIjo5GBE6OXaFjMgW+ZEZQvt0TExO55pprWLRoEWvWrOGpp57i8ssvJy8vj6effpq77rqL5cuXe23BcqmSkpK8RpisVqvXCJO/65OSkoiPj6e2ttYzHNd8OUBMTIxnNOnCyy+8r7q6Os+olD8mk8lzUNA0Tf7T2X/SL97/pWX24R/ia9GU+1eWQbn4eXIFaZl9fOLuS67AIHGXFNcV2hiSuNgiv6+N/Nf2f3LsCu1rHYhLKg5vj9LSUnbv3s2ePXsYMWIEP/zhDzt0f06nk0ceeYRf/vKXLRaHP/744/z85z/3KQ5/7rnnmD59Orm5ubzwwgtMnTqVK664gtdee43evXt7isNTU1O5/vrreeeddygrK5Pi8C5OCiz9+9P+MvqbGomurSA9IzWAM7POBi2u9HRxO87gCt7jhiuuK7Sxs/qkT4yB5C1/xXDfE/L5ayc5doVOe4rDOz1x6gy7du1i3bp1uFwu5s6dy8yZM1myZAkLFy7EYrFw+PBhVq9ejd1uZ8qUKdx8880AnDlzhuXLl1NfX8/IkSNZsGABBoOB6upqnn/+eaxWK9nZ2Tz88MOe5QiWL19OYWEhFouFxYsXB3SWoCRO+iIHH/+WfHaKxZMywrJAofSJ/nRmn7j+/ie0PlloV0wO6v12d/I5CZ2QJk6LFy8mOzubnJwccnJyyM7Opnfvnn3mhCRO+iIHH19KKZ7Zcop/n54dtseXPtGXzuwTZbfj+u2vMNz3JFp0yyUPwpt8TkKn05cjuFB2djZHjx7liy++8FwWFRVFZmamJ5FqTqoSExM7+nBCiCAob3CQHBOU9W+FaJNmMmH4hx+h3t6Adsvd4W6OEB3S4SPnpEmT2LNnD7NmzWLYsGHYbDaKiorYunUrx44d84qNi4vzJFJ33nlnRx9aCHGJ8sttDE6WM5xE6GjDx6C++BhVcBQtZ2C4myPEJetw4rRhwwamT5/OHXfc4XX5j3/8YzZu3MiBAwe45ZZbKC4u5vTp05w6dYovvvhCEichwuhIuY1JOfFtBwoRRNpNd+D6w3IMDz6NJku2iC6qw4lTaWkpOTk5PpdHRkYyf/58li5dynfffcdPfvKTjj6UECJICqoa+Uli5yxSK0RLtIQktDFXorZ+gDbtunA3R4hL0uGUPzMzk71797Z4fW5uLp999llHH0YIESRKKZwuhdEgxaYi9LRp30ft/gJVXRHupghxSTqcOM2dO5evvvqKP//5z37PJDt9+jQNDQ0dfRghRJCU1NrpExf4KrlCBJNmiMDwj7eh3lwb7qYIcUmCUhxeUVHBhg0b2Lx5M9OmTfNssPvdd9/x4YcfMnbs2A43VAgRHEfKbQySwnARRlrfgajoGNSh/WjDRoe7OUK0S1DOR549ezajR49m06ZNvP/++14b3I4ePZqFCxcG42GEEEGQb7UxY0CvcDdD9HDa3J/iWvWfGAYNRzPKCKjoOoK2kEtOTg4PPfQQDoeDkpISGhsbSUlJCWilbSFE6JyubiQzITLczRA9nBYdgzb1+7j++jqGkbmQloFmaf2EBWUtg9KiNmO7TVxFGVrhCVR2PzRLy4szBnp/YX0ueo+rqoRQLYDpc4dGI5mZmcG+WyFEELiUQimIkMJwoQe2Bnh/E673N4Gmoc2/H8OUa/2GurZ+gFq3EpRqNba7xUUqhdI0XB28Pz08Fz3HubZ/CC++7vd1u1i7tlxpbGykqKiIPn36EB3tXSNx6NAhhg0bFuhddWuy5Yq+yLYF552qauSD/EruzA3vtkjSJ/oT6j5R1jJcj9/l/lLz0GDSDDSz9/eLsjXA5x9edA++sRLnP64rtDHccaaBQ+nz2/UEIuARp8OHD7N06VKMRiN1dXXMmzePG2+80XP9kiVLeO211wK9OyFEGEhhuNCN0qKLkiYAhTZ8DNqAod4XHz2E8vkS9BMrcf7jukIbdRXXuoATp7Vr13LXXXcxceJEzpw5w4oVKzhz5gz3338/mqbRwb2ChRAhkG+1MXtoUribIQSkZYCmeSdPBgPa4BG+tSgRRlQgsRInr+GlxrVDwOs4nTp1iokTJwKQnp7O008/TW1tLcuWLQvptFR+fj6LFi3igQce4C9/+YvfmOLiYh5//HEeeOABfve733mSuurqan71q1/x4IMP8txzz9HU1ATA3/72Nx555BH+5V/+hWXLllFfXw+4p9x+9rOf8eijj/Loo4+ybt260DxJITrJmZomWcNJ6IJmSUGbfz80b71iMKD97D6/BbyBxkqcvIYdjgtAwDVO9913H88++ywWi8VzmdPp5KWXXqKqqor8/PyQJBZPPPEE9957L9nZ2Tz11FMsXLjQZ8uX559/nquvvprc3Fyvf69du5a0tDSuu+46r39/8803DB48mMjISDZs2EBERAS33HILpaWlvPDCC/z6179uVxulxklfpJ7GzelSLPnsNP92dVa4myJ9okPh6hNlLYOzZyA1PbAzwgKI7S5xLutZGgtPEJXdD0NbZ9XJa9ihOGN9HWmDBrd4vVdsQFHAqFGj+OSTT7zqmiIiInjooYd45ZVXOHjwYKB3dcmsVitOp9OzwObEiRPJy8vzSpyUUhw+fJhFixYBMGXKFPLy8sjNzSUvL48lS5YAMHXqVNavX891113HiBEjPLcfNGgQeXl57W6b3W7H4XAQHR2NUkqmLnWkuS96ep+crLSR0ytSF6+D9In+hK1PkpLd/wXy2IHGdpe4xGSUORbM5uDcX2e0sbvEJQS+tl3AidOCBQtwOp0+l2uaxr333stNN90U8INeqoqKCq8RL4vF4pOw1dTUEBcX5/nFZLFYsFqtANTX1xMTE+Nz+YW2bNnC5MmTPX8XFRXxr//6r8TFxfHTn/6UgQMH+m3bpk2byMvLY+nSpTQ1NXktAir0wWazhbsJYfVtcS3ZcQZdbYHU0/tEj6RP9Ef6pPO5XK6AYwNOnIxGI0ajkQ0bNpCTk0NOTg6ZmZlEREQAkJISvJ3WH330Ub9P4q677graY/jzzjvvoJTy1HIlJSWxcuVK4uPjOXz4MC+88AK//e1vPc/5QvPmzWPOnDkAREZGYmjHfKnoXEopbDYbZrO5R08LFdRUceOIRKKjw1/jJH2iP9In+iN9EjomU+DHxXYvgPnuu+96iqojIiJIT08nJyeH7OxsT0KVlpbW3rv1smzZMr+XW61Wr1Eiq9VKUpL3GULx8fHU1tailELTNK+YmJgYz6jTxbfdtWsXn376Kb/61a88l5lMJs+LOWTIEBISEigvL/f7/C6M1TRN3uQ61NP75Wy9g9RYk65eg57eJ3okfaI/0iedrz2vb7sTp3Xr1lFaWsqpU6coLCyksLCQI0eOsH37dk+M2Wz2SqSys7O96ogulcViwWAwcPLkSbKzs9m+fbvPPniapjF48GB2795Nbm4u27ZtY+rUqQCMGzeOzz77jOuuu47PPvuM3NxcAI4dO8a6dev493//d8xms+e+qquriYuLw2AwUFRURGVlpddUoRBdhd3pwmiQg68QQnRUu1YO9yc/P5+lS5dy5ZVXctlll+FyucjPz2fr1q3U1tZ64jZu3NjhxoJ7Ic7Vq1djt9uZMmUKN998MwCrV69m1qxZDBw4kDNnzrB8+XLq6+sZOXIkCxYswGAwUF1dzfPPP4/VaiU7O5uHH36YyMhInnnmGQoLC+nVy10cNnToUO6++26+/PJL3njjDSIiIoiIiOCnP/0po0aNarONcladvsgZXHCkvIGdp2u5dXRgezF1NukT/ZE+0R/pk9AxmUykBrhXXYcTpyeeeILBgwdz5513el3e2NjIm2++ySeffMIdd9zBpEmTOvIwXYokTvoiBx9493AFyTFGxmfFh7spgPSJHkmf6I/0Sei0J3HqcAVzQUGBZ3mAC0VFRXHrrbcydOjQSzq9XwgRPLLVihBCBEeHE6fMzEz27t3b4vWXX345+/fv7+jDCCE6oNLmwBLd7pJGIYQQF+lw4nTDDTewY8cONm7c6Dnb7kInTpyQaSshwsjmcBEZIctjCCFEMHT4J+jEiROxWq2sX7+ezZs3M3XqVAYMGADAgQMH2LJli+fsNSFE6B232hhgiQp3M4QQolsIytj97NmzGTlyJG+99RabN2/2GnkaPXo099xzTzAeRghxCfKtNgZZzG0HCiGEaFPQih769evHokWLcDgcFBcX09TUREpKCgkJCcF6CCHEJcgvtzGtf+D7MAkhhGhZ0KtFjUYjWVnh331dCOFW0+QkIcp3myAhhBDtJxWjQnRjdU1Ook3yMRdCiGCRI6oQ3dhRq42BUt8khBBBI4mTEN1YfrmNwcmSOAkhRLBI4iREN5YvI05CCBFUkjgJ0Y3ZHC5iTFIYLoQQwSKJkxDdVLXNQXykJE1CCBFMXW7zqvz8fFatWoXdbmfatGncdNNNPjHFxcUsX76curo6Ro0axYIFC9A0jerqan7zm99QXl5OTk4ODz74IJGRkWzZsoXXX3+dpKQkAObNm8fEiRMB+Mtf/sKnn36KyWTivvvuY9CgQSF9vkJcqnyrjUFS3ySEEEHV5Uac1qxZw0MPPcSLL77Inj17KCgo8IlZv349P/rRj3jppZeoqalh9+7dAPz1r3/lyiuv5Le//S1paWl8/PHHnttMnTqVZcuWsWzZMk/SVFBQwJ49e1i+fDkPP/wwa9asCc2TFCII8sslcRJCiGDrUiNOVqsVp9NJ3759Afc+eXl5eeTk5HhilFIcPnyYRYsWATBlyhTy8vLIzc0lLy+PJUuWAO5Eaf369Vx33XUtPt6uXbuYNGkSERER5OTk4HA4sFqtWCwWn1i73Y7D4SA6OhqlFEqpYD510QHNfdHT+uRYhY0fDkvS5fPuqX2iZ9In+iN9EjrteY27VOJUUVHhlbRYLBYOHjzoFVNTU0NcXByapnlirFYrAPX19cTExPhcDvD555+zf/9+srOzuf3220lMTKSiooIRI0Z4Pd7FbWi2adMm8vLyWLp0KU1NTTQ2NgbviYugsNls4W5CSDU0OXDZG2mwh7slLetpfdIVSJ/oj/RJ53O5XAHH6jJxevTRR/0+ibvuuqtTHi83N5dJkyZhMpn4v//7P/7whz94RqwCNW/ePObMmQNAZGQkBkOXmwXttpRS2Gw2zGazJ6Hu7qz1DpJjo4iOjg53U/zqiX2id9In+iN9EjomkyngWF0mTsuWLfN7udVq9RolslqtnoLuZvHx8dTW1qKUQtM0r5iYmBjPqNOFl8fHx3tuP2PGDN555x0AkpKS2ny8ZiaTyfPCa5omb3Id6kn9kl/hXvhS78+3J/VJVyF9oj/SJ52vPa9vlxoWsVgsGAwGTp48icvlYvv27VxxxRVeMZqmMXjwYE9B+LZt28jNzQVg3LhxfPbZZwB89tlnnssrKys9t9+5c6dnk+Lc3Fw+//xznE4nBQUFGI1Gv9N0F6u0OdqMKau3s7+4jrL61udRJC449/nNWZtun0tnxG0/WUNKrC5/FwkhRJemqS5WdXb48GFWr16N3W5nypQp3HzzzQCsXr2aWbNmMXDgQM6cOcPy5cupr69n5MiRLFiwAIPBQHV1Nc8//zxWq5Xs7GwefvhhIiMjWb9+Pbt378ZgMNCrVy/uuece0tLSAHjjjTfYunUrJpOJe++9lyFDhrTZxvmv7WBm/zhmDUr0e/3m/EpWflWMAjTg/iv7+I2VOP9xXaGNeo8LN6UUDQ0NREdHyy9pnZA+0R/pk9AxmUykpqYGFNvlEqeu4Gev7eC70lom5sRjNnoP6tkcLrYX1Pjc5uJYifMf1xXaqKc4gwav3jCQlJjA5+9DQb4Q9Ef6RH+kT0KnPYmTjOV3oqv7JTA8LcbrsoOl9X6/BC+OlTj/cV2hjXqKcyk4U9Oku8RJCCG6KkmcOolBg4HJZhKivLe8GJRsRgNUG7ESJ69hsOLS4yMRQggRHF2qOLyrMGhw3/g+fn/lp8SYuP/KPhi01mMlTl7DznwNhRBCXBqpceoEhwuKiGtjLK+s3s6ZmibS4yNb/WKTuJYFGnu2romTZbX0TYkjNbbl0Re9P+fOeA3DRWo39Ef6RH+kT0JHisPDrHlrGKEPSikaGxuJioqSg49OSJ/oj/SJ/kifhI7RaGxxncaLSeIURHa7vV2rjwohhBCia5EapyCy2+28+OKLNDQ0hLsp4gINDQ089thj0i86In2iP9In+iN9ok+SOAWRyWQiPT0do1FOVtQTo9FIbm6u9IuOSJ/oj/SJ/kif6JNM1QkhhBBCBEhGnIQQQgghAiSJkxBCCCFEgCRxEkIIIYQIkCROQgghhBABklL9IMrLy2Pt2rUopZg7dy4zZswId5N6pGXLlnHw4EFGjhzJ4sWLAcjPz2fVqlXY7XamTZvGTTfdFOZW9hxlZWWsWLGCqqoqIiIiuPHGG5kwYQLFxcUsX76curo6Ro0axYIFC2SRvxCqq6vjmWeewel04nK5uP7665k5c6Z8VnSgsbGRRx55hKuuuorbbrtN+kRvlAgKh8OhHnzwQVVeXq4aGhrUgw8+qKqrq8PdrB7pwIEDaufOneq5557zXPb444+rEydOKKfTqZ588kl18uTJMLawZ7Farer48eNKKaUqKirUPffcoxoaGtRzzz2ndu3apZRSXv8WoeF0OpXNZlNKKdXQ0KDuu+8+VV1dLZ8VHdiwYYN64YUX1GuvvaaUkuOX3shUXZDk5+eTlZWFxWLBbDYzduxY9u3bF+5m9UgjRowgOjra83fzFjh9+/bFYDAwceJE8vLywtjCniUpKYl+/foBkJiYSEJCArW1tRw+fJhx48YBMGXKFOmTEDMYDERFRQHgcDgA90iHfFbC68yZM5w+fZqxY8cCcvzSI0mcgqSiogKLxeL522KxYLVaw9gi0Uz6Rj+OHTuGy+UiMjKSuLg4z9Sc9El41NXV8eijj3LvvfcyZ84cqqqq5LMSZuvWrePWW2/1/C3HL/2RxEkIERK1tbWsWLGCe+65J9xNEefExsaybNkyVqxYweeff47L5Qp3k3q0nTt3kp6eTkZGRribIlohxeFBkpSU5PUrwGq1MmjQoDC2SDTz1zeB7oItgsNut7Ns2TJuuOEGhg4dilKK2tpalFJomiZ9EmaJiYn07duXoqIi+ayE0ZEjR9i+fTtffvklNpsNh8NBTEyM9InOyIhTkAwaNIjCwkKsVis2m409e/YwZsyYcDdL4B7aNhgMnDx5EpfLxfbt27niiivC3aweQynFypUrGTFiBFOnTgVA0zQGDx7M7t27Adi2bRu5ubnhbGaPU1lZ6dk8tr6+nm+//Zb+/fvLZyWMbr31Vl5++WVWrlzJ/PnzmTFjBjfddJP0ic7IXnVBtGvXLtatW4fL5WLu3LnMnDkz3E3qkZ555hlOnDhBY2MjcXFxLFq0CIDVq1djt9uZMmUKN998c5hb2XMcOnSIp59+mpycHM9lDzzwACaTieXLl1NfX8/IkSNZsGABBoP8lguV/Px8XnnlFcCd3H7/+99n1qxZHD58WD4rOrBlyxYKCgq47bbbpE90RhInIYQQQogAyc87IYQQQogASeIkhBBCCBEgSZyEEN3SzTffTHl5eUCxVquVRx99NKSn4z/99NMUFBSE7PGEEMEhiZMQosf761//yrXXXttmcfr999/PoUOHgvKYP/jBD3jjjTeCcl9CiNCRxEkI0aPZ7XY+//xzJkyYENLHHTduHN9++y1VVVUhfVwhRMfIAphCiG5vx44drFu3jieffJL09HSv644cOYLFYiEuLg4Al8vFH//4Rz7//HOcTifp6ek88cQTbNiwgbKyMp599lk0TeOee+5hypQpfPnll7zxxhtUVFQwbNgw7r33Xnr16sU333zD6tWrmTRpEu+//z4JCQncddddjB49GgCj0ciAAQP4+uuvmTx5cshfEyHEpZHESQjRrX3++eds3LiRp556irS0NJ/rCwoK6NOnj+fv/fv3c/jwYV566SXMZjMnTpwgMjKSe++9l6+//poHHniAYcOGAe61kP74xz/y5JNPkpGRwZ/+9Cd+//vfs3jxYgDOnj2Ly+Xi1VdfZffu3bzwwgusWLHCk6RlZGRInZMQXYxM1Qkhuq1PP/2UN954o8WkCdyrZpvNZs/fERERNDQ0UFRUhKZpDBgwwOv6C3388cdce+215OTkYDQaufHGG9m1axdOp9NzXzfddBNGo5Hx48eTnZ3N3r17PbePjo6mvr4+eE9YCNHpZMRJCNFtvfPOO8yePZvU1NQWY2JiYrDZbJ6/R40axaxZs3jllVeorKxkypQp3HrrrRiNvofL8vJytm7dyttvv+25zGAwUFlZCUBCQgKRkZGe65KTk6moqPD83dDQQExMTEeeohAixCRxEkJ0W4sXL+a3v/0taWlpTJw40W9MTk4OH330kddls2fPZvbs2ZSVlbFkyRJycnK4+uqrfW6blJTELbfcwuzZs32uKy4uprq6mqamJk/yVF5e7rXPWFFREdOmTevAMxRChJpM1Qkhuq20tDR+8Ytf8Nprr3k2FL7Y4MGDsVqt1NbWAnD06FHy8/NxOp1ER0djNBo9yxT06tWL0tJSz22nT5/Oe++9x4kTJwCora1l586dnuudTidvvfUWDoeDXbt2UVhYyOWXXw6Aw+Hg2LFjjBw5shOeuRCis8iIkxCiW8vKyuKxxx5jyZIlPPLII1x22WVe15tMJiZOnMiXX37JzJkzqa+v549//COlpaWYzWYmTJjgOett7ty5/Pd//zd/+MMfuPvuu5k8eTLz589n5cqVlJaWEhcXx4QJE/je974H4JkiXLBgAfHx8Tz88MOewvA9e/YwfPhwEhMTQ/diCCE6TDb5FUL0eOXl5SxdupRf//rXbS6CGajm5Qheeuklv9f/8pe/5J/+6Z/o27dvUB5PCBEakjgJIUQnaCtxEkJ0TVLjJIQQQggRIBlxEkIIIYQIkIw4CSGEEEIESBInIYQQQogASeIkhBBCCBEgSZyEEEIIIQIkiZMQQgghRIAkcRJCCCGECJAkTkIIIYQQAZLESQghhBAiQP8fJeKEvuqA+V8AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The initial position as a vector\n",
    "q0 = [0, 2]\n",
    "\n",
    "# The final position as a vector\n",
    "qf = [1, -1]\n",
    "\n",
    "# The number of steps\n",
    "steps = 50\n",
    "\n",
    "# Create the trajectory\n",
    "traj7 = rtb.mtraj(rtb.trapezoidal, q0, qf, steps)\n",
    "\n",
    "# Plot the trajectory\n",
    "traj7.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"600\"\n",
       "            height=\"400\"\n",
       "            src=\"http://localhost:52005/?53005\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            \n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.IFrame at 0x2ab8edf00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Animate the trajectory\n",
    "env = Swift()\n",
    "env.launch(browser='notebook', realtime=True)\n",
    "obj0 = sg.Sphere(0.03, color=\"#008cff\")\n",
    "obj1 = sg.Sphere(0.03, color=\"#fc0349\")\n",
    "env.add(obj0)\n",
    "env.add(obj1)\n",
    "env.set_camera_pose([0.5, 2.0, 0.5], [0.5, 0.0, 0.0])\n",
    "\n",
    "for q0, q1 in zip(traj7.q[:, 0], traj7.q[:, 1]):\n",
