M368K Workbook - least square approximations.ipynb

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  {
   "cell_type": "markdown",
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   "source": [
    "# Least square approximations/ Approximation of data involving least square fitting\n",
    "\n",
    "by [Richard Tsai](https://www.researchgate.net/profile/Richard_Tsai3)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A motivating example: linear regression\n",
    "\n",
    "Data set: $(x_j,y_j), j=1,2,\\cdots,n$\n",
    "\n",
    "(LSQ) Find a line $g(x)=a_0+a_1x$ which best fit the data:\n",
    "\n",
    "$$ \\min_{a0, a1} \\sum_{j=0}^n | a_0+a_1x_j -y_j |^2 $$\n",
    "\n",
    "$E(a_0,a_1):=\\sum_{j=0}^n | a_0+a_1x_j -y_j |^2$ is a quadratic function.\n",
    "\n",
    "(LSQ) $\\iff$ find the minimum of $E$ $\\iff$ find the critical point of $E$\n",
    "\n",
    "$$\\partial E/\\partial a_0 =0, \\partial E/\\partial a_1=0 $$\n",
    "\n",
    "$$\\iff \\sum_{j=0}^n a_0+a_1x_j -y_j =0, \\sum_{j=0}^n (a_0+a_1x_j -y_j)x_j =0$$\n",
    "\n",
    "Notice that the two equations above depend linearly on the unknown $a_0$ and $a_1$.\n",
    "You can write them in conveniently in the matrix-vector form.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x12944bfd0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.collections.PathCollection object at 0x12e67da50>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f=x-> 2.5.*x.^2+2.*x+2+rand()\n",
    "\n",
    "x=linspace(0,1,50)\n",
    "\n",
    "y=f.(x)\n",
    "\n",
    "#introduce here an outlier\n",
    "y[end]=-1.0\n",
    "\n",
    "using PyPlot\n",
    "\n",
    "scatter(x,y)\n",
    "\n",
    "# g(x)=a+bx, find a and b that best fits the data (x_j, y_j), j=1,2,...\n",
    "\n",
    "\n",
    "#similar to the set up in the interpolation:\n",
    "\n",
    "A=[ ones(length(x)) x]\n",
    "\n",
    "B=A'*A\n",
    "c=A'*y\n",
    "\n",
    "a=B\\c\n",
    "\n",
    "scatter(x, A*a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "18.54752502692956"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cond(A'A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## General description of least square approximation problems\n",
    "\n",
    "**The least square problem**: let $f(x):=\\frac{1}{2}||Ax-b||_2^2$. We want to find where $f$ achieves the minimal value.\n",
    "\n",
    "### Algebraic view\n",
    "$$||Ax-b||_2^2 = (Ax-b,Ax-b)=(Ax-b)^T(Ax-b) = (x^T A^T -b^T)(Ax-b)$$\n",
    "$$ = x^TA^TAx - x^TA^Tb - b^TAx+b^T b$$\n",
    "\n",
    "(Note that $x^TA^Tb = (b^TAx)^T = b^TAx$ is a scalar.)\n",
    "\n",
    "Critical point of $f$ satisfies:\n",
    "\n",
    "$$ f^\\prime(x) = A^TA x - A^T b = 0. $$\n",
    "\n",
    "Solving the least square problem is equivalent to solving the **normal equation**\n",
    "\n",
    "$$A^TAx=A^Tb.$$\n",
    "\n",
    "** $A^TA$ is symmetric, positive definite **\n",
    "\n",
    "### Geometrical view of the least square problem\n",
    "\n",
    "* $y:=Ax$ is a vector in $col(A)$, the column space of $A$.\n",
    "\n",
    "\n",
    "* $b=b^*+b^\\perp,$ where $b^*$ in $col(A)$ and $b^\\perp$ is not.\n",
    "   \n",
    "   \n",
    "* $Ax=b^*$ has a unique solution, *if the columns of $A$ are linearly independent*.\n",
    "\n",
    "\n",
    "* (LSQ) is equivalent to find $b^\\perp$ that is the smallest 2-norm.\n",
    "\n",
    "\n",
    "* The right $b^\\perp$ is the one which is perpendicular to *all* vectors in $col(A)$.\n",
    "\n",
    "\n",
    "\n",
    "**Learning objectives**:\n",
    "\n",
    "* Where does $A$ come from? \n",
    "    * In particular, how do *orthogonal polynomials* come into play?\n",
    "    \n",
    "* Given $A$ and $m\\times n$ matrix, the typical numerical methods to solve the least square problems:\n",
    "    * (Cholesky) or using the backslash operator to solve the normal equation directly, QR and SVD\n",
    "    * Know how to use the \"truncated\" QR and SVD to improve the condition of the least square approximation.\n",
    "    * Know which method is more suitable than the others\n",
    "    * Know for to use the existing code to solve least square problems\n",
    "\n",
    "* Know the geometry of least square problems."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Noticed that the normal equation of a rank-difficient matrix is not invertible\n",
    "\n",
    "So more elaborate methods, such as truncated QR and truncated SVD are needed. See the following discussion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5518221009430436e16"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D=rand(8,4)\n",
    "D[:,2]=copy(D[:,1])\n",
    "\n",
    "cond(D'D)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Orthogonal polynomials\n",
    "\n",
    "Let $q(x)=c_1\\phi_1(x)+c_2\\phi_2(x)+\\cdots+c_n\\phi_n(x).$\n",
    "\n",
    "We would like to use $q(x)$ to **approximate the given data**: $(x_1, y_1),(x_2,y_2),\\cdots, (x_m,y_m), $ and **make prediction** at an arbitrarily chosen $x$.\n",
    "\n",
    "* In general, $m\\ge n$.\n",
    "\n",
    "Least square approximation problem: \n",
    "\n",
    "**Find the coefficients $c_1,c_2,\\cdots,c_n$ such that $q(x_j)$ *best fit* $y_j$, $j=1,2,\\cdots,m$, in l2 norm:** \n",
    "\n",
    "\n",
    "* To fit the data, $(x_j,y_j)\\in\\mathbb{R}^2$, by a straight line, we simply choose $\\phi_1(x)=1$ and $\\phi_2(x)=x$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x138b21f90>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.collections.PathCollection object at 0x138c62910>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f=x-> 2.5.*x.^2+2.*x+2+rand()\n",
    "\n",
    "x=linspace(-1,1,50)\n",
    "\n",
    "n=length(x)\n",
    "x_=collect(x)\n",
    "\n",
    "A_=[ones(n) x_ x_.^2 x_.^3]\n",
    "\n",
    "#Legendre polynomial as basis functions\n",
    "A__=[ones(n) x_ 0.5*(3.*x_.^2-1.0) 0.5.*(5x_.^3-3.0x_)]\n",
    "\n",
    "y_=f.(x_)\n",
    "#y_[n-1]=1.2\n",
    "#y_[n-2]=5.0\n",
    "\n",
    "B=A_'*A_\n",
    "c=A_'*y_\n",
    "\n",
    "a=B\\c\n",
    "\n",
    "scatter(x_,y_)\n",
    "scatter(x_, A_*a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(x^2,x^3)=8.675169359705565\n",
      "(L2,L3)=3.3306690738754696e-16\n",
      "condition number using 1, x, x^2 x^3:             62.23091391105069\n",
      "condition number using Legendre polynomials:      6.281152904350122\n",
      "\n",
      "condition number for R, after computing qr(A_ ):  7.888657294562296\n",
      "condition number for R, after computing qr(A__):  2.506222836132119\n"
     ]
    }
   ],
   "source": [
    "println(\"(x^2,x^3)=\", dot(x.^2, x.^3))\n",
    "println(\"(L2,L3)=\", dot(0.5*(3.*x_.^2-1.0),0.5.*(5x_.^3-3.0x_)))\n",
    "\n",
    "\n",
    "println(\"condition number using 1, x, x^2 x^3:             \", cond(A_'A_))\n",
    "println(\"condition number using Legendre polynomials:      \", cond(A__'A__))\n",
    "\n",
    "#if one uses QR factorization, one only needs to invert R\n",
    "Q,R=qr(A_)\n",
    "println(\"\\ncondition number for R, after computing qr(A_ ):  \",cond(R))\n",
    "Q,R=qr(A__)\n",
    "println(\"condition number for R, after computing qr(A__):  \",cond(R))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## QR factorization\n",
    "\n",
    "QR factorization finds orthonormal basis of the subspace spanned **successively** by columns of $A$.\n",
    "\n",
    "$A=QR$ where the columns of $Q$ are orthonormal and $R$ is an upper triangular matrix.\n",
    "\n",
    "Let $A$ be an $m\\times n$ matrix and $m>n$.\n",
    "There are two versions of QR factorization: the full QR or the \"thin\" QR.\n",
    "\n",
    "* In this note, we shall assume the \"thin\" QR as default: $Q$ is an $m\\times n$ orthonormal matrix, and $R$ is $n\\times n$.\n",
    "\n",
    "Let $a_j$ be the jth column of $A$ and $q_j$ be the jth column of $Q$.\n",
    "\n",
    "**Very important property of $Q$**: span$\\{a_1,\\cdots,a_j\\}=$span$\\{q_1,\\cdots,q_j\\}, j=1,2,\\cdots,n$\n",
    "\n",
    "\n",
    "* Full QR factorization can be thought of  a QR factorization of $A_f$ which is an $m\\times m$ matrix, by padding $A$ with the addition of $m-n$ zero column vectors.\n",
    "    * $Q$ is a $m\\times m$ orthonormal matrix\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4×2 Array{Float64,2}:\n",
       " 0.710726  0.260087\n",
       " 0.659208  0.095578\n",
       " 0.249536  0.401383\n",
       " 0.445615  0.636766"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "4×2 Array{Float64,2}:\n",
       " -0.648658  -0.204324\n",
       " -0.60164   -0.450742\n",
       " -0.227744   0.484354\n",
       " -0.4067     0.721446"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "2×2 Array{Float64,2}:\n",
       " -1.09569  -0.576596\n",
       "  0.0       0.557581"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "2×2 Array{Float64,2}:\n",
       " 1.0          1.14438e-16\n",
       " 1.14438e-16  1.0        "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A=rand(4,2)\n",
    "display(A)\n",
    "\n",
    "Q,R=qr(A)\n",
    "display(Q)\n",
    "display(R)\n",
    "\n",
    "Q'Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4×4 Array{Float64,2}:\n",
       " -0.648658  -0.204324  -0.375731  -0.62954 \n",
       " -0.60164   -0.450742   0.375465   0.542114\n",
       " -0.227744   0.484354   0.757179  -0.374451\n",
       " -0.4067     0.721446  -0.380174   0.411799"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "2×2 Array{Float64,2}:\n",
       " -1.09569  -0.576596\n",
       "  0.0       0.557581"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "4×4 Array{Float64,2}:\n",
       " 1.0          1.14438e-16   1.03458e-16   1.90986e-16\n",
       " 1.14438e-16  1.0           8.2835e-17    1.39189e-16\n",
       " 1.03458e-16  8.2835e-17    1.0          -2.94983e-17\n",
       " 1.90986e-16  1.39189e-16  -2.94983e-17   1.0        "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Qf, Rf= qr(A, thin=false)\n",
    "display(Qf)\n",
    "display(Rf)\n",
    "\n",
    "Qf'Qf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Use QR factorization to solve the least square problems:\n",
    "\n",
    "$A=QR$ \n",
    "\n",
    "1. Project the data vector: $y: = Q^\\top b$\n",
    "2. Solve $Rx=y$.\n",
    "\n",
    "Let's see if this solution satisfies the normal equation.\n",
    "\n",
    "Since $Q$ is an orthonormal matrix (it's columns are orthonormal), so \n",
    "* $Q^\\top Q=I$.\n",
    "* $QQ^\\top$ is a **projection matrix**: $z=QQ^\\top b$ is a vector **in the column space of $Q$**, which is the same as the column space of $A$. Oberve \n",
    "    $$Q^\\top b=\\left(\\begin{array}{c}\n",
    "(q_1,b)\\\\\n",
    "(q_2,b)\\\\\n",
    "\\cdots\\\\\n",
    "(q_n,b)\\\\\n",
    "\\end{array}\\right)\\implies QQ^\\top = Q\\left(\\begin{array}{c}\n",
    "(q_1,b)\\\\\n",
    "(q_2,b)\\\\\n",
    "\\cdots\\\\\n",
    "(q_n,b)\\\\\n",
    "\\end{array}\\right)= (q_1,b)q_1 + (q_2,b)q_2 + \\cdots + (q_n,b)q_n$$\n",
    "    * So $z=QQ^\\top b$ is in the range of $A$; i.e. $Ax=z$ has a unique solution if the columns of $A$ are linearly independent.\n",
    "\n",
    "We can prove our QR algorithm either by geometrical arguments or algebraically.\n",
    "\n",
    "#### Algebraic view\n",
    "\n",
    "$$A^\\top=R^\\top Q^\\top,$$\n",
    "\n",
    "$$ Rx=Q^\\top b \\implies QRx=QQ^\\top b \\implies (R^\\top Q^\\top) QR x = (R^\\top Q^\\top) QQ^\\top b$$\n",
    "\n",
    "$$ Q^\\top Q=I \\implies A^\\top A x = R^\\top Q^\\top b=A^\\top b$$\n",
    "\n",
    "#### Geometric view\n",
    "\n",
    "$Q^\\top b=\\left( q_1\\cdot b, q_2\\cdot b, \\cdots, q_n\\cdot b \\right)^\\top$ is the orthogonal projection of $b$ to $col(A)$, represented in the \"new\" coordinate systems defined by the columns of $Q$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pivoted QR factorization and truncation and applications\n",
    "\n",
    "QR-factorization can be used to solve both **underdetermined**, \n",
    "**square** and **overdetermined**\n",
    "linear systems of equations. \n",
    "\n",
    "It can also be used to compute a numerically \n",
    "stable solution of an **ill-conditioned** system.\n",
    "\n",
    "\n",
    "With pivoted QR-factorization a matrix can be factorized into\n",
    "$$AP=QR$$\n",
    "where $P$ is a permutation matrix, making the diagonal elements $r_{i,i}$ in \n",
    "the uppertriangular matrix $R$ be ordered in decending order, i.e.\n",
    "$\\vert r_{i,i} \\vert \\le \\vert r_{i-1,i-1} \\vert $. \n",
    "\n",
    "$Q$ is orthonormal, i.e. $Q^\\top Q = I$. Assume the matrix $A$ is $n\\times n$. \n",
    "\n",
    "In Julia, $Q,R,$ and $P$ can be computed as follows:\n",
    "\n",
    "```\n",
    "F=qrfact(A, Val{true}) #Val{true} tells Julia to compute the pivoted full QR factorizaton\n",
    "Q=F[:Q]\n",
    "R=F[:R]\n",
    "P=F[:P]\n",
    "```\n",
    "\n",
    "The solution of a linear system of equations $A{\\bf x}={\\bf b}$ is obtained from \n",
    "$$R{\\bf y}=Q^T{\\bf b}, \\quad and \\quad {\\bf x}=P{\\bf y}$$\n",
    "If the matrix $A$ is ill-conditioned $R$ can be written on block form\n",
    "$$R=\\pmatrix{R_{11}&R_{12}\\cr\n",
    "               0   &E\\cr}$$\n",
    "where \n",
    "* $R_{11}$ is an uppertriangular matrices of dimension $r\\times r$, \n",
    "* $E$ is an uppertriangular matrices of dimension $n-r\\times n-r$, and **the elements of \n",
    "$E$ are very small**. \n",
    "    - The smaller the elements of $E$ are the more \n",
    "ill-conditioned is the matrix $A$. \n",
    "    - If the elements of $E$ are exactly zero the matrix $A$ is rank-deficient with $rank(A)=r$.\n",
    "        \n",
    "By setting small but nonzero elements in $E$ to zero we regard the matrix $A$ \n",
    "as rank-deficient even if it isn't that mathematically. Then we cannot \n",
    "find a unique solution. But we can, instead, **find a  least square solution with the smallest 2-norm** (why?) to\n",
    "$\\hat A \\hat{\\bf x} = {\\bf b}$, where\n",
    "$$\\hat A = Q \\pmatrix{R_{11}&R_{12}\\cr\n",
    "                         0  & 0 \\cr} P^T$$\n",
    "according to the following algorithm:\n",
    "\n",
    "1. Compute the vectors $\\hat {\\bf d}$ and ${\\bf d}_E$ from\n",
    "$$Q^T {\\bf b} =\\pmatrix{\\hat {\\bf d}\\cr\n",
    "                         {\\bf d}_E \\cr}$$\n",
    "2. Solve the system \n",
    "$$R_{11}\\hat {\\bf y}=\\hat {\\bf d}$$\n",
    "3. Finally compute\n",
    "$$\\hat {\\bf x}=P\\pmatrix{\\hat {\\bf y}\\cr\n",
    "                            0\\cr}$$\n",
    "\n",
    "\n",
    "\n",
    "The goal of this exercise is to illustrate the following relations:\n",
    "\n",
    "1. the sensitivity of the solution $\\hat {\\bf x}$  from the experimentally computed condition number of $R_{11}$ (see below) as a\n",
    "function of $r$\n",
    "2. the condition number of $R_{11}$ computed with Julia's function 'cond( )' as a function of $r$\n",
    "3. the norm of the matrix $E$ as a function of $r$\n",
    "4. the norm of the residual ${\\bf res}=A \\hat {\\bf x} - {\\bf b}$ as a \n",
    "function of $r$\n",
    "\n",
    "What is important in practice is to find the rank $r$ for\n",
    "which both the residual ${\\bf res}$ and the sensitivity of disturbancies in\n",
    "**b** are \"small\". Often this is a compromize; the norm of the residual\n",
    "increases while the sensitivity (condition number) decreases as the rank $r$\n",
    "decreases.  \n",
    "\n",
    "In the following box, a function named 'gen_illposed_system()' is defined. \n",
    "It creates an ill-conditioned system $A{\\bf x}={\\bf b}$.\n",
    "\n",
    "1. Compute a system of size $n=18$, i.e. $A$ is $18\\times 18$ and ${\\bf b}$ is\n",
    "$18\\times 1$. \n",
    "2. Estimate the condition number $\\kappa (A)$ experimentally\n",
    "from the relation\n",
    "$${\\Vert \\Delta {\\bf x} \\Vert_2 \\over \\Vert {\\bf x} \\Vert_2} = \n",
    "\\kappa (A) {\\Vert \\Delta b \\Vert_2 \\over \\Vert {\\bf  b} \\Vert_2}$$\n",
    "by disturbing ${\\bf b}$ with some small perturbances $\\Delta {\\bf b}$ and see\n",
    "how ${\\bf x}$ is changed, $\\Delta {\\bf x}$. Compare your result with \n",
    "Julia's function `cond()`.\n",
    "3. Write a program showing a table of the following quantities \n",
    "as functions of the rank $r=8,7,6,5$: $\\tt norm(E)$, $\\tt cond(R_{11})$,\n",
    "the experimentally computed condition number of $R_{11}$, $\\tt norm(x)$,\n",
    "and $\\tt norm(res)$. Express your results in a way that describes the \n",
    "behaviour of the relations mentioned above as functions of the rank $r$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "gen_difficient_system (generic function with 1 method)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function gen_illposed_system(n)\n",
    "# ILLPOSED Creates an ill-posed system Ax=b.\n",
    "#    ILLPOSED(N) creates an ill-posed system of size N.\n",
    "#    N >= 2\n",
    "    \n",
    "    r = max(convert(Int,round(0.25*n)),2)\n",
    "    U,S,V = svd(rand(n,n))\n",
    "    S[n-r+1:n]=linspace(1.5e-9,2.45e-12,r)\n",
    "    A = U*diagm(S)*V'\n",
    "    b = A*rand(n,1)\n",
    "    \n",
    "    return A,b\n",
    "end\n",
    "\n",
    "function gen_difficient_system(n)\n",
    "# ILLPOSED Creates an ill-posed system Ax=b.\n",
    "#    ILLPOSED(N) creates an ill-posed system of size N.\n",
