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    "# Problem Sheet 1\n",
    "\n",
    "## Linear regression of time series data\n",
    "\n",
    "Recall the Oxford temperature data considered in the lecture. In this lab we will try to approximate the known values of the temperature in time, and to predict the unknown values in the future. As a by-product, we will refresh our _numpy_ skills.\n",
    "\n",
    "Once again, here is the prediction rule we would like to explore:\n",
    "\n",
    "$$\n",
    "h_{\\boldsymbol\\theta} (x) = \\theta_0 + \\theta_1 x + \\cdots + \\theta_n x^n,\n",
    "$$\n",
    "\n",
    "where $x$ is the time value, and $\\boldsymbol\\theta = (\\theta_0,\\ldots,\\theta_n)$ is the vector of coefficients we will optimise. Given a dataset $D = (\\mathbf{X},\\mathbf{y})$ of months $\\mathbf{X}=\\{x_1,\\ldots,x_m\\}$ and temperature values $\\mathbf{y}=\\{y_1,\\ldots,y_m\\}$, we need to minimise the sum-of-squares loss\n",
    "\n",
    "$$\n",
    "L_{D}(\\boldsymbol\\theta) = \\frac{1}{m}\\sum_{i=1}^{m} (h_{\\boldsymbol\\theta} (x_i) - y_i)^2.\n",
    "$$"
   ]
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   "cell_type": "markdown",
   "id": "51da250e",
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   "source": [
    "## Warm-up\n",
    "- Prove that a vector of $m$ predictions $\\mathbf{\\hat y}:=(h_{\\boldsymbol\\theta}(x_1),\\ldots,h_{\\boldsymbol\\theta}(x_m))^\\top$ can be computed as a product of the _Vandermonde_ matrix \n",
    "$$\n",
    "V = \\begin{bmatrix} 1 & x_1 & \\cdots & x_1^n \\\\\n",
    "     1 & x_2 & \\cdots & x_2^n\\\\\n",
    "     \\vdots &  & & \\vdots \\\\\n",
    "     1 & x_m & \\cdots & x_m^n\n",
    "     \\end{bmatrix} \\in \\mathbb{R}^{m \\times (n+1)}\n",
    "$$\n",
    "and the parameter vector $\\boldsymbol\\theta$, $\\mathbf{\\hat y} = V\\boldsymbol\\theta.$\n"
   ]
  },
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   "cell_type": "markdown",
   "id": "4e41b4b4",
   "metadata": {},
   "source": [
    "## Task (a): sum-of-squares minimiser\n",
    "\n",
    "- **Prove** that any solution of Equation (1.2) in the lecture notes satisfies the first-order optimality conditions (Equation (1.1))\n",
    "$$\n",
    "\\frac{\\partial L_D(\\boldsymbol\\theta^*)}{\\partial \\theta_0} = \\cdots = \\frac{\\partial L_D(\\boldsymbol\\theta^*)}{\\partial \\theta_n} = 0\n",
    "$$\n",
    "in general.\n",
    "Recall that\n",
    "Equation (1.2) is a system of linear equations\n",
    "$$\n",
    "A \\boldsymbol\\theta^* = \\mathbf{b},\n",
    "$$\n",
    "where\n",
    "$$\n",
    "A = V^\\top V, \\qquad \\mathbf{b} = V^\\top \\mathbf{y}.\n",
    "$$"
   ]
  },
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   "id": "e2f4a632",
   "metadata": {},
   "source": [
    "---"
   ]
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J2tdJ/eUtM1mx1pbhrG6jult5mt5TGc7JFxuU+4yKu14f4K1nWtJuPHHhiHw5r1lq93qN/dWGqyWBFgS0amNvOzt5I79xXnvwt8M+LvD3hHx3Mtv4jv8AXJ9K2y6Xq+kvawT3R3B3ik85/NblsBCgI24xmov7vN/dT+dtvv0NI6rXvb5X3+7U+sqK+S/h74D8Yp4I1jSVh8QQaVc+INIuLbz7d7C5+zieIXnyGWR0XajZy3K5IHNej+KPgfZLfeEPD2nprL+EBfXlzf2i6lPsRTbHZGz7/M8vzQrBd33j1xxVWdm/l+X+enoZ8+trf021+n4nqXivxfYeDbWxn1Bblo7y9hsI/stu8xEkrhULBQdq5PLHgd626+ZPFlrrWjeAfhr9p8NeKtV8R6PqcbiTSo5pWgs4rrDLNtcBy0AXAfcW571e8beCPEPiPxR4q8V2llrgvrd9Hm0CJriSJYslftJEIYKWCswcMD09qqMOZ2v1t8tF+r+41ScoqS6q9vn/AMMfRtFfHFkw1T9oZNV1yXUn0u38UTW9rrMKXjRSyqHjisnZXFuI1fvgtuRQepr7GbO0464qFrBS7/194pe7UcO3/B/yOfXx9obSa/m9WODQiFv7qQFYYnK7ym/oWVcFgOm5e5rKt/jT4IuPB934qXxJZr4etGKTX8hZERgASPmAJPPYVxGk2Wj6t8A9U0nUbDVL5ori6g1O10aMvfrd/aXZ3RRzuLESLn+FlPSsDUtS8T6j8GfGMOraB4g8RxSRva6ALzSVGrbniZMzRA8bWI/e8Egk4GKmLur+Sf8AXr0/MOqT6v8Ar+vwPoWxvoNSsre7tZVntriNZYpUOVdGGQw9iDXP+KPiZ4W8F6rpuma5rlppt/qTiO1gnYhpCWCjtwCxABOBmqfwdup7n4YeGkudNv8ASLm2sIbWW01KAwzI8cao2VPbIOD3FcP8eNauZNSg8MjwdrmpaNqlsp1fWNH0z7WzQK5ItFwQQzHd8x4UMxHzEVrUShU5VqrkxblDm62PRtR+JPhjSfFtn4YvNatbfXrtQ8Ni7HewOcc4wCdpwCcmi2+JHhi88YT+FYdatZPEMKb308N+8Axk+xIBzgHIrwDxl4F8Ua94u8SaDJp+rPZ61rNrrGl3VrCVtY9qW3727nz8rwGBykPcoh/ixXU6prWseJvi8bP/AIRLWtGttEnmGjXzaUWs7u8khKG7mmU/LEA5UL1Y5J4Azmr2jfd30+78b6eflrat3Lol17/8P+HnbX2G38Z6Lea1qmj2uoQ3er6ZEs13YwNvmiVgSuVHc44FWPD3iGw8VaPb6nplwLmznGUcDByDggg8ggggg9CK8O+DHw9+IXgv4pXU3iC08Pvp8+lAXmqac9wZLq5MhYud6gbieo7LtA6V6B8IzFcXPjG9sW3aRda3M9rt+4SFVZWX1DSBzkdau35X+52/HdGfNrt1t+F/0PQ6KKKk0CiiigAooooAKKKKACiiigAooooAKKKKACiiigDO1z/j0T/fH8jXz3+018CpfjJ4btZ9Lkji8Q6WWa1WZtscyNjfGT2PygqemRg4BJH0Jrn/AB6J/vj+RrCoA/PC1+I3xu8ExWvhyGTXLBbNfs8Fn/ZqsQq8AKTGSw9CCa9n/Zd/Z71rSvEjfEDxjG1tqMm+WzspOJvMk3b5ZVx8pwxwvXLEnGBn6oooAij/AORg0T/rvJ/6Jkrs64yP/kYNE/67yf8AomSuzoAKK800DwvbeLNe8YXGo3+ts9vrBt4UttcvbaOOMW8DBVSKVVHLMenetz/hVui/8/niL/wptS/+SKAOvorkP+FW6L/z+eIv/Cm1L/5Io/4Vbov/AD+eIv8AwptS/wDkigDr6K5D/hVui/8AP54i/wDCm1L/AOSKP+FW6L/z+eIv/Cm1L/5IoA6+iuQ/4Vbov/P54i/8KbUv/kij/hVui/8AP54i/wDCm1L/AOSKAOvorkP+FW6L/wA/niL/AMKbUv8A5Io/4Vbov/P54i/8KbUv/kigDr6K5D/hVui/8/niL/wptS/+SKP+FW6L/wA/niL/AMKbUv8A5IoA6+iuQ/4Vbov/AD+eIv8AwptS/wDkij/hVui/8/niL/wptS/+SKAOvorkP+FW6L/z+eIv/Cm1L/5Io/4Vbov/AD+eIv8AwptS/wDkigDr6K5D/hVui/8AP54i/wDCm1L/AOSKP+FW6L/z+eIv/Cm1L/5IoA6+iuQ/4Vbov/P54i/8KbUv/kij/hVui/8AP54i/wDCm1L/AOSKAOvorkP+FW6L/wA/niL/AMKbUv8A5Io/4Vbov/P54i/8KbUv/kigDr6a1cl/wq3Rf+fzxF/4U2pf/JFI3wt0X/n78Rf+FNqX/wAkUAdBe/dNcTef8jRpH/XwP5GrN58MNGCn/S/EH/hS6l/8kVzVj4N0/QvGekXNtPqkknnbcXmr3d0mCD/BLKy598ZFAHsVFFFABXjv7RPjaPwevhKO9+I//CrtIv7+SG713zLCLhYWZI999DLEu5h/dyccGvYqx9Y8L2mtazoupzyTLPpMsksCxsArF0KHcCCSMHsRzUyTdreX5jPNfgv8UdX13TtO03WC+rTSWt9d22uSItu+oWsN0Yre4aJUVQZotkm5Qq/N8qgEAR+H/wBoC78TeLPBejW+j6Ppw1/SYNWb+2NdNtcSJIjMyWEQt2+2NEF/eZaLYGQ9GFdf47+FsXjbWNN1SLxFrnhq9tIZbWWTRZYUN3bSFS8EnmxSYBKDDx7JFydrrmseL4D2kaeE7E+K/EMnhvw3HaLb+H3NmbaeS2wYZpZfs/2guGCMdkyqSoBUqWB0i1J3n3/C8v0ce12ui1M5c3vcvy+5aa36372Vt3ocT8Dvi14sex8Fad4g0Ay6Nrs99ZWniCfVzcXr3ELTSAS2/lkLE8cT7H85m+VQyJnjpvFXxA8Y6H+0JoeiRWmlnwLJ4dvtTv5pb91uVaGWAGRYhatuKeYFCiUBhI5OCihuq0X4T6RoOm+FbK3uL14vDl5Ne2hkkQs7yRzRsJMKMjE74xjkLz1zY8R/Dmy8SeMNG8Rvf3tnd6dbXNjJb2/lNBfWs+wyQTLJGx27o42BjKNlcbiCQcYKUIw7pP7+VpX8k2n30utSmrprvb803b5J799dDl/Avxc8Ra9qegHxF4QtvDmj+Jo2k0O4h1Y3d02IjMsd3D5CLBI0Ks2I5JlBVlLfdLebfHf4oa14c+LGr6Tb+N/FXhqG10HT7nS7HQ9At72yur6e4u4gl5czWcq26u0UCAyT268t84wWX1bwJ8ELLwNqFhMfEmv6/ZaTG0GiabrE0EkOkRlSm2FkhSWQ+XiMPcPK4UEBvmYtuan8MdD1vWvEeoajC98viDSoNGvrO42tbvbxNcMAF25yftMgOSRgLgDBztLl6bfj/lf70a03ZTVS13bbbeN7dbWv1v0ueSeLP2v9F8E/ED/hFtTuPC0F1pz2ltrEF54ljtNRFxOiMBZWTxlrpFEiEsXj4JC72UgTwftIeLb/AFSygsvh1aS2mra1qXh3SriXxCEaS9tHuAXnT7OfKt2S2c+YpkkDfL5LDDHsNE+BsnhnVrO/0r4geLLMgW/9pwlrCZNZeFFjWW5MtozCRo0SNnhaIsEXPzANV/TPgnoWktoBhutQb+xdcvtft98iHdcXX2jzFf5OUH2qTaBgjC5JwcvTd/1t/wAG2vqQlHkab10t/wCAy9N5cvTbY5XTPj9rfizSfD9t4a8H2t34x1I3/wBo0vU9Ya1srNbK4NvcubpLeVnXzdqpiHcwdSyphtuVa/GvxprHxO8JRQaLplj4Xn0y/k1q3uNUY3FvcW0qxzGNVtW8wIclP3ieYr5YIRiurm/Z50q3s7D+xfEev+GtXsbu/urfWtNktmulW8nae4gKzQSQvEXYYDRkjYpB3DdWjH8D9HtLjw5PZ6lqlnJo4uEkKyRS/wBpR3Db7hLjzI24d/nJj8tgeFKr8tZSvLWOmv8AXy731vs7b1LkTajt+l/zt8t/lxXwZ/ay0D4xeMU0SxufDcq3tvJeaeujeJItRvViQ8i9tljU2rkEEKGk7hirDFe81wvw9+F03w6meG18Y+INU0GOLybLQdSFm9rYJnKrFIluk5Cj5QJJXwvHYY7qr0srGet32/r+ugUUUUhhRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQBzfxB/5FqT/rtF/6MWq3h/8A490+gqP4tHHgS/J4G6P/ANDWvMPiHbzSeJvhvdSnS7nS4tdgH2W6t5vtCTtwk0UyToq7QT8rxyA57VVvh83b8v8AP+tyJS5VJvor/n/ke8Q/dFTjpXhOrfFfx/dfFm70Pwx4YXUtA0m5gttQdltC7+YoYv5r6hFJEAp4/wBGl3YODWF4i8c6x4w8c+CLm41bQ7LQ28VtY2mhC1c6k7wBw0jTmcL/ALRjEJwCPn54iDU3GK6/ldK/4r+rhUl7OMm+n+Tdvwf9WPpSiuT+K99Lp/w51+eGeW2lFsUWaCRo5E3ELlWUgqeeCDkV5LqHiTX/AIa6l/bPiHVbyKO20CS2hgkle7ikeNlCTmESqJHkZ1GWZW65ZRzU8+rjb+tf8vxNeV2TXXT8Uv1Poaivmvwz+0H44l0bxBp2u6TY2Piiy1Wx0yO4u7aO2t4BdR71lnhgvbsAL0wJwWJUfJmui+IFn42j1L4dW7a14fvvE7alcgakulTQWUaeUefs32l3cgcbfOXJOcrjBqd4W9Yr77fkmheva/y1/wAvU9yor548Z+INW8cfDLwZrGrJoc0dvr9rHqNnLZ3AWeZLkRrLbul0hh2tlsOJQeAR3rc+JnxN8aaD4o8QxaG+hQaL4d0221W7+32k1xcXau7B4Yyk0axHahIkO/lgCmBkqMlKKkno3+Fk7/c/6ehm5KMuV9r/AItW/D+lqe10V4OPjB8Qde+K9xpnh3wvHeeFtNv4bDUHZbQyYZFd5TM2oJJFtDhgn2STeFGG+cFfeKpaxUu//D/imVdXaCivJPBPjyfQfgfrnia+ebWbjSm1a6Mc1xmSRYbicqm9ido2oFBPAGOwrnvC/wAX/H9p4F8Va/4z0aPS7S1sEutK1CGxtSs0smVSIQQanced8xjwxlhDb8fLjdSvu+yuOPvRUu/9fqv6ue+UV85+H/jr47m8O67a6ppmnW/ivTfEGlaQVuraO3iEd48K7nit727AZVkZh++5+XKrmus1/wAQfE7Q5/C/h43/AITl1zWdQuYP7YGm3Itkt47czB/sn2jd5mVZNnnkEYfcPuU91dbf8N/miOZJ2f8AWrX6HsFFfPHj7xFqXjr4N+Dda1OLRZ4l8Q6dDqljcWtxtuJo9TigEtu6XKGHbIvmgP5owArA8k6nxU+LfjHwv4k8Y/2L/YaaH4T0O11y7W+tZprm9Ej3AaCNllRYsrb8SEPgn7jZ4qMXLbvb8tfx/p6GkYuUVKKutPxdv1X3+R7nRXz94j+LnxCv/ivceHPC9paRWVrqVpZstz4bvL2OWB0jkuLg36TxW8DRq7DyHy52AjPmKtfQNJaxUu/9f18+wno7ej+8KK8u8J6Vd+I5vG3iGO9EHiG4nn0qxuZlLLYQRABECE4GXzIxGC2UznauOa+GGnz2K6z4M1qXxBofi6XT0u7nUovFNxrFvcIDtaW0e5Zjb/M3KeTFjd8m4LuGalzJNdUn96v+C1f4XB6N+tv0/Pb8bXPdqK8q/Zf1C71L4KaHLe393qdws15D9pv7qS5nZUu5kTfLIzO5CqBliTx1rR+NkekSeG4E1fV9bsQ8vl2un+H9SlsbrUbgqRHErwMspOecK4HHzZUEVrVj7OTjvZ2/rz7BH3t9D0SivlrxlP4paXSPCWr6nqx1Kx8MtqS31pq9xp8MMyuQ1xdXEEimYRrtHlksJGBJGCTWtrF9qHjDwt4FK6/rX/CyL2zt7i2ttM1OS0too1dfNvbmGNgjRMoIxKHBLBUGckLrp3t+av8Ag/Lz3tMXzWVrO19em3X5rz8tr/R9FfMPjL4u6h/wuvw0l2vjLStOs9a/syKwttA1IWt8pjYPcPIkBjmUtjaodgqqWIU5NetQxSeG/jMsFkzf2fr9hJdXVtk7IriJlAlA/hLqwBxjJTPJJNCV7ed/wV/y/wAvRSko3T6W/F2/M9EooopFhRRRQAUUUUAFFFFAHO6t/wAhCX8P5CqdXNW/5CEv4fyFU6ACiiigDR8G/wDIFf8A6+7n/wBHvWX8Uf8AkC6R/wBh3S//AEsirU8G/wDIFf8A6+7n/wBHvWX8Uf8AkC6R/wBh3S//AEsioA7GvFvA3hc6pfQXt14VNxGb2Rzqx1Zs/LIxDGLd6gDFe01S0nSbbRLJbW0QpCrMwUnPLEk/qaW01Lt/wB/Zt/XU8K8UapqGoaTK0N41hKNN8RfPBux+7ljwcFvvYBGe2SRiui1bxh4mt9SGjac+oXEum2FvJJc2umLP9qlkVj8+WHlr8o6ZPLeld3/wrvQ2UK1qXTy7uLazkgrcsGmB+pA+lVrv4Y6Vd/YyZ7+Ka2gFsZobplkmjByFkI+8AScfU0/spf11/wA0O/updr/jb/Io+Ftc1/xF4ruVupk0y0srS1ll03yQzmSaNiys+eNrL2681yPxGs7y18U+INZe/wDtK2FhB9ms5YyEj3yqCcq4z68ivWNM8PWOj3l1c2sRjluEijk+YkbYwQg/AE1W1jwfpmufbftcLP8AbI0imwxGVRtyj86UtZJx8/yYoO1uby/M8pj8Zatp+oahpOn/AG5ri71a/lNxa232uSJI2QBVRmAxl/XitXVPF/jCPQdIubiC70iH/SFvbuHTxcTKUkVYnaHd8iMpZ2xkqQBXZX3w10W+hZQtxazG7kvRcW0xSVJH+/huwPcdOBSXXw20q4sbG2Se/tWsw6pcW926StvIL7m/i3MAT7+lG0V3G7OTZleOtYfVfgnquo217FLLPpRlW7tSyoWKfeXuBn8aydS8TeKPCd89hPqEGrulmmqGRLYIRGsypJFgHptbIbr8prv7zwppl94Zk8PvbBdJkt/sxgQkDy8YwD9KxG8BwaFperf2RA19qF9H5Ba/nLYjORsDHoqgk4FU3ZtpC3UYv+tv+CaXhLVrvXDqV7JKj2DXJSyEajBiUAb93fccmuI0vxd4k+3aNf3Oo281hfa5caS1gtsF2ovnbXD5zuHlDI6cmvRfDehweGdA0/SrYBYbSFYlx04FU4/BOkxw2USwMEs759RhG88TNvy3/kRuPeh/ErdP+B+hK1Wvn+Tt+NjzvT/iJrMnjDSEh1I6rpOo3M1uzpp/l2qYhkkURTE7nI2DqMHJ5o8Pa5421618MSHX7OAa5pzXUjLYgm1ZVVgUBPzbsnIPTPFdhY/CfQbC/s7pBdO1lKZLOOS4Zo7bKspSNeylXIx7CtjTPB+maRDpUVtCyJpluba2BYnbGQAQfXgCo1toW2un9a/5HmU/xH8SaoumWVmt2lyLI3Fxc6fp4ufMcStGAVLAKp2E8c84r1Pwvf3uqeH7C61GzawvpYg01s3WNu4rGvvhjo15BZxxm6sntQ6RzWk5jkKMxZkJHVdxziumsbKHTbOK1t02QxKFRck4H1NaaWfr/n/wPuM1fS/YnoooqSgooooAKKKKAPI/j1Z20t14Ou9ehe58G2upGTVogpaMZiYQvKB1jWQqT26GuS03WPCk/wC0JpJ8GSWlvbT6TcJqjWSiK2uGGDAoAAVpByeOcV9CTxpNG8ciLJGwwyMMgj0Irh/H3wx0Pxl4fGmSW40x4JBcWd5p6iKW0mHSRCB19R3FAEE//I2aR/13/wDZWr0SvNkie38R6FE8rTukgVpWHLkIQWPua9JoAKKKKAKl/q1lpew3l3Dbb/u+a4XP51aVg6hlIZTyCO9cn4rt7m41ywW20211JvIkBW7ICqMjnkGsy6vj4S0u/wBMmvnFxHpqC1wDlmCsCU/EULVf15h1sd5cXEdrBJNKwSKNS7MewAyTSwypPEkkZ3I6hlb1B5BrgNUvCutavBJdyXbyWkojjilyIB5Wdrx49j83qwFanhezm0vU7SH7ZcXMNzpyyus5yFkUoMr/AHchjxSjq7f11/yFf+vu/wAzq1lRpHRWUumNyg8jPTNPrzm+j/snXPFM8F1dR3MqwMfmL7YzwzquO36VveEJo/tV1FY3s2o6YqKyXEz7yJCTuUN3GAD+NMDbi1qwmvGtI7yB7pSQYVkBYEdRirteaafaTWepLf3MdsmmjV7n99FDtnRzK4Te3dCTj8V7VmWutazNpmr3D3Xk3v2GeS5jW53vFIB8u2PHybTxTNOX3uXzt+Nj16ivM9Ut77TW1kw6pfsLGGC7hDPnMjlt2eOV4Hy9qt3+oO+r3kkuoXMGrQ3CpaWKMQkkWVwduPmyC2T2x7UWI1td/wBdTvo5Ul3bGDbTtODnBHan15ZN5ug2GrpZTzNLJqhW7E1wVMULbiGDY+XJwM+9dV4aubxvB88rSpPIol+zvHN5p2gfKC2OSDkVHN7vN5DtrY6I31ssPmmeMRb9m/cMbs4xn1zxUxIUEngCvN9Sb7RpujaVaadcajax2K3MrQAZEjLiNmz1JO9s+q0+415dWi0/+1L250uMWrE+WSjNcq21lPr67e+ap6XX9f1/wBLW3megWt1FfW8c8DiSKQZVh0IqavO9Fury3s9LsY5Z/wDiZwxGNiMeVtz5hx2+UD8WqK31uebxVcm2nmETx3CvHJPuKlVOP3ePkwRxzyKJ+635X/AULySfe34npNFebxzalo2n200N9eXU15ozXMplG8rKvkgOq9jh2OO+Kh1u+jtdNs49L1Sa802WdvtFzNdlCGC5VfMxxzjinJcrs/66BH3kn3PS5pkt4ZJZG2xxqWZj2AGSaZb3kN4pMMqyAYztOcZAIz+BFebXt9LJpbR6xqcsE0dgz232R8rcMVbPOPnIGBiun8PqsetR7PlaTTIHlXGOQWCsR64yPwFHW39