    "    obj0.T = sm.SE3.Tx(q0)\n",
    "    obj1.T = sm.SE3.Tx(q1)\n",
    "    env.step(0.02)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The attribute `traj7.q` is a matrix with 50 rows and 2 columns, each row being the configuration at a particular time step. Note that we could have used `rtb.quintic` as the first argument to `mtraj` to generate a quintic polynomial trajectory."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "<a id='3'></a>\n",
    "# 3.0 Interpolation of Orientation\n",
    "---"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In robotics, we often need to interpolate orientation. This essentially means that we wish to smoothly transition from one orientation to another and to achieve this we create a sequence of orientations that smoothly approach the desired orientation while starting at the original.\n",
    "\n",
    "More specifically, given two orientations ${^0\\mathbf{R}_a}$ and ${^a\\mathbf{R}_b}$, we require a function $f(s) = \\sigma({^0\\mathbf{R}_a}, {^a\\mathbf{R}_b}, s)$ where $s \\in [0, 1]$ and we have boundary conditions that give $f(0) = {^0\\mathbf{R}_a}$ and $f(1) = {^0\\mathbf{R}_b}$. The function must vary _smoothly_ for intermediate values of $s$."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpolation using RPY Angles\n",
    "\n",
    "A simple approach to interpolation is to convert rotations to roll-pitch-yaw angles, $\\Gamma \\in (\\mathbf{S^1})^3$ and use linear interpolation\n",
    "\n",
    "$$\n",
    "    \\sigma(\\Gamma_0, \\ \\Gamma_1, \\ s) = (1 - s) \\Gamma_0 + s \\Gamma_1\n",
    "$$\n",
    "\n",
    "where $s \\in [0, 1]$. We can then convert the interpolated roll-pitch-yaw angles back to a rotation matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R_0 = \\left[\\begin{matrix}0.29 & 0.84 & -0.45\\\\-0.45 & 0.54 & 0.71\\\\0.84 & 0 & 0.54\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle R_1 = \\left[\\begin{matrix}0.29 & -0.84 & 0.45\\\\0.45 & 0.54 & 0.71\\\\-0.84 & 0 & 0.54\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R0 = sm.SO3.Rz(-1) * sm.SO3.Ry(-1)\n",
    "R1 = sm.SO3.Rz(1) * sm.SO3.Ry(1)\n",
    "\n",
    "rpy0 = np.expand_dims(R0.rpy(), axis=1)\n",
    "rpy1 = np.expand_dims(R1.rpy(), axis=1)\n",
    "\n",
    "ds.display(ds.Math(f\"R_0 = {sym.latex(sym.Matrix(np.round(R0.A, 2)))}\"))\n",
    "ds.display(ds.Math(f\"R_1 = {sym.latex(sym.Matrix(np.round(R1.A, 2)))}\"))\n",
    "\n",
    "traj8 = rtb.mtraj(rtb.quintic, rpy0, rpy1, 100)\n",
    "\n",
    "traj8.plot()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have a sequence of 100 RPY angles. Let's convert them back to orientation matrices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"600\"\n",
       "            height=\"400\"\n",
       "            src=\"http://localhost:52006/?53006\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            \n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.IFrame at 0x2aede7310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Convert the list of RPY angles to a list of SO3 objects\n",
    "pose = sm.SO3.RPY(traj8.q)\n",
    "\n",
    "# Animate the trajectory\n",
    "env = Swift()\n",
    "env.launch(browser='notebook', realtime=True)\n",
    "obj = sg.Axes(0.1)\n",
    "env.add(obj)\n",
    "\n",
    "env.set_camera_pose([0.5, 0.3, 0.3], [0.0, 0.0, 0.0])\n",
    "\n",
    "for R in pose:\n",
    "\n",
