{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Introduction to periodic problems and plane-wave discretisations"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "In this example we want to show how DFTK can be used to solve simple one-dimensional\n",
    "periodic problems. Along the lines this notebook serves as a concise introduction into\n",
    "the underlying theory and jargon for solving periodic problems using plane-wave\n",
    "discretizations."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Periodicity and lattices\n",
    "A periodic problem is characterized by being invariant to certain translations.\n",
    "For example the ``\\sin`` function is periodic with periodicity ``2π``, i.e.\n",
    "$$\n",
    "   \\sin(x) = \\sin(x + 2πm) \\quad ∀ m ∈ \\mathbb{Z},\n",
    "$$\n",
    "This is nothing else than saying that any translation by an integer multiple of ``2π``\n",
    "keeps the ``\\sin`` function invariant. In a more formal one can use the\n",
    "translation operator ``T_{-2πm}`` to write this as:\n",
    "$$\n",
    "   T_{-2πm} \\, \\sin(x) = \\sin(x + 2πm) = \\sin(x).\n",
    "$$\n",
    "\n",
    "Whenever such periodicity exists one can exploit it to save computational work.\n",
    "Consider a problem in which we want to find a function ``f : \\mathbb{R} → \\mathbb{R}``,\n",
    "but *a priori* the solution is known to be periodic with periodicity ``a``. As a consequence\n",
    "of said periodicity it is sufficient to determine the values of ``f`` for all ``x`` from the\n",
    "interval ``[-a/2, a/2)`` to uniquely define ``f`` on the full real axis. Naturally exploiting\n",
    "periodicity in a computational procedure thus greatly reduces the required amount of work.\n",
    "\n",
    "Let us introduce some jargon: The periodicity of our problem implies that we may define\n",
    "a **lattice**\n",
    "```\n",
    "        -3a/2      -a/2      +a/2     +3a/2\n",
    "       ... |---------|---------|---------| ...\n",
    "                a         a         a\n",
    "```\n",
    "with lattice constant ``a``. Each cell of the lattice is an identical periodic image of\n",
    "any of its neighbors. For finding ``f`` it is thus sufficient to consider only the\n",
    "problem inside a **unit cell** ``[-a/2, a/2)``. In passing we note that the definition\n",
    "of the unit cell is itself only unique up to translations. A choice ``[0, a)``,\n",
    "for example, would have done just as well.\n",
    "\n",
    "## Periodic operators and the Bloch transform\n",
    "Not only functions, but also operators can feature periodicity.\n",
    "Consider for example the **free-electron Hamiltonian**\n",
    "$$\n",
    "    H = -\\frac12 Δ.\n",
    "$$\n",
    "In free-electron model (which gives rise to this Hamiltonian) electron motion is only\n",
    "by their own kinetic energy. As this model features no potential which could make one point\n",
    "in space more preferred than another, we would expect this model to be periodic.\n",
    "If an operator is periodic with respect to a lattice such as the one defined above,\n",
    "then it commutes with all lattice translations. For the free-electron case ``H``\n",
    "one can easily show exactly that, i.e.\n",
    "$$\n",
    "   T_{ma} H = H T_{ma} \\quad  ∀ m ∈ \\mathbb{Z}.\n",
    "$$\n",
    "We note in passing that the free-electron model is actually very special in the sense that\n",
    "the choice of ``a`` is completely arbitrary here. In other words ``H`` is periodic\n",
    "with respect to any translation. In general, however, periodicity is only\n",
    "attained with respect to a finite number of translations ``a`` and we will take this\n",
    "viewpoint here.\n",
    "\n",
    "**Bloch's theorem** now tells us that for periodic operators,\n",
    "the solutions to the eigenproblem\n",
    "$$\n",
    "    H ψ_{kn} = ε_{kn} ψ_{kn}\n",
    "$$\n",
    "satisfy a factorization\n",
    "$$\n",
    "    ψ_{kn}(x) = e^{i k⋅x} u_{kn}(x)\n",
    "$$\n",
    "into a plane wave ``e^{i k⋅x}`` and a lattice-periodic function\n",
    "$$\n",
    "   T_{ma} u_{kn}(x) = u_{kn}(x - ma) = u_{kn}(x) \\quad ∀ m ∈ \\mathbb{Z}.\n",
    "$$\n",
    "In this ``n`` is a labeling integer index and ``k`` is a real number,\n",
    "whose details will be clarified in the next section.\n",
    "The index ``n`` is sometimes also called the **band index** and\n",
    "functions ``ψ_{kn}`` satisfying this factorization are also known as\n",
    "**Bloch functions** or **Bloch states**.\n",
    "\n",
    "Consider the application of ``2H = -Δ = - \\frac{d^2}{d x^2}``\n",
    "to such a Bloch wave. First we notice for any function ``f``\n",
    "$$\n",
    "   -i∇ \\left( e^{i k⋅x} f \\right)\n",
    "   = -i\\frac{d}{dx} \\left( e^{i k⋅x} f \\right)\n",
    "   = k e^{i k⋅x} f + e^{i k⋅x} (-i∇) f = e^{i k⋅x} (-i∇ + k) f.\n",
    "$$\n",
    "Using this result twice one shows that applying ``-Δ`` yields\n",
    "$$\n",
    "\\begin{aligned}\n",
    "   -\\Delta \\left(e^{i k⋅x} u_{kn}(x)\\right)\n",
    "   &= -i∇ ⋅ \\left[-i∇ \\left(u_{kn}(x) e^{i k⋅x} \\right) \\right] \\\\\n",
    "   &= -i∇ ⋅ \\left[e^{i k⋅x} (-i∇ + k) u_{kn}(x) \\right] \\\\\n",
    "   &= e^{i k⋅x} (-i∇ + k)^2 u_{kn}(x) \\\\\n",
    "   &= e^{i k⋅x} 2H_k u_{kn}(x),\n",
    "\\end{aligned}\n",
    "$$\n",
    "where we defined\n",
    "$$\n",
    "    H_k = \\frac12 (-i∇ + k)^2.\n",
    "$$\n",
    "The action of this operator on a function ``u_{kn}`` is given by\n",
    "$$\n",
    "    H_k u_{kn} = e^{-i k⋅x} H e^{i k⋅x} u_{kn},\n",
    "$$\n",
    "which in particular implies that\n",
    "$$\n",
    "   H_k u_{kn} = ε_{kn} u_{kn} \\quad ⇔ \\quad H (e^{i k⋅x} u_{kn}) = ε_{kn} (e^{i k⋅x} u_{kn}).\n",
    "$$\n",
    "To seek the eigenpairs of ``H`` we may thus equivalently\n",
    "find the eigenpairs of *all* ``H_k``.\n",
    "The point of this is that the eigenfunctions ``u_{kn}`` of ``H_k``\n",
    "are periodic (unlike the eigenfunctions ``ψ_{kn}`` of ``H``).\n",
    "In contrast to ``ψ_{kn}`` the functions ``u_{kn}`` can thus be fully\n",
    "represented considering the eigenproblem only on the unit cell.\n",
    "\n",
    "A detailed mathematical analysis shows that the transformation from ``H``\n",
    "to the set of all ``H_k`` for a suitable set of values for ``k`` (details below)\n",
    "is actually a unitary transformation, the so-called **Bloch transform**.\n",
    "This transform brings the Hamiltonian into the symmetry-adapted basis for\n",
    "translational symmetry, which are exactly the Bloch functions.\n",
    "Similar to the case of choosing a symmetry-adapted basis for other kinds of symmetries\n",
    "(like the point group symmetry in molecules), the Bloch transform also makes\n",
    "the Hamiltonian ``H`` block-diagonal[^1]:\n",
    "$$\n",
    "    T_B H T_B^{-1} ⟶ \\left( \\begin{array}{cccc} H_1&&&0 \\\\ &H_2\\\\&&H_3\\\\0&&&\\ddots \\end{array} \\right)\n",
    "$$\n",
    "with each block ``H_k`` taking care of one value ``k``.\n",
    "This block-diagonal structure under the basis of Bloch functions lets us\n",
    "completely describe the spectrum of ``H`` by looking only at the spectrum\n",
    "of all ``H_k`` blocks.\n",
    "\n",
    "[^1]: Notice that block-diagonal is a bit an abuse of terms here, since the Hamiltonian\n",
    "      is not a matrix but an operator and the number of blocks is essentially infinite.\n",
    "      The mathematically precise term is that the Bloch transform reveals the fibers\n",
    "      of the Hamiltonian.\n",
    "\n",
    "## The Brillouin zone\n",
    "\n",
    "We now consider the parameter ``k`` of the Hamiltonian blocks in detail.\n",
    "\n",
    "- As discussed ``k`` is a real number. It turns out, however, that some of\n",
    "  these ``k∈\\mathbb{R}`` give rise to operators related by unitary transformations\n",
    "  (again due to translational symmetry).\n",
    "- Since such operators have the same eigenspectrum, only one version needs to be considered.\n",
    "- The smallest subset from which ``k`` is chosen is the **Brillouin zone** (BZ).\n",
    "\n",
    "- The BZ is the unit cell of the **reciprocal lattice**, which may be constructed from\n",
    "  the **real-space lattice** by a Fourier transform.\n",
    "- In our simple 1D case the reciprocal lattice is just\n",
    "  ```\n",
    "    ... |--------|--------|--------| ...\n",
    "           2π/a     2π/a     2π/a\n",
    "  ```\n",
    "  i.e. like the real-space lattice, but just with a different lattice constant\n",
    "  ``b = 2π / a``.\n",
    "- The BZ in our example is thus ``B = [-π/a, π/a)``. The members of ``B``\n",
    "  are typically called ``k``-points.\n",
    "\n",
    "## Discretization and plane-wave basis sets\n",
    "\n",
    "With what we discussed so far the strategy to find all eigenpairs of a periodic\n",
    "Hamiltonian ``H`` thus reduces to finding the eigenpairs of all ``H_k`` with ``k ∈ B``.\n",
    "This requires *two* discretisations:\n",
    "\n",
    "  - ``B`` is infinite (and not countable). To discretize we first only pick a finite number\n",
    "    of ``k``-points. Usually this **``k``-point sampling** is done by picking ``k``-points\n",
    "    along a regular grid inside the BZ, the **``k``-grid**.\n",
    "  - Each ``H_k`` is still an infinite-dimensional operator.\n",
    "    Following a standard Ritz-Galerkin ansatz we project the operator into a finite basis\n",
    "    and diagonalize the resulting matrix.\n",
    "\n",
    "For the second step multiple types of bases are used in practice (finite differences,\n",
    "finite elements, Gaussians, ...). In DFTK we currently support only plane-wave\n",
    "discretizations.\n",
    "\n",
    "For our 1D example normalized plane waves are defined as the functions\n",
    "$$\n",
    "e_{G}(x) = \\frac{e^{i G x}}{\\sqrt{a}}  \\qquad G \\in b\\mathbb{Z}\n",
    "$$\n",
    "and typically one forms basis sets from these by specifying a\n",
    "**kinetic energy cutoff** ``E_\\text{cut}``:\n",
    "$$\n",
    "\\left\\{ e_{G} \\, \\big| \\, (G + k)^2 \\leq 2E_\\text{cut} \\right\\}\n",
    "$$\n",
    "\n",
    "## Correspondence of theory to DFTK code\n",
    "\n",
    "Before solving a few example problems numerically in DFTK, a short overview\n",
    "of the correspondence of the introduced quantities to data structures inside DFTK.\n",
    "\n",
    "- ``H`` is represented by a `Hamiltonian` object and variables for hamiltonians are usually called `ham`.\n",
    "- ``H_k`` by a `HamiltonianBlock` and variables are `hamk`.\n",
    "- ``ψ_{kn}`` is usually just called `ψ`.\n",
    "  ``u_{kn}`` is not stored (in favor of ``ψ_{kn}``).\n",
    "- ``ε_{kn}`` is called `eigenvalues`.\n",
    "- ``k``-points are represented by `Kpoint` and respective variables called `kpt`.\n",
    "- The basis of plane waves is managed by `PlaneWaveBasis` and variables usually just called `basis`.\n",
    "\n",
    "## Solving the free-electron Hamiltonian\n",
    "\n",
    "One typical approach to get physical insight into a Hamiltonian ``H`` is to plot\n",
    "a so-called **band structure**, that is the eigenvalues of ``H_k`` versus ``k``.\n",
    "In DFTK we achieve this using the following steps:\n",
    "\n",
    "Step 1: Build the 1D lattice. DFTK is mostly tailored for 3D problems.\n",
    "Therefore quantities related to the problem space are have a fixed\n",
    "dimension 3. The convention is that for 1D / 2D problems the\n",
    "trailing entries are always zero and ignored in the computation.\n",
    "For the lattice we therefore construct a 3x3 matrix with only one entry."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "using DFTK\n",
    "\n",
    "lattice = zeros(3, 3)\n",
    "lattice[1, 1] = 20.;"
   ],
   "metadata": {},
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "source": [
    "Step 2: Select a model. In this case we choose a free-electron model,\n",
    "which is the same as saying that there is only a Kinetic term\n",
