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T+NAEcYIdW3uxHPyOT9M5qKZ2cGQSynawyrDtU8EkQny0piIOAHYfMPyofeCz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6kcV6VHlVNO+px1VqjgJ9d1zxt4j8F3VprXiO8utU8L6rqVxJo1pax3bieS3WSG3MhMSRKF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\nSu9c7vY0wLysWRWWPheNg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"metadata": {}, "output_type": "display_data", "text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "Let's denote the unknown quantities as $x_1$, $x_2$, and $x_3$. These are the yields of one bundle of inferior, medium grade, and superior rice, respectively. We can then write the problem as:\n", "\n", "\\begin{eqnarray*}\n", "x_1 + 2 x_2 + 3 x_3 &=& 39\\\\\n", "x_1 + 3 x_2 + 2 x_3 &=& 34\\\\\n", "3 x_1 + 2 x_2 + x_3 &=& 26\n", "\\end{eqnarray*}\n", "\n", "The problem then is to determine the values of $x_1, x_2,$ and $x_3$.\n", "\n", "These are _linear_ equations. No term has power other than 1. \n", "\n", "For example, there are no terms involving $x_1^2$, or $x_1x_2$, or $\\sqrt{x_3}$." ] }, { "cell_type": "heading", "level": 2, "metadata": { "internals": { "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "Basic Definitions" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "source": [ "* A _linear equation_ in the variables $x_1, \\dots, x_n$ is an equation that can be written in the form $$a_1 x_1 + a_2 x_2 + \\dots + a_n x_n = b$$ where $b$ and the coefficients $a_1, \\dots, a_n$ are real or complex numbers that are usually known in advance.\n", "* A _system of linear equations_ (or _linear system_) is a collection of one or more linear equations involving the same variables - say $x_1, \\dots, x_n$.\n" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "* A _solution_ of the system is a list of numbers $(s_1, s_2, \\dots, s_n)$ that makes each equation a true statement when the values $s_1, s_2, \\dots, s_n$ are substituted for $x_1, x_2, \\dots, x_n,$ respectively.\n", "\n", "* The set of all possible solutions is called the _solution set_ of the linear system. \n", "\n", "* Two linear systems are called _equivalent_ if they have the same solution set. \n" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "* A system of linear equations has\n", " 1. no solution, or\n", " 2. exactly one solution, or\n", " 3. infinitely many solutions.\n", "* A system of linear equations is said to be _consistent_ if it has either one solution or infinitely many solutions.\n", "* A system of linear equations is said to be _inconsistent_ if it has no solution.\n" ] }, { "cell_type": "heading", "level": 2, "metadata": { "internals": { "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "Interpreting Things Geometrically" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "source": [ "Any list of numbers $(s_1, s_2, \\dots, s_n)$ can be thought of as a point in $n$-dimensional space, called a _vector space_.\n", "\n", "We call that vector space $\\mathbb{R}^n$.\n", "\n", "So if we are considering linear equations with $n$ unknowns, the solutions are points in $\\mathbb{R}^n$.\n", "\n", "Now, any linear equation defines a point set with dimension one less than the space. For example:\n", "\n", "* if we are in 2-space (2 unknowns), a linear equation defines a line.\n", "* if we are in 3-space (3 unknowns), a linear equation defines a plane.\n", "* in higher dimensions, we refer to all such sets as _hyperplanes._\n", "\n", "Question: why does a linear equation define a point-set of dimension one less than the space?" ] }, { "cell_type": "heading", "level": 2, "metadata": { "internals": { "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "Some Examples in $\\mathbb{R}^2$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# No need to study this code unless you want to.\n", "sl.hide_code_in_slideshow()\n", "ax = ut.plotSetup()\n", "ut.centerAxes(ax)\n", "ut.plotLinEqn(1, -2, -1)\n", "ut.plotLinEqn(-1, 3, 3)\n", "plt.legend(loc='best')\n", "print ''" ], "language": "python", "metadata": { "internals": { "frag_number": 6 }, "slideshow": { "slide_type": "-" } }, "outputs": [ { "html": [ "
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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "source": [ "This system of two equations has __exactly one__ solution." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# No need to study this code unless you want to.\n", "sl.hide_code_in_slideshow()\n", "ax = ut.plotSetup()\n", "ut.centerAxes(ax)\n", "ut.plotLinEqn(1, -2, -1)\n", "ut.plotLinEqn(-1, 2, 3)\n", "plt.legend(loc='best')\n", "print ''" ], "language": "python", "metadata": { "internals": { "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "html": [ "
\n", " " ], "metadata": {}, "output_type": "display_data" }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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y5PL5koPBy5U8f74U04f/u9XU1Gjs2LFKSUnR6tWrwzZOp7L79Qs3vj8m5m7Z9f1FopLt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\ngg==\n", "text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "source": [ "This system of two equations has __no__ solutions." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# No need to study this code unless you want to.\n", "sl.hide_code_in_slideshow()\n", "ax = ut.plotSetup()\n", "ut.centerAxes(ax)\n", "ut.plotLinEqn(1, -2, -1)\n", "ut.plotLinEqn(-1, 2, 1)\n", "plt.legend(loc='best')\n", "print ''" ], "language": "python", "metadata": { "internals": { "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "html": [ "
\n", " " ], "metadata": {}, "output_type": "display_data" }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "source": [ "This system of equations has __infinitely many__ solutions." ] }, { "cell_type": "heading", "level": 2, "metadata": { "internals": { "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "Some Examples in $\\mathbb{R}^3$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "sl.hide_code_in_slideshow()\n", "display(Image(\"images/Pic_3-planes.png\"))" ], "language": "python", "metadata": { "internals": {}, "slideshow": { "slide_type": "-" } }, "outputs": [ { "html": [ "
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However the new system is easier to solve.\n", "\n", "We make the following observation: given a set of linear equations, we can __add one equation to another__ without changing the solution set. By definition, any solution of the old system makes each old equation true; therefore any solution of the old system makes each new equation true.\n", "\n", "Another, more obvious fact is that we can multiply any equation by a constant without changing its meaning (and therefore the solution set).\n", "\n", "And an even more obvious fact is that we can change the order of the equations without changing anything.\n", "\n", "Together, these three rules form a set of tools we can use to solve linear systems. Here is an example." ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "We'll do this with the equations and the matrix side-by-side. The basic operation we will repeatedly apply is to _add a multiple of one equation (row) to another._ The goal is to eliminate terms to create a _triangular_ matrix (or system).\n", "\n", "Here is the original system:\n", "\n", "$$\\begin{array}{cc}\n", "\\begin{array}{rcl}\n", " x_1 - 2x_2 +x_3 &=& 5\\\\\n", " 2x_2 - 8x_3 &=& -4\\\\\n", " 6x_1 +5x_2 +9x_3 &=& -4,\n", "\\end{array}\n", "& \n", "\\left[\\begin{array}{rrrr}\n", " 1 & -2 & 1 & 5\\\\\n", " 0 & 2 & - 8 & -4\\\\\n", " 6 & 5 &9 & -4\n", "\\end{array}\n", "\\right]\\\\\n", "\\end{array}$$\n", "\n", "To begin: we add -6 times the first equation to the third equation:\n", "\n", "$$\n", "\\begin{array}{rrrrrr}\n", " &6x_1& +5x_2& +9x_3& =& -4\\\\\n", " + &-6x_1& +12x_2& -6x_3& =& -30\\\\\n", " \\hline\n", " & & 17x_2& +3x_3 &=& -34\\\\\n", "\\end{array}\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "This gives us a new system.\n", "\n", "$$\\begin{array}{cc}\n", "\\begin{array}{rcl}\n", " x_1 - 2x_2 +x_3 &=& 5\\\\\n", " 2x_2 - 8x_3 &=& -4\\\\\n", " +17x_2 +3x_3 &=& -34,\n", "\\end{array}\n", "&\n", "\\left[\\begin{array}{rrrr}\n", " 1 & -2 & 1 & 5\\\\\n", " 0 & 2 & - 8 & -4\\\\\n", " 0 & 17 & 3 & -34\n", "\\end{array}\n", "\\right]\\\\\n", "\\end{array}\n", "$$\n", "\n", "Note that this is not the _same_ system of equations, but it is _equivalent_ -- it has the same solution set.