    "    # Move axes into free space to visualise it more clearly, then rotate\n",
    "    obj.T = sm.SE3.Trans(0.2, 0.2, 0.2) * sm.SE3(R)\n",
    "    env.step(0.02)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For large orientation change we see that the axis, around which the coordinate frame rotates, changes along the trajectory. The motion, while smooth, can look a bit uncoordinated. There will also be problems if either $\\mathbf{R}_1$ or $\\mathbf{R}_2$ is close to a singularity in the particular vector representation of orientation."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Interpolation of unit quaternions is only a little more complex than for 3-angle vectors and results in a rotation about a fixed axis in space. Using the Toolbox, we first ﬁnd the two equivalent unit quaternions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "q0 = sm.UnitQuaternion(R0)\n",
    "q1 = sm.UnitQuaternion(R1)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and then interpolate them in 100 uniform steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.77015115 -0.22984885 -0.42073549 -0.42073549]\n"
     ]
    }
   ],
   "source": [
    "qtraj = q0.interp(q1, 100)\n",
    "len(qtraj)\n",
    "\n",
    "print(qtraj[0].A)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where the object is the initial orientation and the arguments to the `interp` method are the final orientation and the number of steps. The result is a UnitQuaternion object that holds 50 values, which we can animate by"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"600\"\n",
       "            height=\"400\"\n",
       "            src=\"http://localhost:52007/?53007\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            \n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.IFrame at 0x2aede4250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Convert the list of quaternions to a list of SE3 objects\n",
    "pose = [q.SE3() for q in qtraj]\n",
    "\n",
    "# Animate the trajectory\n",
    "env = Swift()\n",
    "env.launch(browser='notebook', realtime=True)\n",
    "obj = sg.Axes(0.1)\n",
    "env.add(obj)\n",
    "\n",
    "env.set_camera_pose([0.5, 0.3, 0.3], [0.0, 0.0, 0.0])\n",
    "\n",
    "for T in pose:\n",
    "    # Move axes into free space to visualise it more clearly, then rotate\n",
    "    obj.T = sm.SE3.Trans(0.2, 0.2, 0.2) * T\n",
    "    env.step(0.02)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quaternion interpolation is achieved using spherical linear interpolation (`slerp`) in which the unit quaternions follow a great circle path on a 4-dimensional hypersphere. The result in three dimensions is rotation about a fixed axis in space."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When moving between two points on a circle, we can travel clockwise or counter-clockwise – the result is the same but the distance travelled may be different. The same choices exist when we move on a great circle. In this example, we animate a rotation about the $z$-axis, from an angle of $+2$ radians to $-2$ radians"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"600\"\n",
       "            height=\"400\"\n",
       "            src=\"http://localhost:52008/?53008\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            \n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.IFrame at 0x2aede6020>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q0 = sm.UnitQuaternion.Rz(-2)\n",
