3_SolvingDiffeqs.ipynb

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    "# Solving Differential Equations using Numerical Methods\n",
    "\n",
    "## 1. Introduction\n",
    "\n",
    "This notebook is an introductory class to how to solve differential equations using numerical simulations. It has been implemented using Julia running on  Jupyter labs. We start by defining our problem as an irreversible chemical reaction in the following form. \n",
    "\n",
    "$$ a + b \\rightarrow c \\tag{1}$$\n",
    "\n",
    "where `a,b,c` are chemical species, and the rate or _speed_ of the reaction is determined by the reaction rate constant `k`. This value can be identified as the probability that a collision between `a` and `b` succesfully produces a molecule `c`.\n",
    "\n",
    "Using the __Mass Action Law__, we can derive the differential equations corresponding to this reaction. The general formulation of the system of differential equations can be expressed as:\n",
    "\n",
    "$$ u' = f(u,p,t) \\tag{2}$$\n",
    "\n",
    "where `f` is a general vector function that depends on the parameters `p` of the system, the time variable `t`. For our particular case, the equations of our system are :\n",
    "\n",
    "$$\\begin{align}\n",
    "\\frac{da}{dt} &= -k \\cdot a \\cdot b \\tag{3}\\\\\n",
    "\\frac{db}{dt} &= -k \\cdot a \\cdot b \\tag{4}\\\\\n",
    "\\frac{dc}{dt} &= k \\cdot a \\cdot b \\tag{5}\n",
    "\\end{align}$$\n",
    "\n",
    "\n",
    "We will write the variables `a,b,c`  in the form of a __state vector__, i.e., a column vector that contains all the variable of the system variables. In this particular problem:\n",
    "\n",
    "$$u=\\begin{bmatrix}\n",
    "a\\\\ \n",
    "b\\\\ \n",
    "c\\tag{6}\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "## 2. Euler Method\n",
    "The Euler method is the simplest most straightforward explicit algorithm to solve numerically a set differential equations. Althgough it is very simple, the Euler method often serves as the basis to construct more complex methods to solve systems of equations nukerically. Here, a differential equation can be thought of as a formula by which the slope of the tangent line to the curve can be computed at any point on the curve, once the position of that point has been calculated. The idea is that while the curve is initially unknown, its starting point (i.e., its in initial condition, which we denote by `u₀`), is know. Then, from the differential equation, the slope to the curve at `u₀` can be computed, and so, the tangent line.\n",
    "\n",
    "<img src=\"Euler_method.png\" width=\"200\"/>\n",
    "\n",
    "Take a small step along that tangent line up to a point `u1`. Along this small step, the slope does not change too much, so \n",
    "the point `u1` will be close to the curve. We can then continue the same reasoning for `u2`,`u3` and so on. \n",
    "\n",
    "Here we will learn how to implement this method on a computer using any programing language. This notebook has been designed using Julia. \n",
    "\n",
    "\n",
    "We start by defining a set of initial conditions for the state vector:"
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   "source": [
    "u₀=[0.02,0.01,0];"
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   "source": [
    "Next, we define a vector `time_span`, that determines the time where the equations will be solved"
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    {
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      "text/plain": [
       "100-element LinRange{Float64}:\n",
       " 0.0,1.0101,2.0202,3.0303,4.0404,…,95.9596,96.9697,97.9798,98.9899,100.0"
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    "tspan = LinRange(0,100,100)"
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   "source": [
    "The results will be saved in a matrix `U`. This matrix will be initialized with the same number of rows of the state vector `u`, and same number of columns equal to the time vector `tspan`."
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   "source": [
    "U=zeros((size(u₀,1), size(tspan,1)));"
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    "The first row of the matrix `U` will be the state of the of the system at `t=0`, so it is equal to the vector of initial conditions `u0`:"
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   "source": [
    "U[:,1]=u₀;"
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    "Finally, we need to set a value for the kinetic rate constant $k$:"
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   "execution_count": 5,
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   "source": [
    "k=1;"
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    "We will use each row of the matrix to save the value of each variable `a,b,c` for each time point in the simulation `a=U[1], b=U[2], c=U[3]`. This way, the set of Eqs 2.3 will be solved iteratively, i.e., the value of `U(t-1)` will be used to calculate the value of `U(t)`. We will iterate as many times as the length of the time vector. We do this by using a `for` loop:"
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   "source": [
    "for i = 2:size(tspan,1)\n",
    "           U[1,i]= U[1,i-1]-k*U[2,i-1]*U[1,i-1] # Eq 1\n",
    "           U[2,i]= U[2,i-1]-k*U[2,i-1]*U[1,i-1] # Eq 2\n",
    "           U[3,i]= U[3,i-1]+k*U[2,i-1]*U[1,i-1] # Eq 3\n",
    "       end"
   ]
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   "source": [
    "Next, we rename each row as the corresponding variable and plot the results in a graph, with the x-axis as the time vector `tspan`, and the y-axis the concentration of each variable `a,b,c`:"
   ]
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   "source": [
    "a=U[1,:]\n",
    "b=U[2,:]\n",
    "c=U[3,:];"
   ]
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  {
   "cell_type": "code",
   "execution_count": 8,
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   "source": [
    "using Plots; gr(); # this is to initialize the plots package in Julia"
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    "plot(tspan,a,label=\"a\",seriestype=:scatter)\n",
    "plot!(tspan,b,label=\"b\",seriestype=:scatter)\n",
    "plot!(tspan,c,label=\"c\",seriestype=:scatter)\n",
    "title!(\"Euler in Julia\")\n",
    "xlabel!(\"Time [s]\")\n",
    "ylabel!(\"Concentration [M]\")"
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   "cell_type": "markdown",
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   "source": [
    "## 3. Euler with integration step\n",
    "\n",
    "The number of times that the equation is solved is very important. If we solved it just a few times, the solution may not be accurate. If you solve the system many times, the numerical simulations can be very slow. To  define how much time passes between diferent solutions of the system, we define a `timestep`. Note that now the `tspan` vector and the number of columns of the state matrix `U` depends on the `timestep` selected."
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  {
   "cell_type": "code",
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     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "timestep=4\n",
    "tspan=LinRange(0, 100, floor(Int,100/timestep))\n",
    "U=zeros((size(u₀,1), size(tspan,1)))\n",
    "U[:,1]=u₀\n",
    "for i = 2:size(tspan,1)\n",
    "           U[1,i]= U[1,i-1]-timestep*k*U[2,i-1]*U[1,i-1] # Eq 1\n",
    "           U[2,i]= U[2,i-1]-timestep*k*U[2,i-1]*U[1,i-1] # Eq 2\n",
    "           U[3,i]= U[3,i-1]+timestep*k*U[2,i-1]*U[1,i-1]  # Eq 3\n",
    "       end\n",
    "a=U[1,:]\n",
    "b=U[2,:]\n",
    "c=U[3,:]\n",
    "plot(tspan,a,label=\"a\",seriestype=:scatter)\n",
    "plot!(tspan,b,label=\"b\",seriestype=:scatter)\n",
    "plot!(tspan,c,label=\"c\",seriestype=:scatter)\n",
    "title!(\"Euler in Julia\")\n",
    "xlabel!(\"Time [s]\")\n",
    "ylabel!(\"Concentration [M]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To compare how close are we to the analytical solutions, we can solve it and add it to the plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
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     "execution_count": 11,
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    "plot(tspan,(U[2,1]/U[1,1])*exp.(k.*tspan.*(U[2,1]-U[1,1])))"
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     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot!(tspan,b./a,seriestype=:scatter,label=\"numerical solution\")\n",
    "title!(\"Coparison between analytical and numerical\")\n",
    "xlabel!(\"Time [s]\")\n",
    "ylabel!(\"a/b\")"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Differential equations solvers\n",
    "\n",
    "Normally, each modern language has implememted solvers for dinamical systems in the form of differential equations. In Julia, we first need to initialize the package for differenetial equations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "using DifferentialEquations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we have to define a function `f` as a set of equations that result from the mass action analysis. To define a system of differential equations in DifferentialEquations.jl, we define our `f` as a vector function with a state vector vector `u` and parameters vector `p`. Thus, for the vector `u = [x,y,z]'`, we have the derivative function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "simpleODE1! (generic function with 1 method)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function simpleODE1!(du,u,p,t)\n",
    "    k = p\n",
    "    du[1] = -k*u[1]*u[2]\n",
    "    du[2] = -k*u[1]*u[2]\n",
    "    du[3] = k*u[1]*u[2]   \n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice here we used the in-place format which writes the output to the preallocated vector `du`. For systems of equations the in-place format is faster.  For our model, the only parameter is the rate constant `k`, therefore we build the parameter collection `p` as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "k=1;\n",
    "p=(k);\n",
    "u₀=[0.02,0.01,0];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we define the `tspan` vector. Note that now, the vector has only two components: the initial and final time point for the simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "tspan = (0.0,100.0);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we define a `ODEProblem` type using the constructor call. This is done by specifying this function `simpleODE`, the initial condition `u0`, the time span `tspan` and the parameters  `p`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mODEProblem\u001b[0m with uType \u001b[36mArray{Float64,1}\u001b[0m and tType \u001b[36mFloat64\u001b[0m. In-place: \u001b[36mtrue\u001b[0m\n",
       "timespan: (0.0, 100.0)\n",
       "u0: [0.02, 0.01, 0.0]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob1 = ODEProblem(simpleODE1!,u₀,tspan,p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we solve the problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "retcode: Success\n",
       "Interpolation: Automatic order switching interpolation\n",
       "t: 9-element Array{Float64,1}:\n",
       "   0.0                \n",
       "   0.15383356961677971\n",
       "   1.6921692657845766 \n",
       "   8.271827791540357  \n",
       "  19.86176245334914   \n",
       "  35.92987335869888   \n",
       "  57.673911215070845  \n",
       "  85.79206764253748   \n",
       " 100.0                \n",
       "u: 9-element Array{Array{Float64,1},1}:\n",
       " [0.02, 0.01, 0.0]                  \n",
       " [0.0199693, 0.0099693, 3.06959e-5] \n",
       " [0.01967, 0.00966995, 0.000330049] \n",
       " [0.018529, 0.00852899, 0.00147101] \n",
       " [0.0169472, 0.00694719, 0.00305281]\n",
       " [0.0153629, 0.00536295, 0.00463705]\n",
       " [0.0139056, 0.00390558, 0.00609442]\n",
       " [0.0126907, 0.00269073, 0.00730927]\n",
       " [0.012254, 0.00225402, 0.00774598] "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol1 = solve(prob1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`sol1.t` stores the time points and `sol1.u` is an array storing the solution at the corresponding time points. \n",
    "\n",
    "However, when dealing with systems of equations, `sol1` also acts like an array. `sol1[i]` returns the solution at the `i`th time point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.6921692657845766, [0.01967, 0.00966995, 0.000330049])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol1.t[3],sol1.u[3]"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Additionally, the solution acts like a matrix where `sol[j,i]` is the value of the `j`th variable at time `i`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Float64,1}:\n",
       " 0.019669951491554746\n",
       " 0.009669951491554744\n",
       " 0.000330048508445255"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol1[:,3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
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       "  298.365,175.417 300.41,176.62 302.456,177.819 304.501,179.015 306.546,180.208 308.592,181.397 310.637,182.582 312.683,183.764 314.728,184.942 316.773,186.118 \n",
       "  318.819,187.289 320.864,188.457 322.91,189.622 324.955,190.783 327,191.941 329.046,193.096 331.091,194.247 333.136,195.395 335.182,196.54 337.227,197.681 \n",
       "  339.273,198.819 341.318,199.954 343.363,201.086 345.409,202.214 347.454,203.339 349.5,204.461 351.545,205.579 353.59,206.694 355.636,207.807 357.681,208.916 \n",
       "  359.727,210.021 361.772,211.124 363.817,212.223 365.863,213.32 367.908,214.413 369.954,215.503 371.999,216.59 374.044,217.674 376.09,218.755 378.135,219.833 \n",
       "  380.181,220.908 382.226,221.98 384.271,223.049 386.317,224.115 388.362,225.178 390.408,226.238 392.453,227.295 394.498,228.348 396.544,229.4 398.589,230.448 \n",
       "  400.635,231.493 402.68,232.535 404.725,233.575 406.771,234.611 408.816,235.645 410.861,236.675 412.907,237.703 414.952,238.729 416.998,239.751 419.043,240.77 \n",
       "  421.088,241.787 423.134,242.801 425.179,243.812 427.225,244.82 429.27,245.826 431.315,246.829 433.361,247.829 435.406,248.826 437.452,249.821 439.497,250.813 \n",
       "  441.542,251.802 443.588,252.789 445.633,253.772 447.679,254.754 449.724,255.732 451.769,256.708 453.815,257.681 455.86,258.652 457.906,259.62 459.951,260.586 \n",
       "  461.996,261.549 464.042,262.509 466.087,263.467 468.133,264.422 470.178,265.374 472.223,266.324 474.269,267.272 476.314,268.217 478.359,269.16 480.405,270.1 \n",
       "  482.45,271.037 484.496,271.972 486.541,272.905 488.586,273.835 490.632,274.762 492.677,275.687 494.723,276.61 496.768,277.53 498.813,278.448 500.859,279.364 \n",
       "  502.904,280.277 504.95,281.187 506.995,282.096 509.04,283.002 511.086,283.905 513.131,284.806 515.177,285.705 517.222,286.602 519.267,287.496 521.313,288.388 \n",
       "  523.358,289.277 525.404,290.164 527.449,291.049 529.494,291.932 531.54,292.812 533.585,293.69 535.631,294.566 537.676,295.439 539.721,296.311 541.767,297.18 \n",
       "  543.812,298.047 545.858,298.911 547.903,299.774 549.948,300.634 551.994,301.492 554.039,302.347 556.084,303.201 558.13,304.052 560.175,304.902 562.221,305.749 \n",
       "  564.266,306.594 566.311,307.437 568.357,308.277 570.402,309.116 572.448,309.952 574.493,310.786 576.538,311.619 578.584,312.449 580.629,313.277 582.675,314.103 \n",
       "  584.72,314.926 586.765,315.748 588.811,316.568 590.856,317.386 592.902,318.201 594.947,319.015 596.992,319.826 599.038,320.636 601.083,321.443 603.129,322.249 \n",
       "  605.174,323.052 607.219,323.854 609.265,324.653 611.31,325.451 613.356,326.247 615.401,327.04 617.446,327.832 619.492,328.621 621.537,329.409 623.582,330.195 \n",
       "  625.628,330.979 627.673,331.761 629.719,332.541 631.764,333.319 633.809,334.095 635.855,334.87 637.9,335.642 639.946,336.412 641.991,337.181 644.036,337.948 \n",
       "  646.082,338.713 648.127,339.476 650.173,340.237 652.218,340.996 654.263,341.754 656.309,342.51 658.354,343.263 660.4,344.015 662.445,344.766 664.49,345.514 \n",
       "  666.536,346.261 668.581,347.005 670.627,347.748 672.672,348.49 674.717,349.229 676.763,349.967 678.808,350.703 680.854,351.437 682.899,352.169 684.944,352.9 \n",
       "  686.99,353.628 689.035,354.356 691.081,355.081 693.126,355.805 695.171,356.527 697.217,357.247 699.262,357.965 701.307,358.682 703.353,359.397 705.398,360.111 \n",
       "  707.444,360.823 709.489,361.533 711.534,362.241 713.58,362.948 715.625,363.653 717.671,364.356 719.716,365.058 721.761,365.758 723.807,366.457 725.852,367.153 \n",
       "  727.898,367.849 729.943,368.542 731.988,369.234 734.034,369.924 736.079,370.613 738.125,371.3 740.17,371.986 742.215,372.67 744.261,373.352 746.306,374.033 \n",
       "  748.352,374.712 750.397,375.39 752.442,376.066 754.488,376.74 756.533,377.413 758.579,378.084 760.624,378.754 762.669,379.422 764.715,380.089 766.76,380.754 \n",
       "  768.805,381.418 770.851,382.08 772.896,382.741 774.942,383.4 776.987,384.057 779.032,384.713 781.078,385.368 783.123,386.021 785.169,386.673 787.214,387.323 \n",
       "  789.259,387.971 791.305,388.618 793.35,389.264 795.396,389.908 797.441,390.551 799.486,391.192 801.532,391.832 803.577,392.47 805.623,393.107 807.668,393.743 \n",
       "  809.713,394.377 811.759,395.009 813.804,395.641 815.85,396.27 817.895,396.899 819.94,397.526 821.986,398.151 824.031,398.775 826.077,399.398 828.122,400.02 \n",
       "  830.167,400.639 832.213,401.258 834.258,401.875 836.304,402.491 838.349,403.105 840.394,403.719 842.44,404.33 844.485,404.941 846.53,405.55 848.576,406.157 \n",
       "  850.621,406.764 852.667,407.368 854.712,407.972 856.757,408.574 858.803,409.175 860.848,409.775 862.894,410.373 864.939,410.97 866.984,411.566 869.03,412.16 \n",
       "  871.075,412.753 873.121,413.345 875.166,413.935 877.211,414.525 879.257,415.113 881.302,415.699 883.348,416.284 885.393,416.868 887.438,417.451 889.484,418.033 \n",