    "#    N >= 2\n",
    "    \n",
    "    r = max(convert(Int,round(0.25*n)),2)\n",
    "    U,S,V = svd(rand(n,n))\n",
    "    S[n-r+1:n]=zeros(r) #linspace(1.5e-9,2.45e-12,r)\n",
    "    A = U*diagm(S)*V'\n",
    "    b = A*rand(n,1)\n",
    "    \n",
    "    return A,b\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.8806043398671156e16\n",
      "1.6266982594353767e12\n",
      "39.051587950468544\n"
     ]
    }
   ],
   "source": [
    "A,b=gen_difficient_system(8)\n",
    "B,c=gen_illposed_system(8)\n",
    "C=rand(8,8)\n",
    "\n",
    "println(cond(A))\n",
    "println(cond(B))\n",
    "println(cond(C))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8×8 Array{Float64,2}:\n",
       "  0.0           0.0          3.10516e-16  …  -1.94289e-16   0.0        \n",
       "  0.0          -5.55112e-17  1.11022e-16      4.16334e-17   2.22045e-16\n",
       "  0.0           0.0          1.11022e-16     -1.11022e-16   0.0        \n",
       "  0.0           0.0          0.0              1.11022e-16  -5.55112e-17\n",
       " -1.11022e-16  -8.32667e-17  1.11022e-16      0.0           0.0        \n",
       "  0.0           0.0          0.0          …  -1.11022e-16   0.0        \n",
       "  0.0          -5.55112e-17  5.55112e-17     -1.11022e-16   1.11022e-16\n",
       " -5.55112e-17   0.0          1.11022e-16     -1.11022e-16   0.0        "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A,b=gen_illposed_system(8)\n",
    "\n",
    "cond(A)\n",
    "\n",
    "F=qrfact(A, Val{true})\n",
    "\n",
    "A*F[:P]-F[:Q]*F[:R]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r= 4, cond(R11)=              4, norm(E)=2.107940247736643, res=3.265439035753067\n",
      "r= 5, cond(R11)=              5, norm(E)=1.819124563223740, res=2.098356841788691\n",
      "r= 6, cond(R11)=              5, norm(E)=1.742291908374359, res=1.318182505319975\n",
      "r= 7, cond(R11)=              6, norm(E)=1.433808658045680, res=1.300341618284477\n",
      "r= 8, cond(R11)=              7, norm(E)=1.333641317527919, res=1.298976821490687\n",
      "r= 9, cond(R11)=              9, norm(E)=1.333376191665098, res=1.106278196424944\n",
      "r=10, cond(R11)=             10, norm(E)=1.206693955418061, res=0.751994761993389\n",
      "r=11, cond(R11)=             12, norm(E)=1.029451211317090, res=0.734402185240326\n",
      "r=12, cond(R11)=             14, norm(E)=0.941082464837174, res=0.726514049652165\n",
      "r=13, cond(R11)=             16, norm(E)=0.785616505731822, res=0.509636518725187\n",
      "r=14, cond(R11)=             17, norm(E)=0.000000002646341, res=0.000000001132107\n",
      "r=15, cond(R11)=     7369804610, norm(E)=0.000000002160661, res=0.000000000563440\n",
      "r=16, cond(R11)=     8493579046, norm(E)=0.000000000814574, res=0.000000000409707\n",
      "r=17, cond(R11)=    17052428790, norm(E)=0.000000000004796, res=0.000000000000034\n",
      "r=18, cond(R11)=  3606927304494, norm(E)=0.000000000000000, res=0.000000000000002\n"
     ]
    }
   ],
   "source": [
    "A,b=gen_illposed_system(18)\n",
    "\n",
    "F=qrfact(A, Val{true})\n",
    "\n",
    "Q=F[:Q]\n",
    "R=F[:R]\n",
    "P=F[:P]\n",
    "\n",
    "n=length(b)\n",
    "\n",
    "for r=4:18\n",
    "    R11=R[1:r,1:r]\n",
    "\n",
    "    E=R[r+1:n,r+1:n]\n",
    "\n",
    "    d=Q'*b\n",
    "\n",
    "    dhat=d[1:r]\n",
    "    dE=d[r+1:n]\n",
    "\n",
    "    yhat=R11\\dhat\n",
    "    x=P*[yhat;zeros(n-r)]\n",
    "    \n",
    "    println(x-)\n",
    "    \n",
    "    #display(R)\n",
    "    #display(E)\n",
    "    \n",
    "    @printf \"r=%2d, cond(R11)=%15d, norm(E)=%5.15f, res=%5.15f\\n\" r cond(R11) norm(E) norm(A*x-b)\n",
    "    \n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Solving least square problems with QR factorization\n",
    "\n",
    "The least squares method is used to fit functions to measured data. In the\n",
    "following box, measurements of the $CO_2$-concentration in the athmosphere is\n",
    "tabulated. \n",
    "The concentration is measured in parts per million and is\n",
    "available for each month from 1980 to 2003. \n",
    "The data are tabulated following teh following format:\n",
    "\n",
    "1980 338.01 338.36 340.08  ........................ 338.21\n",
    "\n",
    "1981 339.23 340.47 341.38  ........................ 339.61\n",
    "\n",
    "Hence each row starts with the year, then follows the 12 measurements for\n",
    "each month. \n",
    "\n",
    "Pick out the monthly values (columns 2 to 13) and store them columnwise in Q\n",
    "\n",
    "```\n",
    "Q=maunaloa[:,2:13]'```\n",
    "\n",
    "Put the measurements  in time increasing order in one column\n",
    "\n",
    "```\n",
    "b=Q[:] \n",
    "using PyPlot\n",
    "plot(b,\"x\")```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "maunaloa=\n",
    "[1980 338.01 338.36 340.08 340.77 341.46 341.17 339.56 337.60 335.88 336.01 337.10 338.21;  \n",
    "1981 339.23 340.47 341.38 342.51 342.91 342.25 340.49 338.43 336.69 336.85 338.36 339.61;\n",
    "1982 340.75 341.61 342.70 343.56 344.13 343.35 342.06 339.82 337.97 337.86 339.26 340.49; \n",
    "1983 341.37 342.52 343.10 344.94 345.75 345.32 343.99 342.39 339.86 339.99 341.16 342.99;\n",
    "1984 343.70 344.51 345.28 347.08 347.43 346.79 345.40 343.28 341.07 341.35 342.98 344.22;\n",
    "1985 344.97 346.00 347.43 348.35 348.93 348.25 346.56 344.69 343.09 342.80 344.24 345.56;\n",
    "1986 346.29 346.96 347.86 349.55 350.21 349.54 347.94 345.91 344.86 344.17 345.66 346.90;\n",
    "1987 348.02 348.47 349.42 350.99 351.84 351.25 349.52 348.10 346.44 346.36 347.81 348.96; \n",
    "1988 350.43 351.72 352.22 353.59 354.22 353.79 352.39 350.44 348.72 348.88 350.07 351.34;\n",
    "1989 352.76 353.07 353.68 355.42 355.67 355.13 353.90 351.67 349.80 349.99 351.30 352.53;\n",
    "1990 353.66 354.70 355.39 356.20 357.16 356.22 354.82 352.91 350.96 351.18 352.83 354.21;\n",
    "1991 354.72 355.75 357.16 358.60 359.34 358.24 356.17 354.03 352.16 352.21 353.75 354.99;\n",
    "1992 355.98 356.72 357.81 359.15 359.66 359.25 357.03 355.00 353.01 353.31 354.16 355.40;\n",
    "1993 356.70 357.16 358.38 359.46 360.28 359.60 357.57 355.52 353.70 353.98 355.33 356.80;\n",
    "1994 358.36 358.91 359.97 361.26 361.68 360.95 359.55 357.49 355.84 355.99 357.58 359.04; \n",
    "1995 359.96 361.00 361.64 363.45 363.79 363.26 361.90 359.46 358.06 357.75 359.56 360.70;\n",
    "1996 362.05 363.25 364.03 364.72 365.41 364.97 363.65 361.49 359.46 359.60 360.76 362.33;\n",
    "1997 363.18 364.00 364.57 366.35 366.79 365.62 364.47 362.51 360.19 360.77 362.43 364.28;\n",
    "1998 365.32 366.15 367.31 368.61 369.29 368.87 367.64 365.77 363.90 364.23 365.46 366.97;\n",
    "1999 368.15 368.87 369.59 371.14 371.00 370.35 369.27 366.94 364.63 365.12 366.67 368.01;\n",
    "2000 369.14 369.46 370.52 371.66 371.82 371.70 370.12 368.12 366.62 366.73 368.29 369.53;\n",
    "2001 370.28 371.50 372.12 372.87 374.02 373.30 371.62 369.55 367.96 368.09 369.68 371.24;\n",
    "2002 372.43 373.09 373.52 374.86 375.55 375.41 374.02 371.49 370.71 370.25 372.08 373.78;\n",
    "2003 374.68 375.63 376.11 377.65 378.35 378.13 376.62 374.50 372.99 373.00 374.35 375.70];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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aMMwQEVFeaWuqNYMMAE9BRld3IwKAXfGtzKpHDICkER+rzSVFOHLb/VcdfZJfN9wXp9+8B2MVwwwREeWVDTsPmEEGAMIhfVGwTrp7GgGpIzuCHFacVkLZjeyox8rvp75ODjJjafWSimGGiIjyhvgyn3L5xXjn+AcIh0KIGwYaN0XNgli7KZd09zQKYkWV08iO/DMAy2XaTv1wxhKGGSIiygvqdAsAfGX+hdGJxk1R1FaWOo6wpBMIRmpkx+n4cCikrbUZq7UzDDNERJQX4onkYl8guVFdR8z9lItafCv2U3IacUl3ZAdw3rHaSdehAcSNC4FGXLeXQDXaeFqavXHjRsyaNQtFRUUoKipCJBLBtm3bAACHDh1CKBTS/nnmmWfMcxw+fBiLFi3CJZdcgokTJ+Luu+/GuXPngv1UREQ06qxsqMGcqReKa+XlzXsPHQcA1FaWuN6xWi6+7To04LifkuBnWXVQhnf1Hl5GLlZyyZtkjtUpJ09hZsqUKXjkkUewd+9e7N27F/PmzcPixYvx+uuvo6KiAkeOHEn689BDD+HSSy/FwoULAQDxeByLFi3C2bNn0dHRgaeeegpPPvkkHnjggYx8OCIiGl1WKl/WaiO5zc0Rx3PoesCIgOC2kV02dquWr6etqda87nAoZF7/WAwyABAyDCOtnsclJSX4zne+g9tvvz3lueuvvx6f/OQn8cQTTwAAtm3bhn/4h3/Au+++i0mTJgEAfvCDH+Cee+7B//3f/6GwsNDVew4NDaG4uBgnTpxAUVFROpdPRER5THzBi2DhpvGcLqCo9ThO5/P6vkD6xcO642vu34az8QTCoRBWzJuW87Uymfr+9l0zE4/H8cwzz+DUqVOIRFKT8CuvvIJ9+/bh+9//vvlYZ2cnZs6caQYZALjppptw55134vXXX8f111+vfa8zZ87gzJkz5s9DQ0N+L5uIiPKMVQiQO/lubo642jXaTfGtbj8l+RrUQCSmeNT3Va9b3W1bhBe3tS5qUFGnytx0Px6tPIeZ/fv3IxKJ4PTp0xg/fjy2bNmCGTNmpLzuiSeewMc//nHU1dWZj/X29iYFGQDmz729vZbvuXbtWjz00ENeL5WIiEYB3QoiObjUVZUlPWcXLHQjF/KoiFUjO3ENal8XuYZFfV/1unW7bXstHpav2W2fmrHAc5iZPn069u3bh8HBQTz77LNYvnw5du/enRRoPvjgA7S1teEb3/iG6/OGQtaJcvXq1Vi1apX589DQECoqKrxeOhERZUG60yu6kNIR6wOAlDoR8feOWF/Sed0sqXYTEMRUlG6ERt36wC5cAfDdJ8Zrn5qxwHOYKSwsxLRp0wAAs2fPRldXF9avX48f/vCH5mt+/vOf4/3338dtt92WdGx5eTlefvnlpMeOHj0KACkjNrJx48Zh3LhxXi+ViIhyQBC9WXS9YXTt/YVoz4A5YiPClFiBJM4nT1OJc7sJCGIVkxpEdAHCqqeN2z2ZdNLtUzMapb1rdiKRSKpnAYanmP7xH/8RH/3oR5Mej0Qi2L9/P44dO2Y+1t7ejqKiIu1UFRER5T95KbOblUJ255FXEIkVPU7nlcOUuqQaGJ6msgsIqxpqzIDgZxWTegyAtHa/Vld0qe+V60XAmeBpZOa+++7DwoULUVFRgZMnT6KtrQ27du3C9u3bzdccPHgQL730ErZu3Zpy/I033ogZM2Zg2bJlePTRR9Hb24uvf/3ruOuuuzjyQkQ0iompIauuu7rpJnV6Sq1nWfJ4p7kU266brzw6sqqhxjwegOsGe4LbzSFl6jGsdQmepzBz9OhRLFu2DEeOHEFxcTFmzZqF7du3o6GhwXzNj3/8Y/z1X/81brzxxpTjw+Ewnn/+edx5552IRCK49NJLsXz5cjz88MPpfxIiIsppdVVliPYMpIxqWE03qat/5NcMF+MOmGHCadpGnTLyw0/RrfrZ1Pcf67UuQfEUZkS/GDvf/va38e1vf9vy+SuvvFI7akNERGOHPL1i15hOPA9Au4WBWGHkdbSkMFyAFfOmuQ4Rfopu1WNaNaFGXuU0FmtdgsK9mYiIKGPEVBGQGkLkkGJXA9IR60O0Z0A7jaRbKm1XbAwgZZrJTaDxU3SrHqPWsuhWPpE/DDNERJQxavGt+NJev+MA4i4b0G9ujpirh9TpKXVjSavRErGUWw09qxpqkgp8rfjZHDLdDSXJvbRXMxEREVlpqa82lz4LjZui5q7PwIWgYUVXdAvYj5bIAWXDzgOI9gykhB55VMYqeLRqNp+Ur6s1jRocCg5HZoiIKKPkrQbEiExdVSnammrNx9U6F930lDyi0hHrs91UUj6XlymioLcgoJHBMENERBnXUl9tBplwKIS2plrzcSB1WshqekqQVzJZcbuFgSxTWxCk2wWZ7DHMEBFRxm3YeSHIxA0jKYjoRkjkwl/5HPJoiFOdi5/Ow0FvQSBCjNX+UuIzcoQnPQwzRESUUW76s+iCgTw95WcfI10wcTOqEuQWBCLEiEJjtW8O4K5xH9kLGYbLcvIcMjQ0hOLiYpw4cQJFRUXZvhwiIrKg67Wiq4URr9VNt8grmbrXLPR9DaKA2G14kN9X9KTxeg75/XWN88ZakMnU9zdXMxERUcaoxbdqLYy84midFHQEq5VMXvjZT8lqC4LuNQtT9oNy8/7imMdePGg+7meTSdJjmCEiooxRN0XULYm2mvqRH/cTIuTzeAlE8vuumDct5XndxplO5EAFIK1wRqlYM0NERIGzW70DALWVJba1MH62D9Dxup9SprYgEIFKECGJezIFg2GGiIgC52Yl0e//Mmg59eNn+wCVn0CUiS0I5ACl7i/ldjsFsscwQ0REgXNaSQTAdnPIILYC8BOIgt6CQHzm2soS1FWVJZ3Dy3YKZI+rmYiIKGN0K4kAfVdf8aXutblcLjeky+Vry4ZMfX9zZIaIiFIE9SXcUl+d1J8FSF2SLY/i1FWVoiPWn/S4eE+rRnd+muO5EcQ94GaTI4NhhoiIUgQVENSVRB2xPsepn9rKUk+N7nRTWkse70zZXFK+Jrsgwq69+YdhhoiIUvjtniuzWklUV1Vm+56Cl86/uq69TtdkhV178w/DDBERJVGnV+SAUFdVmrGVRDJ1espNcFCPEV17xXNuw5h8nbpAwyCTexhmiIgoiTq9IgJCOBRCR6wftZWljudId2m1rtGdU4BQjwGQ1HnXyzYEcqARtT4Au/bmKnYAJiKiJHKH28ZNUTPIxA0DdVWljl/m6RbO+un8a3UMAM9bGQjs2ps/ODJDREQpWuqrEe3pR0esPynIdMT6HUdJ0ike9jM95eYYLyM88nnZtTc/MMwQEVGK4VU7F4JMYbgAbU21jtsByI/7qVfxMz1ldYxQW1mCzc0RV9cusGtvfmGYISKiFPHEhZEY3aiGU82LrnhYDhxWU1Fi48nW9u6UqSir4KCbskqnAJlde/MPwwwREaUIF4hi3xJzKbWu54pd/YvdiqRMNboT0ilAdnPsWOramw8YZoiIKIkaKOx6rjjVv1itSAq60Z0qnc677NqbfxhmiIhGkSBa8OtGJuRAI3fAdZqqURvmAdAGmnQb3dHYxjBDRDSKBDF9Y1Wrom4YqQYZEaTEa9XX1FaWaANNEI3uaGxjmCEiGkWC2IbA6rxOHXlFkKqtLEl6L/n966rKkupVgmx0B3CX6rGKYYaIaJQRK5F0gcDvF7qbjrzJu1+XmcdZBSmrqahVDTW+G91lurCYchPDDBHRKCNWIoVDoaRA4PcL3U39i+C0JNvqnOqxgL9Gd5kamaLcxjBDRDQKyNMravfes/EE/u7fX8Q7xz/w/IXup1+LmympTDS6k99fXJ+fqSrKPwwzRESjgDy9AgAdsX6z6R0AvHP8A8d9lXT1JiJ0iOfF9JRdvxY3U1JBN7pTr13dIJMN7kY3hhkiolFA/dIXAUSEGbHjtd2Uja7eRHTkHa6DSd4tW9c8z8uUlCqdRnfqtYtAJbZj6Do0YPvelN8YZoiIRomW+mqzB4zct0WMkNRVldoGArt6E6tNJuXwks7ICpBeszr5fcQUm7hmtxtkUv5imCEiGkU2N0dQc/+2pGXOciiprSy1Pd6u3kQdZZH3MAL0Iyti1MZuL6OgllOrtUIdsX5fI0SUfxhmiIhGETG9ovIyQmJVwGsVdMRjuiDjZhVRkMup50wtwZ6eAXOnb/XaWTszOjHMEBHlMXlUQ93tOdrTnxQS7L7Q1fPIBbyNm6KYM7UEK8+HEquVSn6XQwe5nDpcEDKDjNV+UDT6MMwQEeUxMaohplfkaRVRL6ILNG7P07gpahYRA9Yrlfwuh1anmOTjnWp8VOkUH1N+Y5ghIsqydGpGkrvulmpHNcQ57Mj1JvJ55AJaEWyswoKb/jIqdYpJXk7dEet3rPGR71M6xceU3xhmiIiyLN2aEflLWxT/ioJbqxU8upA0Z+pwIW9HrD/pPPIIjV1YAODYX8bu2qM9/UnLqZ364sjSWdZN+Y9hhogoS3RTLAAsw4Md3aiI1TSLVUgSwUYEGXl0Zc7UEtRWpoYL8bNYEu5nikddhSSCjJfl1Oks66b8xzBDRJQluhGZde3dWL/jgOeRCbuuu14Ka63O47Q0Wg4y6ueRf7a6djnIFIYL0NZUy5oXco1hhogoS+Qv/I5YH+qqyswv9HAohLamWgDWdTNiZEecQx0V6Yj1YXNzxHxeV5irWw0lTy25CRPpTvGIXb47Yv3aMMYpInLCMENElEXJNSPDLfdFoNmw84D5nK5uRh7Z0YWJaM+AGQqsCnO9robSSXeKR+zyzVVI5BfDDBFRlrXUV5tTSwDwlfmp+yzpvtTl7QsEtR5GFAFbTUEFtRrKL65CoiAwzBARZVnjpqg5tRQ3DKxr70ZhuMDVsZubI2Yg0E0juem9YrUaaiSazXEVEgWBYYaIKIvk6Ry56FWMpKyYN81VjxjdNJKXUQ8/PWKCwFVIFAR30Z+IiAInhw1R7CsTeyw5rSTSTSMB9qMe6saPVucgygccmSEiyhI1bKj1Lh2xPse6EbtpJLejHm63AdB1KpZXVKkrrrzseE2UDoYZIqIsUb/4dVNCdit70i2ebW3vRtehAW1nX3WTSkDfF0ddUaW7NqJMY5ghIsoBfgph0y2eFUui1eZ8ch2PfA63QcnvjtdEfoUMw8i7UvGhoSEUFxfjxIkTKCoqyvblEBGNqHQ2ptS9XjfFZBdExGtEfY0YfVEfY5AhVaa+vzkyQ0SUZ9LdmFImj7bolnZbHaNb+ZSN1VBEAMMMEVFO8TLq4mXPJTtel2VbrXzyumM2UVAYZoiIfAhyqkfmdtTFz4iKFbsOwbrXWq184nYElC3sM0NE5IMIHWo/FvFFLpYrW2nVHAsMf/mL/ZDE81ajLi311WYA8Tu1I5+7e81CrGqo0X4uu+vQfQa78xAFjSMzREQ+6Fb2eJnqsRuBkTd4tBt1cTOiYjeC1Lgpql2WrX4uQbd6Sjwm/q7eH25HQCOBYYaIyKd0pnrchCGxT5Ju1MVtozs3ocnt0m7dtBm3I6BcwDBDROSBOtIhF8+GQyFPIxF2Ychu1MXrnkvq425GkBhEKJ8wzBAReaCOdIjQIXa87jo04Ol8upVETqMuXpvlBVksTJSLGGaIiDyQg8HP9r6Nd45/gLqqUnPKpiPWn7TRozoNo47sqCMwf/fvL+Kd4x/Yjrr4mdrJ1q7YRCOBYYaIyCOxd1FHrB8Akopo1aXKKnlkB0DScut17d1mOPK7RYEVL8uvifINl2YTEfkwZ2oJwiHr5de1lSXasCAvW1aDzKqGGqxqqEka3VGPBWC53HnDzgNolYKS/Li8/Lq2ssR2+bXuHCqrpeVezkEUFI7MEBH5EC4YrpERIx1etwPoiPUh2jNgeYzVCIzXrQx0xb51VWWI9gyknMfLdghBbqlAlC6GGSIij6wKdL3Uo2xujlguvXYKQoD71Um6YmH5HB2xPl/bIaTbZ4coSAwzRDRmBLEFgdMXttt6lHRqWLysTrL6PPI5RKjyGkK4SopyBWtmiGjMSHcLAiB1pEMON6saamzrUdT3c7OFgJUgtjLwew65XkY9h3ieaCRxZIaIxowgpkbkkQ6r5nV2Gy16aXhnJ4jVSX6HIYnGAAAgAElEQVTPoa7Iks/BehnKBk8jMxs3bsSsWbNQVFSEoqIiRCIRbNu2Lek1nZ2dmDdvHi699FIUFRXhM5/5DD744APz+YGBASxduhRFRUWYMGECbr/9drz33nvBfBoiIgfyaqKa+7d5CjLqCh55lEZewSPeQy7iFcfqaljkx90svQ5iZCedc+hWZK2YN831exMFzdPIzJQpU/DII49g2rThX9qnnnoKixcvxquvvoprrrkGnZ2dWLBgAVavXo3vfe97uOiii/CHP/wBBQUXMtPSpUtx5MgRtLe348MPP8SXvvQlNDc3o62tLdhPRkRkwW8DOXUFjxil0a3gUc8pjtUFGS+BKoiRnaBGhwS5XsbvOYjS4SnM3HLLLUk/r1mzBhs3bkQ0GsU111yDlStXoqWlBffee6/5munTp5t//9Of/oQXXngBXV1dmD17NgDge9/7Hm6++WZ897vfxeTJk9P5LEQ0CgVRtKs7zs/0SjrTVEGt/vG6lUGmz2EVCrlbNo0k3zUz8XgczzzzDE6dOoVIJIJjx45hz549WLp0Kerq6hCLxXD11VdjzZo1+Lu/+zsAw1NQEyZMMIMMAMyfPx8FBQXYs2cP/umf/kn7XmfOnMGZM2fMn4eGhvxeNhHlmaD7mYjj6qpK0dZUm1Lf4hSQdCt4aitLbN9PnC+d1T8i1Omuy22oC+IcwsqGGstQyBEZGmmeVzPt378f48ePx7hx43DHHXdgy5YtmDFjBnp6egAADz74IJqamvDCCy/gk5/8JOrr63HgwPAcbG9vLyZOnJh0vosuugglJSXo7e21fM+1a9eiuLjY/FNRUeH1sokoT8n1GaKew+uIhqhXkYOM3GVXrEBq3BR1tapJXcFTV1XmepWUmxVEuu66ItQ1boomrRZyuxKrtb0bXYcGtNfp9nPrPls6dTtEQfE8MjN9+nTs27cPg4ODePbZZ7F8+XLs3r0biUQCAPDlL38ZX/rSlwAA119/PXbu3Ikf//jHWLt2reU5DcNAyKYt+OrVq7Fq1Srz56GhIQYaohwW9NRQuv1MRBCorSyx3EOpIBRK2mPJjjoiIc7hZgrJzRSXbjRK3Q9KnMttqAsXhMzNMOVzN26Kmo+7vZ9B19wQpctzmCksLDQLgGfPno2uri6sX7/erJOZMWNG0us//vGP4/DhwwCA8vJyHDt2LOn5c+fO4fjx45g0aZLle44bNw7jxo3zeqlElCVBTQ3JoSieMBAOhVL6mYjpDrdTQ3VVZSnPewlIVt1/RZ8Zu8Bldax6n6zqa+Sdub02uku+B8OBZv2OA4gbhjnl5lYQNTdEQUq7z0wikcCZM2cwdepUTJ48GW+++WbS893d3Vi4cCEAIBKJYHBwEK+88go+9alPAQBefPFFJBIJzJ07N91LIaIcEVSxqxyKug4NIG5cCDTiXG4DktXojpdVTU4jEqsaarRTSGKKRx35EaMtToFGDUdW2yA4Uf/vIu6nlyADWHcVVj8D0UjxVDNz33334Te/+Q0OHTqE/fv3Y/Xq1di1axeWLl2KUCiEu+++Gxs2bMDPf/5zHDx4EN/4xjfw5z//GbfffjuA4VGaBQsWoKmpCS+//DJ+97vfYcWKFViyZAlXMhGNMun0c9GdQ4xKxI0L/9UvgoCX0Qm1W6065aPjtkdMR6xPez55ikc91vxcmtEMXX2NbprKi5b66qTdvuOGwToXynueRmaOHj2KZcuW4ciRIyguLsasWbOwfft2NDQ0AAC++tWv4vTp01i5ciUGBgZw3XXXob29HVVVVeY5nn76aaxYsQL19fUoKCjArbfeig0bNgT7qYgoJ/jt52Jl76Hj5t/DIX1AsKMGATdTPoC7HjEAEO0ZsD2fKJB1O1KlXq+ob3FzzVYaN0XNERkxxcQ6F8p3nsLME0884fiae++9N6nPjKqkpIQN8ojGiCBa7uv6mQDDIyrhUAhzplovi1avRQ4ecjt+wL6A1WnaTDznpiDWbRGzGnZ0hbpei27lc8jL0hloKN9xbyYiCpQo2gWgHfnoiPVhc3PE9fl0/UwAmH93s5xYDQatmlAj90exmvIRr1fDSKvFCIt6PrcjVbpRGxHaxJJyNdA4Fd3KU1qiRkYtCmbhLuUrhhkiCpRctKv7go/2DHgaobEaURF7ATmNKLS2d2PPW8mFt/I2BLWVJUlf4k5dfHVhxG1BrNuRKl1tjnzNauhwcy/drEDy2kmZKFcwzBBRoFrqq9ER60O0Z8B8TA0kbkcArKZy5L+r/V1U4YIQoj0DKUuy3a6ukpeH62pY5kwtcRUC3C7LBjKzWogrkGg0Y5ghosBtbo6YX9ail4nVKiC7L1l5NEE3lSMfbxWQ0l0mLkaaRMM6tYbFDTaZI8qskGEYeTdJOjQ0hOLiYpw4cQJFRUXZvhwislC1equ5cia29mbzcT89Z9Il3lOMqnh5b7vCWTddg/12RM7EJptE2ZSp72+OzBBRRmzYeSBpCXDjpmhSEBjJIAOkt0xcLr5VO+/qalhUfqd4gt5kk2i04sgMEQXOalmxCDaZGslwc01+RmYEufNu95qFno71y2qXbzVMcYSG8kGmvr8975pNRGRHN/LS1lRrBplwSB9SZGJEws0u1F6vye8Oz+l23vWrpb7anM6qWr1VW0Ts9X4QjTYMM0QUKMuW/9KUk1MQkLcxEK/1Oz1lVXxbW1liGWg27DyAVqmpnt8w1GrzGvU97OjCYLam64hyEWtmiChQ6nSHlyXJMq8dc61Y9VepqypDtGcAHbE+23oULyuR1OkxueZFXItoAuil5kUNg6KwmkGGaBjDDBFlTLpLkoPY28mqlsTtfklums0JasGu+lnVXb7dfB719fIKMQYZomEMM0QEIP2iW93xIgiI58XxXlrw+93bycvnsRv98bISySmoeR1h0hb7alaIEY11rJkhIgDpF93qjpfDgnp8S321bVCwqlNp3BS1fL1cg+L287TUV5thKYidveV6n5r7t5mfwc97yKNC8v2Irb3ZLAoeqUJkolzGMENEANIvuh2Jol3xBa4GGl3gcns9mVilpAYkAL7eY6UmyMgrxPysyiIajTjNRESmdItuM12029ZUa/assatzcXs9dsXJ8YThe9pNDUh+CqDd3A+303VEox3DDBElSbfoNp3jRZ2LLiSIACE3jrMKTHK9jHo98vN2xcliFEh+XFyH3Uokq12+5fsjP+7m/nCTSCJ7DDNElCSdott0j3fbvt8pMKlLonWjJG5GO2orSz1tUKk+36oJNfIqJ46oEAWDYYaITH57wgR1vG7Uwm2di3x+3ZJo+WfA22iH22kzNSCp7yGHF46oEAWHYYaIAKTfEybd44V06lyszi+fx8/1uJ0243QQUXZwNRMRobW9Gx2xPnP6RV0dU1tZYj5u1YLfatomnjBQV1WqnVKxOp/VcmmrwKRb1SOuRz2PeL3bKZ5s7clERO5xZIaIEC4IIdozgLqqspR6E7WY1arw1WpUIlwQQkesH7WVpUmPq3UwctGuGiAaN0UxZ2oJALhe1SO2DdBNR7kdJUln2iwTO38TkR7DDBElTe2saqgxRzoApAQZP6ubxPHiZ90IiwhR0Z5+dMT6zefEUmwAtt1u1esKuv7H6rNYcVvMTETpY5ghIgDJX9RiCTPgrgW/m1EIEZCsztdSX20GmbqqUjOAiJ/l3jJOgqjf8dvbRb0X8vuJYMYNIomCxTBDlOeCnM7Q9WRxU/jqZhTCTSGtmErqiPWj5v5tSaFHfBY3gmgy57eYV3cv1rV3Y/2O4X2VRFAjouAwzBDluSCnM9QaEwCu+sW4mUpy039GBAgRZOTQ4yUAeAkiQde26O6FCDLhUIgbQxJlAMMMUZ4KYjpDLbrVda5dMW9ayvl17JZUe6lfGamdsoVM1LboRmTETtdemxASkTOGGaI8FcR0hq7oVpwHAOqqSrVFwXaBRp1K8lK/km7Rrp9gol5LPGGg69CANgx6GalRR2Ria2/2tS8TETljmCHKU/KXcEesb3hZ9fn/+penM+y+gOVziPCz5PFOAEipVRHH29Wb6EZV3NavBFG063bllN1x4h6qYdDrSE3jpqjliAwDDVGwQoZh5N3mIENDQyguLsaJEydQVFSU7cshyir5v/YBmF+eXpZUi3OIEOJntY3VqIrbqS7dLtUiDInnRaBymk7qiPUh2jPg+fOIWh35Hnr5LOq9qKsqTdoY0yogEo0Vmfr+5sgMUZ6TpzMA4CvzU/clcjOikc5O2emMquh2r7Y6p3qMel75mN//ZdDT51FHlcQUm5ul6UHdCyLyh2GGKM+p0xlqnxg3rKaHnIppAZijJlb1JU5bB/iZGnI6BoCnImKrUaVwKOQ54AWxLJyIvGGYIcpjclM5eTpDfAGvmDfNsbkbAO0X+ZTLL8Y7xz8AYF9M63VURcduJZTXY6w+j/o57K5VbuAnAo3bVUjcbJJo5DHMEOUpp8Ag+sTY7ZlkNxX1zvEPzKkWwH7ExGvBrY6fqS5dkz+vUzxWo0oiJM6ZWmI5rUVEuYFhhihPqV/C6ohJR6zP9gu4pb7aLJQV1HPEEwZqK+1rR/yMquj46S+jHiN2/vYyxaOGPbswxkBDlJsYZoiyIIius/LzVlMlTlMsm5sj5mvsgog6YqJevzxCEg6FPNeF+OkvY3VMXVWZ9vWseSEavRhmiLIg6K6z6XwBO03v6EZM1OsXrxFFyF2HBnRvpeVn9Y/umHjCSJkWk1/vdik0a16I8g/DDFEW+G3uZiWdL2C76R273jGiI7C807XdDtdWo1EihKiByy6I6cJbuCBkvr98jJeAGPQ+TUQ0MhhmiLIkqFoTmdcvY7vpHXFtViMmqxpqzOASDoWS2v/rpomsRqNECKmtLLW8RyqnbsbiXF4DYib2aSKizGOYIcoSETzEiIg8xeN3FMDLl7HT9E5tZYnj1NWcqSXY0zOAuGFod7iWR0h0o1FLHu9EtGdA+z7p7ljtJSAGsWknEWUPwwzRCJK/NOXgIQLNksc7UVdVZjsKYDf6AgC1lSW201fy9gFOje6s3iMpdJ0PMuoUlVOzOxE2dNLdsdrrEu8gNu0kouxhmCEaQfKXpmz21MvREetHtGfAcqRCdw6r0RcRiHSjE362D9Dxu8O1GjZWzJsWWO2QuC6vS7x1IzLyjtdi004iyk0MM0QjSP3SXNVQk9RpNu5i31e3xcNWoxNBFB+ns/+QGjbEfQiidshvwFKvXw4y6o7XRJR7GGaIRpjcrC6pN8v56Rq7LQjkcwDWtSFOoxPpFh/7XQputzpKVzvkhtW2DII67WZHHZGJrb3ZUyAiouxgmCHKgs3NEdTcvy0lyDhtQSDXy6jTNfLzbkYn/NSWCH6WgrsZzfEyNSSIz6sWLKvTbm6a3ambdsrXwUBDlLsYZoiyQG0yp24UCei/NNWaG3n0Zbj7bWnKyhurL2M/tSXpsBrNEWorS5I6EsvXqqNbgSS6//pZgWS1aad8Hez+S5SbGGaIRtiFtvvWTeasvsx1NTfyzwnD3fSP29oS3copeVpH17fGajm17rF0am+CXIGUznUQUfYxzBCNIPlLU2ziaBUm5FEAq+XYYpqotrLEXMHktDeRly9uXWBQd9vWfTa30t2GQb1mvyuQuB8TUX5jmCEaQW6/NNXn5QAhziH3aamrKnP9xevli9vLCiU/y6nT3QcpqBVI3I+JKL+FDMPFWtAcMzQ0hOLiYpw4cQJFRUXZvhyiEaGOfMi1M25DhN+9h8R7i/oa+Rrkx7L1xV+1eqt2BRK79hLllkx9f3NkhijL3AYMdZQESK2Zcfri9rv3kNXKJ7+roYLEFUhExDBDNEKsQosIGB2xPmxujpiPOwUMNUC47b6rvtbNKIZu5RMA36uhgtqdmiuQiAhgmCEaMVajIkK0Z8AMBFYBoyPWByC1H4uXL26vDfPsVj756bTb2t6NrkMD6Ij1p7xeXlLthCuQiEhgmCEaIU6jIuI5q4CxYeeBpH2b1ADh5YvbbcM8t7UnXkJEuCBkjqbodqd2u6SaK5CISGCYIXIpiKkRp1ERq4AR9CiE24Z5usAgHhN/Vz+bl60YRKCRe8O4XVLNFUhEJDDMELnkt3hWDUHyqEg4FEpqZGcVMIIchfCyGaPb5nfq9ThRgxh3pyaidDDMELnkt3hWDUHqVgZdhwYcA4aXAGE3gqRr85+tOhO5yR0A7k5NRL4xzBB54LV4Vj0m2tOftIWB+N8gA4bdCJJVTUo26kzUJdVqDQ0RkVsMM0QeuS2eVY8RQSYcCiWFlyWPdyLaM6A9BgB+d7Av6WeZrlZHF4TEe+iCl5el0EGRi33lJdUMNETkR0G2L4Aon7S2d6NxU1Tbc2XDzgNolRraqeZMLTFHIeQQtLk5Yu7VpGqpr8bfThvec0m8jyACgNj0UT1uVUMN1rV3o+b+bdqw5HQO3WdXr0E+j91nV18rBxn5esXjXIlERF5wZIbIA9EfRR1REKMudv1RwgUXgoxa4JuJRnfqCNKKedM8n0O9fj8F0Co3xcwjOUpERPmPYYbIQas0ciHXuYhRiimXX+zYH8XLCiIdP7U66uooAOZojdtzqPdAHC+uSXyO2soS19NCXFJNREFjmCFyIEYkaitLtGEEAOqqSjFnaon2+KB6xHip1bEKT6saasxw42U/JXEPVjXUpASi4c9f5uo8RESZwDBD5CC5yVvql3ZhuMC2P0pQPWLcNrpzE5687qckHy8HIsD9jt1ERJnCMEPkgm6aB3AXCoKYVvEyTWUVnoTayhJsbo6kNdVFRJRLGGaIXJKneQDnTRa9bH8QZKM7XXjKxKaMuqJiIqJsYJghcklM86isQoGX1T+ZbnQXxFSXHNp0RcXqtRMRjRSGGRrVgtgcUrxWFAGLuhndjtW6jRfdLIdOZ/m1G0FMdXXEhpv36YqKrfrkEBGNBIYZGtWC6I1iFyp0gUbmZUm17rVWy71Humvvhp0HUjoIq0XB7A1DRNniqQPwxo0bMWvWLBQVFaGoqAiRSATbtm0zn7/hhhsQCoWS/txxxx1J5zh8+DAWLVqESy65BBMnTsTdd9+Nc+fOBfNpiBRyJ1y5U6+XZnF2UzRuRiRa6qtdL4eWXyu2PfDS+VcVVNfedO8BEVEmeRqZmTJlCh555BFMmzYNAPDUU09h8eLFePXVV3HNNdcAAJqamvDwww+bx1xyySXm3+PxOBYtWoTy8nJ0dHTgyJEjuO222/CRj3wE3/72t4P4PEQp/DSck6U7ReN2SbXutepeRV6CWGt7t9mxWL1WuajYDTa6I6Jc5inM3HLLLUk/r1mzBhs3bkQ0GjXDzCWXXILy8nLt8b/+9a/xxhtvYMeOHZg0aRI+8YlP4Fvf+hbuuecePPjggygsLPT5MYjs+dkcMghellRbvVYEGq9BLFwQMouH5feUN3lkECGi0cD3RpPxeBybN2/GqVOnEIlEzMeffvpplJWV4dprr8Xq1avx/vvvm891dnZi5syZmDRpkvnYTTfdhKGhIbz++uuW73XmzBkMDQ0l/SGyo06vLHm8M2nEY8njneZzXqZbvLBaDq1Oezm9Vuy07TWIqZs3rmvvRtXqrSmbPBIR5TvPBcD79+9HJBLB6dOnMX78eGzZsgUzZswAADQ2NuLKK6/E5MmT8dprr+Gee+7Bm2++iV/84hcAgN7e3qQgA8D8ube31/I9165di4ceesjrpdIYJhf+AjB3jZ499XJ0xPoR7Rkww4RdIbDVaigxhTNnaknKFIwozgX03XF1K5/salLEJpZeu/bK7yXuRdwwEA6FGGSIaFTxHGamT5+Offv2YXBwEM8++yyWL1+O3bt3Y8aMGWhubjZfN3PmTFxxxRWor69HLBZDVVWV7XlDIetixtWrV2PVqlXmz0NDQ6ioqPB66TSGqF/iqxpqzFBQV1WK2srSpOeswoHVaii5FkXmtqZFfc6qJkX0mfG7QaV43fodBxA3hsNT3DA8BSIiolznOcwUFhaaBcCzZ89GV1cX1q9fjx/+8Icpr507dy4A4ODBg6iqqkJ5eTlefvnlpNccPXoUAFJGbGTjxo3DuHHjvF4qjXEt9dXoiPUh2jOQtNS5I9aPvYeOA4Djbs9W/V/U3bO9Fue6EVTX3sZNUXNEJm4YKTU0RET5Lu0+M4lEAmfOnNE+t2/fPgDAFVdcAQCIRCJYs2YNjh07hokTJwIA2tvbUVRUZE5VEQVpc3MENfdvM+tN2ppqk37e3BxxPIfdaigROPysknISRNdeudi3rak2pahYPh8RUb7yFGbuu+8+LFy4EBUVFTh58iTa2tqwa9cubN++HbFYDG1tbbj55ptRWlqK1157DStXrsRnPvMZzJo1CwBw4403YsaMGVi2bBkeffRR9Pb24utf/zruuusujryQKaiuveL1cuFv46ao62XSMqvVUFaPB/EZglgSrhb7ysGsrqqU/WGIaFTwtJrp6NGjWLZsGaZPn476+np0dXVh+/btaGhoQGFhIXbs2IEbb7wRV199Nb72ta/h1ltvxa9+9Svz+HA4jOeffx7hcBiRSARf/OIXcdtttyX1pSESdSrpNIuTX7+qoQbdaxaa00J1VaXoXrNQu6rI7lxqCLJ7PN3PEESzOzGyoxb7ilVOuuJlIqJ85Glk5oknnrB8rqKiArt373Y8x5VXXomtW7d6eVsaY/zuUyTT9WzR1bmo7+P2XOvau82CYrviXK+fQYzo6AqPhz9Dn7mtgBM2uiOisYJ7M1FOSrdrr1pvIv8sL512qj+xKsKVV0Y5Fed6+QwixIjNG+Xl5W5WXxERjUUhwzDybtJ8aGgIxcXFOHHiBIqKirJ9OZRBcrFu95qFI/a+YoQknjBSal827DyA3x3sQ7ggZNtnRjzu9TOom2DKgYZBhojyWaa+vzkyQzlFLpzVFe+OVJ2HPEJitdu2VahQX++14Fge0SkMXyhrG8ltGIiI8gnDDOUUESLkaZy2plpzibHgdVWTV5mq23G7HFpeJQXAV/dfIqKxgmGGcopcj1Jx+cXoiPUn9UqRf3a747NX6rJqueZFXc5stQRbBBe5KZ+XhndiREdYMW+a62OJiMYahhnKOXOmlgCAucGiboTGT+2I294v6koiEWTEtdRWlprHWW130BHrAwDUVZUlvY+bhnfyCI5cN6MWBTPQEBENY5ihnKMWzooQIX52CjJWoUUEj45YX1LnX7XgVh5Bifb0m9cgtgKQz5uykWPCQNehAXP5tFo/4zQ1Jo/o1FWVJR0vBxo2uyMiuoBhhnKSWjgbDoVSuuxasRotEcSO2XZ1MPJ0lxxk1B418nusa++2DD1qYLLiZgsDNrojIkrGpdmUc9SAIaaWRFBwM8VkVXwrT9uIoKQ7n9mp9/x7imXVdkXA8kiSfJ1Bb0BJRJSvuDSbclq6exGJ4wGkhJCOWD+mXH4x3jn+gesNEp0a1un2U5LFExdGYnQridRpHnUkSVxnJjagJCKiZAwzFAirqR230yvi+NrKEu1S5s/PrgAwHCJqK90HGl1ocdP7JVwQctyqQPcZ5dd6mRojIiL/GGYoEOn2ZUnezXl4BZBYEWR1vFMRrNUmkE69X6y2MFA/n91r5Xob9ochIsoshhlKm5e+LHa87GXkt2YGgGNIcVOEK+heK29qOWdqiWNBMhERpYdhhtLmpS+LE6upITes6m6Ev57wV/jfwdPa9wSA3x0cHgnS1fZY1f3o9mWyGo1ioCEiygyGGUqbPLrxs71vW/ZlcdtnxeteRoKu7kacU67b0Y0U2XXndVv3I87tdlSHiIiCwTBDgZDrRACk9GUB4BgI0tnLSH6NXHfjt25H/Ox1WbVdUOOIDBFRZjDMUCBEnYgYkQGA2srSpJVHdoHAqpC2I9Znu4pIHenxUnejk+7xREQ08gqyfQE0Ooi+LKLBHHAhEABI2nDR6nhdaFBXNgnm8ufzNTKylvpqc5rKz7Jor8e3tnebo0+qDTsPoPV8GCMiosxgmKFAyH1ZutcsNKeTRCCQ90LSWWmzamlVQ425BQGgH8WRA4Vad9O4KeopUFgt6bb77Ovau7Hk8c6k18qBi6GGiChzOM1EaXOqK0m3z4qbqR8RKETdjroVgt/P4qZuJ3ljygHzcXX7BDcFxERE5B3DDKVNnSJSV//Y1b243QbBacm2XIAsVlDJ/V50G0Tq3s9tszyV/Dq5Rkg8xrobIqLMYZihtMkFuFaBwGqEw+02CG6WbM+ZWgIA6Ij1m5s+yiMsYlm0VYAy636U5dNul1XLgQsAC4iJiEYIw8wYlu7mkDpe+6y4WQ7tdupHXKsIMvIIjpsAJep+dE3+3IQRNXBxXyYiopHBMDOGpbs5pI6fPit2NTFep37cjOCox8cTBroODSTV2sjncxPq1Hsmzs19mYiIMo9hZgwLoklckNeiq4lxGukRWxDorr1xU9Sy1kX+7LpuxYD7UKcLMvLfuY0BEVFmMcyMcZloEudn+spqRMXNSI9uFZNc/GsXaNR9pMT7egl1InCJa1GPsSuAJiKi9DHMEOIJA+FQSFvjYTfNYhVaxPRVR6wvqb+M1UhHOtsYJG9hUKoNInLxr/q+coASwcdrqBP3plUTZFrqq22vgYiI0scwQ+g6NIC4cSHQ6EYndKxqbgTR6M5upCOd5dCC/Hp1FZPV8VYByirUucF9mYiIsoNhZoxTe7GI0Ql12kbHqeZGPGc30hHULtNOfWjUz6wLUOIzq6GOiIhyG8PMGNXa3p2ygkd8yYeApOZzdpxqbuwCRpBLw92sYhLiCQO1lSUpx4vPnDi/USbrXIiI8gP3ZhqjRE8VObC01FcjHArBABDChSZ0Tlrq9RszOu1xJKap1MftNpHUkUdaxL5QuvMKKxtqUFdVZr5GPr62shTRngHUVZU5noeIiHIDR2bGKHlERYxiNG6KmrUzccPwFCZ0ocWpqNfL0nCrURzxenlXbnkFGMoAABtxSURBVDc1N/JraitLbFcjsXCXiCi3McyMYfIX+vodB8xeK21NtY4rilqlkROr0OKmqNft0nCrYuOO2HCfmbqqMu1nswsi8nv//i+D2vfmFBMRUe5jmBnjWuqrzSATDoXQ1lRrPg5Yj27I4cLtEma7LQ2cinetRnGiPQOW7+/2mtwWDhMRUW5izcwYt2HngaSpJbk+pKW+GqsaarSjGy311doiWjFKY3eceK18nDxNteTxTu21iusRS7Dl3jK6z9V6Pvg4fX67uh4iIsp9HJnJQ0GtAnLTrM5upGJzc8Q8xkujOXlUB0ht/y/3p1HZde3VfS43n99qas3vZptERDSyGGbyUBAbROoKbeMJw7L9v9UXu59pGnXKyGpPI/UaxHXouvaK17rdhkAOMmogUvvsEBFRbmOYyUNeVgFZ0TWrk5dry1NEdiHJS38X9TN0xPoQ7RmwHNVRp6msRpL8bEMgf351RMZNw0AiIsodIcMw8m7d6dDQEIqLi3HixAkUFRVl+3KyRnwJiyARxJevVWDQndvLa62I7QcKwwXoXrPQ9XWpj4uaH6fzOJ0/yHtJRETJMvX9zQLgPGbVrC7dc6pFtvIXe6um0Zz8vrWVJa4bzXkpvrXb9qCuqtQMMn6LeDNxL4mIaGQwzOSRViUkuF0F5JXdF7u8I7YcLi5M+ZRZrmSS+enaa1XwLKaE3JzH7nq4qomIKD+xZiaPyIW/ot5EtwoIQFqrcOzqYOR6HdGozuv0UhA7ZWfyPE4NA4mIKLcwzOQR9YsaQMqqG3WFkFdelms7Fd1aLSEXq6Z0zfPE824EseN2UIGIiIiyh2Emz8irgESfFdE4TozKyPsUqex61DRuiqas4rHbhsBpSbbVEnKxaqq2slT7+ayo1y6PPKlLx90GkCACERERZRfDTB7a3BwxVwGJQCN+dprqsetRo+6iLYgA1RHrS6qRUet1NjdHUo4DkoPQksc7LbcgcGpSF0R/HZXdVBxHZIiI8gPDzAgJqmuveL0cJMKhkOtVOH571NRVlSUV1rrt2qubkrL6TE6BJIj+OkRENPowzIyQoEYV1C9vMTUkAo2bpnVua16sjgG8de1Vp6RWzJvmO5CIUSKra+cWBEREYw/DzAhJZ1RBjOqI4+Xi3I5YP6ZcfjHeOf6B5VYEVtfjZxsCr117gdSRJADmEmovXXuFuqoyRHsGUq49nekmIiLKXwwzGSZPL+lGROyKdQUxqlNbWaJdZfT52RUAhoNEbaV1oJGvRQ0YjZuimDO1xHFEQ67XUUOQ1RSaVZfgIJrUyT1hON1ERDQ2McxkmDq9JI+IADB7tdjR9XbpiPUBgOWXt26ERFyLuveQmKoCnGt7OmJ9rvdicrPs2eueTuroy7r27qSpLwYZIqKxh2Emw+Qv745YHwrO17aonGo9vNS5WH2ht9Rf2ERRXs4tfhaBRvyvrrYHgHZ0yCpQ2QWM2soSbG6OuG5SpwtHdkXFREQ0NjDMjABds7vklUDJje/szuO1zkU1Z2oJAGiXc4tApU5V6YKM7nOp16MLZuk0qVPDkTpVJi8dJyKisYNhJot0IyV2dNsMxBOGpyXf4u+6uhf1HGptT11VWdrN5dJpUqc2ydPV4ridriIiotGDYWaEiBoXEUTkoFBXVWqOmFix+vKWp4fcLvm223tJUEeB1IZ46mvdCqJJHbcgICIiGcPMCNiw80BS11vxZSyCQltTrePxdl/e6pJsuyXfbjdVdBN4soVbEBARkYxhJsOcesk4BYXW9m7seavf8vjayhLMmVpi1rnYFQe7HdHI9V2kuQUBERHJGGZsBLEFga5oVZ7+Ed1sAf0XcbgghGjPQMoSbruVPVbFwW5GNDiFQ0RE+YZhxka6WxCoYUg9Lp4wHJcmu+0cbDctJK7DanWRHMpaLUaR0p3CCXJvKiIiIhnDjI10tiAAUsOQGBkR5xR/dwoKTj1mnKaFvISyTE3hZGLHayIiIoBhxlE8YZgFtmqQ8NLoDhgOClZhyCkoWPWY8TIt5DeUpTuqIo4X+zGp1+BmSwciIiIrDDMOwgWhpF2pRZBwO6LgpXOvHatpJLcre9K5jnRHVcTxqxpqUjaYBNxt6UBERGSFYcaB3NhOBBqxl5HbMJBu5167aSQv00J+ryPdkR35eHmDSYD7KRERUfoYZjTU3aXlvYtCgOuOvYKfni3iGgD9btC1lSWeVxel0zsm3REmNRAREREFpSDbF5CLxLRI46aoGSTammoRDoVgAGag2bDzgOO55BGM7jULzWkWp2PFNXTE+rTFvnVVZVjVUON6dZHf65C11FebQcjv3lBCYbjA1zUQERGpODKjoXbXbamvRuOmKOKGgXAohLgxXBRsFSScRlX+esJfWY6qqAW1IriI59xO7cjX0nVoIGVaTEyfeRndSWdkR54aU6eZ2L+GiIjSwZEZCy311VjVUIOOWD+qVm81p5Zia282HxeBReU0qnJl6aUALuzXJIjnxXnFNaxr70bN/ds8BxlxLbppMXn6zM3oTrojO+KzqseLx7gFARER+cUwY6OlvtociQmHQuYeSnLI0H2Zi+ejPQPmY3IYaGuqNZ8Xx9st2U5nakcOZbr3amuqdWxWZ7X8222gUfemUo8H7AuZiYiI7HCaSaEW/8pTS42bopgztQQrpS9lv43u3BbUBrHhY7rFu+lu7MiNIYmIKJM8jcxs3LgRs2bNQlFREYqKihCJRLBt27aU1xmGgYULFyIUCuG5555Leu7w4cNYtGgRLrnkEkycOBF33303zp07l96nCJCu+De29mZzNVPXoQujLS311Y5Lo+1GVZyeD6Jo1+176bSef6+VFiGrtb3b8R4A0B4vXxdHZYiIKB2ewsyUKVPwyCOPYO/evdi7dy/mzZuHxYsX4/XXX0963X/8x38gFEqtJ4nH41i0aBHOnj2Ljo4OPPXUU3jyySfxwAMPpPcpAtRSX20GF1Fnoi7PdhsmdKMqbp/3MrXTahNwROhwuhaVKBzWhScR9KxqhoiIiEaSp2mmW265JennNWvWYOPGjYhGo7jmmmsAAH/4wx+wbt06dHV14Yorrkh6/a9//Wu88cYb2LFjByZNmoRPfOIT+Na3voV77rkHDz74IAoLC9P8OMGYM7UEwPDy65r7t2m3MHDitF+S0/NepmacOvSKEGb1Xjpy4bD8WtEw0EufHSIiokzyXTMTj8fxzDPP4NSpU4hEIgCA999/H1/4whfw2GOPoby8POWYzs5OzJw5E5MmTTIfu+mmm3DnnXfi9ddfx/XXX699rzNnzuDMmTPmz0NDQ34v2xUx7SGCTGG4APGEYVmvoi6ndtovSXQUtnq+I9aHuqoy13sh2XXoVYOM1etV6vL0de3dWL/jgLksXRRDExERZZvnMLN//35EIhGcPn0a48ePx5YtWzBjxgwAwMqVK1FXV4fFixdrj+3t7U0KMgDMn3t7ey3fc+3atXjooYe8Xmpa1GkZ0asFcN6fyGlU5XcH+2yf74j1ed4LyarIN54wUFuZOoripvhWDT3qqi4iIqJcEDIMw9NSkrNnz+Lw4cMYHBzEs88+ix/96EfYvXs3Dh48iK997Wt49dVXMX78+OGTh0LYsmULPvvZzwIAmpub8Ze//AXbt283z/f+++/j0ksvxbZt27BgwQLte+pGZioqKnDixAkUFRV5/tBOrKaArKZrMrG/kNU1OL2XPJrUvWZhINdStXor4tKvCfdTIiIiP4aGhlBcXBz497fnkZnCwkJMmzYNADB79mx0dXVh/fr1uPjiixGLxTBhwoSk199666349Kc/jV27dqG8vBwvv/xy0vNHjx4FgJQRG9m4ceMwbtw4r5fqi9MUkZhy0S1xlpd1686rTg/Z8bOcWh1NatwU1Y6ieLkWXedjduwlIqJcknbTvEQigTNnzuDee+/Fa6+9hn379pl/AKC1tRX/9V//BQCIRCLYv38/jh07Zh7f3t6OoqIic6oq2+ymiFY11GDO1BLLJc6iEFe3asnP6h8vy6nVZdxiFKlxU9T3tcjFvnLnYxFouKcSERHlAk8jM/fddx8WLlyIiooKnDx5Em1tbdi1axe2b9+O8vJybdHvxz72MVx11VUAgBtvvBEzZszAsmXL8Oijj6K3txdf//rXcdddd43YyIsTp74xdk3s7Apx/UzNuG2Yp3uPtqZaM4yIERov1yIvR5c7H4vP53YbBCIiokzzFGaOHj2KZcuW4ciRIyguLsasWbOwfft2NDQ0uDo+HA7j+eefx5133olIJIJLL70Uy5cvx8MPP+zr4kea03Jq+X/9dtv18l6C1WiSHGjUJeZO3CwNZ7M7IiLKBZ4LgHNBpgqI7FiNalg9nk4hrtf3cpKJomAiIiKvcqYAeKzy0sQu3f2UgtzLKIi9nYiIiHIZw4xLTrU0gtvpIbuVT+GCkOMGlm54maoiIiLKVwwz5wWxrNppWbf8s24LArEfkuhl4+ca/FwLERFRPmOYOc9pfyNd111Za3s39rzVb1nPUltZkjTaogsWIsio+x65vQZZkFNVREREuYxh5rx0l1WHC0KI9gygrqos6XG7c+hWPsk7c6eztNvttBgREVG+Y5hB6hSTGi7cjGL4DUMt9dXmexWGC5L6wXhd2h1kB2IiIqJ8kXYH4NFA7twrd90Nh0LoiPW77twrugSva+9Gzf3bXI2oWK02ctv5V/c5rLr+dh0aQOv5sEVERDRaMMwgOYQ0boqaQUbsReRlWiadLQjUa5ADjtv3VrcxUDfJ9LqlAhERUa5jmDlPDgJykBH1K0KrzZ5EG3YewJLHO10FEavVRuI966pKkwKO20DT1lRrnqNq9Vbtbt9ERESjCWtmzhN7EYkgo9avAMNhw2nVEwDfWxDI+yHNmVqSdJyX5dRtTbWoWr0V8fPNnRlkiIhoNGOYOS+euDASo+uWK4qA7Qp9Abju66IrxA1qOfWGnQfMIAMA4ZC+KJiIiGg0YJg5L1wQShrBsBtV0a16qq0sQV1VWVpBJIjl1Ck1MudHmsTO2URERKMNwwz8dcuVl1SHQyFsbo5ozzuSy6HVICM+j9g5m4GGiIhGIxYAw356Z1VDjXZURSyplkc+1OfXne/7MlLkqTL588hFwW4LiYmIiPJFyDCMvOtrn6ktxN1SR3LEyEddVWlS0bCXotugGt6xcR4REeWqTH1/M8x4ZBVURKARIzVeu/YCSDnv8OqmPkR7BrgaiYiI8l6mvr9ZM+OR1ZSUvBzaT9feVQ01Zk8ZQbdCioiIiJIxzHhkNUUjlkPrlnXbkQuNdYGGQYaIiMgew0wA1Kknu2XdOnKgKQxfqMn2MsJDREQ0VnE1U5qslnV73YZA3tMJgOd9mYiIiMYqjsykobW9G3vest4qoLayxFPXXhFkAGDFvGkAvG1jQERENBYxzPggViCFC0KI9gygrqrMfM7PCiR1OwRAX0PDQENERJSKYcaHIFcgiSCj2w5Bfg+3IzxERERjDcOMD0GuQHKzuSSb3BEREVlj07w0iFEVtXC3e83CrF0TERFRrsrU9zdXM6WBK5CIiIiyj9NMaeAKJCIiouzjyIxP6gokuW7Ga48ZIiIi8o8jMz5wBRIREVHuYJjxgSuQiIiIcgdXMxEREdGI4GomIiIiIg2GGSIiIsprDDNERESU1xhmiIiIKK8xzBAREVFeY5ghIiKivMYwQ0RERHmNYYaIiIjyGsMMERER5TWGGSIiIsprebk3k9iBYWhoKMtXQkRERG6J7+2gd1LKyzBz8uRJAEBFRUWWr4SIiIi8OnnyJIqLiwM7X15uNJlIJPDuu+/isssuQygUCvTcQ0NDqKiowNtvv81NLD3gffOP984f3jf/eO/84X3zT9y7w4cPIxQKYfLkySgoCK7SJS9HZgoKCjBlypSMvkdRURF/WX3gffOP984f3jf/eO/84X3zr7i4OCP3jgXARERElNcYZoiIiCivhR988MEHs30RuSYcDuOGG27ARRfl5Sxc1vC++cd75w/vm3+8d/7wvvmXyXuXlwXARERERAKnmYiIiCivMcwQERFRXmOYISIiorzGMENERER5jWGGiIiI8hrDjOT73/8+pk6dir/6q7/C3Llz8fLLL2f7knLOgw8+iFAolPTn6quvNp8/ffo07rrrLpSWlmL8+PG49dZbcfTo0SxecXa89NJLuOWWWzB58mSEQiE899xzSc8bhoEHHngAV1xxBS6++GLMnz8fBw4cSHrNwMAAli5diqKiIkyYMAG333473nvvvZH8GFnhdO/++Z//OeV3cMGCBUmvGYv3bu3atZgzZw4uu+wyTJw4EZ/97Gfx5ptvJr3Gzb/Pw4cPY9GiRbjkkkswceJE3H333Th37txIfpQR5ea+3XDDDSm/c3fccUfSa8bafQOAjRs3YtasWWZH5Egkgm3btpnPj+TvG8PMeT/96U+xatUqfPOb38Tvf/97XHfddbjppptw7NixbF9azrnmmmtw5MgR889vf/tb87mVK1fiV7/6FZ555hns3r0b7777Lj73uc9l8Wqz49SpU7juuuvw2GOPaZ9/9NFHsWHDBmzcuBF79uzBpZdeiptuugmnT582X7N06VK8/vrraG9vx/PPP4+XXnoJzc3NI/URssbp3gHAggULkn4Hf/KTnyQ9Pxbv3e7du3HXXXchGo2ivb0dH374IW688UacOnXKfI3Tv894PI5Fixbh7Nmz6OjowFNPPYUnn3wSDzzwQDY+0ohwc98AoKmpKel37tFHHzWfG4v3DQCmTJmCRx55BHv37sXevXsxb948LF68GK+//jqAEf59M8gwDMP4m7/5G+Ouu+4yf47H48bkyZONtWvXZvGqcs83v/lN47rrrtM+Nzg4aHzkIx8xnnnmGfOxP/3pTwYAo7Ozc6QuMecAMLZs2WL+nEgkjPLycuM73/mO+djg4KAxbtw44yc/+YlhGIbxxhtvGACMrq4u8zXbtm0zQqGQ8b//+78jd/FZpt47wzCM5cuXG4sXL7Y8hvdu2LFjxwwAxu7duw3DcPfvc+vWrUZBQYHR29trvmbjxo1GUVGRcebMmZH9AFmi3jfDMIy///u/N77yla9YHsP7dsHll19u/OhHPxrx3zeOzAA4e/YsXnnlFcyfP998rKCgAPPnz0dnZ2cWryw3HThwAJMnT0ZlZSWWLl2Kw4cPAwBeeeUVfPjhh0n38eqrr8bHPvYx3kfJW2+9hd7e3qT7VFxcjLlz55r3qbOzExMmTMDs2bPN18yfPx8FBQXYs2fPiF9zrtm1axcmTpyI6dOn484770R/f7/5HO/dsBMnTgAASkpKALj799nZ2YmZM2di0qRJ5mtuuukmDA0Nmf+1Pdqp9014+umnUVZWhmuvvRarV6/G+++/bz7H+zY8yrJ582acOnUKkUhkxH/f2I8ZQF9fH+LxeNINBYBJkybhz3/+c5auKjfNnTsXTz75JKZPn44jR47goYcewqc//Wn88Y9/RG9vLwoLCzFhwoSkYyZNmoTe3t4sXXHuEfdC9/smnuvt7cXEiROTnr/oootQUlIy5u/lggUL8LnPfQ5XXXUVYrEY7rvvPixcuBCdnZ0Ih8O8dwASiQS++tWv4m//9m9x7bXXAoCrf5+9vb3a30vx3Ginu28A0NjYiCuvvBKTJ0/Ga6+9hnvuuQdvvvkmfvGLXwAY2/dt//79iEQiOH36NMaPH48tW7ZgxowZ2Ldv34j+vjHM2DAMA6FQKNuXkVMWLlxo/n3WrFmYO3currzySvzsZz/DxRdfrD2G99EdwzBQUGA/WMp7CSxZssT8+8yZMzFr1ixUVVVh165dqK+vtzxuLN27u+66C3/84x+T6tmsuL0vY+HeWd03ud5q5syZuOKKK1BfX49YLIaqqirbc472+zZ9+nTs27cPg4ODePbZZ7F8+XLs3r3b8vWZ+n3jNBOAsrIyhMPhlCrrY8eOpaRGSjZhwgTU1NTg4MGDKC8vx9mzZzE4OJj0Gt7HZOXl5QBg+/tWXl6eUnx+7tw5HD9+nPdSUVlZibKyMhw8eBAA792KFSvw/PPP43/+538wZcoU83E3/z7Ly8tTfi/Fz6P93lndN525c+cCQNLv3Fi9b4WFhZg2bRpmz56NtWvX4rrrrsP69etH/PeNYQbD/8f41Kc+hZ07d5qPJRIJ7Ny5E5FIJItXlvvee+89xGIxXHHFFfjUpz6Fj3zkI0n3sbu7G4cPH+Z9lFx11VUoLy9Puk9DQ0PYs2ePeZ8ikQgGBwfxyiuvmK958cUXkUgkzP9HSsPeeecd9Pf344orrgAwdu+dYRhYsWIFtmzZghdffBFXXXVV0vNu/n1GIhHs378/KQy2t7ejqKgIM2bMGJkPMsKc7pvOvn37ACDpd26s3TcriUQCZ86cGfnft7TKlkeRzZs3G4WFhcaTTz5pvPHGG0Zzc7MxYcKEpCprMoyvfe1rxq5du4y33nrL+N3vfmfMnz/fKCsrM44dO2YYhmHccccdxsc+9jHjxRdfNPbu3WtEIhEjEolk+apH3smTJ41XX33VePXVVw0Axrp164xXX33V+Mtf/mIYhmE88sgjxoQJE4xf/vKXxmuvvWYsXrzYuOqqq4wPPvjAPMeCBQuM66+/3tizZ4/x29/+1qiurja+8IUvZOsjjRi7e3fy5Enj3/7t34zOzk7jrbfeMnbs2GF88pOfNKqrq43Tp0+b5xiL9+7OO+80iouLjV27dhlHjhwx/7z//vvma5z+fZ47d8649tprjRtvvNHYt2+f8cILLxgf/ehHjdWrV2fjI40Ip/t28OBB4+GHHzb27t1rvPXWW8Yvf/lLo7Ky0vjMZz5jnmMs3jfDMIzVq1cbL730kvHWW28Zr732mnHvvfcaoVDI+PWvf20Yxsj+vjHMSP7/9u0eRWEggOJ4tnBCJAhKgkjANJ7B0iYgWFoFK1GwsQ2WnsIDeBRbryBYiI2VhQhaWLwtFgRx2Y8mcfD/g1QJw8xjAi8hWSwWajabMsao3W5rvV4XPaWXk6apGo2GjDGKokhpmmq73d7PX69XTadTVatVlctl9ft9HQ6HAmdcjNVqJcdxno7hcCjp6/fs+Xyuer0u13WVJIk2m83DGMfjUYPBQL7vq1KpaDQa6Xw+F7CafP2U3eVyUbfbVRiGKpVKiuNYk8nk6aHjHbP7LjPHcbRcLu/X/OX+3O126vV68jxPQRAoyzLdbrecV5Of33Lb7/fqdDqq1WpyXVetVkuz2Uyn0+lhnHfLTZLG47HiOJYxRmEYKkmSe5GR8t1vH5L0v3c5AAAAr4NvZgAAgNUoMwAAwGqUGQAAYDXKDAAAsBplBgAAWI0yAwAArEaZAQAAVqPMAAAAq1FmAACA1SgzAADAapQZAABgtU8qiLSwj5jh0AAAAABJRU5ErkJggg==",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x137a24350>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{PyCall.PyObject,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x137d6fe10>"
      ]
     },
     "execution_count": 277,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q=maunaloa[:,2:13]'\n",
    "\n",
    "b=Q[:] \n",
    "\n",
    "using PyPlot\n",
    "\n",
    "plot(b,\"x\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We observe that the data seems quite oscillatory.\n",
    "A suitable function to fit to the given data could be\n",
    "$$y(t)=c_1+c_2e^{\\alpha t} + \\sum_{k=1}^{np} \\left(a_k cos({2\\pi kt\\over 12}) +\n",
    "b_k sin({2\\pi kt\\over 12})\\right)$$\n",
    "where $t$ is in months, $\\alpha = 0.00037$. \n",
    "**The other parameters to be computed with the least squares method.** \n",
    "\n",
    "1. Solve the least square problem for $np=1,2,...,12$ by solving directly the normal equation with the backlash operator. This means `x=(A'A)\\(A'b)`. Report also $cond(A'A)$.\n",
    "\n",