df8h9L/10/wAzqKKKKQBRRRQAUUUUAFFFFACV5t4L/wCPWOvSa828F/8AHrHQB3tr92ra1Utfu1bWgB1FFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAHG2/we8HWvjBvFMWhQJrjSNMbgO+3zCMF/L3bNxBPzbc89a7KiijZWQdblK10axsdQvb63tY4bu92G5lQYMpQEKW9SAcZ64AHYVdoooAKKKKACiiigCOeFLmGSKQbo5FKsM4yCMGotN0210exgsrK3jtbSBQkUMS7VRR2AqzRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAGdrn/Hon++P5GsKt3XP+PRP98fyNYVABRRRQBFH/AMjBon/XeT/0TJXZ1xkf/IwaJ/13k/8ARMldnQBxnw9/5Cnjj/sPP/6S21J8TPF1x4Tt9KMWq6Zocd3deTLf6tEZIYxsJ6CSPkkY+9S/D3/kKeOP+w8//pLbVs65ok2qarod1FIiJY3DTSBs5YFGXA49TUyvpbuvz1Guvo/yOY0fxtO1lYXD+JdI8SQXuox2cdxo1iVjXIO5WJuX56fMDx/dNZvhX4sanqWq2kWpacsWmtYXN5PfwhQieXOyDgyF8bRggKSSeOK7PxX4en16bRXgkjjFjfx3UnmE/Mq5yBgdea4zT/hTqNvbW1pcTWcttJYXdhdlXYMiyzGRWQbcNjIBB2/U1d/db69Pu/zHG2t/L83c27f4rWflzSX2lahpcYtnvLdrjymN1Eg3MUCSMQQpB2uFbB6Vr2vim4vPCtxrK6JewMsTTQ2c7wiWZQuVIxIVUEf3iCO4FcPo/wAJ7qz0q9s/7A8JaPObGSzjv9LtyJ5yy7Qznyk8scAlQXz616NDpckfhtNOLL5y2gt93O3ds25+mamp8L5d7afj/wAAmL95XX9af8E8ttfit4it/Dr3WoQwRam1lHfR2z2QRFRrkRDLJcybvlPt6nH3a7Of4m2lvfGM6feSabHOLWfVkMX2eKYsF2kF/MI3ELuCFcnrXP6v8KdT1C1SKO6tFZdJhsMsWxvS4WUn7vTAx65qK2+Eb6d4huJYdA8KX1tPffbRq2oW3mX0OWDMoXy8OQeFbzFwCDg4wajrLXb/AIP+X9dCn8Ctv/wF+v8AXU6vS/iFFrGuSWVro+pSWSXElodUVI2g85CQylQ5kUZVhuZAuR15GYPGPjTUPDfijQdOs9Km1hNQhuXe3tVXzt0fl7SGd1RVw7ZLH0A565Enw71K58fQ60bbSdNEVy0z6ppks0N1dxYO2GeIKEfr95mbpwozxueLdB1y58SaLrWifYJJLCC4he2vpXiWXzTHgB1RtuNhOcHsMc5CVtL+f5C6sbpvxQ0jUBIzJcWiR2ct5I1woUJ5Tsk8Z5zvjZfm7cjBNaV/4ug0vwbJ4ju7S6gt4rX7XJa7VadVxkrgMQW9gTXn+peCns4/DmkNqML+ILu+uLq/ESZElvMxkulUdRHuEagn/Zzya9B8baDN4k8H6rpFq8cU11btDG0uQikjjOATim9nb+v62+TJ6/1/Xn8zNsfiLHdTanb3Gh6rZX1lbx3a2bxJLLcROzKjRiJ2HLIwwxBHUgDmqL/F20s4dT/tLRdU0y70/wCytJZyCGaR0nl8qN0MUjqfmzlc7uOnIynirwHq2rapq17YX8do9zpVtZR7ZZInLxTvIyl0+ZFdW2blO4ZJA4FcxZ/BrU45NVkjtdC0ZL5NOH2bTzIwVra781meQoDKzr/GwBzwc43FR31/rX/Iuy79v0v+b+46WT4vLbSX8dz4Y1u2fTWQ6jvWAraROAUlLCUh1I3HEZZhtOQOM39W+JlnpOoXcZ0+8uNOsXEd9qkRiEFq2AxDBnDsFVlLFFYDPJ4OG+IPBd5q1p4yiimgRtat0ig3lsIVj2Etx0z6Zrn9Q+EpPibU7qLw/wCFdVt9SuRdNf6xa+ZdWrFVV1VfLPmr8u4ZdMbiO2aI6tX/AK2/4JHc9SBzyORS0g44paBhRRRQAUUUUAFeZ/FrWNcudd8LeEdD1I6DJrssxuNWWNXkiiiTcyRbsjzGzgEg4HNemVzvjbwPpvjrTYrXUPPglt5BPa3tnKYri1lHR43HQ447gjgg0Aeb6K+t/D34pWPhG88RXnijR9YsJ7y3l1QI13aSRY3AuiqHRgeMjg10l5/yNGkf9fA/ka5PxN8INY8J3kfi3wnrF9r3iy1Xy5o/EFwkgv7bvbqwVVhPcFQMnrmun82SfXtCklhNvK8qM8LMGKMVOVyODg8UAel0UUUAFFFeMftIeMoPCcfhFNR+IVx8M9GvtQkiu9at5LSNuIWZI991DLGASP7ueOtTKXKM9norxr4LfErWtW0/TNL1gy6s8lpfXlrrdyggmvrSK6MVtM8SoqhpYtkhKhRluFAOBX0H9oDUvEXizwLpMelaNpUXiHSoNUdtW1Z4Z5hIjM8diggYXLRYG8M0eA6nvWlrvTX+pL/21/cZ8yV79P8AgPpo91se20V87fAz4peMY7LwRp+vaJHNoGuz31la61Lqr3F+biJp5VMsPllVieOF9reaWGFDIueOn8XeOvGeh/tD6FpMMelf8II3hy/1K/Mt3ILrMMtuDIsYt2yy+YFVfMAYSOTgqobKElJRk9E039yb/JFN2v5W/FpfqexUV5L4D+LXinWtU8PN4m8K2Og6N4pjaTRJbXU2urpT5TTrHdxGFFicwqzfu3lUMjLu6E+afH74kaz4f+LWr6bB4w8YeHrez0DT7nTbbQNIt7nT5b2e4u4x9uuJbWRYEZooFBeWFcbjuGCRo4yTs1r+JcI+0UpRasremrS32677WPqWivnLxd+17p/gv4jf8IpfSeG0n02S0tdYgudZ+z6g1xOkb4srUxnz0USqSzOmeQu4gipYv2i/HOoapZQ2PgHS5bPV9a1Pw5pM02vFHa8tHuR5k6iA+XbslsxLIXkDcCMjDEtfb+v6uTry8zW1vXVN7eib+R9EUV4dpvx78SeLtJ8PWXhnwpp8/jPUTqH2qx1TVHt7G0WyuPs1w/2hIZHcGXaExFkhwWCYOMu0+MvjjWPij4RWLTdKsPC8ml6g+tWk2oO1xHcW0yxzGMLbkOFxlMum9XywQjFTJqDtL+vP06X2uVyyW6/q9revlvo+x9C0V8//AAR/ay0r4yeMxo1tL4flhvrZ7zTl0fWRe3ccSkcXsPlr9ncg5Cqz+hIPFdLqXxKudH8S/EPWtQvxa+GfCtjFDHa5TZNcOpkaSQ7dwI+RFw2MMcjODQ3yq77X+7/g6f0xL3pcq3vb5/8ADanrdFeCeB/jJqnhbwb4rTxZcya/r2jeTeRmJI086O6AMMIKAD925MbNjgAE5PXPh+J3jvw38TLuXxboNlZLFYWaXFrpmtvc2SQy3JQ3CF4o2Mi5VWVo1znhiK0UW5KP9Xtt69+3UylNRV7/ANd/R9O/Q+i6K8N+JX7RVz4N8I3viG0t/DNrp0OpTWMN54n186bb3Kxjlo3EMhZmYFVUDBwSWFUdY/aQ8RTW8134b8HWWo2Fn4dg8TXk99q/kYt33mSKIJFJvkCoSudqtxllrKMlLby/FX/I0ejUXu/87fmfQFFeU2fxY8R+JvEjf8I74bsZvClgsLarqWp6i8FyvmQiUi3gSKQS7FZQ294+cgZwCfNfB37cGj+JtTvUMOiXlvLYzXunWmh60LzUV2SRxrDew+Wq28jtNGBteRc78kbcm92121+Vr/lt36B0uv6/4br262PqCivnHVfFHxIufEHisalFb+FtZ0/wpFqtnFo+qfbbKV47mdwjebCpUusYjkPlZCsdjkgEe/eH9UGuaHp+oBdgurdJtvpuUHH60unn/wAOv0f3A9Hb+tk/1RoUUUUAFFFFABRRRQAUUUUAcp8T7G21Twbd2d7bQ3lpO8cc1vcRiSORC4BVlIwQR2NchD8IfAfiW001NY8EeG9WTT4Rb2a32kW84toxjCRh0OxeBwuBxXbfEH/kWpP+u0X/AKMWq3h//j3T6CgAvPhj4O1jWNN1e/8ACWhX2raaqpY39zpsMk9qq/dEUhUsgHYKRir1v8P/AAva65d63D4b0iHWbt0kuNRjsYluJmT7jPIF3MV7EniteH7oqdelG2wuliG8srfUbWS2u4Irq3kGHhmQOjd+QeDVTVPDek64pXUdLstQUwvblbq3SQGJxh0+YH5WHUdDWlRSaT0Yzm9N+GnhDRtAuNC0/wAKaJY6Jcp5U+m22nQx20qf3WjVQrD2IqXw/wCAPDHhOws7HRPDekaNZWcjy21tp9jFBHA7/fZFRQFJ7kda36KYdLHJ+IvhH4G8XW1rb674L8Pa1b2pdreLUdKguEhLnLlA6EKWPXHXvWpD4P0G3s3tItE02K1e3SzeBLSMI0CZ2RFcYKLk4XoM1sUULRWQmk9Wc3qHw08Iat4ks/EN94V0S81+zCi21W406GS6gC52hJSu5cZOMHvXSUUUbaD8zldH+FPgnw74iuPEGleDtA0zXrjf52qWemQRXUu85fdKqhjuIBOTyetR6N8IfAnh2y1az0nwV4d0u01ePytRt7PSoIY71MMNsyqgEgwzcNkfMfWuuoo6WA57Rfh34U8N6ZHpuk+GNH0vTo5EmS0srCKGJXRzIjBFUAFXJYHGQTkc1s3Gn2l1dW1zPawzXFqzNBNJGGeIspVihIypKkg46g4qxRTu3uKyOU8Q/CXwP4utbO113wZ4f1q2s2ka2h1DS4J0gMh3SFFdCFLHk46nrWhD4H8OW+nzWEXh/S4rGa0jsJLZLKMRPbIGCQMu3BjUO2EPA3HA5NbdFCbWxR4L4p/ZZt/FHxGvvEdxfaJJBeX9vfm4uvD6zazaGJYwIrTUPOBgj/dAgCIkF5CD83HvVFFJaLlJ3lzdTk7X4eWdrrfiGYvHc6JryBr7Rbq3WSB59oRpRns6AKykEHapGOdzdL+EPgTQ/D+o6Fp3grw7p+iaiMXum2ulQR210MY/exqgV+P7wNddRR0sPzMDwj8P/C/w/tZ7bwv4b0jw3b3DiSaHSLGK1SRgMBmEagE47mjxd8P/AAv8QLWC28UeG9I8SW0DmSKHV7CK6SNiMFlEikA44yK36KHruC02OSuPhH4FutH0vSZ/Bfh6bStKk87T7GTSoGgs3zndChTbGc91ANHir4R+BfHWoRX/AIk8F+HvEF9EgjjudV0qC5lRQchQzoSBntXW0UB5FOTR7Cb7H5llbv8AY2DW26JT5BA2gpx8pxxx2rI0vwclp4v1TxHdXbXt/dRpbQKU2pa265IjQZOSWJZmPJJ7AAV0dFHW4dLBRRRQAUUUUAFFFFABRRRQBzurf8hCX8P5CqM0yW8MksrrHFGpd3Y4CqOSSfSrusMFvpiTgAAk/wDARXwt8fP2tL7XPEEemeD5zBoVhNumuNuft7KeQQf+WfUY70AfXngv4heHfiJZ3N14d1SLUobaUwymPgqw9j2PY9DXRV8T3Wk33gLxNb+NvhLARDBp8V7rug7ziNHXeTt7xnnGPukV9T/Cn4paT8XPCMOuaSWQbvKuLZ/vQSgAlD69cg9wRQB6F4N/5Ar/APX3c/8Ao96Xxh4dfxNo62sNwLW5huIbuCVk3qskUiyJkdxuUUng3/kCv/193P8A6Pet2gDiv7F8df8AQyab/wCC4/8AxVH9i+Ov+hk03/wXH/4quz3ru27hu9M806gDiv7F8df9DJpv/guP/wAVR/Yvjr/oZNN/8Fx/+KrtaKAOK/sXx1/0Mmm/+C4//FUf2L46/wChk03/AMFx/wDiq7WigDiv7F8df9DJpv8A4Lj/APFUf2L46/6GTTf/AAXH/wCKrtaKAOK/sXx1/wBDJpv/AILj/wDFUf2L46/6GTTf/Bcf/iq7WigDiv7F8df9DJpv/guP/wAVR/Yvjr/oZNN/8Fx/+KrtaKAOK/sXx1/0Mmm/+C4//FUf2L46/wChk03/AMFx/wDiq7WigDiv7F8df9DJpv8A4Lj/APFUf2L46/6GTTf/AAXH/wCKrtaKAOK/sXx1/wBDJpv/AILj/wDFUf2L46/6GTTf/Bcf/iq7WigDiv7F8df9DJpv/guP/wAVR/Yvjr/oZNN/8Fx/+KrtaKAOK/sXx1/0Mmm/+C4//FUf2L46/wChk03/AMFx/wDiq7WigDiG0Xx1/wBDJpv/AILj/wDFVXuNJ8cKpz4k0r8dMJ/9mrvWqje/dNAHmGm2fiK38b6Q2q6tY3tt5pAjtrMxNu2nBzk8deK9frzub/kbNI/67/8AsrV6JQAUUUUAJtGc459aY8EcjKzxqzL0ZlBIqhrPiXTPD/lf2jeR2vmZ2b88469BWhDMk8aSRsHjYblZTkEetADRbRLI0giQOwwzbRkj3NSbQMHAyBjpWZ/wkdl9uNpvbzhdfY8bTjzPK83GfTZ3qa+1eHT7q0t3SaWW6fYiwxlsY6s2Oij196BlsxIzFyiliNu7HOPSiKGO3TZEixp/dUACn0UCGmNGUqVUqTkjHHrTBawiR3EMYd+GbaMn61LWTJ4s0iHVv7Me/iW+3BDCc5DEAgemSCPzoDzNQxq2cqpzweOtNaCNpVkMamRRgOVGR+NSUUARtbxNvzGh3jDZUfN9fWljhjhjCRosaf3VGBT6ijuopppokkVpISBIo6qSARn8CKAI7HT4NNgENumyMEkDOcZJOPpycDtUj28UmA8SMAdw3KDg+v1qWigBvlrkHaMr046U1beJZGdYkV2+8wUZP1qSigBuxRjCgYGBx0HpUf2O38kxeRH5ROSmwbc+uKmooAiNrCdgMMZCfd+UfL9PSo7fT4LW6uLiNMTXBUuxOegwAPQVZooAKKKKACiiigAooooAKKKKAErzbwX/AMesdek15t4L/wCPWOgDvbX7tW1qpa/dq2tADqKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigDO1z/AI9E/wB8fyNYVbuuf8eif74/ka4jxl4y0nwD4du9b1u7WzsLdcszdWPZVHdieABQBt0lfHPiD4teM/iXA3xJ8E6jLY2fhfct74cmbgoSSJCBxKGTqDypQ49T9C/Bn40aL8ZfDa31gy2+owgLe6ezZeBvUf3kPZv60Ad5H/yMGif9d5P/AETJXZ1xkf8AyMGif9d5P/RMldnQB5xpevf8IVrniiG+0rWbg32qG9hksNMnuYzGYIUHzopGcxtxnIrU/wCFpWP/AEBPE3/ghuv/AIiuzooA4z/haVj/ANATxN/4Ibr/AOIo/wCFpWP/AEBPE3/ghuv/AIiuzooA4z/haVj/ANATxN/4Ibr/AOIo/wCFpWP/AEBPE3/ghuv/AIiuzooA4z/haVj/ANATxN/4Ibr/AOIo/wCFpWP/AEBPE3/ghuv/AIiuzooA4z/haVj/ANATxN/4Ibr/AOIo/wCFpWP/AEBPE3/ghuv/AIiuzooA4z/haVj/ANATxN/4Ibr/AOIo/wCFpWP/AEBPE3/ghuv/AIiuzooA4z/haVj/ANATxN/4Ibr/AOIo/wCFpWP/AEBPE3/ghuv/AIiuzooA4z/haVj/ANATxN/4Ibr/AOIo/wCFpWP/AEBPE3/ghuv/AIiuzooA4z/haVj/ANATxN/4Ibr/AOIo/wCFpWP/AEBPE3/ghuv/AIiuzooA4z/haVj/ANATxN/4Ibr/AOIo/wCFpWP/AEBPE3/ghuv/AIiuzooA4z/haVj/ANATxN/4Ibr/AOIo/wCFpWP/AEBPE3/ghuv/AIiuzooA4z/haVj/ANATxN/4Ibr/AOIpG+KNj/0BPE3/AIIbr/4iu0prUAcHdfEuydTjQ/E//gguv/iK5yy8Wwa1400i3j03WbRvO3eZf6XPbx8A8bnUDPtXqN7901xN5/yNGkf9fA/kaAPRqKKy/EXijSfCWn/bdY1CDT7YsI1aZsF3PREHVmPZVBJ7Ck2oq7NKdOdWShTTbeyWrNSsnVvDNprGsaPqU7SrcaXJJLAI2AUl0KHcMcjBrmf+E38TeIP+Rb8ISx2x6ah4knOnxkeqwhXmP0dI8+vej/hE/G2r86p45XS0P/LHw5pcURA9DJc+eT9Qq+2Kx9rzfDFv+vO34Ho/2e4f7xVjDybu/moKTT8pWJfH3wqtfHmraZqX9ua1oF5ZRyW7yaNPHEbq3kKmSCXfG/ykoPmTa687WXNc/dfBfQ9Hj8KpeeLtatvDPhuK1S20O6urZbKV7bmGaVzF5xdWCtxKoJQZBGQdv/hTOh3XOq3/AIg11+/9oa3dGM/9sUkWL/xyrNj8F/AOmzCeDwXoIuf+fh9OieU/V2UsfzojKtH4Ypa339bdOl2/V33E6WX681WT6aQVn31c762tqtlaxxlnqvwk8I2fhfTm8faLD/wjt3NeWUdxrdt5jyOk0bBhnLcTvgAA5x+KeIvF3w38TeL9E8RJ4quXvdNguLMw6RE1zFe282wyW8yrE5Zd0cbYQq2VHOCQfXrHTbTTY/Ls7WG1jwBsgjCDjpwBVmp5KtkrrTyfp37aemg/aZdt7Kb/AO34r/3G+vmfPngKP4f+AdStbiLxD4z1m002NodG03VtKu5YNIiIKlLfbaK5+TCBpXkYKMBuWzv6h4k8AatrXiHU77TvE98mvaXBpF9HN4U1N7N7aJp2HP2Xbg/aZNxJxgDpg17JRVWrWs5L7n/mONbL435aU1f/AKeR8n/z78kfOWkWvg/w9q2n3+l+PviHYtCtuL+FdKmkj1doVCLJdeZYsS5jVUZ4zGWVVySQDWppt38KNHbQifEN3YnRtavdetxqUctti5uvtHmK/mRL8v8ApUm1eD93k9/eaKf7/wDmX3P/ADBVcviuVUZ2/wCvkezX/Pvs2vmfO50f4Q6hZ2NvoXxWt9A1mwu727g1TStdshfRfa52muIWWVXQxs7fdeMkbVwQwzXd6X8J/C163hq70XWbrGiCdTJZ3UU4v45yWnS5LI25ZHy52bDkcEDivRruxttQj8u6t4rmPrtmQMPyNcpqHwa8BarL5134L0CacdJzpsIkHrhwu4dMcHpU2qrs/wAP8wk8vrNyfPB/9uz31/uFb4f/AAp/4V1ezfY/FniHUdG8rybTQtSlt5LSxTdkLCVhWXCj5QHkbA47DGR4m+Cdt4u8UayuqeVd+EtZ+y3N/p7vuM1xA2BE8bIyPBIp+dSQSVHYmtb/AIUv4ftedMutd0R+39na5dxx/wDfoyGM/iv8zR/whvjPSfm0rx7JfgdIfEelwXK49A1v9nYfUlvfPSnzzVuaF7dnf772v+IfVsJP+FiLf44tfdy868uhh3H7Lfw2W4vX0rw1ZeGIr6wfT7y28P20NjFcoXV1d1jQZdHUMrdQfUcVNon7PulaauuS6l4i8Q+JtS1jTxpt1qWsXMLTeSpJj2COJI1ZCchgnJwW3Hmtb/hMPFvh/wD5GDwj9ttl+9feGbn7Xgf3mt5FjkH+7H5prpPDXi7R/GFnJcaPfx3iRP5c0YyssD4zsljYBo2x/CwB56VUakZ+536P/g+r2MK2Br0Y+0avFNaxakr6Wu03Z6LR2fkcFqn7O+i3WjeGtP0zXdd8NtoVq9lDd6VNAJp4HA8xJDJC4+c8lkCtk8EVqWnwP8PWdhqVokt+YtQ0RdAmLzAt9mAcAg7fv/O3zHPbivQaK2u7t9Xr+f8Am/vZwdU+q2/D/JfcjzW3+BWmab4ot9Y0vX9e0mExwpf6Ta3ERs9T8qMRo06vEzZ2BQfLZA20ZB5zDpPwDsNO0/VtHuPFHiTV/C99btbReH9QuYHtrJC25fIcQicFCBtLysRgeleoUUnqmn1/r/hu3QPM8YvP2frjTtH1+XTPE+ra54n1jS00GTVvEV3HuhsvNctsEMCrvRJpSnyfM23cepr13S9Pi0nTbWyh/wBTbxLEn0UAD+VWqKd9Lf1/W/3sP6/L/JfcFFFFIAooooAKKKKACiiigDm/iD/yLUn/AF2i/wDRi1W8P/8AHun0FWfiD/yLUn/XaL/0YtVvD/8Ax7p9BQB0sP3RU69Kgh+6KnXpQAtFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAHOatzfzA8jj+Qr4r/AGnP2Xf7NkuvF/hG0Z7Eky6jpcA5i5y0kQ9OuV7da+3dQ0+4nvJHSPcpxg7h6D3qt/ZN0QQYcg8EFh/jQB8CaNo198dvH8Nt8PZNU0LQ/wCybfT9ZvLh8KERcFTjqTzgd/pX2b8P/h/o3wz8M22h6Hb+RaQjLOfvzP3dz3Jre0TwPa+GraW30nSbfTYJZGmeO2VUDOerHnrWj/ZN3/zy/wDHh/jQBL4N/wCQK/8A193P/o963ayfDNjPp+mNFcJ5chuJ5NuQflaVmU8exFa1AH5V/Fvx54k0f42eKrqx1/UrWe11eYwtHdPhNrYGFzjAx0xivVf2Xfj78QvF3xr0PSNb8U3mqabcrMsttcLHtOEJB4UHIIr6H8UfsX/DrxZ4i1HWr2LUVu7+driYRXRVd7cnAxxzWj8O/wBkzwH8MvFlr4i0eK+Oo2qsIjcXO9RuGCcY9KAOw+Kl1Jd6XYeGbaSSK78R3P8AZ5lhYq8VvtZ7iQEcr+6RlDDo7pXaqoRVUdAMCsdvDMcvjBNflneWSGy+x29uQNsO590jg+r4jB/65j1NbVHS39f11+Y3v/X9eXyCiiigQUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFADWqje/dNXmGaq3VvJIp2rn8RQBw83/I2aR/13/wDZWr0SuMl8P6g3iLTroW+YIZdztvXgbSOmc967OgAooooA5nxBHqja9YnTFtd/kSK7Xe7aASOm0dfrWHqEi+FLC/0nzbh5W05Y7Ty0YmRgrhiuOhHU+1e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ov/gI3/xVfO6jcwGQMnGT0Fdn4++HcHgnQ/C2pW2u2+uwa5bzTCS1t5Io4zG4QqpkwzDJ6lV6Hg9aylkeUQnGEqKvLbfor/kuppHOc0nGUo1XaOr27pfm0eq/8N3/ABM/556L/wCAjf8AxVH/AA3f8TP+eei/+Ajf/FV5XpPwY8Za5odnq1ho32mzvI5JrXbdwCa4RCQ5jhL+Y+3BztU469Kk/wCFV63pJ1IarolxcLDpjajFPp+o2xhEYbb5vmL5iyqGyCiNuz3FYvKcju0oRb7c2v5myzPOLKTnJJ9bafkeof8ADd/xM/556L/4CN/8VQf27/iZ/wA89F/8BG/+Kry7VPgl410WzNzd6KERfJLpHeW8kqLMQInaNZC6oxIAcgL78UnhX4P+IPFGvtpphjsIoNRTTLy6nuIVW2mY424aRd54OAp57Uf2TkXK58kLLz9PPzX3ol5pnC1c5fd6+Xk/uZ6Vcft2fEplOYtF/wDAQ/8AxVdd+zv+0p4v+LHxq0bRdbTT1syks/8AosBR9ygY5yeOTXg2ofBPxN/b2s6bYQWuopplz9le6W/tkjkc52IpMu1pGAz5SkuOmK6j9jO3ltf2lNKgmjaKaKC5R43BDKwABBHY15GZZZlUcFVq4aEeZRvo9VpdPc9fAZhmf12nSxE3bms7rTezVz9PaKKK/Hj9TCvEv2mLq7H/AAhtnBZeLtUt7rUJRPp/grVf7OvpwsDsP3v2i3+QHkr5nPHBr22s7UPD9hqupaZf3UJkutNd5LZ97DYzKVY4BweCeuamS5l935jvY+V7X9oLxD4Q8FeFtL0m9n1Ge7s59Xh1DU/D+r+IJvsJuJFtbSYWq+atxsXa80x4ZD8shJI9H0v41eI9