       "  891.529,418.613 893.575,419.192 895.62,419.77 897.665,420.346 899.711,420.921 901.756,421.495 903.802,422.068 905.847,422.639 907.892,423.21 909.938,423.779 \n",
       "  911.983,424.346 914.029,424.913 916.074,425.478 918.119,426.042 920.165,426.605 922.21,427.167 924.255,427.728 926.301,428.287 928.346,428.845 930.392,429.402 \n",
       "  932.437,429.957 934.482,430.512 936.528,431.065 938.573,431.617 940.619,432.168 942.664,432.718 944.709,433.267 946.755,433.814 948.8,434.361 950.846,434.906 \n",
       "  952.891,435.45 954.936,435.993 956.982,436.534 959.027,437.075 961.073,437.614 963.118,438.153 965.163,438.69 967.209,439.226 969.254,439.76 971.3,440.294 \n",
       "  973.345,440.827 975.39,441.358 977.436,441.889 979.481,442.418 981.527,442.946 983.572,443.473 985.617,443.999 987.663,444.524 989.708,445.048 991.753,445.57 \n",
       "  993.799,446.092 995.844,446.612 997.89,447.132 999.935,447.65 1001.98,448.167 1004.03,448.683 1006.07,449.198 1008.12,449.712 1010.16,450.225 1012.21,450.737 \n",
       "  1014.25,451.248 1016.3,451.757 1018.34,452.266 1020.39,452.774 1022.43,453.28 1024.48,453.786 1026.53,454.29 1028.57,454.794 1030.62,455.296 1032.66,455.798 \n",
       "  1034.71,456.298 1036.75,456.797 1038.8,457.296 1040.84,457.793 1042.89,458.289 1044.93,458.784 1046.98,459.279 1049.02,459.772 1051.07,460.264 1053.12,460.755 \n",
       "  1055.16,461.246 1057.21,461.735 1059.25,462.223 1061.3,462.71 1063.34,463.196 1065.39,463.682 1067.43,464.166 1069.48,464.649 1071.52,465.132 1073.57,465.613 \n",
       "  1075.61,466.093 1077.66,466.573 1079.71,467.051 1081.75,467.528 1083.8,468.005 1085.84,468.48 1087.89,468.955 1089.93,469.429 1091.98,469.901 1094.02,470.373 \n",
       "  1096.07,470.844 1098.11,471.313 1100.16,471.782 1102.2,472.25 1104.25,472.717 1106.3,473.183 1108.34,473.648 1110.39,474.113 1112.43,474.576 1114.48,475.038 \n",
       "  1116.52,475.5 1118.57,475.96 1120.61,476.42 1122.66,476.878 1124.7,477.336 1126.75,477.793 1128.79,478.249 1130.84,478.704 1132.89,479.158 1134.93,479.611 \n",
       "  1136.98,480.063 1139.02,480.515 1141.07,480.965 1143.11,481.415 1145.16,481.864 1147.2,482.311 1149.25,482.758 1151.29,483.205 1153.34,483.65 1155.39,484.094 \n",
       "  1157.43,484.538 1159.48,484.98 1161.52,485.422 1163.57,485.863 1165.61,486.303 1167.66,486.742 1169.7,487.18 1171.75,487.617 1173.79,488.054 1175.84,488.49 \n",
       "  1177.88,488.925 1179.93,489.359 1181.98,489.792 1184.02,490.224 1186.07,490.655 1188.11,491.086 1190.16,491.516 1192.2,491.945 1194.25,492.373 1196.29,492.8 \n",
       "  1198.34,493.227 1200.38,493.652 1202.43,494.077 1204.47,494.501 1206.52,494.924 1208.57,495.347 1210.61,495.768 1212.66,496.189 1214.7,496.609 1216.75,497.028 \n",
       "  1218.79,497.446 1220.84,497.864 1222.88,498.28 1224.93,498.696 1226.97,499.111 1229.02,499.526 1231.06,499.939 1233.11,500.352 1235.16,500.764 1237.2,501.175 \n",
       "  1239.25,501.585 1241.29,501.995 1243.34,502.403 1245.38,502.811 1247.43,503.219 1249.47,503.625 1251.52,504.031 1253.56,504.436 1255.61,504.84 1257.65,505.243 \n",
       "  1259.7,505.646 1261.75,506.048 1263.79,506.449 1265.84,506.849 1267.88,507.249 1269.93,507.647 1271.97,508.046 1274.02,508.443 1276.06,508.839 1278.11,509.235 \n",
       "  1280.15,509.63 1282.2,510.025 1284.24,510.418 1286.29,510.811 1288.34,511.203 1290.38,511.594 1292.43,511.985 1294.47,512.375 1296.52,512.764 1298.56,513.153 \n",
       "  1300.61,513.54 1302.65,513.927 1304.7,514.314 1306.74,514.699 1308.79,515.084 1310.84,515.468 1312.88,515.851 1314.93,516.234 1316.97,516.616 1319.02,516.997 \n",
       "  1321.06,517.378 1323.11,517.758 1325.15,518.137 1327.2,518.515 1329.24,518.893 1331.29,519.27 1333.33,519.647 1335.38,520.022 1337.43,520.397 1339.47,520.771 \n",
       "  1341.52,521.145 1343.56,521.518 1345.61,521.89 1347.65,522.262 1349.7,522.633 1351.74,523.003 1353.79,523.372 1355.83,523.741 1357.88,524.109 1359.92,524.477 \n",
       "  1361.97,524.843 1364.02,525.209 1366.06,525.575 1368.11,525.94 1370.15,526.304 1372.2,526.667 1374.24,527.03 1376.29,527.392 1378.33,527.753 1380.38,528.114 \n",
       "  1382.42,528.474 1384.47,528.834 1386.51,529.193 1388.56,529.551 1390.61,529.908 1392.65,530.265 1394.7,530.621 1396.74,530.977 1398.79,531.332 1400.83,531.686 \n",
       "  1402.88,532.04 1404.92,532.393 1406.97,532.745 1409.01,533.097 1411.06,533.448 1413.1,533.799 1415.15,534.148 1417.2,534.498 1419.24,534.846 1421.29,535.194 \n",
       "  1423.33,535.541 1425.38,535.888 1427.42,536.234 1429.47,536.58 1431.51,536.924 1433.56,537.269 1435.6,537.612 1437.65,537.955 1439.69,538.298 1441.74,538.639 \n",
       "  1443.79,538.98 1445.83,539.321 1447.88,539.661 1449.92,540 1451.97,540.339 1454.01,540.677 1456.06,541.014 1458.1,541.351 1460.15,541.688 1462.19,542.023 \n",
       "  1464.24,542.358 1466.28,542.693 1468.33,543.027 1470.38,543.36 1472.42,543.693 1474.47,544.025 1476.51,544.356 1478.56,544.687 1480.6,545.018 1482.65,545.348 \n",
       "  1484.69,545.677 1486.74,546.005 1488.78,546.333 1490.83,546.661 1492.88,546.988 1494.92,547.314 1496.97,547.64 1499.01,547.965 1501.06,548.29 1503.1,548.614 \n",
       "  1505.15,548.937 1507.19,549.26 1509.24,549.582 1511.28,549.904 1513.33,550.225 1515.37,550.546 1517.42,550.866 1519.47,551.186 1521.51,551.505 1523.56,551.823 \n",
       "  1525.6,552.141 1527.65,552.458 1529.69,552.775 1531.74,553.091 1533.78,553.407 1535.83,553.722 1537.87,554.036 1539.92,554.35 1541.96,554.664 1544.01,554.977 \n",
       "  1546.06,555.289 1548.1,555.601 1550.15,555.912 1552.19,556.223 1554.24,556.533 1556.28,556.843 1558.33,557.152 1560.37,557.46 1562.42,557.768 1564.46,558.076 \n",
       "  1566.51,558.383 1568.55,558.689 1570.6,558.995 1572.65,559.301 1574.69,559.606 1576.74,559.91 1578.78,560.214 1580.83,560.517 1582.87,560.82 1584.92,561.122 \n",
       "  1586.96,561.424 1589.01,561.725 1591.05,562.026 1593.1,562.326 1595.14,562.626 1597.19,562.925 1599.24,563.223 1601.28,563.522 1603.33,563.819 1605.37,564.116 \n",
       "  1607.42,564.413 1609.46,564.709 1611.51,565.005 1613.55,565.3 1615.6,565.594 1617.64,565.888 1619.69,566.182 1621.73,566.475 1623.78,566.768 1625.83,567.06 \n",
       "  1627.87,567.351 1629.92,567.642 1631.96,567.933 1634.01,568.223 1636.05,568.513 1638.1,568.802 1640.14,569.09 1642.19,569.379 1644.23,569.666 1646.28,569.953 \n",
       "  1648.33,570.24 1650.37,570.526 1652.42,570.812 1654.46,571.097 1656.51,571.382 1658.55,571.666 1660.6,571.95 1662.64,572.233 1664.69,572.516 1666.73,572.798 \n",
       "  1668.78,573.08 1670.82,573.362 1672.87,573.643 1674.92,573.923 1676.96,574.203 1679.01,574.483 1681.05,574.762 1683.1,575.04 1685.14,575.318 1687.19,575.596 \n",
       "  1689.23,575.873 1691.28,576.15 1693.32,576.426 1695.37,576.702 1697.41,576.977 1699.46,577.252 1701.51,577.527 1703.55,577.801 1705.6,578.074 1707.64,578.347 \n",
       "  1709.69,578.62 1711.73,578.892 1713.78,579.164 1715.82,579.435 1717.87,579.706 1719.91,579.976 1721.96,580.246 1724,580.515 1726.05,580.784 1728.1,581.053 \n",
       "  1730.14,581.321 1732.19,581.589 1734.23,581.856 1736.28,582.123 1738.32,582.389 1740.37,582.655 1742.41,582.921 1744.46,583.186 1746.5,583.45 1748.55,583.714 \n",
       "  1750.59,583.978 1752.64,584.241 1754.69,584.504 1756.73,584.767 1758.78,585.029 1760.82,585.29 1762.87,585.551 1764.91,585.812 1766.96,586.072 1769,586.332 \n",
       "  1771.05,586.592 1773.09,586.851 1775.14,587.109 1777.18,587.367 1779.23,587.625 1781.28,587.883 1783.32,588.139 1785.37,588.396 1787.41,588.652 1789.46,588.908 \n",
       "  1791.5,589.163 1793.55,589.418 1795.59,589.672 1797.64,589.926 1799.68,590.18 1801.73,590.433 1803.78,590.686 1805.82,590.938 1807.87,591.19 1809.91,591.442 \n",
       "  1811.96,591.693 1814,591.943 1816.05,592.194 1818.09,592.444 1820.14,592.693 1822.18,592.942 1824.23,593.191 1826.27,593.439 1828.32,593.687 1830.37,593.935 \n",
       "  1832.41,594.182 1834.46,594.428 1836.5,594.675 1838.55,594.921 1840.59,595.166 1842.64,595.411 1844.68,595.656 1846.73,595.9 1848.77,596.144 1850.82,596.388 \n",
       "  1852.86,596.631 1854.91,596.874 1856.96,597.116 1859,597.358 1861.05,597.6 1863.09,597.841 1865.14,598.082 1867.18,598.323 1869.23,598.563 1871.27,598.802 \n",
       "  1873.32,599.042 1875.36,599.281 1877.41,599.519 1879.45,599.757 1881.5,599.995 1883.55,600.233 1885.59,600.47 1887.64,600.706 1889.68,600.943 1891.73,601.179 \n",
       "  1893.77,601.414 1895.82,601.649 1897.86,601.884 1899.91,602.119 1901.95,602.353 1904,602.586 1906.04,602.82 1908.09,603.053 1910.14,603.285 1912.18,603.517 \n",
       "  1914.23,603.749 1916.27,603.981 1918.32,604.212 1920.36,604.443 1922.41,604.673 1924.45,604.903 1926.5,605.133 1928.54,605.362 1930.59,605.591 1932.63,605.82 \n",
       "  1934.68,606.048 1936.73,606.276 1938.77,606.503 1940.82,606.73 1942.86,606.957 1944.91,607.184 1946.95,607.41 1949,607.635 1951.04,607.861 1953.09,608.086 \n",
       "  1955.13,608.311 1957.18,608.535 1959.23,608.759 1961.27,608.983 1963.32,609.206 1965.36,609.429 1967.41,609.651 1969.45,609.874 1971.5,610.095 1973.54,610.317 \n",
       "  1975.59,610.538 1977.63,610.759 1979.68,610.98 1981.72,611.2 1983.77,611.42 1985.82,611.639 1987.86,611.858 1989.91,612.077 1991.95,612.295 1994,612.514 \n",
       "  1996.04,612.731 1998.09,612.949 2000.13,613.166 2002.18,613.383 2004.22,613.599 2006.27,613.815 2008.31,614.031 2010.36,614.246 2012.41,614.462 2014.45,614.676 \n",
       "  2016.5,614.891 2018.54,615.105 2020.59,615.319 2022.63,615.532 2024.68,615.745 2026.72,615.958 2028.77,616.17 2030.81,616.383 2032.86,616.594 2034.9,616.806 \n",
       "  2036.95,617.017 2039,617.228 2041.04,617.438 2043.09,617.648 2045.13,617.858 2047.18,618.068 2049.22,618.277 2051.27,618.486 2053.31,618.695 2055.36,618.903 \n",
       "  2057.4,619.111 2059.45,619.318 2061.49,619.526 2063.54,619.733 2065.59,619.939 2067.63,620.146 2069.68,620.352 2071.72,620.557 2073.77,620.763 2075.81,620.968 \n",
       "  2077.86,621.173 2079.9,621.377 2081.95,621.581 2083.99,621.785 2086.04,621.989 2088.08,622.192 2090.13,622.395 2092.18,622.597 2094.22,622.8 2096.27,623.002 \n",
       "  2098.31,623.203 2100.36,623.405 2102.4,623.606 2104.45,623.807 2106.49,624.007 2108.54,624.207 2110.58,624.407 2112.63,624.607 2114.68,624.806 2116.72,625.005 \n",
       "  2118.77,625.204 2120.81,625.402 2122.86,625.6 2124.9,625.798 2126.95,625.995 2128.99,626.192 2131.04,626.389 2133.08,626.586 2135.13,626.782 2137.17,626.978 \n",
       "  2139.22,627.174 2141.27,627.369 2143.31,627.564 2145.36,627.759 2147.4,627.953 2149.45,628.148 2151.49,628.342 2153.54,628.535 2155.58,628.729 2157.63,628.922 \n",
       "  2159.67,629.114 2161.72,629.307 2163.76,629.499 2165.81,629.691 2167.86,629.883 2169.9,630.074 2171.95,630.265 2173.99,630.456 2176.04,630.646 2178.08,630.836 \n",
       "  2180.13,631.026 2182.17,631.216 2184.22,631.405 2186.26,631.594 2188.31,631.783 2190.35,631.972 2192.4,632.16 2194.45,632.348 2196.49,632.535 2198.54,632.723 \n",
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       "  1750.59,1204.02 1752.64,1204.29 1754.69,1204.55 1756.73,1204.81 1758.78,1205.08 1760.82,1205.34 1762.87,1205.6 1764.91,1205.86 1766.96,1206.12 1769,1206.38 \n",
       "  1771.05,1206.64 1773.09,1206.9 1775.14,1207.16 1777.18,1207.41 1779.23,1207.67 1781.28,1207.93 1783.32,1208.19 1785.37,1208.44 1787.41,1208.7 1789.46,1208.95 \n",
       "  1791.5,1209.21 1793.55,1209.46 1795.59,1209.72 1797.64,1209.97 1799.68,1210.23 1801.73,1210.48 1803.78,1210.73 1805.82,1210.98 1807.87,1211.24 1809.91,1211.49 \n",
       "  1811.96,1211.74 1814,1211.99 1816.05,1212.24 1818.09,1212.49 1820.14,1212.74 1822.18,1212.99 1824.23,1213.24 1826.27,1213.49 1828.32,1213.73 1830.37,1213.98 \n",
       "  1832.41,1214.23 1834.46,1214.47 1836.5,1214.72 1838.55,1214.97 1840.59,1215.21 1842.64,1215.46 1844.68,1215.7 1846.73,1215.95 1848.77,1216.19 1850.82,1216.43 \n",
       "  1852.86,1216.68 1854.91,1216.92 1856.96,1217.16 1859,1217.4 1861.05,1217.65 1863.09,1217.89 1865.14,1218.13 1867.18,1218.37 1869.23,1218.61 1871.27,1218.85 \n",
       "  1873.32,1219.09 1875.36,1219.33 1877.41,1219.57 1879.45,1219.8 1881.5,1220.04 1883.55,1220.28 1885.59,1220.52 1887.64,1220.75 1889.68,1220.99 1891.73,1221.22 \n",
       "  1893.77,1221.46 1895.82,1221.7 1897.86,1221.93 1899.91,1222.16 1901.95,1222.4 1904,1222.63 1906.04,1222.87 1908.09,1223.1 1910.14,1223.33 1912.18,1223.56 \n",
       "  1914.23,1223.8 1916.27,1224.03 1918.32,1224.26 1920.36,1224.49 1922.41,1224.72 1924.45,1224.95 1926.5,1225.18 1928.54,1225.41 1930.59,1225.64 1932.63,1225.87 \n",
       "  1934.68,1226.09 1936.73,1226.32 1938.77,1226.55 1940.82,1226.78 1942.86,1227 1944.91,1227.23 1946.95,1227.46 1949,1227.68 1951.04,1227.91 1953.09,1228.13 \n",
       "  1955.13,1228.36 1957.18,1228.58 1959.23,1228.81 1961.27,1229.03 1963.32,1229.25 1965.36,1229.48 1967.41,1229.7 1969.45,1229.92 1971.5,1230.14 1973.54,1230.36 \n",
       "  1975.59,1230.58 1977.63,1230.81 1979.68,1231.03 1981.72,1231.25 1983.77,1231.47 1985.82,1231.69 1987.86,1231.9 1989.91,1232.12 1991.95,1232.34 1994,1232.56 \n",
       "  1996.04,1232.78 1998.09,1233 2000.13,1233.21 2002.18,1233.43 2004.22,1233.65 2006.27,1233.86 2008.31,1234.08 2010.36,1234.29 2012.41,1234.51 2014.45,1234.72 \n",
       "  2016.5,1234.94 2018.54,1235.15 2020.59,1235.37 2022.63,1235.58 2024.68,1235.79 2026.72,1236 2028.77,1236.22 2030.81,1236.43 2032.86,1236.64 2034.9,1236.85 \n",
       "  2036.95,1237.06 2039,1237.27 2041.04,1237.48 2043.09,1237.69 2045.13,1237.9 2047.18,1238.11 2049.22,1238.32 2051.27,1238.53 2053.31,1238.74 2055.36,1238.95 \n",
       "  2057.4,1239.16 2059.45,1239.36 2061.49,1239.57 2063.54,1239.78 2065.59,1239.99 2067.63,1240.19 2069.68,1240.4 2071.72,1240.6 2073.77,1240.81 2075.81,1241.01 \n",
       "  2077.86,1241.22 2079.9,1241.42 2081.95,1241.63 2083.99,1241.83 2086.04,1242.04 2088.08,1242.24 2090.13,1242.44 2092.18,1242.64 2094.22,1242.85 2096.27,1243.05 \n",
       "  2098.31,1243.25 2100.36,1243.45 2102.4,1243.65 2104.45,1243.85 2106.49,1244.05 2108.54,1244.25 2110.58,1244.45 2112.63,1244.65 2114.68,1244.85 2116.72,1245.05 \n",
       "  2118.77,1245.25 2120.81,1245.45 2122.86,1245.65 2124.9,1245.84 2126.95,1246.04 2128.99,1246.24 2131.04,1246.44 2133.08,1246.63 2135.13,1246.83 2137.17,1247.02 \n",
       "  2139.22,1247.22 2141.27,1247.42 2143.31,1247.61 2145.36,1247.81 2147.4,1248 2149.45,1248.19 2151.49,1248.39 2153.54,1248.58 2155.58,1248.77 2157.63,1248.97 \n",
       "  2159.67,1249.16 2161.72,1249.35 2163.76,1249.55 2165.81,1249.74 2167.86,1249.93 2169.9,1250.12 2171.95,1250.31 2173.99,1250.5 2176.04,1250.69 2178.08,1250.88 \n",
       "  2180.13,1251.07 2182.17,1251.26 2184.22,1251.45 2186.26,1251.64 2188.31,1251.83 2190.35,1252.02 2192.4,1252.21 2194.45,1252.39 2196.49,1252.58 2198.54,1252.77 \n",
       "  2200.58,1252.96 2202.63,1253.14 2204.67,1253.33 2206.72,1253.52 2208.76,1253.7 2210.81,1253.89 2212.85,1254.07 2214.9,1254.26 2216.94,1254.44 2218.99,1254.63 \n",
       "  2221.04,1254.81 2223.08,1255 2225.13,1255.18 2227.17,1255.36 2229.22,1255.55 2231.26,1255.73 2233.31,1255.91 2235.35,1256.09 2237.4,1256.28 2239.44,1256.46 \n",
       "  2241.49,1256.64 2243.53,1256.82 2245.58,1257 2247.63,1257.18 2249.67,1257.36 2251.72,1257.54 2253.76,1257.72 2255.81,1257.9 2257.85,1258.08 2259.9,1258.26 \n",
       "  2261.94,1258.44 2263.99,1258.62 2266.03,1258.8 2268.08,1258.98 2270.12,1259.16 2272.17,1259.33 2274.22,1259.51 2276.26,1259.69 2278.31,1259.86 2280.35,1260.04 \n",
       "  2282.4,1260.22 2284.44,1260.39 2286.49,1260.57 2288.53,1260.75 2290.58,1260.92 2292.62,1261.1 2294.67,1261.27 2296.72,1261.44 2298.76,1261.62 2300.81,1261.79 \n",
       "  2302.85,1261.97 2304.9,1262.14 2306.94,1262.31 2308.99,1262.49 2311.03,1262.66 2313.08,1262.83 2315.12,1263 2317.17,1263.18 2319.21,1263.35 2321.26,1263.52 \n",
       "  \n",
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       "  298.365,1391.05 300.41,1389.85 302.456,1388.65 304.501,1387.45 306.546,1386.26 308.592,1385.07 310.637,1383.88 312.683,1382.7 314.728,1381.52 316.773,1380.35 \n",
       "  318.819,1379.18 320.864,1378.01 322.91,1376.84 324.955,1375.68 327,1374.53 329.046,1373.37 331.091,1372.22 333.136,1371.07 335.182,1369.93 337.227,1368.79 \n",
       "  339.273,1367.65 341.318,1366.51 343.363,1365.38 345.409,1364.25 347.454,1363.13 349.5,1362.01 351.545,1360.89 353.59,1359.77 355.636,1358.66 357.681,1357.55 \n",
       "  359.727,1356.45 361.772,1355.34 363.817,1354.24 365.863,1353.15 367.908,1352.05 369.954,1350.96 371.999,1349.88 374.044,1348.79 376.09,1347.71 378.135,1346.63 \n",
       "  380.181,1345.56 382.226,1344.49 384.271,1343.42 386.317,1342.35 388.362,1341.29 390.408,1340.23 392.453,1339.17 394.498,1338.12 396.544,1337.07 398.589,1336.02 \n",
       "  400.635,1334.97 402.68,1333.93 404.725,1332.89 406.771,1331.86 408.816,1330.82 410.861,1329.79 412.907,1328.76 414.952,1327.74 416.998,1326.72 419.043,1325.7 \n",
       "  421.088,1324.68 423.134,1323.67 425.179,1322.65 427.225,1321.65 429.27,1320.64 431.315,1319.64 433.361,1318.64 435.406,1317.64 437.452,1316.65 439.497,1315.65 \n",
       "  441.542,1314.66 443.588,1313.68 445.633,1312.69 447.679,1311.71 449.724,1310.73 451.769,1309.76 453.815,1308.79 455.86,1307.81 457.906,1306.85 459.951,1305.88 \n",
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       "  502.904,1286.19 504.95,1285.28 506.995,1284.37 509.04,1283.47 511.086,1282.56 513.131,1281.66 515.177,1280.76 517.222,1279.87 519.267,1278.97 521.313,1278.08 \n",
       "  523.358,1277.19 525.404,1276.3 527.449,1275.42 529.494,1274.54 531.54,1273.65 533.585,1272.78 535.631,1271.9 537.676,1271.03 539.721,1270.16 541.767,1269.29 \n",
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       "  605.174,1243.41 607.219,1242.61 609.265,1241.81 611.31,1241.02 613.356,1240.22 615.401,1239.43 617.446,1238.64 619.492,1237.85 621.537,1237.06 623.582,1236.27 \n",
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       "  646.082,1227.75 648.127,1226.99 650.173,1226.23 652.218,1225.47 654.263,1224.71 656.309,1223.96 658.354,1223.2 660.4,1222.45 662.445,1221.7 664.49,1220.95 \n",