    "2. Use the function `qrfact()` to solve the least squares problem for $np=1,2,\\cdots,12$, truncating $A$ to rank $r$, for $r=1,2,\\cdots,14$. This means, following the notation in teh previous discussion, $R_{11}$ is is an $r\\times r$ matrix . Report also $cond(R_{11})$.\n",
    "\n",
    "3. Present the computed values of the parameters in each case. Plot out the solutions $y(t)$ against the data points.\n",
    "Compare your numerical solutions computed in 1. and in 2. Try to explain the discrepancies that you observe.\n",
    "\n",
    "4. Compute also the residual and write out its 2-norm in each case. Did the residual always decrease as $np$ increases?\n",
    "\n",
    "5. Perturb the data by a small amount: ` b.+=1e-5*rand(size(b))`, and compare your least square solutions with the ones that you computed without the perturbation. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 291,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x1388f3710>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of basis fns=18, rank=12, residual = 13.337487\n",
      "cond(A'A)=272325806629854496, cond(R_{11})=1.493297\n",
      "||x-x_||=516150550135.979065\n",
      "||y-y_||=1.191771\n",
      "\n"
     ]
    }
   ],
   "source": [
    "b.+=1e-5*rand(size(b))\n",
    "\n",
    "m=length(b)\n",
    "α=0.00037\n",
    "\n",
    "t=collect(1:m)\n",
    "\n",
    "y =zeros(m)\n",
    "y_=zeros(m)\n",
    "\n",
    "for np=8:8\n",
    "    \n",
    "   r=min(2+2np, 12)\n",
    "       \n",
    "   A=zeros(m,2+2np) \n",
    "   n=size(A,2)\n",
    "\n",
    "   A[:,1]=ones(m)\n",
    "   A[:,2]=exp.(α.*t)\n",
    "   \n",
    "   for k=1:np\n",
    "     A[:,2+2k-1]=cos.(2π*k.*t/12.0)\n",
    "     A[:,2+2k  ]=sin.(2π*k.*t/12.0)\n",
    "   end\n",
    "\n",
    "   F=qrfact(A, Val{true})\n",
    "\n",
    "   Q=F[:Q]\n",
    "   R=F[:R]\n",
    "   P=F[:P]\n",
    "    \n",
    "   c=A'*b\n",
    "   \n",
    "   #replace the following line by using qr factorization\n",
    "   x_=(A'A)\\c\n",
    "   \n",
    "   #standard QR solution\n",
    "   #x=R\\Q'*b \n",
    "    \n",
    "   R11=R[1:r,1:r]\n",
    "\n",
    "   E=R[r+1:n,r+1:n]\n",
    "\n",
    "   d=Q'*b\n",
    "\n",
    "   dhat=d[1:r]\n",
    "   dE=d[r+1:m]\n",
    "\n",
    "   yhat=R11\\dhat\n",
    "   x=P*[yhat;zeros(n-r)] \n",
    "       \n",
    "   #display(x-x_)\n",
    "    \n",
    "   y=x[1]*ones(m)+x[2]*exp.(α.*t)\n",
    "   for k=1:np\n",
    "            y.+=x[2+2k-1]*cos.(2π*k.*t/12.0)\n",
    "            y.+=x[2+2k  ]*sin.(2π*k.*t/12.0)\n",
    "   end\n",
    "    \n",
    "   y_=x_[1]*ones(m)+x_[2]*exp.(α.*t)\n",
    "   for k=1:np\n",
    "            y_.+=x_[2+2k-1]*cos.(2π*k.*t/12.0)\n",
    "            y_.+=x_[2+2k  ]*sin.(2π*k.*t/12.0)\n",
    "   end\n",
    "    \n",
    "    plot(b,\"x\")\n",
    "    plot(y)\n",
    "    plot(y_)\n",
    "    \n",
    "    @printf \"number of basis fns=%2d, rank=%2d, residual = %f\\n\" 2+2np r norm(y-b)\n",
    "    @printf \"cond(A'A)=%15.0f, cond(R_{11})=%2f\\n\" cond(A'A) cond(R11)\n",
    "    @printf \"||x-x_||=%f\\n\" norm(x-x_)\n",
    "    @printf \"||y-y_||=%f\\n\\n\" norm(y-y_)\n",
    "end\n",
    "\n",
    "#y0=y\n",
    "#y0_=y_;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 292,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Ij0oTVOJ4q32VX9GVw6JFi9DT04M777wTnZ2dmD17NjZt2sRDb8eOHUMw6BhlV1xxBZ588kmsXLkSt99+O2bOnImNGzfiwgsv5NvceuutiEQiWL58Ofr6+jBv3jxs2rQJ9fX1fJv169ejra0NV111FYLBIK677jqsXbvWOfBwGN///vfx/vvvw7ZtnHfeeWhra8M3v/nNYp8SgiAI4mMIr0NlZdhQwaroHCqdQ5X8f9vOPae6nCmJFdPW1oa2tjbtc9u2bXM9dv311+P666/33F8gEMCqVavSrsibOHEinnjiCc/nFy1ahEWLFnkPmiAIgiB8xI9efpUnqHR/y45blegp6uVHEARBEKUg35AfqiSHyrRkh0p9vtIhQUUQBEEQJcBxqHJ9XeU6VOIiL6dcQuXW1UoHCSqCIAiCKAFODlX+q/wqTYCI+WKmTQ4VQRAEQRAFkvcqvwoWIPqQX+WuWkwHCSqCIAiCKAF+hPwqTYBkqqFVaQIxHSSoCIIgCKIEWHmG/HR5SJWCncGhIkFFEARBEERO5N3LT/i74nKotL38nMcq7HDSQoKKIAiCIEqAWtgy19epf1cClsZdkx7LschpOUOCiiAIgiBKgB+9/CpZUJlKc2T1+UqHBBVBEARRlsQNCyue2oPf7vlotIfiC7wpcAGr/CpNf6Tr5QeQoCIIgiCIorP72Bn8evdHeHjb4dEeii/YeYb87CoL+YnNnistJywdJKgIgiCIsiRhJmfbuFEdiTasyKWZ8yo//d+VgC4pXS6lUGEHlAYSVARBEERZwtyNXHOOyhWdW5Pr6yrZoXJCfuRQEQRBEETJYEIqV0enXMm3hUwlt56Ra2gl/1vJSfbpIEFFEARBlCX59r4rX9xuTXavqtzCnlLIjzlU0vOVdTzpIEFFEARBlCVsmX31hPzEv3MQVBXsUEkhP80qxyr5aAGQoCIIgiDKFJ5DVR056Xn35KvsHCrnb21hz8o6nLSQoCIIgiDKEkvT+62S8cehqqxzIffyY485z1fa8aSDBBVBEARRlvDK4pUW5/LA1oS/skESHRV2KsT8N13ZBBJUBEEQBFFkzCpLSs+3h11l51A5f9uaHKpKO550kKAiCIIgyhI28VZNUrogonIK+UmVxSvrXOjrUDnPV9qqxXSQoCIIgiDKEicpvTomXd2Kt6xel6cQKwe0vfyo9QxBEARBlA6WxFxpIsKLfJOxK3lVnG7slENFEARBECWkmh2qXHREJRfC1PXyq+Rmz+kgQUUQBEGUJU7ZhOrItdHlE2VDJSdxZ86hKvWIigcJKoIgCKIs0bUtqWTyDXXpVspVCnJVdGo9QxAEQRAlx8wzibtcybflSmU7VM7fpqZQaxV8rBwSVARBEERZIgmJKmg/k6/jVskOlaURg1QpnSAIgiBKiKmpsl3J5NuTTydKKgVdmLOSjycdJKgIgiCIsqS6c6jy3UdlnQc7Y1J6ZR1POkhQEQRBEGWJ2HKmGtrP5FsuIF9nywvDLF38VB/yI4eKIAiCIEpGvpXFy5W8Q36C/in0NOw53oeLvvM8fvbyB4XtKEv0IT/3Y9UACSqCIAiiLDHt6nKoJCGRxiT6xpO7cf2617StWmwUdh7eOt6HkYSJN4+eLmg/2aKtQ1XBvQnTER7tARAEQRCEDqkPXBVMvNk6VL975yRMy0bXQBTTmhqyFmLZwERNqXLSdCv65FWLJRlGSSCHiiAIgihLRFeqGpLSsykXYNu2W/T4GCJjr0+YpTmfujw4KptAEARBECVEDvmN4kB8IptyAZnKDBSqP0rtUGXu5VeSYZQEElQEQRBEWaKbjCuZbEJ+otAxNJXFC3V02Hk0SqRQtav8PJ6vdEhQEQRBEGVJtYX8RA3jlWSvT+IWny90DClBVaKQn1zt3i0QC8yxLytIUBEEQRBlid/1l0abbEJdpkZE+llmgJWgMkYj5Ec5VARBEARRekyNW1PJZCOMDI2gkpoqFzgGdk5Ll0PlFpHUeoYgCIIgSoitcTcqCdOyPauje4b8tILKeb7QVi1s/4kSVUvXikhyqPLnoYcewvnnn4/6+nq0tLTgjTfeSLv9008/jc9+9rOor6/HRRddhOeee0563rZt3HnnnZg6dSoaGhrQ2tqKgwcPStucPn0aN910EyZMmICmpiYsXboUQ0ND/Plt27bh7/7u7zB16lSMHTsWs2fPxvr16/07aIIgCKIgdOGvSiFuWPir+1/EV3/+Jn8sm15+oiunTUov8DyU2qHS9fKTVy1W1ueajqILqqeeegorVqzAXXfdhV27duGSSy7B/Pnz0d3drd2+vb0dN954I5YuXYrdu3fj2muvxcKFC/Huu+/ybe69916sXbsWDz/8MLZv346xY8di/vz5iEajfJubbroJe/fuxebNm/Hss8/ipZdewvLly/nzr732Gi6++GL86le/wttvv42vfe1rWLx4MZ555pninQyCIAgiayq59UzXQBQf9EbQ/sEp/lg2vfykuk3aVi2FjYvtf3RCfv4n2ZcTRRdU999/P5YtW4YlS5bgggsuwLp16zBmzBg8+uij2u3XrFmDBQsW4Nvf/jZmzZqFVatW4dJLL8WDDz4IIHlBrlmzBitXrsTChQtx8cUX4/HHH0dHRwc2btwIANi/fz82bdqEn/3sZ2hpacG8efPwwAMPYMOGDejo6AAA3H777fje976HK664Ap/+9KfxjW98AwsWLMBvfvObYp8SgiAIIgsquTmyocl/ykYgijlUbCVevk2VdTAhlShZ2QTxb//LQJQTRRVU8XgcO3fuRGtrq/OGwSBaW1vR3t6ufU17e7u0PQDMnz+fb3/kyBF0dnZK2zQ2NqKlpYVv097ejqamJsyZM4dv09raimAwiO3bt3uOt7+/HxMnTvR8PhaLYWBgQPpHEARBFAfdCrFKwUwJFlNynJznvUJdujCnnENV4LhYyK9UldK1IT/x+ZIMoyQUVVD19vbCNE1MmTJFenzKlCno7OzUvqazszPt9uy/mbaZPHmy9Hw4HMbEiRM93/c//uM/8Oabb2LJkiWex7N69Wo0Njbyf+eee67ntgRBEKNBNeWkmBUc8jO04kF03PSv07lYfjo6vA7VqPTyYw+Kz1fW55qOUVnlZ9s2AoGAr9sXss0LL7yAJUuW4Kc//Sn+7M/+zPP1t912G/r7+/m/48ePZ3cABEEQJcC0bCx86FX8j1/sGO2h+IKdhQApV8TCmew4smn2LDtUyYMWt/SrbELp6lC5w7bVGvILF3PnkyZNQigUQldXl/R4d3e3y2FiNDc3p92+ubkZANDV1YWpU6dK28yePZtvoya9G4aBM2fOuN73xRdfxFe+8hX86Ec/wuLFi9MeT11dHerq6tJuQxAEMVp0D0bx1ol+BAL9oz0UX5DERYVNvGroLhwKZLW6TX5d8r++tp5hhT1HoWwC7+UnPF9hH2taiupQ1dbW4rLLLsOWLVv4Y5ZlYcuWLZg7d672NXPnzpW2B4DNmzfz7WfMmIHm5mZpm4GBAWzfvp1vM3fuXPT19WHnzp18m61bt8KyLLS0tPDHtm3bhmuuuQb33HOPtAKQIAiiEnGSmKsjlCKFyyos2cbQ5E5lU9BSLmaacqh8zKEqdcjv41TYs6gOFQCsWLECixcvxpw5c3D55ZdjzZo1iEQiPFdp8eLFmD59OlavXg0AuPnmm3HllVfivvvuwzXXXIMNGzZgx44deOSRRwAAgUAAt9xyC+6++27MnDkTM2bMwB133IFp06Zh4cKFAIBZs2ZhwYIFWLZsGdatW4dEIoG2tjbccMMNmDZtGgBHTN1888247rrreG5VbW1t2sR0giCIckXnilQyuoTmSkFORnfnU3kdj645sq4fXt7jKnHITzf2am09U3RBtWjRIvT09ODOO+9EZ2cnZs+ejU2bNvHQ27FjxxAMOkbZFVdcgSeffBIrV67E7bffjpkzZ2Ljxo248MIL+Ta33norIpEIli9fjr6+PsybNw+bNm1CfX0932b9+vVoa2vDVVddhWAwiOuuuw5r167lzz/22GMYHh7G6tWruZgDgC996UvYtm1bEc8IQRBEcTCUEFnRb/BFxqrgkJ8YUuP1l7KqQ+X8XYxVcSWvQ6Ucj+qcVoOTyijJ962trQ1tbW3a53Ti5frrr8f111/vub9AIIBVq1Zh1apVnttMnDgRTzzxhOfzjz32GB577DHP5wmCICoNyRWpsCRuHdUX8nOe99IRuv6FvuZQCZXSc10glg/q2NXhV9jHmhbq5UcQBFEliP3ZKs3R0VHJZRN09aSyCWGaghIuRi8/XUixmKhlI1RBWE0hPxJUBEEQVYIub6eS0fWBqxREsWLbduqf87zX52NqQn7ieSj0LJQ6L00Oc7rHX2Efa1pIUBEEQVQJUpipCmaqShaIotNk2e4Qn2fIT5M35lUcNL9xOa9PlKB0girg1PFXUw4VCSqCIIgqQRdmqmTkVXGjN458MKz0QsIzKV3jINmQXZ5C0DlgxUQVg64cqiq4ThkkqAiCIKoEw6quHKpKbo5sKiE/dfi5NEf206ESX1+aHCpKSicIgiAqDLHdSXWs8qvcpHTps7DdQshLSFiaMKevzZE1gq2YSO12LFty24DCc8LKCRJUBEEQVUIlt2rRIc73pSpE6ReZPotsWs8Uo7Cn7FCVNofKstxCknKoCIIgqoR3TvTjhQPdmTesAKotKd1PIVFqEmJSuiaHyrNsQsY6VIWNq9R5dmrIj8omEARBVCn/89934GuPvYmewdhoD6Vg5JVllT9RVXKSvbpCUR1+NiE/JyndQQ2ZFTKuRAlCfmpzZMqhIgiCqFJOReKwbeB0JD7aQykYdWVZpeNnhfBSkymHyivUpfsMRZFVcHPk0axDpWk9U2mfazpIUBEE8bGG1eKJJsxRHknhVHLdJh26vnaVgvpZ2Jb38yLasglFqkNVmhwq+e9s63FVIiSoCIL42JKsD5T8O2ZU/rI4MYRTaXWbdFT0Kj8lny3bVX7apHTpdQUKKjHRvyQhP1kgus5DhQnldJCgIgjiY4tYKbo6HCp3H7hKxlLCRZWEWik922RsncvoZ1K6pRFsxcRV2DPN85UOCSqCID62xAVBVQ0OlVFlIT/RQKk0x039LFxJ6Z7Nkd11osTP0s/myKXv5Uer/AiCIKqShFFtDlV1CSq7gkN+qnBxJ2N7vE6TiC/lUBUoLKU6VKPQy0+1qKgOFUEQRBUgughV4VCZpXUfio2p5CFVEuK1ZdtuAeXZy0+TNF68pPQShPyEr5WlPQ9FH0LJIEFFEMTHlngZO1RvHDmNzv5oTq8xqqwOlVrDqJJw16HKPYeKGUhSyK/QcZW4bIKrl5+r9Uxlfa7pIEFFEMTHlkSZ5lAd7hnCf/9JO77+5K6cXmdoJuNK4sSZYRzoHOT/X8nNkcVry8xBUMmfYcqhyuJ12SKex0QJLhK1lx85VARBEFWIWGagnByq7oFk1faTOTpUZoWH/G545HX87YOvYCCaAFD6IpR+Ykohv+wrhMu99nRJ6QWOazQdKirsSRAEUZ2Uq0PFJp1cx1Tpq/xO9kcRNyz0RZKCSpr8R+l4bNvGb3afwPtdg5k3FlDdwmzrL4mmEdvGzxwqMaepNGUT5JIPVNiTIAiiCpHKJpSRQ8XEQzxHQVUuve+Sjkxu729aNh+zNhl7lI7nnY/68c2n3sJtv34np9eZpixus05KVxyqbFcHZj2uEldKl0J+OqeuwpzHdJCgIgjiY4tYNqGcHCo26eUqqBJlkJRumBauXvsKlv5iR06vk3KOUscvCcRROp7+kaRb1jecW69Hdx2qLMsmZGyqXOAqP6lsgv/n9Nm3O3D7b97hn6ca8sv2PFQiJKgIgvjYUq45VGzOiRm5jUl1RUaD7sEY9p8cwLYD3Tm9ThRUutyh0Uqy14m77F4niFvLXW/Ja3+iEDNMtwAptG6TVWQXc80fD+KJ7cew+1hf8v2UcCUV9iQIgqhCyjWHyuSCIrfii+Wwyk8cey7hnIQmoV6e/EfngNiEn6tDlqlSupcwspTX+Z1zJB5HogiCiv0wGRjRLyxQ35EKexIEQVQB5drLT5yE4jkoo3LIobKkCTsHMah1qJznR0sgskMwcwyiSRHtAAAgAElEQVSPZa5D5fE6JYfKb0dHukaKcFJZGDESNwDIAtC23QIqZlj47jN7c3Y0yxESVARBjBrDcQO9Q7FRe/9ih/wSpoXf7D6Bk/0jOb1OnDRjifwcqtEKpeh60WVDXMqh0uTfjNbx+OVQKR9jNpXSky1r1NflNIy0+y/GKj+W6D4USwoqyaHSOG5vHD2Nn796FD/a/L7vYyk1JKgIghg1Fv3kdVx57wu87lCpKXbIb8v+bnzzqbdwz+/fy+l14jyXm0PlTuwuNbo6StkgiltdU+BROx6eQ5Xb6+S2OZqyCVkV9tRUFvczKb0I55R9jhGdoNIU9hyOJX/IRHP44VCukKAiCGLUONwzhOG4mXOLFb+IFznkx9y305HcVoiJk3EuK/2MMkhKF4VHLvlfulV+5dB6ho0h1xwutVK6u1yA/nVqrz1dZfFHXjqM3+75KKfx6N63GCKV7XMoygSV85xtu1vNsO9gpbUW0hEe7QEQBPHxhf1CziWs5SfFdqiYGMp14pJCfjms9Cu7kF8Oxy0KR4O7QvKS+9GAh/xyXuXnbG/nsLotU5mBk/1R/Otz72FCfRh/N3t6TmMCil82gX2nhlLOk62E/FQhyUqXVEM9KnKoCIIYNZiDkWt5AL9IFLk5Mvv1nWtoRRZU+Sal5/SWviElpee9QrEcQ36F5FC5BZSXI6MKUnWz4VSyd74hsmIX9mTH7YT85PdWHapYnt+RcoQEFUEQo4IlhDNGq2SBmLdTVg6VMJR0Ib/HXj2C69e9hsFUDpoh1T4qA4cqBwdEW4eqDBw3tWxCzDCz+jzVFZfusgnp34/9reZMsR8B+Ygh9ZrwW8TYtlPtfijuzqFKjkF+Tb7fkXKEBBVBEKOCeDMfrZIFcg5V8QRVrhOXmaVD9cQbx/Dm0TPYlSqiWA6VxfNNehbdQmeVn7DfURaIpmUjZpj4ix9sw6KftGd8nRp+zbYpsKEk56ubxXnCfu4J6uo14fc5FX+gcIfKJeL013M1FPikHCqCIEYF8WY+eg6VmENVxJBfjvE3caJM51BFUnkqbP+64pilRl6Wn/1xxzUOldwc2YfB5QF3qCwb3QMxdPRH0TWYudSHmMRu2+5yB16fj6mEOVWhIV6zlg2EAhmH4vmeuYRks0H8vJmgUnWS53GTQ0UQBJEfYtHH0cqhEt2AYiTG5xvOMLMM+Y2knD0mpNRikqNB/iE/txgUheVohTDZ21q2nCyfSSQbZnph5BnyU1xG9bB1qyGzxZXH5dM5tVLnQ/wMWVK6+p5eriUJKoIgiDwxpaKao+9QxU3L90k7lmfIL9ukdOYCMGfAKIM6VFJrk1yS0kWHSiMQRzvkB8jiNlN9sMyV0r0cKnkfrjIDhuhQ5Z8or/v/fLnhkdfxVz96SQrd65LSAW+RTWUTCIIg8kRyqMoghwpIipeG2pB/+/ehbELc1J+bZE4PCynqHKqc3tI38q1zFC/bOlQegsqwMKbW+3Vy2YRcQl/yeVBfp1sNmS2ufCYfQn6GaeGNo6cBJEs6MHSFPQHvMDA5VARBEHliFHmFXTaoDorfoUenbEJux5dNYU+2fB5wjkNKhC4Lhyq/kJ9h2a7xl8OqRVHcZrpmJeGTSy8/1+pA7+POVWSqosUPh2pE+DE0Enf+HqIcKoIgiNJQFknphnwT9zv0GDdY0niuDpXzt9e5EScvNjFKeTuj5ejkmZQu5wZZWddtKjbSZ5GQHap0GKYcmnOXTfASFuLfbodKGlsBq0fZ/gtFvA7FkF/MsGCY7s+RcqgIgiB8JiGVLBilwp5FdqjyzqHKyqHSCKoi5BwdOzWMf3vliOSIpcOvOlTq5D9qSemi8M9hVajqFmYrENVeiGkdqizOyZHeCLoHoqlxKGP0Yemk6FCJ1ySQXIXqElQe71kNZRNIUBEEMSroHCrbtvFvrxzBG0dOl2QMag6V/w6VH61n9GOKCAKHuSFmEQp7/uiP7+N7z+7D79/pzGr7fJPS1ebIrlBRGdTVEsVtJldVzWdz16HK/DrTstI6VJnOSfdgFH/xw224/F+3aLf3o1K6KKJU0T0UN9xJ6ZRDRRAE4S9ylfLkTXlvxwC+9+w+3LHx3RKNQRVUPudQ8aTxHHOoshBUUsjP1DhUPgkQ1uC5fySR1fZWni6Z6lBl62wUGy9xmzHkp67yUzb3DvnJ5y99yC/tEPDOiX5le/9DfsMeIT/AaZCczXvmU6i03CBBRRDEqCDeWJkzNJCatFkrlWKjJk37ncsVN/NzqMR5xWvijggTGVsxWYxVfky4Zes2SQ5VAZXS1XM2aq1nPMKvuThUuuTybJKzMyWlZ3KYWGK413vmsmjAi5G4d8hP9z1OF/5WG0pXGkUXVA899BDOP/981NfXo6WlBW+88Uba7Z9++ml89rOfRX19PS666CI899xz0vO2bePOO+/E1KlT0dDQgNbWVhw8eFDa5vTp07jpppswYcIENDU1YenSpRgaGuLPR6NRfPWrX8VFF12EcDiMhQsX+nfABEFkhVzYM9UkOTVpZ6rx49sYSuRQ5SIsgOxW+Y1IIT93UrpfIb9IroJKyqHKLyk96VB577eUeBVZzexQpa+U7l2HKv3qQGkfGU4vq6Sv2zfgU1J6mhyqwRwcKsAZ3x/3deHz//JHvHywp+DxlZKiCqqnnnoKK1aswF133YVdu3bhkksuwfz589Hd3a3dvr29HTfeeCOWLl2K3bt349prr8XChQvx7ruO/X/vvfdi7dq1ePjhh7F9+3aMHTsW8+fPRzTq1L+46aabsHfvXmzevBnPPvssXnrpJSxfvpw/b5omGhoa8I1vfAOtra3FOwEEQXgi5VClbspskso0WfmFOym9HHOo9CJPnCydpHTB5fHpFz4TbvEs3QwpqToHBySuVhZ3OVRZ78pX5DpUpvB3boU9s82hUkOm6Q4702c8FHMcItt2n1N/cqgc0TSi/CAZyNOheuVQL3qH4nj5YG/B4yslRRVU999/P5YtW4YlS5bgggsuwLp16zBmzBg8+uij2u3XrFmDBQsW4Nvf/jZmzZqFVatW4dJLL8WDDz4IIHlBrFmzBitXrsTChQtx8cUX4/HHH0dHRwc2btwIANi/fz82bdqEn/3sZ2hpacG8efPwwAMPYMOGDejo6AAAjB07Fg8//DCWLVuG5ubmYp4CgvAV27ZdNn6lIvfRk4WUH6GI7MYgv4/fDlVMEFS5hDCyWuWXEHOoNCE/nxTIcM4OlfN3LqsbjQw5VKPWm9Ajhyr3OlTy817Xg7pSM911k+mcDAmi27I1Sek+h/xG4qqgcu5V4WAg9Z7e581UfhiM1urffCmaoIrH49i5c6fkAAWDQbS2tqK9Xd+pu7293eUYzZ8/n29/5MgRdHZ2Sts0NjaipaWFb9Pe3o6mpibMmTOHb9Pa2opgMIjt27cXdEyxWAwDAwPSP4IoJf/vxndx6fc240hvZLSHUjByDpXsUPndtNWLojtUefZdEzf1Cn8OC8K6mGUTuKDK8tz4U4fKXTah/FrPeE/2lpJMngz5ZXc84naWLQvUdNvqiAjXiGXbRSnsKYb5VIdKzKEKp7o4p/sc2eXCjlkVaOVO0QRVb28vTNPElClTpMenTJmCzk798tvOzs6027P/Ztpm8uTJ0vPhcBgTJ070fN9sWb16NRobG/m/c889t6D9EUSuvHW8D3HDwoHOyhfzukrpTmVxd3iiGLAJcmyq3UyxcqiA3CYvaZWfRykHcSJjYsT0ubCnbds8pJNXUnqeIT9d2YRRS0oX3lZyqNKU2FA/a10dqmzKJgDpz3tGh0pwiJJh1Nxenw1eldIBOYcqHEzKjXTfA4MvrrBc+64ESr7Kz7ZtBAIBX7f3a5tM3Hbbbejv7+f/jh8/XtD+CCJX2IQ/WpXF/US8saohP6A0ielsshpfXyONwy/yFVRyL7/MrWd0ZRP8EKQxw+ITf7Y5VH4kpetW+ZVDyE/8LNJdn6ozZ9pugZhN2YTkvgoJ+TnXiK0J+fnhBI+kqUOVq0PFxseGRSG/FJMmTUIoFEJXV5f0eHd3t8thYjQ3N6fdnuU7ZdpGTXo3DANnzpzxfN9sqaurw4QJE6R/BFFK+Go4nwtQjgbiZKsmpQOlCfsxB2VcfbJPvO8OlSgScnBr8q+ULrY7yfrtPNG5YJlQK31nS6Y6VKPlUHmG/NKIb5dDpQv5ZSuo0pz3TOdkUBBUpibk53cdKnfIT+NQpfkesMuXHRc5VClqa2tx2WWXYcuWLfwxy7KwZcsWzJ07V/uauXPnStsDwObNm/n2M2bMQHNzs7TNwMAAtm/fzreZO3cu+vr6sHPnTr7N1q1bYVkWWlpafDs+ghgNmKCK+twiZTTQOlSmKKiKP4E6DlVYGocfmJY8geWSTyTOoV6r/OTCnk6olO/DBwGia8CciXxbzxiuVX7e+y0l+SSlq+LZEspApHKzPUseuF2k/B0qMYcql1pYuTCSEFb5pQ35pZLS03wP2LGz67jScqjCxdz5ihUrsHjxYsyZMweXX3451qxZg0gkgiVLlgAAFi9ejOnTp2P16tUAgJtvvhlXXnkl7rvvPlxzzTXYsGEDduzYgUceeQQAEAgEcMstt+Duu+/GzJkzMWPGDNxxxx2YNm0aryU1a9YsLFiwAMuWLcO6deuQSCTQ1taGG264AdOmTeNj27dvH+LxOE6fPo3BwUHs2bMHADB79uxinhKCKAge8qsGh0qqQ+UOZZaidIIr5OfjL2J1/LklpWd2qKTWM6mcM3G+9CPkJ7oP2X4emURk/3ACix/djr+6YAra/nKms/9yXeUnCX+5+a8XbofKWa0XDgYR1zQN1r0fkF7I5pKUbmscqoQPZROyLezJQn5pQ5gp8cjOgd+toIpNUQXVokWL0NPTgzvvvBOdnZ2YPXs2Nm3axENvx44dQzDomGRXXHEFnnzySaxcuRK33347Zs6ciY0bN+LCCy/k29x6662IRCJYvnw5+vr6MG/ePGzatAn19fV8m/Xr16OtrQ1XXXUVgsEgrrvuOqxdu1Ya29VXX40PP/yQ///nPvc5AJVZnZX4+MBDftXgUIlJ6Ql3DpU6kRzuGcKZSBxzzp/o2xjYr//xdf47VKoAyTeHymtMajhO3b/f4Zx8Qn46d+X/23YIb53ox1sn+iVBlWmVn1966pGXDuP373bi8a9dzoV0Orx6+aUTmO4q7071+3AogLiZXWFPIIOjk+EjGXQlpSvXiA8u8HBaQZV8/0AACAVzyaFigqqy7nNFFVQA0NbWhra2Nu1z27Ztcz12/fXX4/rrr/fcXyAQwKpVq7Bq1SrPbSZOnIgnnngi7biOHj2a9nmCKDcsy+Y38WpLSmchzHRJ6V977E2cODOCN26/CmePq/NlDGwSH1fnfw6VKnrzdahihoX/9e87cfa4WvzLtRfxx4eVXn6u/BifQ37ZJ6U7f+vyf95W+ssx1Bwq9cetXw7Vvz73HgDg0VeO4ubWmRm2VkpYSCE/72tFFUGWUPGcCQvvwp7y/6cL+eXSesa03SLVj7IJYp4T+/7UhpIuHBNUwUAAwQCrQ5U5hMlDfhUmqKiXH0FUCKLAqLRfbjrEm3kiJQjE2j6qI9IzGINp2Tgdief1fq9/cAodfSPSY1xQFSEpXRW9uSTZi5t+eCqCTXs7sX77MclhUJPS1fCNLyE/oTBk1nWoMiSlH+4Zcj2W3L+YQ2W53Be/Kr8z+kayu47kkF+eDpWQQxXmgkp/PKpIyiaJW/+cLYXcbNsZV20ocwmDbNE5VCwnkYWlgwEnd8xM67ilQn6UlE4QRDERJ/uqcKiUGTNuWGlDKuzmn0+y+sGuQdzwyOv4P+t38cds23ZCfkVISlcdtlwcFtGd8SryKZVNsCxX+MaPnH6xGnteSekucWChezCm3VbKoTI1q/x8zqHK9rP2WuWXWw6VIxLCKTHjdTzqac4miVtHJG5I146YlF4bZivu/M2hYgKoIVXXjZ2vQCDAnblsykBUalI6CSqCqBCyLSpYKagCI2aYaXOoTC6ocj/2Q91JV+TEmWFh/877s1waPx2qQnKovMRX1KMRrWHa2kToQhGrsfuxyu/9LtmdiiiiUNwHGz93Nnx2qLL9rL0Erfr5DscNHD+dvL7cOVRiUnqGkJ9ynOmcsHQic0BpTJxcdZr8mwsqn0N+jIYaWVAlHarMIT927Oy4YoZVkgK/fkGCiiAqBFFEVUNSuruPnqVMWM7z4gqlfARV50Cyebo4yYj7YZXS/SzVUNgqP/3j4qonVezowkyFIq3yy6M5sno+3z7RJ/2/uApNDPkZQtmEmpSjY9v+ulTZOlReKy7Vz/dvH3gFX7z3BXzQM+S6Ri2hl18oQ8jPr8KeAyNyY2Ix5Ffno6BSi3kCjkPF9i/lUGVxPFLj9Apy40lQEUSFINae8ms5sW3b2HH0tLYrfLFRcynSOVRqvlWudA0kw0xxw+JiVNz/mFRSup/V2dV95bvKT4S5KrZty82RLdtdndtn9yEfh0r9jN9SEtIjHg6Y6FAxQQX461JlWyJDntxN7d+mZeNwT7K/5quHerUFNNXj8Q75KYIqXeuZNOdDFVSm7Q75+b0SlFGfcqgYQSHkx66JoKZxiaERVJWUR0WCiiAqhGI4VK8eOoX/tq4d3/ntXl/2lwuqMIoZlmfSrykJqtxFT1fKoQKcpdxM8AQDQL2POSUMV8gvh317CqrU5x5NWFLNKcOyXaEUP0J+XoInHVIvP2XC3ndS7kE5FBMdMFFAW3w/NSFn5vWzFlXBDpUw3g9POc3Kp0yo98ihSv6daZWfu5df8v91ndOYKDtxZhg3/ex1vPCe0yWkXxVUluPysqR0U7OaMld0odMGRVAFhKR0dm5CGkXFzrV4DZGgIgjCd6JZFhXMhY7+5Kq3o8KEUCrUiSOayNah8kdQMQFSEwqiJiWoihny8yOHiolqNcxilKIOVbYCRMqhkl8zpDih6RwqnnMkOFR+tp/JPodKH34SP98DnYP8b8Nyl7CwtTlUHg6VR7+9kEZRsW1fONCDVw+dwhNvHOPPqTlUtuBQ1dU457SQsF/CtLTfGVVQBQMBBJU6VDpBpQv5VVJiOgkqgqgQZIfKH0HFbtbqzbcUqMv8Y4bl2XxWXMGWj+jplARVIrWf5P5rQ0H+i93P/oHqZ5TbKj/940wEqGEWfR2qrN/Ok5E8cqjkOlR6t4Uh1kkStzXEBGox5DcKDlU2q/zeEwRVzDBdxy2G/DLlUDFBWqNUFk8nQNi4xM9LF/JTHSr1+HJFF+4DgDG1qqCCK4dKKxA1gqqSSsSQoCKICiGqKaBXKMx1UG++fjEYTWC/EuZhqMv8YwnvsgliflA+oqd7wFmqzxwqtp9wKMDzWsolh8pzlZ/BHCr5809YlruYpA/iI+LRy69nMCaFuaT3TRPyY47VhFSZCrlwqD6HKiyE/HzolMLJa5Wfx/X5fteg9LiuUjqvQ8VyqLxCfsxFCrOFEimHKk2IjJ1X8XyqeZFSyC/sTP2F/IjwOof1LkEV4ALKSHM8WoeKBBVBEH6TbWPWXGCTfLGS0r/51B58+ccvY2+Huzq2KjDcSelicnP+Ib+hmCE5IcyhYqsIa0JB7gb46VC5V/l57/sHf3gP/7B+FxdBXsnGjkOlhvzcDpUf4bERj9Yzi37SjvlrXpIKRzLSJaUzgdU0phaAnEMlhXhNp01KWJh4fU1KzyOEGfMomyCG/OKGW9yK4bZ0IT+xH6NTKyqdQ5X8L/suDUsOlRryc96TibXkPvx3qNw5VAGwLnNsrGIol4+FlU0Qc6go5EcQhN/IhT39uckwVyCasPLaZ8K0sP/kgGdiKwuFfNDjdjPUSUctm+BXDpWYPwU4Ew3bT1JQpUJ+hn8Ttiqo0oUqH33lKH73zkl8mKpj5HU+vUN+xcmh8nKoTpwZQTRh4dSQu9q4lJSuHDNzJ84ak6z7JedQyQKaDb+mSCG/bB0qr15+TJBFE6aUgxjTOFSm7QildD3txPfiIj/1PQlrBZUljUt0c/QOVfJv0aEqJIdKVzIB0OVQOSE/dtxBTciPiVepLRU5VARB+I34i9qvsgmigBjMI4/qh88fwJd//DL+sLfT9Zxt2+gdSobadA6YmmcSM0wpT0x1LJzHc5sAuvoVQaXmUIUFQeWrQ5V9Lz8mJJnAyJyUnuqZJtQTKsYqP9mhsl0Omu58pUtKZ59dY8qhYsdrKYnc4iq/ZA2j1L5Hw6HyeEv2+oNdQ67in9pVfkpulO5QxHPAPlv2HU3vUGWZQ8XyuMTK5QUk23m5Rw26kJ/yfjqByM6beA1RyI8gCN+RauD4dJMRXaJ88qg+7E06KsdOD7uei8RNLvzUJdzJ91YFlexQxXzKoeoalAWVWjahJhTgk9xo5FCJYoJNHt6TuBzym5Cq8F6sOlS6XC2xyKrufMnCSE1KT27f1JAcNwvFqgsUpErpwfSuTr5knUPlJW5Tn8XB7kHpcX0OlVjYM8gfc72X8JjTby9NzhHPoUpdP9IiAk3YUUhwd1rB5H/Ne4kddx0qMSk9TU4YOVQEMfo8sf0Y7tj4rufN7/7nD+ChFw6VeFT50zsUQ9+wHE6JFmGVn3jTzWelH3u9rj1Gr9CzTc3nANzuRbqyCYXkUHX2x6T/d5LSxRyqIqzyS6giQb9vUUwwAeNd2FNelclCZ7pK6b708lMFlZKrpXMLxbCV6n6wibJJCfm5QoOWMPkLVbZHe5WfCLtW1WbdccNyV0q3ssuhMiSHSq7er1sVx84R22Y4YfJwsbu4qBBuCwZQ44NI9cqhqq+RpUVAcBmdMbhfZ2rGTjlUBFFivr/pPfz76x/ifeXXIpAM8azdegg/+MMBz5h/ORE3LPz1j17C1T9+GZZlYyhmoHsgqlRptgouyAfIIb98HCo2Jt2SehbuAzxCfjqHqgiV0lkOFZvIeNkEw8mhUhOA/cDlUHnsWzyekYyCKvl8T+qYpjY18H27wky+OFTy9yVhWBnz2aSQnyAWRSeOOVSRVFK6WuMq2Rw5+bfYWLfQkJ84tmx35fWecTP5HVRFhZdD5apDpdFz4vhqlYUSwTSr4th5Ni2bX3fpqrWHAo5DVEjtNXa9qm5TTSgohfRElzGbsglSUnoF9S0lQUVUPDHD5CElnRMiWsZ9w6VvsZIr/SMJnI7E0dEfRcywcOMjr+PKH7zgSq72w6WSQn55rPRjLozWoRIFlS7k5+rlZypJ6XKSsvN4fknp5509BoBQ2NNy6lDVhJxcJL/6xWVb2FMUEyOJ9DlUrLhrd8r9m95Un9q35SpD4UuldJdDJYsFXbFPcRhS7ptwrTXyVX7yAgH+OqVuU8gnh0pdJZjNZ+11Hm07eY2KifWAPofKtMSyCd7iUJdDxZxcXc4R24d4/pjIUccghmqDwQBfZeeHQ8XKYDBqQgGp3EVQ4zKmK5sgjp1yqAjf6R6Mjqq7Ylk2vvOfe/HLnSdGbQxeiCuNdMu4xYmtEgSVeHOMJkwc6h5CNGHhYNeQtJ0fgkp8r3yS0tOG/ITPRRdOZDdN1ph4SNlGrkNVuKD6zORxAIDBWKpsAgv5hQNSexM1nydf1M/HU1AJx+OE/PT7ZCE/JqimNTbwffudQ2VatutzVcWCLodKFCniuRTFFQtVsnuauh/Tsvh+ggHHnTkdiUslMHLFVZ0/i5WtmRYTsPGwayiWcDtUYtmEdDlUTPAFRAdJEEFeY5NczpQA0a00FJPSwz7mUDWmHEdGOBhEjRDT0zVHTieopFIVJKiIQjh2ahjbDjg9mU4NxXDF6q1YsOblnPf1i9eO4uevHil4THtO9OGx147iH59+qygxbdu2cTLVBiVXREGlu9lKgmrEvcy73BDHGzVMHlbrHpRzgfwonRAvNOTHHCrTPRbRodInpSdfOzbVmFgVdHKhR/3EnA3smvjEWbJDJYb8xKX5frWfcYkEDyEY17gLXs4Jc1u7B+WQn227BVyhDpX4A86pJJ9FDpW0yk8vhFkOFatDpcu1YrsJCpP/f1vXjrmrt+R1PID7nHjlAMmv8X4ublh8H6y2ln6Vn1AGQujlp4bt2bkLBwMIBzM7VE5SuluU68poiEnpXFAVFPJLLY5QBFVNKMDbOQGyQHQKe7rlB/XyI3yleyCKG3/6OpY9vgOb3j0JIFk0zrBsHDs9jB5lUk1HJGbgrv/ci+8+sw/vdeqrVWeLeIN/5VBvQfvS8eDWQ5i7eis2vetefp+J3oiYq6MRVMLNpr/CHKqhqMFvxN3KajU16bnQ98or5GewHJj0OVSDGkHFJo9xKUGlvr8YThJv+rmuxGOuzjnj65JjUSulBxVB5VfCf9YOlfO4V1I6a+XBRBOr/D4tFfIDnOsh7EOysTiWUDCAsXVO1e5MKy6lpHQP8dXYoCalu901qWyCICbycVLF/YoMx7IRVN7nMWaYXLBPZILKsFzi2RTEk+jMqLsWazQFlRwnrQBhDpUmiVtdBGHbTpmFYDCAkNLaJh+ckJ/boZJyqITjcRwq9/7Yc6Ymr7ASIEFVZpw1thaXnncWEqaNf3hiNzbv65KU/ptHT2e9L1HZP/d2UpzFDBPfe3YffvzHgzjUPeT1Uhfi5PC8puZQobAu9F5tStIhOVRRA6ZlS8JTnOz7itRixU9Ep0F0dtTaU344VHLZhNwnKjZWncjpHRRDfu7zzibRManJWp0o/Srsyc7TOeOSgoo5cU4dqmTSM7v/+7XSz10pPfuQH5tPpjUmBdOsqRMAJB0q03Lqe01POVSAE75iuTeFpoKxsYypCfF9qgnXudShYtdaTSjAXUkmqHQlJmxNDlWhqNGt4UTmaz5tyM+w+DFMHJsUVDHD7VBJldLFVjqunK7kf0UHyWk9oxtb8r/ijwDuUGn6CYohvxrFAcsHdp+dNK5Welxs5wSwsgnOOID0ApEcKsIXakJBrFk0GwtnT4Np2Xj0lSOSEyMpU/MAACAASURBVPHGEVlQxQ3L03URb+jPvn0Stm3jhfd68G+vHMGP/vg+5q95Ce9+5G4JokNsubDlvW5fly8DzoSbj0tySnRCognc+su38fl/+SPeOt4HQA5H+ZVDtf/kAO7Y+K4k3H675yPc//yBglffiZNLuvH6UdxTCvnlce7ZNZY5Kd3wDG+MrWUhP/n94x6CKtcQhZdDxXOoUjd+v/v5ZetQiduxEAo7V//05c/iF1+7HAs/Nx1A8lhOR+Kw7GQYZcoEx6Fi4UAmfgp3qJJjaagNSWUlvJoFM7zKJrAfNuFgkH/mQ0rZBJaHJPadE8NFjHy/Y2pSeiQrh8r7uZhh8cT9s8YmXZq4cI5qQ06+FE9KF4SEOh5R8PCcozRlE3jIT5PErcuhkkJ+ocKdzN2pe+yl550lPS62cwKUXn5CWNN1PJqkdKpDRRREKBjA314yDUDypiYKAtWh+sqDr+CKe7bgTMSdGyTe7D7ojWBvx4A0aZqWjSO9+ganKqKoOx2JY+eHZwAA737Ujx/+4QB+8uLhrPbjBZvk8nFJTkXkHKpf7Uomzn/3mb0AZMfHrxyqdS8exr+//iF+u+ej1HuYuHnDHqzdegj7T7pLN+RCQhqvt8jxOyk9v7IJaRwqQVDFTcslANkk6oT81KR056Yqhi9yD/mlHKqUoEqOxZRazwBynhAA7O3ox3f+c6+rzlC2iIVDgXRlEzQOVWpCaWyowZf+5ByeuB8zTB76PXtsHeoE95qd31ofVm+JYxlT6zhUag6VTiRKDpYYHhQcKvaZxwwLhunUbWIFIUVBFQoGXDWL8j029XUsnBSJGVpxCKRfCSg6VGfxkJ/Jz4soEK1cQn5Bd9K4Pok7+Zy8yk+/UtS25TAqE3b5/oDoH07wKMfnz58oPRcWVhECydIXAXWVn0YgVnql9HDmTYjRgDWvjBmWJGb2nUyKogn1Nejsj/JeaQe6BvGFT50t7UP9ovz+3ZPSL1pASYBOXbhqlVvdvnYdO4PeoRj+z/pd/LGrZk3GZyaPz/oYRdhkno9LIuXqCJMyCyOKx+hXDlVHXzKBnjlI75xwnL5CQ0ZSzldaQeVzyC+P3BRehyrDKr/k/hNSSwp2Yx2fWnKtFjL1o/WMbdtc9J0thCUGo4aUlA4gGVqPOe/7kxc/wH++1YHPTB6H/+cL52X9ngx2ThpqQkiYhndhT80KLTEhG3C+k9GEyRcnnDO+DoFUwrZh2S6HqmCnNDX+unAIASEcmrEOlS0KYbdbVRMK8jAvkHSJREGlFl4V3Q2+X9vOa/JSQ2yRuIFowsSXfvACmhvr8ezXv+h6TbqGzDGtoHIcqppwEIibqQT05GtEZ6Z/JIHaUJDnF4lJ6aGQmkOVpvWMJg9PdIIMK9nHz3GowFNJ5NcarkUaXuw+nvxRff7ZY9CszCvhUEDJoXJClk5SuncZCPGc+9VmqxSQQ1WmiDkL4gRr2+DuUPsHTnK47gugTnIdfVFXgp+47H3e97fiy6likirq0tXhuMnFHKOQcNoAd6jyCfnpyyZEE8klzeKEdWbYH4eqK5UUzEIWbwjOYa7OkW3b0rjFSao/zXizTUqPxAzv/J0CVvlZls3PrXqtRRNOsi5zTNT9s+OcODbpHJ0Z1j8PqBNz9udX/CzG1IYxvs4JLyYUB4m3n0m9hrmD+ZYrYfth+UJeIT9DchfkVX5s0mGVp6MJCz2pa29yynFj23CHioX8ChRUPGlfyIcRw1mAR8hPSURnwk7cX104xM/3UNz5jopNdXlBSyUpHdAXxcwGnUPVPRBD71Ac+zr0+ZuZktK5oBorrPJj+XkhR9xyh0oIhbX86xb87/U7XeMLBsUQWWYBks7lFK8HXaV09tpowsSV976A//6Tds/jFdl1LBXu++RZUp4v4F7oIfbyS1+HKnnti6ecktKJgmFWfsywXBP0e6mQ0quHTvHH4qnK2WKROfV1w3HDZZ+yG+I7H/WjdyiOI70RDGssVtWhiiVMl8hSiwBmiygo8nFJRIdKLS3w5pHTGetQDUYTuOq+bfjnX72t3X80YeKe37+HPal8Adu20ZmqbcQctTeF3LZcY/63/fodXPa9P+JwT9I+j2cd8sv8Pj2DMVz+L3/E//q/O7XPy61nchNUchFO+fpguWW14SCaU4nV6v7ZjXXSeDmhle/fhzpU4mdRHw5yN2wwavAl+0zwiMU9ASFhOs/QKss7ZK6cZwsTbVK6kz+UHLs75McEFRs3T0rnIb+8hs3hTWyFfJi4YWV0C1Wx49RKSgmqVKhJTExPCG4eg533YMAdHspXLKqfQURIqbBs/WeUMeSX+swmshwqISm9Rgi/MvFTo8Qv/7C3y3kvXZ0o3kzYPV3zc6tZ5ccL1wqOpZSUzkLcqdcyYbnXQ1iq7D6W/GF/6XlnufKhwqGAkkMFHvJLX1fLcn22lENFFExdDRNUpksYRVP9mtoPO4IqYVr47jP78Gd3/QF7O/r5a0VGEpanoDrYNeh6TLedOAb1Qh/2KLgXM8y0rkI0YfEbc6EOldqk97XDvVIOmi6E9vaJfhzuieA/dhzXior7nj+AdS8exsKHXuX7YOdjMLWqcEfKNQRyj/m/ergXcdPiKxzFNi668bJJJxsnbG9HPyJxE2+f6NM+X8gqP9EhUwU3E7nnjKvjS+TVY2GTzqTU6jsVL4dK1+bGi6hQSiAcCmJ8ann3YNTg42HjqxUSrwFxBVp+kzd3qFIJ2F6hSqlsAg/5yXkmdTzkZ/EfDZMnJM8bSy5m38c6vsrPH4eqVnCoXJXSM5RNAJzP2VAcE3ZeIjHDCfkJIeG44FCpbka+x6a+biQu318zJdmrDEQd95fVoYoJIb86YcUlD+NqhAR/LylvTG7Ynbb1jOhy8qT05P9Lok6TlM7ErK6PXrpx7hYdKiVCUhMKunKo1Gr3Ic1pEPsNqsdTCZCgKlN4DlXCcn3J46aFY6eH8VGfUwgzYVp47LWjAIB/fW5/cjvldSNxA1GPkN8+oVyB7qbiFnVucaZzqEzLxpd//DKuuv9Fzy+qKGJydUls28YpoQ6V6kC1f3Aqo0PFfvFbNvC6IFIZrymPdQotYAajCRzoHJRyt3L5RWWYFk72JffHKoVnGu+EhlRCbxYhPzb5etXbEUN+IwkT//DELjyx/VhWYxcFu3rNsPypSeNq+XhVwcbEnLrkmu9TEBryKr/cHSo2sTkOVYILKlZDh4uG1LF4tUXJlnjq/DgOlfI9Tk28uoRiS/kV74T8TF6DavL4pPPHnAv2HfVrlR9zEsLBoJCUnkUdKuV92TaOQ5U8pnHcoXJaDjUITXXZNZUsaaGG/PIVVPL/R2JyQ2595Xfv/YmLgcQcKtWh0vXy0yFWEXc7VN4hP10OFbvenJWGkJLSHUfWkvZlCiUrvOjoG8FQzEBtKIg/bR6fLG0hjC8cdDtU7pCfxnGzbRJUhP/USiE/t6vUrkzy4k3h+OkR12NA8oumXpzsJiyWT8jKoTJMV7KgLtdkMJrABz0RfHhqGB/0OHWvDNNp7ivmDw3FjJxulgNRw/OXP5DMdRInZt0qPzZBAW7xBMghRbZPcbw7PpRXXuZScLNrMMZvokOaEJMu5McclWzaZrDQm9iFXkSdEH/39knc/pt3shp7ul/276ccz2lNDVywqGKZTQIshyrd2EQRlVPIz5AXWoghvwHFoaoJy45AupBfNuFWdn5YUU6pZYthofX+F3Hdw6+lbT3DhAT7gRVNmOgZknOonJYnSh2qAgUVr9AtOlSGrbiFzthjhinlCjHU9ijMuWDFQodiBr8W1AR4QF82wa9VfsMJeXWf7rPWuWHMJWYrQBtqQvwxMSm9VnALxRpTXmW1xJWAvBCm4NR5HY9OlLPrrU64HkxhDDyMmzr3clPr9OeXXdsNtSH+2YgCSk1sF1vPMHR575ZluxxByqEiCoZ9CeKm5ZqgY4YpTepsO8bxM8Oux4Ck0medu9n9iX35xaX+ujYi7EZTI4QXVCdG1/ZFFDssR+hIbwQXfucPuPt3SSetX3AubDuZpJotp4b0leOnpMIh0YT8CzSasFzjFvOudFXgTymr1br6RYfKwEdn5JY5mYSOOB7xtWoFb0AfAmUCICuHKuWmmZatDRF69a1j10W6iSuW5pf9S+/3AACu+PTZfLzqsYg3/PFCc1UmQLxyqPIJ+TFBxcbSNxJ3hfycsBbLoUpVgVeO7d2P+nHRd57Hj/94MO17qyE/8Vx2D0Zx7PQw9hzvk67HESWhmH1PuUNlWE4OlRLyG+FuXMoR8y3kJ+RQqav8Ug7nyf4RXLpqM779y7c1DpUclqpN7UvKoRIWCDAnRnao5LHle2yu1jMxtSF3ZscNcK5RtshlbF1YWkik5i9ZlvPegYBeHInvFQw4jhS73gMBuIQYT0oXvsdqUjoP+bnqUMmFPcXDzFTrTSzSyhAFVHKVnyyowkqMT5cTZli2q8l3zLAK/nFQKkhQlSlifRlVqMQ9XCsGu2ewx1jfrJG4yW/YbBKJGxaO9A5JzlVc00aEvR9zG6IJC9HU/tlkqAsrieGBA51JQbVlfxeiCQv/9soRdPSNuJyLXPKoWA2qs8fKYaPmVNPYmOEOmaq5PKKgOtQ9xJvpOscgn4+uAVlQqXWK0v2i+uO+Llxw5yb87/+7Ez2DMZw44+R8aR0qzSo/LqiycEnEY9ONS9cyBkiK8tb7X8R/ffg1T/vfK+Q3FDOwK5Ww+sWZ5/A+X+qCA0OYRNk1CjihIJavYynCLpfWMMy1YTmJbCXW6UjCLaiCTlhLXF2rXj+7j/chbljYeewM0sHDWBqHSuwhNyR8b9jjapuSesH9YI7qOePkkJ9ah6rwHCrmKGXOofq3l48gEjfxy50nXALE4LWSZIeK3TeGJEEVdJoCC86Meg/0a5XfcNyURJTeoXLvh32m7Ls/ts6p1RUTzhETHGJhz6Rbox+fKHh47zvL+RGsCjEnh0oO3Sdf53bJxJCfmjPoVT9MB7tviCJKElRBubBnIOAOWepywsQxivhRc68UkKAqU9ivTMARGOJKG/UCS5g2n4iAZBiNC6oG1tndcZW4oDJNvPuRvKpDl0fA9sUmx2jC5PlYTMxEBGeJW9HChM3CQGItol+0H3W1HBFzbeKGhYdeOOTZkoY5VJ88e4z0eHPq17tOfKp5Sd2KgHo1Q69CNYeKLfdn97p0dVNeO3wKhmXj9+924m8feEUqPcFzqDLUoWKiNpubjCioIhrnzyt8tundThzpjeCt432eLpWXQ7X9g1NImDbOndiA884egwmpiVOtAebkiwTR1OAIYnYdD8dN/PWPXsT1P2mXc6g0N3uvvCom+tkqubO5oIq5BVXYmcjF1bLq94G3rklz/m3b5gKWHY84RnH/Q8L1P5IKzYoTHyDXhmPnnTtUQcc1Th6H44oUglPmIChNvjpBJRbXVYUcm+zVHCp2HfePJKSq9U7BSeccqN8Dv1b5DcflkF+muloM5jpyh6o2zM9R3HAW2ehyqHTCiI9P+Nx52QTmUEHj1Fls3IKg8iibYElJ6c7nwF4r1Q/L4FAxwRWWHCr573BIdajU0gr6EKbOjaqUPCoSVGWKeHEywcFWKMVNt+uSMC0eFgCAD3oi/MbbmEqWTIb83A4VWxXIYCUYdLkSXFAZFg9tsR5WzKE61D2IK+7ZghVP7ZF+6RxICSrRKXli+zF09sshM9GxWv37/fjBHw5gyc/f1JwloCcVjjtnXJ0kKKc2Oj3OVMGmuj4sz2j2uU0A5PY+4nlmv6jFcGvCtLljNS31nulCfmKD486BKH6dquoO6B0qnZYRRW0mxPfTOlSpz/W6Sz+BT50zFudOTB6DeA6yaZkiiouXDyYF6RdnnoNAIOCE/FKf63++1YHn93ZKybaiQ8VCQf0jCRzuiWDnh2eUSU8ez89fPYKLvvM8dn7o7nPpFKtNfjdYvlbXQMz1XagRJkTREVHfjx2HTtg52xj8+8eK6Xo7VLJYiCYsd2FPpc7P+PowF1lsouJJ6UKIpxDY51Mr5MOoldLZfUHMM3Q7VCkXRQmDNY5xBJXOoRLLJqg/gvJPSnc7VOIPA92PFN0PCsehSo5rnBDyA3QrLp331uUTMXgxzpBY2DN1HoJO6QH1eAwl5Cfev6V2PmJSulLYUzw3mR0q5/NiiH+LOVps7DWKgNLXobKlKvPNE+oxvanBt/6axYYEVZkSCAT4l3Ew5nxpAe+Qn3gz+KB3yOVQiW0SJgiP9Si1m+KGhbYnd+OL39/KJw+Wr8PchpiQQ8UmqUjcwFDMQOv9L6FrIIZf7/5IsqKP9EZcZSAGowZ+l2rczBBDfj9/9SgA2RUCnBsqW2UzcWytlIcjVoRXe8SxRG+2D+bi/M3FUwHIYkIUJGziVUOCrFQDq7eULuTHwjVMQIjVxAezWFUWCDjCLpNDZdtyk2jdKkwmFm5pnYmt3/ovvIXEDqFQaa4O1csHk/lTV86cBABCyC+B3qEYbt6wG19/cjd/TTjkiC7ASVYWkUPS8nF/95l9GEmYPCdPRK3+z2oFHT2VbLkknk9RNIhuXlz5rqm9AHWwa6RpTA3G1bnrUEkOlRLOGo4brsKe4VBQ+kXPEtKT45YdKv9W+TmOEk/YN9RK6cm/xetYfVvmzCUEAQ1AKqfB86vCuqbAAZeozzec6ZdDxXOoUvefMXUhKU2D3QO4Q2U5Ib9ANiE/waFykvPdr2PnRWqOnGqgzahNubOWLZdlUAt7iqcm07XDRY+QB1WriKsaVw6VLDe0vQmF8H4wEMDrt1+FV//5L10dPsoVElRlDBdU3KFyJlJ1MlVdq8PdET5hiZMVs+adkJ9uXyZ+9/ZJdPRH8csdSQclpjpUCWeVH1v2Phw38f3fvyftS60l9EFPxCU49isV11mujSiERPdpwxvHcPF3n8cbR07ziW9sXVjaZtK4Wn5jVh2qZA+qQcxe9Tz+5Xf7+IS24MJmBALJvodMiIjiiX3RVUHFwhFMUKXLbepKCTQm3kSGUsebrpBkXTjIxUGmpPTBmCGFH3WrMNV+dsxlE8WXl0MlFnZNmE6uE+sPOfvcZMNUvspvxMCR3ghsW67VEw4G+ZJzABhX51yvDNGN83KGmhrcr4spSelM/B9PieDxdWGey8EmBMOSQ34uhyqLkB+7RqaMr+fLw70cKvX6HI6bgpvhPC5O2KxkAuAO+YnbFZLMy5sZh4KoDSXPXzLk53YmT6VxqBJqyC91nvkCgWEn5BcOBnkYiX0PVFdG9x7Z4mo940pKd+9Xdw7ZvYaVbBlbF5YEBbsviSE/K03Ij4UDdb38uBCD+3VsbHJhT0O61mo1Y0g6SKywpzuHKlNSOu9TGRZKJQiOVDgoJ6GzFkki2rpawhjTlZcoV0hQlTGsmJ9OULlqUxlyi5rDPUNcKE1oCPP8njOqoDLcq97EfTP3hT3Gl+wLq+VYj7RIzOBtcYDkTUf9xXegc9CzuCiDTVgvplaKAcC5E50cqa3vdWMoZuDNo6d5mHFMbUhyqM4aU8snFjXp/cxwHG8ePYOBqIFftH8IILnseXpTA/50SrIXIXNoOvvl8J5hWjy8UauEYaalBJVXDpVt29yh+puLp7me5yG/NA5VfY3zSzhq6EshMLqVlaDiogE7ldOhNnGd2uT+JZiNQ8XGfSoSg2UnnR8mtFlo59RQDB+eGnbtRw35jdM5VHFZvInHwWCCVsQpm8BCfskxsUNqFN5XzFEUE8Vd16dmNaZKZ2ol6JTGej6xSA6VIG4jikM1IjgM4qQj5lGx/CnAESjsuhMFVSFhPx6iCwWk/DJd1Xoxh8orKV0MIQKQVn+Kwj4sLA4APJbX5+1Qyf8fNZQ6VFkW9jwvlbPJG3zXhiURxASz2PaF7SYYCLjugWoeUygQcNVp0oUKvQp7yg6VEPIT3B923TDhLH6XMoXYmJAWV+q5Q36iQwXXKj+vsgmG5tqvFEhQlTFqDzT2y10M77FfSsnq6c5rD/c4Ib+6sFMjhV2szkoxyyUAxImSrULj4oyt8jOcfCwx5CfmJ8VNy/WL70DXIBdi05saoIMJoOeFlgziF7wr5R5FYga/cY2pDfMcMwA4a2wNn4BcOVQjCb46h52jyROSjWZZyGt7Kux3UsjvMiwLvUNxWHZSBHxyopIIz3KohJvlr3aewFupljWDMaf1zyWfaMInzpKPfyiLibouHORC+7d7OjB71WZJxIqI4UrAqcL98sEezF61Gb/d08GfCysOlYhXwrcuj4+JuEnj6vg+PzVpLACgoz+qXVzgDvm5296Kjo7oDImhpnM0Fdcd10ZOSmeI7yuF/NIkpQ/yHKo0YjZ1jU4ZX+cKYQGyuHWH/Exp8mVIgkoI+akOlSj0Cwn7iavyatPkUKn5lqrYcTtUyfGyhQj9Iwl+TsfVOXWNxErpKvmm1KjnI5awpM9FH/Jz7+fT54yT/p81e2ZilrnWLDQolk0IBtzXDhed0io/+T2DgaRLJR1P6tyLuxuJm9L+HZfMOW+hYICXrzA0DlW2IT81zJf8bwCBgFrYU5eUri+bwFw3cqgIX2FLvVluDctfEnOomKAaVG7Kp4bifMKrDQf5F5shOlSuFjXC5OU4VKmyCQ2OgGPhlLOFpHSxwW3CtFyTcbeQDDxzinxTYi1I2Cq/1z+QW+s4+0gKhWSh0uS2Y2pDGCc4VE2CQ8UElRNiiLtKHbAJ6vIZSUH1ZsqhkkJ+ppOTNEloqQIkPwfmkLHjO9A5iG89/Rb+8em3pHFPqA+joTaEy1PijU0g7DNMlxslOlRA8sb905c+0G6r5sax1kDbDvSgfySBre918+fYjVHnUBmWjZ0fnnblurkcKsNyQl2Cg9I0phbnpM7vlv1dUAkHg7xtBwDpc2SIIlVMmO0QugXoQkNOHSrHFRHv05KgEqqBiyLHy0FNF5plDlVzY72rQjQgO1RDSrmR4bgh9Vxj1AmLTs4Z73ao1OrcAFCAQeXZHFnu5We5KuCrk7GrsGdQdqj6RxLoHUxV1hcEqJOUrl9enw/q62KKQ6X77ulCfp+ZLN+72H2YidneQZYrmbyuxYKnuuuUnRtTElTy9BwIuAuCJhuUy2MejpvSmLUhP9Gh0uRQpSuWLL5GdJ3Y+7DPN6w4VGpSuvZzFRwqXdJ6uUOCqoxhv6rZF55NNGK+FHtMDRskV684zVLFX7eAnEOlTjqio3Ps9DBs2ykKKYb82C9IFkY5PRyXrGzbdq94G44bfHJk4TXG9JRjwxwqcRzMlbAsR9REYgYvvthQG+KCE0iG/NgxswlwWsoR6xmMSy0jACcn5bLzknk/+08OIGFaOCkU8UxYjvisrwlKOVtNY2q4C8iO76O+pBhl4o23DEklWH7h02cDAGZNTZ6HoZgB27a1NzO277pwUBJUAPjKPBVXyC8llNn5E3PUeMhP41CZlo3rHm7HPzyxS3KYXAsjTEtwZmRhNjM1AR3VhfxCASn/iS1JFxlJ6EN+Yvsl3a9q1aEKBgNSvtYEwdUUSwPIOVSqQ5XZSWTCcvKEej7BZLvKbyTuhGzEOac+LDpUzvlVJ6raNCE/27bx610nsC+LBrhOIU5hlZ9huXJtTg7Iq3RVR4/tR0w8BxRBNeT8UNE5VHf8zQUYK/woLLRSOvuBGVVae2XTmxBIpiCIDsxYRVCxHMSzUiFlU6lDpeIU1/R2qAIBdxjMFML2jJGEyX90BIRQmxTyE3OodGUTMpxftSwE4LwP+694XQZ0DpWmmZ/YesZrJWQ5Q4KqjFEnzvGSQyWH/HR5GLEsHSomepzGsc4NPpqw0DMUc+VQibAcKl3fueG4KqicZPbzJ42VbF0WAhuMJmBZtryyK/UFPj0c5zeQ4YRTqHRsrZOUHggkx6nmoE1PuS+9QzEp5wNwfvGLOTYjCVNyqAzTlm4kYs7WxLGOgGPHxyqss+NgCenMvbnu0k/gO397Ae75rxcDSArQ4bjpWlUmvqa+JuQSx7oQGaAJ+aVcESaoxEKbbBKbUB+WJi5AFgLvp2minTBsQUjI4bc/UcSziJpDVReWiwICsmsq1qoRK83rQnBqpXTA+YwB+XoOCxN5OkE1kCbk98CWg3i8/Sg/D80TPBwqjzpUAKtFlfxb/JUulkWRQn7KuUonPJ59+yRW/MdbuHrty66xq4i9/DwrpSs/OgBnIQAXqEritOpQjSRMvo+zx9a6CnuGgsDSeTPw9nfmY2oqTy7vHCqbCSqWj2ryBTdA8pr+1c4TeOSlwwBYrqF7P3XhIM49ywn5s3Ou5lWy69qyIdWhUmHnlA0lmEMOlRoFsG0npBwW+iDKSenOj6iEIuaALMomCEV5GU7IT/4vO2b1O60VllZlJ6Xr78REWaB+Ocfzgo4mYgm5N5mu7QtzZurCQTQov/rFsgnsBji+PoyewZirovWhLicfS/xFzzhb6cU2vj7MRYxaPX04bvAb6ti6MKaf1cATlZmgGhgxXM4W+wKLAmc4ZmBYCPmx8zOhvgahYEBq3wOIDlXMdUNmAqAuHEQgkHLXhBs9kPyyiyuVxJytpjG1UgNbwHGmWLFGVr+KuTehYABf/fMZsG0b4dTS8EGP3oSTx9fj6KlhrUPl5ZQw4RQMJG/o3KFKuQHs+qgNBXkYIhAIYGpTAw51O30XxVVdEeHz1K0O7VIa9zLU8C4j2ddMFlS14aQjkhBaIA2rSbyWhbpgSHGo3OchpiSlA96Ciof8DBtD0Celx4WcQ3WVX/dgFPdtfh9AcvUgkBTC7HPwdqjc7rJa2DN5DOmT0p3jc55Tw1W/EuqeZYInHocCUnNk0bGJm7bUiglwXOm6cDAVIpQdKiYAx9eH+XeNfY6Txte5VvmxcyA2Sc57lZ/iUCVMW2oYnzAtrHp2H4bjJr5yyXQptCoSDAZw3tlj8EFqRSt3qJTPguWJ2RkcKqdaORORAagGTnKVn3I8Ho42u/+KFdfF5EGqwwAAIABJREFUjgNSc2Ql3Kj+rcPpcuDOoRJLfTCCgYArZ4qS0omSks6hYiJhPA/5pVwmwa3oFwWVMKGIk3KybILcVkZN4j4krBgcKySNAskbyHgl50VMDlaX6kdiTjJ7Q01I+pX3iSYn5BdRhBi7uXYrdZXYxNRQG+IOFbPZxUkUcJLge4Zirv58TACI9b9iCctV3ZuNvTYUUFYV1ggOlSyoWJkA3jJEcW8CgQAP3Q7FEtrcnE+kwnoT6mtcNyaWRP30juPSogAmBpmQdIf82NJu+cY1VVktJwsB5/NUQ37JY2QunLwPL4eKXUuNQqV0JqhEonFVYKccqr7CHKoJ2qR077IJonurhrbEa5blw4kOlVeldHVCHBHLJginQbwfnKMpm8A4SxCnarjqnRNyEd90iInHTtFTG6aSxK06VOwtWc4Xr5WkTMLBYMD1Ay0Z8pNDUeLEysVBgXWoRMd+UKlUz74nvUMxT2ERDgZwfmqxBSCG/JRIAAv5WWIOlfe4xKTxkPIdCAYCrvwrU/iRVxMSahemrtNwMOiIUCGcFhLKGrDXi6c00yq/uCbkx0K5LNSnJqWrOVFi5XfRxVVrsFUSJKjKmDrlyykV9kw4oS7A+ZVbJyQtM0GVDPk5k39DrdB3KuH84maTi5rTcVBwqGpDIalqc11NkOf3MM4a69SAivBVeMltRoSCoPU1QSn/R8yhUmtVsS+42CZmOG5wB2xsrZMUzhJB1fPHhEXcsHih0C/OnIT6miAu/WQT345NviMJ0+WUsbGHQ0FJvJ41plbIoXIvJY8mTCfkN96d+M0XF0QNraD6m4unYsVf/Qm+9dd/ioZa+WsbNyw8+cYxfPuXb2Pdi8kE9cM9QzyxnuWFDccNxAyTXxcsdFWjCPcrZ54jTdJi+yDJoVJWhyZMmwveycov+z+ZrBdUNVxQyblMqjvrWmaeOkdSyE/zS52XTRD25+VQ1QoTjCh4RCdOdG/dycDyj4dQMICzx9VxAWx6OFQqkbiRdpVfXTgo5QuqArtxTA2ftEWHyrZtV6g7HbqkdF3ZBLUuG4N9/5zWM2wS/v/Z++44K6rz/WdmbtveC1uApVdBioAgSBEQC/agxpKgJkaMLbEkaowmX2MSY0xiNNEkmlgSTTF2xI6KNClKE0Hpu7DLFrbeNr8/5p6Z95w5c8veu7Lkd9/Phw+7d+fOnKnnmed93ue19kk877k+l0SUbq3TAlRx7wYXDNTQ9lf0nFJw1dwRcARumqqgf1GWiULYc5het6piFRIZKT/2uYMonbQc0hQFXhFQqRKGKmwdX7emmvvVEnmxoqxeWOdtGdyCPYWjD1XIfq2KbCPbvvEZE6dTDRXgVgF3yJpbVOgmALEc5XnQd6yFokczsklRPPTQQ/jFL36B2tpajBkzBr/97W9xwgknOC7/3HPP4Y477sCXX36JwYMH47777sOCBQvMv+u6jh/96Ed49NFH0dTUhKlTp+Lhhx/G4MGDzWUOHz6Ma6+9Fi+++CJUVcW5556LBx98ENnZVuph48aNuOaaa7B69WqUlJTg2muvxc033xz3frW0tCAvLw/Nzc3Izc1N8KhEiXvuATo78d/Pm/Hx4SDyO47ghL2fot/U8bjSezwuX/cyCgMdeGHAJIw9aQxWf7gJExt3YVVBf7T0H4jz33sOamcHmkoq0NEZwKwRZdjaBnx8OIg+LYcw6eB2VJ85F1ce7oOr17+IDl3BK0NOxJDRA7F/zaeYETqEZ/OGot3tw+Ufv4jCvEx85s5DsNOP8ybX4OnNjWiAC4Ma9mDU4d0Y891v4qq1HfjaqhdwKKsAB2fNw5r6IPrVfYEz8oP4P99wDNNbMWvlqwhk5aAlrxDtbZ1YMKEfdvtVLPuiBaNrd+CUrA7cWXoivB4XftCwGs+25+LdmvEIqhpG1e3ALZPL8PTAadj8z1cx5/OV6CwqwUEtE+FAAGdNGQg9Kxt/W70XZ7Z9iRpPCA+NX4gj6z7FyTvX4OPKYZi2+Dw88uY2DN29BYCCF4ZPx8uVtXCv+BBav35AVhYQCODJT+pxUHfjwgmV2PWvVxBQXXhk8nk4eecaLAwewF+zByM49nhMKvPhsxfeRLMvG30uXYQzVr6IT15fgYPFfXDu5AF4e/MBbG/V0ebJwJUTylH7/Kv4wp2L7Fu/hynLXwK+/BI480xg6FD84ukPUbJ1I06aPwkPhSow9aUnUdraiD355dAVYO6IcpT0KQKys6EfOoSG197ClqJqPDxgBu7Y+QYy/J14rPR49D1uCK4a5MMH/1yGF9yVKBo7Eove/ye+2HcYWk1/HF+Rg/9+Uoc2jw/t7gxUtdTh+LrPMeC804D584EHHgAyMhBYeBbueL8WOXt34arSLtzVWYWgpuG2nW+if0UhUFmJdTsOYmtDJ9o9GWh3+3BxzhEc+XgjXhg8FWedPwPVz/wFqKoy9jE7G4/+/r/Ira/DK8Omobq5DmdtehttmTmYMW0k4Pfjn5vq0ezy4aTRVWh+bwUKG+vw1NgF8IQCOGfbe9hU2Bfv1YxDSFXxs35+ZHZ14IrAYIzavg4n71wDT1UlRgzvC/j9QGYmkJ2N17fVo3TjatR4deT96IfAhg2o/8/LeD1/IFZVj8TlEyox9sA2wOXCf4dOQ/NfnsTMpp2oLyjDrk4drnAYQV8GzjppKBAKofP1N/H5kSAennQeTvn8IyzEISjz5gHHH49dX9ZizbOvoSEjD28OOgGLN72OuWojGkorsWJ3C3I8KmaMqwGys/Hmmp0YunkNDuQU488TzsSija+jT2sDlg6ajIEnjsW6tdsxpnY7Zi88CRknnwT8+tfYu20XPvUUIMOtYcbQUiAnB8jOxsaPt6N842psLh2Af4+ahV/sfwc79tTj1SEn4opF05FXfwDYsAENo47HnRvasHjN8/DpIYyYNMqYLF0uIDvbWN/OncCaNcCcOfhbxgBMeuFJFJYVoG7OAvxt2xFM0w9jVFsd/pg9DKqu4xsbXoGSmYnPXblwhYIIaC60eTLQ4fZiTOMeVNXtQuOZ56Jm3HA0/uo32OYtRNepp2HG2H7Axo346P1P8Uz/SRhweD/O2fYeqgdVYW27C62tHdC9PjSqHgyqLsLofduA/fvxxPjTETrchK/vWQnP+HGonzIdf1+zF2cE9qOfD8DFFwPLlgFLlwIVFUBuLhAImNfDvuYu6O8vR7YexO9POBej923DSfs+xYd9hmNt1QhM7ZsD/4cfIaC6UHHlZRiz/GXUvfk+9uWVoEvzQNPDaHd7MWvCQDQ0tkJb/h7a3V7o378Z1W+/iuZVH+ON/uOwuaQGxeEuXKbV4eWDOj4adgIWf/Ia8vfvhmfQAGxv6ICiG8+GdrcPMyt8yP7oAzSVVuCXQ+bi21vfQHFbI/5VPR5f5legqL0Jp7TvwbqsPviweCCuWP088juOoKmsEjVFmdi4/wi6fBnw+zKR01iPiQe2YWPpALwxdjau+PgFtLd3Yd/M+dii5kDZtQunK/U4dNwEPLU3hCXrX0BJphuNxeX4orYZIUXDgAHlKCorBD7/HNi4EZgzB5g2DXjwQSAvDx9PmIk3agOYg8MYF2gATj8dr3+8C+Ne/Qf8vkxUDKtBQ2MrvmgJoM2TgfziPAyp3Qnvnt14cfh0NGTm4ZJPX8fO3DK8NWAilAwfavZ9jgHhNmgXLsJHL76HhdveR1ZFGTBkCPDII0C/fqmbY9FD87few/H3v/9d93g8+p///Gd906ZN+pVXXqnn5+frdXV10uU//PBDXdM0/ec//7m+efNm/Y477