\n", "\n", "Next, we multiply the second equation by $1/2$ to get its leading coefficient to be 1:\n", "\n", "$$\\begin{array}{cc}\n", "\\begin{array}{rcl}\n", " x_1 - 2x_2 +x_3 &=& 5\\\\\n", " x_2 - 4x_3 &=& -2\\\\\n", " +17x_2 +3x_3 &=& -34,\n", "\\end{array}\n", "&\n", "\\left[\\begin{array}{rrrr}\n", " 1 & -2 & 1 & 5\\\\\n", " 0 & 1 & - 4 & -2\\\\\n", " 0 & 17 & 3 & -34\n", "\\end{array}\n", "\\right]\\\\\n", "\\end{array}\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "Next, we multiply the second equation by $-17$ and add it to the third equation:\n", "\n", "$$\\begin{array}{cc}\n", "\\begin{array}{rcl}\n", " x_1 - 2x_2 +x_3 &=& 5\\\\\n", " x_2 - 4x_3 &=& -2\\\\\n", " 72x_3 &=& 0,\n", "\\end{array}\n", "&\n", "\\left[\\begin{array}{rrrr}\n", " 1 & -2 & 1 & 5\\\\\n", " 0 & 1 & - 4 & -2\\\\\n", " 0 & 0 & 72 & 0\n", "\\end{array}\n", "\\right]\\\\\n", "\\end{array}\n", "$$\n", "\n", "And next we can divide the third equation by $72$ to get its leading coefficient equal to 1:\n", "\n", "$$\\begin{array}{cc}\n", "\\begin{array}{rcl}\n", " x_1 - 2x_2 +x_3 &=& 5\\\\\n", " x_2 - 4x_3 &=& -2\\\\\n", " x_3 &=& 0,\n", "\\end{array}\n", "&\n", "\\left[\\begin{array}{rrrr}\n", " 1 & -2 & 1 & 5\\\\\n", " 0 & 1 & - 4 & -2\\\\\n", " 0 & 0 & 1 & 0\n", "\\end{array}\n", "\\right]\\\\\n", "\\end{array}\n", "$$\n", "\n", "We have now put the system and matrix into _triangular_ form. In the matrix, all values below the diagonal are zero." ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end", "slide_type": "subslide" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "slide" } }, "source": [ "At this point, the process shifts a bit to _backsubstitution_. We now have the value for one variable, and we will substitute it into other equations to simply them and get values for the other variables.\n", "\n", "Although we think of its as a somewhat different stage, in reality it still comes down to applying the three rules. First, we substitute the value of $x_3$ into the equations above it. This is actually multiplying equation 3 by the proper value and adding it to equations above it.\n", "\n", "$$\\begin{array}{cc}\n", "\\begin{array}{rcl}\n", " x_1 - 2x_2 &=& 5\\\\\n", " x_2 &=& -2\\\\\n", " x_3 &=& 0,\n", "\\end{array}\n", "&\n", "\\left[\\begin{array}{rrrr}\n", " 1 & -2 & 0 & 5\\\\\n", " 0 & 1 & 0 & -2\\\\\n", " 0 & 0 & 1 & 0\n", "\\end{array}\n", "\\right]\\\\\n", "\\end{array}\n", "$$\n", "\n", "Next, we do the same thing with equation 2, substituting it into equation 1 above it:\n", "\n", "$$\\begin{array}{cc}\n", "\\begin{array}{rcl}\n", " x_1 &=& 1\\\\\n", " x_2 &=& -2\\\\\n", " x_3 &=& 0,\n", "\\end{array}\n", "&\n", "\\left[\\begin{array}{rrrr}\n", " 1 & 0 & 0 & 1\\\\\n", " 0 & 1 & 0 & -2\\\\\n", " 0 & 0 & 1 & 0\n", "\\end{array}\n", "\\right]\\\\\n", "\\end{array}\n", "$$\n", "\n", "Now we can read off the solution: it is $x_1 = 1$, $x_2 = -2$, $x_3 = 0$." ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "Let's get a sense of this process geometrically. Here are the three starting equations:\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "sl.hide_code_in_slideshow()\n", "fig = plt.figure()\n", "xmin = ymin = zmin = -5\n", "xmax = ymax = zmax = 5\n", "axs=[1,2,3]\n", "axs[0] = fig.add_subplot(131, projection='3d')\n", "axs[1] = fig.add_subplot(132, projection='3d')\n", "axs[2] = fig.add_subplot(133, projection='3d')\n", "for ax in axs:\n", " ax.axes.set_xlim([xmin, xmax])\n", " ax.axes.set_ylim([ymin, ymax])\n", " ax.axes.set_zlim([zmin, zmax])\n", " ax.axes.set_xlabel('$x_1$')\n", " ax.axes.set_ylabel('$x_2$')\n", " ax.axes.set_zlabel('$x_3$')\n", "#\n", "ax = axs[0]\n", "eq1 = [1,-2,1,5]\n", "ut.plotLinEqn3d(ax, eq1, 'Brown')\n", "ax.set_title('${}$'.format(ut.formatEqn(eq1[0:3], eq1[3])))\n", "# \n", "ax = axs[1]\n", "eq2 = [0,2,-8,-4]\n", "ut.plotLinEqn3d(ax, eq2, 'Green')\n", "ax.set_title('${}$'.format(ut.formatEqn(eq2[0:3], eq2[3])))\n", "#\n", "ax = axs[2]\n", "eq3 = [6,5,9,-4]\n", "ut.plotLinEqn3d(ax, eq3, 'Blue')\n", "ax.set_title('${}$'.format(ut.formatEqn(eq3[0:3], eq3[3])))\n", "#\n", "plt.subplots_adjust(right = 2.0)" ], "language": "python", "metadata": { "internals": { "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [ { "html": [ "
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yyitx1VVXJR5D2p3qEFaELcLuRLPF4exJmYEEUUbmui7q9Xog4DMO8jo8ZTHN\nAd0oUXse/lzvueceXHPNNdiwYQP+7u/+Dq961avw0pe+NHFfZdidqXJwskZPneVlMEqBhIuJMRbU\nnjZmZmIvujwSiBiyjVhkcM5RbzT8qKVtD77wOQfv1kGK/w/CdV0QQuDlHbDUdXREZFCcG+ccTcOA\nQkjwuYryvvD/hzpV4neEwOMc1PNA6/Xgdz37i/tdJIsWd1xSYhlYWiMVbuQzDAOPPvoorr76apx0\n0kn43ve+h9e//vWJ237iE5/Ali1bxlY6IIknT9Zm0ELDdV20Wq2extqiznMQ4YnkCwsLids8fvhx\nPLX8lP93cBCkOL+uw3PIPYSnmk9BO6xh3pjHYm1x5AxPeJbMWixpK4NwoOUFL3gBfvnLX+Ktb30r\nZmdn8YMf/GCggyPtTjXIqwibZAcmNSyYUopWqwVVVTE/Px8IIU2KqMMDxKtDis+niKzZOCjTccq6\n3tE0DS996Utx00034eMf/zgYY/jpT3860MEpw+5MjYOTNmsTxlla8p2NmNeGsyfagOF5ReN5HqxO\nB5qu9zTWVQ7S23AG4YRQ2rPwCP5jDDzn5yUMi1eCHK5l22g1Gr1OUsTBSuswmRs2QB+xCdM0TRiG\ngfe9730DX7d3717ccsstuO666/Dxj398pGNK8pMlazOMsAxzGcOCByEWN+GJ5HHH2Lu8F48eenR1\nv2mcmzg4sGwvY9leDjI8eR0e13VBKQ2CQkWV0paZJZv0QiMKYwwnnHACPvCBDwx8nbQ71SBOETYN\nSUHaYcOCxXZZr69BtipcCifGXYjXV63sNM7uOI4Dr9tCAMiStjxwznHGGWfgIx/5yMDXlWV3Ku/g\niMjd8vIydF2H3u2HGYbnOKDtNgBACc2FEdkTAEH2ZNjxiyJaCjdVdB0ej1LfMQtleGIdnlCGZ2Jw\n7me+KM3tfAkUTYO5YUNo1/kWGo7jpBKRePe7341//ud/xvLycuZjSEZHZG2Wl5dRy3G/Rh/8kxoW\nHC6FGzaR/GD7IB549oHg50If4AMcHiFakOTwqKoKxljPsONjSbSgCNrtdqph19LuTBZhd44ePZpL\nSTFqd0S2WNO0QrPFwxhUClcWRa7VhN0BgFqtFpvhCQsJrXW7k/ezTTsSoyy7U+lVdjhrEy6TSoMT\n6oEJai67wxt1wyhteB4hpE8UIE0p3NQRk+GprMMz4nFJd1GoFdAs12q1ht7wN998M4477jicf/75\n+PGPfzxFTlGhAAAgAElEQVTyMSXZCNsdMRl8lH05jtPT0Dvs/s+bwYluI2ZMpFncLNvL+MX+X4Dx\n/DMtMjHE4VmsL0JT+h9PRYgWTDN5r0Vpd6pPOFscnQWTlbTZ4jB5e/+i16QQMBlnKVzZxxhmd8Rr\nJml3yu7tybPvSdudSjo4aeQQh+GGPUFK4SgKPNdNlbWJnEym40ahrgvbtmGY5uDIfYmNxWNhRIen\nqu+bKArgedDXr+85x1EiGsMiqT/72c9w00034ZZbboFlWVheXsYf//Ef4wtf+EKuY0rSEe61ATDS\nQ0ps12w2wTkfWxQT6BcSGFYK23E72LFvB1wvvZhK4cQ4PAvGAhbri5jX5zGnzsVullZNbJwLjyou\nNNJEUqXdmQxxPX7RgMUzzwD79gGNBsHMDMfMDDA7C0RvbUL8GVTLy8tjyRZHn4nCqSpq3EVVOdYD\nLWnpdDoTtTuVc3CS5BCzRjXto0cB+KUhHP4FWcsYgR+13t62bX9mQVanqiAmWueaweGpYk0uAN8B\nUxRwSmGsWxfz53IWGh/96Efx0Y9+FADwf//3f/iXf/kXucgomaQevzzZFABBE62maZmH9uY9JuC/\nj7D88yCnihACyih2PLMDlmvlOl5pcGDJXsKSvRQsHDbNbQr6d4ZleEQp3iCHZ5QJ7NOGtDvVJK3d\nmZkB9u9XYJoMrkvAmP86XedoNPy/z8xwqKoDVSXYuNHEzMzwbHGYUexOlhLcUY5TVbI4PMIGTRN5\ngzZpMjhl2p3KODjDsjZZbgpGKdxmM+h5IYT4QgI5bqq8t2G73YamaRPTAC/DiPAEwYaUJ5To8LCu\nE+o4TqElbRzI2yINwO/dYt1ovtFVnRqVNDd8lGMx8jMuirQ7AAI5cJEFEg39ZSMit0tLSzBNM5VT\nxTjDLw/+Eo7m5BcTGBMcPHB4fo1f92R4RA9PGocnLGMqyg87nc7URFrzLjTS1sKHqfLnMO0MU2aM\n2p2FBcAwOGxbgaZx6DqH4xC4LsHSEnDkCOs68ByMGZiba8AwOGZnV50fkfVpNIAi462iRzptCW4a\npv3aG+TwhP8r0u5UsQKo0+lg06ZNmbYp8j1UwsGJyiHGvcEsC43OkSNot9tQFAWNmRlffcd1gYxO\nTt4mcgAwDSNRnU2CHofHU5TgZq9KDw/RtMC5UTStTz2tzIhGmMsvvxyXX3555uNIhpOULc5LVP55\naWkpV5Ahq1MlVJIAZCoNuf/A/ThsHcbsiMqAEyGU4fn10fQOT1jGVCAmdU964HGZSLtTHfIowgLA\nhg1+mRqlBIz5Tg7nQKdDYVk29K4ya6vV6to2gsOHgcOHgXCojxCgVvOdH9/h8Z0fzyOYnc0WzOl0\nOkEJ7tQJJ42RsMNjWVZgV6alpE2sx7LSarVSiZsIirY7lbgiRVStCBlWy7Jw5JlnYOh6j4PB4Q/I\n5N1Fa9FEtd3VHKpLxzKkQqIFRFV7Zg0Vlb0B8kVSJeUgBrAOsjtpnI08Db1FES4NAZDauXn00KN4\neuVpEEx5758gweERggVpHZ5whievw1NFmehWqxXMPpJMFlE2mdXubNzIsW+fmM1CYFkMnmeBMQ9z\nc3Vwnm7N4TtFBJ0OcPAgIJyfVsvAzIyKuTkSyvasZn7CZk0Ec8Q9kdW5mYYStTLPkRASqAIDa7eH\np91uTzSAVgkHJy5FG/eaQTXT4SF2hueBxmm9I3vJWZqLnFIK27ICdbZWtwZeko7YzziFwyOuG0VR\noHbn1fTtN6NRIN2eoHCmT49ZGIyzVERSDuLaGcQwB0cMsYurPc9bJprWqRIzJur1OgzDwNFu3+Ew\ndi/txuOHH898XlNFyOF54ugTsQ5PHGU4PFWg0+ngpJNOmvRpSJB+vdPv4Kz+m1IK27agqn6Pn6aJ\nazW/GhohBJRyrKwQrM5aXN2HYXDU6xy67kDTLGzcOIP5eQWMZRvMOA33i2Bc51p10YJpXe9UwsFJ\nQ9JDX5SZtNtt1Go1mIaBVrdcI7wtOAcbUXoxDtu2QSmdmJDAMcMAh4dSCjfO4cl8iG5WKHKdxAkM\n5CVPD45kcgyyO2GlMjHELs22oxI3YyLtcQ60DuChgw8Vfk6VJ+LwEEJQJ3VsqG/A5vnNWKwtQlX6\nG3/zODylvo0RSkWk3akGaRaKcbaj0fAzKkeOOHBdF7WaCU3TwTnguoCmcSiKLzyQv3s4GcviOHrU\nFyOp1eaxf7/SLVMzsGED6fb69Pf7TJE/MxbSOAt5HJ4qZuInbXemxsEB+iP94Qe9GGLnLC31lBdF\ndgAl1FsxjEELFFF/qqoqGo1G74WVM4IyDWnbypDS4RELkrgMTx8xJYyKrkOPuUFHiWhkbbqTlEPe\nh0E4W1yG/PMguxPu84mbMTHoulyylvDL/b+Udgb+57TkLGHJWcJTradACMGCudAzeDSvwyNKjzzP\nq0yGZ9KRVMnoUEpRq1lgTEcjJqBKKYGq+tI6quo7PK6bTUUtyTGi1A36fKLBHM4ByyKwLODQISCc\n9VEUoF7nfc5Pt1U5kSou1idJGodH2p1+KuHgpI1ohHEcB61Wq2+YVHjAZ3hbvvrDqKcL13Xh2DZM\n0yxMSGDQZ+B5HhzXrcbQzKoS4/C4lIJ5XnKGJ/QZKroO5vbPASmy/wZIP1FcUg3CpbHRbPEwhbQi\nMzjD+nyG2dC228b2fdtBWa8D72e3ESs36FEPjhtWNkz30JwWB4qDQyH+IpFzjqPWURy1jgYZngWz\nW9JWW8zk8IjxAFUqaZv0QkOSjbDtCGeLTzxxBocOJSuVeR6B5xEoCgelBJrmCxF4Xr5rbvV6pqjX\n65mDOYwBrRZBNx4EdHv+mk0T69atZn1Ev8/sLKCqDhizJ37PVJk4h8e27eD7KtrujBLQPeZ7cNIg\nbnihGOS6bqxiUJyDA6w+dBOzOwOOGd6HZVngnI+tJM1xHLiOA1XTArW5SSuMTQVdZ4Zz7i8GB5S0\naaYZ69wAxTs4rVZrOlWrjlGEDRDyz57nBdniso8pyDJjIg7Xc7H9me1w6JCwaRcODsf2y2BUTQU4\n4Dqu7xD02J3+h2bV5abTEnZ4foVfZXJ4xCKwVqsV3sMzrbXwkmyEqw/C2eL5eRUHDgDPPZcsCMs5\n4DgEhuE7N4z5jo7nAZwPE8hY/bfnebCsDhRFRaMxU5iTIfZDKbC8TCBmsvuZIAuMMdTrNbzgBS5O\nOskviQvfM0UoXq41hE0mhMAwjEoMPAakgxMwLNopIqlLS0vQNA3z8/OxD3pH3C0JcMb6VLLSIIQE\ntK4U4yCKuHCizlSPwEK44d5xgkGmPQ7PFDGWiG9CSRsnBG7XqMZleOIEBsQ553Fw5UJjuhAp/+Xl\nZei6jvn5+dT3dxEZHNu20W63U82YiGsuZpxhx74daDmtxO3CMMZg2RYICBqNRqBuqes6GGfBg9N1\n/ICAoq7anbXi3MQR5/CsM9cFg0fDDk/4O6iKaIEMrFSHtN+vsDvRbPFFF3E88ICvqBaXmVl1jvy/\nGYYvGa0oq/NzBiECqY7jwDTNgcqMRWWpw85Uve7bnV/9SgPnNZxxBg3uGTGGY5x9b9NIloHHaexO\n3sCK4zhjVRWNUhkHZxDhtNvMzEyig+E2m7H9NdGbkChKKgeHYDX1R10XtRwp2iyIc/RvdguapgXv\ntcfBCS/WdT2IMAuHR7wmWPB0f64yY4/IEAJV0/xrQVFiMzyqYYBpGiilQeRoVKSDUx3SyP2KcqO5\nubnUEszh/edVUWOModlsglI6Usbolwd+iSOdI6leSymFZVnQDX31oRQykwpRoKgKoALQ0ePwUHfV\n7hKFgHEWlH+NCi+hYXpUOOc4Yh3BEetIn8Mzq85inREvTDKqwyMzOGsfxlgwnyvu3lcU4MUv9sf6\nPf10ksOyes84zmqpmnB0FMXv2Qkj7I7IosT1+RRNnDMVtplPPEFgWRrOO08J/ibuGV9Jzg7uB9F7\nUnWHZxIlvIMGHpcdaJnk91F5B0eUZ4i05KDsSVJ5Wh8pLzAWUl5rzKRP0eaOanRr/F3HgVmrpV7U\nkBiHx3VdcMbgdGfzKN2L9lirZ016r4QQIOzoxmR49MVFAAgeNoqiBK9hjOVadMqFRrVIulcppUFZ\nmKqqmZ2bURALHMMwsLCwkPt+ffjgw9i3sm/wi4jvqDi2A496qNVr0NTuQ3CIYxF2eLjGwcH9Ujbm\nO4YEpCfDM4rDU3WbFXZ4XOqCgGDT7KbYDE+YrA5P3sXRpEtFJOkQIiJiMTroGbNlC4dpArt2+T+L\njE3cvSKcGV33e3MoRV9/DucclFLouj60vzBKVsdb2F1xjQ9ypp55hsBxFFxwAYOqkqDSQg8Fdy3L\nChruw8/pogKTRVPGOWWpKsljd6ZRNKsyDk5cv0t4zoOu61geUn6W5OBE980o9SP3A+bq0G5UgRCC\ner2e8d3kw3Fd/3hxNztPP9NFGABOCHRNA8dqitJ1XRAcuw6PgGhaYt+N/wKC+uJi4FCHDYBweER0\nP4shlQuNahOVf1ZVNaiBz0rWQIc4tm3b0DQtsyMcPt6vj/7aH3g59KCAbdlQFAX1Rj23E0II8R0a\nRQEIoKlakOEJFh4k5OysZbvDfecwKcOzob4B68x1uRwe8VzUNC1TpNXzPDlpviLEfV+it9hxHMzO\nzgbf8zBOPx2o1TgeeECBrvNgwkGS2XFdP5vD2KrTo2kcrZY/7iJcNZL3vaTBF01pQ1W1fhXaGJ57\njuDuu1VceKGH8OmJ4K5weETwUdgcy7KmwuGZNMPsDuD3R+XJ8Ezy866kxUua8zBssZDUf0PQ700S\nVY11cMJRBcMw4JUwOyeKuJBUVS3emSJ+Zby4MHVN8zNTISMwSF1sLTLUuekSFhiIGgAh1SuUtaIZ\nniRDOmldeEkycfLPNKWkfBJpHRxRkgasNqfnZV9zH3Y+t3Po6yilYJxB7/YVFtlDQwiBStSevhTh\n8FCPgrls4g6PX75b0jEju+0paTviOzzra+uxWFvEYn0xtcPTbDb9fqhugCWt3RH7klQPMSxYVdVA\nRMQZpqMc4qSTAMNguPdeBYDfZzPIfFBKQIjfm2NZHEtLHWgawcyMBkrHU5IGALpuZOrPWFoC7rpL\nxUUXeUh6hPZUs3SPJ9Y6WZ7Txzphu8M5R6vVgqZpPXanCuqQw6icg5Mk/yxISpXRTgdeiohHaEd9\nvwr3vogG27wOTtoFSqCS1nU+SocQKCQ0SZnzNevwxH0HRNNS9V8phgFtgCMSZ0ijGZ44Q9rpdKSD\nUzHC8s/RZv5RmmjTbitsnmgmdhwnWARkPd6h9iHc9+x9A4/L0e0toh4U4kc+yxYIGOjwdB2tSTs8\n44RzjsOdwzjcOQwcQWqHB0BPyWQauyOpHuF+l7hhwVntzqZNwCWXMGzfTtBuKzBNBkJ4omoaYxzN\npgvGLNRqJhTFgOM4UFXfQcoyPyct4cUxgJwl3r6Tc+GFHqLzt2Of96HntGEYsffLNCzU01D27KBw\nmXaaHp4qlKhVphtLZG1ECU80bTnsixvYfxNjLLjn9SzcbduG1enANM1MKdq8iLkWnudl6u8pnK4z\no2kaDMNArdvoRwjxm45tG7Ztw3Vd3zCVdNGO5f0Tgq5W5tCXDpOH7ssIdiMepmmi0WgEYhiEkKCu\n+o/+6I/gui6++93vJpZbPvXUU3jFK16Bs88+Gy9/+cvxpS99Kf37k2TGn8nQhGVZmJub66s9L9PB\nEZExYfPq9fpI90HLbeHe/ffCY8kOvJC75oyj3qiDKMXN6skCIQSqokLX/OxRzVztOfTtjgXbseFS\nv6enCg/LMhEOz+NHHsf2Z7bjtidvw93P3I1dh3fhUOcQGF+tNohen1G7I6LijuNgaWkJr33ta+E4\nDn70ox+h0+nEHl/anfHieR5WVlbgui7m5+f7FBLz2J2FBeDSSzkaDQ7HQZCliZoU4Vi5rgvDmIWm\nGQg0RTwC1yXQdQ5FSXf8NOfqeR46nTYIId1+m/x2znGA7dtVHDyYfn0Yfl30fhGVGLZto9VqodPp\nBM7PWrc7eRn2Oe7evRuvec1rYNs2fvaznyVmJMu2O4RX5Bs8cuRIoJKWdLEeOXIkcQ7E0cceQ3tf\nfEMtpRSu6/aVfymaBuo4QY1hdHEjDEHWwYydTge6ridGKDzPg9Xp9EhOW5YFTVUTB4dSSjP14VBK\nwTkfvTk6pC7GPC9eknpE5yTcGFgk0c8gizz4/Omno3HiiYl/b7VaqNfrqZv6OOf4yU9+gve///1Y\nv349HnzwQTz99NN938/+/fuxf/9+bN26Fc899xxe8pKX4L777sPc3Fyq40iy8dxzzwWloUm18UeO\nHMFiV3AiC6LxNS5jFy5LiTbYOl2blOU7dzwHtz5yK5jGEiP/ruvCtm0YphFkbdqdNgzDCIQFwnBw\nUJdmcrpc1wUIoGuj2Z2wMqTnealm8GTFdmxoqla43RHDUeM+07woRMGCuYAar+HkxZOxvr4+Vb+U\n67r40Y9+hA984ANYt24dVlZWcP/99/e9Ttqd8cE5x8GDB/2AYkIzv3CA1kXTFCk4erSNe+7RYFk1\nAICqCnVW0lUes6CqWp9TxbkF1+UwDH+dRIjfn+MvPZLvtWazmSgSEFZJq9VMaF270Go1Ua8nb0Mp\nHbqsIAQ4+2yGk0/mQX/IqOudcGZCZNGLzvBkXTukZdi6My+MscyVJ+12G9/+9rfxr//6r6jVajju\nuOPwne98p+91ZdudypSozc7O9kohJ5DkjzlHjyZuk3RBOq4Lu92GbmSrBR0GISQxSzAuyenCCKV4\nPUUBdd2gka/qQ0fDKVtF02IlxJMwcjxYBkEIwWWXXYaZmRn84Ac/SGz6Pf7443H88ccDADZu3Iiz\nzz4bP//5z/GKV7yi0POR+MzPz6eK0uVJ/8dFNsPiKdGylLx4zMP2Z7aj43VgqP12LFySVm/UEx2g\nKhEuLSGKP4tIU7VgBk8ZDk+VYZzhcOcwLNvCPnsfFKJgXW1dUNK2vhbv8Oi6jiuvvBI33HADfvKT\nnyT2lEm7Mz4IIVi3bl1p2QHTJHjJSyh27uQ4eFDMyuFgzIJl0R5HI4zrKuDcC0rUOPdFCYbNz0m6\n7cIlaWVITnMOPPigAttmeN7zitlnuPdElBGqqpro8Ah13ypQkVwFAKDRaGDbtm0455xz8NWvfnVi\ndqcyDk6aiyTpNZ7jgCak3sV20S/fsiwwIF6xLERRF41QSALiJacJIYVOexiltGbgfkP13QDSDR2d\nsAHI6tyohgFtSNZulHpXYUSH8fjjj+Ohhx7CS17yklzHkQxHUZSBfXajPrx61BtjxFOSjpn23uWc\n497992LJii/RZYyhY3WgKAoaM434XpvqPBcTCTs8aYeODv3uOPrEAKYF4fCIHp7A4QnJUguHp9Pp\noFbzo/nS7lSDYff4qM9vVQUuvpjjvvuAp55aXXvMz/vlYUmPQ85XS9Qo9Z0cxggcpzcTNIxwpiiN\nStoo7NqlYGlJxbnnFr9vQvwhxyIzJDLKVR06Wpb8dJ79hkdiTMruTJ2DE3fTp55/g9V0m6qqaNRq\nmcqW0hJ1ViilsC2r8ExRJSDDh472SFJ3txnb6alqMMsoLfqQ/ptxsLKygje+8Y34t3/7NylKMGGE\n3cmTwRG4rotms5konpKXhw4+hGdbz67+ImR4REmaaZrQdC3WuRkmLlCV6GSUNENHi5rBk5Wy1Nk4\nkvfLOMORzhEs28t4Ek/iRYsvwikLpwDIptwo7U41GLX3jzEGQoCzzvJl559+ug7DMMCY77QIqWjG\n4vt+XJdAVf3+HSEnLRwbIUcd3lYgBFtc103MFHWPVmgAdu9eFZQCF13kO3dFEHd+wp4MGjpaJYdn\nkmSZ+VeW3amMg5OGURwc3h2e53Yn5opeFxIe9hhzvFGb6m3b15efmpK0ESEDHB7qikhr7wye0lKr\niuJ/fxn3n1VgIC1i0vIwXNfF61//erzlLW/Ba1/72lzHkhRH3mtULDTa7TZs28bs7GyqGvG0x/vV\nkV9h99Lu1e26i18OP2LLPDY1JWmjEjd0tHf2V3FDR6sCB4eu+IIwjDN4zANlFCfOnRg4N4Dv4KTp\nI5V2p3rkDawI2XlKKS68cBbHHadh504SPA4p9UvP/B6bhMoYjwR9OJ5Hgseo6/q/F1ke4ayIkjTO\neSklacN49lkFO3aouOACD+OII4vytOjQ0bDDsxYkqfOud5rNZipnpUy7M1UOThLDHBzO/Zncnuf1\nl6SVtLgWCxuhGjKNF3YR9Dg8CUNHAYB1DUVRn1NQG5vj+x3m4ISPkYU0Cw3OOf70T/8U55xzDv76\nr/860/4l1UI87BRFSRRHycvTK0/j0UOP9v3eYx7slg1FHVCStsYhhAQOjXB44oaOit9NS/8O5xyq\nokJT/P4Ayigo6601mjVmcc7Gc3p+lyaSKu3OeBl2vY1yPYpr3DAMLCwsgBCCF7wAME2G++5TIFqd\nGSNgbDWbE3dI4QxFy9PC/TmGATDml2xpml5IX2FejhwB7r7bn5VTxEjBLO9j0Aye8NBRkfUpun+n\nTJnoUUvUkijb7lQmjJW3RI1RCjpg0jilFFa3PydOuYJ7HkjCwiNvX4xYvGualkn6tUpNYqXQvaFF\nHX3NNKF3Qy0i+iMkqb2Ucs6Jh0o57yZKmf03aW74O+64A1/84hfxwx/+EOeffz7OP/98fPe73818\nLEk6RimNTUIICYgAx+zsbCbnZtjxDnUO4f4D9/e8hsNfxDuOA8MwUK/VUzs3a93u9EhSG11J6m7J\nHvOYL0kdsjsjfx4F9vYQEGiKBk3RoBIVjDNQRuF6bt95qoqK8zef35exS1OiJu1O9chjdzqdDmzb\nhqqqfaWwJ54IXHwxg6737lNkcHQdICT+eJ5HwJjfmxM2mZ4H2DaH59mYmTH6lNkmQbMJ3HmnioRJ\nDGNDrHUMw0C9Xg9GRwAIRkeI7L5QfF1LVGG9M1UZnLgb3lleTrwwxIVj1mpBk10UzjkUTQNPoeCW\nBtu24XkedF1fe/02RUP8oaOBcIGiFDJ0lGgamNu/AEhD0eppYdrt9tAMzste9rJUaoKS8ZFloSEy\nt57nodFooNPpFPrAX7FXcM++e3rmooiSNM44DMPIJpU6rA+/5OFxk4AQf+goJRSarvVkcyY9dJSD\nQ1M0KOieU9ehAQCPDw7YnLvpXMwas32/T7PQkHanemS1O81mE4AfyE0aFLxxI3DJJRzbtwO2HR6J\nQYKyNUXhCf01ftZG03j33127wzlUtQZAH9ifk/e95cG2/UzOBRcwbNhQDcdBODwAgpEl0zB0NO8z\nIE1gpWy7M/0OTkx5mphfM87ysPAxxaBMSUa6Dk8Q7eY8s8Oj5MzcCMoUGMjS7CupFmkexiIqp+s6\n5ufnRzLcccezqIXt+7bD9VYXLx7zYHUsqFr3oViF3pJqrCeGIh7cwuFRFRXQemfwBA5PiZLUiqJA\nJap/3G4vjYcYGzYgM/T8hefjhNkTYv8m7U71KPL6cRwHrVYLpmmiXq+DUpo4WBEA5uf9gaB33w20\nWr3nQamfqTGMVanoKP5rKFy3DU0zexbAruv/f9D244JSYMcOBeedx3DiidUzSmFJaqB3Bo+Q187i\n8FQtGNVut3HCCfE2aVxMlYMThxvJQ7quC8e2YZhm6kgmo3SkiIJQSRPHdBxnzaUbJ0KMw+OFFh5u\ndAZP17kZ5bNP039TZkRDMl5GkacXCAl4y7J6JsmPIk4QhTKKHc/sgOX6mWiO7gA92xdN0XUdlm2B\nT9q78EduTDVJtfRCoW2Yw5PmO9eUbokcfIeGIb8zvL62HmduODPx71nUjCTVYZj94Jyj3W7Ddd0e\nAZM0dqdeB176Uo4dO4CjR0nfdo7jZ3NUFT0iBL0qaQ2YpgrGKKI3veP4fTuKgkBuehJwDtx3nwLL\nYjjttGobpkEOz2qmbPwZnlFK8tOIm5RJZRycPLXwnDE4Kyv+v/lqunTYbJs+OPd7NmLE4QkGf8Gi\nDC7zMaPHKTllW2VS30CRhUfPDB5KwSmFglUpx6yfp2qa0IroTExALjSmk0H3pud5aHV7AIsUEuix\nc5zjnn33YNn2gzmMM9iWDcZHH6Dn9xlW2+5M2i5mdXg4IvaMACrU1QbjrtpZVvr2C8BQDWzdvHWg\n/ZSBlelkkN2hlKLVakFVVczPz+eyAYbhl6vdey/w7LP914+QlPbV0gDPC83y69odv1WWQNf7W2Y9\nj8Dz0Cc3vcr47utHH1Vg2xxnnTXZMswstizs8Jim2TODJ27oaNVot9uYne0vmR0nlXFw0hC94d2V\nFfCQhysuhNhtMXghndVDFSVpiqKUXgYnGvDFg7YqtZkTJ7TwULp9N4HD0+3BEc17aYaOplVPK1Nk\nQFI9EuXpu6UhtVoNtVqt75ooKoNz/7P347n2cwB6S9IaZrkqaaI2nCikJ1sxCaqkBhd1eOKGjnrU\n8+2S6vfSePAGDpTNdyLA1s1bUdNqA1/W6XSwadOmYo8tKZ04+yEETDqdDhqNRqxiWRa7o6rARRdx\nPPAAsHt3f/pV9N0w5sJxOlBVM+aYBK4L1Ovx/Te9ctO+QzTo+emX2NkgRAmtd1K9nYE8+SSBbfsl\na5MeT5Nn/RCewQPEDx0VAhNFzuCZ5oqVqXJwgF4P2F5a8jMorguzVhs8LZUMHtbHurJ9fYYhZjva\nHaCXVAZXZDZGHEsL6axH58mkbb5fqyi6Dua6fRkeOyTLmGboaJkCA0A1bnhJL3kMd7g0ZG5ubuiU\n5rwPCM45dh3ehb3Le3tK0moJto4UNDyPo1uG4rjQdC0olRDyypNovq8yClGgaApU+HMu2p02QADb\ns8EcP2JcxAye6ADRM9afgQ31DUO3SzsHRzI+8tw3jDG0Wi0wxjA/P19Y1J4Q4LzzODSN4cEHe/8W\nLUmr19WuExN9nZiPw6HrPOjFCf+d0tX5OZ1Ov50Sx6LUhapqQYCSMQZFIVCU8Py8fO913z7fybnw\nQo8hBN4AACAASURBVIYhZrvyhB0eIW6jqmrQwxMOxExi6GgVArqV+Yqz1sJ7nocjTz8NxhgaMzMj\nP2g5YyCq6useDqCokrQ0hI/FOfeV3vxQyPDm+2MEoZgW/8fVjFeaoaNpBQZGiWgslChiICmHcMCC\nUopmswlN04IZE4O2y3s8ANizvAe7Du8qtCRtGNFjMcb8610jQRM8YwzUo2BuSG1Mnb7hmRw8f2aI\nABo0v0yHe6vCANxXO6upfkYvOnSUun5p2qgOz8bGRrxw/QtTvbYKpSKS7ITtjuu6aDabME2zT/55\n0HZZOPNM377t3es7JFGxJkVR0I0jJooIcO5nc8RsnWg2Z3V+DnrK2sLHqtcb3Tkxq9usin64YCzS\ne5vRHh4+THDXXf6snNrg5OfUIK4HXdcrM3RUOjgZETeumDEB2w7k9tJsm+JFiduFS9KGfWmiHC4L\nYaMUd6ye8oYEtTFxMbucB9kJf5Dd4NKsaWXorJuII9JTWhIZOspUFbbngVpWaRGPTqeDk046qdB9\nSsqHdO8jy7KC0pCkUti4bfM4xIc6h7CrswvUo7AtG5qmoWbWhi/IM65rwlmfuPK3sBJcj9oY4ntR\nCPzyE495UzNAMy0KUYL37jEPlFPEiZ2FISTd0NFUWbHud1vX69h63NbU512FhYYkO8LuiFkpYQGT\nYdvlzeSefLKHTZsYfv5zD+22HYy76BXRWBURSEJITsdlcwDf8XFdoFbjcF3acyz/PYTfD6CqClRV\nAaDFOjyr6zSlq4w4+H2urCBwctai75/UNxgdOprG4REl/lmpQmClUg5OmhvTdV1QSlEjBJ2iH54J\nx3Zd1y+DM01oWWZM5CCqyJaKGIfHpRSsezEHPSjdCzpamjVx8mREFMXPk+ctySH+UlHc3LXjjkOt\nVksV8cj78CiqVEQsmPfs2YOnnnoKJ598Mg4cOABFUXDuuefK+Usl4DgOFEUptDQkiSVrCfcdvA+K\npnRLQ4aU3wryKphx38bZth0osqUh7iHqUhec8aAXpYjSrIlBAJX40tuMMXjcA/MGNykPsw2xTmJS\nVizG4RHDPHU1/XOoqNJYaXeKI83zTgRzVVUtVMBk0DlxzrGw0MY557jYuXMOnCfbHdFbYxgAY/3X\nPWMEjInem/5sD2McrZZfkjY/b4JzDZwPXwNGHR7GeHedw4JelN4MT/xn3en4Ts4FF3hYXBz82VSd\nYUG0QQ6PmMFTdIanCnanUg7OICilwWTwhYUFtJ95JtP2aZwn7nlQVBUslBXgjIHmUWbLCA9lYEY+\nVsjZ0SOlWY5tA4j0olTJ2UmJQkjP9zQq5rp1qSMeeR2coiOpP/vZz3DXXXfhtNNOg2mauP/++/GO\nd7wD5513XuU08avKsM/IcZzgu5+fn8/8mWaNpnbcDrY/sx2UUyieUnpJGodvd+ChEEU2QgiI4s8C\nCzffh0uzVKWiQilC7Yz4Smg9pWdZd5XyvWVxeBhn2LJ+CxbMbGWuRcu1SrtTPrZtw3Ec6Lo+tCQt\nSjgQl2U7USXieR5OPXUOGzcq2L6dw7IGzV7xS850nUNVfUcmCqWr2Z7w30Vpfb3eAGNKkPHpLlFS\noyir6x1N0/qe3YP6d1wX2LFDxdatDJs3l6/qVpX7I+zwGIbRI0kdHToq/p0Vy7JSV1ilIY/dqbyD\nE54xYZomaHdmTdyAzzT7GoqiAJ4Hxhg6nQ4AwDTNbA/+jIsazv0IBDgvpJ+o/3TiS7PSDs+sGoqm\ngcVIekcZMBevj6iC2qCIh1BmE019aSMeRS00hME577zzsHXrVmzevBme5+H8888PSuCqYESnmbCQ\ngJDozPOZZnFwXM/FnU/dicNLhwEAtVotk90hhIDx9DKowvEgSncgcsFKZQpRYkuz0mQqxgUhBJri\nPwYZ97M0Hi9Y7Szj+SSVAW6ub8bx9ePR6XQyzcIoqlRE2p3y4Zyj1WqBUgrTNIOgQdkIRUgAmJmZ\ngaIomJvzZ+Vs3w40m4PPgVJA00ggKc15vJKa78D4c+xUVUW9Xg+VlxE4DqAoQlY6+/vwq/F9h0bT\n1Eg5W7xgAWPAvfcqOPtshlNOqbZkflmEJamB3hk8QsVXfGdp7U7e0rYoo9idStUMRE+SMYaVlRW4\nrov5+fnA0wQAJzLgsyh4V2K4027DNAwoJZejeJ6HdqvVbdQttvErdmHVNZjCc691S1IIIb7ctm3D\ntm24ruvX30f2MekHWFrnJgtqrQZ1SLdh+DPTNK2nXlg8HDqdDhzHgZcwbLSohcbNN9+Me++9F897\n3vPwwAMPwPM83H777di3b5+stc9B9Jr2PA/Ly8uBWpGICpaJxzzc8eQdOLh00HdsiFKqNLLIiAfO\neckyzIQQqIoKXdNhGiZqZg2argXnYtkWbMeGS114bLRhvYPg4NAUzXci4GdjKaOgjGZyDseFsDuL\nM4s477jzYBhGkJW3bVvanTUEpRRLS0tBlcoo1QJpAyvCoWq325ibmwu2FYiBoOvXJ+9rNWMklNT8\nsrQofkmaC9tuwzQVaJoWu55gzM+s6LovYz0KopxN1zWYptEt9/XLOyn1KzNs24HrUtx/P/Doo9Pp\noBedGRIOjwju12q1zHZH7GdURrE7lc3gxM2YEB8k7XTgZcxjEkJS9Wt0Wi2wUEmaW/BiOowvxeqg\nVq/7pXBFz0lIQ0z/TnSWTHhw5iSH7imaVmhZmiCPPPSgiIdt2z0pXhHxaLVahSw0fvWrX+Gpp57C\nOeecg1e/+tW4++678brXvW7izue0E54xUa/Xgwiq+Fse0iw0GGO489d34mDrIBozDShEge3YpQzg\n5PDfo0c91Bt1UErHOW8vII1ggSgJBUf+z6LbR6NCBQcH5b4zwzmHBw8GKbZvZCRltgRURcX5x58P\nhfp2OKvdEb1VoyLtTnH0Nu2vVqmkFRJIs/9hdsfzPDSbzaD8VkTlo4tlXQe2beP4xS+AAweGf9e9\nvTcI+mosywJjDPX6DFzXgWEM67f2/69p+bI5cSQJFohqlocfBpaXOV784uqUk1UBEWgRdmecQ0dH\nsTvq9ddff32hZzMC4gEnVENmZ2f7FhmO4wCtFqxDhzLtm1IaZEmSji0imo3ZWZCQLGxWRS3x0Elq\n1u292etBnSPjPLGZmHPuO2gpbzjhjGS+2LrOjriYNVUNSu5Y18EUhrOo9LlHKdSEaE5wWoriy2Sn\nXWhyDup5/uc55BxnTjoJeoYIpLiWwp+tKPMT2R2RFROO4pve9Cbs3bsXnudhYWEBmzZtin2/t99+\nO175ylfiE5/4BAgh2LZtW99rdu/ejVarhSeeeAKWZeGJJ57A85///ELrXY8lRBpelIbMzc31KAeJ\n8oY8i0Tb9tWBku5D13Vxz557sL+zP8jciN9rmpapMV/YT12LtzuM+0pw4ECtXoOqqEHdfZLdESpq\nae9z8fqsdodE7I4o+RQPUmF3ODhABp+PUDtTiRr0tHjc68vQUI8mflZ5ET1NqUQhUrL1uK1YrC/G\nPouidkdExRnzG66vvPLKoIdsYWEBi4uL0u5UBHG/NpvNnmyxQCwg8zg8oqQ/ad1i2zaazSZqtVpP\n751lWbFDixUFOOEEwLaBpaX+jDfQb0MYE9UiHlqtTrffpg5FUbpl3gpM0++JiZa0+SXB4t8IZKWT\n4purdidbURIhfg+PsDuKomJlRcGRIxwbNjjg3OuxgaOud8Rsn6IFOYatOUcheBZF7I74zERVC7Ba\n/XDppZeCUoqZmRksLi4mjsco2+5UqkSNUorl5WVwzjE/P9/3ZYnoQp7yNEJIYgwwXJJmmmZP/C1t\n5ictwpFSlEgDcca+nbHRvZB1XYem66G6VV+wwLYsuK7rG7mc5z+sVyb47vLsP4VBMubns+936GFX\nU7yNRgOf/vSnMTMzgyeeeAJ/+Id/iJWVldjt3vWud+Ezn/kMbrvtNnz605/Gc8891/eaZ599Flu3\nboXruvjc5z6H++67rxTDdqwg7E6SStoosqtJ24oen537dmK/s79rd8jQ7fJCPYp2yw/g1Oq1yiua\nKUSBpmowdAOaqgULe5GpEGW0YnGlEhWa4juEjDNQRuEyt5Qs2Dh5/sLzcfzs8QDSZRHF4L9arYbZ\n2Vn893//N0zTxF133YU3vvGNifuQdmf82LaNpaUl6LqOubm5PmekLLsjyovm5ub6nJlBxyQEOPdc\njt/4jfTn5DgulpY6qNd1zM72O06UEjDm9+5EH9Xh02AMcBy/ZC2u/K0oFIVA01QsL5u4994aONe7\n83/coJRP9KNUab1WZrYpzb7Ddmf9+vX46le/ClVV8Z3vfAd/9md/lrhd2XanUiVqtm2jVqv16a4L\nxM3nHj2aa//RC1JkUnhEJS08+yEPSUbCn0Ruj0VuuiyiggVDB46OeNMRQvx5N0nDPEdEq9eH9t9E\nyWNMTjjhBADAjTfemBhVW+oKZ/zWb/0WAOCqq67C3XffjVe/+tU9r7vyyiuxuLiIyy67DG9961vx\n8Y9/vHTp4rWMZVloNBqJUbWiFxoianugfQB7rD3Q1ALNcHTwHrqTyB0XtXqt71hZhQkmAgEIJ9BU\nDVp3wrkCJYhaWq61ane6A0cnVVpS5EJjfW09ztxwZs/vsu771FNPhWma+PznP5+4rbQ740dUo8zN\nzSVm+0YNckS3FSVpQnY673V6xhkcpsnx4INKYsxRlPt6Hu0KCahgbHVAaPj8RO+OKGkDCJLiyuLv\nIpsz4lJtIMvLCrZvV/Gbv0nQaKyW0VJK+5TGsjTer/WyN0VRcNppp2HdunX46le/mvi6cdidSoXx\noiVpcTDHAe2qm41CYibF/yOUrtEZlPnJgtXNdNQbjal1bvoIlUeEBQsA0TjsS10K9ZI8GRiiaWAl\nOTcAoCekTsti0LW9Y8cOnHnm6oJmy5YtuOuuu/pet2XLFjSbTXieh8ceewyLi4tyBsUIiJK0ceA4\nDpaWltBmbTzefDzxeiAg2Yd2RkVaOIPVseB5HhozjXyOVEWexQpRoKu6LxCgqOCEAwqg6qofMOra\na+qOT7CgTAzVwNbNWwtbDEm7Uy0IIQOdmyL2H8a2bSwvL8M0TcwMUGpN61Sdcgpw4YUMfgV77zZi\nbcU5R73eCCmR+gNCfTno/n1Suqq0Noyu6Gzsfoqk3Sa4804VR4+uBndFVcbMzExs470QaJpGuxNH\nHqes2WwOFQAYh92pVAZnGIQQuAmlPWm2DRTYus395qABegU9WMQEdOFI5aUoR6tUUgoWBNGO7jZJ\nKJoGnrO7MK1EdFQeuiyKNnYvfOELAQBnnnlmj5GQZGeY8S4ig8M5D1RnFFPBAwceKDVz4jEPVsfy\ngw+mUbpKWhloit9PwhmHxzy4XnygoyerjJCkO/MSB46WIQZQGATYunkralpvZjnPQkPaneoyzK4U\nZXfCvYVFOlSbNwPbtjH87GeAZfm/85XJ7EBlNO569TwCSgkMg0NROBhbfY0QKNB1wHUHP8X9zI/o\nz1nNDBWN4wDbt6u44AKGjRtXv4+o0FC48V4MHI1meMqiapmhomdv5bU7lcrgpPmC6MpK7pteLDLE\nMM1BNzsP5T7zHE80k3Xa7aA2cRBVujgLI9S/Y5omTNMMBBWcUB09ALCoHLWqgo2hzjWPgzOKMRm0\n3cUXX4xHHnkk+Pmhhx7CJZdckus4kuIYtVREyN17nofaTA33PnsvHOoMOWgOu0P8rI3jOui0O8E9\nN+6FfN6+F4Uo0BUdutLNAjMK13MD1bO0BJLuui8La5hGqG/QH9xKKQVHCaqQBezujPVnYEN9w+g7\ngh/MGxbtlHanmoxqdzzPC8qAFhYWUjk3WY+5fj2wbRtFrebPSrEsv81gWCUO4Gdz/CxMXDm/H/tM\n44/5stL+MFExULRoPA/4+c8V7N07ICAb6kNpNBo9ggrtdhvtdhuO40xcjTYLec8zzVDzcdidSjk4\nacjr4AiHI7YkLe71ngcyQn2xSFvWGw3ZiNmFRBweI2QEHcdZnb/DeY+DWRZaowG1APnUohBKI7ff\nfjuefPJJfP/7349VFZFMhjx2R2RwdV1HvVHHPfvvQdttl3B28OWUmT80uDEkgCMgKFbMIIvjT4g/\nZFNTtaAXyGUuXFZsSWpYsMA0TeiGHjh9lm31CBYU8lmM4E9uamzCC9e/MPZveQIrrVZr6EJD2p21\nhchgCrn72dnZUgOos7PABRd00GjQ1HZn9VwJXNcXGVCUaK8iAaV+NifN6Xsegef5/TllJEs4Bx54\nQMHjjw8/GdETaBgG6vU6ZmZmAqcvPHto2ByZqjCtdmeqStQYpfDabegZm8IdxwF13aB+Mi1CFjDL\nxScWNAD86eBrMTNTBMRfYmiqCkopaqa5KljQzfCEpWMVQjKVDfIUktp51dPyloqk2eaGG27AO97x\nDriui7/6q7/Cxo0bc52jpDjy3MNCJU1Igtbrddyz7x4ctdIJpPglqdnsjt2dDdZoNCpZfiWGbBIQ\nMLBA7SzFhoUh5u8Q4s9VM00TjDMwrzvpvDt/J1zONi4bXtfrePFxLy50n61WK1WpiLQ746eM0lix\neGaMBZmUrOeU5Ziu63YdKYIrrqjh5z8nOHw40yG7+/H7b8IiBKt/E9kcDkqH34tZX5+VXbsU2DbH\n2WenD8KK4K5wPuv1+tD5VVnsTlkOUt5qlTQODlC+3ZkqByerPLRQSQMA3TBGVkcbhud5sDodaLre\n1XEv9uZK21cylXT7dzTDAKMUuqIkDhz1Fx7ZHJ44xikw0Ol0hpYpAsDll1+OnTt3juGMJII096l4\n8Kd5bXiAnlhgPHTwIexv7h/5XONwXTeYt0M9WinnRlX8IZsMfk+Mx3IO6i3pLQmHJ83AUb9vsJjZ\nX1EUouD8zedDV5Nnp+UhTakIIO1OFcnqbFBK0Ww2gzlsZfd8iKHIpml2Z7AQbNvG8ctfAvv25QkK\n+WVrfqlZ73BPzn0RAk1bdWCG7YtSAkXxpaWL1inas4fAthVs3coyZ4tE4DxuYC+lNHZwZprvskrB\n9KrYnUo5OENrNpeWUt/0YWfDNE1QSoOZCWlhlPoDJlNsJ4QLaqLuMuMdVfTci2lE0fVVxbRI43CP\nYEG3gU/p3vhZox0CY926XOdZVqmIpLqkvT8dx0Gr1UK9XodpmrBtG48ffhy7W7uzHS9F6RhHV4qV\neqg3/KFn1MshylFkhgTE76NR9cCh8ZDTqZkAUcECxlmPwwP0CxaE4cgX8dyycQsWzOEBl6z7TrvQ\nkFSXYc+bsLPRaDRgmmagYpaVNHaOc94znFRkIgC/NOyCCzgeegh48sl8C27PE0ID/RkYSv2+HEJ6\nHaAkGPP/89Xeis3oHDhAsH27igsv9EZWcxskWGB3q1nEAGQxBLnKVMXuVMrBGYbbzeAMuwFTqaSl\nhKhq8vhc9GaJGiH5xaJdFdadtl7EbJkqomga2CCLFV54dKUZVxceQilJDebvDHsoaI0G1DFKnEoH\nZ7oZ9uAXJWmu6/aoFe1r7sNjhx/LXCoyDMYYOlYHClFQb9ShECVXdmTYg1LInSpIDiKEy848z4PL\nXBCv2jYqbZBCIf5sHagA1zg4eLDwcF3X/3sos5yHk+ZOwsnzJ+fadhhp5Fol1STN9ckYC0rS4oYU\nF004SyR6e+ICx2efzVGrcTzySPw9QQhJrKjx+6VZt/+GgBAOL2RPxOGylKCVNT/nyBHgrrtUXHSR\nh3q9mH0CCOyJHlrrCJsjVHnDGZ6yKLtErWymxsHhjMEZIhGd5GwA+dN3gxY2opFPTKwvCzEgFABc\nIEhZ5s1cVA5C/CxZDqWkxIGj3dd5nhfrFOaVhx6lVKRI2URJcYx6D4VL0ubn54OF7uHOYTz43IP5\n5KAJEqMklFJfuMDoSrF2r/Y8s3OS4OBwbCcolwBWMxe6pkMjmr/YZ15PH01eBbVpgBACAgJF879f\nznmQ4aEeBXNZUMLmMS9V/86cMYezN5499Nh5FxpViaRK+hm1NDbO2Yhul+eckrazbTt4joXXO0nb\nnH46YBgMDz6opHYoxBpOOE2+DLQC01TAuYJwrSqlBGJtn7ZgRryuyP6cZhO4807fycnZ1juQJBn8\n8MBR0a/seV4l1oXtdhvr16+f6DkAFXNwBn0p7sqKr2xG4kfcRkvS4vadS30tIasgnI4iskSDsCwL\njDGYtVpw/izUm0LQm7mYtuwOJ8QvAxylPI/0z9+hngePUr+mNaZ/Z9T5N7JE7dgiyX6Ih74oSRPX\nRdNp4p599/jOTcFOB6UUtXot3+DOFDC+KpQiZKZVovrOjEf/P3vfHjVHWd//eeays7vvLQnkQhIE\nCQRCTEgiRcFqf1i8QNRWPPZUUlEpLRXlqLTaFo8etVVqLaf12lo5qFTrUUsRlB6UY1sVqRLkJhch\nKAgxCXnJ5b3s7lyf5/fH7Hf22dmZ2bnt++4L+zmHAyS7M8/MzvOd7+Xz/XzRbDV7KheL/UJdDET1\n7ziuA8FFV/9OnGCBpmjYvmZ78P1BYBTgLG1E2R2ZkjY2NhYrA14W5T2uOp0Gxx8PGAbHPfcofSll\nlDCm3kWSU/aFmzwANjRNAeedBK/n+S6PT2dLf01l9+dYFvDTn6rYscPDMeUovMciKuAxTbPr36qq\nBpQ26vnJgyKJlfXr1+c6Z5kYqgAnCXZbzz1q4KVlWXAdB9VabSDlurBcNAUdtRRy01kQngYsDwil\n6oT8cOsRlQuZKrEUenoUVfWnhJUppd3e0Kwt0xg1cNQzDDhtZb0iBiAt6GU0wtJE2NFIeulbroU7\n990J2+sz66bP+eTKjxx0ECWt90s5Z3ZJFpUGhFaNKoyKAcd1On00iu+Uq5oaqzwGsTTsziDAArvD\nuqklMQNHt6zcgjE9nU0YVXCemwjbnbSUtCLvM/l8VJ1WVRVTU1Oxx03a86tW+QNBd+9msO3o71NV\nulKpQNd1eJ4LgEFRGFSV/Bm01cY8eJ4D2+4MDheCQdMEFCU9/ay7PyddT08SXBfYvVvFGWdwHHdc\n9P0YxEBOqt4wxlBpi2kt1sBRQrPZxPj4+MDP0w9LLsABOpspiZIWhdwDQtvHlSlpg6Qbua4LyzRR\nMYzkGToRlQty5LnnQQBdQU/RjVW246JoGryy5U0kBNcbyniotRoqbZnGrAZgqXNSRyiOpJe+xz3s\n3r8bLafl/wErTttyPRdmy5+lUzEq5aqktQ+lKiq4y+Garj+QV1PhchccvOeZj1Me83in2dh27NhG\n/OcKujKterdgwbraOkywCViWNdDG4WazidWrV5d+3BGKI+vv7TgOGo1GJCUt6th5KWqEsGBK3PnS\nXMeyZcA55wj89KdAq9UZvyGE8HumHQfVLjZML0eXMbSDHQWqivZw0U6ClwQIDEOB56mpySydnh7/\nv4u4OUIA996rwLI4Tjxx4RI9pDIL9Pbv0AxI13VhWVZP/04/AYulnFhZOgFOSCKaggC9Uuk7qRlA\nLLUtzfeE68Jtl4UNw4A2qMGdtNnbamyZq1HSC9VrK7nRBO9ho7MxVQXPqGpXFoxlywIpzaIGIC2G\nZcOP0IssXHiZh16pVLq+K4TAzw78DDPmTMKRUq4JDIILWLYFxw6//IuDghRFKHDhotFq+GpsbRVI\neR2pjtXeKw5zwDkP+OBRjfhDQWcblOZ+wiuGBAtWjK/AtjXbAmnYuMbh8LOV19EY9f4tXVAzfqvV\ngmmaiZS0ssA5D4ZQZqWkJWFsDHjJSwTuvBM4dMj/M2LDpBm+LkMIwPMU+N0IKkyTAjqGVsuDqtrg\nXAFjcr9y8jFdl+huxWlrDz+swDQFTjtt8APLk0BVZXpm4gQLiM5Wln0eFn9nqAKcuBvrzM11KWy5\nrgshxMAoaTKEEOCOA1tVM1HSGLK/lAT87HCaalTf8zPWFfBE0dnIMSlrrkzqtbUHXhVKlRSALA+d\n1QCMKjjPXRC/Oe6l/8D0A5huTHf9We7ev7ZaFxfpX/4+fTf6XAwsqKZw4VdbXOHCcR04ngMNWiT1\nLWv1KZjxoGrQVK3TiD8EgzQXDAmXU1ErOGPVGcHvmdQ4LAc7eavnjUZjKKgiI+RHq9UCYyyTSlqR\nsRO2bUPTtC7BlLLOZRjA2WcL3HGHh337XOi6XmggutyD4ziArtNcGUBVPQAebNsD5x06m2974qh2\nJGzgH7NIDvbxx/1ZOVu2ZJ+VMyhE9e8kDRwd9PytQWOoAhwgerNQ9YZeAAAyb4qo3p1+oOngAsDE\n5GRnRkvJoAwNANTK1BqUkUBnc2wbAgujzhYct02UFUIMJLCK25isj8BAGgMA+C+BLBmPZrOJYwbd\nfTjCQEDD1xRFieWhP3b4MTw582TPn+dRNvO4B9uywRjz7VzOUoPCFKhMhYAIghp5Jo3r+RVLBoZq\nrTqQAaFJdLaovpRnNZ2NAdtWb0NV6x34m2R3KLAGkLlvcFgcjRF60e/3cxwHruumoqRFIatzSgk9\nVVVznS8tOLdx+unzYMzA7Gz/4df94AclDIoiAnU0f+kqABXj44BtC3ge7/Ihuwb4hi6Vc8C2gWrV\nD3byBjr79vlBzo4dHAPUosqdeGWsd+AozYykfmXGWGB30ib4hyWxMnQBThTsmZmAkqYsUFM4nU/T\ndX9D5BBOT/PQue0p5BXDCKSgFwQsfq7MoOhsjDEwTRtYoJgGar0OJQPFMGwAHMcJMqxZJg6PqCLD\ni6TGWVIromcg6rN7Z/fikUOPlLIWp20PNF2D4CJT0KFAga7o0JSOhHOURLWAaKtA2qgYlfZ+X6Dq\nrWR3aK5Ml0jKMNLZSsLG5RtxTC1dkkO2O4ZhwLbtwPHI0jc4CnCWHqi32DRNaJrWQ4VNg0zMEel8\npEA7iH0nhECr1YJt2xgbq2HbNhdPPSXw+OPlnItzBtdlPRQzxwFUlUHXFbiuGogVULDjU2oZFKWX\nzkZS1LruU9jyFDQOHWL46U99GWnGyhcZKBOMsYC+DyBI6mYdODosdmfoAxwhBGaffhq2ZaFWwve9\nHgAAIABJREFUr4N7HtwB925YltWWYq2BMeZT4jj35YzTBjopHmI6T61djVrQACeEfupsXUFlzqrL\nYgc3QP75NwRSLKlW/cxT2onDw6IqMkI6CCHQaDTgeR4mJydh23ZkRvSZ5jP4+cGfxx8opbKZgO9k\ncM+npHHBA0c2CZqi+bQz+LNYHO74gzZjApbgPG3eOwU7/dY2qOoOA4OiKol0NgiAKfHzQIYJAiKy\nCrVqbBU2LN+Q+7iy3cnSNzgsjsYI6cA5x/z8PABgamoKrVar9Hk24fM1Gg0IITA5OQnHcSIHdxY9\nl3xdk5OTwbN7+ukChiHwyCNKaYx1opjJEtC+YhqDpvmBiqoqPepsfsDjBHQ2SvoqigLH8V2eSsWX\nhM5qhmZn/Vk5W7f6vUhLCaqqolKpxNL34+zOMPg7Qx3geJ6HmelpuJYVUNJosnYe9OuL6VJlk85H\nf6doWvoAJwFR5xFiiEbkxdDZqPfJbCv/ZMmyMl2PnSk0CMT9znL/TRlIM3H49ttvx9GjRwc6L2mE\nYpBf0vIAvcnJySC4D0/enrVmcfeBu/MN8pTAOUfL9Oc/1Md8Shr3oo/JGIOmaIAAXOF2DdnMdJ42\n9c3jiyP0EYU4OhtVLrjHlySdra7XsXXl1kLHkO1Z2r7B733ve3AcZ6BDqEcoD47jYH5+HoZhoNZO\nrhbppekH2c6RH0Lv+EGcp1KpBNclY8MGXxHt/vvTDwTtB5KA1nWfXkbHdV0/+FGUzqBPxuSARwPn\nHbtDtoccec59BTf5+2nRagF33qlj+3YHZQsbLoQ0fxKNVu4bvPHGG1GtVociGTV0bwi6KbZtY3Z2\nFsyyujbFoG6a53loNhpQFKX3fPTwZHiI4tZJCiWR5xlWSA+2qqowDCNQZ7MsC5ZpdjI/EfeIqSrE\nAAxnVjDGUCk4ajgpQCYDQIZ8bGwMhmHgySefxA9+8ANccMEFeOUrX4lf//rXied473vfi02bNmHH\njh1497vfHfRnjTBYUOJhbm4u+P3k/Sk/v6ZrYvf+3XC85OpHUuM/4L/8m80mdF33XwpSpUQIvxqg\nqVpQqRFCwPH8Kk3cfor687jz5OkRWijIIiiapqFiVAJ1NsuyYFlWYHey2haBhakGKUzBttXboKsD\nUt5EtN2pVCrYs2cPfvKTn2Dr1q143eteh7m5ucTjjOzOwoKeP5qpNT8/j/Hx8UJN9/Kxk+wD2bl6\nvd5l58qGZVnBecLXJa9v3TrgzDPL71NxHN8laY/DA+AHO67LYs+lKAyapnbRtSj4M00TrZaFVsuD\nonAwls3u2Dawe7eGgwcHUxEvG/38HaLQ0nOk6zruv/9+3HPPPVizZg0uuuiivrZ5kHZn6AIcooY0\nm01MTEyAtSsdpSBm09u2DbPVglGtJma7eHvQZl44joNWswnDMDJn1Xg7Us7zMi8b9ELVdR1Vw4De\n5gh7ngez7XgQtzWo5S7ymgFAGxvL1H9TFHSfLr30Umzbtg133HEH3vnOd2LVqlWJ33vlK1+JBx98\nEHfddRcajQb+/d//fYFW/NwFUSgsy8Lk5GTi/nS5izv33QnTSW+bwkGOgAic9Fq9horemW+jMhUV\ntQKN+b00rudXatJUisJUMgFfato0TVRr1a7zpFkz99oUzJh+nqjzD8o+UbBnVAxUjSq0tmKS67ow\nLdOX1G4PJl0sGylEN53v9GNPx5RRjBYbHDflu4ccj/e+97048cQT8fDDD+Otb31rX8rIyO4sPDjn\nmJubg+u6mJqa6pl7l7eCE/c98q/IzoUlp/OcL+o7dJ5Wq4WJiYnI84SxciXw4hdzVCpy5ZaD82J7\nWQg/sNA0n7ZG8KlqSAyq/He4Al3XYBiVtly//xu1Wg6aTQucW/A8F5yLVG4O5ww/+5mCp54a4qR2\nDpDdufrqq3Hqqafi3nvvxa5du/rarUHanaELcObm5gI+qKZpECE+aJklW2p6oz6YKApRl/qaEGA5\nUwyWZcG27djzJIGoMUQZ6wy2cgtR9kpBm8pGzZBVw/B/N+Fz+y3bhm2asYHZIHn14eMW7b8Bis2j\nOO644/C6172ur1LeK17xioCG86pXvQo/+MEP8i53hBQQQmBubg6KosRKsZLd4YLjrv13Yc5KzoYH\n34sIJrjwVRM556jVa9BV3Q9o2lUaT3hwuAOXF6t6csFhtsy29Hwdmpre7ggIiLZjQX0wnPt9Pq7n\npg54BgXGGFTFT7IYRjvgaffxOLYv1GA7NlwvXWA4CKybWIfjJ49flHMThBBYvXo1Lrzwwr52a2R3\nFhZCCMzOzkLXdUxMTEQKRZTp73ieh9m2Im0WyemsoKCNcx74cWkxOSnwohc5GBtDVx+M63pwXa9Q\nwENUNV3vBCKe5/+j6+mOSXQ2P+DxE9WcaxCCA7Bg2xZs24Hn8b7BzgMPKNizZ7iDnCLP3vr167Fz\n586+nxuk3Rm6poCJiQlwzgNjPHXKKXAaDbjNZvCZ3D04koEnaWYqsZWNoK+mHUQxxnI1e1IAo6hq\nEI3Scenv5Pux6MpDEp1N0XV4bW4m5xyuQ7KwkjrbAkIvIcDJi7xNd1/4whdw6aWXDmBFIxAY82dM\n9PuMEAL3P30/DjUPZTs+Og3yrufCMi3UjFr75cjhCQ+2Z/d8Jw98Sm0niFI1FVUjmwQ0KZv5dkeB\nCt8R4oJDcD/IC2wQOBgYmMIG1hMT17gvo4sfrvtrTVJnGzQmjUlsPnZzaccTQuRed573wcjuDB6M\nsVjZefkzZVRwaEBxrebbnSTaUV7/ioQv5ufnUa1WM/dh0PdrNeClL1Wwe7eKmZlO37Xs73ieCHyd\nuJk20efwJaX9mEvA81jwZxTvZdFYIPU1wFdnq1Y5hOCwrGh1tjAee8wfCPqCF/A8uk3SdS1coniQ\nKNvuDF2AQ1F78P+6jhWbN+OZe+4Bd93unpiMoEZh3uZwG4YBLSNlSbTXkMYIeJ4Hs9WCXqnkmj5M\naibhB4yaD2nDyJufqj2cc6BtDBYj4FHaimldjkeUOlv785zzgQ4bZSx5/k1a5L2f9LwRXvGKV+DA\ngQM9n/vYxz6G1772tQCAj3zkI5iYmMAb3/jG/AseIRWopywJjx5+FE87T2c+NjXPe64H13ZRrVah\nqErf/p28jobrubAtG4Zh9FBeehfXfR7OObjwE0zhoEJhCqCiK+CR7Q4Hb9sd/+8WUwRAYUqvOhvv\nqLMx+DbU4165w0YFoKs6tq3eFoglLBainp+R3RkuhP2dskGJXMdxYgcUFwXtHZKaph6wfqDrlkdU\ndAQ0fLra3XcrmJ7uDMWV/ZvO9yD9uUgV8PiulR/oUOtwZ2hot8x0+vsACKEAUDA+DriugOtSBcpX\nZ+sI1tB/A3v3+rNytm/nGFBRbUFBynMyFsvuDF2AEwWtXsfy00/H4Qce6KGsZQHRpoQQqKWcDh51\nDEZagwmgQKpaq2UqBVOGIivnOmoiNgs5bbS5Bh3wKJoGHvU7sV51Nsd1waWhUt3Dt/KvM/zS0MbG\noCyyipn8vN12222Jn/3Sl76E7373u/j+978/6GWNkAJ75/biVzO/wlg9XRWWMRb00DAwNFoNAEC1\nVk3n+Od49Gmgp23ZqNVrmRxsoqRRcJOm4kNBBNAJdlzHBVNYEPBQdYc+vxjoUmfT2u8B14HgYiDD\nRres3IIxfXi0YGU7OrI7w4V+ydIiFRwAXdTbNP5OnvPR523bTk19kwUWwsENQVV94YH77mPYt89f\nO11DmK5PCl4U8HSSwH3mELZV1TStI0jgOICmCThO/sDTl5VmMAwG1/XV2fxeIBuACEYAkL9z8KCC\nO+9U8cIXesiRCx8Y8iR0m81mMEaDsFh2Z0kEOABgLF+OyQ0bMLNnTy7RH9pEqqpmHrjYT146DJo8\nbRhGZp5r1uCm5/ucw7YsaG31DyEEBOfgUuBExx8InY0xPwhNYyTbaxBCdOmsx9LZCqy1jOrNQuHW\nW2/FJz7xCfzwhz/sMRQjDAZJ++Bg4yAefObBRLUxcqKpIuJxD47wG9494UFjWo9KWpngggfS89Vq\nNXP1IGtw03N+7gdWekWHrumd6g6Xqsus48QsZnUnSPQovkpSPzpbFht5wuQJWD1WsgYsBktBIYzs\nzvAhb4BDDrSu65HSzGXB87xgvs34+Hhmf4d6c+MSr4wB27YJVKscv/pVr82gPWu0e3/Jf5CrO/5x\n4gOeKElp12UQgkHXRW7paiE6AZSq+kIHFJhRn7LcS/300ww/+pGCs84SGB/PZncWi6kThayztwZp\nd4YuwEn6kcbWroUzP4/5PXsyHdN1XVim6cv+DTCLzznvGn6U9YFj8KlMNCgyK1zXhWPbqEiBFWMM\nLNS/Q0ZAFiigF3mhTcKYPww1x6Aw+ncinY11ZGOz0tnKCnDycOGzvqCuuOIK2LaN8847DwBw9tln\n43Of+1ymY4xQDmbMGdxz4B6/wiH9juSkq0yFJ/wgRp5JQwM0bcuGwhR/GnmGwMEXN0n33Hjcg9ny\np54LLoKKSVqQ0po84yDLd13HDZwM+n5Q3VH94ItoaxRIcfDgOhc74OlHZ5ODnSQ624raCpwyecrQ\nOBo0vyMtRnZnOJHl/UE9v1Z7aHjWPpgsARXN7anVamg2m5mfe8/zYJomdF3va3dOO80Pch5+2A88\nhBDt2SseqlWj3QfTmUsHEG1NtNXN+gc8NMxT1/1ghHpzDKNDY8sDCqA0jWbH+NQ0//y+PyoEDV3l\n+NGPOLZta2L5ct+P1DRtQZg3UcgTODUajUxFhEHanaELcPph6pRTcOTgwdSdYCRZXKvXU00GjwTr\nnqItXBeKqnbRsCiIqrR576ZpZtoRnueh0m46dhxfBYicefp3Emzbhud5MKrVxM/KQUTZYgU076YU\nRNDZvHZQlpXOxhhbVIEBeR1psCdjAD/CYNB0mrhz/51B4KIwBRWlAsH8Co3HPXjotUMC/pwJzjnq\n9TpMy8zfuAuRGBiRrfDlSzW4XnrlNeq3qRpVv+Ik2R1VUaFqamLgISBgW76ISBL1TmEKwAAF3QEP\nyTkvlFhBGkTR2SgZlERnMzQD21Ztg2sNZphxHkdjfn4+UyZ1ZHcWHv1+0yy/OUndA8DU1BRmZ2cH\n0t8jhAj6bcbHx6HreurZJbK/Ua/X4bouWq0WhBDQNC34J8qHOfFEAcMA7r0XME0/gDOMeH+nQ2fz\n/z+NWEGHooZArS1MY8sLz/OPZRh+ICVXhhjrHjb6wAMGtmyxsHy5G9xbCnbyJM8XElkrOIO0O0su\nwGGMYfLUU+E+/ji8hE1FmxBAMGDKz4qWBEUJgizbtuHYduZ+G6Cz6eTAgxqDae6N1b4ORXrAZViW\nBSFErmxNlFgB/RP+XJKxVHQdvMju77/Ynim6SXQ22SHQxsdL678ZplLwCOUh/Js6noPd+3aDcw5d\n1f3smmjA5slJEs45WmYLiqL4doeCk4yGp1+1h+boeK6HutRPmObZDPfbKKrSpT7meR64x+G0nK6/\nV1U1WBcX/pBfhSmo1rJR74KAhzKtEWIFdC2LvdfCdjmKzqaqKl646oWoqBW4GEyAkwfNZjMzHXuE\n4ULaiorjOGg0GsGw17z7pt/5hBCYn58H5xxTU1NddqffOsP9NjREE0BQMXUcB2abbaNpWlDdoetZ\ntcrF6ae38POfV8FYJdN10lrJh4iis1HilHMG12Wo10VAWyMam+sWG+vnOAy67vf5uG70+j0PuO8+\nA1u26Fi7lgcKc3R/KLlL1Z1BIW8FJ49i8CAwdAFOmpup6jrGN23CkfvvB4+oGBRVL0sDygAEQVSO\nacBycBOFwKGvVLpm31iWFWQQvXY1qQzuYlR1J6rCE24IZG3FtIVEPzob0FGh0/tIAA8atm33V7Ma\nYajQdJpYXluOg42DsFwr+POkigpVQMLqZWX33ZAEtMIU1MfqmY7fT0xAYQoUTfGrF+3Pup7bVd1h\nzJ/qTbOvil5fWKyA6GyBA8L9Co/HvPLobDkdlCg628lTJ2NcHUej4QtJOI4TZKHLcj7yNvsOi6Mx\nQj6kCTgsy0Kr1epRL8vbvxMHz/MwNzcHXdcxPj6euUckqd9GUXwaL/Xikq9jtmfokSPvOA6OO66G\n5cs17N4NWFbMCVMgis7mz6/p+DymKaDrHJrmBzyOQz018cFJuvvh9/lQf06U+yQEcP/9CkwT2LBB\nBL8t3R+vrQZMyWiyO4udGBomuzN0AU4aMMag1modZTWp2tCvmlJEkUSGa9swLQuaokTO0elXLeoX\n3IQR1lF3HCeQWSbZ6yDLWsLDLW8SVVVh2zYE59BIuKB9H5mqgrnugFqnUy+2h85GHGTHceC2S+hU\n/SoyB2OpZzRGSIep6hS2VrcCAGatWUw3p/FL95ewhd2jcCZXUyLVy1hOuwPW87y5nguzZUKv6JHB\nBQOLdd7l+TZpxASIMlZRKoDepqTZtq/QCAbP9WALG6rWXd0pApnOJlSfAieEgKZoHVqJaEs7F6Wz\nFVwuYwzHjR+H01adBqAzvV1OfJFNLmp38mBkd57dkKspUepleQKcuO/Yth30VsTNDYw7F1Uf6Php\naHlEVQMQOPLUh2tZFnTdw2/9loa7766g2Sy+rzp0NjUIGqlPhuSefcEBpR2YsNxy0jKoMqSqAGPR\nQdOjjyqwLIHTT+9UtuX7wzlHs9kMJMGBjt0pUuHJGxwPk91ZkgEOoUtZrWA1pR/kH9sl3vvYGNQc\n54mbb5MWjuPAdRxUDQNKu9pCEb1t28EGUBUFSgnC6gEFTip9+9nLdkVH6kUKFIoWk1pC1LR2FnVy\n9WoIxoL7Q39XZkCYhKxNdyMMFyaNSUwak1iBFaiP13HIPITp5jQONg/CtE2fksYU1Oq1gQ67JNEC\n6rfJAuq3AfLJNVNwwz2OWrUGpjAILnqqytS/o6hKoYCHgkYAqNVrYGDB+mV1Ng4e0EoWWqygrtdx\nxqozgv8nO0KDFKOq7nLAkzUDnhXD5GiMEI00zn6UsioN1MxTTckCEi2wbTtxjk7U+ZMkoLOcn6oU\nExMTwb5yHAeKYmHz5ibuv7+K+XkdqqqAFZxpxTmHZZlQFBWGUQvO51d3BAAOVeVwHAbXBTTNr8Jw\nXszu0FweWclNxq9/zWCaCrZt44jLk1Sr1eBZcV23x+7krSov5crx0AU4aW6mnGUYW7sW1uwsDv3q\nV9A0LTa7EP5e3jXJogVapZKJmpW1ahMF2uxysNET0XsePM5h2X72s8hL1c9ksB4KHG0a7rpQ2vc1\nTqyA1hh3jkFCGx+H1i7tkmy2TGUjPqtc3Um6R3nWO0wbfoRopLU7mqJh7cRarJ1YC9u2sf/wfsxN\nzOGodxSzVnRTr1/NzWl3BCBYt2hBlkpAnvk2UcegYMOoGkEQwRS/aqpDh0B3koXsDvXvZAk8fCfD\ngqJ2q8/RMcLqbIshVqAwBdtXb4emdF6h4d+equ5hu+OrP/Ge6k6ZDefAyO48GxD1m1uWFfRXle3v\nyAlMqhABSD1Hh1BGcEOVCUVRMCYlreVe3LExgZe8xMXPfuZh/36n6++z+jucezBNK+j9oe9GiRVU\nqxye58/KYQxQVQee5wdYSbN3+v0e5E5G9ec8/TTD7t0KduzgCDPeZV+QMdZFZ6P+JvIdw9WdsoPj\nYUqsDF2AkwZyVsOyLGDVKkw2m/Dm5lJ9Lw8450H2n0QLOI2+TSjNyt8vEtzIwUatVkv8rKKqUNpN\nsXJ1x7Htrmb9JEEEzjks0wzm6YTB2sEN0F+sQObdLnR1JywP3dW7g2g+q6xWEmXURxS15yZku0NS\nrGuPWRvsD9uzMd2cxnRjGtOtadhuR5Agt90RHFbT6hUtiF2kNCG8hOAmLtjoPS2DpmrQVC1Ytxzw\nKEzxqWx9qju0D/UYuyMjq1hBmQHP5pWbMWlE9/ZF2QfZ7sh9BiSVC8TT2fI+O6MA59kB2W9pNptw\nHCexmlIGXNfNJFogr7Ffv03a8zebTRiG4dudmGP4yVcd55wD/PznDE8+6ffRRFVNk5IIruvCtm1U\nKpW+99UXIVDAmMDYGGDb/jk1jUMIrz1Dp1udLbzm/tcf3Z9z+DDDT36i4swzPfRxA4Nzhf0d13Xh\neV5fOltef7XVamH16vJngeXBkg1wfM3wBjzPw9TUFNiWLXjm3nvhNpuln08IEQzP7MqYcO5LI/eR\nrC4a3FCPTVywkYS46k6SFLXnebAtC3rMZlc0LfGa+4kVyJ8bVAVHwKfYV5YtS/xcFJ9VdsyAbnnG\nPBgFOM8eeJ6HZtvGyCpCAFBRK1g3sQ7rJtYBAI6aR3GwcRBPHX4Ks/ZsrvOZLRMVo+JnFDOKCWTp\nt4mC67ldwzuzgMQKdM2v7nCPw+MebMcGt3ikFLXjOnBsBxWjEgRKmc8ZIVYQNXunn/x2EtZPrsf6\nifW5vkuQ7Y7RHg8QR2fLopAnY2R3hh9pf1OyO4qi+P5ORqZLVpDEeFaRpqz9NlGwbRumaaJWq6X2\ndxgDtm4VMAyGX/5S70nu2rYFIdDj78jqZPI8nXRggaS0rqtwXQ0AR70u0Gpxye+R70X630PuzwE6\nk1Hm5xEEORMTGZaL9sgMeQh8DJ2tCHV/mCj5SzLAoQyqruuYnJz0fwhVxYrNm/HMPfdEKqsBvsOb\ndcM7juNLxYaDGzpmQoBDGwzI328TNbyzCOTqDoDgpUpSy0xRwDnvGtong6437X0MixXIwY5cwqah\ndKVWdxQFlYwKanG0EqKzAdlVkkaZ1OFH2ueOsoppsprLqsuwrLoMx9ePh+VamBfzmG5O45nmM7C9\neLnpoN9F+PuwomdzMqh6krdqETe8My8YpCxijBQ1WJv6YVTLsXMRs3eCQIdzcI+DKb7dyUJnmzQm\nsfnYzYXX17PePnQ2wHf80tLZAN/RWL58eelrHWHhQQM1qb8rDbIGOEKIIHlD822yQPZ18vbbmKYJ\n13UxNjaWyw6ceqo/EPShhxiA5OQlVVaEQI7gpgPP8wOXSkXAthlcV0G12k7aOJ1Ek1/VQrCfo6o7\n0cf3/y1LVJumH+Ts2OFh2bJ8yfMkOlvY7mShszWbTYyPj2dezyAwdAFOvxtIahqVSqXnJmr1eqSy\nWl5Qv42fbYx+ASYNtnRdN6hm5EHa4Z1FIFda/CZiP9CILe+GemyyQqazEa9fNkDhzxUJePTxcbAC\nzlJUeZekYNPS2YBRgLPUQfRQz/NQrVZzZacqagXr6+uxfnI9hBA4Yh7xhQoaBzFnzwV7igsOy7Qg\nIHqUE/uuEzSYzrdJeSgswfBOkTy8swhkKWqapyO4f72mZXaqO6oKpuSrPkWdE6of8FiWBab4zg/a\nDkcasQJN0bB99fbYe1K0v5IQprMRnSSrOlur1cL69cUqTSMsHiiRK4Q/FLOMURBxoCGhYbp52nUC\nSE3xijs/UaaKiiaccIKAYQjce68/z4YgJxE499riSX71p9UyCyoeMti2Lx+tKAKOw8CYX1FyXRWe\nJ+C6To80Nbk8nfsef92O46+V1NtcF7jrLhUveAFHGXmMsL8j9+1kUWcbJn9n6AKcOFB2gYKbuKBB\nVlbrQcqMBuc8GDY1NjYWvFQi18U5FFXtUhIjxxeAlC1QgkApjbJZ3uGdeUF0rJrkvMm9KQKAputQ\ngFKUxwKFJIlIGkVny9W/0/6Nw/03ZYE4wf3obLTWYdrwI2QDUWGpipsnWUHPivz/K2orsKK2Aqce\ncyos18LB5kHsn92PvYf3gikMVaOaejo40Om30VQNHvO67I6maqmCha7hndVswzvzQD5fpe7398hi\nBY4pNQ2XIEUtn8+oGl1DS/uKFTBg66qtqOsLT70gu2cYRhedjWxznDrbMGVSR8gGCjiA7qb6LEhb\nwXEcB/Pz86hWq6hWq5iZmUl9DqpMGIYROMTNZjOonKShdhP9TtO00vydNWuAs87iuOsupadZn4Ib\nRVF73uWk0MaYLxmdla7leQyeB+i6gOv6Qz1V1RcvUNVu8YLw7J0wnS0q2BEC0iwe/7/vvVfFSScp\n2LSp8G3rgd/jlKzOFmV3hsXfGcoAJ7wxPc/D/Py8L/k7OQnTNBM37tjatXAbDTT27es5bj9EDQn1\nOdsJUJSgjkiOeTj7yj0PrufBsm1ACCgxSh/U1KuqaqJCSlmgrCBlC2V0GVZVhWOa8NpiC1kDtjTn\ni6SzcQ4uBT4U8KShafTrv8kLOm8/OpuiKHj00Uexd+9enHLKKQNZywiDQ1iKlap3WdHP0TA0A6ur\nqzHujWPrsVvREA1MN6bxhPcELNF/kp3cb0OqZfTnaYMFcpY1Xcvc75MHlEQKn08WKxAVUZoUddz5\ngASxAkmK+vlTz8ex1WPBOV/weTbhylAadbZ7770XR48e7StIM8LiIuodRgEHUWHn+ognJSHJ7lBl\nOjwkNG1gJPfbUGJP/nPq85X7zcKZf8dx0Gq1UK1WSx/KvmIFcPbZHLt3KzBN/5xxIiayv+b7GRyu\n63X1Kvv/pJOidhwGRREAXMzN2TAMHYahdgVb8uwdgCo6kkhKQnWH+nM0zZevfuQRHYqi4NRTizOX\nZNB1pqGzqaqK//u//4NlWUMT4Cyspc4B27YxOzsbUNLS8o8nTz4ZRkYH17ZtmK0WqrVats3WNgay\nckgYStuhr9VqqNZqUBQloB6YphkM7jRNE7qul77Zo8DbwRxNJI+D0hZnpz6ker2OSts4WLaNZrMZ\n0PmSDCPnPNX5CIwxKG3DGc4GyU25YfGC9pcz99/0QxIFhcq79BvTC2PPnj345je/iXe84x248MIL\n8cADD6Q61zXXXANFUXD48OEyL2GEGIR/V8uyMDc3F/yWZODLFsWgynSz2cTExASq1SqOqR2D0449\nDS9Z9xKce8K52LJqC9aMr+mSJCbQPhBC+MMvJcedggWjYqBWr6HaprqSQlHLbPmzdRwbpuWLGVT0\neKW0suB6/oTyfudjYIEjXzV8aiA59bZto9X0lewc1wlm5ESBlMr0ip7q+hTmV710XYeX1OVPAAAg\nAElEQVSmaVg1vgqbjt0UZKvJVlPGl1AWRS0LZLtTr9cxNjYGXddx//334+abb8aFF16Iiy66CHv3\n7k11vJHdWTwQJY0a/EmtNa/dSXoWiW5tWRYmJycz+Ru0D4iCH/bJqJG9Xq9jYmIiuA7LsjA7Oxuc\nt9VqodVq+f7EgPydiQk/yBkfF0GwYhhGYn+Rf02dd3m9Xoemae0kiRUoaPbzd2zbQ6NhY2ysAl3X\n4LoKNE2Asejv0LgKsjua1hFC8CtLLlzXA+cCnBMdmcHzGCoVgccfZ7jvPgUlv6IiQXaH/EGyOz/+\n8Y9x22234ZxzzsEll1ySOjgflN0ZygoO0NnslmX1NLyFKR9RYIxh+emndymrJRkKmjNRi5kzkfQg\nu2355SzNf/L10EuTroma9cqggsUhrXgB07TIWT9ZpahJCS5Oma0f5MpOWKyA/lv+rFaw/6YoKGv1\nxje+EY8++ii2b98O13WxLEXQ/dRTT+G2227DCSecsAArHYFAdiVOirWIoxH1PZmGEjVngjGGilrB\n8+rPw/OmngcuOA63Dge9O7PmbGoJ6IBuJc2t8cVFXP8YYPBcye4MIMgpKl6QR4qalNnyiiXU9Bpe\neNwLUdF8B0wWRyF77brugld14kB257LLLsN9992Ht73tbXj88ccxlYKuO7I7iweZCjs5Odn1rBax\nO1F+EjFiVFXtiDSFvhd3PlkgKA1lPKqPlRK5lBBwHAdCiMS+jiKoVgW2bWtg926GVquaWUxArkBR\ndSdJihpAlzKbEL6/QrQ1xvxenTB1TkbU7B353vt/1vmNOWeoVoHp6c6snKIq4lkSNnSPPvCBD+DO\nO+/Epz/9adxxxx2pKLKDtDtDGeAIIYLILyzFCqTf8Iqu91VWI+oCzZnIioAaommJggNJoEwA0QlI\np7wIFSwJjuPAdZy+4gXMH9Hb93iyAQB6pajp98rbgBh3TrkZUg52PM9DZXKyPe1Y6frcYqDZbGL9\n+vV4yUtekurzV155Jf7+7/8ev/d7vzfglY0gw/M8zM3NQVXVSCnWMis4RH9LO2cC8CsLx9aPxTG1\nY7Bx+UbMm/M4ZB7CdGsah1qH4PFkufowSEGspteC/5df2ml7d9IgEC/g5YkX9JOiVpgSKNHlCW5o\nmKehdajCPdRjqYJGjhqpnZVld/JWhhqNBjZu3IiXv/zlqT4/sjsLD8ZYDxV2kFVA27bRaDQyK7IB\n5cy3of1B/Ta0b/L07qQ9ny+vLfCyl9Vx//0Knn46//H861ahKL3JXZKiZu3RiIYhK7P5ktKq2qm8\nUMAjRArb37YjqqpKAU4n6AEEbNuF6ypwHOCuuxRs386xAF0OPXBdF5s3b8aWLVtSfX6QdmcoA5y5\nuTlompb6xZ+EQFnt5z8H0F2JcV0XlmmikqJkGZeBLUJLIA4sY93DO+W1pO3dSYtAvKDPvWWM+aIM\nfWb8REGu7ti2HSjRObYNx7ahto1XGQZMXq+qqm35WQ8Tq1YFxoCcEACFAp68v3WWprubbroJ69ev\nx9atWzOfZ4T8oKQKNXKX6WSE7Qe9zPvNmYiyO7KTMWaMYbw6jhOWnQAuOA61DvmDRpvTaNjx/UJx\nwzvl6k6Zjf7U3M8YQ7U2GPECWYpa6H4w5XkeVFWFbdlwmBP0J6W9ho0rNmJFbUXiZyjgkVX2AHRV\n42V7s5CJlpHdGX5QFZcCjiiUUTmm3lfTNPtKQPezO3mDm7jhnXJ1J23vThpQVUxV1YAmt2MHxwMP\nMDz1VDn7MFzdocqUoijtxDmDqnZUVrslpX2hAMaSqzlhyHOxHMcBIKDrFUkIAJieFrjjDoEXvUig\nXs93rUV827TfG7TdGcoAZ3JyMnFDZ93wpKx2dM+eoF/Gsiy4joNqrZbL0e4JbtovsrTrSju8U1FV\nVEIGIE91Rw6mUslNqmruihSBgik5UE0z0C4vqDJVrdcxfuyxAUUtiVaSVYo3D8KOxite8QocOHCg\n53Mf/ehHcfXVV+N73/te8Gdl93yMEA3GWF8aTxpqbNz36OVD9LcwDSUN5J6P8DOrMAUr6yuxsr4S\nANB0mjjYOIjp5jQOmYc6z32K4Z1pGv1TK7PFBFODgoDoKDTWa4Eym+ACrud2Nw0nSFGvGV+Dk5af\n1P98bbvqOE7QI0qQlZlk5zBrkqWsxMrI7gwfFEXpS1suUjkmuzM/Pw/OeSQjpt/3ZUpa3ndlmuGd\nRN2XxTPyVnfiginGgC1b/Fk5e/aU994P7JyiBOeLEwDxE68qdJ2BMQSqaz67P90+p0qYP7Ow2mN3\n/OBOYM8eD6ef7iepFoLNEm4XABbX7gxlgEMN+HHIs+HH1q2D3WigsWdPIL9abzcP94N8vq7p4NJ3\ns9DU8g7vDPfuZFJmM82+wRRB0fXIvpssICcjHEyFAwpZ7rRIhcpxHLiui2qtBmNqqqv/Jo5WIsut\nCiH60krKcjRuu+22yM898MADePzxx3HGGWcAAPbu3YsXvvCFuPPOO7Fq1arM5x0hG5T2kNs4FHU0\nZmdnkWcSeVbeOwDU9TpOXHYiTlx2Ijzu4ZnmM9g3uw/7Z/aDGelnc0X17tCecS032DdJymxJwVSZ\noBlCiqKgYnSCKbqGilIBdEldrq2SBCBYv6qqGNPHsHVV/4wi9YlyzjE2NtYbdIZmXsi/Y1lV5SR4\nntdFCR7ZneFEP7tStIIzMzOTif5WxO6EQVWNrMM7o3p30lZ30gRTp5ziBzkPPMBSUcSSwLkvA00C\nAZ1gqvsawlLUluUrqFWrClxXg6oCitK/mkNJFQCRstqy3Tl4UMXpp7tQ1ex2p6wKzmLanaEMcPoh\n74YfO/FEHD14EGhH9lkg93jE/egixcNQ5vDONNUdAMHsoDT9L0qMqEBakEGLkoGOQpQRy1qhCs8M\n6jf/JsrxkLPjMq2kDKej0Wikooq84AUvwNMSQfj5z38+fvazn2HFimSazAgLg7x2h56tWq2Wec6D\nnAVMqyAZhsIUTCgTOGXyFJyx5gw03WZAZTtsHs5Uleqq7iC+uiPgc+urRrVUKmockmSgs1yDa7vY\nsWIHXNsF0+Pl6KkaByBQ2UuCzKGn9aa1O4OmiozszrMTNLNkbGwsl79TlJJW5vDONNUdoqSnDaaO\nP96nit1zT/dA0CyIk52OQpwUdbPpArBQqagQQoVhKPA8FYiwYVGVoiRwrmD/fg3Pf34nQb+YbBYZ\nC2F3lmSAkwe0ESY2bgR/4gm4GYboAR1HI+kB6Fe9SYq6iyJc3cmjzMb6ZLD7IWulqOf8ERUqj/PE\nClVUpSiLPHiU4xGu7tDnKJOVFTRnICsG2Ww6wuBBmbZWq9XTZ5cW9AzmDW5IFU5RlMARH6+MY7wy\njucve75f3Wk9EwQ8LSe9XUyjzOa6LgTEwJTZgGKVovA1bFm5BcfWjw0oLqTuRP+QHaB7mrdPNM7u\nyE3L9Lk8QXURqsfI7iws0lRwsryXqbJYZJ6e7PTmeR4GMbyTEFXdCSuzkZBBv96d1auBF73IHwjq\nONnWSHLxuRQh22IFlUrnGnw776HRsMAY2YbO0HA/uDF7Bob2wxNPsCDAycJmyZNYWYi+nSxYkgFO\nlkyqzHufmJjA7OwspjZvxqF7741VVos7H6mtxfaMCAGmqj2N+fLwzoWYbwN0ZvKQU9UlpxpVGWmL\nCsDLLipAx7ctKzPtLgn9pKghBJiidBlwpqrQC8y/SaKVyGpJWWgl1HSYFb/61a8yf2eE/OhnYLPa\nnUajAc/zMD4+HshBpwUlU2joH72sdV1P/SzF8dBlqIqK1WOrsXpsNQBgzp7DdMMPdo6YRxLny0TB\n8zyAATVj8MpsAArLQMs4fvJ4HD91PICO0AtlimkgIQU4ZTtucXaHKtrUUEzXmPYZyLO+kd0ZLmTq\n7ZWk58fGxoIKShrQM6eqKizLCoIEmsuS9pkb5PDOKMjKhbVaLXhHR/XuRAVsy5d3BoK2Wv33i0yX\nq1ZlpbT8IModoKFarUDTOEzTA2MOWi2rHeCIHhpcGrRaDAcOAGvW9P5dHJtFTrLIwW4/WJaV+zcf\nhN0ZygCnLEeDNjtjLJgzwRiDWqsFympJxwkkoBUlqBAEPSOmGTnvhTEG+Yjk+Oed/5IHpmn2ZIzD\nMs5y746qaVArFSjtwV1ZQT1FhmGUJmUdhsy5pUoRa2+4VqsVBJy1iQk/+CkBsvKRZVm+xG1IJSlt\neXeUFV36SGt3wnMmgPQZdTmgppcZvbApUKC9oOt6bEU2DQ89ChOVCUxUJnDS8pPgchfPNDvVHdM1\nY78n978YVSNRma1f706q+9SmwLmOGwwwLYJJYxKbV27u+XOlnUAxDAOu6waqTJzzQO0zqwPYD7Ld\noR4hwzAC5wMon0Y7wvAird0JS89TQi4NZLtDg8YpwHZdN3jHyk3+YbtDFWvbtoPhmIOG53loNBqo\nVCpd6pdZe3fGxztBztxc8oBUv7nfK8XuRIPBdVVUKgoURYemeWi1TCiKCs69Ln8nrTjTr3+tYM2a\n5GRV2O6o7eQygJ6qclxyNy0df6EwlAFOP6TZ8P3mTJCy2sxjj0V+P67fJghm2gaAqGCBMo8QUNGR\n8HPbJcxBOf7hNaepFIV7dwRjcNoyp1mU2YBOc38ZPUVpEEeDo0yxV6lgbm5OmgZcbHiY3CQZp5Ik\nZz3CYgUjNaLnFqLmTORxMmTeO2MMlUoFlUoleNZc14VpmvA8r+dZz9PUGwVN0bBmfA3WjPupv1lr\nNgh2jppHg+qOzEPXdC0yWEnTu6OqKjRV61vdKXumjqZq2LFmR+JxqBpWq9UC2yo7gJRUKiJrK0Pu\n8ZH7F2TKcZJISj869QjPLkRJz2dR5Irqt6E+D9nuUHVGpm7Se5gEN8LvyUEhTaUoqneHbE64umMY\nCs4+26erHT4c3XfXocQXH2HSD5wzOI4LISwYRhW6rsJ1Wde+9xk53VLUUes6dIhhdhboR24h5kGY\nfptWJKXRaOSaJzkoLMkAhxDH9zNNM+h7CD/4ssMxtm4d3GYTjX37uj6Tdr4NZc9og7uuC+44sDkH\nOAcDoFcqCxPcpJSdDkOtVCBcF0qb5pVl7k64uX/QoGuMqobRGpevXQttbAyu68K2bTSbzSDzRPSe\nLIZfNtpJaiVJTcN5e3dGGC4kBSsUCEfNmaDfPlGgJGVTr+xEAx0nm1729Jl6vV66kzFpTGLSmMSG\n5RvgchfTzWnsm9mHfTP7UDEq0NR0r5MkZTayKXHVHVkGuoyZOowxnLHqDNT1+Jcy3dtwNSzKAYxz\nnrLaHQpuaH6HfE7533F2p9Fo5OqDHGHhUYSxIlPww9LzaZIrReyOTN0EUKgnLSssy4JlWZkqRXLv\nDlVEo6o727drePDBCg4c6E5mWpZfRUnT3F8G6P5Wq1VomtLuyyGp+e6gLUqKOlzdeeIJhq1bkxlL\njUYjkn4b1TMYJVZAs+SGBUMZ4KTZ8FGgze66buycifCmnzz5ZLjNJqyjRwEUG95Jw56ot0dRlIC+\nVXRAZxJyy063Z93I9yNc3Ynq3VEUJfj/VDN1SkCaHh+mqqhMTYG11ykbsaSm4SiUoZLkeR6+/e1v\n49ChQ3kve4QFRF5Hg14MQojMcyaADo0CyD4IkpxsVVUD+pSiKJFZ1jLtjspULNeWY2xiDNvWbMO8\nO+9XdxrTOGodzVS5lKs7QPysLEVRYFs2VE0tbabOSctOCvqPokBUv36OVNgBDDtPAFJVleMyqHGI\nszvXX389Go34Ya8jLB0k2Z0wBT8LKChO20sqg6ibqqrCdd0gmKZ3ZlkMijCSGBVZEVfdcRwLGzY0\nwbmB3/zGD2ZkpbRBBzdESfY8N+jx8bzOvBwAUBQOx1F6BBfCUtSM+VLUqqpi3z4Vp50mEFXsoneY\nruupBl1HiRW4rosvfOELmJubK+9mFMRQBjhpQJuefgjivSuKgsnJydQPIWMMyzZtwvTdd8NpNhOz\nGP0QVBiqVWhS9iwuUEhLA0tCXooYUxRA9A5l6vpMOGvjeXDaL22C67oDCdpkpO3xqUxMBH05BNmI\nAb2ZpyhecVYnIwqMMdxwww34xje+gbvvvjvz90cYPkQ5GkSF1XW9J9se9V357+MoaVkRR9WIetbl\nfpG856PKJgkoKIqCKXUKU8YUTl5+MhzPwXRzGgebB/FM8xnYnp3p+EFlXK7uuB4sx2ovwLf3RZXZ\njqkdg40rNsZeI/UT5KH6xTlPSVXlpAxqlvN+9rOfxcMPP4zbb7898/dHWBog8ZFqtRr7rMQFRmXZ\nHTn4p/drPxpYEcpsHG2zDERVd844w4VhWPjFL1hwLwO7MyB/R+7xCQ/wBADHYVAUASEYdF3AdQF5\njk+cFDUlWh55BNi4kXW9A6jiS72GeXHVVVdh5cqVuPbaa3Mfo2ws2QBHRprNTghveiEEoKqY2rQJ\nh++/P9WgziiEqyiMjo3oQCFMA8uz+XNTxBjzJaGzXitj4BLnf1BBm4ygjylFAFdJIQ8tNw3LtBLK\neKuqGhixvMGNEAJf/vKX8d3vfhff+ta3FqzKNcLCgAIVeoHX6/W+L4You1PGED3btmOpGuFnnSqZ\nlNnPk2UliWTGWKyToas61k6sxdqJtQCAo+bRoHdnxprJXN0B/ICmUqlAVdTcvTsyDM3AttXbItdf\nZpYYiKfGyFVlsju6rucObjjnuPrqq3Hw4EF8+ctfXpD5QyMUR5bKMQXecRT8KMiJlbLsTlyfX1oa\nWJJAShTKCP6zgO75CSc4GB+v46GHNLgu7+63VlWoqgLG8ieLZNBv6/t08b4H5wycA5omoKoAYyJS\n4tr/fbulqPfv97BhgwnL8t8BVIGrVqu5gxvXdfHud78bJ554Ij7wgQ8MFR1/yQY4lPGyLCuS954G\nXcohY2NYvmkTjjzwQObG8J7hnSJaLpoQNaAz/MJOUscgA5OXIpZnmGcURaxf0FaUkkf3tZoy0Og3\n4DMMOfCsVquBw0FZDZLnzWKMhRD453/+Z+zevRvf/OY3F0wWfITiSEuNpQqGbduYmJjIrBaUlvfe\n7xhZmnrlikK1Wo3NsibJUNNsi7Q0BsKy6jIsqy7DKStOge3ZXdUdx0u2Q1Ey0Hl6d2QoTMH21dth\naL0vdMoSCyFKzxITwlVlx3GCuTpk85LUqqLAOccHPvABcM7x+c9/fiQw8CwCOdvELPA8L5aCH/6e\njDLsTtbhnVGVTJpZQ895PxXCNHL3ZSJcvZ2cVDE2BtxzjwbPC42saPtRakF/R/bp0tpW12VgTEDT\nfOqav5Tk5L7rajh6tI7jjuNd0vemacJxnMy9yo7j4LLLLsOZZ56JP//zPx+q4AYAmBhCmSfKTCbh\n6NGjgUrV+Ph46mwVNUHpuh652Ru/+Q1mf/nL1GslfnV44ym6njmIADpyfF67uqK2X3Iyx7LIMM08\n68oqAy0bgDzKbEB3dSoNFFXFqrPP7qGopUWYgwp0lNloFkW/pmEhBK655ho89thjuO666xZMFnyE\nckAv3yQcPnw4+F2zZPdnZmaCbGfefht5nUUHTcqQs6xuWyo+HNgPYraFEAJHrU51Z9aa7WSqc8hA\nB+pCvNvuhKs7m47dhOcve37keopSU7OC6CF0X+WqMg1q7ucEep6Hv/iLv8AxxxyDv/3bvx0FN0sM\n9HvHQQiBI0eOBH5Amp5QwpEjRzA1NRUEF0UoaWUP75RVCMnu0HNOdiev3H1eyPTbsbGxrr109Chw\n110KbLubZiwEh+f519Ld5J+uulOGgIGqioC65rrJ31+2TOCss+xAFZKCT/m3SNOrbFkWLrnkEpx3\n3nm4/PLLhy64AZZogON5HmZmZqBpGiYmJjLdWJpPQbSMqO/OPPYYmiFltTD6STKn6XHpB1kOkIyT\nEKIr+5cFTNMyU/CCHh/DyO+Qtas7nuelqu6Q5GqWkqmxfDlWbNmSa31pOKhhJxAAwv0Mf/M3f4OZ\nmRl89rOfHdFDliD6BTiu62J2dhaGYST220RhZmYmcNSLOBmDzmbKWVYK7El2WJZIHgQs1/KrO42D\n+M3R38D22kmVHDLQcnWHezyo7qybWoffWvdbPfdtoSkwQLf0dJw9j3ICZadDCIF3vvOd2LhxI97/\n/vcPpZMxQjL62R3btjE/P49arZb52Txy5AjGx8cBoJDdGfTwznBgT4lnzjnGxsYWJFmYpF5IaDSA\nO++MHwgaTu4CydUdzj2YplWKEAxjAmRGfPc5+liu62L79nkcd1wt9r7K6pw064/8HaJnX3zxxfiD\nP/gDvOUtbxlau7PkUsw0Z4LoWVluLJV5KXiKe6lMbtgAT1JWCyPN8E7BOZiq+tIXOSHLUFOzsKqq\ncNsPnZ+dVFNVRZiiADzbVPKyZKDTKLOpigK0N06/OT5RSNN/EwVyMvoZ7qSm4Te84Q04cuQIli1b\nhk9+8pOjDOoSRdIzTlQuxlguu0MvhUqBgb8Lkc2UOfSUzXRdF5qmwTTNzrybDPSptDA0A+sm1mGZ\nsgwbJzbCUiw803oGB5sHMWdlU+aJUmarKlWcOnUqZmdnu5r8ybEJDwscJOKkp8NIkqJ+6UtfCk3T\nsHHjRrzhDW8Y+JpHWFgQbck0/QG7ee2OaZrBns2zhoUY3ikH7oZhoNlsBqwJUofMM+ohLdImOMbG\ngHPO8QeCzs5G973QdcjVnajeHc59XzRvwjoMIRhsG1AUgUpFgHP0VHPIj5yeHsfxx8ffwzi7MzMz\ngzPPPBPLly/HS1/6Upx77rlDG9wAQ1rBATrUL4LMex8fH0er1QqymGkgO6VRtKMw95y7Lg7dcw/c\nNt+UkGV4Z16aWhiWZfkvaGnjhas7SVkCxhigKLE9QWGQUctaRckDubpDBjmPvOQx27ah0m+KVQhp\nMqj94Hke3vOe94Bzjnq9jh/+8Ie48847R8ICSxBRlWNyfh3HwcTEBObn5zNlFOWAPmx3+nHP5WNQ\nU2+9Xl+Q6qDci0KUmKgsaxrJ9bRIcjJM1wyobNPNaXg8W+JIVVScs/4cTFQmuugYdB3UFF22rG0U\nKLgp4jCapolLL70Ua9euhWma+MUvfoEf/ehHQ+1sjBCNqAqOLD0/Pj6OmZmZTBL08l6Noh2lqRbI\nfX6DmKsVhSj6bRx9Sq4oFAExOLIkOFwXuPtuBc88ky3glKs7ZHcGkSwCAF3nbXqxH/x05uoY0DQF\n/+//cWR1U44cOYJLLrkEW7ZswYEDB9BqtXDDDTeUuu4ysSQCnPBmVxQlkGZN44DHNdcJIYISXBQH\n1Gu1cOjeewO1MapopM7yFazgpA005I3DPQ9oBwnU85Il0CJnKk8VJS/kviJq8M/Su6OoKladc04m\nA1GGk+E4Di6//HJs3boV73vf+0bOxRJHOMDhnGNubg6KogQNtbOzs6kDYnoxA939NuHyf1J2Um7q\nzUqLy4u02cws19EPMk20H/VOCIHD5mEcbBzEdHMa8/Z83+OfsfoMrJtY1/VnZAPIttJ7YJDZYqrC\n5ZGeJjQaDbz5zW/Grl278Ed/9Ecju7PEEQ5wPM/D3Nxcl/T80aNHMTExkeqZkYe+hu2O7O/IsvHh\n45INKKImmhVpA41w4FZE/j4tgyMKnAP33cewf3+2wM9xHNi2HZwvb+9OGvi0NYFWy4Ftd0tPn3wy\nx8aN6d3/6elp7Nq1Cx/84Afxyle+svDaFgJDG+DYth04CFFzJmjz9cuUy/0r/V6aUdlJPj+P2Ycf\nzl3RYIoCkZEaBvTv8Un8rufBazsf0DQo0uZJugc0xyevgEEeJA3wTNu7Y6xYgRUveEHqc6Yd3pcE\ny7Jw6aWX4nd+53dwxRVXjJyMZwHkACdOen52drbvyzCLFCvZHXI8qMeOMpOtVmtR+kKy9vgUybKm\npWvFoeW0gsrOM61neqo7x08ejy2ruvvz4mzAILPFNH29SHAzOzuLiy66CG9/+9vxxje+MfdaRhge\nyHaHKPhh6fk0AU5WuyNXMWVhEarcLJRqGZC/xyfuOtKwQMrwAwDgoYcYnniif5Aj9/HSAE/577L0\n7qQFPVuMuRgbq8J1FdDcnEpF4OUv50hTmDtw4AB27dqFj3/843jZy16Way2LgaEOcEzTjJ0z0S/A\nybLZoyAPyZvfuxfNX/86yHRkKdXmoakFA0ML8PUBXw7ac124bTWerqpI6DqSAo1BIYs6W5Iy2+SG\nDZh43vNSnbMMJ6PVauEtb3kLXv/61+OSSy4ZBTfPIlCfSavVipSeJxXGuJdwEbsT7u3inAdc6CT5\n5rJQZo9POMsap0BYlpNB4ILjUOtQEPBoioaz153dJVSQxQZEZYuzVneoEu84To8yUxYcPnwYF110\nEd73vvfhNa95Ta5jjDB8oOdDpuCH9wKpMMb2/JZgd6iyQNQp6hccpN0hBzxullfWY4UFUqJaEMIy\n0GX4O7/6FcMjjzDIQzfDa0sa4Bn+bFFltu5z8rbAjS8n7XkMnud/f+tWjvXrk0OAp556ChdffDE+\n9alP4UUvelHf8w4ThlJkgOQ6k+ZMEDcz7vtFh1nJ06VXnHQSdABzTz0F13GAdiNuqgb/jNWbrJLM\ncWCqCu55YOgWU5DnRlBVhP68WvCcWZBlgCcQPSzV4xyWbcPWtK5ZHnHHKyO4mZ+fx65du/C2t70N\nb3rTm0bBzbMIZHeS5kz0sztF5kwwxgJlLCEE6vV6kPWjCvIgGvwH8cJPM+yP/ryscwL+jJuV9ZVY\nWV8JoHfIYdYBnv0GdPbraZDPWSS4efrpp7Fr1y585CMfwXnnnZfrGCMMJ4gKCwCTk5ORz8hC2R3G\nGGq1WkDfb7VaA6Ns5tmP/a5DHqkhtyDIdofuVRnnJJx0kkC1Ctx/vz+IU0Z3oNGf7uf/hioURQ0q\nalnn7pBNBzriFEIAts2gqgK6zuE4Cp54giUGOI899hj++I//GNdeey3OOOOMrLdl0TG0FZzZ2dnE\nrCVNnq/X611/XnSz0zHCTb1CCBz5+c9hHT2aqcEfzJ++kOY2BwNDC0gy+6dMJ5EInuYAACAASURB\nVCrAPQ92u7oDIKjqZK1SZQUZnTJoN4qq4tgXv7iL5kMGWeYWl5FBPXr0KHbt2oUrrrgCF154YaF1\njzB8EEIEMtBxz2Vc5Vjutylid+KaeuMotEWpUwvdSEzXQecEEJllHcR5y77OftUdAME5s8wuCWPf\nvn3YtWsXrrnmGvz2b/924XWPMFxIY3fiqLFx/TZZkNTnl0ShLWp3+kkylwmyz+Q3Aui6jrLszvS0\nLz5AFRI50ChDoTFNdQdA33NSb45tM7zoRRzHHNN7roceeghvf/vbcf3112PTpk2F1r1YGNoAx5Ec\n7yjILw5CGZs9aeNFKavFUqekICENTS2zgEEMGGN+9SbFvJvwOemFTUIFcuBWFsq6TkK4/ybKEaTs\nV5ES+KFDh3DRRRfhqquuwvnnn1943SMMJ4iiEYdwgFNGtRjIPrwzS8NwWecsA1QlY4x1VaiShv2V\ncc5BO1NRvTuAb4+LJFWeeOIJvPWtb8XnPvc5nHnmmWUueYQhQlg1NowwNbYsu5NleKdMoXUcJ1GF\ntqxzloWwcIpcVY5KihZZ08wM8NBDClyXh3q35cCx+ztRr5x+nxGCfhNS6fSCzzDG2u+ocDWp+xiK\nAqxeLbB5c/df3HfffXjXu96Fr33ta9iwYUOfKx5eLNkAxzTNYNrsQm52t9nsUlaLOobnefDaf69q\nGjTDgJJQXjZNE4qilCLJnCaYSqPOlqlKlRJyVqEsTJ50EsbWr4/8O3JsPM8LJsjLA6vSXgs12H3s\nYx/DueeeW9raRxg+9AtwaBYO0TjKsDtFh3eGX9Zyw3DcM55HGrUo+qmzxVWpimRZFyuIm5/3ld0U\nRcndu/Poo4/iT/7kT3DddddhS84hxiMsDfSzO7JqbFl2p+jwTpkCljY5Idu6QY+gIPRTaIyqUhWt\njpOto99sIVXoyE7KAWgWhbmf/vSn+Ou//mt885vfxPHHHz/oZQ8USzbAkSlHC73ZrSNHcOSBB/rS\nzihI4JzD4xyqVN1hjJWuWsY0DaJP5SaPOptcpYqSoU7z/UHN1Tlm+3ZUJiYizxnO2uZxoPbu3Ys3\nv/nN+Kd/+iecffbZmdfneR7OPPNMrF+/Ht/+9rezX+AIC4o0lWMhBGq1WmEqLFD+8M5woy3nvOcZ\nH/RU8ijITkZaGxAnQ502ObEYTkaWOR5JvTsPPvggLr/8cnzlK1/BqaeemnkdI7uztJC2cmwYRikU\n/LKHd6ah0C7EoOIw8ti6pOp4miAhj60riihbJ9sd6t3pRy/84Q9/iI985CP4z//8T6xZsybzOobN\n7gylyACQPFWc/r6sfpusKh7G8uWYOOkkzP7yl4mfUxSl4zSrKlzL8jMFbUlIAZQ2xZalmLmTN6BK\navAnoYK46g5VqMjYlQlF06CPj/f8OdFgwllb+Tqq1WqXA9VqtYLqDjVdPvnkk7jkkkvwr//6r9i+\nfXuuNX7yk5/E6aefHjSRjrC0QcIjZfTbyM3nZdFAw4224Wec7OZiOBlZzxk1TZuO1S/LuphORrhC\nRZltunZZoVNu4gb898F9992HK6+8El//+tdx0kkn5VrLyO48+yDbnSIUfKL3l9lkH/VuJVU2qnoD\nWFC7k1ehkdg0YWGRRqMBIDlIKGN4eFbE2TrZ7sj+jmVZaDabQeDGOYdhGPj+97+Pa665BjfffDOO\nPfbYXGsZNrsz+NG0A4KsLgT0D4jijtFqteA4TqQ0YxLG1q1D/bjjUn9eaRsAwzCgahoEENCmWs0m\nrHbwkwdMUYC28lIcSDmtYhiFN57S3hi1Wg3VWs0fitpuHDZNM8iCc8+D2Z7jMYjNXpma6vndswwo\nIwdqbGwMk5OTqNVqAICf/OQnOOGEE7Bz5078/u//Po7L8DvL2Lt3L/7rv/4Ll156aSqRiRGGG6Ru\nRs4pkM/uUJafnIxByrLTM16v14M9qOs6TNPE3NxcYP8G9XyS/K18/jwgB6pWq2FiYiK4b7ZtY3Z2\nFvPz84ENdRwHjUYD1Wp1UTKo/foKyIEiu0OO1I033ogNGzbgD//wD/G2t70Ny5cvz7WWkd1ZeujX\n+wL4DrvTh36eBM55QJ0s0heWBvSMk0gT7d9WqxXYHblXrUxQ8ogUU4tUqChIILtD982yLMzOzqLR\naMCyrCCgo7EmCx3c9LN1lPgyDAPj4+OB3eGc4zOf+QxOPfVUvOMd78Cf/dmf9Z0tGYdhtDtDW8GJ\nA1EwqImKBoFmbU6VqQR5FW4mTz4ZXqsF6+jR/utu016oyV52vonKRgEbCRSk4n8yBjCWqJgWSDIP\nQAY6qrrjeh4s04RAqIpVMipTU13/X4SSIl/H8uXLccYZZ+DVr3417r77bvzLv/wLPvShD2Ve33ve\n8x584hOfwOzsbObvjrA4iHtmyO7QS4L2Ku3TtL0Vi9FgK9M1JyYmgipOOKMnV0SK7lmiwRCNuOwg\nLinLStUdus5B3+Mi1SI5y3rcccdh27ZtePnLX45bbrkFiqLgsssuy7yekd159oD2KT3PruvCNM3M\noiJF+/zyII6uSb6OaZqRFNoikCtUZQdxcnU8LH9vmiaAzkiOhbA7RapFsr/8vOc9Dzt27MDZZ5+N\n6667DhMTE3jta1+beT3DaHeGNsCJejjk5jpSK5PpC7IMYBJ9oazNzhjDstNP71FWiwL3PFiuCwb0\nRMjhICAwAK1W35k7TNMgErI6JD1dXaAGW0VVoQLwXDf4bWRnMGrIaF5Uli0L/ltums6bgQCA3bt3\n433vex++/vWv48QTT8x9nO985ztYtWoVtm/fjv/93//NfZwRFh8yFTbK7lDmrp+E6mL0viTRpuSX\nNQU75HhQ4JZHVWiQTkYU6GXNOQ+SRxRgyfOxBiFDTe+Sor/prbfeik9+8pO48cYbsWLFitzHGdmd\nZw9ku0M0xqiAvp+oyGL0vsSJmPQkREMU2qz9LjJkhcYisuxpQdfieV4gPON5XiCAVWbCKIy8tF8Z\nQghcf/31uPXWW/GNb3wDtVoNV111Va5jDavdGVqRAXLyCVn6bcJNYvILjl7gZW72fspq1NivV6vQ\nMm466ndxXber30XTtL6KaVQtKuLwZ0XSAM8ohbm8MtSKpmH1OecExy2Db3/77bfjQx/6EG644Ybc\ntDTCVVddhX/7t3+DpmkwTROzs7N4wxvegOuvv77QcUcYLGgCNoGcCSC53yZOQpWcDuKjl9XUm/Za\n8igWFVEVWizVsrg5V3kU5tKiLL79jTfeiC9+8Yu44YYbMBWqSmfFyO4sTYTFTdKOvJBFRaKEcyzL\n6prntxDI63znaYon9FNoHATkRE54tpacMCpb/p7ub5F3iRACn//85/GTn/wEX/nKVwon3IbV7iyJ\nAKfIfBtZylDeNDRMs6yNEKes5nkebMuCXqlAN4y+wzeT0KVmBoC1MzvhisggVcuSQPc5zaDSKBnq\n1LQ8ANVjjsHyzZtLy6B+//vfx8c//nHceOONWLlyZe7jROEHP/gB/uEf/mEoVEVGSAYFOEWlWMMK\nYACChvky7U4cyszahgdaxlVEhs3JiPqsfC1FsqxlORlf+9rXcMMNN+A//uM/uma6lYGR3Vk6KNPu\nULBDlQWj3Xe7EEN8swo2JR1LTlQn7dXFEBTJMlurTPl7sutFaL9CCPzjP/4jHn30UVx33XWlJ9yG\nye4MLUUNKGeYFWXsHMfp4s+noZRkQZSyWk/vC+dgihL04+S9Fp3oMe2Nb5lmQGVjjMF1nNKkp9Mi\noMKldGyIlkdrJCOWhpYH+P03ZWVQv/Od7+Bzn/scvv3tb+du7O2HhXD2RigOuT+liN2hYN2yLGia\nhkqlkppSUgSyBGxZvS9xvHNKopDyoGmaC9rYLzsZaSgpcfSYrLS8vOpM4bVfd911+O///m/ceOON\nA6uyj+zO0gHZHRoYXsTu2LYd+DZEES+zihC19larBc/zSlFni1ODpDYEYrGQ3VnIxv6sVeo4hbmw\nimK/Pk7LsgLhhLx2nXOOj370ozh8+DC++MUvDqyqNyx2Z6grOKSKUyTjmdTUK0fVZXEmZ/bsQXP/\n/sDhD1cz0syqSQJjDFCUnkoQbRqi15QxmDMtyqbCES0vacjo1NatcBWlsJNxww034Ctf+QpuuOEG\nTETM0xnhuQVyBorOt4nr80uaUxM3EyUtslQzygBlJokGA3QoJUWvJc25o6TgixwvLssqX0sZToYQ\nAp/5zGdwzz334Prrr1+wfqwRhhdEYS1qd+L6/NLMqckLcvgZY32rGWUgbHfkhFHRa+mHsqvUcTOy\n5GtJouBmXfv73/9+KIqCa665ZuDvh2HA0AY4V199NX784x/j/PPPx/nnn4/Vq1dnfpiyNPXGDZXL\nMnmajrP/rrvgzMxEZjIVTYvt1UmDuO8TFa7SDqiCfpd2gFhmc78M0zQHSoWTaXl0LYquY9mOHYWy\nNkIIfPWrX8XNN9+Mb3zjG6jX6yWvfISliPe85z148sknccEFF+DVr341li1bltnuZKGHRdkdUtXK\nslcXo/cF6Dj8FFAVGZCXFgtBhYsa9kcqVkWkZ4UQ+MQnPoEnnngC11577YL1Y40w3HjTm94EVVVx\nwQUX4LzzzsN4xHy3JGQd3hmmsuVN7i6WKiQ5/PTeDieqByEqshBUuDAdWK5gFamMeZ6HK6+8EmvW\nrMGHP/zh50RwAwxxgCOEwN69e3HzzTfjlltuQaPRwMtf/nLs3LkTp512Wl+udZFJveFmt7SUEnrx\nKgAaDz8Mry0dKEPO5GZFnKhAUmM/0JFu9jwPEKJQcz+BtOZJUWqhYNs2lMlJLNu0KTbL2g9CCFx7\n7bX40Y9+hK9+9asL2qc0wnBDCIHHHnsMN910E2699VYIIfCqV70KO3fuxIknntiXa03DO/M09UY1\nxKehlMQpFg0S8rVGZRXz2tB+kJ2MhZS7pfledL481GbOOT784Q+j0Wjg05/+9II1fY8w/OCc48EH\nH8S3vvUt3HbbbRgfH8f555+PCy64AGvWrOlrd4pUbuU+Zdd1U0vfl9X/mnWtSdea14b2w2Jcqzwv\nDeimumWxO67r4vLLL8fmzZvxV3/1V0NDH1sIDG2AE8bs7CxuvfVW3HTTTdizZw9e/OIX44ILLsDZ\nZ5/dlSUtm6aRllISpqR4rVasslqeKo6iaRDtJkQZWXtfijb30zEs01zwPh/6DVZu3oyJ9esjs6z9\nDLMQAp/61Kfw4IMP4otf/GKm9T/11FO4+OKLcfDgQaxcuRJ/+qd/iosuuqjMSxxhiCCEwKFDh3DL\nLbfg5ptvxr59+/DSl74UO3fuxI4dO7ocVM45Wm2p+DJoGmkpJYshPU29L0KIVDY2S8NwEhbLoSLZ\nV/pdo9Ty5N6dKHDO8Zd/+Zeo1+v4+Mc/num9NLI7zy0IIbBv3z7cfPPN+M53voO5uTmce+65eM1r\nXoNNmzZFCnukGWyd9txhBcWoYL6MPrQ8a6MexjQ2Ni3ttB/KkGTOirCIAYBcNtS2bVx66aV42cte\nhiuuuCLT8/FssDtLJsCR4TgObr/9dtx000244447cPLJJ2Pnzp3YtGkTbrnlFrz97W8fGE0jilJC\n1IwwZSpOWa2fvHMYrC1QED5OGb0vtFm45wHtDIGqKLHN/bzNfdUrlQWlV8iB3MoXvhB6qISfRmKS\nc46/+7u/w4EDB/D5z38+cwb1wIEDOHDgALZt24ZnnnkGZ511Fu67775R785zBK1WC//zP/+Dm266\nCXfffTe2bt2KnTt3YtWqVdi9ezcuvvjiBaNM0d4rSpnKs46iVLg8dODFcjLkeT5xCZMoGWrZ7nie\nh3e961044YQT8MEPfjDzPRvZnec25ubmcOutt+Lmm2/GI488grPOOgs7d+4EAOzfvx+vf/3rB1LN\njJO+pz8fxADfOJRBS41KiPaj0C5mIJdkY9PIULdaLbz1rW/F6173Olx66aXPSbuzJAMcGZxzPPTQ\nQ/jUpz6Fr371q/jd3/3dgMq2du3agTectVqt4AGLesgav/lNl7IagExKaowxgLGuzw9KBjpq5o6c\nlZT7fBaSXkGBnGEY0AwDq1784sTPhw1zq9XCZZddhlqthomJCXzpS18qhYP62te+FldeeSXOPffc\nwscaYWmB8//f3rlHRVWuf/w7M9wUFFHBQrxLKuJd8UYIIgKzSetYJwO8lPdfSV6yUjuuUtOOWp7K\nzsrKU3lOq4tF7EERwRuKmhe8JGaaeUN0QCAIgWGY2fv3B+7diFzmsvcAw/NZq9WSYL/vNt7vvM/7\nPs/34XDq1Cls3LgRu3btQkxMDCZMmICoqCh06NBBdt0pLy8XDUUEN0JL6wUtRci3F2z2pRjHnBPj\nxtpkmGsDa/ozppsorVaL1157DQaDAUFBQVi7dq0kf2ekOy0Xg8GAzMxMvP322zh27BiefPJJREZG\nIiIiAm3btpV1bGH9CylTctXY1cTafl710VAKLQDJ3SjNwZoDpJo3VefPn8eWLVuQn5+PadOmYf78\n+S1Wd5p9haNSqcRjjz2G48eP47vvvsOQIUOQnJyMJUuWoLi4GGFhYWAYBv3795e0sEpIXeB5Hm3a\ntBFP6gQbQ+E61MXHB63KylCh1f71sxwHhUrVYE8chUIBhZPTA7c9QtNQYTFKifK+LbOzs/MDAiAE\nUzzPw8XFpVGCG+GWytkMETe1mBRc7Hx9fXHhwgXk5OQgKioKaWlpNs3rypUruHDhAoKCgmx6DtE8\nUSqV6NWrF86fP4/9+/fDx8cHGo0Gs2fPhsFgQEREBBiGQa9evSS3YxUci4QNjRAgSG19b4ocmwzg\nwbxy04OJyspK8YNeSDduSieotVHT2tbLywtt2rTBzZs3sXXrVuTl5eGzzz6zaW6kOy0bJycn+Pr6\n4vbt2zh16hQ4jgPLspg6dSpcXV0RFRUFhmHQuXNnSXVH2HirVCrRAEHYH8hpfS/Xza1wGO3s7PyA\ndbOQjirM354NUq29pappQ+3r6wue58HzPJYvX468vDy8+eabNs2tuepOs7/BETBN2xC4d+8e9uzZ\nA41Gg4sXL2LEiBFgGAZjxoyxKYfbnCjb9CSvqqoKZZcvw1haKm46zElTq/k9jZUeJritqFQqMZWt\noT41UlBZWQkAD2yo2vbuDXdfX7OfYTAYsHDhQvj7+2PlypUAqq/1fS14Rk1KS0sRGhqKVatWYfLk\nyVY/h2j+1NQdnudRXFws1u3cvHkTwcHBUKvVGDFihE0fluY4Fslhfd+Y6WFCKomw6ZCrj4eA6UbO\nlnTD8vJyzJgxA08//TRmzpwJjuNw9+5dPPLII1bPjXSHEKhNd/Ly8pCcnIydO3eisLAQoaGhYBgG\nAwYMsOlwty7Le9Ox5bC+N3VotPfNrdFohEqlsslR1xKE4MbW2/HCwkLExsZi+fLlUKvV0Ov1KC4u\nho+Pj9Vza8664zABTkMYDAYcPXoUGo0GmZmZ6NatG9RqNSZOnIi2bdua/QtljWMRz/PQ63TIz8pC\n1b171bUurq5QAXUKT83gxmAwoEqvt3t6WG0mBrUZFUjdc6cu++mOw4bB2cyO33q9HnPnzsWoUaOw\nePFiSeZWVVUFhmGgVquxaNEim59HODaVlZXIyMhAUlISTp48if79+4NhGISFhVlkTW7NDYoU1vdS\n9H2xlNpqX+Ts4yEg1SajtLQU8fHxmDVrFqZOnWrzvADSHcIyysrKkJ6eDpZlkZ2djeHDh4NhGAQH\nB1t0uGvN4Yat1ve2ulFaS20mBuaaLtiCVPbTeXl5iIuLw9q1azF+/Hib5wU0f91pMQGOKTzP49df\nfwXLstizZw+cnZ0RFRUFtVqNLl261PlLa6tjkaG8HAVnz8JYWVlt28zzgNH4kG2z0smp+qbk/v+a\nhmyg5cIcE4Pa+tTY0nOnPvtplYtLg/U3AjqdDs8//zyio6Mxb948yeoFZsyYgY4dO+K9996z+XlE\ny4LjOJw9exYsy2Lfvn1o3749oqOjERUVBR8fnzp/R6WoQbHUtrkhG2i5MNcpqb6CYWs2RKYHV7aY\nthQXFyM2NhaLFy+W7LSTdIewBaPRiGPHjkGj0eDw4cPw8/ODWq1GZGQkPD096zTPkKIGxVLbZns3\nKxYwJz2sLtMFW3ruSOUMmZubi/j4eGzevBljxoyx+jmmOILutMgAxxSe55Gfn4+dO3ciOTkZd+/e\nxbhx4xATE4OBAweKOeCmjaVsuS41dVZTOjvDUFn54G2Ik1N16tf9E1ZLbaClorb0MHMQg537NtiW\n9NwRNlV11Re18vZGu379GnxOWVkZpk2bhtjYWEybNk2yv7fMzEyEhIRg4MCB4jPXr1+PqKgoSZ5P\ntBx4nsfNmzfFPl86nQ7h4eFgGAZ9+vQRa/r0er3kJ5kNpZQAEOt56nIPkwNrc9DrcjIztx5AqhPU\nu3fvIi4uDv/4xz8QGRlp9XNqQrpDSAXP87h8+bLY50ulUiEqKgrR0dHo1q2bqDuVlZWSBxkN3cIK\n6WH2blZsrXlKzf5BlqbQCsGNram/V69exQsvvICPP/4YQ4cOtfo5NXEE3WnxAU5NysvLkZ6eDo1G\ng/Pnz2PQoEEoLi6Gv78/VqxYI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"text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": { "internals": { "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "The starting point and the finishing point:\n", "\n", "$$\n", "\\begin{array}{rcl}\n", " x_1 - 2x_2 +x_3 &=& 5\\\\\n", " 2x_2 - 8x_3 &=& -4\\\\\n", " 6x_1 +5x_2 +9x_3 &=& -4\n", "\\end{array}\n", "\\hspace{0.5in}\n", "\\begin{array}{rcl}\n", " x_1 &=& 1\\\\\n", " x_2 &=& -2\\\\\n", " x_3 &=& 0\n", "\\end{array}\n", "$$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "sl.hide_code_in_slideshow()\n", "fig = plt.figure()\n", "xmin = ymin = zmin = -5\n", "xmax = ymax = zmax = 5\n", "axs=[1,2]\n", "axs[0] = fig.add_subplot(131, projection='3d')\n", "axs[1] = fig.add_subplot(132, projection='3d')\n", "for ax in axs:\n", " ax.axes.set_xlim([xmin, xmax])\n", " ax.axes.set_ylim([ymin, ymax])\n", " ax.axes.set_zlim([zmin, zmax])\n", " ax.axes.set_xlabel('$x_1$')\n", " ax.axes.set_ylabel('$x_2$')\n", " ax.axes.set_zlabel('$x_3$')\n", "ax = axs[0]\n", "eq1 = [1,-2,1,5]\n", "eq2 = [0,2,-8,-4]\n", "eq3 = [6,5,9,-4]\n", "ut.plotLinEqn3d(ax, eq1, 'Brown')\n", "ut.plotLinEqn3d(ax, eq2, 'Green')\n", "ut.plotLinEqn3d(ax, eq3, 'Blue')\n", "ut.plotIntersection3d(ax, eq1, eq2, 'Brown')\n", "ut.plotIntersection3d(ax, eq2, eq3, 'Green')\n", "ut.plotIntersection3d(ax, eq1, eq3, 'Blue')\n", "#ax.mouse_init()\n", "#\n", "ax = axs[1]\n", "eq1 = [1, 0, 0, 1]\n", "eq2 = [0, 1, 0, -2]\n", "eq3 = [0, 0, 1, 0]\n", "ut.plotLinEqn3d(ax, eq1, 'Brown')\n", "ut.plotLinEqn3d(ax, eq2, 'Green')\n", "ut.plotLinEqn3d(ax, eq3, 'Blue')\n", "ut.plotIntersection3d(ax, eq1, eq2, 'Brown')\n", "ut.plotIntersection3d(ax, eq2, eq3, 'Green')\n", "ut.plotIntersection3d(ax, eq1, eq3, 'Blue')\n", "#\n", "plt.subplots_adjust(right = 2.0)" ], "language": "python", "metadata": { "internals": {}, "slideshow": { "slide_type": "-" } }, "outputs": [ { "html": [ "
\n", " " ], "metadata": {}, "output_type": "display_data" }, { "output_type": "stream", "stream": "stderr", "text": [ "/Users/markcrovella/canopy/lib/python2.7/site-packages/matplotlib/delaunay/triangulate.py:104: DuplicatePointWarning: Input data contains duplicate x,y points; some values are ignored.\n", " DuplicatePointWarning,\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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lbBrDrkTjrbxnZ2fXvoNdkEKiTX/JjeGDMNnwtLQvz6xvX24wmxaGVVqxUF/g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DAAAg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\nf/11jBw5MuLX31XQKhohQKyJi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"text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "source": [ "$$\n", "\\left[\\begin{array}{rrrr}\n", " 1 & -2 & 1 & 5\\\\\n", " 0 & 2 & - 8 & -4\\\\\n", " 6 & 5 &9 & -4\n", "\\end{array}\n", "\\right]\n", "\\hspace{0.5in}\n", "\\left[\\begin{array}{rrrr}\n", " 1 & 0 & 0 & 1\\\\\n", " 0 & 1 & 0 & -2\\\\\n", " 0 & 0 & 1 & 0\n", "\\end{array}\n", "\\right]\n", "$$" ] }, { "cell_type": "heading", "level": 2, "metadata": { "internals": { "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "Verifying the Solution" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "source": [ "TBD" ] }, { "cell_type": "heading", "level": 2, "metadata": { "internals": { "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "Row Equivalence" ] }, { "cell_type": "markdown", "metadata": { "internals": { "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "source": [ "Elementary Row Operations include the following:\n", "1. (Replacement) Replace one row by the sum of itself and a multiple of another row.\n", "2. (Interchange) Interchange two rows.\n", "3. (Scaling) Multiply all entries in a row by a nonzero constant.\n", "\n", "Two matrices are called _row equivalent_ if there is a sequence of elementary row operations that transforms one matrix into the other.\n", "\n", "If the augmented matrices of two linear systems are row equivalent, then the two systems have the same solution set." ] }, { "cell_type": "heading", "level": 2, "metadata": { "internals": { "slide_type": "subslide" }, "slideshow": { "slide_type": "slide" } }, "source": [ "Fundamental Questions" ] }, { "cell_type": "markdown", "metadata": { "internals": {}, "slideshow": { "slide_type": "-" } }, "source": [ "Two fundamental questions about a linear system are as follows:\n", "1. Is the system _consistent;_ that is, does at least one solution exist?\n", "2. If a solution exists, is it the only one; that is, is the solution _unique?_\n" ] }, { "cell_type": "markdown", "metadata": { "internals": {}, "slideshow": { "slide_type": "-" } }, "source": [ "Example of an inconsistent system." ] }, { "cell_type": "markdown", "metadata": { "internals": {}, "slideshow": { "slide_type": "-" } }, "source": [ "Example of a non-unique system." ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": { "internals": { "slide_helper": "subslide_end" }, "slide_helper": "slide_end", "slideshow": { "slide_type": "-" } }, "outputs": [], "prompt_number": 10 } ], "metadata": {} } ] }