       "  666.536,1220.21 668.581,1219.46 670.627,1218.72 672.672,1217.98 674.717,1217.24 676.763,1216.5 678.808,1215.76 680.854,1215.03 682.899,1214.3 684.944,1213.57 \n",
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       "  707.444,1205.64 709.489,1204.93 711.534,1204.23 713.58,1203.52 715.625,1202.81 717.671,1202.11 719.716,1201.41 721.761,1200.71 723.807,1200.01 725.852,1199.31 \n",
       "  727.898,1198.62 729.943,1197.92 731.988,1197.23 734.034,1196.54 736.079,1195.85 738.125,1195.17 740.17,1194.48 742.215,1193.8 744.261,1193.11 746.306,1192.43 \n",
       "  748.352,1191.75 750.397,1191.08 752.442,1190.4 754.488,1189.73 756.533,1189.05 758.579,1188.38 760.624,1187.71 762.669,1187.04 764.715,1186.38 766.76,1185.71 \n",
       "  768.805,1185.05 770.851,1184.39 772.896,1183.73 774.942,1183.07 776.987,1182.41 779.032,1181.75 781.078,1181.1 783.123,1180.45 785.169,1179.79 787.214,1179.14 \n",
       "  789.259,1178.5 791.305,1177.85 793.35,1177.2 795.396,1176.56 797.441,1175.92 799.486,1175.27 801.532,1174.63 803.577,1174 805.623,1173.36 807.668,1172.72 \n",
       "  809.713,1172.09 811.759,1171.46 813.804,1170.83 815.85,1170.2 817.895,1169.57 819.94,1168.94 821.986,1168.32 824.031,1167.69 826.077,1167.07 828.122,1166.45 \n",
       "  830.167,1165.83 832.213,1165.21 834.258,1164.59 836.304,1163.98 838.349,1163.36 840.394,1162.75 842.44,1162.14 844.485,1161.53 846.53,1160.92 848.576,1160.31 \n",
       "  850.621,1159.7 852.667,1159.1 854.712,1158.49 856.757,1157.89 858.803,1157.29 860.848,1156.69 862.894,1156.09 864.939,1155.5 866.984,1154.9 869.03,1154.31 \n",
       "  871.075,1153.71 873.121,1153.12 875.166,1152.53 877.211,1151.94 879.257,1151.35 881.302,1150.77 883.348,1150.18 885.393,1149.6 887.438,1149.02 889.484,1148.43 \n",
       "  891.529,1147.85 893.575,1147.27 895.62,1146.7 897.665,1146.12 899.711,1145.55 901.756,1144.97 903.802,1144.4 905.847,1143.83 907.892,1143.26 909.938,1142.69 \n",
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       "  973.345,1125.64 975.39,1125.11 977.436,1124.58 979.481,1124.05 981.527,1123.52 983.572,1122.99 985.617,1122.47 987.663,1121.94 989.708,1121.42 991.753,1120.9 \n",
       "  993.799,1120.38 995.844,1119.85 997.89,1119.34 999.935,1118.82 1001.98,1118.3 1004.03,1117.78 1006.07,1117.27 1008.12,1116.75 1010.16,1116.24 1012.21,1115.73 \n",
       "  1014.25,1115.22 1016.3,1114.71 1018.34,1114.2 1020.39,1113.69 1022.43,1113.19 1024.48,1112.68 1026.53,1112.18 1028.57,1111.67 1030.62,1111.17 1032.66,1110.67 \n",
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       "  1096.07,1095.62 1098.11,1095.15 1100.16,1094.68 1102.2,1094.22 1104.25,1093.75 1106.3,1093.28 1108.34,1092.82 1110.39,1092.35 1112.43,1091.89 1114.48,1091.43 \n",
       "  1116.52,1090.97 1118.57,1090.51 1120.61,1090.05 1122.66,1089.59 1124.7,1089.13 1126.75,1088.67 1128.79,1088.22 1130.84,1087.76 1132.89,1087.31 1134.93,1086.86 \n",
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       "  1157.43,1081.93 1159.48,1081.49 1161.52,1081.05 1163.57,1080.6 1165.61,1080.16 1167.66,1079.73 1169.7,1079.29 1171.75,1078.85 1173.79,1078.41 1175.84,1077.98 \n",
       "  1177.88,1077.54 1179.93,1077.11 1181.98,1076.68 1184.02,1076.24 1186.07,1075.81 1188.11,1075.38 1190.16,1074.95 1192.2,1074.52 1194.25,1074.09 1196.29,1073.67 \n",
       "  1198.34,1073.24 1200.38,1072.81 1202.43,1072.39 1204.47,1071.97 1206.52,1071.54 1208.57,1071.12 1210.61,1070.7 1212.66,1070.28 1214.7,1069.86 1216.75,1069.44 \n",
       "  1218.79,1069.02 1220.84,1068.6 1222.88,1068.19 1224.93,1067.77 1226.97,1067.36 1229.02,1066.94 1231.06,1066.53 1233.11,1066.12 1235.16,1065.7 1237.2,1065.29 \n",
       "  1239.25,1064.88 1241.29,1064.47 1243.34,1064.06 1245.38,1063.66 1247.43,1063.25 1249.47,1062.84 1251.52,1062.44 1253.56,1062.03 1255.61,1061.63 1257.65,1061.22 \n",
       "  1259.7,1060.82 1261.75,1060.42 1263.79,1060.02 1265.84,1059.62 1267.88,1059.22 1269.93,1058.82 1271.97,1058.42 1274.02,1058.02 1276.06,1057.63 1278.11,1057.23 \n",
       "  1280.15,1056.84 1282.2,1056.44 1284.24,1056.05 1286.29,1055.66 1288.34,1055.26 1290.38,1054.87 1292.43,1054.48 1294.47,1054.09 1296.52,1053.7 1298.56,1053.31 \n",
       "  1300.61,1052.93 1302.65,1052.54 1304.7,1052.15 1306.74,1051.77 1308.79,1051.38 1310.84,1051 1312.88,1050.62 1314.93,1050.23 1316.97,1049.85 1319.02,1049.47 \n",
       "  1321.06,1049.09 1323.11,1048.71 1325.15,1048.33 1327.2,1047.95 1329.24,1047.57 1331.29,1047.2 1333.33,1046.82 1335.38,1046.44 1337.43,1046.07 1339.47,1045.7 \n",
       "  1341.52,1045.32 1343.56,1044.95 1345.61,1044.58 1347.65,1044.21 1349.7,1043.83 1351.74,1043.46 1353.79,1043.09 1355.83,1042.73 1357.88,1042.36 1359.92,1041.99 \n",
       "  1361.97,1041.62 1364.02,1041.26 1366.06,1040.89 1368.11,1040.53 1370.15,1040.16 1372.2,1039.8 1374.24,1039.44 1376.29,1039.07 1378.33,1038.71 1380.38,1038.35 \n",
       "  1382.42,1037.99 1384.47,1037.63 1386.51,1037.27 1388.56,1036.92 1390.61,1036.56 1392.65,1036.2 1394.7,1035.85 1396.74,1035.49 1398.79,1035.13 1400.83,1034.78 \n",
       "  1402.88,1034.43 1404.92,1034.07 1406.97,1033.72 1409.01,1033.37 1411.06,1033.02 1413.1,1032.67 1415.15,1032.32 1417.2,1031.97 1419.24,1031.62 1421.29,1031.27 \n",
       "  1423.33,1030.93 1425.38,1030.58 1427.42,1030.23 1429.47,1029.89 1431.51,1029.54 1433.56,1029.2 1435.6,1028.85 1437.65,1028.51 1439.69,1028.17 1441.74,1027.83 \n",
       "  1443.79,1027.49 1445.83,1027.15 1447.88,1026.81 1449.92,1026.47 1451.97,1026.13 1454.01,1025.79 1456.06,1025.45 1458.1,1025.12 1460.15,1024.78 1462.19,1024.44 \n",
       "  1464.24,1024.11 1466.28,1023.77 1468.33,1023.44 1470.38,1023.11 1472.42,1022.77 1474.47,1022.44 1476.51,1022.11 1478.56,1021.78 1480.6,1021.45 1482.65,1021.12 \n",
       "  1484.69,1020.79 1486.74,1020.46 1488.78,1020.13 1490.83,1019.81 1492.88,1019.48 1494.92,1019.15 1496.97,1018.83 1499.01,1018.5 1501.06,1018.18 1503.1,1017.85 \n",
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     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "plot(sol1,label=[\"a\",\"b\",\"c\"])\n",
    "title!(\"ODE solver in Julia\")\n",
    "xlabel!(\"Time [s]\")\n",
    "ylabel!(\"Concentration [M]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One interesting feature is that, by default, the solution is a continuous function. So you do not need to extrapolate to a curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Float64,1}:\n",
       " 0.013761040160814916 \n",
       " 0.0037610401608149106\n",
       " 0.006238959839185087 "
      ]
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     "execution_count": 22,
     "metadata": {},
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   ],
   "source": [
    "sol1(60.4)"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see how the implemented ODE solver chooses the time variable depending of the stiffness of the solution of the ODE. This saves a lot of time and computer power. Quite often, each ODE solver handles the integration time diferently, and choosing one or the other is impontant and depends on the problem to solve. We can see that the stock solver in Julia only solves the following few points"
   ]
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  {
   "cell_type": "code",
   "execution_count": 23,
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   "source": [
    "sol1 = solve(prob1,dense=false)\n",
    "plot(sol1,label=[\"a\",\"b\",\"c\"],seriestype=:scatter)"
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    "### 5.1 A DSL for Parameterized Functions\n",
    "\n",
    "In many cases you may be defining a lot of functions with parameters. There exists the domain-specific language (DSL) defined by the `@ode_def` macro for helping with this common problem. Using this feature in Julia, we can rewrite the `simpleODE!` function as:"
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   "execution_count": 24,
   "metadata": {},
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    {
     "data": {
      "text/plain": [
       "(::abetterway{getfield(Main, Symbol(\"##3#7\")),getfield(Main, Symbol(\"##4#8\")),getfield(Main, Symbol(\"##5#9\")),Nothing,Nothing,getfield(Main, Symbol(\"##6#10\")),Expr,Expr}) (generic function with 2 methods)"
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     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
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    "simpleODE3! = @ode_def abetterway begin\n",
    "  da = -k*a*b\n",
    "  db = -k*a*b\n",
    "  dc = k*a*b\n",
    "    end k"
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  {
   "cell_type": "code",
   "execution_count": 25,
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       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 253.911, 1420.78)\" x=\"253.911\" y=\"1420.78\">0.000</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip4100)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 253.911, 1110.76)\" x=\"253.911\" y=\"1110.76\">0.005</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip4100)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 253.911, 800.733)\" x=\"253.911\" y=\"800.733\">0.010</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip4100)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 253.911, 490.71)\" x=\"253.911\" y=\"490.71\">0.015</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip4100)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 253.911, 180.687)\" x=\"253.911\" y=\"180.687\">0.020</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip4100)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:84px; text-anchor:middle;\" transform=\"rotate(0, 1299.59, 73.2)\" x=\"1299.59\" y=\"73.2\">ODE solver using DSL</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip4100)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:66px; text-anchor:middle;\" transform=\"rotate(0, 1299.59, 1590.4)\" x=\"1299.59\" y=\"1590.4\">Time [s]</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip4100)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:66px; text-anchor:middle;\" transform=\"rotate(-90, 57.6, 783.233)\" x=\"57.6\" y=\"783.233\">Concentration [M]</text>\n",
       "</g>\n",
       "<polyline clip-path=\"url(#clip4102)\" style=\"stroke:#009af9; stroke-width:12; stroke-opacity:1; fill:none\" points=\"\n",
       "  277.911,163.187 279.956,164.427 282.002,165.662 284.047,166.894 286.092,168.123 288.138,169.347 290.183,170.569 292.229,171.786 294.274,173 296.319,174.21 \n",
       "  298.365,175.417 300.41,176.62 302.456,177.819 304.501,179.015 306.546,180.208 308.592,181.397 310.637,182.582 312.683,183.764 314.728,184.942 316.773,186.118 \n",
       "  318.819,187.289 320.864,188.457 322.91,189.622 324.955,190.783 327,191.941 329.046,193.096 331.091,194.247 333.136,195.395 335.182,196.54 337.227,197.681 \n",
       "  339.273,198.819 341.318,199.954 343.363,201.086 345.409,202.214 347.454,203.339 349.5,204.461 351.545,205.579 353.59,206.694 355.636,207.807 357.681,208.916 \n",
       "  359.727,210.021 361.772,211.124 363.817,212.223 365.863,213.32 367.908,214.413 369.954,215.503 371.999,216.59 374.044,217.674 376.09,218.755 378.135,219.833 \n",
       "  380.181,220.908 382.226,221.98 384.271,223.049 386.317,224.115 388.362,225.178 390.408,226.238 392.453,227.295 394.498,228.348 396.544,229.4 398.589,230.448 \n",
       "  400.635,231.493 402.68,232.535 404.725,233.575 406.771,234.611 408.816,235.645 410.861,236.675 412.907,237.703 414.952,238.729 416.998,239.751 419.043,240.77 \n",
       "  421.088,241.787 423.134,242.801 425.179,243.812 427.225,244.82 429.27,245.826 431.315,246.829 433.361,247.829 435.406,248.826 437.452,249.821 439.497,250.813 \n",
       "  441.542,251.802 443.588,252.789 445.633,253.772 447.679,254.754 449.724,255.732 451.769,256.708 453.815,257.681 455.86,258.652 457.906,259.62 459.951,260.586 \n",
       "  461.996,261.549 464.042,262.509 466.087,263.467 468.133,264.422 470.178,265.374 472.223,266.324 474.269,267.272 476.314,268.217 478.359,269.16 480.405,270.1 \n",
       "  482.45,271.037 484.496,271.972 486.541,272.905 488.586,273.835 490.632,274.762 492.677,275.687 494.723,276.61 496.768,277.53 498.813,278.448 500.859,279.364 \n",
       "  502.904,280.277 504.95,281.187 506.995,282.096 509.04,283.002 511.086,283.905 513.131,284.806 515.177,285.705 517.222,286.602 519.267,287.496 521.313,288.388 \n",
       "  523.358,289.277 525.404,290.164 527.449,291.049 529.494,291.932 531.54,292.812 533.585,293.69 535.631,294.566 537.676,295.439 539.721,296.311 541.767,297.18 \n",
       "  543.812,298.047 545.858,298.911 547.903,299.774 549.948,300.634 551.994,301.492 554.039,302.347 556.084,303.201 558.13,304.052 560.175,304.902 562.221,305.749 \n",
       "  564.266,306.594 566.311,307.437 568.357,308.277 570.402,309.116 572.448,309.952 574.493,310.786 576.538,311.619 578.584,312.449 580.629,313.277 582.675,314.103 \n",
       "  584.72,314.926 586.765,315.748 588.811,316.568 590.856,317.386 592.902,318.201 594.947,319.015 596.992,319.826 599.038,320.636 601.083,321.443 603.129,322.249 \n",
       "  605.174,323.052 607.219,323.854 609.265,324.653 611.31,325.451 613.356,326.247 615.401,327.04 617.446,327.832 619.492,328.621 621.537,329.409 623.582,330.195 \n",
       "  625.628,330.979 627.673,331.761 629.719,332.541 631.764,333.319 633.809,334.095 635.855,334.87 637.9,335.642 639.946,336.412 641.991,337.181 644.036,337.948 \n",
       "  646.082,338.713 648.127,339.476 650.173,340.237 652.218,340.996 654.263,341.754 656.309,342.51 658.354,343.263 660.4,344.015 662.445,344.766 664.49,345.514 \n",
       "  666.536,346.261 668.581,347.005 670.627,347.748 672.672,348.49 674.717,349.229 676.763,349.967 678.808,350.703 680.854,351.437 682.899,352.169 684.944,352.9 \n",
       "  686.99,353.628 689.035,354.356 691.081,355.081 693.126,355.805 695.171,356.527 697.217,357.247 699.262,357.965 701.307,358.682 703.353,359.397 705.398,360.111 \n",
       "  707.444,360.823 709.489,361.533 711.534,362.241 713.58,362.948 715.625,363.653 717.671,364.356 719.716,365.058 721.761,365.758 723.807,366.457 725.852,367.153 \n",
       "  727.898,367.849 729.943,368.542 731.988,369.234 734.034,369.924 736.079,370.613 738.125,371.3 740.17,371.986 742.215,372.67 744.261,373.352 746.306,374.033 \n",
       "  748.352,374.712 750.397,375.39 752.442,376.066 754.488,376.74 756.533,377.413 758.579,378.084 760.624,378.754 762.669,379.422 764.715,380.089 766.76,380.754 \n",
       "  768.805,381.418 770.851,382.08 772.896,382.741 774.942,383.4 776.987,384.057 779.032,384.713 781.078,385.368 783.123,386.021 785.169,386.673 787.214,387.323 \n",
       "  789.259,387.971 791.305,388.618 793.35,389.264 795.396,389.908 797.441,390.551 799.486,391.192 801.532,391.832 803.577,392.47 805.623,393.107 807.668,393.743 \n",
       "  809.713,394.377 811.759,395.009 813.804,395.641 815.85,396.27 817.895,396.899 819.94,397.526 821.986,398.151 824.031,398.775 826.077,399.398 828.122,400.02 \n",
       "  830.167,400.639 832.213,401.258 834.258,401.875 836.304,402.491 838.349,403.105 840.394,403.719 842.44,404.33 844.485,404.941 846.53,405.55 848.576,406.157 \n",
       "  850.621,406.764 852.667,407.368 854.712,407.972 856.757,408.574 858.803,409.175 860.848,409.775 862.894,410.373 864.939,410.97 866.984,411.566 869.03,412.16 \n",
       "  871.075,412.753 873.121,413.345 875.166,413.935 877.211,414.525 879.257,415.113 881.302,415.699 883.348,416.284 885.393,416.868 887.438,417.451 889.484,418.033 \n",
       "  891.529,418.613 893.575,419.192 895.62,419.77 897.665,420.346 899.711,420.921 901.756,421.495 903.802,422.068 905.847,422.639 907.892,423.21 909.938,423.779 \n",
       "  911.983,424.346 914.029,424.913 916.074,425.478 918.119,426.042 920.165,426.605 922.21,427.167 924.255,427.728 926.301,428.287 928.346,428.845 930.392,429.402 \n",
       "  932.437,429.957 934.482,430.512 936.528,431.065 938.573,431.617 940.619,432.168 942.664,432.718 944.709,433.267 946.755,433.814 948.8,434.361 950.846,434.906 \n",
       "  952.891,435.45 954.936,435.993 956.982,436.534 959.027,437.075 961.073,437.614 963.118,438.153 965.163,438.69 967.209,439.226 969.254,439.76 971.3,440.294 \n",
       "  973.345,440.827 975.39,441.358 977.436,441.889 979.481,442.418 981.527,442.946 983.572,443.473 985.617,443.999 987.663,444.524 989.708,445.048 991.753,445.57 \n",
       "  993.799,446.092 995.844,446.612 997.89,447.132 999.935,447.65 1001.98,448.167 1004.03,448.683 1006.07,449.198 1008.12,449.712 1010.16,450.225 1012.21,450.737 \n",
       "  1014.25,451.248 1016.3,451.757 1018.34,452.266 1020.39,452.774 1022.43,453.28 1024.48,453.786 1026.53,454.29 1028.57,454.794 1030.62,455.296 1032.66,455.798 \n",
       "  1034.71,456.298 1036.75,456.797 1038.8,457.296 1040.84,457.793 1042.89,458.289 1044.93,458.784 1046.98,459.279 1049.02,459.772 1051.07,460.264 1053.12,460.755 \n",
       "  1055.16,461.246 1057.21,461.735 1059.25,462.223 1061.3,462.71 1063.34,463.196 1065.39,463.682 1067.43,464.166 1069.48,464.649 1071.52,465.132 1073.57,465.613 \n",
       "  1075.61,466.093 1077.66,466.573 1079.71,467.051 1081.75,467.528 1083.8,468.005 1085.84,468.48 1087.89,468.955 1089.93,469.429 1091.98,469.901 1094.02,470.373 \n",
       "  1096.07,470.844 1098.11,471.313 1100.16,471.782 1102.2,472.25 1104.25,472.717 1106.3,473.183 1108.34,473.648 1110.39,474.113 1112.43,474.576 1114.48,475.038 \n",
       "  1116.52,475.5 1118.57,475.96 1120.61,476.42 1122.66,476.878 1124.7,477.336 1126.75,477.793 1128.79,478.249 1130.84,478.704 1132.89,479.158 1134.93,479.611 \n",
       "  1136.98,480.063 1139.02,480.515 1141.07,480.965 1143.11,481.415 1145.16,481.864 1147.2,482.311 1149.25,482.758 1151.29,483.205 1153.34,483.65 1155.39,484.094 \n",
       "  1157.43,484.538 1159.48,484.98 1161.52,485.422 1163.57,485.863 1165.61,486.303 1167.66,486.742 1169.7,487.18 1171.75,487.617 1173.79,488.054 1175.84,488.49 \n",
       "  1177.88,488.925 1179.93,489.359 1181.98,489.792 1184.02,490.224 1186.07,490.655 1188.11,491.086 1190.16,491.516 1192.2,491.945 1194.25,492.373 1196.29,492.8 \n",