    "(and no potential) in the model."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Model(custom, 1D):\n    lattice (in Bohr)    : [20        , 0         , 0         ]\n                           [0         , 0         , 0         ]\n                           [0         , 0         , 0         ]\n    unit cell volume     : 20 Bohr³\n\n    num. electrons       : 0\n    spin polarization    : none\n    temperature          : 0 Ha\n\n    terms                : Kinetic()"
     },
     "metadata": {},
     "execution_count": 2
    }
   ],
   "cell_type": "code",
   "source": [
    "model = Model(lattice; terms=[Kinetic()])"
   ],
   "metadata": {},
   "execution_count": 2
  },
  {
   "cell_type": "markdown",
   "source": [
    "Step 3: Define a plane-wave basis using this model and a cutoff ``E_\\text{cut}``\n",
    "of 300 Hartree. The ``k``-point grid is given as a regular grid in the BZ\n",
    "(a so-called **Monkhorst-Pack** grid). Here we select only one ``k``-point (1x1x1),\n",
    "see the note below for some details on this choice."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "PlaneWaveBasis discretization:\n    Ecut                 : 300.0 Ha\n    fft_size             : (320, 1, 1), 320 total points\n    kgrid type           : Monkhorst-Pack\n    kgrid                : [1, 1, 1]\n    num. irred. kpoints  : 1\n\n    Discretized Model(custom, 1D):\n        lattice (in Bohr)    : [20        , 0         , 0         ]\n                               [0         , 0         , 0         ]\n                               [0         , 0         , 0         ]\n        unit cell volume     : 20 Bohr³\n    \n        num. electrons       : 0\n        spin polarization    : none\n        temperature          : 0 Ha\n    \n        terms                : Kinetic()"
     },
     "metadata": {},
     "execution_count": 3
    }
   ],
   "cell_type": "code",
   "source": [
    "basis = PlaneWaveBasis(model; Ecut=300, kgrid=(1, 1, 1))"
   ],
   "metadata": {},
   "execution_count": 3
  },
  {
   "cell_type": "markdown",
   "source": [
    "Step 4: Plot the bands! Select a density of ``k``-points for the ``k``-grid to use\n",
    "for the bandstructure calculation, discretize the problem and diagonalize it.\n",
    "Afterwards plot the bands."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing bands along kpath:\n",
      "       -½ -> ½\n",
      "\rDiagonalising Hamiltonian kblocks:   6%|█               |  ETA: 0:00:08\u001b[K\rDiagonalising Hamiltonian kblocks: 100%|████████████████| Time: 0:00:00\u001b[K\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=6}",
      "image/png": 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       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "cell_type": "code",
   "source": [
    "using Unitful\n",
    "using UnitfulAtomic\n",
    "using Plots\n",
    "\n",
    "plot_bandstructure(basis; n_bands=6, kline_density=100)"
   ],
   "metadata": {},
   "execution_count": 4
  },
  {
   "cell_type": "markdown",
   "source": [
    "!!! note \"Selection of k-point grids in `PlaneWaveBasis` construction\"\n",
    "    You might wonder why we only selected a single ``k``-point (clearly a very crude\n",
    "    and inaccurate approximation). In this example the `kgrid` parameter specified\n",
    "    in the construction of the `PlaneWaveBasis`\n",
    "    is not actually used for plotting the bands. It is only used when solving more\n",
    "    involved models like density-functional theory (DFT) where the Hamiltonian is\n",
    "    non-linear. In these cases before plotting the bands the self-consistent field\n",
    "    equations (SCF) need to be solved first. This is typically done on\n",
    "    a different ``k``-point grid than the grid used for the bands later on.\n",
    "    In our case we don't need this extra step and therefore the `kgrid` value passed\n",
    "    to `PlaneWaveBasis` is actually arbitrary."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Adding potentials\n",
    "So far so good. But free electrons are actually a little boring,\n",
    "so let's add a potential interacting with the electrons.\n",
    "\n",
    "- The modified problem we will look at consists of diagonalizing\n",
    "  $$\n",
    "  H_k = \\frac12 (-i \\nabla + k)^2 + V\n",
    "  $$\n",
    "  for all ``k \\in B`` with a periodic potential ``V`` interacting with the electrons.\n",
    "\n",
    "- A number of \"standard\" potentials are readily implemented in DFTK and\n",
    "  can be assembled using the `terms` kwarg of the model.\n",
    "  This allows to seamlessly construct\n",
    "\n",
    "  * density-functial theory (DFT) models for treating electronic structures\n",
    "    (see the Tutorial).\n",
    "  * Gross-Pitaevskii models for bosonic systems\n",
    "    (see Gross-Pitaevskii equation in one dimension)\n",
    "  * even some more unusual cases like anyonic models.\n",
    "\n",
    "In this tutorial we will go a little more low-level and directly provide\n",
    "an analytic potential describing the interaction with the electrons to DFTK.\n",
    "\n",
    "First we define a custom Gaussian potential as a new \"element\" inside DFTK:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "struct ElementGaussian <: DFTK.Element\n",
    "    α  # Prefactor\n",
    "    L  # Extend\n",
    "end\n",
    "\n",
    "# Some default values\n",
    "ElementGaussian() = ElementGaussian(0.3, 10.0)\n",
    "\n",
    "# Real-space representation of a Gaussian\n",
    "function DFTK.local_potential_real(el::ElementGaussian, r::Real)\n",
    "    -el.α / (√(2π) * el.L) * exp(- (r / el.L)^2 / 2)\n",
    "end\n",
    "\n",
    "# Fourier-space representation of the Gaussian\n",
    "function DFTK.local_potential_fourier(el::ElementGaussian, q::Real)\n",
    "    # = ∫ -α exp(-(r/L)^2 exp(-ir⋅q) dr\n",
    "    -el.α * exp(- (q * el.L)^2 / 2)\n",
    "end"
   ],
   "metadata": {},
   "execution_count": 5
  },
  {
   "cell_type": "markdown",
   "source": [
    "A single potential looks like:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=1}",
      "image/png": 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      ]
     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "cell_type": "code",
   "source": [
    "using Plots\n",
    "using LinearAlgebra\n",
    "nucleus = ElementGaussian()\n",
    "plot(r -> DFTK.local_potential_real(nucleus, norm(r)), xlims=(-50, 50))"
   ],
   "metadata": {},
   "execution_count": 6
  },
  {
   "cell_type": "markdown",
   "source": [
    "With this element at hand we can easily construct a setting\n",
    "where two potentials of this form are located at positions\n",
    "``20`` and ``80`` inside the lattice ``[0, 100]``:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=1}",
      "image/png": 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       "  771.158,1381.77 772.341,1382.25 773.524,1382.68 774.707,1383.05 775.89,1383.38 777.073,1383.65 778.256,1383.87 779.439,1384.04 780.622,1384.16 781.805,1384.22 \n",
       "  782.988,1384.24 784.171,1384.2 785.354,1384.11 786.537,1383.97 787.72,1383.78 788.903,1383.54 790.086,1383.24 791.269,1382.9 792.452,1382.5 793.635,1382.05 \n",
       "  794.818,1381.55 796,1381 797.183,1380.39 798.366,1379.74 799.549,1379.04 800.732,1378.28 801.915,1377.47 803.098,1376.61 804.281,1375.7 805.464,1374.74 \n",
       "  806.647,1373.73 807.83,1372.67 809.013,1371.56 810.196,1370.4 811.379,1369.19 812.562,1367.93 813.745,1366.62 814.928,1365.25 816.111,1363.84 817.294,1362.38 \n",
       "  818.477,1360.88 819.66,1359.32 820.843,1357.71 822.026,1356.06 823.209,1354.35 824.392,1352.6 825.575,1350.8 826.758,1348.95 827.941,1347.06 829.124,1345.11 \n",
       "  830.307,1343.12 831.49,1341.08 832.673,1339 833.856,1336.87 835.039,1334.69 836.222,1332.47 837.404,1330.2 838.587,1327.89 839.77,1325.53 840.953,1323.12 \n",
       "  842.136,1320.67 843.319,1318.18 844.502,1315.64 845.685,1313.06 846.868,1310.43 848.051,1307.76 849.234,1305.05 850.417,1302.3 851.6,1299.5 852.783,1296.66 \n",
       "  853.966,1293.78 855.149,1290.86 856.332,1287.89 857.515,1284.89 858.698,1281.84 859.881,1278.76 861.064,1275.63 862.247,1272.47 863.43,1269.27 864.613,1266.03 \n",
       "  865.796,1262.74 866.979,1259.43 868.162,1256.07 869.345,1252.68 870.528,1249.25 871.711,1245.78 872.894,1242.28 874.077,1238.74 875.26,1235.16 876.443,1231.55 \n",
       "  877.626,1227.91 878.809,1224.23 879.991,1220.52 881.174,1216.77 882.357,1212.99 883.54,1209.18 884.723,1205.34 885.906,1201.46 887.089,1197.56 888.272,1193.62 \n",
       "  889.455,1189.65 890.638,1185.65 891.821,1181.62 893.004,1177.56 894.187,1173.48 895.37,1169.36 896.553,1165.22 897.736,1161.04 898.919,1156.85 900.102,1152.62 \n",
       "  901.285,1148.37 902.468,1144.09 903.651,1139.79 904.834,1135.46 906.017,1131.1 907.2,1126.73 908.383,1122.33 909.566,1117.9 910.749,1113.45 911.932,1108.98 \n",
       "  913.115,1104.49 914.298,1099.98 915.481,1095.44 916.664,1090.89 917.847,1086.31 919.03,1081.72 920.213,1077.1 921.395,1072.47 922.578,1067.82 923.761,1063.15 \n",
       "  924.944,1058.46 926.127,1053.76 927.31,1049.03 928.493,1044.3 929.676,1039.54 930.859,1034.78 932.042,1029.99 933.225,1025.19 934.408,1020.38 935.591,1015.56 \n",
       "  936.774,1010.72 937.957,1005.87 939.14,1001 940.323,996.129 941.506,991.243 942.689,986.345 943.872,981.438 945.055,976.52 946.238,971.592 947.421,966.656 \n",
       "  948.604,961.711 949.787,956.757 950.97,951.796 952.153,946.827 953.336,941.852 954.519,936.869 955.702,931.881 956.885,926.887 958.068,921.887 959.251,916.883 \n",
       "  960.434,911.874 961.617,906.862 962.8,901.845 963.982,896.826 965.165,891.803 966.348,886.778 967.531,881.752 968.714,876.723 969.897,871.694 971.08,866.663 \n",
       "  972.263,861.633 973.446,856.602 974.629,851.572 975.812,846.542 976.995,841.514 978.178,836.487 979.361,831.462 980.544,826.44 981.727,821.42 982.91,816.403 \n",
       "  984.093,811.39 985.276,806.38 986.459,801.375 987.642,796.374 988.825,791.378 990.008,786.388 991.191,781.403 992.374,776.424 993.557,771.451 994.74,766.485 \n",
       "  995.923,761.526 997.106,756.574 998.289,751.63 999.472,746.694 1000.65,741.766 1001.84,736.847 1003.02,731.936 1004.2,727.035 1005.39,722.144 1006.57,717.263 \n",
       "  1007.75,712.391 1008.94,707.531 1010.12,702.681 1011.3,697.842 1012.48,693.014 1013.67,688.199 1014.85,683.395 1016.03,678.604 1017.22,673.825 1018.4,669.059 \n",
       "  1019.58,664.306 1020.77,659.566 1021.95,654.84 1023.13,650.128 1024.31,645.43 1025.5,640.747 1026.68,636.078 1027.86,631.424 1029.05,626.785 1030.23,622.162 \n",
       "  1031.41,617.554 1032.59,612.962 1033.78,608.386 1034.96,603.826 1036.14,599.283 1037.33,594.757 1038.51,590.248 1039.69,585.755 1040.88,581.281 1042.06,576.823 \n",
       "  1043.24,572.384 1044.42,567.962 1045.61,563.559 1046.79,559.174 1047.97,554.807 1049.16,550.46 1050.34,546.131 1051.52,541.821 1052.71,537.53 1053.89,533.259 \n",
       "  1055.07,529.007 1056.25,524.775 1057.44,520.563 1058.62,516.371 1059.8,512.199 1060.99,508.047 1062.17,503.916 1063.35,499.805 1064.54,495.715 1065.72,491.646 \n",
       "  1066.9,487.598 1068.08,483.571 1069.27,479.565 1070.45,475.58 1071.63,471.617 1072.82,467.675 1074,463.755 1075.18,459.857 1076.36,455.98 1077.55,452.126 \n",
       "  1078.73,448.293 1079.91,444.483 1081.1,440.695 1082.28,436.929 1083.46,433.185 1084.65,429.464 1085.83,425.765 1087.01,422.089 1088.19,418.435 1089.38,414.804 \n",
       "  1090.56,411.196 1091.74,407.61 1092.93,404.048 1094.11,400.508 1095.29,396.991 1096.48,393.497 1097.66,390.026 1098.84,386.578 1100.02,383.153 1101.21,379.752 \n",
       "  1102.39,376.373 1103.57,373.018 1104.76,369.686 1105.94,366.376 1107.12,363.091 1108.31,359.828 1109.49,356.589 1110.67,353.372 1111.85,350.179 1113.04,347.01 \n",
       "  1114.22,343.863 1115.4,340.74 1116.59,337.64 1117.77,334.563 1118.95,331.509 1120.13,328.479 1121.32,325.472 1122.5,322.487 1123.68,319.526 1124.87,316.589 \n",