    "q1 = sm.UnitQuaternion.Rz(2)\n",
    "\n",
    "qtraj2 = q0.interp(q1, 100)\n",
    "\n",
    "# Convert the list of quaternions to a list of SE3 objects\n",
    "pose = [q.SE3() for q in qtraj2]\n",
    "\n",
    "# Animate the trajectory\n",
    "env = Swift()\n",
    "env.launch(browser='notebook', realtime=True)\n",
    "obj = sg.Axes(0.1)\n",
    "env.add(obj)\n",
    "\n",
    "env.set_camera_pose([0.5, 0.3, 0.3], [0.0, 0.0, 0.0])\n",
    "\n",
    "for T in pose:\n",
    "    # Move axes into free space to visualise it more clearly, then rotate\n",
    "    obj.T = sm.SE3.Trans(0.2, 0.2, 0.2) * T\n",
    "    env.step(0.02)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which is a path that takes the long way around the circle, moving 4 radians when we could travel just $2 \\pi - 4 \\approx 2.28$ radians in the opposite direction. We can request that the shortest path be taken"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"600\"\n",
       "            height=\"400\"\n",
       "            src=\"http://localhost:52009/?53009\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            \n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.IFrame at 0x2ab8ee710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qtraj3 = q0.interp(q1, 50, shortest=True)\n",
    "\n",
    "\n",
    "qtraj2 = q0.interp(q1, 100)\n",
    "\n",
    "# Convert the list of quaternions to a list of SE3 objects\n",
    "pose = [q.SE3() for q in qtraj3]\n",
    "\n",
    "# Animate the trajectory\n",
    "env = Swift()\n",
    "env.launch(browser='notebook', realtime=True)\n",
    "obj = sg.Axes(0.1)\n",
    "env.add(obj)\n",
    "\n",
    "env.set_camera_pose([0.5, 0.3, 0.3], [0.0, 0.0, 0.0])\n",
    "\n",
    "for T in pose:\n",
    "    # Move axes into free space to visualise it more clearly, then rotate\n",
    "    obj.T = sm.SE3.Trans(0.2, 0.2, 0.2) * T\n",
    "    env.step(0.02)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and the animation clearly shows the difference."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Your Understanding\n",
    "\n",
    "#### Question 1\n",
    "\n",
    "Can we linearly interpolate using $\\mathbf{SO}(3)$ matrices? Why or why not?\n",
    "\n",
    "#### Question 2\n",
    "\n",
    "Given two orientations $\\mathbf{R}_1 = \\mathbf{R}_x(30^\\circ)$ and $\\mathbf{R}_2 = \\mathbf{R}_z(60^\\circ)$, interpolate between the two using\n",
    "\n",
    "* ZXY RPY representation\n",
    "* XYX Euler angles\n",
    "* Unit Quaternions\n",
    "* Euler vector representation\n",
    "\n",
    "Animate the resulting trajectories and reflect on what changes between the angular representations."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "<a id='4'></a>\n",
    "# 4.0 Interpolation of Pose\n",
    "---"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another common requirement in robotics is to ﬁnd a smooth path between two 3D poses in $\\mathbf{R}^3 \\times \\mathbf{S}^3$ which involves change in position as well as in orientation. In robotics, this is often referred to as Cartesian motion. We represent the initial and final poses as $\\mathbf{SE}(3)$ matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "T0 = sm.SE3.Trans([0.4, 0.2, 0]) * sm.SE3.RPY(0, 0, 3)\n",