       "  1198.34,493.227 1200.38,493.652 1202.43,494.077 1204.47,494.501 1206.52,494.924 1208.57,495.347 1210.61,495.768 1212.66,496.189 1214.7,496.609 1216.75,497.028 \n",
       "  1218.79,497.446 1220.84,497.864 1222.88,498.28 1224.93,498.696 1226.97,499.111 1229.02,499.526 1231.06,499.939 1233.11,500.352 1235.16,500.764 1237.2,501.175 \n",
       "  1239.25,501.585 1241.29,501.995 1243.34,502.403 1245.38,502.811 1247.43,503.219 1249.47,503.625 1251.52,504.031 1253.56,504.436 1255.61,504.84 1257.65,505.243 \n",
       "  1259.7,505.646 1261.75,506.048 1263.79,506.449 1265.84,506.849 1267.88,507.249 1269.93,507.647 1271.97,508.046 1274.02,508.443 1276.06,508.839 1278.11,509.235 \n",
       "  1280.15,509.63 1282.2,510.025 1284.24,510.418 1286.29,510.811 1288.34,511.203 1290.38,511.594 1292.43,511.985 1294.47,512.375 1296.52,512.764 1298.56,513.153 \n",
       "  1300.61,513.54 1302.65,513.927 1304.7,514.314 1306.74,514.699 1308.79,515.084 1310.84,515.468 1312.88,515.851 1314.93,516.234 1316.97,516.616 1319.02,516.997 \n",
       "  1321.06,517.378 1323.11,517.758 1325.15,518.137 1327.2,518.515 1329.24,518.893 1331.29,519.27 1333.33,519.647 1335.38,520.022 1337.43,520.397 1339.47,520.771 \n",
       "  1341.52,521.145 1343.56,521.518 1345.61,521.89 1347.65,522.262 1349.7,522.633 1351.74,523.003 1353.79,523.372 1355.83,523.741 1357.88,524.109 1359.92,524.477 \n",
       "  1361.97,524.843 1364.02,525.209 1366.06,525.575 1368.11,525.94 1370.15,526.304 1372.2,526.667 1374.24,527.03 1376.29,527.392 1378.33,527.753 1380.38,528.114 \n",
       "  1382.42,528.474 1384.47,528.834 1386.51,529.193 1388.56,529.551 1390.61,529.908 1392.65,530.265 1394.7,530.621 1396.74,530.977 1398.79,531.332 1400.83,531.686 \n",
       "  1402.88,532.04 1404.92,532.393 1406.97,532.745 1409.01,533.097 1411.06,533.448 1413.1,533.799 1415.15,534.148 1417.2,534.498 1419.24,534.846 1421.29,535.194 \n",
       "  1423.33,535.541 1425.38,535.888 1427.42,536.234 1429.47,536.58 1431.51,536.924 1433.56,537.269 1435.6,537.612 1437.65,537.955 1439.69,538.298 1441.74,538.639 \n",
       "  1443.79,538.98 1445.83,539.321 1447.88,539.661 1449.92,540 1451.97,540.339 1454.01,540.677 1456.06,541.014 1458.1,541.351 1460.15,541.688 1462.19,542.023 \n",
       "  1464.24,542.358 1466.28,542.693 1468.33,543.027 1470.38,543.36 1472.42,543.693 1474.47,544.025 1476.51,544.356 1478.56,544.687 1480.6,545.018 1482.65,545.348 \n",
       "  1484.69,545.677 1486.74,546.005 1488.78,546.333 1490.83,546.661 1492.88,546.988 1494.92,547.314 1496.97,547.64 1499.01,547.965 1501.06,548.29 1503.1,548.614 \n",
       "  1505.15,548.937 1507.19,549.26 1509.24,549.582 1511.28,549.904 1513.33,550.225 1515.37,550.546 1517.42,550.866 1519.47,551.186 1521.51,551.505 1523.56,551.823 \n",
       "  1525.6,552.141 1527.65,552.458 1529.69,552.775 1531.74,553.091 1533.78,553.407 1535.83,553.722 1537.87,554.036 1539.92,554.35 1541.96,554.664 1544.01,554.977 \n",
       "  1546.06,555.289 1548.1,555.601 1550.15,555.912 1552.19,556.223 1554.24,556.533 1556.28,556.843 1558.33,557.152 1560.37,557.46 1562.42,557.768 1564.46,558.076 \n",
       "  1566.51,558.383 1568.55,558.689 1570.6,558.995 1572.65,559.301 1574.69,559.606 1576.74,559.91 1578.78,560.214 1580.83,560.517 1582.87,560.82 1584.92,561.122 \n",
       "  1586.96,561.424 1589.01,561.725 1591.05,562.026 1593.1,562.326 1595.14,562.626 1597.19,562.925 1599.24,563.223 1601.28,563.522 1603.33,563.819 1605.37,564.116 \n",
       "  1607.42,564.413 1609.46,564.709 1611.51,565.005 1613.55,565.3 1615.6,565.594 1617.64,565.888 1619.69,566.182 1621.73,566.475 1623.78,566.768 1625.83,567.06 \n",
       "  1627.87,567.351 1629.92,567.642 1631.96,567.933 1634.01,568.223 1636.05,568.513 1638.1,568.802 1640.14,569.09 1642.19,569.379 1644.23,569.666 1646.28,569.953 \n",
       "  1648.33,570.24 1650.37,570.526 1652.42,570.812 1654.46,571.097 1656.51,571.382 1658.55,571.666 1660.6,571.95 1662.64,572.233 1664.69,572.516 1666.73,572.798 \n",
       "  1668.78,573.08 1670.82,573.362 1672.87,573.643 1674.92,573.923 1676.96,574.203 1679.01,574.483 1681.05,574.762 1683.1,575.04 1685.14,575.318 1687.19,575.596 \n",
       "  1689.23,575.873 1691.28,576.15 1693.32,576.426 1695.37,576.702 1697.41,576.977 1699.46,577.252 1701.51,577.527 1703.55,577.801 1705.6,578.074 1707.64,578.347 \n",
       "  1709.69,578.62 1711.73,578.892 1713.78,579.164 1715.82,579.435 1717.87,579.706 1719.91,579.976 1721.96,580.246 1724,580.515 1726.05,580.784 1728.1,581.053 \n",
       "  1730.14,581.321 1732.19,581.589 1734.23,581.856 1736.28,582.123 1738.32,582.389 1740.37,582.655 1742.41,582.921 1744.46,583.186 1746.5,583.45 1748.55,583.714 \n",
       "  1750.59,583.978 1752.64,584.241 1754.69,584.504 1756.73,584.767 1758.78,585.029 1760.82,585.29 1762.87,585.551 1764.91,585.812 1766.96,586.072 1769,586.332 \n",
       "  1771.05,586.592 1773.09,586.851 1775.14,587.109 1777.18,587.367 1779.23,587.625 1781.28,587.883 1783.32,588.139 1785.37,588.396 1787.41,588.652 1789.46,588.908 \n",
       "  1791.5,589.163 1793.55,589.418 1795.59,589.672 1797.64,589.926 1799.68,590.18 1801.73,590.433 1803.78,590.686 1805.82,590.938 1807.87,591.19 1809.91,591.442 \n",
       "  1811.96,591.693 1814,591.943 1816.05,592.194 1818.09,592.444 1820.14,592.693 1822.18,592.942 1824.23,593.191 1826.27,593.439 1828.32,593.687 1830.37,593.935 \n",
       "  1832.41,594.182 1834.46,594.428 1836.5,594.675 1838.55,594.921 1840.59,595.166 1842.64,595.411 1844.68,595.656 1846.73,595.9 1848.77,596.144 1850.82,596.388 \n",
       "  1852.86,596.631 1854.91,596.874 1856.96,597.116 1859,597.358 1861.05,597.6 1863.09,597.841 1865.14,598.082 1867.18,598.323 1869.23,598.563 1871.27,598.802 \n",
       "  1873.32,599.042 1875.36,599.281 1877.41,599.519 1879.45,599.757 1881.5,599.995 1883.55,600.233 1885.59,600.47 1887.64,600.706 1889.68,600.943 1891.73,601.179 \n",
       "  1893.77,601.414 1895.82,601.649 1897.86,601.884 1899.91,602.119 1901.95,602.353 1904,602.586 1906.04,602.82 1908.09,603.053 1910.14,603.285 1912.18,603.517 \n",
       "  1914.23,603.749 1916.27,603.981 1918.32,604.212 1920.36,604.443 1922.41,604.673 1924.45,604.903 1926.5,605.133 1928.54,605.362 1930.59,605.591 1932.63,605.82 \n",
       "  1934.68,606.048 1936.73,606.276 1938.77,606.503 1940.82,606.73 1942.86,606.957 1944.91,607.184 1946.95,607.41 1949,607.635 1951.04,607.861 1953.09,608.086 \n",
       "  1955.13,608.311 1957.18,608.535 1959.23,608.759 1961.27,608.983 1963.32,609.206 1965.36,609.429 1967.41,609.651 1969.45,609.874 1971.5,610.095 1973.54,610.317 \n",
       "  1975.59,610.538 1977.63,610.759 1979.68,610.98 1981.72,611.2 1983.77,611.42 1985.82,611.639 1987.86,611.858 1989.91,612.077 1991.95,612.295 1994,612.514 \n",
       "  1996.04,612.731 1998.09,612.949 2000.13,613.166 2002.18,613.383 2004.22,613.599 2006.27,613.815 2008.31,614.031 2010.36,614.246 2012.41,614.462 2014.45,614.676 \n",
       "  2016.5,614.891 2018.54,615.105 2020.59,615.319 2022.63,615.532 2024.68,615.745 2026.72,615.958 2028.77,616.17 2030.81,616.383 2032.86,616.594 2034.9,616.806 \n",
       "  2036.95,617.017 2039,617.228 2041.04,617.438 2043.09,617.648 2045.13,617.858 2047.18,618.068 2049.22,618.277 2051.27,618.486 2053.31,618.695 2055.36,618.903 \n",
       "  2057.4,619.111 2059.45,619.318 2061.49,619.526 2063.54,619.733 2065.59,619.939 2067.63,620.146 2069.68,620.352 2071.72,620.557 2073.77,620.763 2075.81,620.968 \n",
       "  2077.86,621.173 2079.9,621.377 2081.95,621.581 2083.99,621.785 2086.04,621.989 2088.08,622.192 2090.13,622.395 2092.18,622.597 2094.22,622.8 2096.27,623.002 \n",
       "  2098.31,623.203 2100.36,623.405 2102.4,623.606 2104.45,623.807 2106.49,624.007 2108.54,624.207 2110.58,624.407 2112.63,624.607 2114.68,624.806 2116.72,625.005 \n",
       "  2118.77,625.204 2120.81,625.402 2122.86,625.6 2124.9,625.798 2126.95,625.995 2128.99,626.192 2131.04,626.389 2133.08,626.586 2135.13,626.782 2137.17,626.978 \n",
       "  2139.22,627.174 2141.27,627.369 2143.31,627.564 2145.36,627.759 2147.4,627.953 2149.45,628.148 2151.49,628.342 2153.54,628.535 2155.58,628.729 2157.63,628.922 \n",
       "  2159.67,629.114 2161.72,629.307 2163.76,629.499 2165.81,629.691 2167.86,629.883 2169.9,630.074 2171.95,630.265 2173.99,630.456 2176.04,630.646 2178.08,630.836 \n",
       "  2180.13,631.026 2182.17,631.216 2184.22,631.405 2186.26,631.594 2188.31,631.783 2190.35,631.972 2192.4,632.16 2194.45,632.348 2196.49,632.535 2198.54,632.723 \n",
       "  2200.58,632.91 2202.63,633.097 2204.67,633.283 2206.72,633.469 2208.76,633.655 2210.81,633.841 2212.85,634.027 2214.9,634.212 2216.94,634.397 2218.99,634.581 \n",
       "  2221.04,634.765 2223.08,634.95 2225.13,635.133 2227.17,635.317 2229.22,635.5 2231.26,635.683 2233.31,635.866 2235.35,636.048 2237.4,636.23 2239.44,636.412 \n",
       "  2241.49,636.594 2243.53,636.775 2245.58,636.956 2247.63,637.137 2249.67,637.318 2251.72,637.498 2253.76,637.678 2255.81,637.858 2257.85,638.037 2259.9,638.217 \n",
       "  2261.94,638.396 2263.99,638.574 2266.03,638.753 2268.08,638.931 2270.12,639.109 2272.17,639.287 2274.22,639.464 2276.26,639.641 2278.31,639.818 2280.35,639.995 \n",
       "  2282.4,640.171 2284.44,640.347 2286.49,640.523 2288.53,640.699 2290.58,640.874 2292.62,641.049 2294.67,641.224 2296.72,641.399 2298.76,641.573 2300.81,641.747 \n",
       "  2302.85,641.921 2304.9,642.094 2306.94,642.268 2308.99,642.441 2311.03,642.614 2313.08,642.786 2315.12,642.958 2317.17,643.13 2319.21,643.302 2321.26,643.474 \n",
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       "  298.365,795.463 300.41,796.666 302.456,797.866 304.501,799.062 306.546,800.254 308.592,801.443 310.637,802.628 312.683,803.81 314.728,804.989 316.773,806.164 \n",
       "  318.819,807.336 320.864,808.504 322.91,809.668 324.955,810.83 327,811.988 329.046,813.143 331.091,814.294 333.136,815.442 335.182,816.586 337.227,817.728 \n",
       "  339.273,818.866 341.318,820 343.363,821.132 345.409,822.26 347.454,823.385 349.5,824.507 351.545,825.625 353.59,826.741 355.636,827.853 357.681,828.962 \n",
       "  359.727,830.068 361.772,831.17 363.817,832.27 365.863,833.366 367.908,834.46 369.954,835.55 371.999,836.637 374.044,837.721 376.09,838.802 378.135,839.88 \n",
       "  380.181,840.955 382.226,842.027 384.271,843.095 386.317,844.161 388.362,845.224 390.408,846.284 392.453,847.341 394.498,848.395 396.544,849.446 398.589,850.494 \n",
       "  400.635,851.539 402.68,852.582 404.725,853.621 406.771,854.657 408.816,855.691 410.861,856.722 412.907,857.75 414.952,858.775 416.998,859.797 419.043,860.817 \n",
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       "  482.45,891.083 484.496,892.018 486.541,892.951 488.586,893.881 490.632,894.809 492.677,895.734 494.723,896.657 496.768,897.577 498.813,898.495 500.859,899.41 \n",
       "  502.904,900.323 504.95,901.234 506.995,902.142 509.04,903.048 511.086,903.952 513.131,904.853 515.177,905.752 517.222,906.648 519.267,907.542 521.313,908.434 \n",
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       "  543.812,918.093 545.858,918.958 547.903,919.82 549.948,920.68 551.994,921.538 554.039,922.394 556.084,923.247 558.13,924.099 560.175,924.948 562.221,925.795 \n",
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       "  646.082,958.759 648.127,959.522 650.173,960.283 652.218,961.043 654.263,961.8 656.309,962.556 658.354,963.31 660.4,964.062 662.445,964.812 664.49,965.56 \n",
       "  666.536,966.307 668.581,967.052 670.627,967.795 672.672,968.536 674.717,969.275 676.763,970.013 678.808,970.749 680.854,971.483 682.899,972.215 684.944,972.946 \n",
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       "  727.898,987.895 729.943,988.589 731.988,989.281 734.034,989.971 736.079,990.66 738.125,991.347 740.17,992.032 742.215,992.716 744.261,993.398 746.306,994.079 \n",
       "  748.352,994.758 750.397,995.436 752.442,996.112 754.488,996.786 756.533,997.459 758.579,998.131 760.624,998.8 762.669,999.469 764.715,1000.14 766.76,1000.8 \n",
       "  768.805,1001.46 770.851,1002.13 772.896,1002.79 774.942,1003.45 776.987,1004.1 779.032,1004.76 781.078,1005.41 783.123,1006.07 785.169,1006.72 787.214,1007.37 \n",
       "  789.259,1008.02 791.305,1008.66 793.35,1009.31 795.396,1009.95 797.441,1010.6 799.486,1011.24 801.532,1011.88 803.577,1012.52 805.623,1013.15 807.668,1013.79 \n",
       "  809.713,1014.42 811.759,1015.06 813.804,1015.69 815.85,1016.32 817.895,1016.95 819.94,1017.57 821.986,1018.2 824.031,1018.82 826.077,1019.44 828.122,1020.07 \n",
       "  830.167,1020.69 832.213,1021.3 834.258,1021.92 836.304,1022.54 838.349,1023.15 840.394,1023.76 842.44,1024.38 844.485,1024.99 846.53,1025.6 848.576,1026.2 \n",
       "  850.621,1026.81 852.667,1027.41 854.712,1028.02 856.757,1028.62 858.803,1029.22 860.848,1029.82 862.894,1030.42 864.939,1031.02 866.984,1031.61 869.03,1032.21 \n",
       "  871.075,1032.8 873.121,1033.39 875.166,1033.98 877.211,1034.57 879.257,1035.16 881.302,1035.75 883.348,1036.33 885.393,1036.91 887.438,1037.5 889.484,1038.08 \n",
       "  891.529,1038.66 893.575,1039.24 895.62,1039.82 897.665,1040.39 899.711,1040.97 901.756,1041.54 903.802,1042.11 905.847,1042.69 907.892,1043.26 909.938,1043.83 \n",
       "  911.983,1044.39 914.029,1044.96 916.074,1045.52 918.119,1046.09 920.165,1046.65 922.21,1047.21 924.255,1047.77 926.301,1048.33 928.346,1048.89 930.392,1049.45 \n",
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       "  993.799,1066.14 995.844,1066.66 997.89,1067.18 999.935,1067.7 1001.98,1068.21 1004.03,1068.73 1006.07,1069.24 1008.12,1069.76 1010.16,1070.27 1012.21,1070.78 \n",
       "  1014.25,1071.29 1016.3,1071.8 1018.34,1072.31 1020.39,1072.82 1022.43,1073.33 1024.48,1073.83 1026.53,1074.34 1028.57,1074.84 1030.62,1075.34 1032.66,1075.84 \n",
       "  1034.71,1076.34 1036.75,1076.84 1038.8,1077.34 1040.84,1077.84 1042.89,1078.34 1044.93,1078.83 1046.98,1079.33 1049.02,1079.82 1051.07,1080.31 1053.12,1080.8 \n",
       "  1055.16,1081.29 1057.21,1081.78 1059.25,1082.27 1061.3,1082.76 1063.34,1083.24 1065.39,1083.73 1067.43,1084.21 1069.48,1084.7 1071.52,1085.18 1073.57,1085.66 \n",
       "  1075.61,1086.14 1077.66,1086.62 1079.71,1087.1 1081.75,1087.57 1083.8,1088.05 1085.84,1088.53 1087.89,1089 1089.93,1089.47 1091.98,1089.95 1094.02,1090.42 \n",
       "  1096.07,1090.89 1098.11,1091.36 1100.16,1091.83 1102.2,1092.3 1104.25,1092.76 1106.3,1093.23 1108.34,1093.69 1110.39,1094.16 1112.43,1094.62 1114.48,1095.08 \n",
       "  1116.52,1095.55 1118.57,1096.01 1120.61,1096.47 1122.66,1096.92 1124.7,1097.38 1126.75,1097.84 1128.79,1098.3 1130.84,1098.75 1132.89,1099.2 1134.93,1099.66 \n",
       "  1136.98,1100.11 1139.02,1100.56 1141.07,1101.01 1143.11,1101.46 1145.16,1101.91 1147.2,1102.36 1149.25,1102.8 1151.29,1103.25 1153.34,1103.7 1155.39,1104.14 \n",
       "  1157.43,1104.58 1159.48,1105.03 1161.52,1105.47 1163.57,1105.91 1165.61,1106.35 1167.66,1106.79 1169.7,1107.23 1171.75,1107.66 1173.79,1108.1 1175.84,1108.54 \n",
       "  1177.88,1108.97 1179.93,1109.4 1181.98,1109.84 1184.02,1110.27 1186.07,1110.7 1188.11,1111.13 1190.16,1111.56 1192.2,1111.99 1194.25,1112.42 1196.29,1112.85 \n",
       "  1198.34,1113.27 1200.38,1113.7 1202.43,1114.12 1204.47,1114.55 1206.52,1114.97 1208.57,1115.39 1210.61,1115.81 1212.66,1116.24 1214.7,1116.66 1216.75,1117.07 \n",
       "  1218.79,1117.49 1220.84,1117.91 1222.88,1118.33 1224.93,1118.74 1226.97,1119.16 1229.02,1119.57 1231.06,1119.99 1233.11,1120.4 1235.16,1120.81 1237.2,1121.22 \n",
       "  1239.25,1121.63 1241.29,1122.04 1243.34,1122.45 1245.38,1122.86 1247.43,1123.27 1249.47,1123.67 1251.52,1124.08 1253.56,1124.48 1255.61,1124.89 1257.65,1125.29 \n",
       "  1259.7,1125.69 1261.75,1126.09 1263.79,1126.5 1265.84,1126.9 1267.88,1127.3 1269.93,1127.69 1271.97,1128.09 1274.02,1128.49 1276.06,1128.89 1278.11,1129.28 \n",
       "  1280.15,1129.68 1282.2,1130.07 1284.24,1130.46 1286.29,1130.86 1288.34,1131.25 1290.38,1131.64 1292.43,1132.03 1294.47,1132.42 1296.52,1132.81 1298.56,1133.2 \n",
       "  1300.61,1133.59 1302.65,1133.97 1304.7,1134.36 1306.74,1134.75 1308.79,1135.13 1310.84,1135.51 1312.88,1135.9 1314.93,1136.28 1316.97,1136.66 1319.02,1137.04 \n",
       "  1321.06,1137.42 1323.11,1137.8 1325.15,1138.18 1327.2,1138.56 1329.24,1138.94 1331.29,1139.32 1333.33,1139.69 1335.38,1140.07 1337.43,1140.44 1339.47,1140.82 \n",
       "  1341.52,1141.19 1343.56,1141.56 1345.61,1141.94 1347.65,1142.31 1349.7,1142.68 1351.74,1143.05 1353.79,1143.42 1355.83,1143.79 1357.88,1144.16 1359.92,1144.52 \n",
       "  1361.97,1144.89 1364.02,1145.26 1366.06,1145.62 1368.11,1145.99 1370.15,1146.35 1372.2,1146.71 1374.24,1147.08 1376.29,1147.44 1378.33,1147.8 1380.38,1148.16 \n",
       "  1382.42,1148.52 1384.47,1148.88 1386.51,1149.24 1388.56,1149.6 1390.61,1149.95 1392.65,1150.31 1394.7,1150.67 1396.74,1151.02 1398.79,1151.38 1400.83,1151.73 \n",
       "  1402.88,1152.09 1404.92,1152.44 1406.97,1152.79 1409.01,1153.14 1411.06,1153.49 1413.1,1153.84 1415.15,1154.19 1417.2,1154.54 1419.24,1154.89 1421.29,1155.24 \n",
       "  1423.33,1155.59 1425.38,1155.93 1427.42,1156.28 1429.47,1156.63 1431.51,1156.97 1433.56,1157.32 1435.6,1157.66 1437.65,1158 1439.69,1158.34 1441.74,1158.69 \n",
       "  1443.79,1159.03 1445.83,1159.37 1447.88,1159.71 1449.92,1160.05 1451.97,1160.39 1454.01,1160.72 1456.06,1161.06 1458.1,1161.4 1460.15,1161.73 1462.19,1162.07 \n",
       "  1464.24,1162.4 1466.28,1162.74 1468.33,1163.07 1470.38,1163.41 1472.42,1163.74 1474.47,1164.07 1476.51,1164.4 1478.56,1164.73 1480.6,1165.06 1482.65,1165.39 \n",
       "  1484.69,1165.72 1486.74,1166.05 1488.78,1166.38 1490.83,1166.71 1492.88,1167.03 1494.92,1167.36 1496.97,1167.69 1499.01,1168.01 1501.06,1168.34 1503.1,1168.66 \n",
       "  1505.15,1168.98 1507.19,1169.31 1509.24,1169.63 1511.28,1169.95 1513.33,1170.27 1515.37,1170.59 1517.42,1170.91 1519.47,1171.23 1521.51,1171.55 1523.56,1171.87 \n",
       "  1525.6,1172.19 1527.65,1172.5 1529.69,1172.82 1531.74,1173.14 1533.78,1173.45 1535.83,1173.77 1537.87,1174.08 1539.92,1174.4 1541.96,1174.71 1544.01,1175.02 \n",
       "  1546.06,1175.34 1548.1,1175.65 1550.15,1175.96 1552.19,1176.27 1554.24,1176.58 1556.28,1176.89 1558.33,1177.2 1560.37,1177.51 1562.42,1177.81 1564.46,1178.12 \n",