       "  1126.05,313.674 1127.23,310.782 1128.42,307.913 1129.6,305.067 1130.78,302.245 1131.96,299.445 1133.15,296.668 1134.33,293.914 1135.51,291.182 1136.7,288.474 \n",
       "  1137.88,285.788 1139.06,283.125 1140.25,280.484 1141.43,277.866 1142.61,275.27 1143.79,272.697 1144.98,270.146 1146.16,267.618 1147.34,265.111 1148.53,262.627 \n",
       "  1149.71,260.166 1150.89,257.726 1152.08,255.308 1153.26,252.912 1154.44,250.538 1155.62,248.186 1156.81,245.855 1157.99,243.546 1159.17,241.259 1160.36,238.993 \n",
       "  1161.54,236.748 1162.72,234.525 1163.9,232.323 1165.09,230.142 1166.27,227.982 1167.45,225.843 1168.64,223.725 1169.82,221.628 1171,219.551 1172.19,217.496 \n",
       "  1173.37,215.46 1174.55,213.445 1175.73,211.451 1176.92,209.476 1178.1,207.522 1179.28,205.588 1180.47,203.674 1181.65,201.78 1182.83,199.905 1184.02,198.05 \n",
       "  1185.2,196.215 1186.38,194.399 1187.56,192.602 1188.75,190.825 1189.93,189.067 1191.11,187.328 1192.3,185.608 1193.48,183.906 1194.66,182.224 1195.84,180.56 \n",
       "  1197.03,178.914 1198.21,177.287 1199.39,175.679 1200.58,174.088 1201.76,172.516 1202.94,170.962 1204.13,169.425 1205.31,167.906 1206.49,166.405 1207.67,164.922 \n",
       "  1208.86,163.456 1210.04,162.007 1211.22,160.576 1212.41,159.162 1213.59,157.765 1214.77,156.384 1215.96,155.021 1217.14,153.674 1218.32,152.344 1219.5,151.03 \n",
       "  1220.69,149.733 1221.87,148.452 1223.05,147.187 1224.24,145.939 1225.42,144.706 1226.6,143.489 1227.79,142.288 1228.97,141.102 1230.15,139.932 1231.33,138.777 \n",
       "  1232.52,137.638 1233.7,136.514 1234.88,135.405 1236.07,134.311 1237.25,133.232 1238.43,132.168 1239.61,131.118 1240.8,130.083 1241.98,129.063 1243.16,128.057 \n",
       "  1244.35,127.065 1245.53,126.087 1246.71,125.124 1247.9,124.174 1249.08,123.239 1250.26,122.317 1251.44,121.409 1252.63,120.514 1253.81,119.633 1254.99,118.766 \n",
       "  1256.18,117.912 1257.36,117.071 1258.54,116.243 1259.73,115.428 1260.91,114.626 1262.09,113.837 1263.27,113.061 1264.46,112.298 1265.64,111.547 1266.82,110.809 \n",
       "  1268.01,110.083 1269.19,109.369 1270.37,108.668 1271.56,107.979 1272.74,107.302 1273.92,106.637 1275.1,105.983 1276.29,105.342 1277.47,104.713 1278.65,104.095 \n",
       "  1279.84,103.489 1281.02,102.894 1282.2,102.311 1283.38,101.74 1284.57,101.179 1285.75,100.63 1286.93,100.092 1288.12,99.5655 1289.3,99.0497 1290.48,98.545 \n",
       "  1291.67,98.0512 1292.85,97.5682 1294.03,97.096 1295.21,96.6346 1296.4,96.1838 1297.58,95.7437 1298.76,95.3141 1299.95,94.8949 1301.13,94.4863 1302.31,94.088 \n",
       "  1303.5,93.7 1304.68,93.3223 1305.86,92.9549 1307.04,92.5976 1308.23,92.2504 1309.41,91.9133 1310.59,91.5863 1311.78,91.2692 1312.96,90.962 1314.14,90.6648 \n",
       "  1315.33,90.3774 1316.51,90.0999 1317.69,89.8321 1318.87,89.574 1320.06,89.3257 1321.24,89.087 1322.42,88.858 1323.61,88.6385 1324.79,88.4286 1325.97,88.2283 \n",
       "  1327.15,88.0375 1328.34,87.8561 1329.52,87.6843 1330.7,87.5218 1331.89,87.3688 1333.07,87.2251 1334.25,87.0908 1335.44,86.9659 1336.62,86.8503 1337.8,86.744 \n",
       "  1338.98,86.6469 1340.17,86.5592 1341.35,86.4808 1342.53,86.4116 1343.72,86.3516 1344.9,86.3009 1346.08,86.2594 1347.27,86.2271 1348.45,86.2041 1349.63,86.1903 \n",
       "  1350.81,86.1857 1352,86.1903 1353.18,86.2041 1354.36,86.2271 1355.55,86.2594 1356.73,86.3009 1357.91,86.3516 1359.1,86.4116 1360.28,86.4808 1361.46,86.5592 \n",
       "  1362.64,86.6469 1363.83,86.744 1365.01,86.8503 1366.19,86.9659 1367.38,87.0908 1368.56,87.2251 1369.74,87.3688 1370.92,87.5218 1372.11,87.6843 1373.29,87.8561 \n",
       "  1374.47,88.0375 1375.66,88.2283 1376.84,88.4286 1378.02,88.6385 1379.21,88.858 1380.39,89.087 1381.57,89.3257 1382.75,89.574 1383.94,89.8321 1385.12,90.0999 \n",
       "  1386.3,90.3774 1387.49,90.6648 1388.67,90.962 1389.85,91.2692 1391.04,91.5863 1392.22,91.9133 1393.4,92.2504 1394.58,92.5976 1395.77,92.9549 1396.95,93.3223 \n",
       "  1398.13,93.7 1399.32,94.088 1400.5,94.4863 1401.68,94.8949 1402.87,95.3141 1404.05,95.7437 1405.23,96.1838 1406.41,96.6346 1407.6,97.096 1408.78,97.5682 \n",
       "  1409.96,98.0512 1411.15,98.545 1412.33,99.0497 1413.51,99.5655 1414.69,100.092 1415.88,100.63 1417.06,101.179 1418.24,101.74 1419.43,102.311 1420.61,102.894 \n",
       "  1421.79,103.489 1422.98,104.095 1424.16,104.713 1425.34,105.342 1426.52,105.983 1427.71,106.637 1428.89,107.302 1430.07,107.979 1431.26,108.668 1432.44,109.369 \n",
       "  1433.62,110.083 1434.81,110.809 1435.99,111.547 1437.17,112.298 1438.35,113.061 1439.54,113.837 1440.72,114.626 1441.9,115.428 1443.09,116.243 1444.27,117.071 \n",
       "  1445.45,117.912 1446.63,118.766 1447.82,119.633 1449,120.514 1450.18,121.409 1451.37,122.317 1452.55,123.239 1453.73,124.174 1454.92,125.124 1456.1,126.087 \n",
       "  1457.28,127.065 1458.46,128.057 1459.65,129.063 1460.83,130.083 1462.01,131.118 1463.2,132.168 1464.38,133.232 1465.56,134.311 1466.75,135.405 1467.93,136.514 \n",
       "  1469.11,137.638 1470.29,138.777 1471.48,139.932 1472.66,141.102 1473.84,142.288 1475.03,143.489 1476.21,144.706 1477.39,145.939 1478.58,147.187 1479.76,148.452 \n",
       "  1480.94,149.733 1482.12,151.03 1483.31,152.344 1484.49,153.674 1485.67,155.021 1486.86,156.384 1488.04,157.765 1489.22,159.162 1490.4,160.576 1491.59,162.007 \n",
       "  1492.77,163.456 1493.95,164.922 1495.14,166.405 1496.32,167.906 1497.5,169.425 1498.69,170.962 1499.87,172.516 1501.05,174.088 1502.23,175.679 1503.42,177.287 \n",
       "  1504.6,178.914 1505.78,180.56 1506.97,182.224 1508.15,183.906 1509.33,185.608 1510.52,187.328 1511.7,189.067 1512.88,190.825 1514.06,192.602 1515.25,194.399 \n",
       "  1516.43,196.215 1517.61,198.05 1518.8,199.905 1519.98,201.78 1521.16,203.674 1522.35,205.588 1523.53,207.522 1524.71,209.476 1525.89,211.451 1527.08,213.445 \n",
       "  1528.26,215.46 1529.44,217.496 1530.63,219.551 1531.81,221.628 1532.99,223.725 1534.17,225.843 1535.36,227.982 1536.54,230.142 1537.72,232.323 1538.91,234.525 \n",
       "  1540.09,236.748 1541.27,238.993 1542.46,241.259 1543.64,243.546 1544.82,245.855 1546,248.186 1547.19,250.538 1548.37,252.912 1549.55,255.308 1550.74,257.726 \n",
       "  1551.92,260.166 1553.1,262.627 1554.29,265.111 1555.47,267.618 1556.65,270.146 1557.83,272.697 1559.02,275.27 1560.2,277.866 1561.38,280.484 1562.57,283.125 \n",
       "  1563.75,285.788 1564.93,288.474 1566.12,291.182 1567.3,293.914 1568.48,296.668 1569.66,299.445 1570.85,302.245 1572.03,305.067 1573.21,307.913 1574.4,310.782 \n",
       "  1575.58,313.674 1576.76,316.589 1577.94,319.526 1579.13,322.487 1580.31,325.472 1581.49,328.479 1582.68,331.509 1583.86,334.563 1585.04,337.64 1586.23,340.74 \n",
       "  1587.41,343.863 1588.59,347.01 1589.77,350.179 1590.96,353.372 1592.14,356.589 1593.32,359.828 1594.51,363.091 1595.69,366.376 1596.87,369.686 1598.06,373.018 \n",
       "  1599.24,376.373 1600.42,379.752 1601.6,383.153 1602.79,386.578 1603.97,390.026 1605.15,393.497 1606.34,396.991 1607.52,400.508 1608.7,404.048 1609.89,407.61 \n",
       "  1611.07,411.196 1612.25,414.804 1613.43,418.435 1614.62,422.089 1615.8,425.765 1616.98,429.464 1618.17,433.185 1619.35,436.929 1620.53,440.695 1621.71,444.483 \n",
       "  1622.9,448.293 1624.08,452.126 1625.26,455.98 1626.45,459.857 1627.63,463.755 1628.81,467.675 1630,471.617 1631.18,475.58 1632.36,479.565 1633.54,483.571 \n",
       "  1634.73,487.598 1635.91,491.646 1637.09,495.715 1638.28,499.805 1639.46,503.916 1640.64,508.047 1641.83,512.199 1643.01,516.371 1644.19,520.563 1645.37,524.775 \n",
       "  1646.56,529.007 1647.74,533.259 1648.92,537.53 1650.11,541.821 1651.29,546.131 1652.47,550.46 1653.66,554.807 1654.84,559.174 1656.02,563.559 1657.2,567.962 \n",
       "  1658.39,572.384 1659.57,576.823 1660.75,581.281 1661.94,585.755 1663.12,590.248 1664.3,594.757 1665.48,599.283 1666.67,603.826 1667.85,608.386 1669.03,612.962 \n",
       "  1670.22,617.554 1671.4,622.162 1672.58,626.785 1673.77,631.424 1674.95,636.078 1676.13,640.747 1677.31,645.43 1678.5,650.128 1679.68,654.84 1680.86,659.566 \n",
       "  1682.05,664.306 1683.23,669.059 1684.41,673.825 1685.6,678.604 1686.78,683.395 1687.96,688.199 1689.14,693.014 1690.33,697.842 1691.51,702.681 1692.69,707.531 \n",
       "  1693.88,712.391 1695.06,717.263 1696.24,722.144 1697.43,727.035 1698.61,731.936 1699.79,736.847 1700.97,741.766 1702.16,746.694 1703.34,751.63 1704.52,756.574 \n",
       "  1705.71,761.526 1706.89,766.485 1708.07,771.451 1709.25,776.424 1710.44,781.403 1711.62,786.388 1712.8,791.378 1713.99,796.374 1715.17,801.375 1716.35,806.38 \n",
       "  1717.54,811.39 1718.72,816.403 1719.9,821.42 1721.08,826.44 1722.27,831.462 1723.45,836.487 1724.63,841.514 1725.82,846.542 1727,851.572 1728.18,856.602 \n",
       "  1729.37,861.633 1730.55,866.663 1731.73,871.694 1732.91,876.723 1734.1,881.752 1735.28,886.778 1736.46,891.803 1737.65,896.826 1738.83,901.845 1740.01,906.862 \n",
       "  1741.19,911.874 1742.38,916.883 1743.56,921.887 1744.74,926.887 1745.93,931.881 1747.11,936.869 1748.29,941.852 1749.48,946.827 1750.66,951.796 1751.84,956.757 \n",
       "  1753.02,961.711 1754.21,966.656 1755.39,971.592 1756.57,976.52 1757.76,981.438 1758.94,986.345 1760.12,991.243 1761.31,996.129 1762.49,1001 1763.67,1005.87 \n",
       "  1764.85,1010.72 1766.04,1015.56 1767.22,1020.38 1768.4,1025.19 1769.59,1029.99 1770.77,1034.78 1771.95,1039.54 1773.14,1044.3 1774.32,1049.03 1775.5,1053.76 \n",
       "  1776.68,1058.46 1777.87,1063.15 1779.05,1067.82 1780.23,1072.47 1781.42,1077.1 1782.6,1081.72 1783.78,1086.31 1784.96,1090.89 1786.15,1095.44 1787.33,1099.98 \n",
       "  1788.51,1104.49 1789.7,1108.98 1790.88,1113.45 1792.06,1117.9 1793.25,1122.33 1794.43,1126.73 1795.61,1131.1 1796.79,1135.46 1797.98,1139.79 1799.16,1144.09 \n",
       "  1800.34,1148.37 1801.53,1152.62 1802.71,1156.85 1803.89,1161.04 1805.08,1165.22 1806.26,1169.36 1807.44,1173.48 1808.62,1177.56 1809.81,1181.62 1810.99,1185.65 \n",
       "  1812.17,1189.65 1813.36,1193.62 1814.54,1197.56 1815.72,1201.46 1816.91,1205.34 1818.09,1209.18 1819.27,1212.99 1820.45,1216.77 1821.64,1220.52 1822.82,1224.23 \n",
       "  1824,1227.91 1825.19,1231.55 1826.37,1235.16 1827.55,1238.74 1828.73,1242.28 1829.92,1245.78 1831.1,1249.25 1832.28,1252.68 1833.47,1256.07 1834.65,1259.43 \n",
       "  1835.83,1262.74 1837.02,1266.03 1838.2,1269.27 1839.38,1272.47 1840.56,1275.63 1841.75,1278.76 1842.93,1281.84 1844.11,1284.89 1845.3,1287.89 1846.48,1290.86 \n",
       "  1847.66,1293.78 1848.85,1296.66 1850.03,1299.5 1851.21,1302.3 1852.39,1305.05 1853.58,1307.76 1854.76,1310.43 1855.94,1313.06 1857.13,1315.64 1858.31,1318.18 \n",
       "  1859.49,1320.67 1860.68,1323.12 1861.86,1325.53 1863.04,1327.89 1864.22,1330.2 1865.41,1332.47 1866.59,1334.69 1867.77,1336.87 1868.96,1339 1870.14,1341.08 \n",
       "  1871.32,1343.12 1872.5,1345.11 1873.69,1347.06 1874.87,1348.95 1876.05,1350.8 1877.24,1352.6 1878.42,1354.35 1879.6,1356.06 1880.79,1357.71 1881.97,1359.32 \n",
       "  1883.15,1360.88 1884.33,1362.38 1885.52,1363.84 1886.7,1365.25 1887.88,1366.62 1889.07,1367.93 1890.25,1369.19 1891.43,1370.4 1892.62,1371.56 1893.8,1372.67 \n",
       "  1894.98,1373.73 1896.16,1374.74 1897.35,1375.7 1898.53,1376.61 1899.71,1377.47 1900.9,1378.28 1902.08,1379.04 1903.26,1379.74 1904.45,1380.39 1905.63,1381 \n",
       "  1906.81,1381.55 1907.99,1382.05 1909.18,1382.5 1910.36,1382.9 1911.54,1383.24 1912.73,1383.54 1913.91,1383.78 1915.09,1383.97 1916.27,1384.11 1917.46,1384.2 \n",
       "  1918.64,1384.24 1919.82,1384.22 1921.01,1384.16 1922.19,1384.04 1923.37,1383.87 1924.56,1383.65 1925.74,1383.38 1926.92,1383.05 1928.1,1382.68 1929.29,1382.25 \n",
       "  1930.47,1381.77 1931.65,1381.25 1932.84,1380.67 1934.02,1380.03 1935.2,1379.35 1936.39,1378.62 1937.57,1377.83 1938.75,1377 1939.93,1376.12 1941.12,1375.18 \n",
       "  1942.3,1374.19 1943.48,1373.16 1944.67,1372.07 1945.85,1370.94 1947.03,1369.75 1948.22,1368.51 1949.4,1367.23 1950.58,1365.89 1951.76,1364.51 1952.95,1363.08 \n",