    "T1 = sm.SE3.Trans([-0.4, -0.2, 0.3]) * sm.SE3.RPY(-np.pi/4, np.pi/4, -np.pi/2)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `SE3` object has a method `interp` that interpolates between two poses for normalised distance $s \\in [0, 1]$ along the path, for example the midway pose between `T_0` and `T_1` is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   0.09754  -0.702     0.7055    0         \n",
       "   0.702     0.551     0.4512    0         \n",
       "  -0.7055    0.4512    0.5465    0.15      \n",
       "   0         0         0         1         \n"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T0.interp(T1, 0.5)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where the object is the initial pose and the arguments to the `interp` method are the final pose and the normalized distance. The translational component is linearly interpolated, while rotation is interpolated using unit quaternion spherical linear interpolation as introduced above. A trajectory between the two poses in 101 steps is created by"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "Ts = T0.interp(T1, 101)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and the result is an `SE3` object with 101 values representing the pose at each time step. We can visualise this with another animation "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"600\"\n",
       "            height=\"400\"\n",
       "            src=\"http://localhost:52010/?53010\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            \n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.IFrame at 0x2aede66b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Animate the trajectory\n",
    "env = Swift()\n",
    "env.launch(browser='notebook', realtime=True)\n",
    "obj = sg.Axes(0.1)\n",
    "env.add(obj)\n",
    "\n",
    "env.set_camera_pose([0.1, 0.7, 0.3], [0.0, 0.0, 0.2])\n",
    "\n",
    "for T in Ts:\n",
    "    obj.T = T\n",
    "    env.step(0.02)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The translational part of this trajectory is obtained by"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left( 101, \\  3\\right)$"
      ],
      "text/plain": [
       "(101, 3)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P = Ts.t\n",
    "P.shape"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which is an array where the rows represent position at consecutive time steps. This is plotted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<Axes: xlabel='Time (s)', ylabel='Joint coordinates (rad,m)'>]"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rtb.xplot(P, labels=\"x y z\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and the orientation as roll-pitch-yaw angles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<Axes: xlabel='Time (s)', ylabel='Joint coordinates (rad,m)'>]"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rpy = Ts.rpy()\n",
    "rtb.xplot(rpy, labels=\"roll pitch yaw\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the position coordinates vary linearly with time, but that the roll-pitch-yaw angles are non-linear with time and that has two causes. Firstly, roll-pitch-yaw angles are a non-linear transformation of the linearly-varying quaternion orientation. Secondly, this particular trajectory passes very close to the roll-pitch-yaw singularity, at around steps 24 and 25, and a symptom of this is the rapid rate of change of roll-pitch-yaw angles around this point. The coordinate frame is not rotating faster at this point – you can verify that in the animation – the rotational parameters are changing very quickly, and this is a consequence of the particular representation.\n",