       "  1566.51,1178.43 1568.55,1178.74 1570.6,1179.04 1572.65,1179.35 1574.69,1179.65 1576.74,1179.96 1578.78,1180.26 1580.83,1180.56 1582.87,1180.87 1584.92,1181.17 \n",
       "  1586.96,1181.47 1589.01,1181.77 1591.05,1182.07 1593.1,1182.37 1595.14,1182.67 1597.19,1182.97 1599.24,1183.27 1601.28,1183.57 1603.33,1183.87 1605.37,1184.16 \n",
       "  1607.42,1184.46 1609.46,1184.76 1611.51,1185.05 1613.55,1185.35 1615.6,1185.64 1617.64,1185.93 1619.69,1186.23 1621.73,1186.52 1623.78,1186.81 1625.83,1187.11 \n",
       "  1627.87,1187.4 1629.92,1187.69 1631.96,1187.98 1634.01,1188.27 1636.05,1188.56 1638.1,1188.85 1640.14,1189.14 1642.19,1189.42 1644.23,1189.71 1646.28,1190 \n",
       "  1648.33,1190.29 1650.37,1190.57 1652.42,1190.86 1654.46,1191.14 1656.51,1191.43 1658.55,1191.71 1660.6,1192 1662.64,1192.28 1664.69,1192.56 1666.73,1192.84 \n",
       "  1668.78,1193.13 1670.82,1193.41 1672.87,1193.69 1674.92,1193.97 1676.96,1194.25 1679.01,1194.53 1681.05,1194.81 1683.1,1195.09 1685.14,1195.36 1687.19,1195.64 \n",
       "  1689.23,1195.92 1691.28,1196.2 1693.32,1196.47 1695.37,1196.75 1697.41,1197.02 1699.46,1197.3 1701.51,1197.57 1703.55,1197.85 1705.6,1198.12 1707.64,1198.39 \n",
       "  1709.69,1198.67 1711.73,1198.94 1713.78,1199.21 1715.82,1199.48 1717.87,1199.75 1719.91,1200.02 1721.96,1200.29 1724,1200.56 1726.05,1200.83 1728.1,1201.1 \n",
       "  1730.14,1201.37 1732.19,1201.64 1734.23,1201.9 1736.28,1202.17 1738.32,1202.44 1740.37,1202.7 1742.41,1202.97 1744.46,1203.23 1746.5,1203.5 1748.55,1203.76 \n",
       "  1750.59,1204.02 1752.64,1204.29 1754.69,1204.55 1756.73,1204.81 1758.78,1205.08 1760.82,1205.34 1762.87,1205.6 1764.91,1205.86 1766.96,1206.12 1769,1206.38 \n",
       "  1771.05,1206.64 1773.09,1206.9 1775.14,1207.16 1777.18,1207.41 1779.23,1207.67 1781.28,1207.93 1783.32,1208.19 1785.37,1208.44 1787.41,1208.7 1789.46,1208.95 \n",
       "  1791.5,1209.21 1793.55,1209.46 1795.59,1209.72 1797.64,1209.97 1799.68,1210.23 1801.73,1210.48 1803.78,1210.73 1805.82,1210.98 1807.87,1211.24 1809.91,1211.49 \n",
       "  1811.96,1211.74 1814,1211.99 1816.05,1212.24 1818.09,1212.49 1820.14,1212.74 1822.18,1212.99 1824.23,1213.24 1826.27,1213.49 1828.32,1213.73 1830.37,1213.98 \n",
       "  1832.41,1214.23 1834.46,1214.47 1836.5,1214.72 1838.55,1214.97 1840.59,1215.21 1842.64,1215.46 1844.68,1215.7 1846.73,1215.95 1848.77,1216.19 1850.82,1216.43 \n",
       "  1852.86,1216.68 1854.91,1216.92 1856.96,1217.16 1859,1217.4 1861.05,1217.65 1863.09,1217.89 1865.14,1218.13 1867.18,1218.37 1869.23,1218.61 1871.27,1218.85 \n",
       "  1873.32,1219.09 1875.36,1219.33 1877.41,1219.57 1879.45,1219.8 1881.5,1220.04 1883.55,1220.28 1885.59,1220.52 1887.64,1220.75 1889.68,1220.99 1891.73,1221.22 \n",
       "  1893.77,1221.46 1895.82,1221.7 1897.86,1221.93 1899.91,1222.16 1901.95,1222.4 1904,1222.63 1906.04,1222.87 1908.09,1223.1 1910.14,1223.33 1912.18,1223.56 \n",
       "  1914.23,1223.8 1916.27,1224.03 1918.32,1224.26 1920.36,1224.49 1922.41,1224.72 1924.45,1224.95 1926.5,1225.18 1928.54,1225.41 1930.59,1225.64 1932.63,1225.87 \n",
       "  1934.68,1226.09 1936.73,1226.32 1938.77,1226.55 1940.82,1226.78 1942.86,1227 1944.91,1227.23 1946.95,1227.46 1949,1227.68 1951.04,1227.91 1953.09,1228.13 \n",
       "  1955.13,1228.36 1957.18,1228.58 1959.23,1228.81 1961.27,1229.03 1963.32,1229.25 1965.36,1229.48 1967.41,1229.7 1969.45,1229.92 1971.5,1230.14 1973.54,1230.36 \n",
       "  1975.59,1230.58 1977.63,1230.81 1979.68,1231.03 1981.72,1231.25 1983.77,1231.47 1985.82,1231.69 1987.86,1231.9 1989.91,1232.12 1991.95,1232.34 1994,1232.56 \n",
       "  1996.04,1232.78 1998.09,1233 2000.13,1233.21 2002.18,1233.43 2004.22,1233.65 2006.27,1233.86 2008.31,1234.08 2010.36,1234.29 2012.41,1234.51 2014.45,1234.72 \n",
       "  2016.5,1234.94 2018.54,1235.15 2020.59,1235.37 2022.63,1235.58 2024.68,1235.79 2026.72,1236 2028.77,1236.22 2030.81,1236.43 2032.86,1236.64 2034.9,1236.85 \n",
       "  2036.95,1237.06 2039,1237.27 2041.04,1237.48 2043.09,1237.69 2045.13,1237.9 2047.18,1238.11 2049.22,1238.32 2051.27,1238.53 2053.31,1238.74 2055.36,1238.95 \n",
       "  2057.4,1239.16 2059.45,1239.36 2061.49,1239.57 2063.54,1239.78 2065.59,1239.99 2067.63,1240.19 2069.68,1240.4 2071.72,1240.6 2073.77,1240.81 2075.81,1241.01 \n",
       "  2077.86,1241.22 2079.9,1241.42 2081.95,1241.63 2083.99,1241.83 2086.04,1242.04 2088.08,1242.24 2090.13,1242.44 2092.18,1242.64 2094.22,1242.85 2096.27,1243.05 \n",
       "  2098.31,1243.25 2100.36,1243.45 2102.4,1243.65 2104.45,1243.85 2106.49,1244.05 2108.54,1244.25 2110.58,1244.45 2112.63,1244.65 2114.68,1244.85 2116.72,1245.05 \n",
       "  2118.77,1245.25 2120.81,1245.45 2122.86,1245.65 2124.9,1245.84 2126.95,1246.04 2128.99,1246.24 2131.04,1246.44 2133.08,1246.63 2135.13,1246.83 2137.17,1247.02 \n",
       "  2139.22,1247.22 2141.27,1247.42 2143.31,1247.61 2145.36,1247.81 2147.4,1248 2149.45,1248.19 2151.49,1248.39 2153.54,1248.58 2155.58,1248.77 2157.63,1248.97 \n",
       "  2159.67,1249.16 2161.72,1249.35 2163.76,1249.55 2165.81,1249.74 2167.86,1249.93 2169.9,1250.12 2171.95,1250.31 2173.99,1250.5 2176.04,1250.69 2178.08,1250.88 \n",
       "  2180.13,1251.07 2182.17,1251.26 2184.22,1251.45 2186.26,1251.64 2188.31,1251.83 2190.35,1252.02 2192.4,1252.21 2194.45,1252.39 2196.49,1252.58 2198.54,1252.77 \n",
       "  2200.58,1252.96 2202.63,1253.14 2204.67,1253.33 2206.72,1253.52 2208.76,1253.7 2210.81,1253.89 2212.85,1254.07 2214.9,1254.26 2216.94,1254.44 2218.99,1254.63 \n",
       "  2221.04,1254.81 2223.08,1255 2225.13,1255.18 2227.17,1255.36 2229.22,1255.55 2231.26,1255.73 2233.31,1255.91 2235.35,1256.09 2237.4,1256.28 2239.44,1256.46 \n",
       "  2241.49,1256.64 2243.53,1256.82 2245.58,1257 2247.63,1257.18 2249.67,1257.36 2251.72,1257.54 2253.76,1257.72 2255.81,1257.9 2257.85,1258.08 2259.9,1258.26 \n",
       "  2261.94,1258.44 2263.99,1258.62 2266.03,1258.8 2268.08,1258.98 2270.12,1259.16 2272.17,1259.33 2274.22,1259.51 2276.26,1259.69 2278.31,1259.86 2280.35,1260.04 \n",
       "  2282.4,1260.22 2284.44,1260.39 2286.49,1260.57 2288.53,1260.75 2290.58,1260.92 2292.62,1261.1 2294.67,1261.27 2296.72,1261.44 2298.76,1261.62 2300.81,1261.79 \n",
       "  2302.85,1261.97 2304.9,1262.14 2306.94,1262.31 2308.99,1262.49 2311.03,1262.66 2313.08,1262.83 2315.12,1263 2317.17,1263.18 2319.21,1263.35 2321.26,1263.52 \n",
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       "  298.365,1391.05 300.41,1389.85 302.456,1388.65 304.501,1387.45 306.546,1386.26 308.592,1385.07 310.637,1383.88 312.683,1382.7 314.728,1381.52 316.773,1380.35 \n",
       "  318.819,1379.18 320.864,1378.01 322.91,1376.84 324.955,1375.68 327,1374.53 329.046,1373.37 331.091,1372.22 333.136,1371.07 335.182,1369.93 337.227,1368.79 \n",
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       "  359.727,1356.45 361.772,1355.34 363.817,1354.24 365.863,1353.15 367.908,1352.05 369.954,1350.96 371.999,1349.88 374.044,1348.79 376.09,1347.71 378.135,1346.63 \n",
       "  380.181,1345.56 382.226,1344.49 384.271,1343.42 386.317,1342.35 388.362,1341.29 390.408,1340.23 392.453,1339.17 394.498,1338.12 396.544,1337.07 398.589,1336.02 \n",
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       "  1198.34,1073.24 1200.38,1072.81 1202.43,1072.39 1204.47,1071.97 1206.52,1071.54 1208.57,1071.12 1210.61,1070.7 1212.66,1070.28 1214.7,1069.86 1216.75,1069.44 \n",
       "  1218.79,1069.02 1220.84,1068.6 1222.88,1068.19 1224.93,1067.77 1226.97,1067.36 1229.02,1066.94 1231.06,1066.53 1233.11,1066.12 1235.16,1065.7 1237.2,1065.29 \n",
       "  1239.25,1064.88 1241.29,1064.47 1243.34,1064.06 1245.38,1063.66 1247.43,1063.25 1249.47,1062.84 1251.52,1062.44 1253.56,1062.03 1255.61,1061.63 1257.65,1061.22 \n",
       "  1259.7,1060.82 1261.75,1060.42 1263.79,1060.02 1265.84,1059.62 1267.88,1059.22 1269.93,1058.82 1271.97,1058.42 1274.02,1058.02 1276.06,1057.63 1278.11,1057.23 \n",
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      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob3 = ODEProblem(simpleODE3!,u₀,tspan,p)\n",
    "sol3 = solve(prob3)\n",
    "plot(sol3,label=[\"a\",\"b\",\"c\"])\n",
    "title!(\"ODE solver using DSL\")\n",
    "xlabel!(\"Time [s]\")\n",
    "ylabel!(\"Concentration [M]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Reversible reactions and equilibrium \n",
    "\n",
    "Now we will use the same approach  to solve the reversible reaction \n",
    "\n",
    "$$ a + b \\leftrightarrow  c \\tag{7}$$\n",
    "\n",
    "with rate constants `k1`, and `k2` for the forward and reverse reaction. Based on mass action kinetics, the differential equations to solve now are:\n",
    "\n",
    "\n",
    "$$ \\frac{da}{dt} = -k_1 \\cdot a \\cdot b + k_2 \\cdot c \\tag{8}$$\n",
    "\n",
    "$$ \\frac{db}{dt} = -k_1 \\cdot a \\cdot b + k_2 \\cdot \\tag{9}c$$\n",
    "\n",
    "$$ \\frac{dc}{dt} = k_1 \\cdot a \\cdot b - k_2 \\cdot \\tag{10}c$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, $p$ that holds the parameters required to solve the system is a vector of two components  $k_1$, and $k_2$. So"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "k1=1\n",
    "k2=0.01\n",
    "p = (k1,k2); # we could also make this an array, or any other type!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "simpleODErev! (generic function with 1 method)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function simpleODErev!(du,u,p,t)\n",
    "    k1,k2 = p\n",
    "    du[1] = -k1*u[1]*u[2]+k2*u[3]\n",
    "    du[2] = -k1*u[1]*u[2]+k2*u[3]\n",
    "    du[3] = k1*u[1]*u[2]-k2*u[3] \n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
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       "<g clip-path=\"url(#clip4500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 686.581, 1494.48)\" x=\"686.581\" y=\"1494.48\">20</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip4500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 1095.25, 1494.48)\" x=\"1095.25\" y=\"1494.48\">40</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip4500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 1503.92, 1494.48)\" x=\"1503.92\" y=\"1494.48\">60</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip4500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 1912.59, 1494.48)\" x=\"1912.59\" y=\"1494.48\">80</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip4500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 2321.26, 1494.48)\" x=\"2321.26\" y=\"1494.48\">100</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip4500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 253.911, 1420.78)\" x=\"253.911\" y=\"1420.78\">0.000</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip4500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 253.911, 1110.76)\" x=\"253.911\" y=\"1110.76\">0.005</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip4500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 253.911, 800.733)\" x=\"253.911\" y=\"800.733\">0.010</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip4500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 253.911, 490.71)\" x=\"253.911\" y=\"490.71\">0.015</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip4500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 253.911, 180.687)\" x=\"253.911\" y=\"180.687\">0.020</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip4500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:84px; text-anchor:middle;\" transform=\"rotate(0, 1299.59, 73.2)\" x=\"1299.59\" y=\"73.2\">ODE solver in Julia</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip4500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:66px; text-anchor:middle;\" transform=\"rotate(0, 1299.59, 1590.4)\" x=\"1299.59\" y=\"1590.4\">Time [s]</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip4500)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:66px; text-anchor:middle;\" transform=\"rotate(-90, 57.6, 783.233)\" x=\"57.6\" y=\"783.233\">Concentration [M]</text>\n",
       "</g>\n",
       "<polyline clip-path=\"url(#clip4502)\" style=\"stroke:#009af9; stroke-width:12; stroke-opacity:1; fill:none\" points=\"\n",
       "  277.911,163.187 279.956,164.426 282.002,165.66 284.047,166.889 286.092,168.113 288.138,169.332 290.183,170.546 292.229,171.756 294.274,172.961 296.319,174.161 \n",
       "  298.365,175.356 300.41,176.546 302.456,177.732 304.501,178.913 306.546,180.09 308.592,181.262 310.637,182.429 312.683,183.591 314.728,184.749 316.773,185.903 \n",
       "  318.819,187.052 320.864,188.196 322.91,189.336 324.955,190.472 327,191.603 329.046,192.729 331.091,193.852 333.136,194.97 335.182,196.083 337.227,197.192 \n",
       "  339.273,198.297 341.318,199.398 343.363,200.494 345.409,201.586 347.454,202.674 349.5,203.758 351.545,204.837 353.59,205.913 355.636,206.984 357.681,208.051 \n",
       "  359.727,209.114 361.772,210.172 363.817,211.227 365.863,212.278 367.908,213.324 369.954,214.367 371.999,215.406 374.044,216.44 376.09,217.471 378.135,218.498 \n",
       "  380.181,219.521 382.226,220.54 384.271,221.555 386.317,222.566 388.362,223.573 390.408,224.577 392.453,225.576 394.498,226.572 396.544,227.565 398.589,228.553 \n",
       "  400.635,229.538 402.68,230.518 404.725,231.496 406.771,232.469 408.816,233.439 410.861,234.405 412.907,235.368 414.952,236.327 416.998,237.282 419.043,238.234 \n",
       "  421.088,239.182 423.134,240.127 425.179,241.068 427.225,242.005 429.27,242.939 431.315,243.87 433.361,244.797 435.406,245.72 437.452,246.641 439.497,247.557 \n",
       "  441.542,248.471 443.588,249.38 445.633,250.287 447.679,251.19 449.724,252.09 451.769,252.986 453.815,253.88 455.86,254.769 457.906,255.656 459.951,256.539 \n",
       "  461.996,257.419 464.042,258.296 466.087,259.169 468.133,260.04 470.178,260.907 472.223,261.771 474.269,262.631 476.314,263.489 478.359,264.343 480.405,265.195 \n",
       "  482.45,266.043 484.496,266.888 486.541,267.73 488.586,268.568 490.632,269.404 492.677,270.237 494.723,271.067 496.768,271.893 498.813,272.717 500.859,273.538 \n",
       "  502.904,274.355 504.95,275.17 506.995,275.982 509.04,276.79 511.086,277.596 513.131,278.399 515.177,279.199 517.222,279.996 519.267,280.79 521.313,281.582 \n",
       "  523.358,282.37 525.404,283.156 527.449,283.939 529.494,284.719 531.54,285.496 533.585,286.27 535.631,287.042 537.676,287.81 539.721,288.577 541.767,289.34 \n",
       "  543.812,290.1 545.858,290.858 547.903,291.613 549.948,292.366 551.994,293.115 554.039,293.862 556.084,294.607 558.13,295.348 560.175,296.087 562.221,296.824 \n",
       "  564.266,297.558 566.311,298.289 568.357,299.017 570.402,299.743 572.448,300.467 574.493,301.187 576.538,301.906 578.584,302.621 580.629,303.335 582.675,304.045 \n",
       "  584.72,304.753 586.765,305.459 588.811,306.162 590.856,306.863 592.902,307.561 594.947,308.257 596.992,308.95 599.038,309.641 601.083,310.329 603.129,311.015 \n",
       "  605.174,311.698 607.219,312.38 609.265,313.058 611.31,313.735 613.356,314.409 615.401,315.08 617.446,315.749 619.492,316.416 621.537,317.081 623.582,317.743 \n",
       "  625.628,318.403 627.673,319.061 629.719,319.716 631.764,320.369 633.809,321.02 635.855,321.668 637.9,322.314 639.946,322.958 641.991,323.6 644.036,324.239 \n",
       "  646.082,324.877 648.127,325.512 650.173,326.144 652.218,326.775 654.263,327.403 656.309,328.03 658.354,328.654 660.4,329.276 662.445,329.895 664.49,330.513 \n",
       "  666.536,331.129 668.581,331.742 670.627,332.353 672.672,332.962 674.717,333.569 676.763,334.174 678.808,334.777 680.854,335.378 682.899,335.977 684.944,336.573 \n",
       "  686.99,337.168 689.035,337.76 691.081,338.351 693.126,338.939 695.171,339.526 697.217,340.11 699.262,340.693 701.307,341.273 703.353,341.852 705.398,342.428 \n",
       "  707.444,343.003 709.489,343.575 711.534,344.146 713.58,344.715 715.625,345.281 717.671,345.846 719.716,346.409 721.761,346.97 723.807,347.529 725.852,348.086 \n",
       "  727.898,348.641 729.943,349.195 731.988,349.746 734.034,350.296 736.079,350.843 738.125,351.389 740.17,351.933 742.215,352.476 744.261,353.016 746.306,353.554 \n",
       "  748.352,354.091 750.397,354.626 752.442,355.159 754.488,355.69 756.533,356.22 758.579,356.748 760.624,357.273 762.669,357.798 764.715,358.32 766.76,358.841 \n",
       "  768.805,359.359 770.851,359.877 772.896,360.392 774.942,360.906 776.987,361.417 779.032,361.928 781.078,362.436 783.123,362.943 785.169,363.448 787.214,363.951 \n",
       "  789.259,364.453 791.305,364.953 793.35,365.452 795.396,365.948 797.441,366.443 799.486,366.937 801.532,367.428 803.577,367.919 805.623,368.407 807.668,368.894 \n",
       "  809.713,369.379 811.759,369.863 813.804,370.345 815.85,370.825 817.895,371.304 819.94,371.781 821.986,372.257 824.031,372.731 826.077,373.203 828.122,373.674 \n",
       "  830.167,374.143 832.213,374.611 834.258,375.077 836.304,375.542 838.349,376.005 840.394,376.467 842.44,376.927 844.485,377.385 846.53,377.842 848.576,378.298 \n",
       "  850.621,378.752 852.667,379.204 854.712,379.655 856.757,380.105 858.803,380.553 860.848,380.999 862.894,381.444 864.939,381.888 866.984,382.33 869.03,382.771 \n",
       "  871.075,383.21 873.121,383.648 875.166,384.084 877.211,384.519 879.257,384.952 881.302,385.384 883.348,385.815 885.393,386.244 887.438,386.672 889.484,387.099 \n",
       "  891.529,387.524 893.575,387.947 895.62,388.369 897.665,388.79 899.711,389.21 901.756,389.628 903.802,390.045 905.847,390.46 907.892,390.874 909.938,391.287 \n",
       "  911.983,391.698 914.029,392.108 916.074,392.517 918.119,392.924 920.165,393.33 922.21,393.735 924.255,394.138 926.301,394.54 928.346,394.941 930.392,395.34 \n",
       "  932.437,395.738 934.482,396.135 936.528,396.531 938.573,396.925 940.619,397.318 942.664,397.71 944.709,398.1 946.755,398.489 948.8,398.877 950.846,399.264 \n",
       "  952.891,399.649 954.936,400.034 956.982,400.416 959.027,400.798 961.073,401.179 963.118,401.558 965.163,401.936 967.209,402.313 969.254,402.688 971.3,403.063 \n",
       "  973.345,403.436 975.39,403.808 977.436,404.178 979.481,404.548 981.527,404.916 983.572,405.283 985.617,405.649 987.663,406.014 989.708,406.378 991.753,406.74 \n",