       "  1954.13,1361.6 1955.31,1360.06 1956.5,1358.49 1957.68,1356.86 1958.86,1355.18 1960.04,1353.46 1961.23,1351.69 1962.41,1349.87 1963.59,1348.01 1964.78,1346.09 \n",
       "  1965.96,1344.14 1967.14,1342.13 1968.33,1340.08 1969.51,1337.98 1970.69,1335.84 1971.87,1333.65 1973.06,1331.41 1974.24,1329.13 1975.42,1326.81 1976.61,1324.44 \n",
       "  1977.79,1322.03 1978.97,1319.57 1980.16,1317.07 1981.34,1314.53 1982.52,1311.95 1983.7,1309.32 1984.89,1306.65 1986.07,1303.93 1987.25,1301.18 1988.44,1298.38 \n",
       "  1989.62,1295.55 1990.8,1292.67 1991.98,1289.75 1993.17,1286.79 1994.35,1283.8 1995.53,1280.76 1996.72,1277.69 1997.9,1274.57 1999.08,1271.42 2000.27,1268.23 \n",
       "  2001.45,1265 2002.63,1261.74 2003.81,1258.44 2005,1255.1 2006.18,1251.73 2007.36,1248.32 2008.55,1244.88 2009.73,1241.4 2010.91,1237.88 2012.1,1234.34 \n",
       "  2013.28,1230.76 2014.46,1227.15 2015.64,1223.5 2016.83,1219.82 2018.01,1216.11 2019.19,1212.37 2020.38,1208.6 2021.56,1204.8 2022.74,1200.97 2023.93,1197.1 \n",
       "  2025.11,1193.21 2026.29,1189.29 2027.47,1185.35 2028.66,1181.37 2029.84,1177.37 2031.02,1173.34 2032.21,1169.28 2033.39,1165.2 2034.57,1161.09 2035.75,1156.96 \n",
       "  2036.94,1152.8 2038.12,1148.62 2039.3,1144.41 2040.49,1140.18 2041.67,1135.93 2042.85,1131.66 2044.04,1127.36 2045.22,1123.04 2046.4,1118.7 2047.58,1114.35 \n",
       "  2048.77,1109.97 2049.95,1105.57 2051.13,1101.15 2052.32,1096.72 2053.5,1092.26 2054.68,1087.79 2055.87,1083.3 2057.05,1078.8 2058.23,1074.28 2059.41,1069.74 \n",
       "  2060.6,1065.19 2061.78,1060.63 2062.96,1056.05 2064.15,1051.45 2065.33,1046.85 2066.51,1042.23 2067.7,1037.6 2068.88,1032.95 2070.06,1028.3 2071.24,1023.63 \n",
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       "  2084.26,971.753 2085.44,966.997 2086.62,962.238 2087.81,957.474 2088.99,952.708 2090.17,947.938 2091.35,943.166 2092.54,938.392 2093.72,933.616 2094.9,928.839 \n",
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       "  924.944,1058.46 926.127,1053.76 927.31,1049.03 928.493,1044.3 929.676,1039.54 930.859,1034.78 932.042,1029.99 933.225,1025.19 934.408,1020.38 935.591,1015.56 \n",
       "  936.774,1010.72 937.957,1005.87 939.14,1001 940.323,996.129 941.506,991.243 942.689,986.345 943.872,981.438 945.055,976.52 946.238,971.592 947.421,966.656 \n",
       "  948.604,961.711 949.787,956.757 950.97,951.796 952.153,946.827 953.336,941.852 954.519,936.869 955.702,931.881 956.885,926.887 958.068,921.887 959.251,916.883 \n",
       "  960.434,911.874 961.617,906.862 962.8,901.845 963.982,896.826 965.165,891.803 966.348,886.778 967.531,881.752 968.714,876.723 969.897,871.694 971.08,866.663 \n",
       "  972.263,861.633 973.446,856.602 974.629,851.572 975.812,846.542 976.995,841.514 978.178,836.487 979.361,831.462 980.544,826.44 981.727,821.42 982.91,816.403 \n",
       "  984.093,811.39 985.276,806.38 986.459,801.375 987.642,796.374 988.825,791.378 990.008,786.388 991.191,781.403 992.374,776.424 993.557,771.451 994.74,766.485 \n",
       "  995.923,761.526 997.106,756.574 998.289,751.63 999.472,746.694 1000.65,741.766 1001.84,736.847 1003.02,731.936 1004.2,727.035 1005.39,722.144 1006.57,717.263 \n",
       "  1007.75,712.391 1008.94,707.531 1010.12,702.681 1011.3,697.842 1012.48,693.014 1013.67,688.199 1014.85,683.395 1016.03,678.604 1017.22,673.825 1018.4,669.059 \n",
       "  1019.58,664.306 1020.77,659.566 1021.95,654.84 1023.13,650.128 1024.31,645.43 1025.5,640.747 1026.68,636.078 1027.86,631.424 1029.05,626.785 1030.23,622.162 \n",
       "  1031.41,617.554 1032.59,612.962 1033.78,608.386 1034.96,603.826 1036.14,599.283 1037.33,594.757 1038.51,590.248 1039.69,585.755 1040.88,581.281 1042.06,576.823 \n",
       "  1043.24,572.384 1044.42,567.962 1045.61,563.559 1046.79,559.174 1047.97,554.807 1049.16,550.46 1050.34,546.131 1051.52,541.821 1052.71,537.53 1053.89,533.259 \n",
       "  1055.07,529.007 1056.25,524.775 1057.44,520.563 1058.62,516.371 1059.8,512.199 1060.99,508.047 1062.17,503.916 1063.35,499.805 1064.54,495.715 1065.72,491.646 \n",
       "  1066.9,487.598 1068.08,483.571 1069.27,479.565 1070.45,475.58 1071.63,471.617 1072.82,467.675 1074,463.755 1075.18,459.857 1076.36,455.98 1077.55,452.126 \n",
       "  1078.73,448.293 1079.91,444.483 1081.1,440.695 1082.28,436.929 1083.46,433.185 1084.65,429.464 1085.83,425.765 1087.01,422.089 1088.19,418.435 1089.38,414.804 \n",
       "  1090.56,411.196 1091.74,407.61 1092.93,404.048 1094.11,400.508 1095.29,396.991 1096.48,393.497 1097.66,390.026 1098.84,386.578 1100.02,383.153 1101.21,379.752 \n",
       "  1102.39,376.373 1103.57,373.018 1104.76,369.686 1105.94,366.376 1107.12,363.091 1108.31,359.828 1109.49,356.589 1110.67,353.372 1111.85,350.179 1113.04,347.01 \n",
       "  1114.22,343.863 1115.4,340.74 1116.59,337.64 1117.77,334.563 1118.95,331.509 1120.13,328.479 1121.32,325.472 1122.5,322.487 1123.68,319.526 1124.87,316.589 \n",
       "  1126.05,313.674 1127.23,310.782 1128.42,307.913 1129.6,305.067 1130.78,302.245 1131.96,299.445 1133.15,296.668 1134.33,293.914 1135.51,291.182 1136.7,288.474 \n",
       "  1137.88,285.788 1139.06,283.125 1140.25,280.484 1141.43,277.866 1142.61,275.27 1143.79,272.697 1144.98,270.146 1146.16,267.618 1147.34,265.111 1148.53,262.627 \n",
       "  1149.71,260.166 1150.89,257.726 1152.08,255.308 1153.26,252.912 1154.44,250.538 1155.62,248.186 1156.81,245.855 1157.99,243.546 1159.17,241.259 1160.36,238.993 \n",
       "  1161.54,236.748 1162.72,234.525 1163.9,232.323 1165.09,230.142 1166.27,227.982 1167.45,225.843 1168.64,223.725 1169.82,221.628 1171,219.551 1172.19,217.496 \n",
       "  1173.37,215.46 1174.55,213.445 1175.73,211.451 1176.92,209.476 1178.1,207.522 1179.28,205.588 1180.47,203.674 1181.65,201.78 1182.83,199.905 1184.02,198.05 \n",
       "  1185.2,196.215 1186.38,194.399 1187.56,192.602 1188.75,190.825 1189.93,189.067 1191.11,187.328 1192.3,185.608 1193.48,183.906 1194.66,182.224 1195.84,180.56 \n",
       "  1197.03,178.914 1198.21,177.287 1199.39,175.679 1200.58,174.088 1201.76,172.516 1202.94,170.962 1204.13,169.425 1205.31,167.906 1206.49,166.405 1207.67,164.922 \n",
       "  1208.86,163.456 1210.04,162.007 1211.22,160.576 1212.41,159.162 1213.59,157.765 1214.77,156.384 1215.96,155.021 1217.14,153.674 1218.32,152.344 1219.5,151.03 \n",
       "  1220.69,149.733 1221.87,148.452 1223.05,147.187 1224.24,145.939 1225.42,144.706 1226.6,143.489 1227.79,142.288 1228.97,141.102 1230.15,139.932 1231.33,138.777 \n",
       "  1232.52,137.638 1233.7,136.514 1234.88,135.405 1236.07,134.311 1237.25,133.232 1238.43,132.168 1239.61,131.118 1240.8,130.083 1241.98,129.063 1243.16,128.057 \n",
       "  1244.35,127.065 1245.53,126.087 1246.71,125.124 1247.9,124.174 1249.08,123.239 1250.26,122.317 1251.44,121.409 1252.63,120.514 1253.81,119.633 1254.99,118.766 \n",
       "  1256.18,117.912 1257.36,117.071 1258.54,116.243 1259.73,115.428 1260.91,114.626 1262.09,113.837 1263.27,113.061 1264.46,112.298 1265.64,111.547 1266.82,110.809 \n",
       "  1268.01,110.083 1269.19,109.369 1270.37,108.668 1271.56,107.979 1272.74,107.302 1273.92,106.637 1275.1,105.983 1276.29,105.342 1277.47,104.713 1278.65,104.095 \n",
       "  1279.84,103.489 1281.02,102.894 1282.2,102.311 1283.38,101.74 1284.57,101.179 1285.75,100.63 1286.93,100.092 1288.12,99.5655 1289.3,99.0497 1290.48,98.545 \n",
       "  1291.67,98.0512 1292.85,97.5682 1294.03,97.096 1295.21,96.6346 1296.4,96.1838 1297.58,95.7437 1298.76,95.3141 1299.95,94.8949 1301.13,94.4863 1302.31,94.088 \n",
       "  1303.5,93.7 1304.68,93.3223 1305.86,92.9549 1307.04,92.5976 1308.23,92.2504 1309.41,91.9133 1310.59,91.5863 1311.78,91.2692 1312.96,90.962 1314.14,90.6648 \n",
       "  1315.33,90.3774 1316.51,90.0999 1317.69,89.8321 1318.87,89.574 1320.06,89.3257 1321.24,89.087 1322.42,88.858 1323.61,88.6385 1324.79,88.4286 1325.97,88.2283 \n",
       "  1327.15,88.0375 1328.34,87.8561 1329.52,87.6843 1330.7,87.5218 1331.89,87.3688 1333.07,87.2251 1334.25,87.0908 1335.44,86.9659 1336.62,86.8503 1337.8,86.744 \n",
       "  1338.98,86.6469 1340.17,86.5592 1341.35,86.4808 1342.53,86.4116 1343.72,86.3516 1344.9,86.3009 1346.08,86.2594 1347.27,86.2271 1348.45,86.2041 1349.63,86.1903 \n",
       "  1350.81,86.1857 1352,86.1903 1353.18,86.2041 1354.36,86.2271 1355.55,86.2594 1356.73,86.3009 1357.91,86.3516 1359.1,86.4116 1360.28,86.4808 1361.46,86.5592 \n",
       "  1362.64,86.6469 1363.83,86.744 1365.01,86.8503 1366.19,86.9659 1367.38,87.0908 1368.56,87.2251 1369.74,87.3688 1370.92,87.5218 1372.11,87.6843 1373.29,87.8561 \n",
       "  1374.47,88.0375 1375.66,88.2283 1376.84,88.4286 1378.02,88.6385 1379.21,88.858 1380.39,89.087 1381.57,89.3257 1382.75,89.574 1383.94,89.8321 1385.12,90.0999 \n",
       "  1386.3,90.3774 1387.49,90.6648 1388.67,90.962 1389.85,91.2692 1391.04,91.5863 1392.22,91.9133 1393.4,92.2504 1394.58,92.5976 1395.77,92.9549 1396.95,93.3223 \n",
       "  1398.13,93.7 1399.32,94.088 1400.5,94.4863 1401.68,94.8949 1402.87,95.3141 1404.05,95.7437 1405.23,96.1838 1406.41,96.6346 1407.6,97.096 1408.78,97.5682 \n",
       "  1409.96,98.0512 1411.15,98.545 1412.33,99.0497 1413.51,99.5655 1414.69,100.092 1415.88,100.63 1417.06,101.179 1418.24,101.74 1419.43,102.311 1420.61,102.894 \n",
       "  1421.79,103.489 1422.98,104.095 1424.16,104.713 1425.34,105.342 1426.52,105.983 1427.71,106.637 1428.89,107.302 1430.07,107.979 1431.26,108.668 1432.44,109.369 \n",
       "  1433.62,110.083 1434.81,110.809 1435.99,111.547 1437.17,112.298 1438.35,113.061 1439.54,113.837 1440.72,114.626 1441.9,115.428 1443.09,116.243 1444.27,117.071 \n",
       "  1445.45,117.912 1446.63,118.766 1447.82,119.633 1449,120.514 1450.18,121.409 1451.37,122.317 1452.55,123.239 1453.73,124.174 1454.92,125.124 1456.1,126.087 \n",
       "  1457.28,127.065 1458.46,128.057 1459.65,129.063 1460.83,130.083 1462.01,131.118 1463.2,132.168 1464.38,133.232 1465.56,134.311 1466.75,135.405 1467.93,136.514 \n",
       "  1469.11,137.638 1470.29,138.777 1471.48,139.932 1472.66,141.102 1473.84,142.288 1475.03,143.489 1476.21,144.706 1477.39,145.939 1478.58,147.187 1479.76,148.452 \n",
       "  1480.94,149.733 1482.12,151.03 1483.31,152.344 1484.49,153.674 1485.67,155.021 1486.86,156.384 1488.04,157.765 1489.22,159.162 1490.4,160.576 1491.59,162.007 \n",
       "  1492.77,163.456 1493.95,164.922 1495.14,166.405 1496.32,167.906 1497.5,169.425 1498.69,170.962 1499.87,172.516 1501.05,174.088 1502.23,175.679 1503.42,177.287 \n",
       "  1504.6,178.914 1505.78,180.56 1506.97,182.224 1508.15,183.906 1509.33,185.608 1510.52,187.328 1511.7,189.067 1512.88,190.825 1514.06,192.602 1515.25,194.399 \n",
       "  1516.43,196.215 1517.61,198.05 1518.8,199.905 1519.98,201.78 1521.16,203.674 1522.35,205.588 1523.53,207.522 1524.71,209.476 1525.89,211.451 1527.08,213.445 \n",
       "  1528.26,215.46 1529.44,217.496 1530.63,219.551 1531.81,221.628 1532.99,223.725 1534.17,225.843 1535.36,227.982 1536.54,230.142 1537.72,232.323 1538.91,234.525 \n",
       "  1540.09,236.748 1541.27,238.993 1542.46,241.259 1543.64,243.546 1544.82,245.855 1546,248.186 1547.19,250.538 1548.37,252.912 1549.55,255.308 1550.74,257.726 \n",
       "  1551.92,260.166 1553.1,262.627 1554.29,265.111 1555.47,267.618 1556.65,270.146 1557.83,272.697 1559.02,275.27 1560.2,277.866 1561.38,280.484 1562.57,283.125 \n",
       "  1563.75,285.788 1564.93,288.474 1566.12,291.182 1567.3,293.914 1568.48,296.668 1569.66,299.445 1570.85,302.245 1572.03,305.067 1573.21,307.913 1574.4,310.782 \n",
       "  1575.58,313.674 1576.76,316.589 1577.94,319.526 1579.13,322.487 1580.31,325.472 1581.49,328.479 1582.68,331.509 1583.86,334.563 1585.04,337.64 1586.23,340.74 \n",
       "  1587.41,343.863 1588.59,347.01 1589.77,350.179 1590.96,353.372 1592.14,356.589 1593.32,359.828 1594.51,363.091 1595.69,366.376 1596.87,369.686 1598.06,373.018 \n",
       "  1599.24,376.373 1600.42,379.752 1601.6,383.153 1602.79,386.578 1603.97,390.026 1605.15,393.497 1606.34,396.991 1607.52,400.508 1608.7,404.048 1609.89,407.61 \n",
       "  1611.07,411.196 1612.25,414.804 1613.43,418.435 1614.62,422.089 1615.8,425.765 1616.98,429.464 1618.17,433.185 1619.35,436.929 1620.53,440.695 1621.71,444.483 \n",