    "\n",
    "However, the motion has a velocity and acceleration discontinuity at the first and last points. While the path is smooth in space, the distance $s$ along the path is not smooth in time. Speed along the path jumps from zero to some finite value and then drops to zero at the end – there is no initial acceleration or final deceleration. The scalar functions quintic and trapezoidal discussed earlier can be used to generate the interpolation variable s so that motion along the path is smooth. We can pass a vector of normalized distances along the path as the second argument to `interp`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<Axes: xlabel='Time (s)', ylabel='Joint coordinates (rad,m)'>]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ts = T0.interp(T1, rtb.trapezoidal(0, 1, 101).q)\n",
    "P = Ts.t\n",
    "rtb.xplot(P, labels=\"x y z\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"600\"\n",
       "            height=\"400\"\n",
       "            src=\"http://localhost:52011/?53011\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            \n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.IFrame at 0x2abc227a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Animate the trajectory\n",
    "env = Swift()\n",
    "env.launch(browser='notebook', realtime=True)\n",
    "obj = sg.Axes(0.1)\n",
    "env.add(obj)\n",
    "\n",
    "env.set_camera_pose([0.1, 0.7, 0.3], [0.0, 0.0, 0.2])\n",
    "\n",
    "for T in Ts:\n",
    "    obj.T = T\n",
    "    env.step(0.02)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The path is unchanged, but the coordinate frame now accelerates to a constant speed along the path and decelerates at the end, resulting in the smoother trajectories shown. The Toolbox provides a convenient shorthand `rtb.ctraj` function for this"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "Ts = rtb.ctraj(T0, T1, 101)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where the arguments are the initial and final pose and the number of time steps."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test your Understanding\n",
    "\n",
    "#### Question 1\n",
    "\n",
    "Using `T0` and `T1` as above, create a trajectory that moves from `T0` to `T1` in 101 steps, but do so using Twists and the `mtraj` method. Plot the translational and rotational components of the trajectory and also create an animation. How does this trajectory differ from the one created using `SE3.interp`? Do you see any advantages or disadvantages of using twists?\n",
    "\n",
    "#### Question 2\n",
    "\n",
    "Using `T0` and `T1` as above, create a trajectory that moves from `T0` to `T1` in 101 steps, but do so using a combination of RPY angles and translations using the `mtraj` method. Plot the translational and rotational components of the trajectory and also create an animation. How does this trajectory differ from those previously created? Do you see any advantages or disadvantages?"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "egh432",
   "language": "python",
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