       "  993.799,407.102 995.844,407.462 997.89,407.821 999.935,408.179 1001.98,408.536 1004.03,408.891 1006.07,409.246 1008.12,409.599 1010.16,409.951 1012.21,410.302 \n",
       "  1014.25,410.652 1016.3,411.001 1018.34,411.348 1020.39,411.695 1022.43,412.04 1024.48,412.385 1026.53,412.728 1028.57,413.07 1030.62,413.411 1032.66,413.751 \n",
       "  1034.71,414.09 1036.75,414.428 1038.8,414.765 1040.84,415.1 1042.89,415.435 1044.93,415.768 1046.98,416.101 1049.02,416.432 1051.07,416.763 1053.12,417.092 \n",
       "  1055.16,417.42 1057.21,417.748 1059.25,418.074 1061.3,418.399 1063.34,418.723 1065.39,419.046 1067.43,419.368 1069.48,419.689 1071.52,420.009 1073.57,420.328 \n",
       "  1075.61,420.646 1077.66,420.963 1079.71,421.279 1081.75,421.594 1083.8,421.908 1085.84,422.221 1087.89,422.533 1089.93,422.844 1091.98,423.154 1094.02,423.463 \n",
       "  1096.07,423.772 1098.11,424.079 1100.16,424.385 1102.2,424.69 1104.25,424.994 1106.3,425.297 1108.34,425.6 1110.39,425.901 1112.43,426.201 1114.48,426.501 \n",
       "  1116.52,426.799 1118.57,427.097 1120.61,427.394 1122.66,427.689 1124.7,427.984 1126.75,428.278 1128.79,428.571 1130.84,428.863 1132.89,429.154 1134.93,429.444 \n",
       "  1136.98,429.733 1139.02,430.022 1141.07,430.309 1143.11,430.596 1145.16,430.881 1147.2,431.166 1149.25,431.45 1151.29,431.733 1153.34,432.015 1155.39,432.296 \n",
       "  1157.43,432.576 1159.48,432.856 1161.52,433.134 1163.57,433.412 1165.61,433.689 1167.66,433.965 1169.7,434.24 1171.75,434.514 1173.79,434.787 1175.84,435.06 \n",
       "  1177.88,435.331 1179.93,435.602 1181.98,435.872 1184.02,436.141 1186.07,436.41 1188.11,436.677 1190.16,436.944 1192.2,437.209 1194.25,437.474 1196.29,437.738 \n",
       "  1198.34,438.002 1200.38,438.264 1202.43,438.526 1204.47,438.787 1206.52,439.047 1208.57,439.306 1210.61,439.564 1212.66,439.822 1214.7,440.079 1216.75,440.335 \n",
       "  1218.79,440.59 1220.84,440.844 1222.88,441.098 1224.93,441.351 1226.97,441.603 1229.02,441.854 1231.06,442.105 1233.11,442.355 1235.16,442.603 1237.2,442.852 \n",
       "  1239.25,443.099 1241.29,443.346 1243.34,443.592 1245.38,443.837 1247.43,444.081 1249.47,444.325 1251.52,444.568 1253.56,444.81 1255.61,445.051 1257.65,445.292 \n",
       "  1259.7,445.532 1261.75,445.771 1263.79,446.009 1265.84,446.247 1267.88,446.484 1269.93,446.72 1271.97,446.955 1274.02,447.19 1276.06,447.424 1278.11,447.657 \n",
       "  1280.15,447.89 1282.2,448.122 1284.24,448.353 1286.29,448.583 1288.34,448.813 1290.38,449.042 1292.43,449.27 1294.47,449.498 1296.52,449.725 1298.56,449.951 \n",
       "  1300.61,450.177 1302.65,450.402 1304.7,450.626 1306.74,450.849 1308.79,451.072 1310.84,451.294 1312.88,451.515 1314.93,451.736 1316.97,451.956 1319.02,452.176 \n",
       "  1321.06,452.394 1323.11,452.612 1325.15,452.83 1327.2,453.046 1329.24,453.263 1331.29,453.478 1333.33,453.693 1335.38,453.907 1337.43,454.12 1339.47,454.333 \n",
       "  1341.52,454.545 1343.56,454.756 1345.61,454.967 1347.65,455.177 1349.7,455.387 1351.74,455.596 1353.79,455.804 1355.83,456.012 1357.88,456.219 1359.92,456.425 \n",
       "  1361.97,456.631 1364.02,456.836 1366.06,457.04 1368.11,457.244 1370.15,457.447 1372.2,457.65 1374.24,457.852 1376.29,458.053 1378.33,458.254 1380.38,458.454 \n",
       "  1382.42,458.654 1384.47,458.853 1386.51,459.051 1388.56,459.249 1390.61,459.446 1392.65,459.642 1394.7,459.838 1396.74,460.034 1398.79,460.228 1400.83,460.423 \n",
       "  1402.88,460.616 1404.92,460.809 1406.97,461.002 1409.01,461.193 1411.06,461.385 1413.1,461.575 1415.15,461.765 1417.2,461.955 1419.24,462.144 1421.29,462.332 \n",
       "  1423.33,462.52 1425.38,462.707 1427.42,462.894 1429.47,463.08 1431.51,463.265 1433.56,463.45 1435.6,463.635 1437.65,463.818 1439.69,464.002 1441.74,464.184 \n",
       "  1443.79,464.367 1445.83,464.548 1447.88,464.729 1449.92,464.91 1451.97,465.09 1454.01,465.269 1456.06,465.448 1458.1,465.626 1460.15,465.804 1462.19,465.981 \n",
       "  1464.24,466.158 1466.28,466.334 1468.33,466.51 1470.38,466.685 1472.42,466.86 1474.47,467.034 1476.51,467.207 1478.56,467.38 1480.6,467.553 1482.65,467.725 \n",
       "  1484.69,467.896 1486.74,468.067 1488.78,468.237 1490.83,468.407 1492.88,468.577 1494.92,468.746 1496.97,468.914 1499.01,469.082 1501.06,469.249 1503.1,469.416 \n",
       "  1505.15,469.582 1507.19,469.748 1509.24,469.914 1511.28,470.078 1513.33,470.243 1515.37,470.407 1517.42,470.57 1519.47,470.733 1521.51,470.895 1523.56,471.057 \n",
       "  1525.6,471.218 1527.65,471.379 1529.69,471.54 1531.74,471.7 1533.78,471.859 1535.83,472.018 1537.87,472.177 1539.92,472.335 1541.96,472.492 1544.01,472.649 \n",
       "  1546.06,472.806 1548.1,472.962 1550.15,473.118 1552.19,473.273 1554.24,473.428 1556.28,473.582 1558.33,473.736 1560.37,473.889 1562.42,474.042 1564.46,474.194 \n",
       "  1566.51,474.346 1568.55,474.498 1570.6,474.649 1572.65,474.8 1574.69,474.95 1576.74,475.099 1578.78,475.249 1580.83,475.397 1582.87,475.546 1584.92,475.694 \n",
       "  1586.96,475.841 1589.01,475.988 1591.05,476.135 1593.1,476.281 1595.14,476.427 1597.19,476.572 1599.24,476.717 1601.28,476.861 1603.33,477.005 1605.37,477.149 \n",
       "  1607.42,477.292 1609.46,477.435 1611.51,477.577 1613.55,477.719 1615.6,477.86 1617.64,478.001 1619.69,478.142 1621.73,478.282 1623.78,478.422 1625.83,478.561 \n",
       "  1627.87,478.7 1629.92,478.838 1631.96,478.976 1634.01,479.114 1636.05,479.251 1638.1,479.388 1640.14,479.525 1642.19,479.661 1644.23,479.796 1646.28,479.932 \n",
       "  1648.33,480.066 1650.37,480.201 1652.42,480.335 1654.46,480.468 1656.51,480.602 1658.55,480.735 1660.6,480.867 1662.64,480.999 1664.69,481.131 1666.73,481.262 \n",
       "  1668.78,481.393 1670.82,481.523 1672.87,481.653 1674.92,481.783 1676.96,481.912 1679.01,482.041 1681.05,482.17 1683.1,482.298 1685.14,482.426 1687.19,482.553 \n",
       "  1689.23,482.68 1691.28,482.807 1693.32,482.933 1695.37,483.059 1697.41,483.185 1699.46,483.31 1701.51,483.435 1703.55,483.559 1705.6,483.683 1707.64,483.807 \n",
       "  1709.69,483.93 1711.73,484.053 1713.78,484.176 1715.82,484.298 1717.87,484.42 1719.91,484.542 1721.96,484.663 1724,484.783 1726.05,484.904 1728.1,485.024 \n",
       "  1730.14,485.144 1732.19,485.263 1734.23,485.382 1736.28,485.501 1738.32,485.619 1740.37,485.737 1742.41,485.855 1744.46,485.972 1746.5,486.089 1748.55,486.206 \n",
       "  1750.59,486.322 1752.64,486.438 1754.69,486.553 1756.73,486.668 1758.78,486.783 1760.82,486.898 1762.87,487.012 1764.91,487.126 1766.96,487.239 1769,487.353 \n",
       "  1771.05,487.466 1773.09,487.578 1775.14,487.69 1777.18,487.802 1779.23,487.914 1781.28,488.025 1783.32,488.136 1785.37,488.246 1787.41,488.357 1789.46,488.466 \n",
       "  1791.5,488.576 1793.55,488.685 1795.59,488.794 1797.64,488.903 1799.68,489.011 1801.73,489.119 1803.78,489.227 1805.82,489.334 1807.87,489.441 1809.91,489.548 \n",
       "  1811.96,489.654 1814,489.761 1816.05,489.866 1818.09,489.972 1820.14,490.077 1822.18,490.182 1824.23,490.286 1826.27,490.391 1828.32,490.495 1830.37,490.598 \n",
       "  1832.41,490.702 1834.46,490.805 1836.5,490.907 1838.55,491.01 1840.59,491.112 1842.64,491.214 1844.68,491.315 1846.73,491.416 1848.77,491.517 1850.82,491.618 \n",
       "  1852.86,491.718 1854.91,491.818 1856.96,491.918 1859,492.017 1861.05,492.117 1863.09,492.215 1865.14,492.314 1867.18,492.412 1869.23,492.51 1871.27,492.608 \n",
       "  1873.32,492.705 1875.36,492.802 1877.41,492.899 1879.45,492.996 1881.5,493.092 1883.55,493.188 1885.59,493.284 1887.64,493.379 1889.68,493.474 1891.73,493.569 \n",
       "  1893.77,493.664 1895.82,493.758 1897.86,493.852 1899.91,493.946 1901.95,494.039 1904,494.133 1906.04,494.226 1908.09,494.318 1910.14,494.411 1912.18,494.503 \n",
       "  1914.23,494.595 1916.27,494.686 1918.32,494.777 1920.36,494.868 1922.41,494.959 1924.45,495.05 1926.5,495.14 1928.54,495.23 1930.59,495.32 1932.63,495.409 \n",
       "  1934.68,495.498 1936.73,495.587 1938.77,495.676 1940.82,495.764 1942.86,495.852 1944.91,495.94 1946.95,496.028 1949,496.115 1951.04,496.202 1953.09,496.289 \n",
       "  1955.13,496.376 1957.18,496.462 1959.23,496.548 1961.27,496.634 1963.32,496.72 1965.36,496.805 1967.41,496.89 1969.45,496.975 1971.5,497.059 1973.54,497.144 \n",
       "  1975.59,497.228 1977.63,497.312 1979.68,497.395 1981.72,497.479 1983.77,497.562 1985.82,497.645 1987.86,497.727 1989.91,497.81 1991.95,497.892 1994,497.974 \n",
       "  1996.04,498.055 1998.09,498.137 2000.13,498.218 2002.18,498.299 2004.22,498.38 2006.27,498.46 2008.31,498.54 2010.36,498.62 2012.41,498.7 2014.45,498.78 \n",
       "  2016.5,498.859 2018.54,498.938 2020.59,499.017 2022.63,499.095 2024.68,499.174 2026.72,499.252 2028.77,499.33 2030.81,499.408 2032.86,499.485 2034.9,499.562 \n",
       "  2036.95,499.639 2039,499.716 2041.04,499.793 2043.09,499.869 2045.13,499.945 2047.18,500.021 2049.22,500.097 2051.27,500.172 2053.31,500.247 2055.36,500.322 \n",
       "  2057.4,500.397 2059.45,500.472 2061.49,500.546 2063.54,500.62 2065.59,500.694 2067.63,500.768 2069.68,500.841 2071.72,500.915 2073.77,500.988 2075.81,501.061 \n",
       "  2077.86,501.133 2079.9,501.206 2081.95,501.278 2083.99,501.35 2086.04,501.422 2088.08,501.493 2090.13,501.565 2092.18,501.636 2094.22,501.707 2096.27,501.778 \n",
       "  2098.31,501.848 2100.36,501.919 2102.4,501.989 2104.45,502.059 2106.49,502.129 2108.54,502.198 2110.58,502.267 2112.63,502.337 2114.68,502.405 2116.72,502.474 \n",
       "  2118.77,502.543 2120.81,502.611 2122.86,502.679 2124.9,502.747 2126.95,502.815 2128.99,502.882 2131.04,502.95 2133.08,503.017 2135.13,503.084 2137.17,503.151 \n",
       "  2139.22,503.217 2141.27,503.284 2143.31,503.35 2145.36,503.416 2147.4,503.482 2149.45,503.547 2151.49,503.613 2153.54,503.678 2155.58,503.743 2157.63,503.808 \n",
       "  2159.67,503.873 2161.72,503.937 2163.76,504.001 2165.81,504.066 2167.86,504.129 2169.9,504.193 2171.95,504.257 2173.99,504.32 2176.04,504.383 2178.08,504.446 \n",
       "  2180.13,504.509 2182.17,504.572 2184.22,504.634 2186.26,504.697 2188.31,504.759 2190.35,504.821 2192.4,504.882 2194.45,504.944 2196.49,505.005 2198.54,505.067 \n",
       "  2200.58,505.128 2202.63,505.188 2204.67,505.249 2206.72,505.31 2208.76,505.37 2210.81,505.43 2212.85,505.49 2214.9,505.55 2216.94,505.61 2218.99,505.669 \n",
       "  2221.04,505.728 2223.08,505.788 2225.13,505.847 2227.17,505.905 2229.22,505.964 2231.26,506.022 2233.31,506.081 2235.35,506.139 2237.4,506.197 2239.44,506.255 \n",
       "  2241.49,506.312 2243.53,506.37 2245.58,506.427 2247.63,506.484 2249.67,506.541 2251.72,506.598 2253.76,506.654 2255.81,506.711 2257.85,506.767 2259.9,506.823 \n",
       "  2261.94,506.879 2263.99,506.935 2266.03,506.991 2268.08,507.046 2270.12,507.101 2272.17,507.157 2274.22,507.212 2276.26,507.266 2278.31,507.321 2280.35,507.376 \n",
       "  2282.4,507.43 2284.44,507.484 2286.49,507.538 2288.53,507.592 2290.58,507.646 2292.62,507.7 2294.67,507.753 2296.72,507.806 2298.76,507.859 2300.81,507.912 \n",
       "  2302.85,507.965 2304.9,508.018 2306.94,508.07 2308.99,508.123 2311.03,508.175 2313.08,508.227 2315.12,508.279 2317.17,508.331 2319.21,508.382 2321.26,508.434 \n",
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       "  1239.25,1063.15 1241.29,1063.39 1243.34,1063.64 1245.38,1063.88 1247.43,1064.13 1249.47,1064.37 1251.52,1064.61 1253.56,1064.86 1255.61,1065.1 1257.65,1065.34 \n",
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       "  1300.61,1070.22 1302.65,1070.45 1304.7,1070.67 1306.74,1070.9 1308.79,1071.12 1310.84,1071.34 1312.88,1071.56 1314.93,1071.78 1316.97,1072 1319.02,1072.22 \n",
       "  1321.06,1072.44 1323.11,1072.66 1325.15,1072.88 1327.2,1073.09 1329.24,1073.31 1331.29,1073.52 1333.33,1073.74 1335.38,1073.95 1337.43,1074.17 1339.47,1074.38 \n",
       "  1341.52,1074.59 1343.56,1074.8 1345.61,1075.01 1347.65,1075.22 1349.7,1075.43 1351.74,1075.64 1353.79,1075.85 1355.83,1076.06 1357.88,1076.27 1359.92,1076.47 \n",
       "  1361.97,1076.68 1364.02,1076.88 1366.06,1077.09 1368.11,1077.29 1370.15,1077.49 1372.2,1077.7 1374.24,1077.9 1376.29,1078.1 1378.33,1078.3 1380.38,1078.5 \n",
       "  1382.42,1078.7 1384.47,1078.9 1386.51,1079.1 1388.56,1079.3 1390.61,1079.49 1392.65,1079.69 1394.7,1079.88 1396.74,1080.08 1398.79,1080.27 1400.83,1080.47 \n",
       "  1402.88,1080.66 1404.92,1080.86 1406.97,1081.05 1409.01,1081.24 1411.06,1081.43 1413.1,1081.62 1415.15,1081.81 1417.2,1082 1419.24,1082.19 1421.29,1082.38 \n",
       "  1423.33,1082.57 1425.38,1082.75 1427.42,1082.94 1429.47,1083.13 1431.51,1083.31 1433.56,1083.5 1435.6,1083.68 1437.65,1083.86 1439.69,1084.05 1441.74,1084.23 \n",
       "  1443.79,1084.41 1445.83,1084.59 1447.88,1084.78 1449.92,1084.96 1451.97,1085.14 1454.01,1085.32 1456.06,1085.49 1458.1,1085.67 1460.15,1085.85 1462.19,1086.03 \n",
       "  1464.24,1086.2 1466.28,1086.38 1468.33,1086.56 1470.38,1086.73 1472.42,1086.91 1474.47,1087.08 1476.51,1087.25 1478.56,1087.43 1480.6,1087.6 1482.65,1087.77 \n",
       "  1484.69,1087.94 1486.74,1088.11 1488.78,1088.28 1490.83,1088.45 1492.88,1088.62 1494.92,1088.79 1496.97,1088.96 1499.01,1089.13 1501.06,1089.3 1503.1,1089.46 \n",
       "  1505.15,1089.63 1507.19,1089.79 1509.24,1089.96 1511.28,1090.12 1513.33,1090.29 1515.37,1090.45 1517.42,1090.62 1519.47,1090.78 1521.51,1090.94 1523.56,1091.1 \n",
       "  1525.6,1091.26 1527.65,1091.43 1529.69,1091.59 1531.74,1091.75 1533.78,1091.91 1535.83,1092.06 1537.87,1092.22 1539.92,1092.38 1541.96,1092.54 1544.01,1092.7 \n",
       "  1546.06,1092.85 1548.1,1093.01 1550.15,1093.16 1552.19,1093.32 1554.24,1093.47 1556.28,1093.63 1558.33,1093.78 1560.37,1093.94 1562.42,1094.09 1564.46,1094.24 \n",
       "  1566.51,1094.39 1568.55,1094.54 1570.6,1094.7 1572.65,1094.85 1574.69,1095 1576.74,1095.15 1578.78,1095.3 1580.83,1095.44 1582.87,1095.59 1584.92,1095.74 \n",
       "  1586.96,1095.89 1589.01,1096.03 1591.05,1096.18 1593.1,1096.33 1595.14,1096.47 1597.19,1096.62 1599.24,1096.76 1601.28,1096.91 1603.33,1097.05 1605.37,1097.2 \n",
       "  1607.42,1097.34 1609.46,1097.48 1611.51,1097.62 1613.55,1097.77 1615.6,1097.91 1617.64,1098.05 1619.69,1098.19 1621.73,1098.33 1623.78,1098.47 1625.83,1098.61 \n",
       "  1627.87,1098.75 1629.92,1098.88 1631.96,1099.02 1634.01,1099.16 1636.05,1099.3 1638.1,1099.43 1640.14,1099.57 1642.19,1099.71 1644.23,1099.84 1646.28,1099.98 \n",
       "  1648.33,1100.11 1650.37,1100.25 1652.42,1100.38 1654.46,1100.51 1656.51,1100.65 1658.55,1100.78 1660.6,1100.91 1662.64,1101.05 1664.69,1101.18 1666.73,1101.31 \n",
       "  1668.78,1101.44 1670.82,1101.57 1672.87,1101.7 1674.92,1101.83 1676.96,1101.96 1679.01,1102.09 1681.05,1102.22 1683.1,1102.34 1685.14,1102.47 1687.19,1102.6 \n",
       "  1689.23,1102.73 1691.28,1102.85 1693.32,1102.98 1695.37,1103.11 1697.41,1103.23 1699.46,1103.36 1701.51,1103.48 1703.55,1103.61 1705.6,1103.73 1707.64,1103.85 \n",
       "  1709.69,1103.98 1711.73,1104.1 1713.78,1104.22 1715.82,1104.34 1717.87,1104.47 1719.91,1104.59 1721.96,1104.71 1724,1104.83 1726.05,1104.95 1728.1,1105.07 \n",
       "  1730.14,1105.19 1732.19,1105.31 1734.23,1105.43 1736.28,1105.55 1738.32,1105.67 1740.37,1105.78 1742.41,1105.9 1744.46,1106.02 1746.5,1106.14 1748.55,1106.25 \n",
       "  1750.59,1106.37 1752.64,1106.48 1754.69,1106.6 1756.73,1106.71 1758.78,1106.83 1760.82,1106.94 1762.87,1107.06 1764.91,1107.17 1766.96,1107.29 1769,1107.4 \n",
       "  1771.05,1107.51 1773.09,1107.62 1775.14,1107.74 1777.18,1107.85 1779.23,1107.96 1781.28,1108.07 1783.32,1108.18 1785.37,1108.29 1787.41,1108.4 1789.46,1108.51 \n",
       "  1791.5,1108.62 1793.55,1108.73 1795.59,1108.84 1797.64,1108.95 1799.68,1109.06 1801.73,1109.17 1803.78,1109.27 1805.82,1109.38 1807.87,1109.49 1809.91,1109.59 \n",
       "  1811.96,1109.7 1814,1109.81 1816.05,1109.91 1818.09,1110.02 1820.14,1110.12 1822.18,1110.23 1824.23,1110.33 1826.27,1110.44 1828.32,1110.54 1830.37,1110.64 \n",
       "  1832.41,1110.75 1834.46,1110.85 1836.5,1110.95 1838.55,1111.06 1840.59,1111.16 1842.64,1111.26 1844.68,1111.36 1846.73,1111.46 1848.77,1111.56 1850.82,1111.66 \n",
       "  1852.86,1111.76 1854.91,1111.86 1856.96,1111.96 1859,1112.06 1861.05,1112.16 1863.09,1112.26 1865.14,1112.36 1867.18,1112.46 1869.23,1112.56 1871.27,1112.65 \n",
       "  1873.32,1112.75 1875.36,1112.85 1877.41,1112.95 1879.45,1113.04 1881.5,1113.14 1883.55,1113.23 1885.59,1113.33 1887.64,1113.43 1889.68,1113.52 1891.73,1113.62 \n",
       "  1893.77,1113.71 1895.82,1113.8 1897.86,1113.9 1899.91,1113.99 1901.95,1114.09 1904,1114.18 1906.04,1114.27 1908.09,1114.36 1910.14,1114.46 1912.18,1114.55 \n",
       "  1914.23,1114.64 1916.27,1114.73 1918.32,1114.82 1920.36,1114.91 1922.41,1115.01 1924.45,1115.1 1926.5,1115.19 1928.54,1115.28 1930.59,1115.37 1932.63,1115.46 \n",
       "  1934.68,1115.54 1936.73,1115.63 1938.77,1115.72 1940.82,1115.81 1942.86,1115.9 1944.91,1115.99 1946.95,1116.07 1949,1116.16 1951.04,1116.25 1953.09,1116.34 \n",
       "  1955.13,1116.42 1957.18,1116.51 1959.23,1116.59 1961.27,1116.68 1963.32,1116.77 1965.36,1116.85 1967.41,1116.94 1969.45,1117.02 1971.5,1117.11 1973.54,1117.19 \n",
       "  1975.59,1117.27 1977.63,1117.36 1979.68,1117.44 1981.72,1117.53 1983.77,1117.61 1985.82,1117.69 1987.86,1117.77 1989.91,1117.86 1991.95,1117.94 1994,1118.02 \n",
       "  1996.04,1118.1 1998.09,1118.18 2000.13,1118.26 2002.18,1118.35 2004.22,1118.43 2006.27,1118.51 2008.31,1118.59 2010.36,1118.67 2012.41,1118.75 2014.45,1118.83 \n",
       "  2016.5,1118.91 2018.54,1118.98 2020.59,1119.06 2022.63,1119.14 2024.68,1119.22 2026.72,1119.3 2028.77,1119.38 2030.81,1119.45 2032.86,1119.53 2034.9,1119.61 \n",
       "  2036.95,1119.69 2039,1119.76 2041.04,1119.84 2043.09,1119.92 2045.13,1119.99 2047.18,1120.07 2049.22,1120.14 2051.27,1120.22 2053.31,1120.29 2055.36,1120.37 \n",
       "  2057.4,1120.44 2059.45,1120.52 2061.49,1120.59 2063.54,1120.67 2065.59,1120.74 2067.63,1120.81 2069.68,1120.89 2071.72,1120.96 2073.77,1121.03 2075.81,1121.11 \n",
       "  2077.86,1121.18 2079.9,1121.25 2081.95,1121.32 2083.99,1121.4 2086.04,1121.47 2088.08,1121.54 2090.13,1121.61 2092.18,1121.68 2094.22,1121.75 2096.27,1121.82 \n",