tDdbrf+ySefmMv87Gc/0/Py8vT//Oc/+oYNG/QzzzxTr6mp0Ts6Osxl5s+fr48ZM0b/6KOP9OXLl+uDBg3SL7zwQvPvzc3NellZmX7xxRfrn376qf7MM8/oGRkZ+h/+8Ie49625uVkHoDc3N3fjyESJ8nI98kKT/pf+l/6X/pf+l/73//e/+vrUzrF6z8zfPc5QTZo0CRMnTsTvfvc7AEA4HEZ1dTWuvfZa3Hrrrbblv/a1r6GtrQ0vvfSS+dnkyZMxduxYPPLII9B1HRUVFbjpppvwve99DwDQ3NyMsrIyPP7441i0aBG2bNmCESNGYPXq1ZgwYQIA4LXXXsOCBQuwd+9eVFRU4OGHH8YPf/hD1NbWwuMxUgC33nornn/+eWzdutU2Lln0GEN1991AQwNWf7obdfvqEVI1bOgzBLfseQ/e7duwunIE1lSNwMk716DSHcbeoIatJf0xa8dq5He2YsXwKXinbCj6tBjfPWVYCQ4daMCBffVoc/vQNHAoFq/6D1z79+HloVNRl12EKbs3otwVwk4lC4fLqjD10+XwBgP456jZaKnqB8+hg+hUXbh4XB+8+/EX0FuO4FBWPgJ9KnHVB/9AqKkZT409Fe5QALNavkTnkXbszi5GbmUZRnz0BnRNw5+PPx2tviyU+NvQBhUXHVcGvfUIlq/7Ekf6VOGCaYMR+r97oUPB/m98C598sAGjGvdA9wews7ASs4eWQH35JTT5cvCnCQvhVXR4OtsR0Ny4ckI5fJ3tQHs7MGoUcOgQwg/8GoczcvDnCQtxXO12THe14mBzB9bmV6O8tQFTd20EamqA664DGhuNN1lNwz+Xf4aupmZMq87BY51FGHvgM5z76VvYWVCB/Ysug3/pMgwItaIg24uXXX0wsm4HxtRuR2D8BPyoeBJKWw/julmD8JcVuxBoaUWWvwMLRpbhl835mLP5fczauQY48UTgvPOAV18FGhvxWZMfH+T1w7n1m5G7awfeGDgRrw+egoojhxBSVFx+Yn8U6X6gtRVwu4EJE3Dw3vtRumUDNpwwG3XDjkPWu2+iBAHklhXh5XARztqxAkXN9dh91iL8rr0YE11tGDugBP9dtxdZ/k5k+TvQ5snA4f6D8MN1/zbeRr/zHaC4GHjnHWzeWYe93jwMmzQaOf/8OzKCXXj/tK9jzmmTgdpavLClHtv2NiIr0IEsfweOnzgMT+4K4Kb3n0RpsB3KbbcBbW3AqlWA34+9eWX4uEXHvDVL0aa68fvJ58GVk41bJ5cDHg/+9u5naDnUiLMH5+GvB13oCOm46b2/IaC58LtpF6Jfwz4Mqd8NTQ9jxMyJCHf5kfHcP3Agtxi/n3w+JlZk47xhBcbx6egAWlvx0kef411vH1w5wIMhj/0GqK7Guou+ha3PL0NV80GMrcpDzqTxwO7d0P/1L2woH4S1Z1+G4KEGHGw4gpCiIivUhe9PrQL8fnxcNgjrn3kZl338Ejb0GYzh99yCjHfeBurqcKgjiGeCJRh74DNM/3IdNoydhjG3X489m3bgseU7kZ/lwQ1TKoHWVjzxwRd4t3AgFm5+Fwu3vIulgyfj4wkzMXL9BxjsDWFXexibSwfgus7PoH28FvjmN/FM6XHYsmoThlUW4KITqo1j29qKN3c04q/+Yixe/Tym7toA9epv4/ZdbkzZ8TFm981CRnEhMGIE6v7wF+TU7sWfJpyFbdVD8bsZZcaxCoWM66q1FcjLA4YNA+68E10bP8WDky/A3EmD0WfDSnyyow6hsnLkDhmA6n8/A1+wC4/NuBhHisuAujr4NRfc4RAy/R3I8nfCXV2JjV0e3L/maeR0tuLZs76FnZ/txflKHQbmeYCaGrz65RFMfP2faPFmYdl538K35o7AYy9+jM0NncjWg3B3tGNO32xMmT8ZCIXQ8J3r0OTywX/HjzC8aR/e+Pc78HcFsL24L66bUgk8+igwYgTwgx8Y10BHh8HARa6HzZ/X4ud1Psx0t+Ls//wBnxVV47nZF6H/tg2oaDmEijwv3vRWoG9TLc7f9h4wexYuy56MovZmqHoYYUVFdqgL984dgFBnFy7ZBEzcuQHXbXgB6ty5eKDfdOQsfxuFHS3IzfJi/NlzsPyvL2D2jtVYOWkuft/3RNw6OgePf/gldCjIDBjH6oqTalB16ixsuve36PfKv7D+5DOQdc5CrH/078jtakOny4OcSRNR8vZSDN+9GU+MOx3v1ozHJHcbLpxSg5+9sgXlriCKw37sbg9j3DlzkPHA/Zixaz3WXbAYT7Vk4cquHWhuaMaXIQ+mnTENpf99Dp3bd+LlBZfiymvPwdoVm/DIij3QwiF8Z3wZjitwAQUFwODBwO23A5s2GXOTz4ePn3kJn+86hPLhAzH95DHAY4/h4KFm3DXufGT3q8TPZ1Tgw90teOLd7cgKdODEMh+OmzwSP3h3H3741p+R5e/Atutuw8qVWzD4wA4UuoBNGSWoKM/Huatfxia/G/898wr89IJxBmv6jW+kbn6NRE/M3z1a5ef3+7F27Vrcdttt5meqqmLOnDlYsWKF9DsrVqzAjTfeyH02b948PP/88wCAL774ArW1tZgzZ47597y8PEyaNAkrVqzAokWLsGLFCuTn55tgCgDmzJkDVVWxcuVKnH322VixYgWmT59ugim2nfvuuw+NjY0oKCiwja2rqwtdXZYouqUltpdLt+LOOwEAL7+wCY9/+KX58eJnfoHFt/4N20r6QVdU3Hfy5bj3nNG47d+fAAAy/J04KasL+0ur8ek+a2yDv3kCPthRjz9E9DXj+xXg7Ed+jEW3P4edRVXmcjedMgT3L/sMRVkeBKZfgYJwF3ZlFqE422M6Up93+xw89KdV2BzxIzquKg9XPfkzfPOBZXi309AofX/eUDz50S4caO7EGWMq8OG4SzBjWBn+vcc4dqyyZ+Gts1CZn4HO1XswrDQbrr75mNo0BAEduPGiqbij8FOMrszDJ/sMIe26O07Bjb9+BSsbgmj38H5J3/rJqYCgu7l/1Gn48yeN6PAYmqUXl0zDw+9+jlc+qQUATPN24MnbFxqTCoknH/oA6/c04Y7TR+BvL23GP90afn3ypTjgy8fVpwzDb3OnYt7IMlx2Yn/84NGVgK7j2dOqMWLicDz942UAgG/fMR/337PM1JBVXj4RTz++Gk+PmI0t3xqNjP7VhijihhsAAL99Zh1e3LAf+oJheHHZOqwL8Pv3tVtmAgW8M/sr/U/EQ//4EJNOHIkcnwvP9JmNASVZOH98Ne57bSu23PBD/HJuDT6vD+HZx9dga1Ue/BOr8buMT7n1DCzJwg+fvAdoajLAFAD86Ee4/oF38VldKx66aBxuKDNSb1PH1WDOJcZ99eqTa/Hqp7XmepbMHIRn3/4cH0yehw9umGakW0hURf49/c5W/PilLehyeVCZn4Fbb50FABhydgOWb69HyZzB+MPtr0LXgX8cdwrCiga/iz9Hb9w4HUs31eGhirPQ6fIgrGroHFuB8xYdzy33yG+X49N9LVhw+UQMufcOIDMTbTsbcVvXcADAO987GTkRcfG/392Cm17ZgTkjyvBlQztX6XjT3Qugqgq2r96Nuw9V4pfTL0G724d1X5uLjG8aD/sP1u3Dr/6xHgDgC3TiwpOHYcwZI9E0qRlPtL+PPnk+3HDLbADAg/csw+E2P94adAJuOfVadLp9GNc3H3/oOxXzR5bjtU3Gcf323fOQGQ4CPh/2v74Nfw0NwOUn9gfOHGmO7aOXN+Pd5V/g3QHjUebWsfKe0/H8na/hqVGn4J3vnWyKp6/KnY7NuxsQ0NxGNdp3ToVjzJ+PxQ+/j/d3t2DoorFoueJbuOLPqzCiTy7mjCjDhaVzoOph+HweZHo01FfYtVkn9C/Eqi8P47/fvwJfn1iF95/7BC8U7kfJ6SMwcFoNAGD5fz7Bd4YshA4F50+oBs4bgw+O9MXb2w6Zla8Fc4dgyixDznHZwUp8WtuKx089AcOHluIGfalZAHDdz04Dfv5zU8n/8Ds7UJztMdYbiS1r9+Kd5zYgPKQEj46aj70tXcjLcKO5j3HdnDS4GMu31wMAvvzp/bj65EH48J5l3H55XCruve5UaAAWbdiPQ0fOhzr1SUBR8NmTa/GqZxAAYMqAIgy/YAy+2zQMHk3BuH4FWLPzMGpPPR7+Pvvx+uY6swL3tMumoKp/IZZffxdOG/I1nDu+GgvHVuDHX+SZ2710Sj+8PeBk7Dls6QY7++Ri7vxReGVnESrzM1CU7cHGvc0orRmM3yy8BdUFPiwcW4XX3/4cFSdeiJVfHMaWAy14YtEJ2Hf+JVj8xBocV5WHK6dOxf7sGiyrXwcAWHDG8ThuDGmPtXQpdwxeyz8ef3xvJ66aPgDTFwwHrr4af3hpM155/wuMqc4HzpmKhg37sbS2BACgjKvCgMl9sWbHhzj70vsBADedOAT/DvRHuz+EwaXZ2H6wFZNqClH5o1vNcWHGNGDGDOfrtJdFjwKq+vp6hEIhlJWVcZ+XlZU5skC1tbXS5Wtra82/s8+iLVNaWsr93eVyobCwkFumpqbGtg72Nxmguvfee/HjH//YeYdTHGKVX1Z2BraW8mOm5pIdHh/q+5QjQ2L0R4XjGW4N3pwcDkxR88+WzgACvmzk5JcATR2c+7nHpXLVcz6XBuTlob28AvjSaIFSkOkxBYod/iAasvKhlpYAe4ySbcaJsjFdMNF64HUVFqO5I4BDEaFrttcFTVXMapatag7aPbwI1qUqNhEzAPhLy9HhsR4+HpfKVSDq1VU2MAVY1YGsYs7nVlGfX4YgqQAyROmR7yoKMgf2h48I/5vaA1yDYeYJ5XFpyBjQz7ZNdh5bA2HUZRYAQuWUKLAHAJfbhUPZhQiEwvBHhOMtHQFz3Hm5WUBxMTJbDMf5tq6gzT0diIhJXS4LTEWCVVt1BkLwu9zwu9xRHcRZm6LCwlwbmKKRmZeDLpcnsg3rWp00oAiTBhhmp+wa6XTLu8x3BsJ46qNdaPdk4LiqPGzc2xy1ys/rVg2NEJxF6UpODqAo8AutZwCjos+naqYrOAP0XDuZyPke1zcfE/sX4rIT+3P7SMdH18/2kY2FuqirigL4jL9fMKEaTe0BA1CRoH5FvlwDPLHKOFrl1xEMI6AZ24jlMwRFQZca8Vaixp6sObKiIKxoEQG/fBVclZ/LBZl3UV6GG7piLFcUuTfFZtK0sk1xuQBFMa8PsUMEA1N1LZ2477WtyPRoHKCyRN+Ax+sC0MVVblKBelNHQGrqScXWZ47he3LS51BuhssUkesAZ5vwyNfHoz0QwlkPfYDPD7bywnDFMPUUn/8yH6qwbtkMeFyqrQ2RpqrmGLgKOkWBEtXYM0aVX9B+LkVDT77KD6YI3vyMCObZtXKsi9KPSpWfrutS+/1klk/FMiz76bTMbbfdhubmZvPfnj17Yow8uRBBgtel2T4T23R4JJ5TorGnz21fj9etEq8Z4zgww06+0Sbvus5uBFpFmJ/pNm8mVhXmFYCYMQ775ceABasWy/Jq5rq6gmHONoFFhscONth+0vC4VLO9DQDOMZtbX+R7jRFgkuHWzIeFZZtgN/Z0adYDbX8z7x7NGL4sSeNfgPcTkzVHlh0r2l+NPZCbOwLmuFn5PKtA6vCHpIBKBkYBcMedBW0zIvpQ7YlU3JXlyr17WFAjUplbcjzx+qZa7G/uRH6m25zUQrIqP7Oi1DruzFvIpfLWF9QNXARU7PiKjbb9HKAyvlNVkInbFgw3q0rF5sjBUFja4oT5mtFt0wm0ujAT95w1iivXN8Ztr5qj3kMsQlzFn7ylCg2ul59jc2TLgFe0T2HXp2WboEfGa11vFNCyZtqiDQSdWCk4iBasktXoi2gtS0vy2UsKXRUFV03tAekxijbRUx+qHJ+bq7Bj41AVA0xke62KRlZVR8cnuy9lxp5mNSZxP7cAlWKC67BuVRGqKmy2CZyxZ4zWM6z/H60wNVvPMMd08jeZbQJgWUiwc0Hd3LUEMEJviR5lqIqLi6FpGurq+P5dBw8etDFMLMrLy6MuX15eDgCoq6tDnz59uGXGjh1rLnPw4EFuHcFgEI2Njdx6ZNsB7OwXC6/XC683+mSRyhDfUDwuFV5NNd8OFAXIFECDW1Ntn4nGntQ2gYUMZBVm2QGH2MaG/UyBggGojHUxQ0a3Zlg3dAas1IBPwrqwhzIDThkeF9yais6AYXUQCuuRElzVnMxkrUro2Fi4NYUz6hMb5YrfY8ycz6OhM3LMmR+SS+Ub+jJwluHWcKQryPWYAyzvJydXc2qbIJtsxX0BADeZ5Ng1EQjppi8Qs49ggLPNAVA5ORKzByD1m2ITlfg5YFkYlEhsIWjQa0V8a403nly5G4DB2rBjKmOo2LGk11pJjhc/XDAcOT4XZz5I3cDbBFsDdnxFjzY68XQIFiEsrEnTWIdoUsqCfY+CtHhe0unEZQIq4j3EQjw8zBzVKeS2CbojEMvLcHPHh71ssWNkTcLWTtGWQ+ze1GyO2uRnCfMmC45JDYWtCdsENYr0JYW+MDR1BKT2DNEcvDmGigAq2sCYvrCb5ppCc2RVsQMqlfTyY+nQkK6bYMxF7EZMexdVNa+FsE4bD1vMVdBkx6xtySxIaDArFTpG0zZB5YEVYAA4mVO6yVC5LGsRk0VMM1R8eDwejB8/Hm+++ab5WTgcxptvvokpU6ZIvzNlyhRueQBYtmyZuXxNTQ3Ky8u5ZVpaWrBy5UpzmSlTpqCpqQlr1641l3nrrbcQDocxadIkc5n33nsPgUCA287QoUOl6b6jETTN44o43noFg047i6XaGBuvLeWncg665roE35Mcn5tbv8dlOGpzKb/IeilDRVN+rCGvW1O4icbrUqVOuBZDZYCCTLdmjouBlKIsD/c2LE5gdBs0PC6VA1QFMQBVE2WoImNlaR23S0VBlgffmjEA188ZbB5z1u6G+iMBMHuVZccAVK1dQZu/kUbePGnQNAz9zpcNhnszA3kMwLT7g1KGT7ZuACR9QH2YiLFlBGSwa4s5sBdm2dOoNOgx6O5Dk5mmnjy0hJgCkmNQ34b1e5o4zzMaV04fgEUn9OU+Y8ehtTNoY0AYKGjp4BkqatbJgJJ4/4k+VGL3ABZmOxRyvOM5PnTiYl5yJivB3xKbAAAgAElEQVRBLiVxn2JNmuzvnLGnwFCxUBT7tW2xDgzs2921eYbKYg5pUFbGBAcxGCp6jCno5Rkq+3VPGarmdnnKT2wJQ8Mp5QdYx5/uj8US8Wk3l2R8qmK4pdPt0ObIbk0xj11HwHJcN0EoB1Ysv6jupPwCEnDsFhgqOp/IevkpigWWTUCVTvlFjxtvvBF//OMf8cQTT2DLli24+uqr0dbWhm9EVPuXXnopJ1q/7rrr8Oqrr+L+++/H1q1bcdddd2HNmjVYsmQJAOPEXH/99fjJT36CF154AZ988gkuvfRSVFRU4KyzzgIADB8+HPPnz8eVV16JVatW4YMPPsCSJUuwaNEiVFQY6YGLLroIHo8HixcvxqZNm/CPf/wDDz74oE0QfzSDgid2A9GLVGaA6JEAKo+mcaCDTYB0XdI0oItvAMyM5ujbPnNgz/aKgIoHIC5N5ZgkGeMCWClM5iqe4dHMG5WxI9leFzIJy+GU8vOKTJ2mcSk/Z4bK2F5jW8Acq/WgigCqyO+3nToc188ZYvuuyFAxQOXIULGUX6fllM7OmU/y4AfAsQaU1WBgjqX8Mt0uczlxXIBzyk8zAZU1ObV0WGkQs59kZOzsQSjr90iDXiviW2uiUUhMZNlEr+s6Ln5sJc57+EOTMXG63miw49lI3OZ9JssSO+XHGCrR6JYxLqyXXZtgAMqCnW/KUMYjjZCl/NhcFK3hrQio/v3xXjz09ufm73TS5DVUdpCR5XHZn0XChB0r5cckBuJESgEIZagoQ5oj3Ff0GFOtHwU1smuCHvumDr8UuHWHoeK3bS3PGFqx/YuqKvBo/PgMAKJw2wnpfH9RS7vKnru8sSffekZI+Qmp3GghO5duIdXHt56RAWUQhoqBbxzTgKrHe/l97Wtfw6FDh3DnnXeitrYWY8eOxWuvvWam1Xbv3g2VIP4TTzwRzzzzDG6//Xb84Ac/wODBg/H8889j1KhR5jI333wz2tracNVVV6GpqQnTpk3Da6+9Bp/PSjU89dRTWLJkCWbPnm0ae/7mN78x/56Xl4elS5diyZIlGD9+PIqLi3HnnXfiqquu6ulDEndw4IkBKs6lXLOxSh7N7lwugiwfaeTZQd7gRaaCASrGBjCA55Wk/Chgoym/DpLyy5CAOjHYZMsASKZHM1NbbHL0ujSufYNTyq+7DBW7uTmGSnhQObE6bL/2NfGicktDJR8rmxCaSZoh1+dGuz/kCAY8ZJLzB60Dwr4vpvwAJMhQRdIHZOIK68ZkleNzm5MP6wHJIhFAlexDsyDTQxgqY8cPtXZxLWmAxABVUwS4Z3mM894ZsDRPYp/LRFJ+sRiqDBNQWfqXeEKLlvIjk6To+h0kLIQ/GMaNz24AYLjy9yvK4vpWmtdaUM5QZXo024RpidLlvfwAvvWPE0NFj4NGwMFh4vouvjy1ORRPsNOlOjBUNJra5U7p0c4LdTfPzXBzLDw7njKGih0jzildYFVpioydj3CYT6Wyrgf0GmJDCgttXax0I2OorG3F38vP2hd2/bL/uZSfYmfZFVitdExRevjYZqi+kubIS5YsMRkmMd555x3bZ+effz7OP/98x/UpioK7774bd999t+MyhYWFePrpp6OOa8yYMVi+PHbX9aMVYnoPEACVJOUnCtDNz9x2MMOvS7M9YLwujZv82E0sS/kxoJDh1ji2iwl13arCaWecWKUc0qoBiACqyHYttkHlbrZEROnsLRiQa8To+tjE6pOI0kX6WtymOKEzwJHtIEpnLA+dJHJ8LtS2OIMB2kRW9tZcEEm9Gb3xFG7yL83xmuAqpoZKaDHT3BEwABUTIwsgkfblkwUvSpcfx/9eMxVPfrQL7f4QXv7kgOO6KHhnE8Pnda225WR6GTGY8JpNwFlel3kdmgxVXCk//nhQwKfruiNDxe7LLknLlWghZagkWiMbQ0V+337wiPkz21cu5ceOTSgsFf9neV22CdMUpZsaKsZqWOMtIkJ0lqIWrwlp65mwzvXjFNPkbULDYxZWlVtskN0VDNt6itIxyIICu1yfPOVHXwZd4jGK/K9piu1lWSEaKjY3hMI613qGMecdROvJ9fIjGjJahMH+ziJWFagsfTtvZDk27mnGohOMqko6flVRbAUospRfMBzm2uMca/GVAKp0dC+ohkrGUMmayIpVeMZ65OwQn/KT6LHcfMqP/Z2ySywdxUAcSzNZ1SaRG0/oJ+j0dijqMDI8LnOcTN8gVjs6aahoqkxV2Nuakfarb+1Cea5cPM1SmrTxMqPmaXNk6XcdUn40XSkL9jmdJBi4FN9UWfAaKvsytIox0+Myx9C/KBNel2YCKrGXHwsGtETxeXNHAFUFIA26eUYqFkOV6dFMLzInMDemOh9jqvPxk5c2R12P12U162bgZvtBO6CS2U6IId5L2T6XWYTgJErnU35Bc1zcegmDFArrtp5/LNgLBwOwsp5vspCK0iVVfiLbQoHG5v2Wb10XKXAA7KJ02WRLX3yASO82oWrYKrW3luuTl4FrZw1CSY7XHLMtNST0hAOM40j7Etr6Kjr0YrSq3JSoqTsWhyW9D6Om/ASGioIvmYaKASDGMrHtFWZ6bM9jmvKjIns/Yf7EzIDYy482X2b7wc4nrYaMpa/zEyE8i+JsL+477zjzdwqgWCERDV6UblVcmsL8NEOVjlSGV2CQAP6G9bo02yRgVNNJGCqPnR2i6/dJLBm8LpWzZWBj4G0TIgyVh29MLGpjXKoiHYMY2V5+MpYxVGJD5kynlJ/bDkgB4FcXjMGuhjYMKMmWfc1u7+BSLYbKHx9DxcALA28snFJ+7LhRX53sCFCRVUMCgoZKqAz0uXlgnenRzDEd37cAO+vbzL+Jb8IsnBgqVgnFPhdBYn5mdEClKAqyPS4c6Qo6HkcWIthjnmSABRjFlBplWwDjWownfSDeS8VZXhwMG6lbUUPlcxupQMr6tTuk/GjVWjCsS1kPwGK2GICNG1DJbBMkKT+RoaK/M6NeAKRi1AJA9P7plFQpZnlc3Dg0xWJY/JHmumyiFJs53zR3KPd7NA2VyfbpOg4TAyzx+qcpPwq2aEl+PCD7cLsdUEW1TYiioWLARbY/7DpijaZLc72SKj/TZss8tjaGSlblR8B1mFTQ0ecHWxcLWVqXhizlJ4bNNkHCUFm2Cdb+WJWIxx6gis2Dp+OoBcdGRS5++hBwSvlRsKFExIAZEkE4r8eyV/l5XRoHANjyspRfZYHhudOvyHDzljFnFPg4aqgELxsDUBk3FiuFFscVD0NF9236kBJcMqW/9Dt0n8yxeiSi9BiAigU7LiycGKp8gdXxuFRz/E7pKg/HUPETiuixRY/RuL75ZjEB4PzgYhOkaOPAgJkoSmcRi6ECLGAZ66EpHmd6TkU2hk0C24WUnxMgjbWt4hyrWpWxAGziZsA/QI5Nu4Mone5jkDBUom8TS8uzuSxeDUl3U34UDFKGiu0jnTTp/dPutwOqTC//cqcSHyVWYh/PJAxINFQOVX6UzQ2GeTsHmvKjYItqiOJJAx+OvAzR/Y8bUGW4uPQeS5VyonQz5WeMkbHGZTk+uFSF+z6noSIAhLFbbk0xGa9OWuVHWD2ZKJ2BGHp5BEN2FpIGe944vYyx8Vhjl1dvyvfn2GWo0oCqF0c8KT8bCBLE3x7NsDoQndLFdfkkbJdY5WcBKvu6pgwowhPfPAH3nDXK3C4Nl6oiSzAXlYWox8lwU4YqkvJz84ybo20Cx1DFN6kaY+PHLhelO6X8+O2M6JPD/e7EUOWKgIr4fTkdK8uHSreZgeYLgIpeE8f3LeCuB+eUH/+2y6KlMwCdpBpEYBAfoIoIV2M8NMXUKt0PphETbQk+F1J+TilT+7YEQJVtsQQmyIhsg11zVNjdQVLENLi0T8hiqEQNX6agr4t3PpGl/Nh3aZZPJB2CJNVDGSoz5ceYAo1/znTIABV58QFEhopPITq9jJjfFRgsDlQQoNggpONkJqvGduUpv/gYqkBkzHYhuSxsKT+OoWIaKpkoXWSofFAUHsgqsGwTGKNj2CZYzJ+Y8nOpvLEnBZSUHQ6Ew44msLIISFJ+YnAAWyZKV6Ibe6YZqnSkNPiUnx1QxcNQsb/Hsk3wOrin5/jsuif6xs/Ah6oqmDGkxKzUsaciFekYxLAzVFY5tlXlpwoMlZOxJ2Wo4r85RQAjtU1wYqjIMdRUBSMr8ri/OwEqTVWQ6+PBKzveTnozqqESUx4FQtqtlrSyGVaeYwPdsjB9qAQNVUtHgGOtcgQbBCeAS4MB9VhO6eJxpuNmoJEyVIfb/LaJtlVsT+IQ4liKs71cWkQnHjmWCSep8gtEr/Izxhg2J3s7i8hfG/G+odP1W4AqdsqPpYr2NnZw2jB7yk/hNEeylF+mhxelU6dvcX2xznlcPlQ60NDKV6xS4NTaFYOhcjD2FKMxci3Rl45oYmm2z4oCZHtcMW0TGBgOhAzmkp0H1m2A3vuGKF1gdHSdO65snAz0aqrCGXvSKkJ63wdDekJO6bI2QmLwGioj7U4PnaLYW8+EdP2YFqWnAVUvDqkPlaCropQu+zsv/rb0Uuz6ZJOSCM5kVX7UkoAt75Wk/MQQH5puTUWm1552FMMuSpdV+WmChsop5SfXUMUKGaCSadVkQSf8muIsG1vjVOUH8KySW1NiM1SqBahipfzqSXrEpfH6qlhVfp2SKj8KqCgIzstwx+WdxL4j6mnEsAEqMm4GGmlrF8ZOVZFUqzj+eLclMlR0kmHHT57y469hNpkAwHf/vg5/fG8nAAlDJTJbcU4oNK2X6+PToFzKT+cndMaKUHYKiFTyhXWT3WLXmch+0MjyaIJmxlqeMUdWlV8shkpx/J1tIhwBz9y46bkQnNJZUBfuuBgqBqgSTPlle11QBQDB0mgUKDNAEgyFLe89t1VdTZl1I0Vm/Ew1R0GSfnMLL0GOPlQq/4wOhMJCejj6PROMg210C9eD+JlCPqeMWzrll44eCVGADvA+JzLWyqOpyPDYl6FpP5mGytHYk7Impm2CnaESQwZA+JSf/HvxaajUuCwYZIA0nrBpqNyqDSA6vWXT7w4ty7ExcU6eWQAv5qZNqGOn/MK2N0onYfiASB+4uFJ+poZKxlAZnykKz7rFk+4DrOMQU0MljI0ei/wMkaEKm4L0QaXygoNoYU/5eTidGk3vyVN+8io/OsYPPm8wvaxE0CteK/H2O6WaJsYoR+vlx+4FNhFT/RRgnG8K0E3na9MKRaahcvEpPxlDFbS7a8tC/LuoI2L7Ql8SAJ5VcTb2tNYTjaFiY2hos2uoor0EsH1mwFYhICgoY6iI6aupn8r1Wv5MHENlN/YME2NPWuXHsJGq8E7pVJROj7PBwFrjCsRM+dkrNsWg9y4bt+hNxVKG7NqnWrh0yi8dKQ2qAfJK2CH2GedW61K5N2QKJNgDnE22NtsEqYbKXtHHASqHtzwRwLg0XhjvlPITNVSZHs18S2OAyufWOBbOqeFwtxkqYVkqSjfXF0fKb6iQWgOcRekAD0Z4DVWslJ9uAz3iZP2Xb0zEhH4FePSyCcY+UUAVo8pPZHieWLELl/5pFQB7y6J4AVW8KT8xVcsBKsZQsQmDOMH3Lcx09BlzCgZQWRTneK3+fgJDJab8dF03fahkgEo2OXCAX7NboMQgcsygbAybPKOl/NjLGdufz+r4qkhjX61zzsbF7iGZhipLsE0wqsisYwdYVW4xGSrhnHPGnkQPFI2hanNqPUNar0RjqMoiliqsW4IIFp2iusAoyhlIAD07FwxQcRoq0yk9zOmnWHg4UCJzFtdBGxWLLyBGyzLj57DONx5WiDA9GOYd8GOK0sNWmtEp6DXPfqTHTlGAq6YPwOnH9cG4fka7N8PYM/KdYxBQpW0TenHQtxNZ6xn2QBbb0TjpY/7vnNHYXncEAyN2AWL60K6h0jgbA5Oh4qoDnUr67QCEMlSOtgk+WcqPnxxsDJVbfhmLE1a8IddQ2QGifJvWd4eU5djWJe4fDQpG3JqKmcNK8fInBzB3ZLl0eToxxWKoZg4txcyhpebv/DUi3xe2zyJYA4CttUci3+V1fHEzVF7GpCST8rNrqNhx8Lk1lOZ4pT5C8W6rhKb8QmFukhFTfl3BsPmGL7u2ZZPwEDLpujS78WG8tgkyBpMCD4BnqqiJIgBsi5zLHK9hZeEPhjkfIhNQRUn5ZXpccGnWsVYVy4lcNAqNBaji0VCFZCk/cn44hipkjZe2dolWrFCW68W+pg5Tj6dGpBVhPTqIGFSajaXXT0d5ngWKjPHzFXYs6LPNBFSkm4PYD4991XRK16nY3+6tpamqub1AKGwWJjBmyK2pCIRCCAR5DVUs2wSzOXKconQGInmhutHc/IIJ1djd0G4cB103043HIkOVBlS9OGKJ0j2a5DPBc4o+NGYMKcGMISXcsiycWs/AZ2e7ZFV+YojrcmkKMpTYVX4ig5NFjD2tcfEMVTwaqlgPcRrihEid0mOtzyswVOLbvJMoHeBBkNelYlzfArx108mOy0d7mIkMlRichipOH6qx1fkozvYix+fCf9btA2C0YqHjEKsLnYKlpmIVC4ggn7J1rMqPnYtQWCfmkQruPWc0zntkBa6eMTCuMYkPcF6UbrVcoeksBhZoGkx2T9B1f3/eUGR5NJwzvgp3vbjZ3AfxmooXUJ11fCXe3nYQM4ZYgNkCHsbvVB9jtYTR0RkImc20R1fl4cMdDegKhk0GQlGs68BkqGQaKi/fBotL+YXC0HVLGxOLlRRBtqyXX1i3i+N5DZVclB6vDxVjN5mflaYocKkq/KFwTDuLoeV8Za+qAgjJRekaEaUfMlN+Fhijz29Zyo/un+gXBvBO6fQ4WH33WMqRr/KL2Tg7DoaKidB1naT8KEMFel7Zenk392Mt0oCqF4cIlMTPGBtCH8ReFy84jjbpcsaebs3GKomfeSWAKhENlc9trcsJUIkaI2qbQLcZj22C0WDUeAgmlvITNVQyUbr8Zqe98voWZmL34Xbu79FSfvkZVJQee7zRKmwY2HCKeFJ+YlVXUZYHj0VShrXNnVixswEAusVQnTm2Ahv3NmPh8ZVRl4vGUMmq/Gj64/i+Bfj0rnmObKgYomYpw6NxOiCzmkpVrKa2kUnIctBXpQCVfjZ9cAlGV+VB13WT9TAAlcDMxHnJ+twa/nDJBGFfjP8Z60DTObQlzOcHWxHWDYF/Zb4h5O8i6U1Z81tJeztkCMaetExeTJcmzlDZfw4TgOZ1qegKhnmGihOly1J+vIbK41I5wMHc/ztJTzwGjBJlTkRgIGOoguEwDkfSi6zCD7C3b2HXBH12d5kCdEnamJjadgWd07iUvQJi2ybIXO9l4daM42qK0jnWylqOseFUlJ7u5ZeOlIZHAErGZ3ZdVTSGKhqQENevKAr3YPG6VKiKfXsyY89o6wb4qjXAmdlSVQXZXhdau4LwuVWoqt2/xM5QOV/GXpcBqGI1QqVh86GSaKicHiSiC7JNlB4nQxUPAJQ9cNgbYSymKK6Un2DsSSfMRy4Zj1v/tRFTBhZxxyJeQDWsPBdPXjEp5nLidcTZJmQIGqqwbqUiIscvXjAlhphaCYTCgiM1/9bPBOlO26MT/ICSrMg2DJakIxCCR1NsaeVkysZtKT/KUEVeGIKhsKmfGlKWY7IhRsovMmGSa0y8JqlrvUxDRX2oqHg/lrFntCo/9jMFPxkeLQICLV8tZ1G6xX5Qhirb68LhoJVCZBYm7LApCjs/4YSZE3F5GZAIhHTUtdgZKnrMFVisDmWuzPZeqj3l5yJV4BRQseUsDZfO9/KLoaEyKzZjpexVBX5YzKIIus2fI6sJ6WlRejp6KBSiQ5Aae5I8uPWZ8WBjF2NUQOWyAyOxipBqlWQpP8cKNJltAufW7jwuxuKw5UWxsDiuaL5HjMVLhKESdWEZkpSfU6XPFSfVYObQEjx88TjzuzQyHY4XYNdQxQrR+E9VDKsGl6qY4linyIgr5Wd8bgIqwUDy4a+Px6VT+neLoYo3bKljMgZRQ0XtI2JN2rGC7QdlqGiag6YCAee2MyxoSpCCajYxul0ShioFgIoBCMo40JTftgigGlqeY76sUYbKpdmfNyzE9k/RfKgoQxXLKkNMV3MTL0tfkQmf3VN+omejBAvXHNmBoRKZY9FoV1MtdixWylIMERfQ/TGNPUNhHDxiaKhKqIZKqJSzgL517DtJw3YZ6JWl/Nj1QZteJ6ShYveZK/qxYNePNOVHU5+KxX6yayUtSk9HyoPR2ewG4nRVpijdTiFneDQcEfQtYogaKvOzLrZ+DdmShsayRsti2KtNBFF6FGCR7XMBLXIDUmOsvD9WVEAlqYSMFbZefm7VNgl4HB4kxdle/OUbJ1jfJRYWWR4t6kOCskrxAkC3poDN1W5NxV+/eQKa2gPcQ1kWvgRSfubvDhNJzwIqfptUIJ9rMlTG9kNhy709kfMtC7YflpcS70htps0iE0+7g0u6GHavN+v6NFgQJSU+PGKVH7UVoqL0z2otQLW30aiQpOlNPuVnvw9Z5W2Wl2dxqQ+V6JMWC+zOHl6KPnk+HIiY0aoxGCqfWXFpfCYauUo1VIIPlcgc5woNvzVS4h+rkEIM8TzKU3666UPFMVRCikymoeoKWi8R9hcQmvKzujyYInHCUHEaqiiAStf5eyFauE1Axf9ufEaAJVkPu1bSxp7pSHkwywAvBTyRMBsmS7RWDIw4VeEBYvrQvi4nhirX58a3pg/Ad04e6DiBiFSwx6Xwxp5RJh6LobJrxNi4OA1VlDSaT1IJGSs8msq9VcpE6bEeJHRd7IEWLd0HJJ7yA3jg6tFUVBVkYlRlXpRvGEHPm9MEFy31QoMXpacYUAnHgVo4sPHwVX6MRUotoOJTflZFnpXyi85QsehflMX9zu47th0+JdL98bNj8tyavfj1G5/xonRim8Aq/IaW5ZjnsSsY4vaVhXhNUr87GUPlpexeyErjxPLX8rk1fHf2YPN3ajJJK9asbfMMVbvQfJpvjmyth6bNMtz8PS++GFBX70RTUSIw4HyoIs+Rlo6A2RjdMeUnMfYEKFBSbWOjVX4yptn0wRI0VNFsE4ISPZ5TsOuHjUG0TWBBH6cmoDoGGao0oOrlYWmnZIBKkvKLfMYeMokyVKLA3XDVtoOS2xYMx83zhzmuW6SCXSrfEicaQ8UqwBwBlVtFQaYHoypzcXzffI75EkNmYhorFMWu94rXKV22Lrav0QTpAN8gOV4AKDv38UQionRzOQcQ2ZMMlXgcZBYOdJxs0kik1ZAsZCm/QBwpv2jXNWA1D2dh3d88YwAkl/Jj31315WH8+o3tJnACrPPd3B7A/ggLNLgsx3FfWdiYYo7h4QtYVEVM+cXXdobFeeOrzJ+rSPpalr5ix5xtg+qnxGV14kPFFe+4+HSZ2J+SGmEmOtGLAFKRMFR1kXSf2D/VyzmlOzBUAXvrGRa0lx9bzs1lNKzrOBQnQ0UrAGO2EYr8ne0yfdGhx4EeU3a+jkVAlU759fJgb1Hm/7Eq/wSdU7waKjlDxYCAG52Brqhslxg2AOJSTd1CZyDsqL0ytmdclhkmoOJvLJ/bSJ29cM20SINN5xtPJtyPJ3xujUvjiDd3IhodlhqJ5kEFAHmZiQMqulxC1hAJGHuavzul/HqSoRLGJmsjQ8dlNa9ODUPlIW/wJmtDmtCySZxV+WU4FEgUZ3tR39qFcwlQAIiGiukhSco9mQlF3H2a6mLXbn3EBdzrUpGX4bYYpVDY9NeKBtgpyyljqKjxbDzO2jTcmorVP5yDL+rbMKTMsiFgX+dSfoKGqk1M+cmaIxN9KtueW1PN68umoSLtgxKv8nP+nQGMlg5jzOJLl6ihYr1SS3O8ZgEKq0R0q3ZzZtrLjzJZ4vaDkV6VLKIxVH4ufRuDoVJZyo+9MBCGShinuP40oEpHysMEOoyh0uyARxSlAxa7E626TSZKZ+tXFAs0ZHs11LcmljazAarIzVGUZRjmFUapQhNF6bKWOEB8GpPuMFQAb17qc2ncgwBI1NfKWDZa2xlAEKXHEHuyoG+I8X6HjglwBod2hiq2hkqciJINcWxzR5bh3c8OoQ8xTqTj7IzRvDreYOvnROm0Ca0pJo7YJrC2Mw4vCi9dOw2f1R3BdOIDB1j3MDuPvA4peYaKhQ7Lf4lNoiw1Jjbh7gqEpVVcdk8wvjDEJQAq6kMls2GIFSU5XpsW0GRbSPGBaCDa5nf2p6LAko6f9TJlPJ6ooaJ+XIlq20RgwGuHjJ9bOg3LBPFFU2w9c+upwzBvVBmmDy6BpigI6jrHUEWr8rNMPSnraL0w8L38ojFU8evhRA2VU5UfTYumGap09FhYDYl5LRXgbJsAyBsgixGtLyCzUQAsd+9EQIkIvtjD9lcXjMGuhnb0LXKuQmPby3BI+UVjt8QQU6bxBgViqqrYNDmJVPowNiiWhsqwgzCYMapvixY8mI5/H+MRpWu2t135cnRdPVnlpyrAool9UZ7rw5jqfPNzqgnpCFjC2+7EHaePwH/X78M1Mwdx2/eHwmZ/MxdhqPxCys9JQ1We5+Pcs1mIaXtuf5MRpQvfZZOUqlrAmKXGPAI77Q/JU3ROnmCsbY6Y8qPLt0e2lWwpvCak/CgTZmmonFN+tMpPZPvpeGUpv+4zVFEAVeSYscbv4vUjaqgKsjyYNazMWI+qAGGdiNLtrWdUkvIzt0k1VMy2IawLlZHOgCqQgB6O7R8bg5MPFc9QWeD/WIs0oOrl0b8oExv2NKFvoQFA6EQra0djidKNU5swQ2UCKms7oyvzsOXAEY56jxVORpiTBhRh0oCiqN9l/fzY277UwT3OEJm3RL/HJg0RQCWyPktDFRsk5We40e4Pxc02RavCimdM0b5n996Sj6kwy4PLT+yPXJ8rqvt0d4Jeoy7VSBvPHl7mOE7Tk6ebDNXiaTVYPK3Gtn3OmymahhGTiWAAACAASURBVCpB3ysR8POgpDt7YIQ4GZkAhKSu7AyVlTqTMUq2lF/kGsr02u9TEbC0pygVSy0ygEjFpQkEjTGLVX68KN1K+bkjBSOhsM61UBLbd7HtikUQ8YaIC2Q+VGxc4nZFWxRuTLZUnmJ/kSXjZsFpqBi7FxSc0sPOKb9E0rfsRZQBL1l/P/Z3lsL0EzPVYy3SgKqXx33nHoclMwdhcATMyEXpdpFjd0XpIv0PAD89azRunjcMBQk0m5X5UMUbs4aX4ZVPa3Hq6HLpuhKZtM30YQx2SAx2PNikIQqyE6ki88XJUAFAXqYH+5s7OfYwWlDxdUKi9Diq/OwVQ84PuLvOHBn3thMJcZKWhapaD+OOFKX8xO0HQrw3ky3lF6UxcrSwV/mR/U2BDxULxqRRtpUxVCI7bVT52QXMTiarLJVNrxfNxlAlxxyyEEXpUoZKTPlJqvzY8fG6VIMRJgyVV9IoXlEsLVLCVX5iyk+1P69ZiEUNXMoP8vuRvUS4VNX24qeRlB8Leo0xtjIYjt+HKpECA/Z8slJ+9Lja05OBkJ5O+aWj58Ln1kwwBQiASqIPYj8PjjReHVBiNWAVI5oei6YWVVVJCEwB9nL3RCa4sdX5eOPGGdJxAtFNQcX4xtQaeN0qzhjTJ+7vGNvQuG0lI0pnE0+sKj/AqvSL34eqmym/OPoc2q0ivvoHHD3O0bbPHsadKWJCWFhO6bStDZnETYYq4pSeQDoa4I092bpZpFJDxQOQCEMVOVYi021U+dl9hpw0VGY1LhVQqxarEwrrplA8WTsLEVC5VL6aEJBV+Ulaz0TWw4pPPC4LRMkaxWtEQ5WwD5VY5Ud+Fu1XoqX8nMTtVusZuQ+VuH0Zq+0P6aA69Gi9/NiLRTzPG5cgSndiqKxlLI+rtLFnOno8PJIJVDapXjNzEBaOrYyqVWI3q6pYExd9qKRqnFTQ2a112UTp8Y9tREUufnLW6IS3aQEqeaVhd9Jr8TBUrEou3vVH07hEC1W12gw5V/l1n5VLVXAMVYxGrIGQnrSGSgw+5Udazzim/BJ7pIosM6+h6v64xVNlVk4pVosbBnIsnSZjqEiVn8v+bGHBXjYY+0tZXLOhsqaiIxwyQU7SGipV2B9VIaCXr/LL8blwpDMoMFT8ZE1berF99bnljuPd1VCJuJiyTuJLiy3lJ1T50WD3o2UVIqny09SoL4PUqV2PU5SeCEPlisJQifsjmramW8+ko8eDE6ULZp8ezRKSq6oSFUzR7/ncmvk9KkpPJro70csiGQ1Vd8NM+XmYhqr7jFu/iJljTXFWjCWB+aPKUV2YgamDiuNaN/e2meBxqcjzQVUMDZQsEkn59VTQCSKamarZkyxs1/4kE5wonavys5grwJrEs+LQydEQq3hFYXd3w5byC9KUn/E3W8qPMFSMjaOVnU6i9CyJvYnol9QhsGHdDVUy6VIxPQC0RbRhrIVNQCpKN36n2lGWZve5tYjg2tquQrRnCVf5CeeRvljZj6mzbYKQITOPMcNBLs2e8pMxVPS+pmA03l5+iWioiiLPFtMol9omiJowdm6PYaf0NEN1jIW8YTIPrOJelwQ8pQpQcRN9khOxyMB9FVSwTZQuUNWJgIsbTxmC00b3wciK3JjLLhxbiYVjK+Net4yxjDf+dPlENLT6HdvUJJPmTFWoqtWOJdobq32sKUr5UYaKq/Kz3uwBoKHVaKxblBW95Y8YYpWfaD3Q3RCrr6gonR1HJkoX/ez4Xn7OGj123ZRG/peNne0XAzkpq/Jjky6xsLA0VAZQLMh0Y/dhUUNlidIB3liVFYL43KrZJ7NLIuZPpspPFOuL67Kl/KIyOvx2ZCk/TQao6EuKaZvAV/lFNfZM4KXlllOHYfqQErMy0ck2gY0VSNsmpOMrDBn4cXcTUFXmZ0BTFfQl7TBkDZC7E5zhZJLgjPbN+yrYKUCW8qMPocSB6+iq2O1guhN8FVZiD6CBJdkYWOL8d1kbi6MRbk1FMByK+oAVx5rosXDeNptw5FV+rLKsoc0AVMXZiWkNCyPLF5ipXvoG3/196HTwYtKkonSN+5+ycdGq/E4d1QfZXhemDS62jV0TAItpm5CiKj+LoVLNymeRoWK9MWVVfqYonTBUotyB9VFly3e3yo++AGZ5NO68isdDTPlRM2VxqyKDQw1nzfXHqvIjDBVX5ReNoSK9A2NFn7wMnDPOMrPl9ldkqESwnAZU6ejpiOZuniiDUJbrw+s3TOdMNq2HSuoYqnj73sWzrkTc2pMJJtpmDBW9uRNlgnoyKFhNFSvDojcwVGy7HYHomg1xrMlecyyoaSRf5cfrduqPGK7jRdmJMVRfn9wPBZkezB/JKloJy5PE4T7U2sX9zsZJfahYdZjIcHcFQpxejIXYzifDreH8CdXm7zIPLbeQXkz23mFghBPZR8Azm+iZSSZLN0l9qESGilT5WY3iNQDByHbR7So/uriooxTXJRY1cAyVcOhEpt7tstsmSKv8VPszIxjS46/ykxQsxBs0W2Hz5xLAclqUno4ejyyvy8xHi73uuqNPGChUAcp8qLoTfLl16lJ+Xx1DxTN1MiFnb4hoZe3JhvjAPFpvjOyaTIShSpYVNdfjoCuiKb/OQMhsbFuSIKDK9blx4Ql9zd9dEmF3d+JgCw+ouoguRRT3i2l+w8TULgy2CbVthRp2hop9h6UXk7132NcZi+EionT2WWO7wRaWRpoMxydKt4ToPsJQmdsl2rOEGSoCHMSUXixROh2DU4rMXJfENsGl2iUS/MtuBIyG4+/lJytYiDcoyy0eRXMsIfu1d6xEGlAdY+HWVPznOyeaPwNyg8/uhslQJWBNIAt6syVL8/MM1VcDqCoLMrj/ZW91vSFoZVWqQAQLG0N1FFN+QAzbBFvRQKpSflZqj+qKqCi9PsIGeTQVuRnJPVJTlfITGSr61i+eR9F7zh8MIxCxGojGgNqNX+1gkD2bGOBMlbEnZajE1jONbQZDVZbr5ZYFAOYGwAAfK8jIz/SYzz5ZuypNUaSl//EEBTSidYp4PKLZJohhS/lJWs/INFRyY09BQ0XsQJ5euRtzR5SbRU6ygoV4I1rRhWiJkUxRxtGKNKA6BkP0lmIMkCcFLtUmM5NC24RkJze6rmTHFW9cMKEa/YuyMK5vAQCharEXvTlRR/VUM1TieTtaDBWbdKJpuGwaqpSL0q00GE35+UNhS5Ce7UkKBAFiyq/767I1CKaidAeGiv0f5hruRmGoRIZEmvIzPmtuN0BOVoLGp2LIqvxEY88mxlDl+LjPAZg6ITb2G08ZguOq8jFvZDk+2tkAgFRPc9YvFlhJnKGyfs70JJjyi8JQ2VrKaJaYnjJ44nUUj7FnWDeO1csbD+AnL2/B5gMt+NUFY/HhjnrsbewwvtuNe8zFvTDwf9PMsVitbY61SAOq/4FIJuUnxvxRffDRzsM4d3xV7IXjGJP4c7fWRUXpXxFD5dZUzrogGXuCnoxoouFkwz5hHj0NFRD9ARttck8mZMaeNOUXCIVNhqooQUG6LLgqqCR24eGvj8N1z6w3maEAEfqKx0YEVACkRpw2fY5NFE1Tfvx3WBouHi+2aMG2GSTAiLae8QfDZnNkxlDJROls6P2KssxWQ6apsUvCUKlWf79EG4BTICTuv802IZEqP+F31qrLpSlgNQmaptiuI5kVRiDEAyrAOMas2KKlI4AVOxpw0aMrzb9353lAmX4RUPUGm5ZkIw2o/geC0cQZKQAbg0qz8eQVk5JeDxNDhvXU+lB9VRoqMejN3ZvenFLJBIohaqhSJfRONCyGKn5AlXJjTyJK10g1VZCk/IoT1E/Jgqbjkkl5zBpWhg0/movL/rIKy7fX81V+wrESvbAAqx+e04uEokhE0RKGih2/RsZQJQmo7J5KhC0Mhkx2SlWsAgGn5shiWBXOfAqULX/DKUMwuiofc0eUJzRmjQNU0TVUYsqPvkCKl4N4/BnQM45HyNy23TaB6kGtFwbRzDMYDpuNpv0hHau/PMz9vTssMJfSFlRU4v4ci6L03vOqnY5ux7TBJTh/fBWuPnnQ0R4KF+xmTZbZoA/qZO0cuj8G+1tdbwi+Ciu1x6a3MFRsoouuoeoZvRebNEJhnWtC6yZAq76VWSakAFARNjZZDYlKwBMtRbdbTLD71HLVbjMBFWGHJWJmGvQcmKJ0lvLrMI5Ror0OxRAnWY6hCoZN4JaX4SbaKrsDuCydekJNITI9GibVGM3bxXQbY7MSbYBNN2Wv8hMYKtHYk2Oo+PXSx1Cuz2Xz/jLWb7dNcElewgKhMASCCsGwbrJ9gWDY1n6seym/KPsTxYD0WIk0Q/U/ENleF35x/pijPQxbeLTorU0SWQ+Lo8VQ9VpROscgpJih6gW9/ABqehmNoeInkVS93VKGwEqDKWbahKb8UgGoUlXlJ66D9bNTFbv5I+dtpxmtYlgrHZdD0YNsbNFE6QzUxNPPMlrIzCxpWpalFgsyPRy7qOs6FEUx3cBl18e8keX45K55trEDqeurKGrIbM2Ro4jSRX0eBSB5mVYakqu2lIjSeVbbYlptDFVIN/3DAqEwcn0CGOxWyo+mtKOn+I5FUXrvmRnS8T8XVn+yZBkq6/tHi6HiW+n0nhudc7LuYR+qo9HLD6AaqvhE6alk0ugxtdy+rTSTrlsWBYmaesqCr/JLenX2dh6qXZROARUDkGbKz6HoQXYu5D5U/HKiKDvRkFkHUIaKpfzyM90cGGGAThSli+HkN5cMuKXftTFUCVT5iSOg683PsK493oRY5kNlZ9v9Ug1V2LzmA6GwDXB153lDtx1tf2S/HwuRBlTp6LFgN2sqSqXZc/RoMVTJOKX3ZHCtZ1J8bERG6mgzVPFqqFLJILo01dzvVpIGo2zN/maj6iklDFWKqvzM9amWvoit0ynlB1jXk5nyU+XXl+xc0PtU9KFikWivQ9k2aNAqv0DISvkVEBsEwAKUJkMVx7FNFUPFpfwSrPLzkjS+CGg4QOXIUNmbI8tazwRlgIowVEzwz6+nGwyVUDlJIxZjdSxE75kZ0vE/F5Z/UHKXmULSFMkajnY3eq1Teg9qu2ST19EIj3kdRdFQ9eD5kbVPoce9trkTQIo0VFGquroTbJJiDI2q2u9HWTurNokRp8wQUgwR/NoAVZIMlQgyKUPVFQybKb/8TA83XmZGGSnUjGuy5gFV98ccrcrPBqiiiNIDAqCi66WVh+J5shcP2O+VYNie8guFdY6hEhsmd+d5E42BFfHZsQio0hqqdPRYWOXYyd8Y3ogey/cV2SaIwRlo9qKUX0+2nrFV+R0124Sjx1ABRrujNn8IraTBL70eDjBAlZOClF8UjUl3whSlB51Tfnw7qwig8tur/DjXbidApSrww5rsRXCbmSRDJbIatFF1IBRGk8lQuc3+e6Gwju/+fZ1hWEoc42MFfXlLXcpPc/wbEL05sthfj0/5yQGVtDky1RuSxtKiOXogFEZ7wAJU/hC/QLdE6VGqWO1Vxb3nORtvpAFVOnos4tG+xL0ulwp0HT2GSlZq3BuiJ32oxIn3qDVHNqvQnB+wPSnON0EGsRJQyWTNItUpv1TMJ6KzuEyUTqtDmTmwrMovLobKpQL+kCkeF6/J5EXpdoaKtsxpjPgmsYo0JrJfvr2e+148l3I8ADKeoF8VNWQG+66YDKJoXEy3KzJE8aT85Mae9nMaDOtSHypmmxAIyhiq7qT8nDVUtl6FaVF6OtJhRao0VMY6jJvrqFX59aD4O5ngNFQp96HqHSk/du6jATqOoUox8BMBFbsW+DYahm4n2RArtJINNplGs02QpfzMNjsJaKjo8qYPVYpF6fIqPwOEBIhtAgMYTpP+0Uv52V8I2THzue1992iIDBFdbx5hqFwiQyUcM5l3ndTYM6Sb1Z7+kG6mTWXbiTeipbTTovR0pCNKWIAq+RvD6gR/lHyoJDR5bwgnjUsqorf4ULEJP14NVcpTfhHWoFUQatNrojDLk5IJINUaKo2kdIDorWcA+wuLWwK2AOdzwUA9A3LiuUiWobKniRSTkfSHrCo/Bm6d2nHFk/LjqvxSZptg3392PmKBTRHQOFX5idWYUY09zaKFMAQCyqjyY6L0YIhrMg10N+UXRUPVS5qxJxNpQJWOHgvLNiH5yyxVTZu7G1oPApdkokdTfseoU3rKU35uS/QMEIaKHO++hZkp2RbXeiYlVX7GOrpIc2TxPEYFVBxQjc2euYRzJV6TyWqo7CyGyvlQHSa2CYAzaxtPCs+TqpQfOQQyp3h2fYsVfmKw1kfmeuPxodKi9/Jj11sorEOXpvyYhkq3A6puHJNovfzE9aUBFYnDhw/j4osvRm5uLvLz87F48WK0trZG/U5nZyeuueYaFBUVITs7G+eeey7q6uq4ZXbv3o3TTjsNmZmZKC0txfe//30Eg3wj0HfeeQfjxo2D1+vFoEGD8Pjjj3N/f++993DGGWegoqICiqLg+eefT8k+p4OPeAwZE13XV9Uc2bb9XipKl5n0pSp6S5WfVS16tBgqUZxvZ15PHlqakm3xguLk18fOIRVjR/OhElN0Tr38nMA1W7cpShcBVZIMs5yhsrZx6IjhCWYxVPJxxidKTw1bGDvlZ/w9lgN7ICTaJlg/O6X8pFV+knslJKny6/RbrFQgFEYgKKjWuxFcLz9BRSX2wjwWRek9BqguvvhibNq0CcuWLcNLL72E9957D1dddVXU79xwww148cUX8dxzz+Hdd9/F/v37cc4555h/D4VCOO200+D3+/Hhhx/iiSeewOOPP44777zTXOaLL77AaaedhpkzZ2L9+vW4/vrrccUVV2Dp0qXmMm1tbRgzZgx+97vfpX7H02FGSjVUEdbhaDFUPZlaSyZS2YRaDJuG6ihX+cXrlJ56DZXgbh05LnT+mTUsVYAqtQyVqaEiVX42UbrE2FM2HiagZuuRhUdkqDhTXjXpgg6psSdZ55FO4+WaASqneyJRDVUybEmQACEZQ2UCqhhgszSHL3pwEqXLDEnp8EWNFSAXpTd3BKx9IK2XWDC9WiIRrfl3ea6P+/1Y7OXXI1V+W7ZswWuvvYbVq1djwoQJAIDf/va3WLBgAX75y1+ioqLC9p3m5mb86U9/wtNPP41Zs2YBAP7yl79g+PDh+OijjzB58mS8/vrr2Lx5M9544w2UlZVh7NixuOeee3DLLbfgrrvugsfjwSOPPIKamhrcf//9AIDhw4fj/fffxwMPPIB58+YBAE499VSceuqpPbHr6SCRSg0Ve9jEeuj0VHBO3Ecp9SULrtdailN+asSokT1nj9Z+Mwfywiiib46h6qEqP3NbkeuasSEAMLIiNyXb4srKUyFKZxqqkJXyE8EBBYwiQ0X9jdjfA6FQlJQfD7goKEnWg4qu19yeAKhYmCk/h3si4ZRfEuC2I2ABERlDx64nJ4bqz5dPwEc7D+Ps4yu5z+mYeKd0kvJTrPMRjgA7sQoQMCwZNJXffksnD5g6/CKg8kvHGy2iaQTL8zK431NhbPtVR488IVesWIH8/HwTTAHAnDlzoKoqVq5cKf3O2rVrEQgEMGfOHPOzYcOGoW/fvlixYoW53tGjR6OsrMxcZt68eWhpacGmTZvMZeg62DJsHclEV1cXWlpauH/pcA7mP5WKifjbMwbinHGVmDqoOOl1dScU4jCd6gk7mehJHyqg51q6JBIXntAXv7pgDBZPG+C4TE9q3ETWRjwOfQszbf5I3Q1+wkl+fez8WU2B7QyerMqPxeDSbO539ncnQMXGr0pE6TJ2JtEQT62mKVwTaMB46WLFK44MVYKi9GTORScBVDKGzhKlywHVrGFl+MGC4bbvdgYsTZNjlZ+QggVE+wvj51gMFWB5k7FoaEscUEVrPVOe58zAHSvRI4CqtrYWpaU8Be5yuVBYWIja2lrH73g8HuTn53Ofl5WVmd+pra3lwBT7O/tbtGVaWlrQ0dHR/Z0CcO+99yIvL8/8V11dndT6/teD3bipEEvPHl6GX10wNiUP5e6G2c29NzFUPazt4kwAj9IDLsvrwjnjqjjhrRhfRZWfuf7IMSmKeB1deVJNyrYlYxeSCXEdakxjT2tfK/MzkOPjj3ksPRs7NjIfKifAkEjINFR0XIBh6snCmaGKva1UpfwoQyULdswSZd+PEAaJGh7L/MLocZO9JMmc0ls6eADFXNNZdOe6p2MTX0LKhJTf/zyguvXWW6EoStR/W7dudfw+6/idSMT7nWjLsOqFZN8ib7vtNjQ3N5v/9uzZk9T6/tejusCofKoqyIix5LERqdSEpSq45rU94NHFP3x7z36LwTul93TKz1j/36+ajF+cdxy+PrlfyrYVrddZd8JWih5LlE5+HlqeY1tfLIbKJkpPMUNl11DZX9qqCqyKS6c0+FcpShdTZWKwYxZLlC4Gs/EA+GuF6tbYeXLqJEBTfoygYvvtxFDds3AkPrptNk4aXJLQeIHoVX59/gdSfgld4TfddBMuv/zyqMsMGDAA5eXlOHjwIPd5MBhEY2OjjT1iUV5eDr/fj6amJo6lOnjwoPmd8vJyrFq1ivseqwKky4iVgQcPHkRubi58Ph4BJxperxdeb/JuyP+/xHdnD8bckWUYVZF3tIeSkmAPg97kQ8XZJvQA4NEkeoveGD0pzrdZCUSOyeCyHAwus4OOZIJWYKXiDd3udh/dNoH+PESyb2ZfRYd7QLS4oCnp1KT8YjNUp4/pYxtPrPXIgrJ1yZyKWAyVqaFKmKEKSj93SVJ6vCjdrgelVX4el4quYNimoWIWCl63hvK87s2l9BkigtQCgYHWetFzNt5I6AovKSlBSUlsVDplyhQ0NTVh7dq1GD9+PADgrbfeQjgcxqRJk6TfGT9+PNxuN958802ce+65AIDPPvsMu3fvxpQpU8z1/vSnP8XBgwfNlOKyZcuQm5uLESNGmMu88sor3LqXLVtmriMdX114XCqOq8qPveAxEuzh02ud0nuaoerFgKqne/nR6ElxvptjRZJfn6wqzpbyc+jXN7Sc108BlKGSHwOxCtBLGaoeSPmx7dS3WgUCpx9nFT2J7VLM9XyFVX6dMVN+0TVUTnGkU15lJ9PhqaodRAEWuAoQDZXXpeIIgBYHhiqZ5x9vm8CHoigozvagvtXQZh2LDFWPPBmGDx+O+fPn48orr8SqVavwwQcfYMmSJVi0aJFZ4bdv3z4MGzbMZJzy8vKwePFi3HjjjXj77bexdu1aXH755ZgyZQomT54MAJg7dy5GjBiBSy65BBs2bMDSpUtx++2345prrjGZo29/+9vYsWMHbr75ZmzduhW///3v8eyzz+KGG24wx9fa2or169dj/fr1AAyrhfXr12P37t09cTjS8T8S7l7OUPVEKlJLMWPSU/HV+lD13HHg3uBTwVBJzBKp7s4AWAkwVDFc62uKswBYRqeer4ihYlGY5UFhllXx1uRQ2h+XKD1Fxp7xp/wSOz405UeDpfxcqmKmAun+yqr8QgRQMcAkpvxYG5pk7q9YxrW0H2Zvft44RY8pfJ966iksWbIEs2fPhqqqOPfcc/Gb3/zG/HsgEMC2bdvQ3t5ufvbAAw+Yy3Z1dWHevHn4/e9/b/5d0zS89NJLuPrqqzFlyhRkZWXhsssuw913320uU1NTg5dffhk33ngjHnzwQVRVVeGxxx4zLRMAYM2aNZg5c6b5+4033ggAuOyyy2wmoOlIBwtNkl442uHUvDZVwd4o6cO5N8ZXqaHqyfOf8tYzwqSkChoqkW2gAGRgiZ2hEqv4xLhl/jBcNKmfCazcKWaobFV+kf0ryHSjsT2Aa2cN4v4uggLxe9HCk6JzETPl101Rumj0aa5P0llAdXjh0Aigoik/AGjpFEXp9obZiQYvSrf/vSTHi621R2zjP1aixwBVYWEhnn76ace/9+/f32Z17/P58NBDD+Ghhx5y/F6/fv1sKT0xZs6ciXXr1jn+/eSTT7ZtOx3piBVm1WIvAlQFmR5M7F+AbK+rR6r8ZKLW3hhfZZVfT6Y+ucmuBwCV2BxZtIT4or7N/FnWN9PUUEVpPcPAFCBU+aWAoRJBPRvH01dOxpYDLTavpiYHr6R4ABKX8kviXIRjTDWxbBOcgoFIEYjJKjEdNVTkemMAzeMgSmfti9xJSAti3TslxLy0lz9ypHH0atDTkY5jLNjDoDel/FRVwbPfmtJj7JFM9Nsbg3NK72Efqp48FryTdM8AKkUxzD1DYd32cnD++Cos21yHaQ5+b2wyjVcwTI9Vso2RATuw0SLrH94nF8P72M1VRZbF/F6ixp49OLv3i6RH+xMgGk/89ZuT8POlW3HrqcO4z2Vu9nzKT26Fwtz0TYbKgd1LSkNFviv6XgE8oOrNjLhTpAFVOtIRZ1g93HoXuOjJB8+xyFA5NcTtbnyVGiqqb0qlsae1TktfEwrrtkKGU0aU4bXrT0L/IvnkHouhEoMeu1T4UCXaX7IyPwP7muz+g/EM35uiAoErT6rBo8u/wOJpNdK///C0Efj65H4YVGpPsUaL0VV5+Ntie5GX1apJDgidzHqZmz47x4yREiOZ4he67aCEuivJPrar6NOAKh3piDPYm19vao7c0+FKcAI9WqFxk0RPp/x6ssovtUUAdoYqsh3NKI0XwaKiKBhW7txGx2tW+cU3tlSL0kWmKNY4Hr10An75+jYMLc/Bw+/sMNahxPcSkqoqv1tPHY6FYyulDBrbTirtN0TrCiC2U7o4nnjW352gAE4muynJObYBVe961U5HOnpxsMql6sLMGEv+70RvTHPKoiebVzv5UPVEcGXlPaGhIr3dAOD/tXfvwVGW9x7Av+/ecpFsQshlE0hCAkjkFpVL3KFFMDlJKPWgcM6gRoWWwmBDT7kISk+L1pkOHnvaTmuRmY7nFGeqokyljgjaCCSMGkBSKAKCwqSNBdacorlwCbk95w/cN/vu/fLuvrvvx49DhwAAG5xJREFUfj8zGci+77s8749n8/7yXC2m0FqNzC4zyII733VQuvpdfoHKManQiv9dNhN3FA0v3xJscpRidF2HKvz/C6NBwpTRmTFr5ZW7/CTvyblypp3n9YHqRESD0l3qt7cVLWaVZof93vGALVREQfrvf6/A2n+51evsJ71y/iCOpw2hvYnqLD+PvfyiOcvP+7iXcHnM8pPHxDkTqtDuJdA6VL7OB4D0FBXWofIxyy8Q11XIg02O1NocOda8t1B5HgduJu1mo6SYMRhojFQkY6hcWxi9LQ5akJmG99bdjYzUxExNErPURBpINRuTKpkCEqeFyvU3X7UXOI3lLD/FuBdVxlApY2GUlAmyr61ZfBl+WAd3vkXlQemee/kFVxDXGYvhdFfG2bBJv4bHUPno8nOvEwZlQuX+C4Sv9w/Xh0/eg97+QcWGzq5CHUsWTxKomhBRrCXKoHRFl4bKrWmxXYdK7Vl+yu8NbglyqAnV8MKewV3nej+qDEr3sVJ6IKkuSXGwLX9GgyS/f2K1UHmZ5eejyw/wTLCmjlZuFebe4hvpLyyFWWko0+kvpkyoiMgn5w9f9x+68UY5hkrtWX7DD2NJim5yqZzlp0ZC5dkaAQy3soWaUFlTb7Yq3BJk950kSfIDWJUWqhBn+TmlWcJbAsEZn4RKqLysZu9afo/9Hd2+nz/FpqgXWekWxfF4m+UcT9jlR0Q+OR/IidRCpXqXn0sXSLQTS4NBgkG6uRikGs8tj61nnF1+zkVqQ4xV/V3FMBokLJlZFPQ1y79Ris+/vCZP6oiEx7IJQSbPrklxKHXZYjLgWt9g3Nd/VwVfj03Ktw6PUXKttu512L21MTPNjOrb8vH2x5cAAFlpZvxfz/BeifG0sHG8YUJFRD4NL+wZ3w+UWO3lF4uxZM4lDdRoFXFvjTG4tVCF+nDMy0jFf1RNCOmaJ+rKA58UJM9ZfqGPoQolqs74RHNhT7WV26zYucquWEvMGTeDFLiVT5Ik/OvthXJC5T7WyXVpD1JiqklEPiXOGCrvqz+rwbV1IxbrcQXaLy8Uni1Uyn/DfcB9vHMPSdBjqFxaGb0tKOmLRe7yC/qSuDBzbLZyGxc/Ox54W01/7sRcGKSbydTokWmK4+zy840tVETkk7zuUJz/EFW0UKk+yy9629p442wFi8bmyO4Jstrdo9EWbpefawtVn48VwL0JdSHTeOWsS97qr3vrs0G6mWgf+c9qDA0JPL//nOJ4vC/yqyUmVETkk7PlJ95/iCrGUEVxL79YdfkB6oyhUnsdKq2FO8vPNZHo97aipA8PzCzGO6ccmDYmK/DJcWx47JxnvDzqyNfn5ny9DYxr7CwmQ0LusRcrTKiIyKfhdaji+8EbzTFUrglaLBY4Nas4Vd/X3nfhrkOltXBn+bkKpctvxZwyrJhTFvK/EW+c1dZb/XX/vLjXO9cxUxyQ7h+jQ0Q+uU+zj1f+1tmJlMloiOngfFMUx1AZ3FoqEq2FCvC9vhL5NtzlF7iFyv171yQq3ienaC3xPk1EFDOmBEmoXFvQovFbtLMlJxYtdd4WZgyXr4elKUHHUAHKAeLxviVSvJD/370kRO512r3amRUJFePtD6NDRD75+0EcT6LZ5QcAKV8Pao7lLD81hqr4TKgSdJYfoGy5YwtVcPwNSnet05LkuSk3E6rgcQwVEfnkPuYmXkVzc2RguIUqFg+UeysKMSQu4PaiyAdC++rys3296GOhlw1q451ymyEmVMFwhsnbwrTKTZQ94+n6eUq0MXexxoSKiHxKlFl+yq1notnlF/04NMwbj4Z541V5L19bz2ysm4i6KTbcVTZKlX8nloxsoQqZv5Zm14TJ2z6HlhgvG5LImFARkU8mFcfzRFPUu/y+7hqL9z0N3bk/IJ0tEBmpZswen6NFkSLmOtMv3rui44XBbcshV65Jt7duZsWgdK6S7ldi/XQgophKlGUTXB8KUenyM8euhUpN7hvfxntiHAzO8gudPIbKS7zMAeLJMVTBY3SIyCfnCtOuW3fEo2iulA7Edpafmjy2nkms4nsV7iy/ZF5DyV+XX8AxVOzyCxq7/IjIp/vvGI0LX13HQ7OKtS6KX4pB6VHolhvu8kusFhH3B6Qaa1tpLdxZfhaTAX0hrJKuJ/728nN9zVs4LS5JWDInpcFgQkVEPhVlp+O//m2a1sUIyBSjWX6J1uXn2UKVWOX3JtxZfsm8KKU8yy/A5sjuK9G7X5OI65bFEhMqIkp41jQzrKkmZKSao5I0DI+hSqwHiscYqiRuoUrm7ip5Lz8v8XJ9zVv9UI6hSvz6E01MqIgo4aWajXhv3d0wGaOzeWuidvl5zPJLsPJ7E34LVfImVP66/FxbXb19djgoPXhMqIhIF/Ks0VukMlEHpQfapy0Rud5CKPeTzItSOsPkfVC6weXvntdauDly0BgdIqIAhldKT6yExNdK6YnM2dpiNEghtUYmc+vK8B6O3galB1opnS1UwWJ0iIgCGN7LL7F+ZOqxhcrZjRnqvdjH3VwVPt5X/Y8GZ6Jk8bIwZ+CtZzgoPVjs8iMiCqAoOx0AMHpkmsYlCY0kSTBIwJC4+b0eBqUPt7aEdi8b6ybClpmKmkn50ShWXJNXSvfaQuWybIKXfIktVMFjQkVEFMBDs4oxbXQmJhdatS5KyEyG4fWXEqyBzStDmC1U6RYTVt09LhpFinvBLuzpdS8/bj0TNCZUREQBGA0SKoqytC5GWIwGCRi8+fdE67L0xnkLbC0Jnrz1jLdZfgFXSueg9GAxOkREOqbc+07Dgqgk3DFUyayiKBMmg4SKMZ6/FLgm2YEW9mQS6x9bqIiIdCzQoONEYwhzDFUyW3j7aNROtsl7c7oyKWb5eV5r4V5+QWN0iIh0TLEStg6SELZQhcdbMgUE7vKzcJZf0BgdIiIdM7CFivwIadmEBFuHLdaYUBER6ZjeWqict6CHe4kHgeqH0SD53VyZhjE6REQ6ZtRZQuVv1W8Knet2Sr6qhzORYkLlH6NDRKRjuhuUzjFUqlKMofIRU+c4KjPHUPnF6BAR6ZhuW6g4nkcVyhYq7zF1JlJch8o/RoeISMcUY2R00ELFWX7qCqZ+ODdQ9rYXIA1jQkVEpGNGxcKNGhZEJZzlpy7Xlj5f+TbHUAUnqtH58ssvUV9fD6vViqysLCxfvhxXrlzxe01vby8aGhowatQojBgxAosXL8YXX3yhOKe9vR0LFixAeno68vLysGHDBgwMDCjOaWpqwp133omUlBSMHz8e27dvVxzfsmULZs6ciYyMDOTl5eG+++7D2bNnVblvIqJ44foM1EOrDmf5qSuYWaBpX69hleZjLSu6KaoJVX19PU6dOoXGxkbs3r0bBw8exMqVK/1es3btWrz11lvYuXMnmpubcfHiRSxatEg+Pjg4iAULFqCvrw8ffvghXnrpJWzfvh2bN2+Wz2lra8OCBQswb948HD9+HGvWrMH3vvc9vPvuu/I5zc3NaGhowKFDh9DY2Ij+/n7U1NTg6tWr6geCiEgjihYqPXT5cZafqoKpH+v+5VY8fFcxbk/Q/SxjRkTJ6dOnBQDx0Ucfya/t3btXSJIkLly44PWazs5OYTabxc6dO+XXPvnkEwFAtLS0CCGE2LNnjzAYDMLhcMjnbNu2TVitVnHjxg0hhBAbN24UkydPVrz3kiVLRG1trc/ydnR0CACiubk56Hvs6uoSAERXV1fQ1xARxdKiFz4QJU/sFiVP7BZ9A4NaFydiDS+3ipIndotH/+ew1kXRhf1nvpDrxyNJFNNoPL+jluK3tLQgKysLM2bMkF+rrq6GwWDA4cOHvV7T2tqK/v5+VFdXy6+Vl5ejuLgYLS0t8vtOnToV+fn58jm1tbXo7u7GqVOn5HNc38N5jvM9vOnq6gIAZGdn+zznxo0b6O7uVnwREcUz14HGuhiUzjFUqlJuPaNhQXQgagmVw+FAXl6e4jWTyYTs7Gw4HA6f11gsFmRlKZsV8/Pz5WscDocimXIedx7zd053dzeuX7/u8e8ODQ1hzZo1mD17NqZMmeLznrZs2YLMzEz5q6ioyOe5RETxwBjEOkOJhLP81OXadaqHhFtLISdUTz75JCRJ8vt15swZn9cLISCF+J8W7DX+zhFC+DynoaEBJ0+exI4dO/y+/6ZNm9DV1SV/ff755wHLRESkJecsLr0kIM6f4VyHSh3KWX6MaSRMoV6wfv16LFu2zO85ZWVlsNls6OjoULw+MDCAr776yqP1yMlms6Gvrw+dnZ2KVqqOjg75GpvNhiNHjiiuc84CdD3HfWZgR0cHrFYrUlNTFa+vXr1aHjA/ZswYv/eVkpKClJQUv+cQEcUTeWVxnTwsnbMWjRyUrgrlLD8NC6IDISdUubm5yM3NDXie3W5HZ2cnWltbMX36dADA/v37MTQ0hMrKSq/XTJ8+HWazGfv27cPixYsBAJ9++ina29tht9vl9/3Zz36Gjo4OuUuxsbERVqsVkyZNks/Zs2eP4r0bGxvl9wButlj94Ac/wK5du9DU1ITS0tIQI0FEFP+cD0y9tFBxDJW6TDqbBaqlqOWjt912G+rq6rBixQocOXIEH3zwAVavXo0HHngAhYWFAIALFy6gvLxcbnHKzMzE8uXLsW7dOhw4cACtra1YtmwZ7HY77rrrLgBATU0NJk2ahEceeQR//etf8e677+LHP/4xGhoa5NajVatW4fz589i4cSPOnDmDF154Aa+//jrWrl0rl6+hoQF/+MMf8MorryAjIwMOhwMOh8PrGCsiokRl1FlCxb381KW3MXZaimoD38svv4zy8nJUVVXhW9/6Fr7xjW/gd7/7nXy8v78fZ8+exbVr1+TXfvWrX+Hb3/42Fi9ejDlz5sBms+GNN96QjxuNRuzevRtGoxF2ux0PP/wwHn30UTzzzDPyOaWlpXj77bfR2NiIiooK/OIXv8CLL76I2tpa+Zxt27ahq6sLc+fORUFBgfz12muvRTMkREQx5Xxg6uVZyRYqdZldxlDppVtYKyF3+YUiOzsbr7zyis/jY8eOlQeLO6WmpmLr1q3YunWrz+tKSko8uvTczZs3D8eOHfN53P3fJSLSI7ZQkT9GLpugGg5BIyLSMb2NoXImVNxXTh2ucWSXX2RYI4mIdMw5G04vA46HZ/np4360pmyhYkwjwYSKiEjH9JaAlIy65es/0zUuiT6YOIZKNVEdQ0VERNrSWwtVfWUxZo/PwVgmVKpQLJvAJpaIMKEiItIxvY2hkiQJpTm3aF0M3WCXn3qYjxIR6ZjeZvmRulyXTWBCFRkmVEREOqa3dahIXUbF1jOsJJFgQkVEpGN66/IjdZldBk6xgSoyTKiIiHTMILdQ8WlJngwGSU6kOMsvMkyoiIh0jC1UFIizlYoLe0aGCRURkY5xUDoFYmQrpiqYUBER6ZizG4cPS/LFxIkLqmBCRUSkY0YjW6jIPxPriCqYUBER6RjHUFEgztX0JbZiRoQJFRGRjjkflpzBRb44F/dkHYkMEyoiIh1zLoTNFiryhYu/qoMJFRGRjhmNnBJP/smD0llHIsKEiohIx+QxVHxWkg8mZ9LNLr+IMKEiItKxopHpN//MTte4JBSvhicuaFyQBGfSugBERBQ9s8ePQuPaOSgZdYvWRaE45Vw2gS1UkWFCRUSkY5IkYUJ+htbFoDjmnAnKhCoybOAjIiJKYmbO8lMFEyoiIqIkxv0e1cGEioiIKIk5x1BxpfTIMKEiIiJKYibnavpsoYoIEyoiIqIklpVuBgBYU80alySxcZYfERFREnu8ZiJmjs1G1W15WhcloTGhIiIiSmJF2el4+K4SrYuR8NjlR0RERBQhJlREREREEWJCRURERBQhJlREREREEWJCRURERBQhJlREREREEWJCRURERBQhJlREREREEWJCRURERBQhJlREREREEWJCRURERBQhJlREREREEWJCRURERBQhk9YFSGRCCABAd3e3xiUhIiKiYDmf287nuBqYUEWgp6cHAFBUVKRxSYiIiChUPT09yMzMVOW9JKFmepZkhoaGcPHiRWRkZECSJNXet7u7G0VFRfj8889htVpVe99kwNiFh3ELH2MXHsYtfIxdeFzjlpGRgZ6eHhQWFsJgUGf0E1uoImAwGDBmzJiovb/VauWHJUyMXXgYt/AxduFh3MLH2IXHGTe1WqacOCidiIiIKEJMqIiIiIgiZHz66aef1roQ5MloNGLu3LkwmdgrGyrGLjyMW/gYu/AwbuFj7MITzbhxUDoRERFRhNjlR0RERBQhJlREREREEWJCRURERBQhJlREREREEWJCRURERBQhJlRxaOvWrRg7dixSU1NRWVmJI0eOaF2kuPL0009DkiTFV3l5uXy8t7cXDQ0NGDVqFEaMGIHFixfjiy++0LDE2jl48CDuvfdeFBYWQpIk/OlPf1IcF0Jg8+bNKCgoQFpaGqqrq/HZZ58pzvnyyy9RX18Pq9WKrKwsLF++HFeuXInlbcRcoLgtW7bMow7W1dUpzknGuG3ZsgUzZ85ERkYG8vLycN999+Hs2bOKc4L5fLa3t2PBggVIT09HXl4eNmzYgIGBgVjeSswFE7u5c+d61LtVq1Ypzkm22G3btg3Tpk2TVz+32+3Yu3evfDyW9Y0JVZx57bXXsG7dOjz11FP4y1/+goqKCtTW1qKjo0ProsWVyZMn49KlS/LX+++/Lx9bu3Yt3nrrLezcuRPNzc24ePEiFi1apGFptXP16lVUVFTgt7/9rdfjzz33HH7zm99g27ZtOHz4MG655RbU1tait7dXPqe+vh6nTp1CY2Mjdu/ejYMHD2LlypWxugVNBIobANTV1Snq4Kuvvqo4noxxa25uRkNDAw4dOoTGxkb09/ejpqYGV69elc8J9PkcHBzEggUL0NfXhw8//BAvvfQStm/fjs2bN2txSzETTOwAYMWKFYp699xzz8nHkjF2Y8aMwbPPPoujR4/i6NGjuOeee7Bw4UKcOnUKQIzrm6C4MmvWLNHQ0CB/Pzg4KAoLC8WWLVs0LFV8eeqpp0RFRYXXY52dncJsNoudO3fKr33yyScCgGhpaYlVEeMSALFr1y75+6GhIWGz2cTPf/5z+bXOzk6RkpIiXn31VSGEEKdPnxYAxEcffSSfs3fvXiFJkrhw4ULsCq8h97gJIcTSpUvFwoULfV7DuN3U0dEhAIjm5mYhRHCfzz179giDwSAcDod8zrZt24TVahU3btyI7Q1oyD12Qghx9913ix/+8Ic+r2Hsbho5cqR48cUXY17f2EIVR/r6+tDa2orq6mr5NYPBgOrqarS0tGhYsvjz2WefobCwEGVlZaivr0d7ezsAoLW1Ff39/YoYlpeXo7i4mDF009bWBofDoYhVZmYmKisr5Vi1tLQgKysLM2bMkM+prq6GwWDA4cOHY17meNLU1IS8vDxMnDgRjz32GC5fviwfY9xu6urqAgBkZ2cDCO7z2dLSgqlTpyI/P18+p7a2Ft3d3XKrQzJwj53Tyy+/jJycHEyZMgWbNm3CtWvX5GPJHrvBwUHs2LEDV69ehd1uj3l945r1ceSf//wnBgcHFf+xAJCfn48zZ85oVKr4U1lZie3bt2PixIm4dOkSfvrTn+Kb3/wmTp48CYfDAYvFgqysLMU1+fn5cDgcGpU4Pjnj4a2+OY85HA7k5eUpjptMJmRnZyd1POvq6rBo0SKUlpbi/Pnz+NGPfoT58+ejpaUFRqORcQMwNDSENWvWYPbs2ZgyZQoABPX5dDgcXuuk81gy8BY7AHjooYdQUlKCwsJCnDhxAk888QTOnj2LN954A0Dyxu7jjz+G3W5Hb28vRowYgV27dmHSpEk4fvx4TOsbE6oEIISAJElaFyNuzJ8/X/77tGnTUFlZiZKSErz++utIS0vzeg1jGDwhBAwG/43XyR7PBx54QP771KlTMW3aNIwbNw5NTU2oqqryeV0yxa2hoQEnT55UjG/0Jdi4JHvsXMfgTZ06FQUFBaiqqsL58+cxbtw4v++p59hNnDgRx48fR2dnJ/74xz9i6dKlaG5u9nl+tOobu/ziSE5ODoxGo8cMhI6ODo8MmoZlZWXh1ltvxblz52Cz2dDX14fOzk7FOYyhJ5vNBgB+65vNZvOYEDEwMICvvvqK8XRRVlaGnJwcnDt3DgDjtnr1auzevRsHDhzAmDFj5NeD+XzabDaPOun8Pplj501lZSUAKOpdMsbOYrFg/PjxmDFjBrZs2YKKigr8+te/jnl9Y0IVRywWC6ZPn459+/bJrw0NDWHfvn2w2+0aliy+XblyBefPn0dBQQGmT58Os9msiOGnn36K9vZ2xtBNaWkpbDabIlbd3d04fPiwHCu73Y7Ozk60trbK5+zfvx9DQ0PyD3MC/vGPf+Dy5csoKCgAkLxxE0Jg9erV2LVrF/bv34/S0lLF8WA+n3a7HR9//LEiIW1sbITVasWkSZNicyMaCBQ7b44fPw4AinqXjLFzNzQ0hBs3bsS+vkU0lJ5Ut2PHDmGxWMT27dvF6dOnxcqVK0VWVpZiBkKyW79+vWhqahJtbW3igw8+ENXV1SInJ0d0dHQIIYRYtWqVKC4uFvv37xdHjx4Vdrtd2O12jUutjZ6eHnHs2DFx7NgxAUD88pe/FMeOHRN///vfhRBCPPvssyIrK0u8+eab4sSJE2LhwoWitLRUXL9+XX6Puro6cccdd4jDhw+L999/X0yYMEE8+OCDWt1STPiLW09Pj3j88cdFS0uLaGtrE++995648847xYQJE0Rvb6/8HskYt8cee0xkZmaKpqYmcenSJfnr2rVr8jmBPp8DAwNiypQpoqamRhw/fly88847Ijc3V2zatEmLW4qZQLE7d+6ceOaZZ8TRo0dFW1ubePPNN0VZWZmYM2eO/B7JGLtNmzaJgwcPira2NnHixAnx5JNPCkmSxJ///GchRGzrGxOqOPT888+L4uJiYbFYxKxZs8ShQ4e0LlJcWbJkiSgoKBAWi0WMHj1aLFmyRJw7d04+fv36dfH9739fjBw5UqSnp4v7779fXLp0ScMSa+fAgQMCgMfX0qVLhRA3l074yU9+IvLz80VKSoqoqqoSZ8+eVbzH5cuXxYMPPihGjBghrFar+M53viN6eno0uJvY8Re3a9euiZqaGpGbmyvMZrMoKSkRK1as8PilJxnj5i1mAMTvf/97+ZxgPp9/+9vfxPz580VaWprIyckR69evF/39/TG+m9gKFLv29nYxZ84ckZ2dLVJSUsT48ePFhg0bRFdXl+J9ki123/3ud0VJSYmwWCwiNzdXVFVVycmUELGtb5IQQoTWpkVERERErjiGioiIiChCTKiIiIiIIsSEioiIiChCTKiIiIiIIsSEioiIiChCTKiIiIiIIsSEioiIiChCTKiIiIiIIsSEioiIiChCTKiIiIiIIsSEioiIiChC/w8JYtRinf8zggAAAABJRU5ErkJggg==",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x13087a7d0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{PyCall.PyObject,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x132b72a10>"
      ]
     },
     "execution_count": 292,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(y_-y0_)\n",
    "plot(y-y0,\"r\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Singular value decomposition (SVD)\n",
    "Let $A$ be an $m\\times n$ matrix. \n",
    "\n",
    "* Assuming that $m\\geq n$.\n",
    "\n",
    "The reduced singular value decomposition of $A$ is denoted as\n",
    "$$A = U \\Sigma V^\\top.$$\n",
    "\n",
    "$\\Sigma$ is and $n\\times n$ diagonal matrix, containing the \n",
    "singular values of $A$.\n",
    "\n",
    "$$\\Sigma = \\begin{pmatrix} \\sigma_1 \\cr & \\sigma_2 \\cr &&\\ddots \\cr &&& \\sigma_n \\cr \\end{pmatrix},$$\n",
    "where $\\sigma_1 \\geq \\sigma_2 \\geq \\cdots \\geq \\sigma_n \\geq 0$.\n",
    "\n",
    "$U \\in \\mathbb R^{m\\times n}$ matrix with orthonormal columns.\n",
    "\n",
    "$V \\in \\mathbb R^{n\\times n}$ matrix with orthonormal columns: $V^\\top V=I=VV^\\top$. *$V$ is unitary.*\n",
    "\n",
    "* Assuming that $m<n$\n",
    "\n",
    "\n",
    "$U \\in \\mathbb R^{m\\times m}$ matrix with orthonormal columns: $U^\\top U=I=UU^\\top$. *$U$ is unitary.*\n",
    "\n",
    "$V \\in \\mathbb R^{m\\times n}$ matrix with orthonormal columns.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Verify that USV' = A:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "4×5 Array{Float64,2}:\n",
       " 1.0  0.0  0.0  0.0  2.0\n",
       " 0.0  0.0  3.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  2.0  0.0  0.0  0.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " A = [1. 0. 0. 0. 2.; \n",
    "      0. 0. 3. 0. 0.; \n",
    "      0. 0. 0. 0. 0.; \n",
    "      0. 2. 0. 0. 0.]\n",
    "\n",
    "println(\"Verify that USV' = A:\")\n",
    "U, S, V = svd(A)\n",
    "\n",
    "U*diagm(S)*V'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using SVD to solve the least square problem\n",
    "\n",
    "$$\\min_x ||Ax-b||_2^2$$\n",
    "\n",
    "* SVD is particularly useful when $A$ is rank-difficient.\n",
    "* If the number of linearly independent columns of $A$ is smaller than the number of rows, $A$ is rank-difficient. In a least square problem, A has more rows than columns, and is a typical rank-difficient case.\n",
    "\n",
    "#### Algorithm: \n",
    "\n",
    "1. Compute the SVD of $A$:   `U,S,V=svd(A)`\n",
    "2. Make a decision on rank: choose $r$ so that $\\sigma_r>tol>0$.\n",
    "3. Truncate U,S,V accordingly: \n",
    "```\n",
    "Vr=V[:,1:r]\n",
    "Sr=S[1:r,1:r]\n",
    "Ur=U[:,1:r]\n",
    "```\n",
    "4. `xr=Vr*(Sr\\Ur'b)`\n",
    "5. General solution is: `x=xr+V[:,r+1:n]*rand(m-r)`, where `m=size(A,1)`\n",
    "\n",
    "`Ur'b` projects the data vector `b` to the column space of `Ur`.\n",
    "\n",
    "Left multiplication of `Vr` transform the solution to coordinates using teh standard basis.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Principal component analysis (PCA) and dimension reduction\n",
    "\n",
    "* An important application of the Singular Value Decomposition.\n",
    "\n",
    "* PCA is used as a preprocessing steps for certain machine learning applications.\n",
    "\n",
    "Assuming that the columns of $A$ corresponds to the data points and each row of $A$ have zero average.\n",
    "This way the  principal components correspond to the eigenvalue/eigenvectors of the covariance matrix: $AA^\\top$.\n",
    "\n",
    "$AA^\\top x = US^2U^\\top x = US^2(U^\\top x)$\n",
    "\n",
    "(Typically in data science, the data matrix is $A^\\top$ in our discussion)\n",
    "\n",
    "### Reduction of the dimension of data by projection onto a subset of signular vectors\n",
    "\n",
    "Objectives: Keep a few directions (dimensions) in which the data have the largest variance. Ignore the dimensions in which the data is more or less constant.\n",
    "\n",
    "Similar to the truncation in the previous excercises involving stablizing least square approximations,\n",
    "one can truncate the last few singular values.\n",
    "\n",
    "0. \"Centering the data\"\n",
    "1. `U,S,V=svd(A)`\n",
    "2. Truncation: \n",
    "```\n",
    "Ur=U[:,1:r]\n",
    "Sr=S[1:r,1:r]\n",
    "```\n",
    "3. Projection of the data vectors onto the truncated subspace: `Y=Ur'A`\n",
    "4. Change back to the original coordinates: `Af=Ur*Y`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Array{Float64,2}:\n",
       " -0.713174  -0.700987\n",
       " -0.700987   0.713174"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "2-element Array{Float64,1}:\n",
       " 23.3837 \n",
       "  4.89087"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "80×2 Array{Float64,2}:\n",
       " -0.185567     -0.0235426 \n",
       " -0.0932554    -0.00778115\n",
       " -0.166326     -0.297977  \n",
       " -0.160997     -0.0996631 \n",
       " -0.178109      0.0406689 \n",
       " -0.14907      -0.0667124 \n",
       " -0.176169      0.265094  \n",
       " -0.128763     -0.029455  \n",
       " -0.159981     -0.0543919 \n",
       " -0.162165     -0.0493364 \n",
       " -0.161807     -0.0168546 \n",
       " -0.149208     -0.239077  \n",
       " -0.130688      0.164556  \n",
       "  ⋮                       \n",
       "  0.0250313     0.0164761 \n",
       "  0.0603593    -0.0392587 \n",
       "  0.0109195     0.0170029 \n",
       "  0.0349341    -0.164569  \n",
       "  0.0255703    -0.0311581 \n",
       "  0.0491881    -0.0771716 \n",
       " -0.000908313  -0.160983  \n",
       "  0.0102047    -0.123192  \n",
       "  0.0148357     0.114992  \n",
       "  0.0326755    -0.087626  \n",
       "  0.0509278     0.0173434 \n",
       "  0.0487088     0.0440463 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x1415d4f10>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v1=[2.5 2.5]'\n",
    "v2=[0.5 0.5]'\n",
    "\n",
    "g1=v1.+0.5*randn(2, 20)\n",
    "g2=-v1.+0.5*randn(2, 20)\n",
    "\n",
    "g3=v2.+0.45*randn(2, 20)\n",
    "g4=-v2.+0.45*randn(2, 20)\n",
    "\n",
    "A=[g1 g2 g3 g4]\n",
    "\n",
    "C=sum(A,2)./size(A,2)\n",
    "\n",
    "Ac=A.-C\n",
    "\n",
    "using PyPlot\n",
    "scatter( Ac[1,:], Ac[2,:])\n",
    "\n",
    "U,S,V=svd(Ac)\n",
    "\n",
    "#display(C)\n",
    "display(U)\n",
    "display(S)\n",
    "display(V)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×80 Array{Float64,2}:\n",
       " -3.63056  -3.65038   -3.35191   …   0.327275   0.950424   0.62948 \n",
       " -0.54416  -0.393849  -0.110378     -0.155035  -0.517233  -0.971075"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y=U'*Ac"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x141482090>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject Text(24,0.5,u'u2')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(Y[1,:],\"r\")\n",
    "plot(Y[2,:])\n",
    "\n",
    "title(\"Strengths of data in each principal direction\")\n",
    "xlabel(\"u1\")\n",
    "ylabel(\"u2\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x141496690>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.collections.PathCollection object at 0x1412e6d10>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y[2,:].=0.0\n",
    "\n",
    "xp= U*Y\n",
    "\n",
    "scatter(xp[1,:], xp[2,:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x14146d490>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.collections.PathCollection object at 0x138dfd910>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z=U[:,1]U[:,1]'*Ac\n",
    "\n",
    "scatter( Z[1,:], Z[2,:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Sparsity promoting algorithms for least square fitting problems"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Due to noise in the data, a sensible formulation of the problem is:\n",
    "$$\\min_{x\\in \\mathbb{R}^n} ||x||_1~~~s.t.~~~||Ax-b||_2<\\epsilon.~~~~~~~(Bu)$$\n",
    "\n",
    "One way to find a solution is to solve *a sequence of unconstrained problems*:\n",
    "$$x^{k+1}\\leftarrow\\min_{x\\in \\mathbb{R}^n} ||x||_1 +\\frac{\\lambda}{2}||Ax-b^{k+1}||_2^2,~~~~~~~(Bk)$$\n",
    "where $$b^{k+1} := b+(b^k-Ax^k).$$\n",
    "\n",
    "Problem (Bk) can be in turn replaced by a linearized version (LBk) so that (LBk) can be solved by a simple analytical formula component-by-component, decoupled.\n",
    "\n",
    "$$x^{k+1}\\leftarrow\\min_{x\\in \\mathbb{R}^n} \\mu'||x||_1 +\\frac{1}{2}||x-\\left(x^k+A^\\top(Ax^k - b^{k+1})\\right)||_2^2+\\frac{1}{2\\delta}||x-x^k||_2^2 ,~~~~~~~(LBk)'$$\n",
    "\n",
    "where \n",
    "\n",
    "$x^k-A^\\top(Au^k - b^{k+1})$ is a lienar approximation of $\\frac{1}{2}||Au-b^{k+1}||_2^2$ around $u^k$.\n",
    "\n",
    "Equivalently, we have the linearized Bregman iterations defined as:\n",
    "\n",
    "$$x^{k+1}\\leftarrow\\min_{x\\in \\mathbb{R}^n} \\mu||x||_1 +\\frac{1}{2}||x-\\left(x^k-\\delta A^\\top(Au^k - b^{k+1})\\right)||_2^2,~~~b^{k+1} := b+(b^k-Ax^k).~~~~(LBk)$$\n",
    "\n",
    "(LBk) has an explicit solution component-by-component. See teh code below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The shrinkage formula\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "shrink (generic function with 1 method)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function shrink(f, μ)\n",
    "   absf=abs(f)\n",
    "    \n",
    "   (absf> μ? f-μ*f/absf:0.0)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "linearized_Bregman_iterationsv2 (generic function with 1 method)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function linearized_Bregman_iterations(A, f, u; δ=0.01, μ=10.0, kmax=14)\n",
    "    v=zeros(size(u))\n",
    "    \n",
    "    μδ=μ*δ\n",
    "    \n",
    "    for k in 1:kmax\n",
    "        #compute vk\n",
    "        v=v+δ*A'*(f-A*u)\n",
    "        \n",
    "        #apply shrinkage component by component\n",
    "        for j in eachindex(u)\n",
    "           u[j]=δ*shrink(v[j], μδ)\n",
    "        end\n",
    "    end\n",
    "    \n",
    "    display(u)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "25-element Array{Float64,1}:\n",
       "  0.0       \n",
       "  0.0       \n",
       "  0.0       \n",
       "  0.0       \n",
       "  0.0       \n",
       "  0.0       \n",
       "  0.350467  \n",
       "  0.0       \n",
       "  0.0       \n",
       "  0.0       \n",
       "  0.0       \n",
       "  0.246383  \n",
       " -0.359498  \n",
       "  0.0       \n",
       "  0.00961444\n",
       " -0.10298   \n",
       "  0.0       \n",
       "  0.0       \n",
       "  0.0       \n",
       "  0.0       \n",
       "  0.534656  \n",
       "  0.0       \n",
       "  0.0       \n",
       "  0.208761  \n",
       "  0.0       "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "5-element Array{Float64,1}:\n",
       "  7.32747e-15\n",
       " -1.44329e-15\n",
       " -3.34177e-14\n",
       "  1.40998e-14\n",
       "  2.19269e-14"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A=rand(5,25)\n",
    "f=rand(5)\n",
    "u0=ones(25)\n",
    "u=copy(u0)\n",
    "\n",
    "linearized_Bregman_iterations(A,f, u0,δ=0.01,kmax=15000)\n",
    "\n",
    "display(A*u0-f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x1288fec10>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{PyCall.PyObject,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x12f4b9610>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using PyPlot\n",
    "\n",
    "plot(u0,\"x\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using SVD to solve under-dertermined systems"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5-element Array{Float64,1}:\n",
       "  4.44089e-16\n",
       "  3.33067e-16\n",
       " -2.22045e-16\n",
       " -5.55112e-17\n",
       "  5.55112e-17"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "25-element Array{Float64,1}:\n",
       "  0.0154101\n",
       "  0.0414672\n",
       " -0.0523315\n",
       " -0.103508 \n",
       "  0.153444 \n",
       " -0.0190207\n",
       "  0.194119 \n",
       " -0.0179502\n",
       " -0.0347809\n",
       "  0.0436796\n",
       "  0.156676 \n",
       "  0.135425 \n",
       " -0.212702 \n",
       "  0.0295795\n",
       "  0.112708 \n",
       " -0.148172 \n",
       " -0.142455 \n",
       "  0.126139 \n",
       "  0.105599 \n",
       "  0.0151803\n",
       "  0.332523 \n",
       "  0.0453137\n",
       "  0.0860937\n",
       "  0.203467 \n",
       "  0.0366871"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "U,S,V=svd(A)\n",
    "\n",
    "# Ax = USV'x = b\n",
    "y=U'f #SV'x=U'b=:y\n",
    "z=y./S #V'x=S\\y\n",
    "x=V*z\n",
    "\n",
    "#verify the solution\n",
    "display(A*x-f)\n",
    "\n",
    "display(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x136ae5250>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{PyCall.PyObject,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x136ad7150>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using PyPlot\n",
    "\n",
    "plot(x)\n",
    "plot(u0,\"rx\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SVD solution has 2-norm: 0.643792266407551\n",
      "l1 solution has 2-norm:0.8080260187438496\n"
     ]
    }
   ],
   "source": [
    "println(\"SVD solution has 2-norm: \", norm(x))\n",
    "println(\"l1 solution has 2-norm:\", norm(u0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.564430965964316"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm(x,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8123601048701816"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm(u0,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "length(find(u0))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 0.6.1",
   "language": "julia",
   "name": "julia-0.6"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "0.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}