       "  1622.9,448.293 1624.08,452.126 1625.26,455.98 1626.45,459.857 1627.63,463.755 1628.81,467.675 1630,471.617 1631.18,475.58 1632.36,479.565 1633.54,483.571 \n",
       "  1634.73,487.598 1635.91,491.646 1637.09,495.715 1638.28,499.805 1639.46,503.916 1640.64,508.047 1641.83,512.199 1643.01,516.371 1644.19,520.563 1645.37,524.775 \n",
       "  1646.56,529.007 1647.74,533.259 1648.92,537.53 1650.11,541.821 1651.29,546.131 1652.47,550.46 1653.66,554.807 1654.84,559.174 1656.02,563.559 1657.2,567.962 \n",
       "  1658.39,572.384 1659.57,576.823 1660.75,581.281 1661.94,585.755 1663.12,590.248 1664.3,594.757 1665.48,599.283 1666.67,603.826 1667.85,608.386 1669.03,612.962 \n",
       "  1670.22,617.554 1671.4,622.162 1672.58,626.785 1673.77,631.424 1674.95,636.078 1676.13,640.747 1677.31,645.43 1678.5,650.128 1679.68,654.84 1680.86,659.566 \n",
       "  1682.05,664.306 1683.23,669.059 1684.41,673.825 1685.6,678.604 1686.78,683.395 1687.96,688.199 1689.14,693.014 1690.33,697.842 1691.51,702.681 1692.69,707.531 \n",
       "  1693.88,712.391 1695.06,717.263 1696.24,722.144 1697.43,727.035 1698.61,731.936 1699.79,736.847 1700.97,741.766 1702.16,746.694 1703.34,751.63 1704.52,756.574 \n",
       "  1705.71,761.526 1706.89,766.485 1708.07,771.451 1709.25,776.424 1710.44,781.403 1711.62,786.388 1712.8,791.378 1713.99,796.374 1715.17,801.375 1716.35,806.38 \n",
       "  1717.54,811.39 1718.72,816.403 1719.9,821.42 1721.08,826.44 1722.27,831.462 1723.45,836.487 1724.63,841.514 1725.82,846.542 1727,851.572 1728.18,856.602 \n",
       "  1729.37,861.633 1730.55,866.663 1731.73,871.694 1732.91,876.723 1734.1,881.752 1735.28,886.778 1736.46,891.803 1737.65,896.826 1738.83,901.845 1740.01,906.862 \n",
       "  1741.19,911.874 1742.38,916.883 1743.56,921.887 1744.74,926.887 1745.93,931.881 1747.11,936.869 1748.29,941.852 1749.48,946.827 1750.66,951.796 1751.84,956.757 \n",
       "  1753.02,961.711 1754.21,966.656 1755.39,971.592 1756.57,976.52 1757.76,981.438 1758.94,986.345 1760.12,991.243 1761.31,996.129 1762.49,1001 1763.67,1005.87 \n",
       "  1764.85,1010.72 1766.04,1015.56 1767.22,1020.38 1768.4,1025.19 1769.59,1029.99 1770.77,1034.78 1771.95,1039.54 1773.14,1044.3 1774.32,1049.03 1775.5,1053.76 \n",
       "  1776.68,1058.46 1777.87,1063.15 1779.05,1067.82 1780.23,1072.47 1781.42,1077.1 1782.6,1081.72 1783.78,1086.31 1784.96,1090.89 1786.15,1095.44 1787.33,1099.98 \n",
       "  1788.51,1104.49 1789.7,1108.98 1790.88,1113.45 1792.06,1117.9 1793.25,1122.33 1794.43,1126.73 1795.61,1131.1 1796.79,1135.46 1797.98,1139.79 1799.16,1144.09 \n",
       "  1800.34,1148.37 1801.53,1152.62 1802.71,1156.85 1803.89,1161.04 1805.08,1165.22 1806.26,1169.36 1807.44,1173.48 1808.62,1177.56 1809.81,1181.62 1810.99,1185.65 \n",
       "  1812.17,1189.65 1813.36,1193.62 1814.54,1197.56 1815.72,1201.46 1816.91,1205.34 1818.09,1209.18 1819.27,1212.99 1820.45,1216.77 1821.64,1220.52 1822.82,1224.23 \n",
       "  1824,1227.91 1825.19,1231.55 1826.37,1235.16 1827.55,1238.74 1828.73,1242.28 1829.92,1245.78 1831.1,1249.25 1832.28,1252.68 1833.47,1256.07 1834.65,1259.43 \n",
       "  1835.83,1262.74 1837.02,1266.03 1838.2,1269.27 1839.38,1272.47 1840.56,1275.63 1841.75,1278.76 1842.93,1281.84 1844.11,1284.89 1845.3,1287.89 1846.48,1290.86 \n",
       "  1847.66,1293.78 1848.85,1296.66 1850.03,1299.5 1851.21,1302.3 1852.39,1305.05 1853.58,1307.76 1854.76,1310.43 1855.94,1313.06 1857.13,1315.64 1858.31,1318.18 \n",
       "  1859.49,1320.67 1860.68,1323.12 1861.86,1325.53 1863.04,1327.89 1864.22,1330.2 1865.41,1332.47 1866.59,1334.69 1867.77,1336.87 1868.96,1339 1870.14,1341.08 \n",
       "  1871.32,1343.12 1872.5,1345.11 1873.69,1347.06 1874.87,1348.95 1876.05,1350.8 1877.24,1352.6 1878.42,1354.35 1879.6,1356.06 1880.79,1357.71 1881.97,1359.32 \n",
       "  1883.15,1360.88 1884.33,1362.38 1885.52,1363.84 1886.7,1365.25 1887.88,1366.62 1889.07,1367.93 1890.25,1369.19 1891.43,1370.4 1892.62,1371.56 1893.8,1372.67 \n",
       "  1894.98,1373.73 1896.16,1374.74 1897.35,1375.7 1898.53,1376.61 1899.71,1377.47 1900.9,1378.28 1902.08,1379.04 1903.26,1379.74 1904.45,1380.39 1905.63,1381 \n",
       "  1906.81,1381.55 1907.99,1382.05 1909.18,1382.5 1910.36,1382.9 1911.54,1383.24 1912.73,1383.54 1913.91,1383.78 1915.09,1383.97 1916.27,1384.11 1917.46,1384.2 \n",
       "  1918.64,1384.24 1919.82,1384.22 1921.01,1384.16 1922.19,1384.04 1923.37,1383.87 1924.56,1383.65 1925.74,1383.38 1926.92,1383.05 1928.1,1382.68 1929.29,1382.25 \n",
       "  1930.47,1381.77 1931.65,1381.25 1932.84,1380.67 1934.02,1380.03 1935.2,1379.35 1936.39,1378.62 1937.57,1377.83 1938.75,1377 1939.93,1376.12 1941.12,1375.18 \n",
       "  1942.3,1374.19 1943.48,1373.16 1944.67,1372.07 1945.85,1370.94 1947.03,1369.75 1948.22,1368.51 1949.4,1367.23 1950.58,1365.89 1951.76,1364.51 1952.95,1363.08 \n",
       "  1954.13,1361.6 1955.31,1360.06 1956.5,1358.49 1957.68,1356.86 1958.86,1355.18 1960.04,1353.46 1961.23,1351.69 1962.41,1349.87 1963.59,1348.01 1964.78,1346.09 \n",
       "  1965.96,1344.14 1967.14,1342.13 1968.33,1340.08 1969.51,1337.98 1970.69,1335.84 1971.87,1333.65 1973.06,1331.41 1974.24,1329.13 1975.42,1326.81 1976.61,1324.44 \n",
       "  1977.79,1322.03 1978.97,1319.57 1980.16,1317.07 1981.34,1314.53 1982.52,1311.95 1983.7,1309.32 1984.89,1306.65 1986.07,1303.93 1987.25,1301.18 1988.44,1298.38 \n",
       "  1989.62,1295.55 1990.8,1292.67 1991.98,1289.75 1993.17,1286.79 1994.35,1283.8 1995.53,1280.76 1996.72,1277.69 1997.9,1274.57 1999.08,1271.42 2000.27,1268.23 \n",
       "  2001.45,1265 2002.63,1261.74 2003.81,1258.44 2005,1255.1 2006.18,1251.73 2007.36,1248.32 2008.55,1244.88 2009.73,1241.4 2010.91,1237.88 2012.1,1234.34 \n",
       "  2013.28,1230.76 2014.46,1227.15 2015.64,1223.5 2016.83,1219.82 2018.01,1216.11 2019.19,1212.37 2020.38,1208.6 2021.56,1204.8 2022.74,1200.97 2023.93,1197.1 \n",
       "  2025.11,1193.21 2026.29,1189.29 2027.47,1185.35 2028.66,1181.37 2029.84,1177.37 2031.02,1173.34 2032.21,1169.28 2033.39,1165.2 2034.57,1161.09 2035.75,1156.96 \n",
       "  2036.94,1152.8 2038.12,1148.62 2039.3,1144.41 2040.49,1140.18 2041.67,1135.93 2042.85,1131.66 2044.04,1127.36 2045.22,1123.04 2046.4,1118.7 2047.58,1114.35 \n",
       "  2048.77,1109.97 2049.95,1105.57 2051.13,1101.15 2052.32,1096.72 2053.5,1092.26 2054.68,1087.79 2055.87,1083.3 2057.05,1078.8 2058.23,1074.28 2059.41,1069.74 \n",
       "  2060.6,1065.19 2061.78,1060.63 2062.96,1056.05 2064.15,1051.45 2065.33,1046.85 2066.51,1042.23 2067.7,1037.6 2068.88,1032.95 2070.06,1028.3 2071.24,1023.63 \n",
       "  2072.43,1018.96 2073.61,1014.27 2074.79,1009.58 2075.98,1004.88 2077.16,1000.17 2078.34,995.446 2079.52,990.72 2080.71,985.987 2081.89,981.248 2083.07,976.503 \n",
       "  2084.26,971.753 2085.44,966.997 2086.62,962.238 2087.81,957.474 2088.99,952.708 2090.17,947.938 2091.35,943.166 2092.54,938.392 2093.72,933.616 2094.9,928.839 \n",
       "  2096.09,924.062 2097.27,919.285 2098.45,914.508 2099.64,909.732 2100.82,904.958 2102,900.185 2103.18,895.415 2104.37,890.647 2105.55,885.883 2106.73,881.122 \n",
       "  2107.92,876.365 2109.1,871.613 2110.28,866.867 2111.47,862.125 2112.65,857.39 2113.83,852.661 2115.01,847.939 2116.2,843.224 2117.38,838.517 2118.56,833.818 \n",
       "  2119.75,829.128 2120.93,824.447 2122.11,819.775 2123.29,815.114 2124.48,810.462 2125.66,805.822 2126.84,801.193 2128.03,796.576 2129.21,791.97 2130.39,787.377 \n",
       "  2131.58,782.797 2132.76,778.231 2133.94,773.678 2135.12,769.14 2136.31,764.616 2137.49,760.107 2138.67,755.613 2139.86,751.135 2141.04,746.673 2142.22,742.228 \n",
       "  2143.41,737.8 2144.59,733.39 2145.77,728.997 2146.95,724.622 2148.14,720.266 2149.32,715.928 2150.5,711.61 2151.69,707.312 2152.87,703.033 2154.05,698.775 \n",
       "  2155.24,694.538 2156.42,690.321 2157.6,686.127 2158.78,681.954 2159.97,677.803 2161.15,673.675 2162.33,669.569 2163.52,665.487 2164.7,661.428 2165.88,657.394 \n",
       "  2167.06,653.383 2168.25,649.397 2169.43,645.436 2170.61,641.5 2171.8,637.589 2172.98,633.705 2174.16,629.846 2175.35,626.014 2176.53,622.209 2177.71,618.431 \n",
       "  2178.89,614.68 2180.08,610.957 2181.26,607.262 2182.44,603.595 2183.63,599.957 2184.81,596.348 2185.99,592.767 2187.18,589.216 2188.36,585.695 2189.54,582.204 \n",
       "  2190.72,578.743 2191.91,575.312 2193.09,571.913 2194.27,568.544 2195.46,565.207 2196.64,561.901 2197.82,558.626 2199.01,555.384 2200.19,552.175 2201.37,548.997 \n",
       "  2202.55,545.853 2203.74,542.741 2204.92,539.663 2206.1,536.618 2207.29,533.607 2208.47,530.629 2209.65,527.686 2210.83,524.777 2212.02,521.903 2213.2,519.064 \n",
       "  2214.38,516.259 2215.57,513.49 2216.75,510.756 2217.93,508.057 2219.12,505.395 2220.3,502.768 2221.48,500.178 2222.66,497.623 2223.85,495.106 2225.03,492.625 \n",
       "  2226.21,490.181 2227.4,487.774 2228.58,485.404 2229.76,483.071 2230.95,480.777 2232.13,478.519 2233.31,476.3 2234.49,474.119 2235.68,471.976 2236.86,469.871 \n",
       "  2238.04,467.805 2239.23,465.777 2240.41,463.788 2241.59,461.838 2242.78,459.927 2243.96,458.055 2245.14,456.222 2246.32,454.429 2247.51,452.675 2248.69,450.961 \n",
       "  2249.87,449.287 2251.06,447.653 2252.24,446.058 2253.42,444.504 2254.6,442.99 2255.79,441.516 2256.97,440.083 2258.15,438.69 2259.34,437.337 2260.52,436.026 \n",
       "  2261.7,434.755 2262.89,433.525 2264.07,432.336 2265.25,431.188 2266.43,430.081 2267.62,429.015 2268.8,427.99 2269.98,427.007 2271.17,426.065 2272.35,425.165 \n",
       "  2273.53,424.306 2274.72,423.488 2275.9,422.713 2277.08,421.978 2278.26,421.286 2279.45,420.635 2280.63,420.026 2281.81,419.459 2283,418.934 2284.18,418.45 \n",
       "  2285.36,418.009 2286.54,417.609 2287.73,417.252 2288.91,416.936 2290.09,416.663 2291.28,416.431 2292.46,416.242 2293.64,416.095 2294.83,415.989 2296.01,415.926 \n",
       "  \n",
       "  \"/>\n",
       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "cell_type": "code",
   "source": [
    "using LinearAlgebra\n",
    "\n",
    "# Define the 1D lattice [0, 100]\n",
    "lattice = diagm([100., 0, 0])\n",
    "\n",
    "# Place them at 20 and 80 in *fractional coordinates*,\n",
    "# that is 0.2 and 0.8, since the lattice is 100 wide.\n",
    "nucleus   = ElementGaussian()\n",
    "atoms     = [nucleus, nucleus]\n",
    "positions = [[0.2, 0, 0], [0.8, 0, 0]]\n",
    "\n",
    "# Assemble the model, discretize and build the Hamiltonian\n",
    "model = Model(lattice, atoms, positions; terms=[Kinetic(), AtomicLocal()])\n",
    "basis = PlaneWaveBasis(model; Ecut=300, kgrid=(1, 1, 1));\n",
    "ham   = Hamiltonian(basis)\n",
    "\n",
    "# Extract the total potential term of the Hamiltonian and plot it\n",
    "potential = DFTK.total_local_potential(ham)[:, 1, 1]\n",
    "rvecs = collect(r_vectors_cart(basis))[:, 1, 1]  # slice along the x axis\n",
    "x = [r[1] for r in rvecs]                        # only keep the x coordinate\n",
    "plot(x, potential, label=\"\", xlabel=\"x\", ylabel=\"V(x)\")"
   ],
   "metadata": {},
   "execution_count": 7
  },
  {
   "cell_type": "markdown",
   "source": [
    "This potential is the sum of two \"atomic\" potentials (the two \"Gaussian\" elements).\n",
    "Due to the periodic setting we are considering interactions naturally also occur\n",
    "across the unit cell boundary (i.e. wrapping from `100` over to `0`).\n",
    "The required periodization of the atomic potential is automatically taken care,\n",
    "such that the potential is smooth across the cell boundary at `100`/`0`.\n",
    "\n",
    "With this setup, let's look at the bands:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing bands along kpath:\n",
      "       -½ -> ½\n",
      "\rDiagonalising Hamiltonian kblocks:  94%|███████████████ |  ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 100%|████████████████| Time: 0:00:00\u001b[K\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=6}",