       "  2098.31,1121.89 2100.36,1121.97 2102.4,1122.04 2104.45,1122.11 2106.49,1122.17 2108.54,1122.24 2110.58,1122.31 2112.63,1122.38 2114.68,1122.45 2116.72,1122.52 \n",
       "  2118.77,1122.59 2120.81,1122.66 2122.86,1122.73 2124.9,1122.79 2126.95,1122.86 2128.99,1122.93 2131.04,1123 2133.08,1123.06 2135.13,1123.13 2137.17,1123.2 \n",
       "  2139.22,1123.26 2141.27,1123.33 2143.31,1123.4 2145.36,1123.46 2147.4,1123.53 2149.45,1123.59 2151.49,1123.66 2153.54,1123.72 2155.58,1123.79 2157.63,1123.85 \n",
       "  2159.67,1123.92 2161.72,1123.98 2163.76,1124.05 2165.81,1124.11 2167.86,1124.18 2169.9,1124.24 2171.95,1124.3 2173.99,1124.37 2176.04,1124.43 2178.08,1124.49 \n",
       "  2180.13,1124.56 2182.17,1124.62 2184.22,1124.68 2186.26,1124.74 2188.31,1124.81 2190.35,1124.87 2192.4,1124.93 2194.45,1124.99 2196.49,1125.05 2198.54,1125.11 \n",
       "  2200.58,1125.17 2202.63,1125.23 2204.67,1125.3 2206.72,1125.36 2208.76,1125.42 2210.81,1125.48 2212.85,1125.54 2214.9,1125.6 2216.94,1125.66 2218.99,1125.72 \n",
       "  2221.04,1125.77 2223.08,1125.83 2225.13,1125.89 2227.17,1125.95 2229.22,1126.01 2231.26,1126.07 2233.31,1126.13 2235.35,1126.19 2237.4,1126.24 2239.44,1126.3 \n",
       "  2241.49,1126.36 2243.53,1126.42 2245.58,1126.47 2247.63,1126.53 2249.67,1126.59 2251.72,1126.64 2253.76,1126.7 2255.81,1126.76 2257.85,1126.81 2259.9,1126.87 \n",
       "  2261.94,1126.93 2263.99,1126.98 2266.03,1127.04 2268.08,1127.09 2270.12,1127.15 2272.17,1127.2 2274.22,1127.26 2276.26,1127.31 2278.31,1127.37 2280.35,1127.42 \n",
       "  2282.4,1127.48 2284.44,1127.53 2286.49,1127.58 2288.53,1127.64 2290.58,1127.69 2292.62,1127.75 2294.67,1127.8 2296.72,1127.85 2298.76,1127.91 2300.81,1127.96 \n",
       "  2302.85,1128.01 2304.9,1128.06 2306.94,1128.12 2308.99,1128.17 2311.03,1128.22 2313.08,1128.27 2315.12,1128.33 2317.17,1128.38 2319.21,1128.43 2321.26,1128.48 \n",
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       "  298.365,1391.11 300.41,1389.92 302.456,1388.73 304.501,1387.55 306.546,1386.38 308.592,1385.21 310.637,1384.04 312.683,1382.88 314.728,1381.72 316.773,1380.56 \n",
       "  318.819,1379.42 320.864,1378.27 322.91,1377.13 324.955,1376 327,1374.86 329.046,1373.74 331.091,1372.62 333.136,1371.5 335.182,1370.38 337.227,1369.27 \n",
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       "  359.727,1357.35 361.772,1356.29 363.817,1355.24 365.863,1354.19 367.908,1353.14 369.954,1352.1 371.999,1351.06 374.044,1350.03 376.09,1349 378.135,1347.97 \n",
       "  380.181,1346.95 382.226,1345.93 384.271,1344.91 386.317,1343.9 388.362,1342.89 390.408,1341.89 392.453,1340.89 394.498,1339.89 396.544,1338.9 398.589,1337.91 \n",
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       "  993.799,1159.37 995.844,1159 997.89,1158.65 999.935,1158.29 1001.98,1157.93 1004.03,1157.58 1006.07,1157.22 1008.12,1156.87 1010.16,1156.52 1012.21,1156.16 \n",
       "  1014.25,1155.81 1016.3,1155.47 1018.34,1155.12 1020.39,1154.77 1022.43,1154.43 1024.48,1154.08 1026.53,1153.74 1028.57,1153.4 1030.62,1153.06 1032.66,1152.72 \n",
       "  1034.71,1152.38 1036.75,1152.04 1038.8,1151.7 1040.84,1151.37 1042.89,1151.03 1044.93,1150.7 1046.98,1150.37 1049.02,1150.03 1051.07,1149.7 1053.12,1149.37 \n",
       "  1055.16,1149.05 1057.21,1148.72 1059.25,1148.39 1061.3,1148.07 1063.34,1147.74 1065.39,1147.42 1067.43,1147.1 1069.48,1146.78 1071.52,1146.46 1073.57,1146.14 \n",
       "  1075.61,1145.82 1077.66,1145.5 1079.71,1145.19 1081.75,1144.87 1083.8,1144.56 1085.84,1144.25 1087.89,1143.93 1089.93,1143.62 1091.98,1143.31 1094.02,1143 \n",
       "  1096.07,1142.7 1098.11,1142.39 1100.16,1142.08 1102.2,1141.78 1104.25,1141.47 1106.3,1141.17 1108.34,1140.87 1110.39,1140.57 1112.43,1140.27 1114.48,1139.97 \n",
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       "  1136.98,1136.73 1139.02,1136.45 1141.07,1136.16 1143.11,1135.87 1145.16,1135.59 1147.2,1135.3 1149.25,1135.02 1151.29,1134.73 1153.34,1134.45 1155.39,1134.17 \n",
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       "  1198.34,1128.47 1200.38,1128.2 1202.43,1127.94 1204.47,1127.68 1206.52,1127.42 1208.57,1127.16 1210.61,1126.9 1212.66,1126.64 1214.7,1126.39 1216.75,1126.13 \n",
       "  1218.79,1125.88 1220.84,1125.62 1222.88,1125.37 1224.93,1125.12 1226.97,1124.86 1229.02,1124.61 1231.06,1124.36 1233.11,1124.11 1235.16,1123.86 1237.2,1123.62 \n",
       "  1239.25,1123.37 1241.29,1123.12 1243.34,1122.88 1245.38,1122.63 1247.43,1122.39 1249.47,1122.14 1251.52,1121.9 1253.56,1121.66 1255.61,1121.42 1257.65,1121.18 \n",
       "  1259.7,1120.94 1261.75,1120.7 1263.79,1120.46 1265.84,1120.22 1267.88,1119.98 1269.93,1119.75 1271.97,1119.51 1274.02,1119.28 1276.06,1119.04 1278.11,1118.81 \n",
       "  1280.15,1118.58 1282.2,1118.35 1284.24,1118.11 1286.29,1117.88 1288.34,1117.65 1290.38,1117.42 1292.43,1117.2 1294.47,1116.97 1296.52,1116.74 1298.56,1116.52 \n",
       "  1300.61,1116.29 1302.65,1116.07 1304.7,1115.84 1306.74,1115.62 1308.79,1115.39 1310.84,1115.17 1312.88,1114.95 1314.93,1114.73 1316.97,1114.51 1319.02,1114.29 \n",
       "  1321.06,1114.07 1323.11,1113.85 1325.15,1113.64 1327.2,1113.42 1329.24,1113.2 1331.29,1112.99 1333.33,1112.77 1335.38,1112.56 1337.43,1112.35 1339.47,1112.13 \n",
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       "  1464.24,1100.31 1466.28,1100.13 1468.33,1099.96 1470.38,1099.78 1472.42,1099.61 1474.47,1099.43 1476.51,1099.26 1478.56,1099.09 1480.6,1098.91 1482.65,1098.74 \n",
       "  1484.69,1098.57 1486.74,1098.4 1488.78,1098.23 1490.83,1098.06 1492.88,1097.89 1494.92,1097.72 1496.97,1097.55 1499.01,1097.39 1501.06,1097.22 1503.1,1097.05 \n",
       "  1505.15,1096.88 1507.19,1096.72 1509.24,1096.55 1511.28,1096.39 1513.33,1096.22 1515.37,1096.06 1517.42,1095.9 1519.47,1095.73 1521.51,1095.57 1523.56,1095.41 \n",
       "  1525.6,1095.25 1527.65,1095.09 1529.69,1094.93 1531.74,1094.77 1533.78,1094.61 1535.83,1094.45 1537.87,1094.29 1539.92,1094.13 1541.96,1093.97 1544.01,1093.82 \n",
       "  1546.06,1093.66 1548.1,1093.5 1550.15,1093.35 1552.19,1093.19 1554.24,1093.04 1556.28,1092.88 1558.33,1092.73 1560.37,1092.58 1562.42,1092.42 1564.46,1092.27 \n",
       "  1566.51,1092.12 1568.55,1091.97 1570.6,1091.82 1572.65,1091.67 1574.69,1091.52 1576.74,1091.37 1578.78,1091.22 1580.83,1091.07 1582.87,1090.92 1584.92,1090.77 \n",
       "  1586.96,1090.63 1589.01,1090.48 1591.05,1090.33 1593.1,1090.19 1595.14,1090.04 1597.19,1089.89 1599.24,1089.75 1601.28,1089.61 1603.33,1089.46 1605.37,1089.32 \n",
       "  1607.42,1089.17 1609.46,1089.03 1611.51,1088.89 1613.55,1088.75 1615.6,1088.61 1617.64,1088.47 1619.69,1088.33 1621.73,1088.18 1623.78,1088.05 1625.83,1087.91 \n",
       "  1627.87,1087.77 1629.92,1087.63 1631.96,1087.49 1634.01,1087.35 1636.05,1087.22 1638.1,1087.08 1640.14,1086.94 1642.19,1086.81 1644.23,1086.67 1646.28,1086.54 \n",
       "  1648.33,1086.4 1650.37,1086.27 1652.42,1086.13 1654.46,1086 1656.51,1085.87 1658.55,1085.73 1660.6,1085.6 1662.64,1085.47 1664.69,1085.34 1666.73,1085.2 \n",
       "  1668.78,1085.07 1670.82,1084.94 1672.87,1084.81 1674.92,1084.68 1676.96,1084.55 1679.01,1084.43 1681.05,1084.3 1683.1,1084.17 1685.14,1084.04 1687.19,1083.91 \n",
       "  1689.23,1083.79 1691.28,1083.66 1693.32,1083.53 1695.37,1083.41 1697.41,1083.28 1699.46,1083.16 1701.51,1083.03 1703.55,1082.91 1705.6,1082.78 1707.64,1082.66 \n",
       "  1709.69,1082.54 1711.73,1082.41 1713.78,1082.29 1715.82,1082.17 1717.87,1082.05 1719.91,1081.93 1721.96,1081.8 1724,1081.68 1726.05,1081.56 1728.1,1081.44 \n",
       "  1730.14,1081.32 1732.19,1081.2 1734.23,1081.08 1736.28,1080.97 1738.32,1080.85 1740.37,1080.73 1742.41,1080.61 1744.46,1080.49 1746.5,1080.38 1748.55,1080.26 \n",
       "  1750.59,1080.15 1752.64,1080.03 1754.69,1079.91 1756.73,1079.8 1758.78,1079.68 1760.82,1079.57 1762.87,1079.45 1764.91,1079.34 1766.96,1079.23 1769,1079.11 \n",
       "  1771.05,1079 1773.09,1078.89 1775.14,1078.78 1777.18,1078.66 1779.23,1078.55 1781.28,1078.44 1783.32,1078.33 1785.37,1078.22 1787.41,1078.11 1789.46,1078 \n",
       "  1791.5,1077.89 1793.55,1077.78 1795.59,1077.67 1797.64,1077.56 1799.68,1077.46 1801.73,1077.35 1803.78,1077.24 1805.82,1077.13 1807.87,1077.03 1809.91,1076.92 \n",
       "  1811.96,1076.81 1814,1076.71 1816.05,1076.6 1818.09,1076.5 1820.14,1076.39 1822.18,1076.29 1824.23,1076.18 1826.27,1076.08 1828.32,1075.97 1830.37,1075.87 \n",
       "  1832.41,1075.77 1834.46,1075.66 1836.5,1075.56 1838.55,1075.46 1840.59,1075.36 1842.64,1075.25 1844.68,1075.15 1846.73,1075.05 1848.77,1074.95 1850.82,1074.85 \n",
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       "  1873.32,1073.76 1875.36,1073.66 1877.41,1073.57 1879.45,1073.47 1881.5,1073.37 1883.55,1073.28 1885.59,1073.18 1887.64,1073.09 1889.68,1072.99 1891.73,1072.9 \n",
       "  1893.77,1072.8 1895.82,1072.71 1897.86,1072.61 1899.91,1072.52 1901.95,1072.43 1904,1072.33 1906.04,1072.24 1908.09,1072.15 1910.14,1072.06 1912.18,1071.96 \n",
       "  1914.23,1071.87 1916.27,1071.78 1918.32,1071.69 1920.36,1071.6 1922.41,1071.51 1924.45,1071.42 1926.5,1071.33 1928.54,1071.24 1930.59,1071.15 1932.63,1071.06 \n",
       "  1934.68,1070.97 1936.73,1070.88 1938.77,1070.79 1940.82,1070.7 1942.86,1070.61 1944.91,1070.53 1946.95,1070.44 1949,1070.35 1951.04,1070.26 1953.09,1070.18 \n",
       "  1955.13,1070.09 1957.18,1070 1959.23,1069.92 1961.27,1069.83 1963.32,1069.75 1965.36,1069.66 1967.41,1069.58 1969.45,1069.49 1971.5,1069.41 1973.54,1069.32 \n",
       "  1975.59,1069.24 1977.63,1069.16 1979.68,1069.07 1981.72,1068.99 1983.77,1068.91 1985.82,1068.82 1987.86,1068.74 1989.91,1068.66 1991.95,1068.58 1994,1068.49 \n",
       "  1996.04,1068.41 1998.09,1068.33 2000.13,1068.25 2002.18,1068.17 2004.22,1068.09 2006.27,1068.01 2008.31,1067.93 2010.36,1067.85 2012.41,1067.77 2014.45,1067.69 \n",
       "  2016.5,1067.61 2018.54,1067.53 2020.59,1067.45 2022.63,1067.37 2024.68,1067.29 2026.72,1067.21 2028.77,1067.14 2030.81,1067.06 2032.86,1066.98 2034.9,1066.9 \n",
       "  2036.95,1066.83 2039,1066.75 2041.04,1066.67 2043.09,1066.6 2045.13,1066.52 2047.18,1066.45 2049.22,1066.37 2051.27,1066.29 2053.31,1066.22 2055.36,1066.14 \n",
       "  2057.4,1066.07 2059.45,1066 2061.49,1065.92 2063.54,1065.85 2065.59,1065.77 2067.63,1065.7 2069.68,1065.63 2071.72,1065.55 2073.77,1065.48 2075.81,1065.41 \n",
       "  2077.86,1065.33 2079.9,1065.26 2081.95,1065.19 2083.99,1065.12 2086.04,1065.05 2088.08,1064.97 2090.13,1064.9 2092.18,1064.83 2094.22,1064.76 2096.27,1064.69 \n",
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       "  2139.22,1063.25 2141.27,1063.18 2143.31,1063.12 2145.36,1063.05 2147.4,1062.99 2149.45,1062.92 2151.49,1062.85 2153.54,1062.79 2155.58,1062.72 2157.63,1062.66 \n",
       "  2159.67,1062.59 2161.72,1062.53 2163.76,1062.47 2165.81,1062.4 2167.86,1062.34 2169.9,1062.27 2171.95,1062.21 2173.99,1062.15 2176.04,1062.08 2178.08,1062.02 \n",
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       "  2200.58,1061.34 2202.63,1061.28 2204.67,1061.22 2206.72,1061.16 2208.76,1061.1 2210.81,1061.04 2212.85,1060.98 2214.9,1060.92 2216.94,1060.86 2218.99,1060.8 \n",
       "  2221.04,1060.74 2223.08,1060.68 2225.13,1060.62 2227.17,1060.56 2229.22,1060.5 2231.26,1060.44 2233.31,1060.39 2235.35,1060.33 2237.4,1060.27 2239.44,1060.21 \n",
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      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob4 = ODEProblem(simpleODErev!,u₀,tspan,p)\n",
    "sol4 = solve(prob4)\n",
    "plot(sol4,label=[\"a\",\"b\",\"c\"])\n",
    "title!(\"ODE solver in Julia\")\n",
    "xlabel!(\"Time [s]\")\n",
    "ylabel!(\"Concentration [M]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "or, using the DSL notation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(::abetterway{getfield(Main, Symbol(\"##11#15\")),getfield(Main, Symbol(\"##12#16\")),getfield(Main, Symbol(\"##13#17\")),Nothing,Nothing,getfield(Main, Symbol(\"##14#18\")),Expr,Expr}) (generic function with 2 methods)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simpleODE2_rev! = @ode_def abetterway begin\n",
    "  da = -k1*a*b+k2*c\n",
    "  db = -k1*a*b+k2*c\n",
    "  dc = k1*a*b-k2*c\n",
    "    end k1 k2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
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       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:66px; text-anchor:middle;\" transform=\"rotate(0, 1299.59, 1590.4)\" x=\"1299.59\" y=\"1590.4\">Time [s]</text>\n",
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       "  277.911,163.187 279.956,164.426 282.002,165.66 284.047,166.889 286.092,168.113 288.138,169.332 290.183,170.546 292.229,171.756 294.274,172.961 296.319,174.161 \n",
       "  298.365,175.356 300.41,176.546 302.456,177.732 304.501,178.913 306.546,180.09 308.592,181.262 310.637,182.429 312.683,183.591 314.728,184.749 316.773,185.903 \n",
       "  318.819,187.052 320.864,188.196 322.91,189.336 324.955,190.472 327,191.603 329.046,192.729 331.091,193.852 333.136,194.97 335.182,196.083 337.227,197.192 \n",
       "  339.273,198.297 341.318,199.398 343.363,200.494 345.409,201.586 347.454,202.674 349.5,203.758 351.545,204.837 353.59,205.913 355.636,206.984 357.681,208.051 \n",
       "  359.727,209.114 361.772,210.172 363.817,211.227 365.863,212.278 367.908,213.324 369.954,214.367 371.999,215.406 374.044,216.44 376.09,217.471 378.135,218.498 \n",
       "  380.181,219.521 382.226,220.54 384.271,221.555 386.317,222.566 388.362,223.573 390.408,224.577 392.453,225.576 394.498,226.572 396.544,227.565 398.589,228.553 \n",
       "  400.635,229.538 402.68,230.518 404.725,231.496 406.771,232.469 408.816,233.439 410.861,234.405 412.907,235.368 414.952,236.327 416.998,237.282 419.043,238.234 \n",
       "  421.088,239.182 423.134,240.127 425.179,241.068 427.225,242.005 429.27,242.939 431.315,243.87 433.361,244.797 435.406,245.72 437.452,246.641 439.497,247.557 \n",
       "  441.542,248.471 443.588,249.38 445.633,250.287 447.679,251.19 449.724,252.09 451.769,252.986 453.815,253.88 455.86,254.769 457.906,255.656 459.951,256.539 \n",
       "  461.996,257.419 464.042,258.296 466.087,259.169 468.133,260.04 470.178,260.907 472.223,261.771 474.269,262.631 476.314,263.489 478.359,264.343 480.405,265.195 \n",
       "  482.45,266.043 484.496,266.888 486.541,267.73 488.586,268.568 490.632,269.404 492.677,270.237 494.723,271.067 496.768,271.893 498.813,272.717 500.859,273.538 \n",
       "  502.904,274.355 504.95,275.17 506.995,275.982 509.04,276.79 511.086,277.596 513.131,278.399 515.177,279.199 517.222,279.996 519.267,280.79 521.313,281.582 \n",
       "  523.358,282.37 525.404,283.156 527.449,283.939 529.494,284.719 531.54,285.496 533.585,286.27 535.631,287.042 537.676,287.81 539.721,288.577 541.767,289.34 \n",
       "  543.812,290.1 545.858,290.858 547.903,291.613 549.948,292.366 551.994,293.115 554.039,293.862 556.084,294.607 558.13,295.348 560.175,296.087 562.221,296.824 \n",
       "  564.266,297.558 566.311,298.289 568.357,299.017 570.402,299.743 572.448,300.467 574.493,301.187 576.538,301.906 578.584,302.621 580.629,303.335 582.675,304.045 \n",
       "  584.72,304.753 586.765,305.459 588.811,306.162 590.856,306.863 592.902,307.561 594.947,308.257 596.992,308.95 599.038,309.641 601.083,310.329 603.129,311.015 \n",
       "  605.174,311.698 607.219,312.38 609.265,313.058 611.31,313.735 613.356,314.409 615.401,315.08 617.446,315.749 619.492,316.416 621.537,317.081 623.582,317.743 \n",
       "  625.628,318.403 627.673,319.061 629.719,319.716 631.764,320.369 633.809,321.02 635.855,321.668 637.9,322.314 639.946,322.958 641.991,323.6 644.036,324.239 \n",
       "  646.082,324.877 648.127,325.512 650.173,326.144 652.218,326.775 654.263,327.403 656.309,328.03 658.354,328.654 660.4,329.276 662.445,329.895 664.49,330.513 \n",
       "  666.536,331.129 668.581,331.742 670.627,332.353 672.672,332.962 674.717,333.569 676.763,334.174 678.808,334.777 680.854,335.378 682.899,335.977 684.944,336.573 \n",
       "  686.99,337.168 689.035,337.76 691.081,338.351 693.126,338.939 695.171,339.526 697.217,340.11 699.262,340.693 701.307,341.273 703.353,341.852 705.398,342.428 \n",
       "  707.444,343.003 709.489,343.575 711.534,344.146 713.58,344.715 715.625,345.281 717.671,345.846 719.716,346.409 721.761,346.97 723.807,347.529 725.852,348.086 \n",
       "  727.898,348.641 729.943,349.195 731.988,349.746 734.034,350.296 736.079,350.843 738.125,351.389 740.17,351.933 742.215,352.476 744.261,353.016 746.306,353.554 \n",
       "  748.352,354.091 750.397,354.626 752.442,355.159 754.488,355.69 756.533,356.22 758.579,356.748 760.624,357.273 762.669,357.798 764.715,358.32 766.76,358.841 \n",
       "  768.805,359.359 770.851,359.877 772.896,360.392 774.942,360.906 776.987,361.417 779.032,361.928 781.078,362.436 783.123,362.943 785.169,363.448 787.214,363.951 \n",
       "  789.259,364.453 791.305,364.953 793.35,365.452 795.396,365.948 797.441,366.443 799.486,366.937 801.532,367.428 803.577,367.919 805.623,368.407 807.668,368.894 \n",
       "  809.713,369.379 811.759,369.863 813.804,370.345 815.85,370.825 817.895,371.304 819.94,371.781 821.986,372.257 824.031,372.731 826.077,373.203 828.122,373.674 \n",
       "  830.167,374.143 832.213,374.611 834.258,375.077 836.304,375.542 838.349,376.005 840.394,376.467 842.44,376.927 844.485,377.385 846.53,377.842 848.576,378.298 \n",
       "  850.621,378.752 852.667,379.204 854.712,379.655 856.757,380.105 858.803,380.553 860.848,380.999 862.894,381.444 864.939,381.888 866.984,382.33 869.03,382.771 \n",
       "  871.075,383.21 873.121,383.648 875.166,384.084 877.211,384.519 879.257,384.952 881.302,385.384 883.348,385.815 885.393,386.244 887.438,386.672 889.484,387.099 \n",
       "  891.529,387.524 893.575,387.947 895.62,388.369 897.665,388.79 899.711,389.21 901.756,389.628 903.802,390.045 905.847,390.46 907.892,390.874 909.938,391.287 \n",
       "  911.983,391.698 914.029,392.108 916.074,392.517 918.119,392.924 920.165,393.33 922.21,393.735 924.255,394.138 926.301,394.54 928.346,394.941 930.392,395.34 \n",