R+Ieh2upW9t4Q8P32mxXsNjq2jXb3eoM1sZXjju96QW8qPvU28iNKywO4AU5Xpta/Z18F6zeXN4ItY0q9uLqa8e60TXr7TplebaZlV7eZCkbsodo1IQvlyNxJOxJ8I/D9x4ytPE1zJrF9f2YX7Pb3mtXk9lE6x+WJVtXlMIl25/eBN3zMc5Yk023d9X/AMH791917JtsSUU31Vv8vu67bXtslb5zj/aV8c/ETwP4sk0hF0wX3hi91jTbyXwlrFkNH8tFdYpbmYpFdSPG7bZIWjCvFuCyKePX/Fd942s/2WdXv11zTU8ZReHZbr+1YbOZIAwiL7lj88yB9nAbzDh8Ngj5a6Hwz8C/CfhH+04tOj1T+zNQtpLOTRbrWby40yKF/vRw2ckrQwrj5QI0UBTgYHFb+jeBNI0XwWnhRUur/RRbPaNFqt5NeySQsCGR5ZmZ3GGI+ZjgYHQVlVg506kYaOSSXqub/NetjWE+WpCUtVFtvzvy9Pk9Nlc8n0nxl8U9VWy0LSdQ8KPq2jaHaanrN9qGnXLR3zXBk8mKBBdbocLA+6V2kyWGF4Ira+KHjeXxJ+zPeeKtJXVLRtU0eC9gi02c298qyhG2Rybk2SYbaG3Lg9x1rQuv2cPBV5HpCyJrnm6ba/YVuk8Q363F1bBy4gupRNvuogWbCTF1AdgAAxB7nVvCula14ebQ7qzX+yTGkX2WEmJVRSNqrtIwBtHA9K6KjU3Pzen3v/gelvVvmhGUIxV9Uv6/XX/gJfL2j/FnU/hjofiVtOj8T2qTarZ6NaaR4zF94h1LSr1opJZ55UgkmlmgMPkskcMrKSr/ADR5cr1el/HLx94q0/wnYaRZaXYazq19f2M2pa7oeoWUDrb2xmS4ispnjnCucJtd+CGIY459T8ZfBfwn491SfUtWsrr+0JraO1a6stQuLSQLHL5sTq0TqVljcsUlGHTe4VgHYG1o/wALNB0VdCKnU9Qn0Rp2srrVtVur64UzKyybpZpGeTKsQN5OB0xio3T5v60S/Rv563shzi7pwf8AV9f0Xyvpdo8e8PftF+LrTTdK8QeKdM0UaNqmm6hNDY6UJftFvc2QfzC0zvteOQROQAilMgEvyav6x40+Kmn+H9UsNavfC1vq2raDc6lpV3pVlchNOljQMYZQbjdPhW4mQw8p9z5gB6fb/CHwnbWmk2q6SsltpYultYZpZJEVbgOJwwZiHDCR+GzjPGKoeDPgR4O8BrdrptleTrcWpsVXVNTub8W1qetvbieR/Ih4X93FtX5F4+UYmS5lJJ7rT8f81r5dt6p3ilz7/wDAj/lL1vqeHXX7QfjjwX4H+H+lST2+p+Irjw3DrN9qkXhLVtWjuQVQJAI7R3aKVt3M0rlcgkIc4H074V1qXxJ4Y0jVprGbTJr60iuXsrlSstuzoGMbAgEMpODkDp0FcNcfs5+DZ9L0OxjOv2P9ixNb2V5YeJNQtrxYGIPkNcRzrK8QIXEbMVG1cAYFek20C2tvFCjOyxoEDSOXYgDGSxJJPuTk1vKSld21bb+V3+ll8r9WRGLiox7L8dP+D99uhLRRRWRoFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAHN/EH/kWpP+u0X/AKMWq3h//j3T6CrPxB/5FqT/AK7Rf+jFqt4f/wCPdPoKAOlh+6KnXpUEP3RU69KAFooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAryr9mn/AJJ1q/8A2Ofiz/1IdRr1WvKv2df9E8N+LtKbibT/ABnr/mL3H2jUZ71PzS6Q/QigD1WvKvjJ/wAlF+BP/Y53P/qPazXqteY/HbT7qGx8JeLLS2mvW8Ha9HrU9tboXle2a2uLO5KKOWZILyWQKOW8vAySKAPTqKr6fqFrq1hbX1jcw3llcxrNBcW7h45Y2AKsrDgggggjrmrFABRRXi3xMu/F83x68Haf4W1z7AY/DWr6k+l3XNjqMkd1psaxz4BZflmkCyp80bNnDrujcA9pormfA/juz8bWtyqwTaZrFg4h1LR7zAubKUjIVwCQysOVkUlXXlSRXTUAFFFFAHi37QRx4l+H/wD1/t/6Mgr2mvFP2hP+Rm+H3/X+3/oyCva6ACvJvjX5WqeLvhp4c1TJ8N6vq8y30LD9zdSRW0ksFvL2KM67tp4YxhTnOK9ZrI8VeE9J8baLNpOtWUd/YSlWMcmQVZSCrqwwVZSAQwIIIyDSfkHkefftJaXZ2/wQ8XzxWkEU62PliRIlDBTIh25A6cDj2qtH/b/xO8ceM7GHxXqHhay8OTw2NpBpKw75JHt0maafzEfcpLqFUbRhTyd3HQJ8DfDTWOo2d5Pr2r21/bfZJotV1+9u18vcrYXzJW2nKj5lweOtXfFPwh8N+LtXfU7uO/tL6aFba5l0vUriy+1xDO2OcQuolUZYAPnAZh0JqeX3r+X4/wBfnfoHX+v6/rzPIvAvjTxf8X9e8JWk/iSfQbK+8Jvf350aONWlukuxEJYWkR9qsFY4wcqw+tZ0HxU8b61Y+DvC4Gsajf3U2sR3+peHfsMN7OljcLDHtN1IkSlt6s5XJ+U4UAkj6D0/wLoWk61aapZafHaXdpp40qDySVjjtQwYRqgO0AEDnGe1YuofBXwnqWl2ti1jcWwtL6bUrW6s76e3ube4mZmleOZHEibt7AgNgg4xiq6rtr+d19y/yH/wPyt+f+Y34O3Hi2TwrcR+MbO7tLy3vZorR9Re2a6mtAQYnm+zu8QkwSDtPO3OBnFeWP8AEzVY/iJ4P1PQtR8T6v4X1/XG0yW61GKzj0mRGimIFsny3OVaIYfaUYBvmIINe9eHfDtr4Y0mPT7R7qaFCxMl9dSXUzknJLySMzMfqTxgVxem/s9+B9J1TS76DT7wvpN62oabby6ncyW9hMwcMYIWkKRqRI+VUBeenAq1bnT6L+n/AF3I+y16lX44at4gs9Q+Hum6BrD6KdY8QrY3s8caOxtvstw7qu5SA2UUg44IHUcV53r3iXx/rHivxdoXh5fF92fCgt7GwudMk0nZdXJtkm829FzLG7hmdRtjVVwrYOTx9Aa34W0zxFeaPdX9uZp9Ju/t1mwkZfLm8t492ARu+WRxg5HPsKwPEnwh8O+JvEMmuTDUtP1WaFLe4udI1S5sWuY0JKLL5MiiQLlsbs4DEd6hLSz7/ov+D99zVtaelvndv8rfdY880Sbxn8QviP4k0LVPFF74Tj0/Q9Iu30/RzbtNb3k6zebiR0cGMGPGOQSOoxzl/D/x94p+MV14f0G612fQBHpNzfXupaRHGk+ovFfSWkbRl1dY0Ii8xgAf9YoBA69Xc/Aez1/4q+KfEGqR3NraXmn2FjZ3OlanPZ3DRxCbzYnMLqTGS6HaSQSM9q6zVvg74V1XTdEsksJdJTRIzBp0ui3UthNaxFQpjSSFlYIQBlc4OASMgUR7tdX+tv0/pIzW1vT9L+t9Sh8GfEGrapa+KdJ1i9OrT+Htbm0qLU2jVHuohFFKjPtwpdRLsYqACyE4HSvRKyfC/hbTPBujxaZpNt9mtEZnOXZ3kdiWeR3YlndiSSzEkk5JrWqu3ovy1fz3Dv8AP+vkFFFFIYUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAHM/E7/knXiX/ALB0/wD6Aa4r9mY58A3v/YRk/wDRUVdp8Tv+Sc+Jv+wdP/6LNcT+zJ/yIN7/ANhKT/0VFQB67RRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAGdrn/Hon++P5GsKt3XP+PRP98fyNYVABRRRQB4V+2d/yRS4/6/rf/wBDr4Hr9MPjJ8M/+FweGrbwr/aX9k/bLpX+1+R52zy1Z8bNy5ztx17147/w7oH/AEUH/wAov/3RX6fwznWAy/BSo4mpyycm9m9LLsn2PzriHKcbjsXGrh4c0eVLdLW77tdzwD9nv4yx/BDxrca5NpbatFNaNbGFJhEwyQQQSD6V9G/8PEdN/wChJuv/AAYL/wDG6o/8O6B/0UH/AMov/wB0Uf8ADugf9FB/8ov/AN0V34zGcM5hV9viJ3lttUX5I4sJheIcDT9jQjaPrB/mz5t+N3xNT4vfES98TR2DaZHPHHEtu0vmEBRjJOB1z6Vr/Dr4vWng34c+I9EuLe6m1aXe+jXEe0x2sksflylskEZX0zzXvf8Aw7oH/RQf/KL/APdFH/Dugf8ARQf/ACi//dFd8s6yGWHjhva+5G1tJ9Pl8n3RxLKM6Vd4n2fvu/WPX5nmY/aV02PUPBdymkTE2VvKNbYxxlp53i8kyRhiwfEYHEgAJyCMVX0r47aTpceo6LJeS33h68sWgiceENMt/sUnmb/+PRXMM6t/FuZTnkCvVP8Ah3QP+ig/+UX/AO6KP+HdA/6KD/5Rf/uiuT+0eHrW9p/5LJ9W1vF7N6W6aO6OmOAz2Luqf/k0eyT2lreyve+uqszzXRv2itL07SPEGlak+o63baxNb20lzbadb6VIlisOxljSCQrG6nG0cqwBDcGvB7r7Fa6xJ/Z8txcafHPmGS5iWOVowcgsiswDY7BiPevsL/h3QP8AooP/AJRf/uij/h3QP+ig/wDlF/8AuiuvDZ3keFlKVKtbmtf3ZW002UbL5f5HJiMmzjFQVOpS0V7e9Hr581/vPl34reLLPxz8QtZ12wjmis7yXfGlwoWQDAHIBI7etcnX2d/w7oH/AEUH/wAov/3RR/w7oH/RQf8Ayi//AHRXVS4kyajTjTjW0St8Mun/AG6ZVshzavUlVnS1k7vWP+Z8Y0V9nf8ADugf9FB/8ov/AN0Uf8O6B/0UH/yi/wD3RWv+tGUf8/v/ACWX/wAiY/6uZp/z6/8AJo/5nxjRX2d/w7oH/RQf/KL/APdFH/Dugf8ARQf/ACi//dFH+tGUf8/v/JZf/Ih/q5mn/Pr/AMmj/mfGNFfZ3/Dugf8ARQf/ACi//dFH/Dugf9FB/wDKL/8AdFH+tGUf8/v/ACWX/wAiH+rmaf8APr/yaP8AmfGNFfZ3/Dugf9FB/wDKL/8AdFH/AA7oH/RQf/KL/wDdFH+tGUf8/v8AyWX/AMiH+rmaf8+v/Jo/5nxjXZeMfGVl4g8D+BtGto7hLrQ7e6iuWlVQjGSYOuwgkkYHOQOfWvpz/h3QP+ig/wDlF/8Auij/AId0D/ooP/lF/wDuisp8R5NUlGTraxd17suzX8vZmkcgzWEZRVL4lZ6x7p9+6PGPCfxm0TQW8AG4ttQb+wNK1GyuvLjQ75LjOwplxkDPOcewNR6b8YtFs/hzZaA9tfm8h8NXejM6xp5fnSzrIrA787MA5OM57Gva/wDh3QP+ig/+UX/7oo/4d0D/AKKD/wCUX/7orz3muQSfM6z3vtLvJ/y/3mdn9l51y8vsult4/wB1d/7qPGbj42aOfFvjDVorW/MOrabZ2ttGyICJITETv+c4U7DgjJ5HFXLz4v8Ag3S/7QudIj1y7utR8R22uzR3tvDCkSo2WiVlkYseThiBnjgda9a/4d0D/ooP/lF/+6KRv+CdI/6KCf8AwS//AHRU/wBqZBp++elukulrfZ/uouWW53UjKEqSs79Y9U1/N2k/+HPI/wDhdHhuOz1HT4Lm9tYhrMms2OoXHhux1CRWkOWRoZ5SIypxiRJMnHIqL9kHVv7Y/achvbvNze3aXEouNqxDJILExqNoLccDge9er3P/AATuEan/AIuAT/3Bv/uitX4N/sqD4N/FrR9f/wCEo/tfG+3+z/2f5H3x13ea3THTFedjs0yj6nWp4areUo2+F/nyrf1sejhMvzWWKp1MTC0VK795d77c3S76X6H2HRRRX5WfpAUUV4z+0XdeI7WbwbN4Zvb+DULS/l1D7FYylRqKwQs72rpuCuJEDoA3AdkbqopOSjrJ2X5efy3GlfRHs1FfPGs/Ee+8afF7wJqei63PaeCLG7+zXH2e4KQahcTafcXDibjDpCiQEENgO8gIygxhL+0v4vtNN8eyq2ka/LpmhNrGlzjw3qmkWhcS7PK865ZlvYiChFxb7VI52crTs07Na6/hr+KTa8vNpESkorme2n46fm0mfUlFeE33xW8ZeFZ/Gei+ItT8NxatY2On6lpmp2ej3ksOy7mniFubNJ3mupkNs+0RMhlLqAqc1n+DfjV418f6No+i6bLpOneK7zUNRt31jVvD19a2wgtPLJk/syeaK5SRxNEojeYbfnfcwCqxre3W1/y/K6/S+pT92yf9aXX3r/g2Poaivl/XP2lPF9vb6ZpEcVnaeIJrzWUn1HSvCmq+JbVYrG8FsqC2s2WVHkLqS7uFQoy4ckY7r4meMtY1v9lPWvEpsNU8O65deHTdvYW0stne2szRZaNHbypI3BJAZvLYcE7ezSvHmX9f1/XQU2qbalur38rf16eZ7NRXyZpPxL1L4W6T4yn0vTvFunFb7TNJg8O+MLq98Tahp91MzeZeFIp7mWaAxNGVignYO0Eijym3mug0v45fETXrXwrpVpaWOnaxq3iG70b+2de8LalpkFxDHp8l0l1Fp9xLHOoDr5ZVpSG8tyHXcNtKLldx1t/kn+q+/wAnalr+P4X/AMmvVdrN/SdFfNfhP9oXxqsfhrV/EtroMukatLq2mNZaVBMk8d1p63Je4E0kpUxy/ZXxDszHvXMsmDm7e/ED4lr4UibVNU8MxT+KtFubzSJNK024B0mVbZpwsrG7/wBKGwEeYnkfMAduG4mScb6bf8H8+V/qFrSUJaNu342f3PT8j6Hor5E0349ePvCvw7+Hekm6Os69ceF4NZu9Wh8F6vrn2rKII7cx2krtFK2SWuJZCpIyI+cD1n4x+JNS1X9n5dXTTtb03Ub+Czll0vTbx7HUI2kZC8CTb4WjcZK5Lx9OSKqpFwvbWzt+NvzT+7zV1tv2v+F/y/rc9ior5I0j4sax8OdF1a30iHxLY/btbTTLTS/FVvqPirUdFkSIvcSTRwTTT3CONpRYp2j6nzF5Fdjo/wAYviL4wl8H6Rplppfh/U9WTUBc6h4i0C/t/wDj327Jo7CWSGYJJu+5JICP7zd43do6/wDDX/J/5bO0Smo25v61t+f9bX+hqK8C0T4rfEP4hXVjomgv4Z8P65aWMl5qt3qVlPf205SZoVW3jS4hZFYoW3szbc4wxGTNa/G7xFrGreBrkiz8MeGdZt0ea9vdFur9Li4MhRrYTxyxpZnIG15wwfcAoyMUR96zXW343t+T8/LVDlJRTb6b+Xl/Wnnoz3eivljwz4s8V3fxM8C3WmXui+HfDEltrk9/oNhpMoW5MMybnytyqeY2QQzI2CX67uOq0v4uePLPR9H8Ta0/hufQ/EkFw+naZp1nMLnT3WCSeIS3BnZblSsRDFIocHGM54y9pH2Krva1/wA7ffZ2/GwJ3m4db2/K/wB11c99or5lvvjJ4i8OWfg3xT4v0bw3rN7c+HtY16NNK0+VbiyjhhtnFtDNJI7MXLkO4Rd2E+QbeX+G/j18RtY8O+JHi0SbVLu1tbW8t9RPgTWtKigWSVlmj+yXREl88KASYgkVpA20KpA3byi46Pf/AILXp0eu3mXpyKfRq/yvb+lv5bn0vRXNfDnxA/ijwXpepS6tZ63PNH+9vbCwlsIncEhh9nlkkkhZSCpjdiykEHBGK6Wk1Z2Ji+ZXQUUUUhhRRRQAUUUUAc38Qf8AkWpP+u0X/oxareH/APj3T6CrPxB/5FqT/rtF/wCjFqt4f/490+goA6WH7oqdelQQ/dFTr0oAWiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACvKtK/4oH4+axYyfu9K8dWyanaN0UanaxJDcx/70lsts6jqRbTntx6rXMfETwPF4+8O/YftT6bqNtPHfabqUShpLK7iO6KZQfvAHIZTw6M6H5WNAHT0Vx3w/8eSeJBPpGtWq6P4w01E/tLSwxK85CzwMf9ZA5B2uOmCrBXVlHY0AeY6h8Mdd8J39zqXw41i20lbiRp7rw3q8bzaXPIxLM8W1g9o7Eklo90ZJLGJmJaq//C4vEugfu/Ffwt8R2bDreeHXh1m0b12+Wy3H/fVuvtk5A9WooA8q/wCGm/Aq8TDxTaSd4rvwZrMEg+qPaBh+Vc/4d8c6b8Sv2kvD+p6BBq02nab4S1a2urq90a8so45ZbzTWjTdPEgZmWGUgDPCGvdaKAOP8ceAD4hurbW9GvBofi6wQpZ6qse9XjJybe4TI82Bj1QkEH5kKuAwd4H8fDxNNdaRqlkdD8V6eqm/0iSTfhSSFngkwPOgcg7ZAAequqOrIvXVy/jjwHa+M4bWdLmbSNd09ml03WrQDz7RyBuAzw8bYAeNsq4AyMhSADqKK4jwX49ubzVH8MeKLaLSfF9vEZfKiJ+zajCCAbm0ZuWTJAeMkvEWAbIZHft6APFP2hP8AkZvh9/1/t/6Mgr2uvFP2hP8AkZvh9/1/t/6Mgr2ugAooooAKKKKACiik3DcFyNxGQO9AC0UUUAFFFFABRTJZo4F3SOsa5xuY4GT0pzMEUsxCqOpPSgBaKKKACiiigAooooAKKKaJFZmUMCy9RnkUAOooooAKKKa8ixqWdgqjqzHAFADqKKKACiuZ1yygvvEUSXEKzItoSFcZAO8c1kwt4cuPElxoEcNu+sW9pHfy2ohOVgkd0R84xgtE4xnPy9OlHkPzO8orzfVNa8G6LJqaXs+n276YsD3qsOYBMdsO7A6ueAOproG8N6euc6dCAOD+7oF1sdRRXLf8I5p+Af7Phweh8us+8j8PafqVpp9xBbxXl1HLLDEYidyxgGQ5AwAAw6kdeKAO5orjNJsNE13S7bUbC0gubK5jEsMyxEB1PQjIzgis661DwrYXUNtdRw2txPNNBDFcWzxtM0UZlkKBlG9VQE7lyvGAc8UPTcD0SiuJ0W10LxFo9lqunW0F1p97Es1vOsRUSIwyCAQDyPUVX8SzeGvB+jy6rrEdvY6fE8cbztCWAZ3CIMKCeWYDp3o2FfS531Fcs3h3To2w2nwg+6Cj/hHdO27v7Ph2+vl8UDOporlv+Eb08Yzp8PPT931pf+Eb0/8A6B0PTP8Aq6AOoorz+6uPDdprQ0l7VX1ApFIYYLOSXYkjMqMxRSFUlG5YgDGTgEVr/wDCN6ftB/s+HB6Hy6AOporl/wDhGrDj/iXQ/wDfukHh3TmUkafCQOp8ugDqaK5b/hHdO27v7Ph2+vl8UL4d05vu6fCfpHQB1NFcsfDmnKMnT4QP+udN/sDTM4+w2+euNgoA6uisHwpDHbLqkUSCOJLvCovQfuozx+JNb1AHMfE//knPib/sHT/+izXE/sx/8iBe/wDYSk/9FRV23xP/AOSc+Jv+wdP/AOizXEfsxf8AJP73/sJSf+ioqAPXqKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAztc/49E/3x/I1hVu65/x6J/vj+RrCoAKKKKAIo/+Rg0T/rvJ/wCiZK7OuMj/AORg0T/rvJ/6Jkrs6AON+IzTSf2Lbx3d1aRzXbCVrOcwuyrE7bdw7ZAr5z0/48JfXVrD9g19POkRN3/CTSnG4gZ/1XvX0j4+tbmZtGngtLi8jgumaVbZQzhTG65AJ9SK84j+FnhaHwzZ6VF4U1qO4tZFmXUhbL57SAg5Y7uQcfd6fjzXw+b0MZVxDeGmo23ur30jZLR+Z9/kuIwNHDJYuDlfaztbWV27Nf3e/kel/D3zo9Lv7ea7uL37NfzQpLdSGSQqpGAWPWsPxf8AGJvCviG902Lwfrut2unwR3F/qenvZiC0jfOCyy3CStgAk7EbgfhXQ+BYLmPTb2W5tZbN7m9mnWKYYcKxGMivOfiB8FLvxp4u8R65HLd2l6tra/2YyahKtpcSR7maO4tVkEUqE4H71GxnI6V9Xhrxow/r/g/qfHYu0q1TXX/gr/gnTn4vSXnjSXQNF8H65r8FultLc6vZy2UdrAs670JE1wkrfLydsbfia1T8TtI/4WQPBey4OpG2M/nhV8gMAG8onOd+wh8Yxg9c8V5PF4V15fjDL4p1H4feKJ/t0GntG+jeJYra0s3jjZZUngF7Es4UngmOQEdPSq7/AAp+KfzeJRquivqP9uf22ugyaaxuVG7Z9nF8LoIVEROMxY6D3r0bLmXb/hvy1e3S19bnFL+7rpH77Xf46Wb0v5HcXXx8WzvdakfwR4lfw5o95LZ33iKH7HJbQmI4kk8pbg3BRT1IhOBk4wCa6Hw/8WNG8S+PtX8J2kdyLzTraC6F06r9nuUlQOPKYMSSFZc5A+8Otee6fZ+OtOh8aeF7TwPchdc1S9nt/EF3fWf2COGc/edFmacsqk/L5XLADIB3CHUvhL4r0O88Qar4Yt7Q67ZzWY0Oe8mCRTRizit5w+MlVBXftPUxKO+aLLXtZerel/uvf7zaUYc01F7bferfer+m512o/HzSbb/hLVsdG1fWJ/Dt/b6a8VqkKfbJ5igCwPLIiEKz7WLMoBU9a6/Q/Fct14Zm1nXtGu/BqW6yST2+s3FqWhjTJMjvBNJGFwCc7+B1xXjPiz4ManYeC/EWk6Zo13q1vI+lNFb2GoLa3V35LxtOUmMsZR+GO4up962rjRvEWo/CXV/CmleCdZ0mDUdH1W32+I/EEd9dxXDR4gUyG4nLrIZH5MvyBACACMY07yhK/wASbXyXX569zGC56yi9Iu2vre/3af5nb/8AC7fh6YpJf+E58O+XHfLpjt/akOFum5WAndxIey9T6VF8SPjF4c+HFrdQ3WraY3iIWMl9Z6HPfJDc3iIrE7FOWI+RuQp+6fSvOPEvwX1O+TxZ9k0GzLXnw5j8N2ePJXNwPtOYBz8q/vIueF6elUvF3gXxmNB8beGbfwZH4iXxNHb3EGqy3lsLe1aO2hjMcyyP5m9XgLRmNGXLISyfMV35Y81r/wBbf8H8OzIqKSp3W7/DRP56vlt3Tfe30ZG2+NWxjIzTqZEpWJFPUAA0+shhRRRQMKKKKAEZtqknOBzwM1yvgn4iWfjq81y2tdP1KwbSrhbd/wC0rfyGl3LuDqjHeF6j51U8Zxggnq64zwd4dv8ASfGnjXULqER2mpXNvJavvU71WEKxwDkc+tTd8y7Ay7qPxO8IaPr8Wh33ijR7PWpiVj0+e+iSdyBuICFtx456dKhs/iRoniHTdL1Lw5rmhazpt7ei0F3Hqa+W5/iWJkDiSQf3MjPqK848Z/B+98Rt4736FZXo1jVtNuYvPELefFBsJLbv7pDYDfh1q1ffDTXG8aXV/b6fGtnL4ptNV3LLGu6JIQjyEZznIAx1OBUQm20muq/Nf5v7iaj5Ytx31/X/ACX3nf6f8VfBerapPptj4s0W81G3ga6ltYL+J5Y4VJVpGUNkKCrAnoMH0pvjD4n+GfBXha78QalrFnHp8Fk2oB/tMY82EDIZCzAEHIAOcEkc15d4d+C+q2ngTwtpkulW1nqNrd6rJcyK8f7r7T56iQlT8xYSJnGT69Kh0nwf418QaXHp994WbQIrHwtPoaTXl/byNcXGAiuqxO+ImC5BYhhnBUVdR25lHdO3qrXuvwRtJRj1vr+tvy1O9k+NXgWbwxoGvTeK9HsdN15U/s6W6v4UFw7Afu0O7DOCcEKTzRef8jRpH/XwP5GvHfGXw18Z6t/Yd+NM8W2cNz4cTQNR03w/qGircQbeG8w3YkjMbDJBhk3eq969Rs9PbSdU8J2MG421r5cB+0MGlwseFyVG0njkjj0rWXKk2u/4Xt/wfn5a4xvon2/r/L/hz1eiiioKCs+/0Gx1TUNOvrmDzbrT3aS2k3sPLZlKscA4OQSOc1oUUAchpvwj8HaPpdnptj4ftLXT7S9uNRhtYwREJ5xKJnK5w28Tygqcj5unAxh6T+zn4C0ex1K0i03ULqDULQ2E41LW769YWxYN5KNNM5jjBAIRCoGTgDJz6XRRs7rcTSa5Xscf4s+EnhbxtNez6rYTNdXkFrbyXdpfXFpcItvJJJAY5YZFeJlaaX54yrEOQSRxXDePvgXb2/guw0Xwb4XtNUki1Br9ptV8Y6ppN3FK0ZV501CBJ7kyOPlfLDeGbcTkg+00Umr/ANen+S+4pyct9f8AhrfloeN+Ff2a9Ai8A6LpHiGKQatZ3V5qH23w7qd5pklvLdzNNPDFcW8kcxiyyqQzfvPLR3Bbp6XqXhHS9Y8KyeHL+GW90iS2FpJFcXMrySRgAYaUt5jHA5YsWPUnNbNNjkWVQyMrqejKciqvroTa6tLX/g7/AHnIeMvhD4T8fXkt3rmmSXNzLaCyaaG8nt28sSLKjAxOuJI5FDxyjEkZJKMu45NH+EvhvRY9DWOPUr6TRLqW9sLjVtZvNQnhlkieJz5txK7sCkjrtYkDOQAea7GihNxVkPfV/wBaW/LT0OQs/hJ4SsYtIih0dBHpN3d31mjzSOsc115v2hiCx3B/Pl+Vsgb+AMDFPwh8D/BngWW6fSNMuFSeFrZYL3Ubq8htoW+9DbRzSOltEf8AnnCEXAUY4GO7opS97WWpTlJ7v+tzzSf9nXwNNpej2CWusWSaOjxWNxYeI9StbqGFiCYPtEVwsrQ5C4hZzGu1cKMDHb6p4Z07WtHj0y+ga6sozGQkkzliUIKkvu3E5A5J575rSkkSJdzsqL6scCnU7siye5w3i34K+D/G2qXWparptwdRuY4o3vLLUbmzmHlMWjdHhkQpIuSBIpDgEruwSK5XxP8As66b4h8QeDw1xqLaDoVpdweZJr+oDVA0oABS9Ev2jsQSZQSMDkcV7HRU2X9elv1CXvb+X4W/y+4861X9n3wHq1jotp/Y02mx6PAbWzfR9SutOlWAnLQvJbyo8sbHJZJCysSSQSSav6p8G/Cus6ppF7dWl8U0pUW106HVbuLThsOUL2SSi3kKnBBeNiCAewrtPMTzPL3LvxnbnnHrinVXM783Xf59xvVWfa3y7ehxqfCHwpDcaJcQ6fNbT6NcTXNlJbX9xEyNKcyqxWQeYjHkxvuQkD5eBVDQfgL4H8M317c6dpM8Quo5YRaSaldS2lqkufMW1t3lMVqGBwfIRMjHoK9BorPkjy8ttNh3a1Rys/wu8LXS6Slxo8NzFpVjPptpDcM8ka20yossTIxKurLGgO8Hge5zi6Z8BfCuj+H9R0WzuPFEOn3xj3qPF+rmSIIcqsEhut8C9isTICOCCOK9EpryJHtDMq7jtXccZPoK0bvv/XX89Qu7KPRbeRleFfCul+CdBtdH0e2NrYW4O1XleaRmJLM8kjlnkdmJZndizEkkkkmteimvIsa7nYKM4yxx14FDbk7slK2iHUUUUhhRRRQAUUUUAc38Qf8AkWpP+u0X/oxareH/APj3T6CrPxB/5FqT/rtF/wCjFqt4f/490+goA6WH7oqdelQQ/dFTr0oAWiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigDl/HHgG28aQ2k6Xlzouu6ezPp2tWG0XFozY3AbgVeNgAGjcFWwCRlVI5Jfi5e/DphZ/FG2h0iFeIvFthFIdHuB6zE7jZP6rMxj5G2VzkD1WkZQykEZB4INAEGn6ha6tYwXtjcw3tnOgkiuLeQSRyKejKwOCD6irFeZah+z34aW+nv8Awzc6r8P9RncyTTeE7v7JFK55LyWpVraR8/xPEx5PPJqt/wAIv8X9B+TTPHfh/wAS2w6L4k0Foro/We1mjj/KAf0oA9Woryr+1PjfZ8f8Iz8P9Yxxn/hIr6wz74+wz4x0xznrkdKd4T+JXjST4nWng7xl4S0HRJb7R7vV7S70LxDPqYIt57aJ0kWWxttpP2pCCC33WyBxQB6nTZJEhjaSRlRFBZmY4AA6kmq+qapZ6Jpt1qGo3UNjYWsTTT3VxII44o1GWZmPAAAJJNeax6be/HCRbnWbWbTvh6CGt9GuozHPrfpJdoRlLc9Vtz8zjBlAGYiAV5I3+POr6Pf2qmy8D6NfR6jZaso23erXEZ+V7Z+sVrglTIPmnVmVcREtL65SKoVQAMAcACloA8U/aE/5Gb4ff9f7f+jIK9rrxT9oT/kZvh9/1/t/6Mgr2ugArxj9o64tYn8IRX8mkrYyXk4kj1vxBLo1s2IGIzPGrEsOoUjB56Yr2eoLqxt76MJc28VwgOQsqBhn1waTA8UsfFfie48WXzWfiGCPw/Z6/b6HDp0NtHKrQS2FvL5gnILMyvJlTwCCdwbIx5xpnxW8W+FPDPhnSrbxFJq10zXcjX17c6bAbi6W7aMWUpnaMAKMErHmX516AYP1qtvFGMLGijIOAoHIGB+lRSaZZzKBJaQOA/mANGp+b+906+9O7v8Ad+Ct+d3+ApJS200/X+kcR8PdS17xFqHjCfUdX/cW2oy6daWcNvGFtgqId+7BLtlz1O3AHHUnwnwUvia/sfCLWPjmaTXrTw/rzS6ldW0FxMjx3VriB1xtABA3ZG/BwCpwR9aKqrnaoXJycDqaYlrDGSUhjUsSSVUDOev507vlsu1vnZq/43/A0py5L82uv4a6HgHhz4y+KfEHxasNKZY7W0kMCHTnurFEnge2WV7lEeQXTMGYgbFKYQ9Tkjc8ZeOLLwn4l+I1lq2uJplxe6RbNpFtcXPlvO5inQi2UnLPv2jCZbJX1FewmxtmuEnNvEZ4xtSTYNyj0B7UTWVvcyRSTQRSyRHMbOgJQ+oJ6dKmcVOLh0d/xM4+7JS7W+8+cbi1v7H4pS6zfx/Y9PstT061n13+2LjzLTNtGTE9qQIfKkY7DJvJBlyV7jv28Waj4d+CE2r20+bxLiSI3lwrTC2je9MbzsOrLEjGQjpiPHAr1NoY5FZWjVlb7wKgg/Wl8tdhTauw8FccVUnzf16f5f09SaceS13f/hz56vY7r4h/2Bp83jBPE+j2PiaAx6qllZzRaivkebsbEZiJjfIDRgY4/iXNVPj5JqEPinx1E/iSaGxn8Du9tosyxeRJKssgZ1GA7FRtLYbowzxivo2G1gtokihhjijTlURQAv0A6USW0UzBpIkkZQQCygkA9RTT5fx/FJfp/W5tTl7OSk/L8JX/AK/pHzv46+JHjL4eQ3WkXOtyagjahCp12NLC0ls4JLYyCM/aClvzIjKpc52sB8zc12viLxl4m/4VX4T1CK7t9J1zVr/TrSe4hWK6RVnmVHZMM0bEqcggsMnuK9Sns4LqNo5oY5kbG5ZEDA46ZBpywRrGkYjURpjaoUYXHTA7Uo73lrqvu7ER923kv6Z8x618bfG2n6x45t4rlIptFstTCW15Lp/7tbaJjDdiESC5YyMquQUEe2QYwBuPQWvjTxvoviqaC98Tx6pZafr2n6a8D6dDEbmO8ijdt7LyDGX+TbjgfPvPI94bT7V7hp2toWnZdhkMY3FfTPpUvkxkk+WuSQeg6joacWo2uv6uXeOt13/G1vu/U+ZdT+IHiPxZ4J1023jRv7Sv9GvLm80qwt4BP4cliwRF93eDy0ZMuSSNybccadl8W/Eh+J2ieH7PU01HT1SyjimkutNjj1eGWFXlugC6yuVJYL9nUpmNs5zhfoRLOCOSV0gjV5v9YyoAX+p7/jTP7NtN8L/ZYd8IxE3ljKD0Xjj8KhK0ub0/C/z69f8AK0y96/z/ABt+Vjxb4u6hpEviXV7PxVe2sENvYRT6JY6prMukWV3ISwlLXEYJMgIAxhiAchec1zeveItQ1C60+aDWn8F2Vtf6E888YhdxHLBLmOeeZMuobaAWxkn3xX0fdWNvfKq3NvFcKpyFlQMAfXmnSWsMyMkkMbq2NysoIOOmfpSSsreaf3O/47ESTbuuzX3q3/BPN/iN4o8Q6X440qw0a6K26aHqWry2MUCPJeyW72wjhDMCVDeaykqM8jGDXkejfHLxTqWj6fNeeJ7XRrG91a2tbnV7qTTbg2QktriSWMLBI6xqpjQq0/zDnfuAIr6n2LuDbRuAwGxzj0rC1rwNpGvTaZLcWyodPvft6LCqqsknlSR/vBj5htlbj1xVxtpf+tb/AJafI2urbdH+Wn4nh1x8XNcksIEu/HNjoMdva3Vzp+qPawsviNo53jiVQw24ZURikOHbzQUKgcv8c/FPVrW88Y2l5qEEksWjLdW2irFaXNtB/qS4uV5mSUFzw+I2BG3JBr6GextpFhV7eJlhIMasgIQjoV9PwoFjbCWWUW8QklGJH2DL/U96cXytN6/1/X3eooySd7f1p/l+J86af4v1bw3/AGtpd78Q20+K58T3sF1rF+lrnR4lDSQx4ZNiebxtMoIwPlHIrY0vxj458V6lLa6dr8cZsdBXUI/KsIj/AGlL9quYlc7h8qSJCjYXHJBBA4PuUun2s6yrJbQyCXBkDRg78dM+uKg1bSf7T0u5tIbqfS5JovKW7sdizRD1QsrAEe4NRG8Ypdkl9ytf+tPV6hdNu63/APkr/lp/Vjg/Bniafxnqd1rYlD6VdRldOVVA/coyqz56ndIHx7Bcda8f+Lng3T/Ffxd8fT309/G+m/DyC5tvsV9La+XMLi/KS5jZSWUrxkkDJ4r3hrTTPCF3p2nweVYWFtp4t7dGO1QqsAAPwqY65pLMWN5almG0kuuSPQ+3J/OpqR5vhdt/yav+Nx05cqaave3/AKUn+lj4U8X6HoHiPR/H2s6+wfWb7RfCGrzyy6hLC0isY/tFxsEgGwZO5gNq+1djoes6LLqHiS60DxXf3/xGtviC1lpWnf2vLI39n/a4w0UcDPte2+ztKxfBAO75gVAH1s2paHJ9+exb5PL+bYfk/u/T26VheEfD/hPwRJqsmm3MPm6lqNxqc0k0iMyyzNudUIAKpnovatYu1Tm6a6f9vJ2+5W/4cyirU+Vu791fdFq/zbv/AMMeC/DPVrTQfjAdK1HWdO8ZvrE2rLNr2leJLgXVvbrmTbqemyfLAqAGNZo2ABWP5V35r0PxbqS3N54on0iZXis9PsvDGlyQyeaBc3jKSwOTnaklu2c8qSSa9TXUdCSaWZZrBZpRtkkAQM49GPUj61IutaQi4W7tFGQcBlHIGAfyA/Kp0aSf9f0m1+Jd9W111+e/6fcfIPxim0rRtD8cwanr15oPjLR9a0/TvDGn2Wpy28v9mB7ZYRFAjAPE6mXe+0jO4EjGBf8AE9rpuofFTQ9T1+5ZjZ+MPEFnaz3d9JHHGw05HhhX5wuS/RO/IweRXuPiD4aeGPFHiSTU9T8VardWMtxFcyaFJfRPYtJGVK43RmVE3IrGNJFQsM7eTnvZdW0Wb/WXFlJ8/mfMVPzf3vr71Nrxd3q1b/0nX1dnf1uTLVq2yd/z09FdfkfIsWgXHg3wH4PHhq81c6n4i+HutfalW+mle6mjs1eBkTdhJFc4UxhTziqHxv8AiRofjyzig0/xW97oo8E2U97cabdNIkTnVLQFyVyBMFzn+Nc84zX2Wut6QpQi8tAUGFIZflHoPSootQ0GBSsUunxqTkqgQA/gKXL71/62l/8AJfgTJc1L2d/n/wCA/wDyP4nlfwg1bQdP+InjCy8Ma39u8BRwaeYbmTUjd2i6jK0iyRQzu7EuyiEsgY4Zl4BJFcfperaLNceKNU1LXpofjDb6rqMOmaTJqksczFQ4s4Fsw+14GTYc7NpySWr6Fj1TRIYRFHPYxxBt4jTaFDZznA7570v9qaIboXRuLE3IG0T/AC+Zj03dcU7efRrz1t+Wy8i4vld7dtOnz9d35nxb4x8QWen/AArjvfAvi3Ur3Xr3whqdx4tkGqTTTwTLbqyzTqWP2W4W4LKqgIcbxgheOh+I3gO08M/8Lck0/WNfhGieA7TxDYRnWrkrBqRF5m7GX++fIjyD8nB+Xk19YLqWhxtMVmsVM5zKV2DzD/tf3vxp7a1pDbt13aNuXa2WU7h6H1HJ496u+rf9Lfb7/wAPSzi+WKi9bf8A2v6Jr5/f4Dq2t3upweHvFKXcynVPHGk6eslvKR51vADG6nGMhpfNBXoSteJL8QLoeIPD2sWniW0tLzXYNYgu7KHWrm+1VyLK5kzfcxwWrqyIFhSHKlDiQ4Ir7I8UeH/Dni3VPDt3e6xJHDod6NRgsLeeNLea4UERvKNpY7CSyhWUZOSGreW/0FZHkWTT1eRtzsAgLH1JxyeT+dZThzQnHa7fyTjFfjZ3/q0RXLJPokvwbf6r/hj5X0X4cWE39kifV/EE6X/wwXWryNtbuttxfxhNl22JOJB5j/dwORkHArjrjxp4r163vL7WtW0201yPQtIm8N3uoeJruwvMvZxu09rZQ2sq3jvcGRWGSTtClVByft/+2tIGMXdoMLsHzL930+ntUbalockkLtPYs8P+qZthMf8Aunt+FaPVt9/w1k/wTS9F6WiEXG13fS34RX/trf8A299/zRZ643hT46Rz3+qaf431TUNd+zRR6V4guLXWNNLwtm3m0x/3UtshGBICmFIYg4yer8dfbviV8WfhZo3iPRtb8K6bd/2z9q0ltWjX7cqQQMhdrSZgVVjuALAgj0zn2z+09D+1G68+x+1EbfP+TzMYxjd16VKdc0pmVje2pZfusXGRnrg0dLf1/X9b6myfLLmX9bnyl8KvtvhWP4Na1Y3et69rGtLq9rfQ3GqNI+oxQxyGCHE0gjBTy0Csdp45bkmvpvwvJPqtxJq+oaDdeHtUnt0gls7y5imdUR5CuTDI8fO5jkHPPPQVoLrWjrsxd2Y2fdwy/Lnrj0p//CQaZ/z/ANv/AN/BUtN2u9hykm24q3/D/wBL5Gj4b/1mrf8AX5/7RirarB8KTx3K6pLE6yRNd/K6nIP7qMcfiDW9VEHMfE//AJJz4m/7B0//AKL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    }
   },
   "cell_type": "markdown",
   "id": "31dfe8e4",
   "metadata": {},
   "source": [
    "## Task 0: fetching this problem sheet on the Noteable Jupyter server\n",
    "\n",
    "The problem sheets (and solutions) will be uploaded to a Github repository: https://github.com/james-m-foster/MA50290_24\n",
    "\n",
    "To download these materials, click **Git -> Clone a Repository**, enter https://github.com/james-m-foster/MA50290_24.git and click **Clone**.\n",
    "\n",
    "Each week, you can download the latest materials by clicking **Git -> Pull from Remote**. Whilst this shouldn't overwrite the files that you've changed (and saved), I would still recommend that you write your problem sheet solutions in a **different folder**.\n",
    "\n",
    "This is summerised in the following screenshots:\n",
    "\n",
    "![Using Github in Noteable.jpg](<attachment:Using Github in Noteable.jpg>)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "097efae5",
   "metadata": {},
   "source": [
    "- Look at the sub-folder `Week 1` in the folder `MA50290_24`\n",
    "\n",
    "Here you will find a Jupyter notebook file `ProblemSheet1.ipynb`, which is a copy of this problem sheet, and a data file `OxfordTemp.txt`, containing monthly average temperatures in Oxford starting from January 2022."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca172105-eec5-4b86-be0c-df62a1e14a94",
   "metadata": {},
   "source": [
    "## Task 1: read and split the data\n",
    "\n",
    "- The file `OxfordTemp.txt` contains the dataset $\\mathbf{D} = \\{(x_1,y_1),\\ldots,(x_m,y_m)\\}$ in the form of two columns separated by a tab. **Read about** the _numpy_ **function** `np.loadtxt` (https://numpy.org/doc/stable/reference/generated/numpy.loadtxt.html) which can be used to load simple text data as a _numpy_ array. \n",
    "- **Write Python code** that loads the file `OxfordTemp.txt` into a _numpy_ array, and extracts the first column as a _numpy_ array $\\mathbf{x}\\in\\mathbb{R}^m$, and the second column as an array $\\mathbf{y}\\in\\mathbb{R}^m$. You can use the cell below. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "fbc489b3-d86f-4ac5-bb9b-b843b5c12de0",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b052418-98b4-4184-bc53-ab6af2e35b10",
   "metadata": {},
   "source": [
    "## Warm-up: polynomial features\n",
    "\n",
    "- (Without using `np.vander`) **Write** a Python **function** ``features(x,n)`` that takes as input a _numpy_ array $\\mathbf{x}\\in\\mathbb{R}^m$ and an integer number $n \\ge 0$, and constructs and returns the Vandermonde matrix $V\\in \\mathbb{R}^{m \\times (n+1)}$ as a _numpy_ array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "66feb849-5561-4f55-b6cf-5c4e5658bce6",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "c4025559-60ce-4eb5-9b0a-34def5a90dcf",
   "metadata": {},
   "source": [
    "## Task 2: optimisation of the parameters\n",
    "- **Write** a Python **function** `optimise_loss(V,y)` that takes as **input** the matrix $V$ constructed in the previous task and the vector $\\mathbf{y}$ loaded from the file. This function should compute the matrix $A = V^\\top V$, the vector $\\mathbf{b} = V^\\top \\mathbf{y}$, solve the linear equations $A \\boldsymbol\\theta^* = \\mathbf{b}$, and **return** the vector $\\boldsymbol\\theta^*$.\n",
    "\n",
    "_Hint: you can recap on numpy functions `@` (matrix multiplication) and `np.linalg.solve`_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7c72d97c-4cac-442f-8b0c-a0b8dd35c68d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "a8fdad29-68cc-44e3-bb23-c6fa48abac80",
   "metadata": {},
   "source": [
    "## Task 3: results\n",
    "- **Write** Python **code** to compute the optimised parameter $\\boldsymbol\\theta^*$ using the functions from the previous tasks and the training arrays $\\mathbf{x},\\mathbf{y}$.\n",
    "- **Compute** the prediction $h_{\\boldsymbol\\theta^*}(\\hat x)$ for $\\hat x$ ranging from $1$ to $17$ (inclusive). \n",
    "\n",
    "_Hint: `np.arange` can produce an appropriate array_ $\\mathbf{\\hat x}$\n",
    "\n",
    "- **Plot** both the training data $\\mathbf{y}$ as a function of $\\mathbf{x}$, and the prediction $\\mathbf{\\hat y} = h_{\\boldsymbol\\theta^*}(\\mathbf{\\hat x})$ as a function of $\\mathbf{\\hat x}$ on the same graph.\n",
    "\n",
    "_Hint: recap on `matplotlib.pyplot.plot`_\n",
    "\n",
    "- **Vary** $n$ from 1 to 10 and rerun this experiment. Which $n$ gives the most accurate prediction of the known values of the temperature? Which $n$ gives the most \"reasonable\" prediction for the unknown value at $x=17$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dda05aca-2c3e-46a5-8248-0db31cbc3e8d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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