      "image/png": 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6stKuouIIIKahMTIlJVRWVpbpdORTGu8Sa4R8wuPHiIh4IhAMBVSrqoYPGRKdlITffqMqSBijooLJk3HlCi5cyBAX7wAYAR2Ki80CAp4JBEyHI3WBCiFpFJ4/x6ZNcHSEgwPU1e0kJVcCoaqqOyZO7MV0NEJq2Ni0VVV9xmKdYrHOSEsn7t5tqKEBb2+EhKDFtKw1T1QICZMyMmrqn6UloqJqdkF6+HDdihVKXl7+J0+utLKyYjojITXExMRCQ0/NmBE5bdrdmJiTYWGSkZGwtoavL9q2rdkZiipiU0R9hKQhPH36NCEhoVu3burq6gDy8xEUhIAA3L2L/v3B4aBfP3yuGZ+QxishAf7+OHYMFRUYNOj1XsE8Hu/atWuysrLdu3dnOmNL9IV9hDT3nNQ7f/9TM2ZsqKpykZFZ9uOPR0NDO928CScneHvjxAma/E6aAxMT+PrC1xeiQc4TJ4LHw/DhvKCgfi9fdmGzC52c/j51ivYKbqSoEJJ6t2LFjtzcE4B6SYnt3r0HVq9e6e9P+/+R5snUFKam8PVFeDg2b45JStITCNYDuHWr5yf2AyDMoj5CUl9KSnDoEAYNwqNHrYDnACQk0saPbzV0KFVB0vzZ2WH5cmUVlReAEKguKCjs2VN69WqkpjKdjLyHCiGpYxUVCAyEtzfat8fRoxg2DOHhKwwMZrRubW9pGThnzlSmAxLSQAwMDCZOdFRXt2rd2nbnzp82b5bMzET37jW3jE+eMJ2P/B8NliF1o7ISly/XLExlZgYOB2PGQE3t9Qk8Ho/WQyctEJ/PZ7PZtTuqvrNYIIeDceNgYMBsxmaLJtST+pKbm9utm4empo2j46CsrELR/Z+WFlavhrU1Hj9GaCh8fN6qggCoCpKWSUxM7M19xdlsODpi0yZkZGDXLhQUwMEBNjbYtAmZmZg/f7mmpqWent21azcZzNzS0B0h+WqTJs3bv9+ezx/OYh2SlExwcvp9xAgMGQJVVaaTEdIEcbkICYG/P06diigvX8vlHgNy27RxT0+/x3S0Jo/uCEndq6zEmTM4fz6LzzcDIBSaOTm9DA7G5MlUBQn5RhIS6N8f+/Zh375sMTETgAWoZ2UJt24VZmUxHa5loNYq8nm1/X9BQTAxwcCB3gEB35eWchQVjy5a9AfT6QhpJlxcnDU0fsvKkpGRedq1q/3jxywLCxgagsMBhwNtbabzNV9UCMlHvVP/OBysWQNNTQB958xpe+/evW7d/u3YsSPTMQlpJhQVFWNirpw7d651a2sXFxcWC+vX484dBATAyooqYj2iPkICADt2/HPy5JUePSwXL/bh8yXeqX8jR4rqHyGEGXx+TUU8duytihgYeH7LlsOdOrVbuXKBkpIS0zEbHdqP8F1UCD/m4MFjM2YEFRf/Iil50NBQIjNzmakp1T9CGqM3K6KWVvTjx/PLyjaLi4e7uFy5ePEQ0+kaHRosQ75IWRl2775dXDwd6FRd/WNxcWjt/AeqgoQ0NmJiNbMv0tNhbx9eXu4FmPJ4E+/eTX7+nOlwTRYVwhaqvLxm/RcdHWRl2UtL7waeSktv4nAc3pn/RwhphCQlMXly11atjgCPxMT2KykZ2trWrFmTnMx0uKaGCmHLUliIgIC35r8nJyM5edRff3V3dv55wQLZP//8memMhJAvYmVl9fffPi4uy6dMSYyJ2VE7Q9/ZuaYiPnrEdMQmgvoIm6enT5+eOXO+c2ejPn36ACgoQGAgAgIg2v+Iw8GgQaCedUKapdpV3I4fh7IyOByMGAETEwBITk4OCrpkbm7i4uLCdMyGQPsRtlyJiYnOzmNzc2cpKOzv1Suaz19QW/8OHQLtA0NI8yZaxc3RERs24PZtBAVh4EBISaFbt9gTJyYVFc1QUtrz009xS5bMYTppY0F3hM3QvHmr16/XBzgAT07O8d9/77q7Q1aW6ViEEIYIhbhzBz4+yyMjLYCBQLWubq/nz8OYzlXvaNRoi/PsGdavh6Mjdu9uJy5+BxACkZaWWsOHUxUkpEVjseDggGnT2snK3gEA3M3L09XXx/z5uH0bAgHD8RhHhbDJS03Fpk1wdISNDR48wMKFePVqxLhx0NGxtbVdceDABqYDEkIahQkTxg4bVqajY2Nn91dy8rrAQKirY8ECaGrC2xuBgeBymY7IEGoabRrKy8tDQ0N1dXVNRF3eQHx8zeIv6eno1w8cDvr1w+caAAgh5F2pqTh7FgEBePQI7u7gcODmBikpAHj16lVkZGTnzp11dXWZjvktaLBM81FYWGhp2aegwEVcPNbLq4+Kytxjx1BRgUGDsHEjHBzApht7Qsi30tODjw98fPD8OU6exObNGDsWTk7o1i1206YJVVUDpKR+O3To9z59mu1AU7ojbAL8/A5NnvySy50P8MXFuy1ceG/YMFhaMh2LENJMvXyJ06exYsWcly+HAM7AU3v7hbdvH2c611ejwTJNXlUVzp/H999j9mxFgeAlAKCwTRuxlSupChJC6pGWFqZPx8iRimJimQCAzHv3FN3dsWcPcnIYzlYfqBA2OhUVNYufaWnhjz9gaIjw8AH9+r1SV7fX0nLZtWsV0wEJIS3CL7/4GBvvbt3a0cBgQWzs0unTcesWjIzg6IjVq/H4MdP56g71ETJDIBBER0erqKjo6emJjuTnIygIQUEIDoaZGTgcrF4NLS3RF9lBQX6VlZXS0tLMRSaEtCyqqqpxcddq//IYG8PTEzwe7t5FQACcndGqFTgceHrC2rrmkoKCgqSkJDMzM3l5eSajfyUqhAzgcrndu3umpmqzWC9GjOjVpcviwMDXi5/t2fPhxc+oChJCGt47f3nExd9dtmb0aPB48PSEiUn4r7/+wOPZS0qGXbly2NjYmKnMX4sKIQNCQ0OTkjoVF28CBDt22I4bt+D778X8/SEjw3QyQgj5MrULua1ahagonDqFefM2l5XtB8yAGytW7Dh8eDPTGb8UFcKGIxAgIgKnT+PIEanS0lIAAE9Njb9vH5vFYjgbIYR8GxYLNjawsUFcnFRgYAkAoOTkSSlvbwwejL59ISfHcMLPosEy9Y7Pr9nntm1bjBmDigocPGjv6SlUV++lrt5t+fIfWVQGCSFN39q1i9q0mamh4aGvv+Levbmurti3D9ra6NMHmzbh5Uum830c3RHWDaFQeO/ePSkpKXNzc9GR8nJcuVKz+Iu+Pjw8EBICIyPRF1k9evyTl5cnKysrQ+2hhJBmoWPHjs+e3cvJydHQ0GCxWJ07w9sbZWW4ehUBAfjtt5q/hKNG1f4lRGZm5uPHj62srBQUFBhMToWwDggEgl69hiUkKAPljo4qQ4bsEO3817UrPDzeHPz5FlVV1QZPSggh9YjNZmtqar55RE4Onp5vDTd1dYWSEjw9oagYuHHjHzyevazs3Dt3zrRp04ap2FQI60BiYmJcnGxBwT4AZ8/2kpIqmDCh1dGjTaBlnBBCGsabw03Dw3H6NH77bWN1dSCgVlh4fMuW/WvW/MJYNqaeuBmorsaNGwgMxKlTssXF+QAAgYpKyd9/S1IJJISQD2KzYW8Pe3tcvy4bEVEAqAF5W7bIpabC0xPu7lBTa/BIDf2ETV9+PgIC4O0NTU0sXgwVFZw+rTd9uo2aWlc1Nev587+TozJICCGfs3Pnch2dERoarp07H3v0aPKIEQgJQceOsLGBry+iohouCS26/WHl5eUHDx6pruZ6e3spKioCSElBYCCCghARUdP5x+FAW/utS8TFxSUlJespPyGENDNCobC4uFjpjTVEKisRGipqaYO4OPr0gYcH+vaFpCSEQuHp02ceP342fPhAfX39L/n+X7joNhXCDzM3752U5C4QSGpoHBk9+ta5c+K5uejbF56e6N8fTWrxIEIIaZLi4xEUhMBAxMbC2Rnl5YsjIgrLyuzV1TfevXuidn3KT6D9CL9RWRmCg1+mpMhXVc0HkJX1oLQ08cCBzpaWoPl+hBDSYExNYWqKhQuRmYmgIPj4hFRWRgCsV68Ev/9+fsWKGR8ckP8NqBBCIMCjR4iIwN27uHsXT57AzExFIEgH8gHJVq3iV6zQppkOhBDCFG1tTJmCXbtU79+PAbpISobGxg7t0gWysrCzQ7dusLODldWHV6n8klbPljVY5uzZ+FmzfgFQVISQEPj6wtMTrVvD1RUnTkBPD1u3IjcXd+9K+fuvNjDwaN/edePGBTThjxBCGHfs2FYrq0W6unYzZuhGRLi/eoU7dzBuHHJysHAhWreGqSm8vbF7N+LjIRDg/PlgXV3rsLCUz37nltVHOGXKEOA7dfVfSkstunaFnV3NR8OP1iWEEFKHKisRHY3wcISH4+5dFBejvNymsvJySIiCi8tn2j5bVtOoUMgWF2+3YkX++PHU4UcIIc2HtHTN9ESR7GwYGQkqK5W5XP5nr21ZTaPAIm3tsNGju1MVJISQZkxDA6NH95WVHZibm/DZk1tWIWSx1EtLq8vKypgOQgghpH4lJT3l8Tqoqip/9syWVQj5/IX5+e4rV96LiwP/87fLhBBCmp6MDJw6hfDw1Orq9VVVOp89v2X1EUpIpIuJ3UhLmzxiBDIyYGUF0ZAZW1u0bfvuyS9evODxeO3bt2cgKCGEkPcUFBRkZWV16tSJzX7rLq64GJGRCA9HRAQiIsDjoWtXyMrKlZVFtG5t9dlv27IKoZLSqK1bfx02rD2AkhLExCAqCmfOYP58VFbCxgbW1rC2hr09li5dfOJEJCDZq1ebY8d2Mh2cEEJauqNHT86evYrF6qim9jws7HxGhnxUFKKiEBaG+HiYmqJ7dwwZgpUrYWICFgtPn/49efIi4DfA5NPfuWVNn/jEEmvPnyMiouYNRVRUYUWFJ59/C4Cq6uDw8HUGBgYNG5YQQshb2rfvlpYWAsizWOslJVt16vSdrS3s7NC1K0xNIf6h2zpaYu3rtGmDNm0wbBgA5OWhQwdBQQEAFBTwPTxYgwejf384OHz435oQQkg9SU7G+fO4cAHPn7MAAQBxcf769awffqizp2hZg2W+kKqq8rhxLurqvdTV+44a1f7gQX1lZfz8M1RU4OmJ3buRkcF0REIIab4qKxESgkWLYGoKJyfcv4/Jk/Hvv4tbt+7duvUIY+MLEyaMqMOn+1TTaFlZWW5urri4uJqampSUVB0+KyO+avcJAFlZWXw+X0fn9Yij3Fxcu1azGZOWFjw94eoKZ2dISODp06erV++UkpL8+eeZWnW1ECwhhDRfPB5vy5Y9ERHxXl7unp7uAFJTcfkyQkJw+TIMDODhAU9PWFm9Xv+kuLj41atXenp67wyW+Zhvbxq9ffv2/v37r169+uTJE9ERMTExc3NzNze3iRMndujQ4ctfZ5Omqan5zhE1NXA44HDA5+PBAwQGYtEipKWhR4+ya9dGFBauZLPLLl4cmpx8m0Uz9gkh5JPmzftt715uefnYc+d+GzBA5vHjXunp6NkTHh7YvRvKH5r+p6ioKNogtm69dUd45cqVBQsW3L9/v3379g4ODh07dlRRUeHxeHl5ebGxsXfu3MnLy/Pw8FizZo2RkVGdR6lvX3tH+IUyMrBzZ9SaNXuqq3cCkJf3DAjY7eam9WXvVwghpCV6/hw2Nt1zcq4CUsClbt1ubdu2ss53u/vqO8KTJ0+OGzdu8uTJe/futbS0fP9UPp9/5cqVvXv3mpubJycnt2vXri7zNlk6Opg3z2D37sicnKdAKZAxb55GXh769YO7O9zcPvy+hhBCWhoeD2FhuHAB58/j5UvIy1uIie3n84cpKh758ceBVp+f71dfXhfCzp07P3369P32wFpiYmJubm5ubm4PHz6sj5vTpktZWTkgYOPChT/KyEhv2rS/c2f2s2cIDsbx45g69cMt3YQQ0kK8eoXr198aXbF+PXr2REXFnz4+v96/7+Xl5cHhDGUwIc0jrF+VlQgNRUgIzp5FXh769oWnJ9zcsGzZsiNHzkhIsHfs+GPgwP4NGYkQQupDZmZmv35js7OL2+qEU14AACAASURBVLVTv3Dh8LNnrUJCEBiI2Fg4O8PTEwMGQOfz653VpS9sGv18IRQKhQ8fPszOzhZ96urqWjcBGxwjhfBNyck4dw4XLiAs7D6Xu4rL9QeKtbR6ZmZGMxWJEELqyqhRP/j7DxQK+7FYh6SlHxkarnB3R//+6N6dsRnYdTahfvDgwbm5ubWzCJpuIWRcx47o2BFz5yIwMG/0aH0ulwUo5eSIT5/OGzBAvHdvyMoyHZEQQr6SQID793HhAi5cyBUKDQEIhYa9e4cGBTGd7It9phAWFRXxeLywsLCGSdNCuLo6amsve/lyqaRkupOTvaWl+K5dGDUKFhY1cxOtrZmOSAghn5SfjytXEBKCoCBIS8PVFXPmTNq2zbu8fJC8/PGlS7cxHfArfKYQKioqKtOox7omIyMTE3M1ODhYRcWtR48eAKZMQXk5bt9GYCCGDQObjT594OqKvn0hGpb04sWL48fPGBi09fDwoEmKhJCGERMTc+XKTXt7G/v/b/0eH4+gIISE4N492NrCwwM//4z/zyHo6+1tGB0dbWd3sk2bNsyl/mqf6iPctGlTZWVlaGiovLy8hYWF6ODChQsbKlsdY7yP8MulpNSMsLpzBxYWcHbO3LVrQH7+THn5qOHDpf/5Zz3TAQkhzd/Vq9dHjFial/e9svLRMWO8udxR585BSgqurvDwgJsbGv+CY3XWR+jo6FhHkciX0teHjw98fFBSgpAQbNoUnJ8/SSicVFIy6cwZ27IyyMkxHZEQ0qwJBPjzz+N5eWsBu8JCl8OHf/jjj1Fv3Pw1K58qhD4+Pg2Wg3yQggKGDIGycruhQ/8pLPwBeFJVJaelha5d0a8f+vWDmRnTEQkhzUhODi5dwsWLuHwZLFZbMbE7fL6dmNhtD4/206YxHa7evLUOmJ+fX1RUVO2ncXFxRUVFtZ/ev3+fSiMjevXqNWlSBx2drmZm0+/c2ZqVhUWLkJuLkSOhqYkRI+DnB9GmUYQQ8rX4fERFYfVqODrC0BD+/nB2RmQknj2b5e7+QFvbpkcP/w0bljEdsx691UfYrl27adOmLV68GIBAIBATEzty5MioUaNEXz18+PCYMWOa7gT8JtRH+OVSUhAS8nqxdlHbfdeuvBEjvr97N65VK7lTp3Y1xYVhCSF1rrq6esiQSVFRiaqqCmfO7FFQMLx0qWbkS+12Ok5OkJRkOmjdoY15WwR9fUyZgilTUFmJmzdx6RKmTsWLF4fLytrw+fuysx+OHz8/PLzpTOchhNSbvXv3X71qVFl5IDs72tz8Jzm5U336wNMTW7eidWumwzGKmUIYGBi4d+9eAJMmTRo4cOD7Jzx58uT333/PzMx0dnb+6aefauv53r17T548KS8v/+OPP3br1g1AcXHxTz/9VHuhp6enh4dHg7yIxkVaGm5ucHPDunWYNy97wwYTAECHmJi8JUvg5gYHB3zuXREhpHl69AiXLmHz5uzKSlMAgJGq6qtnz0Cb5Igw8M8QFhbm7e09duxYb2/vCRMm3Lp1650TqqqqevfuraOjs3jx4qCgoCVLloiO//vvvytXrvTx8XFxcenbt29aWhqA8vLyf/75x/r/aFNcADNmDGvderWExEYVFc60aeMUFbFyJdTV0acPVq/GG73AhJBmq7QUISHw8YGeHnr1QlQUZs/mqKktl5DYqKIy/KefJlAVrMXAHeHmzZtnzpzJ4XAAPHz4cPPmzaJJ5bWOHz/eqlWrlStXAti+fXvPnj1/++03GRmZjRs3rly5sm/fvgBu3LixZ88e0TlsNnvKlCkN/0IaLX19/ejo8yEhIUZGS21tbQEsXIi8PFy9ipAQDB0KcXG4usLVFX361OwSdfFi8IkTIU5OVmPHjqQJ+4Q0FVFRUXv3Hu/Uqe306ROlpKQEAkRH14wbEE14d3XF8eO1i1V1Gj486OrVq6amK6wY3PSo8Xm3EAYHB5eWltZ+euzYsbi4ONHj+Pj4OnnK+/fvT5gwQfTYwcHBz8/v/RMcHBxEj83Nzblc7pMnT4yNjePi4mqPOzg4nD9/XvSYz+dPmjRJXFzcxcWFw+HQ33EAWlpa48aNe/OIqio4HHA4wP+H2AQEYMoUGBhAT+/CpUtbSkrmHzt2ND09a8mSOcyEJoR8jaSkpH79ZuTmLpeWDvf39zE03HnuHJSV4eqK2bPRpw+kpd+9REdH552/DATvF8Lr169fv3699tPTp0+fPn26bp8yOztbRUVF9FhFRSUrK+v9E9q2bSt6zGKxROeoqakJBILaC1VVVUUXSkpKzps3z9zcPC8vb/78+ZGRkWvWrPnYU1+7dq12z2FdXd3Dhw/X7UtrKtTVMXo0Ro9GRQXCwsQXL75QUrIE6F5SYrFjx6hhwybr6DTVscGEtBDl5ay//grOy5sMuFVWuj14YDN+fOWyZTwNjZpfXi4XXC6zGZknEAikpKS+btRoVFQUn8+vz1QAICcnV1FRIXpcXl6uoKDwzgny8vKVlZW1n4rOkZeXB1BRUSFa+7SsrEx0oYqKyurVq0VnWllZ9e7de+XKlZIfGf9raWnp6+sreiwlJfX+U7c0ogn7GRmdFy06WVZmLSbmLyXVpUcPeVGHopsbnJ0hL890SkIIAEAgQFQULl9GcDCiotCxo6W09LqKilEs1h1zc+2pU9+7AWzxRNMnPnvaW4VQTU2t3vK81q5du9TU1J49ewJITU2tvfmr1bZt24iICNHjgoKCwsLCtm3bKigoKCsrp6SkiIbDfPBCQ0PD6urq4uLij70QZWVla9rZ4T0//DDp2bMVZ8+62tlZ7djxh7x8zbq6Gzdi5EgYGdV0KDo7vx53WlhYmJiYaGpqqihaFJwQUhf4fP79+/fV1dXbt29fezArC7duITAQ589DSQmurpgxQ7Qiv+OWLYlbt/bv0EF/9+6dzKVu+oQNbv369Y6Ojlwul8fjOTs7r127VnR8+/bt6enpQqHw8ePH8vLyKSkpQqFwzZo1Tk5OohOmTp3q7e0tFAqLior09fUDAwOFQmF6enpFRYVQKOTz+YsWLerYsePHnnf//v1jx46t5xfX3JSVCS9fFi5cKLS2FiooCD08hLt2Cc+ejdTQsFJVnampaREbG8t0RkKaicrKSgsLFzW1yWpqLosX/1X7q6euLuRwhLt2CdPSmI7Y1PD5/Orq6s+e9roQ+vv7z549OzMz89MXxMTEDB06NDk5+ZuTlZWVubi46Onp6evr9+7du7S0VHRcTk4uODhY9HjlypUqKirW1ta6urr3798XHczIyDAzMzMzM9PU1JwwYQKfzxcKhTt27FBUVOzcubO2traxsXFkZOTHnpcK4X+UkSHct0/o5SWUlBwPRAFC4PbAgVOZzkVIMxEUdEFObgEgBPgslqWrq2D1auH9+0KBgOlkTdYXFsLXS6ylpKRMmjQpLCysb9++w4YNs7Oz69SpE5vNBlBdXR0TExMWFnbs2LGIiIixY8du27ZN/r/1HT19+hSAgYFB7ZGKigopKSn2/+e25OXlZWZmdurU6c0OP4FAkJSUpKCgoKurW3uwoKDgxYsXysrKurq6nxgy2iyXWGMEhzPt+PHRgDMQLCFxztp6k6jt1N6+WS3OREjDSEysmfBw5cq1ysoAPn87UKmhYZ+VFc10tCbvC5dYe3c/wnPnzm3ZsuXy5csCgQCAsrIyj8cTTaiQlpbmcDhz586tHXjZtFAhrCtPnz7t3XtkVZWmrGzOlSsn8vPbvDNvydUVlpa0aAUhH5WTgxs3EBKCixfB5cLREa6u6N9fMHWqd1TUS6Ewf/XqBd99N5rpmE3eNxZCkZcvX16/fj0uLi47O1tKSqp169a2trY9evRo0iMjqBDWIYFAkJOTo6Gh8eYteGkp7t6teW+bno6ePeHqCjc38HhP3N3HFxZWdeigffnyUVlZWQaTE9KQfvll9a5dh8TE8OefP3M4o+7cqfkFSU6GnV3Nu8Z3BvDl5ubKy8tLvz8HkHy9/1QImyUqhA0pLa3mF/7qVZSWjiovnwfYSkhs8/Wt/vnnuUynI6QhpKSk2NlNz829AFRLSHSTkrpnZyfh4gJXV1hZQUyM6XwtAO0+QZjUrh0mTcKkSRAKYWSUn5ysB4DL1d+0KbSwEL17o0cPyMkxnZKQeiAQ4MEDXL2KU6fy8/LaAWxAWk5O+dGjcg0NJabTkQ+gQkjqF4sFX98ps2YNq6hwk5c/vm3b4adPsW4dhg9/PUOxRw9ISTEdlJD/pnZz0KtXa2b7zZplUVT05PnzBWJiRY6O7agKNlrUNEoaQnJycnx8vIODg4aGhuhIRQXCwhAairCwmlE23bvD0RHOznjxInXkyJkvX2YPHdp/48bltHgsaTzOnr0wd+5yAGvW/DxsmOfLlwgNfX/MC9q0qTmfy+WGhITIyMg4OzvTT3LDoz7Cd1EhbLQKC3HjBq5exZUryMwE4FFQ8CtgraDwg59f/8GDBzEdkBAAKC8vb9+++6tX1wC2tHRvbe0rZWVKvXqhd2+4uEBfn+l85D3UR0iaDGVlDBqEQYMAIDsbpqY5gA3AKilx+vXXp1lZ6NULnToxnZK0YLm5uHEDgYGvCgoMAGUA4uJGGze+9PBQotu8ZoAKIWlcNDQwdmy/f/6ZWlLipKq6cdKkw9HR+OsvlJXByamm+ZTWiyUNoKQE4eFvzXZwcWmrq5uTmblBKBTT0Ul1d+9AVbB5oEJIGp0NG37r2fNsYuLT4cOPdOjQQXQwMxNhYQgJwcaNqKxEjx5wdUX37jA1RWJi4tixc/Py8n/4wXvBgpnMhidNy+3bd7//fnFFRcXSpT7ffTf6zbmwouLXvTv+/BNOTqJVk1gzZ5738zssFArHjbsgRhMgmgvqIyRNz5MnuH4d167h+nVISKCw0LmoaAdgqKIy4uLFJba2tkwHJE2Gjo5lZmYg0EpGxr1DB7/U1HbduqFXL/TsCVtbiNOdQhNHfYSk2TI0hKEhJk8GgKQkdO1aDpgAKChwmjfv8YQJtk5OMDRkOCRpzPLzERqKK1fKX71SBEQLF3edPDl16tR2tF5uC0TLQZKmrVMnuLqay8ktYbGOqKkdHD68V3g43NygpYURI7BpE6Ki0GJaPcin5OQgMBCLFsHGBu3bY8sWtGola2ioIC29hs3+V03t2nff2VAVbJnojpA0eceO7Tx06OizZ8/Hjz/Zvr2W6GBtn+Lu3cjNRdeuNXO8LC0RFHRhxoylXC5/yhSv5ct/YjY8qVu3boV5e/9YUVE9fLj71q2/i7a0FU1XffwYXbvC1RUbN6Jr15qdUhYuDNi//1B+fv6kSef+4446pOn6cB9hWFgYi8VycHAAUFFR8euvv4aHh9va2q5YsUJGRqbBQ9YN6iNssTIycOMGbt7EzZvIyhKWl1tUVd0EFFRVPW/dWmtsbMx0QFJn9PTsnj07A2hISnqrq0/lch179ICTE5yd0bkz7YjS4nxhH+GHfy7GjRsXGRkpeuzr67t27VqBQLBnz54pU6bUcUxC6p+ODry8sHMnEhIQG1stLS0HKAHs/HwjL6/sZctw8SKKi5lOSb4Vj4fISGzciOHDkZ7OAzQBllBoMn9+VnY2jh/H7NkwN6cqSD7qAz8apaWlqampjo6OAPh8/r59++bMmXPr1q2AgICjR48WFRU1eEhC6oyurpSTU0clpVkyMisNDO6sXWsnJ4dt29C+PUxNMXUq/PyQmvruVQ8fPoyJiWEiL0FGRsadO3eqqqrePFhWhtBQrF4NT0+oq2PkSNy/Dzc3DBnSS1n5OympNVpaxydMcGUqM2laPtA0mpmZqaOj8+zZs3bt2kVGRtra2t6+fdve3r6yslJGRubBgwfm5uaMZP2PqGmUiAgEguDg4OLiYg8Pj9rNEXk8xMTUdCbduAExMTg61szf//PPqTduFAiF4ra27PPnDzIbvqX5559DCxfuEArNFRXvnT9/8fFjFdEStdHRMDau+R/UuzdUVV9fcu3atZcvX7q7uysrKzMXnDQK3z59Ql1dnc1mP3nypF27dsePH1dUVLSxsQEg2qee5pCSpo7NZvfr1++dg+LisLaGtTV8fAAgKQlhYbh1C1u25KSkPBUKQwDcuTM0NvZply4GDZ+5ZeLxsHTpltzca4BMfv52G5sAF5epjo5YswY2NvjYCM9evXo1bEzS5H2gEEpISPTr12/atGkcDmfnzp1Dhw4VldO4uDg2m92mdll1QpqvTp3QqRMmTkRhoaShYVlenhBglZUVOzhI6evDzg729rCzg7Ex9TzVsZcvER6OO3cQHo7791FVJQ6UATKSkkWbN2tPnMh0PtIcffiXePfu3Z06dfr3338dHR3//PNP0cF///3X3NxcSYm21CItiLKy8vTpQ9XUuqqrd5sxw7GwUPfIEfTogfBwjBiBVq3g6AgfHwQEICen5pLg4CtWVv26dx/y4MEDRrM3RkVFRWPGzDQ2dvb1/UvUL8PlIioKmzbB2xumpjA2xrZtkJHBvHlITcW5cys0NFxbt3azsAj18hrJdHzSPNESa4R8XllZmVAofH+eWV4ewsMRHo67dxEeDnV1WFrmXrzoXlJyCijW0RmTnh7JpnvGN3h5zQgIsOHxONLS852cehYWjnr4ECYm6NYNdnaws8P/F5d9jcfjFRUVqb7ZDUjIl6mDJdZ4PF5aWlp2drZoQiEhLZacnNwHj6uqwt0d7u4AIBDg0SMcPZoSGGgL6AA6OTma3t559vbqlpYwN8dHvkfzx+cjKQnR0YiOxpkzcTzeWkCmsnJ4ScmVdetGWVvj05OTxcXFqQqSevXh96p8Pn/p0qXKysqGhoYjRowQHfTx8Zk6dWoDZiOkKWGzYWKChQtN1dTuslhnxcQO6uqWuLmpJydjwQK0bg1tbXh6wtcXgYGv21EBXL16rWfPEV5eMzIyMpiL/414PN6yZasdHIb88cdGgUDw/4OIj4efH3x84OgIJSW4uuLoUcjLo39/N1nZxcDNVq3WrFzZ19HxM1WQkAbw4abRX375Ze3atXPnzlVWVt6yZcuLFy8ABAUFjR49Ojc3V0pKqsFz1gFqGiUN49mzZ+vW7ZGTk5k/f5qamproII+HpCRERSEhAfHxuHMHkpKwtoahYdq+faOLivaxWClmZmtjY68wG/5rLVu2Zu3awoqK6TIyfw0ZYqKmNi0qCjExaNsW1tYwNYWJCRwcXk9v4PP5e/f63bkTN3bsAFdXF0azk+bvC5tGP1AIuVyuqqrq8uXL58yZc+PGjTFjxogK4YsXL9q0afPkyRMDgyY5fJwKIWk8BAI8fYr79xEQEHj6dDSfvwyAhIQdh3OnUyd2hw4QfXxwaFpeXl5wcHC7du3qqc/i2bNnoaGhlpaWpqam73+1uhopKUhOxuPHePwYx44NLyxcB7QDHrZtu27Jkn2WlujcGdLS9RGNkK/z7X2Er169KikpcXNze+e4aLxofn5+Ey2EhDQebHZNqXN0tLp1a2VOTn8xsVQDA+XBg9kpKbhwAevW4fFjiIlBX7/mw8QEpqZQVs52cuqXl+clK3tm8uQra9Ys/exzJScnnz17oUsX4/d/qd8XEXFvwIAfiovHKCjM3LHDp3v3wQkJSEmp+YiPR0oKtLVfp/L07HHixPry8ikKChsWL3aiRRhJU/SBQqigoMBms1++fGliYvLm8bi4OABaWloNFI2QFkBHR+fMmc2rVu3S1lZbvvyguvpbX83MfH3vdeoU1qxBcvJ5Hm+SUDizqkqwfbsdi7VUURFKSnjzv8rKNY8lJPDw4cNevb7LzZ2lpLR/7tzYX3+dD6CwEEVFKC5GcXHNg6KimoMnTx7KzV0P9MjL44wa9UObNoNrb0979ECHDtDTw5tvr/n8mebmu0JC1gwc6Dx16oQG/bcjpI58uI+wZ8+efD7//Pnz0dHRXl5eL168KCws9PT0LC0tjY6ObviUdYKaRkkzcO7c+dGjg0pKtgPpGhpj5s699WYxE9W2wkIUFqK4GJKSYLF+LyszAYYAXHFxJzm5O0VFUFJ6q3aKHrRqBUVF3Ly56soVFR5vKosVPHBgwOnTe5h+xYR8u/80fWLTpk3Ozs5GRkYmJibFxcXjx4+/dOlSUVFRSEhIPUQlhHwpd/f+Q4ZcunjRSkFB+siRLba2nzq5rAx//91+0aKwioohLFa4jY3uhQv49AKcs2fPGjDAOylpj5aWyvbt/9ZpdkIaqY9OqH/y5Mny5csvX76clZWlpKTUs2dPX19fCwuLBs5Xh+iOkLRAAoFg0qR5ly/fatNG299/Gy2RSFqU/zqh3tDQ0M/Pr65TEUIaFJvN3rdvA9MpCGnUaPEnQgghLdqH7wh/+umn4o/s2L1r1676zEMIIYQ0qA8Xwps3b+bm5tZ+WlxcnJubKysrq6mp2VDBCCGEkIbw4UIYHh7+zpGEhAQvL68FCxbUfyRCCCGk4XxpH6GJicnmzZunTZtWXl5er4EIIYSQhvQVg2U6depUUlKSlJRUf2kIIYSQBvYVhTAwMBC0xBohhJDm5YtGjfJ4vCdPnty6datPnz40XoYQQkhz8kWjRsXFxXV1df/888+ZM2c2VDBCSJ3JzMxUV1f/7PoahLRMXzpqlBDSSFRUVISHh+vo6HTo0OGzJxcXF3fvPjAnR57NzvD339qjR/fPXpKfnx8dHW1iYkL9IKSF+OgSa4SQRqiwsNDKyq2w0FFMLG7BgiE//fTDm18VCGr2oCgpQWkpSkpw4MD+hIQRAsEPQObYsd47doTIy0NBoWbfCQUFSEm99f0TExN79fKqqnKTkFh8+PCfrq69G/TlEcKE14Xw1atXT548+ewF9vb29ZmHkBZHKBQ+fPhQWVn50ytiFxcjNRV//302PX0Un/8jwF22zOHixR+KilBUVFP5ysuhrAwFBSgoQFTwsrKqhUI1AIBMQQF369aaAinatqmkBEIhFBReX/Xs2d/Z2WsBFyD1hx/m/ftvbz09fPrOsKSk5PHjx506dZKTk6vLfxdCGsrrQhgUFDRx4sTPXvCx3SoIId+Ay+U6Og5MTVUFMmbO9Fy27Mfqajx7htTUdz+qqqCnB2lpeTY7kc8HUKKkJL5kyet7O3l5yMu/+/1zcsZ17epeVnaXxYrevfuXwYPfPaG6GiUlr+8jN2yQy8zMEQgA5JSVyc+bh9RUFBVBXx96eu9+KCnh/v37AwZM5vNtxMXvXb16xMjIqCH+1QipU6+3YcrOzv6SOYJOTk71HKm+0DZMpLHh8XDw4JUZMwLLyzcCAgkJGw2NyFev2Lq6H6g6rVuLLuG5u4998OA5m126f//6vn1dPvsslZWVsbGxenp66urqnz05Ly/PyWlIbi5bVrYsOPiwqBuyvBwpKR+ozRIS4PG8i4vnApbATTc3/xMntr5fjAlhyldvw6ShoaGhoVHPqQhp/tLS0tau3S0vLzNv3jQ1NbXa4zwenjxBfDwSEhAfj8REPH4MFRUJLrdS9HV5ecGtW6w2bSAm9tFvLi4uHhx8tLy8XFpams3+onnA0tLSXbt2/cLwqqqq8fE3S0tL5d8oaLKyMDODmdm7J+fmYtgwiZs3RfkrIyPFNTTQujWMjWFmVvNfIyMoKLy+hM/n//33gbt347y83F1dP1/FCWkANFiGkLpUVlbm6Dg0I2MZm10cEDBkw4ZborKXkICEBCgrw9QUJibo3RszZ8LSEjIyju7uO6Oj3YTCgt9+m9O+PetLnkVWVrZeX4X8l93Wqalh9+4Frq5eXG5baekXN2+eaNsWmZk1lf7uXfz9N2JioKBQ86pNTXHjxqozZ3LLyoacPv378eNivXv3rNcXQsiX+OgO9eHh4f7+/ikpKaWlpW8ev3z5coMEq3vUNErqVWYmYmNx7lzEnj37q6q2ARATc+/bd7+Fhbro9sjICNLSH742KytLTk5O4c1bp6aDy+VmZWVpa2uLfehOViDAs2eofTfg7+9UWXkJkAFCLC2vLFq0qnNndOz4qZtgQr7Zf9qh/siRI2PHjm3Tpk11dbW0tLSSklJCQoKkpGS3bt3qISohjVpiYuKCBWu4XN7q1fPNzc1FBysrER+P2Niaj5gYsNkwN0fHjgZSUveqqjKAEk3NrMBA1S9pv2zSCzZJSEh8Yrwrmw19fejrw8MDALjczgEBx3g8jrT0cT09Z39/LFmCzEwYG8PcHJ07o0sXmJtDVbXm8sLCwgULfk9MTJ0+faSXF6dBXhBpcT5cCH/55RcOh3Po0KHJkyfr6OisXLkyNTV1+PDhTXekDCHfhsfj9ekzJiNjByBx7953ixaFxsXJJiTg0SO0a1fT4jdnDkxNoa8vukJ10KBVCxdOlJGR2bbtny/sxms5duz4g8VaEhX1z8iRHr6+o1gsAKiuxuPHiIpCVBTOnUNMDHg8mJjA2hrXr8+Mj+/L5/8QHz+zfXsdBwcHpl8BaYY+UAjLyspSU1MPHz4sauiorq4GoKent3v37u7du/v4+CgqKjZ0TEIaVlUV4uMRE4PQ0IxXr/QAOwClpRaJiU/79u08fz6MjfGx5hY3Nxc3NxoG8mFKSkqHDm1956CkJExNYWoKb++aI2lpiI1FXByePEni8w8CKCjw8vGJGDPGoUsXWFhARaWBg5Pm7AOFsKKiQigUKikpAVBVVa1ddNTExKSqqurJkydWVlYNmpGQOvXo0aMZM3wLCgqXL5/j4dFPdLCgAPHxNTclb97wGRvrKiml5eaGCIUS6uox27YZysgwG79FaNcO7drB0xMREZ3Pn9/K5TopKe3z8PgzNRXnzuHBA0hI1NyOW1vD2hpGRjW9jGlpadOnL83MzFq4cMro0cOZfh2kafhAIVRVVZWXl09LSzMyMurYsePKlStFY6mvXLkC4M3h4IQ0Rf37j3/2bAegOWbM8LFjzZ4+1Y2NRVUVLCzQpQt698bcuTA1haSk6HSxCRMCli7dwOPxHbOdOQAAIABJREFUfvvtsAyVwYZ18ODmFSs2xMWtnzFj/oABNqKDQiFSUxETg5gYnDoFX1+8egUzM5ibIyhoUkbGMsB41qzRXboYm5qaMpufNAkfHjU6ePBgTU3NnTt3lpSU6OnpycnJdezY8datW926dbt27RqL9UUjvBsbGjXakhUWIiYGsbG4f7/y4ME+PN4tABISi8eOdRk61NXcHJ9c3Yw0dkVFNUOWFiywrai4B4DFWte1q46Hxyhzc3TpgnbtmI5ImPCFo0Y/3JP/zz///PLLLwAUFBSuX7/u5uYmFApnzZp1+vTpJloFSTOWlJTUtesAff1u69fvrD2YmYnAQPj6YsQImJqiXTvMm4d792BhIa2nJy0u/i9wQU3t8tq1Vh4eVAWbPCUl9OiBmTNhb68nKbkFuKKicmzKFAceD7t3o3dvKCvD0RFTp2LTJoSGory85sLw8HtdurgaGjocOODP6CsgTProPMLmh+4ImysTk56JiVuAjnJynH79lr18aRMXB1VViG4FzM1hYQF9fdS+hSsoKPjrr+15ecXz5k3q2LEjo9lJHSstLV2/fmdaWtbs2eNq57oAyM3Fgwc1ramxsUhOhr4+unTBuXNWxcWnARV1dffIyINt27ZlMDypc/9pHuHPP//s6elJG02QxkkoREoKYmIQFyf6o1YGdAZQUdFLTi551SqbLl2grPzRy1u1avXHH0saLi5pQPLy8suWzX//uJoaXF3h6lrzaXU1EhNx7175mTMKQFsAubl2Q4akODu37dIFXbrAxOSjqx+Q5ufDTaMBAQEODg5GRkZ//vlnRkZGA2ciLdzDhw87dnTU1LQePvx7Pp8PoLgYUVHw84OPDxwdoaiIHj2wYwfy8zFoEBwdO8vILGOxAtTVD6xa1dPJ6VNVkBAAkpIwN8fkybJmZnJSUuvZ7INaWldXrbJu1w537mD2bKirw8AAnp7w9UVAAOLjIWo727PnoLa2pZaW5bZt+5h+EaTOfLhptLq6+tKlSwcOHDh9+jSfz7e3t/f29h4zZkyT3m+MmkabCnPzPrGx24EOkpKLzMws8vNH5ebCzKymnVO0+IiS0uvzuVzu/v2Hnj3L/O67kQYGBswFJ01PeXn5nj37CwtLpkwZp/XGvotcLhITa+YyilpTKythaloSFdWroiIMYKmpOSUlnVeh+YyN2xc2jX6mjzA7O/vw4cP79++PiYlRVlYeOXLkzp07P3F+Y0aFkEElJSXp6ekdOnSQ/P+khDe9eIGHDxEXh7g4PHyIBw/shMIwQJzF8hs3rmDZMh89PdAKLYRZubkICXk+ZcqskpLTAFisUbq6K6ysOojeopmZoWNHiH+or+np06fS0tI6OjoNnZjUVSGsdevWrXHjxqWlpTXdwTVUCJly82boiBE+QqGZrGzC7dtn5eS0Hj+umb2ekIDYWHC5NVsTiOZHBwdv2LbtZmlpDxWVA+HhZ2j8Amk8unVzT0joIhSKdep07/Tpi9HRbNF64lFRSEmBvv7rfTZMTGBsLPT09L53rwQoHjeu57p1y5iO3+LUTSEUCARXrlzZv3//qVOnysvLu3fvHhoaWqc5Gw4VQkZUVMDGxiMhYSvQnsUKUFBIFAqXmZjUvIkWvZt+f5GG8PDwJ0+e9OnTp7VoO1pCGgcej3fu3DmhUDhgwIB3/rxWVCAhoaZVQ/TfkpK4yspVXO5hQKik1C0u7lqbNvW7fxZ5x38aNQogKSnpyJEjfn5+qampOjo6s2bNmjhxIo01JyKXLgWHhNzt18/RxaX3m8erqpCYiIQEPHz4P/buO66J+40D+BNCEggjIRD2UlEQVFQUB4p7a1Vwz1brqritddS6d1tt3aNVXFTcuAcqbhFBQUBlKLJHICF73u+Pw0gxJOmvjmqe94uXr3D55PheTO65XO6eq7ryTn4+UCgUAA0AAKiHDaPs2AEGT0Zt1apVq1atPtToEfp/mZub9+/fX+ddlpZV/d60bt+m9O2rFggAACQSTWAgmJtD48ZVlyz294dGjWo2TX316tWePYfd3BzHjRvNYDA+3IKg6nQXwh49ely+fNnS0jIsLGznzp1dunTBJvpIa9++w7NmHeXzx+3Z8+uyZfw6dcKq7x1yda3aNRQWBosXQ6NGkJi4KCxsEEH4Wlllr1hxBlsyIBPRrl2jLl1sbt3qBSCaMGHQqlVMsqUt+X45frzm9wJubiVTp4aVls5nMDJPnBh75cpfn3oJTIXuXaNhYWG9e/ceMmTIl3ShCdw1+i8JhfD8OaSnw+LFw3JyVgL4AKRZW6/r1SuS3LwNCID69XUfLyCVSvPz8729vc113o3Qlys3N9fS0rK2Ls35+ZCaWlUdb948lZGRShCLAIDJDN6w4YGfH6VhQ6h2NCv6Z/7VrtETJ058gCGh/yiRSNSr16gXL/IcHW3Pn48kL7JaUlJ1EYb0dEhPh+fPgccDX1/w8wM3N9/8/Asq1TQG4/y0ab6rVxv+E5aWlj4+Ph98SRD679Fz1WIAcHMDNzfo3h0AIDW1focO23m8WQA5TCYtOZly9CikpYFCAX5+4O8Pfn7g5wcNG0KdOkClgkajGTFi6vXrD6ys6NHRW1u0CNLzh5Ae+jbPeTxefn6+UqmsPjEoCJ/rL83atVsfPOipVE4uLb3Rrt1P7u57nz0DMzNo2BAaNgQ/P+jdG3x9wcur6rs9ieSHcePm3LvXokOHtj/9tP5TDx+hL0RAQMDKlcM3bOhib8/Zu3eX9soZ5eVV26PPnsGNG/DsGRQWQv36YGt7Nj6erlAkArweNWrMs2c3PuXoP2e6C2FaWtrkyZNv3br17l2f7+kTJuXChUt7955u2rTBnDlTanzlnpcHL15ARgZkZMDz5/DiBWRllarVwQBAEH4AJWvXQsOGOo7k1GIymX/9tf1DLwJCJmjy5K8nT/66xkQOB0JCICTk7RSpFJ4/h61bS+7e9QUAAPcXL8RubtCgATRoAPXrQ4MG4OsLdevWvHx0TMy5gwfPBQX5zZo1WedJvaZJdyEcNmxYSUnJxo0bfX19De5dRf81d+/eHTXq5/LylWfOXL5/f8Ho0b9mZ1d9CfHiBZibQ926ULcu+PvDmDFQty4oFCP7959QWTnC2vrM+vXT2rf/1AuAENLL0hKaNoUVK/qeP9+rvFzEZMZPmRI+Z07V2zw7G+LjITsbnj8HR8eq93vduqBW31i/fotAsOzs2XOvXv20ffvaT70c/xU6DpaprKxks9nHjx8fOHDgJxnTB/JZHyyTk5Nz5MhJb2+3QYPC3z2ClyAgPx+ysiA7G7Kz4eTJNampvgBhAASd3io8PJ7cPCS3E3Ue/5Sbm3vr1q2mTZv6+/t/jOVBCL0P5eXlV65c8fb21nm6kUIBL19W7fjJyIDz55fm5bUE6AOgZjJDJk26TxbIevXA2xt0nqzx8OHDq1dvtW0b1KFDhw++MB/Avz2PUP8XvP9SZWXlo0ePHBwcGjdurDOgVqsTEhKUSmVwcHD1z+8lJSXJycl16tSp3lKSIIjExESRSBQcHPxFXkA8Ly+vVauBJSUzrKzunD59a+HC38mCp6182dlgbw/a13SfPkE5OXtEorbm5hd69258+LDhP+Hh4TFixIgPvygIofeJw+EMHTq0tnvpdPD1BV/fql9Pnw4aM+ZwZWWQuXlMs2bN3NwgLQ3OnoXsbHj9Gpyc3q5DyBuvX8dOmrSivHwim/3Lzz/njh8/6iMt1UenoxDa2tr26tXrzJkzLVq0+BB/MjExsXfv3k2bNn3x4kX79u0jIyNrBCQSSbdu3SQSiZWVVVlZWVxcnJOTEwDExMSMGzeuVatWiYmJERERixYtAgCVSvXVV1+9evXKxcUlIyPjxo0bdevW/RDDfr+Sk5M3bPjDyclu4cLpOvv28vmQmws5OfD6NZw7d7WkZDxBjBWJxkZFtUxMfPti7dq16sbfNwC6e3nl/vnn+MBAv19//fVjLRNC6D+tf/9+y5cXHDgwPigo4Oef19vYvL1LrYbc3Leb1ydOQHY2pKScUCjWAbTi8zv++OMUPn+Upyd4eICnJ7i46GiLodFodu3ad+1aQr9+oaNHD/uYi/Yv6T6P8MqVK+PHjx84cGCvXr24XG71u/79UaM9evQIDQ1dtGgRn8/39/c/cuRI+79/K7V169ZDhw7dunWLSqUOGzbM09Nz/fr1Go3Gx8dn/fr1gwYNysrKaty4cWZmpqura3R09LJlyx49emRhYTFt2jSRSLR3r+7Lo3zoXaNlZWXm5uZsI64AVFxcHBjYt7h4vbl5bsOGUVu3XiALXm4u5ObCq1eQmwsA4OEB3t7g4QEqVVxU1E6x+ADA84CAiKdPr32gRUAIIa3ly39evZqQy783MzvcosXDkJCNublVa6rycnBzA09P8PQELy/w8AAPD7h8efPu3Wki0Tcs1qbffus3duxwg39CoVCUlJS4urp+oJ4t/6rXqLOzc3Fxsc4H/MujRskvIHNycshdr5MmTbK0tNy0aVP1TOfOncPDw6dOnQoA58+fj4iIyM7OTkhI6NKlC4/HI8/I7tix49ChQ6dMmTJ06NCGDRsuXboUAB4+fNilS5fKykqdf/qfFsKSkhKVSuXq6mpMeOzYmRcuPAaQT5w4cOXKedrpAgEUFkJJCRQUQEkJFBdDQQGkpp5/9OiBRrMMAKjUNq1b3/L2NidfSeSrytPzb5cZAoBFi9bu33/MwcE+Kuo3Pz8/IxcBIYT+b3K5fOTIiPv3k/z96x85ss3Ozq7aXVUb7q9fg3Y7/tatgVLpZgB3gCcODpt79Njj6AjOzuDsDI6O4OoKjo7g6Pj2SjL37t0PC5tCEJ5sdtm9e2erz782QqGwrKzMy8vLyML5r74jjI6OVigUxvyZfyo/P9/MzMzd3Z381cvLKzExsUYmNzfXy8tLG8jPzycIIi8vz9XVVduXxMvLKy8vjwz37NlTO1EoFPL5/No+lp05kzh9+tx27YIBwNraWvvAd82evezw4RsA9O7d/fbv/+3dAJ8PfD4IBCAQwLNnWSdPZguFNwCIX35pnZg4paLCprAQiouBwQAXF3B0BGdnwskJnJwgNBTat/efM2cVn/8NQK6Pj/nNm2ZvWnG+pfn7hBUr5q1YMe/NXTXDCCH03tFotOjondpfq695aLSq7xGr++GHZlu27JPJJlla7h88uHnbtkRJCRQWwtOnUFwMRUWUkhLg8cDenqyLxMOHy3i8kwDepaV7p0zZM378XDabYLGAzQYWq+aJHwBw8uTZ775bDuDl7Fxx504Mk2mgg/nz58+/+WbeL7+sCwkxcAyg7kIYGhqq/2H/N5lMRqPRKG/2LjMYDKlUWiMjl8u1BZxOpyuVSpVKRT5Qm2EwGBKJRDtDbRgApFJpbYVQLD6xY8fIhIRKCwsWi+WoVncCAKUSxGIKAKhUIBJRAEAsFuzefVUiuQMAJ070EwqzVSrvykqKQEARCEAgoAgEFFtbgsUCFouwtSWoVLlCQX5HRzE3pw8ZIvH0NHd21jg6EhYWOgfiwGJ9v3btVAcHu59/3kEuCEIIfdbmz58qkfx8586oHj1CFi0aZWYmfjejVkNpKaW0lFJYSElJUQJYAABBWCQlyVev1ggElIoKqKykVFZS6PS361g2G2xtiUuXVguF1wBsy8s3jBt3pH37UQDAYBDkERJ0OjCZBADQaGBlRQDAqFETX7/eCmC4p5W+zjIvX75MTU0VCAQjR44EgMrKShqN9i8Py3R2dpbJZGKxmLzYfWlpqcs7ffScnZ15PB55u6yszMHBgUajVZ9IPpBs2VUjTKVS9Vy4hyDqajQ9yspCbW17yOXw++8AADQaWFsDAJibA/ntsVJJA6j63E2lUkNCwNfXXLudwmaDnR0AkLWcAgAEEdCnDy0hYQiAeMCANl9/7WTweQgPHxAePsBgDCGEPhfW1tZbt64xGGOxgOy3yGT+MHZsP42muZXVo7i4s87O1OoxkYgiEACfT/4LAgFcvw7kmpkgqDwe5elTBgDIZEB+mFIoQCwGAFAqQSQCACgokAE0KShQGx46oYtIJAoPDycDbm5u5MRx48b16NFDZ954arXa29v77Nmz5K9t2rTZvXt3jcy0adMmTpxI3l6zZk2/fv0IgigvL7e0tMzIyCAIQqlUOjo63rx5kyCIZcuWDRw4kAzv2bOndevWtf3pyMhIS8sDrq7Ny8vLDY5z0qQfuNzuXG7fQYMmGLloqampmZmZRoYRQgiVlZU9evRIKpUaEz58+BiX25LLHeXv314oFBrMd+s2zMJiTVyc4RW+7kL49ddf29vb79+/PyoqSlsIr127RqfTxWKxMSPWY/PmzfXq1fvrr79mz57t7u5OLg952KdSqSQI4tmzZ7a2tr/88ssff/zBZrOvX79OPjAiIqJ169bHjh0bNmyYtuAVFBRwOJxly5YdOHDAycnp2LFjtf3dyMjI5s3bvXr1yshx5uTkZGdn/5slRQgh9B7xeLynT5+qVCpjwlKpdOPGbRkZOQaTOo4alclkbDZ7z549o0aNiouLGzlyJHlYSnFxsbOz87Nnz3y152f+vw4fPnzhwgVnZ+dp06Z5enoCQEFBwc6dO5csWUIeC5SYmLh7926FQjFq1KhOnTqRj1KpVNu3b3/w4IGPj8/MmTO1XwQ+e/Zs27ZtlZWVgwYN6tu3b21/9LPuLIMQQuif+v9Pn8jPz3d3d09PT/fz86teCPl8vp2d3cOHDz/QifYfGhZChBAyKUYWQh2nYnA4HBqN9uzZsxrT79+/T6FQtCc2IIQQQl8AHYXQ0tKyb9++CxYsePnypfY8hxcvXsyaNatTp041Gs0ghBBCnzXdp09s3rw5NDTUz8/P29u7vLy8VatWSUlJ9vb2MTExH3l8CCGE0Aelu0uNm5tbYmLi0qVLXV1dPTw8qFTqnDlzHj9+XL9+/Y88PoQQQuiDqvWEehaLtWDBggULFnzM0SCEEEIf2Qdp+I0QQgh9LnR/IhwyZEhFRcW7021sbOrUqTNw4MB27dp94IEhhBBCH0OtnwgfPnx448aNkpISgiDy8/NjY2OfPn1aVlZ24MCB0NDQ9evXf8xRIoQQQh+I7kLYpk0bb2/v58+fP3ny5OrVq2lpaUlJSQwGY8aMGbm5uRMnTly8eHFtFyxECCGEPiM6CqFSqVy2bNlvv/1Wt9rFpgIDA5cuXbp06VIGg7Fx40YKhXL37t2POE6EEELog9BRCMvKygQCgYODQ43pXC43IyMDACwtLT08PIRC4ccY4Ht15szTRYvWGpNMSUnp0mVYhw6D7t9/YOTMJRKJXC7/F6NDCCHTQhCEQCAwMlxWVjZixNQWLfrs3XvImPz16zfr1m19+3amwaSOg2U4HI6VldW+ffs2bNhQfbj79u3T9lcjLxNo3OD/QxSKq1u2fFOnztM6dRpVv3avpSVUv4Kura26e/cxRUV7ARgDBozKyLhhQ16osHbTpv3411+XAZRz5oyfPz/CmMEUFhYymUwWi/X/LAlCCP33KBSKoqIiV1dXc3N9F7slJSYmffXVOJWK4+RE3L592uBqdsiQKXFxwzSaNrNnT3Jx8W7UKEShqLpLo4Hq9VQiAbkcRo6cW1JylkrlGByJjrEyGIy5c+cuX748NTW1b9++XC63oKAgOjr67t27e/fuBYC4uDiBQBAUFGRw7v81KpWVUum3fXsxm93o3WeNRBBQXl4kFHoBNAWA4uJmLi5ZFhZNWayqesliAZ0ONjbAZAKDAWw2SKUv9+59JBbHA2jWrGkVGDjO0ZFpZwe2tsBiwbvtXjUaTe/eo5KSeARR8eOPE6dP/9a4wauMeW0hhNB7ZPyaJy0trXv3USpVHQuLnJs3T5BXFqqBvMQu+fPtt4vz86MB6peW7gwL2xMUNEskAoUC+Pyqy+1WVoJCAZWVIJWCTAYVFa8AwgGAzx8cFpZobx9Cp1fN1swMqn+mIFfOfL4awLG83PCFeXUv3pIlS9hs9vr16y9cuEBO8fHxOXTo0IgRIwAgMDAwOzvbycnwddj/a2i0Na6ut27fXmZpqS+m0bj4+BS+enUawMLNLSkhwZdKffufIRCAXA4iEYjFoFBARQXk5UkIgtzoMJPLrdaskYvFTO3/N50OLFbVj60tsNkgk92Ni7OWyQ4DKBcvDq5ffzyHQ+FwgPx50961+ng0YWHj795No9EU+/dv7NKl44d5ehBC6K3y8vIuXYbk54vt7KiXLx/SecUFoRDKy6GiAsrLYe7cdfn5OwFaAlzs0eO35s1/0dY8gQAqK4HPf7syZLGgsFAKYAcAGg1HIim1swN396pPFwwGMJlgY1O1/rSwAEtLGDcu8MKFX+Xytvb2f8TG/h4YaGD848Z1OHnyGxubtQAGqpWOyzBVV1ZWVlRU5O7uzq6+J/HztH///sjIyJiYGCsrK4Ph/Pz8lSt/l8uVixZNrVevnv4wQRCdOoWnprIAJF272kdFbat+r1gMNV4NDx7Ebdt2VCrdAqCxsAgKDX1UUWFGvpLKy8HOrqoiam/weGdPnYqVyzcClLm6fhUbe9feHuztwayWk18Igpg9e+nx4+fq1PGKitrs6upq9JOEEPpiaTSaadN+PHPmso9P3cOHf3d2dq4tWVkJPB4sWrQkOtpXrR5BocT5+h7o0WOPdjWlLX4Mxts1VWrqqJKS7wECAa4FB5+ePv236mXP1hbs7P72V06ePDNx4iq1ui2Tef3evRgPDw/945dIJOvXb0lPz5k0aXDnzh2NWeRr1675+/vrWVKSgUL4Jfmg1yMkCCIhIYHBYDRp0sRgWK1Wh4YOyMiwBiicOvWrJUtmV5sPvPtSu3bt4OnTxWr1HAA1nd6qTp0EHg94PLCzA7Ii2tsDh/P2dkbG8R07YqXSLRRKXPv22+Piog0Oafv2P0+ciG3fvtmCBTMMXrsLIfQfcebM+c2bD/v6eq1cOc/gAQf79h2eOjVeItlIoVxu2vRARMRBHg/KyoBcn/B4UF5edcPCAjgcEApnlJeHA4QCZHt4fD9r1nHtjitt8dPunASAxMTEPn2+Vaub0+mJN25E+/j4GBx/QUFBRkZGUFCQtbX1v3wqdPrHF+bNysq6c+dO8+bNGzVqdPToUalUqvMBY8aMec8j/Vj+UxfmJQgiPT2dxWK5ubkZDFdUVDRv3p3H606nP4mI6Lh06VwAIIi/vXCr346LW5ue7gMwCEBNobS1sHigLZYODuDg8LeqyeHAnTtHli8/KxT+aGl58LvvaD///JPBIZ07dyE29n6PHu169Oj2Hp4OhBAAAGRnZ+/adcjVlTtx4tcW1Q/h0yUpKalbt7k83u/m5g/ato3dtOlQaanu1QJZ7YTCZRpNc4B+AEomM3To0HvkSsDBoebGNFnenjx50r37N1Jpfwbj4sGDK3r06Gpw/EKhMDs7u379+kwm8708If/SPy6Ee/fuHTdu3OrVqxcsWODk5FRSUqLzAZ/vJ8j/VCH8p8RicVxcnKenZ6NGjQyGU1JSOnf+tqxsno3N5UmT3JYt+0n7rtBu/VV/q6SlzRAKhwK0BahgMIY2a3aZfEtot/60t8k3yYkTh2bPPsHnj2Ozd27fPnbYsHCDQ7px48ajR8m9enX19/d/H88HQp8HPp9/+HC0tTVz6NDBDAZDf7ikpCQwsGdx8UIGIyskJDEm5oh251D196x2YkbGjsJCGsB4AKBSWzZu/FBb1d7dUeTgAFlZj3r0iODx5traXpg2zWflyvkGx19cXBwfHx8YGKjzyJf/vn9cCKVSKZ/Pt7W1tbKyKikpUat1H2nj4uLynkf6sXzWhfCfSklJiY4+GxjoGx4+kPLu4Td/d+DAXxERFysrF1tYHBg2DCZOXFr9zaa9rX0TCoXDCGIVQD2ANC53XffukXZ2QP6Q+0yq/zCZsGnTzmXLLvP5/e3tt50/vzk4uKX+8RAEcfp0zPPn2WFhffHKX+g/RSwWR0YeIghizJgRBg/3l8lkAQEdcnNHmZvzAwMf3Lt3VqWq+r6joqLmT3k5pKWdevQoVa1eBAAUSjCD8cDenlJje1Rb4TgcKC5OnDx5XkXFFnPzB506Xbx8Ocrg+B8/fnzs2PmgoIABA74yuGb4AhhZCN8eNWppaWn55mBKR0fHDzg09OE1bty4cePGRoZHjx4mEAiPHVvYoUPQokUzq+/012nWLL9t284qFNPp9LOdOvn17Fn1Ts7JgcePa763CQLU6miV6iSALY/nOnLk8e7dW7LZwGIBmw12dqC9Td5gMGDWrCV//lkkFLb/5Zdht29HNWjQQP94RCLR+vVbX70qnDFj9Od4Vg/6hHg83po1m/l80fffT/D19dUfJggiOLhXZuZAgjDbvLlnaupNMzMqnw8VFVVnBfD5f7uRmfkkL6+FUjlNqYSHD7vZ2FRIpXY6txpdXSEgAJo1q//s2bbKypkAOXXr0jIzDRaq5nT6jC1bljdo4Ll69XZjlrdp06ZNmzY17rkxIbWeHUIQxN27d1NTU1Uq1XfffQcA+fn5DAbjczyPHhkUETEhImKCkeFVq+YVF39/925whw5td+1ar39/j1QKAwZ4XblylyB6Mhh32rTx9vcHPh/KyiAzE8iVSPU1CJUKCsVFtfoBAKW0lDpo0Lng4AY2NmBrC+S/bDZof7WxATYbBg0af/t2qEIx4OLF7+Ljj3h7e+sff3x8woQJC8Ri8eLF08eOHWbMImdlZanVaoMlGX0IJSUlRUVFDRs2NOYwrvT09DFj5vB45dOnj5s5c6LBfMeOg9LTx6vV3PPnR9y/f5VKtRMKobKy6lh/8rZQCEIh8PlQUPA6K8tRoZgFABkZD+3sMoRCv3c35sgb3t7g6el261aKQiEDENvZlb54YVvjsMl3BFhYjFq/vpu9PWfv3t3GPDkDBvQbMKCfMUmkh+6jRsvKyvr37092E3XfmGCXAAAgAElEQVRzc8vLywOAadOmJScnx8XFfewxvicmtWv0P6WoqGjQoMkvX+a1b9/ywIHf9a/OJBJo165vUtISgCAm87upU3s1aNC/+vqoouJvqyeBACoqWgI8BAAKZZO3N9fdfSSTWVUprayAyazaQ6udOGZMUGnpcQAHDqfPtWuRDRt66/8QPHbszAsXMgFo7dvbHz++x+Dy3rt3f+HCjUymxa+/LjT4IQMAxGLxxYsXHRwcOnToYDAMAARB5OXl2dnZGX+gnUgkMj6sUqny8vJcXV3pBncOAABARkbGo0ePWrdubXATBAAkEskPP6yKj08ZMaLPjBmTDOYPHTo6a9YvAA3t7J7Hx1/Qf2BkRQUEB4dmZm4HqGdrO2jduhVcbjOJpOoUJpEIJBIQiUAgAHJiRYU4Obm3Wk2u0+Yxmb3Y7E7kZhZ5xH/1TS47O2AwJDNmhAgE1wHMOJzOSUmxnp4GDtTcuXP/qlWb6XT61q3Le/ToYnB50fv1j3eNVjdp0qTc3NwrV64QBPHNN9+QE4cPH759+3ahUGhwzzhC1Tk7O9++fcrIMJMJx49vHjo0orCwJCys57p1Xxn8IqN5c87jx9cIIoDFOrtmzUYXF5BIqorlm/Ud5OVVTeTzZXw+E8AbAPj8Nu3bZ8lk3kolsNlAp4O1dVVPCm3/IDOzspiYJ1LpdQC4dKn/Dz+89PKqY24OVlZAp1ed50ung5UVUKlgawsCQUX//hGlpfsBKlNSRubkPNT/TYxYLA4M7FxU1IdOf9mv34nIyN/0L6xcLm/X7qvcXAuNJm/r1sWDBw/QnxeLxR06hOXmyszNBadO7WnZsoX+fEFBQbt2AyQSTzOzrIsXIw2eDnThwuUxY5aJRAOtrYecPLmpXbu2+vNTpy46fNhbodienr6AweB27x5G9qlQKEAsBrUaKiuBIIDPBwAQCGDt2l/Ly2MBrHi8zX36RLu6TiB7jgiFoFQCnw9yeVV5UyrBzg4EAilAAACIRB23bXtRv34zcmOIzQYrq7e7E95MtOrfX5qf/wjA0dHx1uPHswwdAsFks1fNnt0LANat+8lgFQSASZPGTJr0uR5pbzp0FEKJRBITExMdHd21a9fqn/8aNGigVqtzc3PxwD/0QdWpUyc+/pzx+ZiYP777bnFubuG8eZOHDjX4zahF27bsxMRflEpnV9crqakLbW0BACoqQKl82zCIzwelEoRCKC2lnjtX1dCQIGRCIfXpU1Crq2LvrsRlsoyyslYA/gCQm+tkZlZqa+tIpQIAsFhVPRDY7Kr+QXZ2wOPdysnpqlL9JBbDkSMtJRKNjY1Z9e1XGxuo3t/q1atTT560VSqXAIgmTuySnf22ENboMkWKjY18/Li3Wj0D4FV4+KQff7xUI1C9vyAAnD695dWrhQQxACA5PHzNkCFR1Q+bEwhAo3n7K58PN27sLSv7E8BXJusUFrYzMLAtWZMAQHtDKASVCgCgshLU6kcAqwEshcIxc+fGOjmFkRsTNBpYW1dtTJDPDPmMEYQZgALAysxMVq+edd++VT1HrK2BTq/afLGyqtouAYB+/fxjY5fKZP6OjocvXz5v6ERquHp1f0TEMoGgcuXKFcYcCdi/f+/+/XsbjKHPi45CyOfzVSqVn5+fzgfUdn4hQp+Ku7t7TMxe4/NXrx7544/9PF7exIlnbMn17ps1r66jxOyysnocOBACYD5gQKtt2wwcRC4UNvT1vV9YGEehVNarV56R4agtHnw+kF9EaG9UVMCLFw4LFmRUVhIAfCZTPWSImbZ+vJlhVRUhpaerCYLcY2muVmsqKt7epdFA5jt99rOzxRoN2VqIU1kpffSoZqBGx3mpVDt/ulyuIj/panl7/62fEZsNhYUOpaUZBOFLpb5o25YbEfG2JllbVzXa1dZyW1uYNSt0z541Umk4m7358OHvevXS/3RCaOji8eM7A3i4ukq2b48xeHLa8eO7IyMP5eRkjht3zGA/EQDw8/O7etXwwZboC0e8QyaTWVpaHj58mCCIGzduuLm5kdOPHj1qZmZWXl7+7kM+C5GRkaNGjfrUo0CfJR6PV1paamQ4LS1t+PCpEybMzcvLMyY/bdqPXG4TN7fm589fNhgWiUQBAaFc7igut/WePQcN5vPy8tzdm9nZzXFwCDl06KjB/MuXL93cmnG53zg5Nbt//4HBfGFhYWBgV0fHoJYtexmzcpDL5atXb+rXb9yRI8cNhkkSiSQ3N1ej0RiZR0hLrVYrFAqDMd0Hy4wZM+bGjRvHjh2TyWQjRozIy8u7ffv28OHDg4KCTp0y9sue/xo8WAZ9GdRqdVpamrOzM5fLNSYvFAoTEhLq1atn5DnRUqk0IyOjTp06eDQA+tz94xPqqysvL+/Ro0dCQgKHwxEKhY6Ojvn5+Q0aNLh+/frn28EZCyFCCJmUf3XUKIfDuXPnTlRU1OXLl0tKSmxtbTt06DB+/HhjrtuAEEIIfUZqPaGeTqePHTt27NixH3M0CCGE0EdWyxXtEEIIIdOAhRAhhJBJw0KIEELIpGEhRAghZNKwECKEEDJpWAgRQgiZNCyECCGETBoWQoQQQiYNCyFCCCGThoUQIYSQScNCiBBCyKRhIUQIIWTSsBAihBAyaVgIEUIImTQshAghhEwaFkKEEEImDQshQgghk4aFECGEkEnDQogQQsikYSFECCFk0rAQIoQQMmlYCBFCCJk0LIQIIYRMGhZChBBCJg0LIUIIIZOGhRAhhJBJw0KIEELIpGEhRAghZNKwECKEEDJpWAgRQgiZNCyECCGETBoWQoQQQiYNCyFCCCGThoUQIYSQScNCiBBCyKRhIUQIIWTSsBAihBAyaVgIEUIImTQshAghhEwaFkKEEEImDQshQgghk/ZpCuHBgwdDQ0NDQ0MPHDigM5CcnDxgwIDg4ODvv/9eKpWSEwmC2LBhQ5s2bbp3737lyhVyIp/PH1LNsWPHPtIyIIQQ+iKYf/w/GRsbO2vWrKioKDMzs2HDhjk7O3fr1q16QCKRdOvWbd68eV27dp07d+7333+/ZcsWANi+ffsff/yxf//+V69eDRo06NGjRz4+PjKZ7OTJk4cPHyYf6+/v//GXCCGE0OeLQhDER/6TYWFhzZo1W7x4MQCsXr06Pj7+1KlT1QP79u3bunXrw4cPASA1NbV169aFhYXW1tYBAQFLliwZMmQIAIwdO9bJyWn9+vVFRUVeXl5yudzg392/f/+VK1dq+wyKEELoC6PRaNRqNY1G0x/7BLtGnzx5EhwcTN5u1arVkydP9AQCAgIIgsjKylIqlenp6dUfmJycTN5WqVTh4eFDhw7dtWuXWq3+KAuBEELoC/FBdo0WFBRkZ2fXmEihUEJCQgCgpKSEzWaTE+3s7IqLi2skS0tLvby8tL9yOJzi4mIul0sQxLsPtLCwWLVqVWBgYGlp6apVq5KSkrZv317bwC5dulSnTh3ytqen59mzZ//VciKEEPoP02g0DAbD4CfCD1II7927t3nz5hoTqVRqbGwsANja2kokEnKiSCTS1jYtGxsbbQAAhEIhm822tbUFAIlEQua1D2Sz2fPnzyeT/v7+bdq02bRpE4PB0Dmw9u3bb9iwgbxNo9FsbGz+3YIihBD67yJ3jRqMfZBCGB4eHh4eXtu9derUycjI6NSpEwBkZmZW//BH8vb2vnXrFnm7tLRUKBR6enpaW1s7ODhkZGS4urrW9kA3NzeVSiUWi2srhEwms27duv/3ciGEEPryfILvCEeMGLF79265XK5QKHbt2jVy5Ehy+po1a8gdqsOGDbtx40Z6ejoAbN26tVOnTs7OzuQDt2zZQhAEj8eLiooiH5iRkVFRUQEASqVy5cqVTZo04XA4H3+hEEIIfaY+QSEcP368t7e3h4eHh4eHu7v7hAkTyOk///zzy5cvAcDLy2vdunVt27b18fGJiorS7mVdvHhxYWGhp6dn/fr1w8PDu3btCgB37tzx9PT08PCwt7dPSkqKior6+EuEEELo8/UJTp8g8Xg8ALC3t68tIJPJysrK3NzcKBRK9elFRUVMJpP8ypCkUCjIA3Csra31/EU8fQIhhEyKkadPfIIT6kl6SiDJwsLC3d393enkbtLq6HS6ziRCCCFkEPYaRQghZNKwECKEEDJpWAgRQgiZNCyECCGETBoWQoQQQiYNCyFCCCGThoUQIYSQScNCiBBCyKRhIUQIIWTSsBAihBAyaVgIEUIImTQshAghhEwaFkKEEEImDQshQgghk4aFECGEkEnDQogQQsikYSFECCFk0rAQIoQQMmlYCBFCCJk0LIQIIYRMGhZChBBCJg0LIUIIIZOGhRAhhJBJw0KIEELIpGEhRAghZNKwECJkmFqtVqlUxud5PF5lZaXx+YyMjNLSUiPDKpXqyZMnRUVFRuZlMllCQoLx85dIJImJiQKBwMi8VCpNS0uTy+VG5pVKZUFBAUEQRuYBwPiZI/R/wEL4yajV6n+ULy0tVSgURoYVCsWTJ094PJ6R+aKiotOnT2dlZRmZv3///s8//5aQkGBMWK1Wb9/+55gxMy9cuGRMns/nf/vt3DZtBkRGRhmTf/HiRevW/erVa7Nx405j8hcuXPHyauni0mzlyk3G5Dds2O7iEuTi0mLp0l+MyY8dO7NhwzAfn27Llv1qMKxWq0NDB4SELAgIGLBhwzaDebFY3KRJp27dNjVpEr5r136D+eLiYj+/dr167QkI6Hvq1FmD+ezs7AYN2vXsucPXt9O9e/cN5lNSUurVC+nUaW29em0yMzMN5uPjH3p5BTdvPtnfv31FRYXB/J0799zcmnl4dOzadYhSqTSYv3v3fr16bVxcms2evdRgGADi4xOaNu1Wv37IoUNHjcmnpKT07Dm6e/eRjx8/NiafnZ09Zcr8efOWl5WVGZMvLi7etGnrkSPRRq4fKisrY2JikpOTjQkDgFwuf/LkSXl5uZF5giCKior+0crqn67Z/gso/2i77LO2f//+mTN/Xbhw0ty5UwyGjx2LmTNnpUajWbp01vjxIw3mf/1154YNO6hUs/XrF44YEW4wP3HivFOnrpqZqbdsWTFo0Ff6w0qlsnPnQS9eyACKt21bER7eT3+ex+MFB/cWCgMAnu7a9dOAAX3151NSUrp2HSuRDLSwuLR793yD+ejok5Mn76ioGMXh7N27d+5XX/XWn58/f9WWLaVi8SA7u1V//TWne/eu+vO9e4++fLmbWt2RxYo4dGhu27ah1e9Vq6HGZ60ePTpmZv4O0IDNHrJ585KGDYN0zlYiAbkcCIIYNqxZefl1ABsWq9/GjZs8PHwBQKkEkUjHo6RS4bRpXSor7wGYWVt3XLLkiK2ts57B5+Y+37jxB7H4FIDGyqrV/PlxNBpTTz4r6/qBAydkss0AKiurlhERiQAUPfnU1EMXL+aqVPMBZLa2oVOmxOsJA8Ddu7/cvu1AEGMBKuztB3777Q39+YsX5z150gmgF8BzD48fR4wwUB6OHfs6KysCoAXA9aZNTw4b9rv+/Nat/XJzNwHUMzOL7Nq1KDz8B/35JUs6FBVFAbjS6UsnTWrQvv2IdzMMBjDfPMejR7cuKjoB4GJjM3LFioiAgLZmZsBi1Tr/3r2bl5ScBOBwOL1Pnz7k6uqpvcvCAiwt/xZWKpWBga2KinYDUF1cxmVl3bGskfg7oVDYsGHHgoLlZmb8Bg12pqXd1L+w5eXlTZp0LSycbGmZ1blzcUzMPv350tLSoKCeFRV9GYxHs2Z1XbRopv58cXFx69Z9xeImFEryn3+u7NOnh/58YWFh+/YDRCIujVZ45cohPz8//fnc3Nzu3UfyeHI3N5urV4/Y29vrz2dnZ/fv/21paWXz5n6nTv1Jp9P159PT0wcPnsrj8fv167pz5zoKRd87BQDi4xPGjp2zffuOjh0b6k+a67/7CyOXX1q1amydOp28vf30bIwqFLJvv/1JILgFYD5nTmc2uzuLxdUzWx6vYPnyQwJBPIBy6tQQO7u+NBqDXO3qlJWV8Ndfr4XCRADRhAntCeIrmQyk0lrnn5R05uHDRnL5KgDht992zczUXQjFYiA/MT54cPDlywkE8S1Axfjx/e/f70sQwOfXOv8rV/aXlGwA6CISjR83buLhw33fPA8gFuvIJyZGV1RsAahfXt5szJiffXzeFkKdS52Xd1WhOANgXVEx76uvLjCZbwvhu1UNAACeARwAAIFgxODBDy0s/lYIqVSwtf1bOidHDNAEAASCTj/99JzD0V0ImUxgMECjUYhEVgB2ACCRBGzdWmBn5wsANBpYW+t4lEwmlsvtAagAoFY7JyRUslj6CqFIpCQIcq1sRhB0Hk/FYOiJg0hEAajaGKVQCDYb9L+7bWxoFIoMAACUVCrFzk5fGABsbOgUipggAEBCo5kbzFtZ0SgUGUEAgJTBMJyn0SgAGgAA0CgUYPAznkKhBLAEAIJgVlQoHj0ykBeJZAAOAKBUut66xde5P1guB4mk6nZ5uRLAFQAkkiZ//JHv5AQaDdS2l1ejkZSX2wB4AQCf33rIkGxLy7eFUCoFmaxGPk8o9AEIAoDCwkZM5ksA/+oBS0uwsHj7q0r1VCQKIYg+ajW8eLHf25tHpf6tNlAowGa//ZXPv1VUNFCjmSgWw6VLwd26Ee9uFVV/ob58eSYv7xuCiBCJVKtXt83MnFlbKbGyAjod7tyJzMmZThCjAcq+/nrI+PE93h1DdadObc7Onk8QAwEeDhq0evr0WvdAmJuDjQ38+uvK58+XEEQXHu/IqFG/jhu3SmdYu2kyd+78p0/XALSKjV0ze/beAQMm1TZ/0qRJ07OztwL4HTo01cPjbJs2tX4ksLYGGg3Cwqbl5x8xN3fVP1swtUKoULDl8mYLFuTa2vrpeYfL5RVSqTuADQBIpb4//1xkba2vEAqFpRJJfQAaAE0icVq7tpJO59Z4S1RXXMyXycj3m7VUah4drba0pOrZsszMlKtU5GufoVara1vXWFmBlRXAm3UlQQCAwtycamcHFArUq1fr/EtL7V6/zlGrAeCVtzdn8OCq6XR61Qxr+P137wsX7qhU9c3N7/Tt6z1r1tu7yGJTw9y5Tc6cOaxSDbe2jl63rv3w4W/v0rm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       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "cell_type": "code",
   "source": [
    "using Unitful\n",
    "using UnitfulAtomic\n",
    "\n",
    "plot_bandstructure(basis; n_bands=6, kline_density=500)"
   ],
   "metadata": {},
   "execution_count": 8
  },
  {
   "cell_type": "markdown",
   "source": [
    "The bands are noticeably different.\n",
    " - The bands no longer overlap, meaning that the spectrum of $H$ is no longer continuous\n",
    "   but has gaps.\n",
    "\n",
    " - The two lowest bands are almost flat. This is because they represent\n",
    "   two tightly bound and localized electrons inside the two Gaussians.\n",
    "\n",
    " - The higher the bands are in energy, the more free-electron-like they are.\n",
    "   In other words the higher the kinetic energy of the electrons, the less they feel\n",
    "   the effect of the two Gaussian potentials. As it turns out the curvature of the bands,\n",
    "   (the degree to which they are free-electron-like) is highly related to the delocalization\n",
    "   of electrons in these bands: The more curved the more delocalized. In some sense\n",
    "   \"free electrons\" correspond to perfect delocalization."
   ],
   "metadata": {}
  }
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