       "  932.437,395.738 934.482,396.135 936.528,396.531 938.573,396.925 940.619,397.318 942.664,397.71 944.709,398.1 946.755,398.489 948.8,398.877 950.846,399.264 \n",
       "  952.891,399.649 954.936,400.034 956.982,400.416 959.027,400.798 961.073,401.179 963.118,401.558 965.163,401.936 967.209,402.313 969.254,402.688 971.3,403.063 \n",
       "  973.345,403.436 975.39,403.808 977.436,404.178 979.481,404.548 981.527,404.916 983.572,405.283 985.617,405.649 987.663,406.014 989.708,406.378 991.753,406.74 \n",
       "  993.799,407.102 995.844,407.462 997.89,407.821 999.935,408.179 1001.98,408.536 1004.03,408.891 1006.07,409.246 1008.12,409.599 1010.16,409.951 1012.21,410.302 \n",
       "  1014.25,410.652 1016.3,411.001 1018.34,411.348 1020.39,411.695 1022.43,412.04 1024.48,412.385 1026.53,412.728 1028.57,413.07 1030.62,413.411 1032.66,413.751 \n",
       "  1034.71,414.09 1036.75,414.428 1038.8,414.765 1040.84,415.1 1042.89,415.435 1044.93,415.768 1046.98,416.101 1049.02,416.432 1051.07,416.763 1053.12,417.092 \n",
       "  1055.16,417.42 1057.21,417.748 1059.25,418.074 1061.3,418.399 1063.34,418.723 1065.39,419.046 1067.43,419.368 1069.48,419.689 1071.52,420.009 1073.57,420.328 \n",
       "  1075.61,420.646 1077.66,420.963 1079.71,421.279 1081.75,421.594 1083.8,421.908 1085.84,422.221 1087.89,422.533 1089.93,422.844 1091.98,423.154 1094.02,423.463 \n",
       "  1096.07,423.772 1098.11,424.079 1100.16,424.385 1102.2,424.69 1104.25,424.994 1106.3,425.297 1108.34,425.6 1110.39,425.901 1112.43,426.201 1114.48,426.501 \n",
       "  1116.52,426.799 1118.57,427.097 1120.61,427.394 1122.66,427.689 1124.7,427.984 1126.75,428.278 1128.79,428.571 1130.84,428.863 1132.89,429.154 1134.93,429.444 \n",
       "  1136.98,429.733 1139.02,430.022 1141.07,430.309 1143.11,430.596 1145.16,430.881 1147.2,431.166 1149.25,431.45 1151.29,431.733 1153.34,432.015 1155.39,432.296 \n",
       "  1157.43,432.576 1159.48,432.856 1161.52,433.134 1163.57,433.412 1165.61,433.689 1167.66,433.965 1169.7,434.24 1171.75,434.514 1173.79,434.787 1175.84,435.06 \n",
       "  1177.88,435.331 1179.93,435.602 1181.98,435.872 1184.02,436.141 1186.07,436.41 1188.11,436.677 1190.16,436.944 1192.2,437.209 1194.25,437.474 1196.29,437.738 \n",
       "  1198.34,438.002 1200.38,438.264 1202.43,438.526 1204.47,438.787 1206.52,439.047 1208.57,439.306 1210.61,439.564 1212.66,439.822 1214.7,440.079 1216.75,440.335 \n",
       "  1218.79,440.59 1220.84,440.844 1222.88,441.098 1224.93,441.351 1226.97,441.603 1229.02,441.854 1231.06,442.105 1233.11,442.355 1235.16,442.603 1237.2,442.852 \n",
       "  1239.25,443.099 1241.29,443.346 1243.34,443.592 1245.38,443.837 1247.43,444.081 1249.47,444.325 1251.52,444.568 1253.56,444.81 1255.61,445.051 1257.65,445.292 \n",
       "  1259.7,445.532 1261.75,445.771 1263.79,446.009 1265.84,446.247 1267.88,446.484 1269.93,446.72 1271.97,446.955 1274.02,447.19 1276.06,447.424 1278.11,447.657 \n",
       "  1280.15,447.89 1282.2,448.122 1284.24,448.353 1286.29,448.583 1288.34,448.813 1290.38,449.042 1292.43,449.27 1294.47,449.498 1296.52,449.725 1298.56,449.951 \n",
       "  1300.61,450.177 1302.65,450.402 1304.7,450.626 1306.74,450.849 1308.79,451.072 1310.84,451.294 1312.88,451.515 1314.93,451.736 1316.97,451.956 1319.02,452.176 \n",
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       "  1505.15,469.582 1507.19,469.748 1509.24,469.914 1511.28,470.078 1513.33,470.243 1515.37,470.407 1517.42,470.57 1519.47,470.733 1521.51,470.895 1523.56,471.057 \n",
       "  1525.6,471.218 1527.65,471.379 1529.69,471.54 1531.74,471.7 1533.78,471.859 1535.83,472.018 1537.87,472.177 1539.92,472.335 1541.96,472.492 1544.01,472.649 \n",
       "  1546.06,472.806 1548.1,472.962 1550.15,473.118 1552.19,473.273 1554.24,473.428 1556.28,473.582 1558.33,473.736 1560.37,473.889 1562.42,474.042 1564.46,474.194 \n",
       "  1566.51,474.346 1568.55,474.498 1570.6,474.649 1572.65,474.8 1574.69,474.95 1576.74,475.099 1578.78,475.249 1580.83,475.397 1582.87,475.546 1584.92,475.694 \n",
       "  1586.96,475.841 1589.01,475.988 1591.05,476.135 1593.1,476.281 1595.14,476.427 1597.19,476.572 1599.24,476.717 1601.28,476.861 1603.33,477.005 1605.37,477.149 \n",
       "  1607.42,477.292 1609.46,477.435 1611.51,477.577 1613.55,477.719 1615.6,477.86 1617.64,478.001 1619.69,478.142 1621.73,478.282 1623.78,478.422 1625.83,478.561 \n",
       "  1627.87,478.7 1629.92,478.838 1631.96,478.976 1634.01,479.114 1636.05,479.251 1638.1,479.388 1640.14,479.525 1642.19,479.661 1644.23,479.796 1646.28,479.932 \n",
       "  1648.33,480.066 1650.37,480.201 1652.42,480.335 1654.46,480.468 1656.51,480.602 1658.55,480.735 1660.6,480.867 1662.64,480.999 1664.69,481.131 1666.73,481.262 \n",
       "  1668.78,481.393 1670.82,481.523 1672.87,481.653 1674.92,481.783 1676.96,481.912 1679.01,482.041 1681.05,482.17 1683.1,482.298 1685.14,482.426 1687.19,482.553 \n",
       "  1689.23,482.68 1691.28,482.807 1693.32,482.933 1695.37,483.059 1697.41,483.185 1699.46,483.31 1701.51,483.435 1703.55,483.559 1705.6,483.683 1707.64,483.807 \n",
       "  1709.69,483.93 1711.73,484.053 1713.78,484.176 1715.82,484.298 1717.87,484.42 1719.91,484.542 1721.96,484.663 1724,484.783 1726.05,484.904 1728.1,485.024 \n",
       "  1730.14,485.144 1732.19,485.263 1734.23,485.382 1736.28,485.501 1738.32,485.619 1740.37,485.737 1742.41,485.855 1744.46,485.972 1746.5,486.089 1748.55,486.206 \n",
       "  1750.59,486.322 1752.64,486.438 1754.69,486.553 1756.73,486.668 1758.78,486.783 1760.82,486.898 1762.87,487.012 1764.91,487.126 1766.96,487.239 1769,487.353 \n",
       "  1771.05,487.466 1773.09,487.578 1775.14,487.69 1777.18,487.802 1779.23,487.914 1781.28,488.025 1783.32,488.136 1785.37,488.246 1787.41,488.357 1789.46,488.466 \n",
       "  1791.5,488.576 1793.55,488.685 1795.59,488.794 1797.64,488.903 1799.68,489.011 1801.73,489.119 1803.78,489.227 1805.82,489.334 1807.87,489.441 1809.91,489.548 \n",
       "  1811.96,489.654 1814,489.761 1816.05,489.866 1818.09,489.972 1820.14,490.077 1822.18,490.182 1824.23,490.286 1826.27,490.391 1828.32,490.495 1830.37,490.598 \n",
       "  1832.41,490.702 1834.46,490.805 1836.5,490.907 1838.55,491.01 1840.59,491.112 1842.64,491.214 1844.68,491.315 1846.73,491.416 1848.77,491.517 1850.82,491.618 \n",
       "  1852.86,491.718 1854.91,491.818 1856.96,491.918 1859,492.017 1861.05,492.117 1863.09,492.215 1865.14,492.314 1867.18,492.412 1869.23,492.51 1871.27,492.608 \n",
       "  1873.32,492.705 1875.36,492.802 1877.41,492.899 1879.45,492.996 1881.5,493.092 1883.55,493.188 1885.59,493.284 1887.64,493.379 1889.68,493.474 1891.73,493.569 \n",
       "  1893.77,493.664 1895.82,493.758 1897.86,493.852 1899.91,493.946 1901.95,494.039 1904,494.133 1906.04,494.226 1908.09,494.318 1910.14,494.411 1912.18,494.503 \n",
       "  1914.23,494.595 1916.27,494.686 1918.32,494.777 1920.36,494.868 1922.41,494.959 1924.45,495.05 1926.5,495.14 1928.54,495.23 1930.59,495.32 1932.63,495.409 \n",
       "  1934.68,495.498 1936.73,495.587 1938.77,495.676 1940.82,495.764 1942.86,495.852 1944.91,495.94 1946.95,496.028 1949,496.115 1951.04,496.202 1953.09,496.289 \n",
       "  1955.13,496.376 1957.18,496.462 1959.23,496.548 1961.27,496.634 1963.32,496.72 1965.36,496.805 1967.41,496.89 1969.45,496.975 1971.5,497.059 1973.54,497.144 \n",
       "  1975.59,497.228 1977.63,497.312 1979.68,497.395 1981.72,497.479 1983.77,497.562 1985.82,497.645 1987.86,497.727 1989.91,497.81 1991.95,497.892 1994,497.974 \n",
       "  1996.04,498.055 1998.09,498.137 2000.13,498.218 2002.18,498.299 2004.22,498.38 2006.27,498.46 2008.31,498.54 2010.36,498.62 2012.41,498.7 2014.45,498.78 \n",
       "  2016.5,498.859 2018.54,498.938 2020.59,499.017 2022.63,499.095 2024.68,499.174 2026.72,499.252 2028.77,499.33 2030.81,499.408 2032.86,499.485 2034.9,499.562 \n",
       "  2036.95,499.639 2039,499.716 2041.04,499.793 2043.09,499.869 2045.13,499.945 2047.18,500.021 2049.22,500.097 2051.27,500.172 2053.31,500.247 2055.36,500.322 \n",
       "  2057.4,500.397 2059.45,500.472 2061.49,500.546 2063.54,500.62 2065.59,500.694 2067.63,500.768 2069.68,500.841 2071.72,500.915 2073.77,500.988 2075.81,501.061 \n",
       "  2077.86,501.133 2079.9,501.206 2081.95,501.278 2083.99,501.35 2086.04,501.422 2088.08,501.493 2090.13,501.565 2092.18,501.636 2094.22,501.707 2096.27,501.778 \n",
       "  2098.31,501.848 2100.36,501.919 2102.4,501.989 2104.45,502.059 2106.49,502.129 2108.54,502.198 2110.58,502.267 2112.63,502.337 2114.68,502.405 2116.72,502.474 \n",
       "  2118.77,502.543 2120.81,502.611 2122.86,502.679 2124.9,502.747 2126.95,502.815 2128.99,502.882 2131.04,502.95 2133.08,503.017 2135.13,503.084 2137.17,503.151 \n",
       "  2139.22,503.217 2141.27,503.284 2143.31,503.35 2145.36,503.416 2147.4,503.482 2149.45,503.547 2151.49,503.613 2153.54,503.678 2155.58,503.743 2157.63,503.808 \n",
       "  2159.67,503.873 2161.72,503.937 2163.76,504.001 2165.81,504.066 2167.86,504.129 2169.9,504.193 2171.95,504.257 2173.99,504.32 2176.04,504.383 2178.08,504.446 \n",
       "  2180.13,504.509 2182.17,504.572 2184.22,504.634 2186.26,504.697 2188.31,504.759 2190.35,504.821 2192.4,504.882 2194.45,504.944 2196.49,505.005 2198.54,505.067 \n",
       "  2200.58,505.128 2202.63,505.188 2204.67,505.249 2206.72,505.31 2208.76,505.37 2210.81,505.43 2212.85,505.49 2214.9,505.55 2216.94,505.61 2218.99,505.669 \n",
       "  2221.04,505.728 2223.08,505.788 2225.13,505.847 2227.17,505.905 2229.22,505.964 2231.26,506.022 2233.31,506.081 2235.35,506.139 2237.4,506.197 2239.44,506.255 \n",
       "  2241.49,506.312 2243.53,506.37 2245.58,506.427 2247.63,506.484 2249.67,506.541 2251.72,506.598 2253.76,506.654 2255.81,506.711 2257.85,506.767 2259.9,506.823 \n",
       "  2261.94,506.879 2263.99,506.935 2266.03,506.991 2268.08,507.046 2270.12,507.101 2272.17,507.157 2274.22,507.212 2276.26,507.266 2278.31,507.321 2280.35,507.376 \n",
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       "  2302.85,507.965 2304.9,508.018 2306.94,508.07 2308.99,508.123 2311.03,508.175 2313.08,508.227 2315.12,508.279 2317.17,508.331 2319.21,508.382 2321.26,508.434 \n",
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       "  1055.16,1037.47 1057.21,1037.79 1059.25,1038.12 1061.3,1038.45 1063.34,1038.77 1065.39,1039.09 1067.43,1039.41 1069.48,1039.74 1071.52,1040.06 1073.57,1040.37 \n",
       "  1075.61,1040.69 1077.66,1041.01 1079.71,1041.33 1081.75,1041.64 1083.8,1041.95 1085.84,1042.27 1087.89,1042.58 1089.93,1042.89 1091.98,1043.2 1094.02,1043.51 \n",
       "  1096.07,1043.82 1098.11,1044.13 1100.16,1044.43 1102.2,1044.74 1104.25,1045.04 1106.3,1045.34 1108.34,1045.65 1110.39,1045.95 1112.43,1046.25 1114.48,1046.55 \n",
       "  1116.52,1046.85 1118.57,1047.14 1120.61,1047.44 1122.66,1047.74 1124.7,1048.03 1126.75,1048.32 1128.79,1048.62 1130.84,1048.91 1132.89,1049.2 1134.93,1049.49 \n",
       "  1136.98,1049.78 1139.02,1050.07 1141.07,1050.36 1143.11,1050.64 1145.16,1050.93 1147.2,1051.21 1149.25,1051.5 1151.29,1051.78 1153.34,1052.06 1155.39,1052.34 \n",
       "  1157.43,1052.62 1159.48,1052.9 1161.52,1053.18 1163.57,1053.46 1165.61,1053.74 1167.66,1054.01 1169.7,1054.29 1171.75,1054.56 1173.79,1054.83 1175.84,1055.11 \n",
       "  1177.88,1055.38 1179.93,1055.65 1181.98,1055.92 1184.02,1056.19 1186.07,1056.46 1188.11,1056.72 1190.16,1056.99 1192.2,1057.26 1194.25,1057.52 1196.29,1057.78 \n",
       "  1198.34,1058.05 1200.38,1058.31 1202.43,1058.57 1204.47,1058.83 1206.52,1059.09 1208.57,1059.35 1210.61,1059.61 1212.66,1059.87 1214.7,1060.13 1216.75,1060.38 \n",
       "  1218.79,1060.64 1220.84,1060.89 1222.88,1061.14 1224.93,1061.4 1226.97,1061.65 1229.02,1061.9 1231.06,1062.15 1233.11,1062.4 1235.16,1062.65 1237.2,1062.9 \n",
       "  1239.25,1063.15 1241.29,1063.39 1243.34,1063.64 1245.38,1063.88 1247.43,1064.13 1249.47,1064.37 1251.52,1064.61 1253.56,1064.86 1255.61,1065.1 1257.65,1065.34 \n",
       "  1259.7,1065.58 1261.75,1065.82 1263.79,1066.06 1265.84,1066.29 1267.88,1066.53 1269.93,1066.77 1271.97,1067 1274.02,1067.24 1276.06,1067.47 1278.11,1067.7 \n",
       "  1280.15,1067.94 1282.2,1068.17 1284.24,1068.4 1286.29,1068.63 1288.34,1068.86 1290.38,1069.09 1292.43,1069.32 1294.47,1069.54 1296.52,1069.77 1298.56,1070 \n",
       "  1300.61,1070.22 1302.65,1070.45 1304.7,1070.67 1306.74,1070.9 1308.79,1071.12 1310.84,1071.34 1312.88,1071.56 1314.93,1071.78 1316.97,1072 1319.02,1072.22 \n",
       "  1321.06,1072.44 1323.11,1072.66 1325.15,1072.88 1327.2,1073.09 1329.24,1073.31 1331.29,1073.52 1333.33,1073.74 1335.38,1073.95 1337.43,1074.17 1339.47,1074.38 \n",
       "  1341.52,1074.59 1343.56,1074.8 1345.61,1075.01 1347.65,1075.22 1349.7,1075.43 1351.74,1075.64 1353.79,1075.85 1355.83,1076.06 1357.88,1076.27 1359.92,1076.47 \n",
       "  1361.97,1076.68 1364.02,1076.88 1366.06,1077.09 1368.11,1077.29 1370.15,1077.49 1372.2,1077.7 1374.24,1077.9 1376.29,1078.1 1378.33,1078.3 1380.38,1078.5 \n",
       "  1382.42,1078.7 1384.47,1078.9 1386.51,1079.1 1388.56,1079.3 1390.61,1079.49 1392.65,1079.69 1394.7,1079.88 1396.74,1080.08 1398.79,1080.27 1400.83,1080.47 \n",
       "  1402.88,1080.66 1404.92,1080.86 1406.97,1081.05 1409.01,1081.24 1411.06,1081.43 1413.1,1081.62 1415.15,1081.81 1417.2,1082 1419.24,1082.19 1421.29,1082.38 \n",
       "  1423.33,1082.57 1425.38,1082.75 1427.42,1082.94 1429.47,1083.13 1431.51,1083.31 1433.56,1083.5 1435.6,1083.68 1437.65,1083.86 1439.69,1084.05 1441.74,1084.23 \n",
       "  1443.79,1084.41 1445.83,1084.59 1447.88,1084.78 1449.92,1084.96 1451.97,1085.14 1454.01,1085.32 1456.06,1085.49 1458.1,1085.67 1460.15,1085.85 1462.19,1086.03 \n",
       "  1464.24,1086.2 1466.28,1086.38 1468.33,1086.56 1470.38,1086.73 1472.42,1086.91 1474.47,1087.08 1476.51,1087.25 1478.56,1087.43 1480.6,1087.6 1482.65,1087.77 \n",
       "  1484.69,1087.94 1486.74,1088.11 1488.78,1088.28 1490.83,1088.45 1492.88,1088.62 1494.92,1088.79 1496.97,1088.96 1499.01,1089.13 1501.06,1089.3 1503.1,1089.46 \n",
       "  1505.15,1089.63 1507.19,1089.79 1509.24,1089.96 1511.28,1090.12 1513.33,1090.29 1515.37,1090.45 1517.42,1090.62 1519.47,1090.78 1521.51,1090.94 1523.56,1091.1 \n",
       "  1525.6,1091.26 1527.65,1091.43 1529.69,1091.59 1531.74,1091.75 1533.78,1091.91 1535.83,1092.06 1537.87,1092.22 1539.92,1092.38 1541.96,1092.54 1544.01,1092.7 \n",
       "  1546.06,1092.85 1548.1,1093.01 1550.15,1093.16 1552.19,1093.32 1554.24,1093.47 1556.28,1093.63 1558.33,1093.78 1560.37,1093.94 1562.42,1094.09 1564.46,1094.24 \n",
       "  1566.51,1094.39 1568.55,1094.54 1570.6,1094.7 1572.65,1094.85 1574.69,1095 1576.74,1095.15 1578.78,1095.3 1580.83,1095.44 1582.87,1095.59 1584.92,1095.74 \n",
       "  1586.96,1095.89 1589.01,1096.03 1591.05,1096.18 1593.1,1096.33 1595.14,1096.47 1597.19,1096.62 1599.24,1096.76 1601.28,1096.91 1603.33,1097.05 1605.37,1097.2 \n",
       "  1607.42,1097.34 1609.46,1097.48 1611.51,1097.62 1613.55,1097.77 1615.6,1097.91 1617.64,1098.05 1619.69,1098.19 1621.73,1098.33 1623.78,1098.47 1625.83,1098.61 \n",
       "  1627.87,1098.75 1629.92,1098.88 1631.96,1099.02 1634.01,1099.16 1636.05,1099.3 1638.1,1099.43 1640.14,1099.57 1642.19,1099.71 1644.23,1099.84 1646.28,1099.98 \n",
       "  1648.33,1100.11 1650.37,1100.25 1652.42,1100.38 1654.46,1100.51 1656.51,1100.65 1658.55,1100.78 1660.6,1100.91 1662.64,1101.05 1664.69,1101.18 1666.73,1101.31 \n",
       "  1668.78,1101.44 1670.82,1101.57 1672.87,1101.7 1674.92,1101.83 1676.96,1101.96 1679.01,1102.09 1681.05,1102.22 1683.1,1102.34 1685.14,1102.47 1687.19,1102.6 \n",
       "  1689.23,1102.73 1691.28,1102.85 1693.32,1102.98 1695.37,1103.11 1697.41,1103.23 1699.46,1103.36 1701.51,1103.48 1703.55,1103.61 1705.6,1103.73 1707.64,1103.85 \n",
       "  1709.69,1103.98 1711.73,1104.1 1713.78,1104.22 1715.82,1104.34 1717.87,1104.47 1719.91,1104.59 1721.96,1104.71 1724,1104.83 1726.05,1104.95 1728.1,1105.07 \n",
       "  1730.14,1105.19 1732.19,1105.31 1734.23,1105.43 1736.28,1105.55 1738.32,1105.67 1740.37,1105.78 1742.41,1105.9 1744.46,1106.02 1746.5,1106.14 1748.55,1106.25 \n",
       "  1750.59,1106.37 1752.64,1106.48 1754.69,1106.6 1756.73,1106.71 1758.78,1106.83 1760.82,1106.94 1762.87,1107.06 1764.91,1107.17 1766.96,1107.29 1769,1107.4 \n",
       "  1771.05,1107.51 1773.09,1107.62 1775.14,1107.74 1777.18,1107.85 1779.23,1107.96 1781.28,1108.07 1783.32,1108.18 1785.37,1108.29 1787.41,1108.4 1789.46,1108.51 \n",
       "  1791.5,1108.62 1793.55,1108.73 1795.59,1108.84 1797.64,1108.95 1799.68,1109.06 1801.73,1109.17 1803.78,1109.27 1805.82,1109.38 1807.87,1109.49 1809.91,1109.59 \n",
       "  1811.96,1109.7 1814,1109.81 1816.05,1109.91 1818.09,1110.02 1820.14,1110.12 1822.18,1110.23 1824.23,1110.33 1826.27,1110.44 1828.32,1110.54 1830.37,1110.64 \n",
       "  1832.41,1110.75 1834.46,1110.85 1836.5,1110.95 1838.55,1111.06 1840.59,1111.16 1842.64,1111.26 1844.68,1111.36 1846.73,1111.46 1848.77,1111.56 1850.82,1111.66 \n",
       "  1852.86,1111.76 1854.91,1111.86 1856.96,1111.96 1859,1112.06 1861.05,1112.16 1863.09,1112.26 1865.14,1112.36 1867.18,1112.46 1869.23,1112.56 1871.27,1112.65 \n",
       "  1873.32,1112.75 1875.36,1112.85 1877.41,1112.95 1879.45,1113.04 1881.5,1113.14 1883.55,1113.23 1885.59,1113.33 1887.64,1113.43 1889.68,1113.52 1891.73,1113.62 \n",
       "  1893.77,1113.71 1895.82,1113.8 1897.86,1113.9 1899.91,1113.99 1901.95,1114.09 1904,1114.18 1906.04,1114.27 1908.09,1114.36 1910.14,1114.46 1912.18,1114.55 \n",
       "  1914.23,1114.64 1916.27,1114.73 1918.32,1114.82 1920.36,1114.91 1922.41,1115.01 1924.45,1115.1 1926.5,1115.19 1928.54,1115.28 1930.59,1115.37 1932.63,1115.46 \n",
       "  1934.68,1115.54 1936.73,1115.63 1938.77,1115.72 1940.82,1115.81 1942.86,1115.9 1944.91,1115.99 1946.95,1116.07 1949,1116.16 1951.04,1116.25 1953.09,1116.34 \n",
       "  1955.13,1116.42 1957.18,1116.51 1959.23,1116.59 1961.27,1116.68 1963.32,1116.77 1965.36,1116.85 1967.41,1116.94 1969.45,1117.02 1971.5,1117.11 1973.54,1117.19 \n",
       "  1975.59,1117.27 1977.63,1117.36 1979.68,1117.44 1981.72,1117.53 1983.77,1117.61 1985.82,1117.69 1987.86,1117.77 1989.91,1117.86 1991.95,1117.94 1994,1118.02 \n",
       "  1996.04,1118.1 1998.09,1118.18 2000.13,1118.26 2002.18,1118.35 2004.22,1118.43 2006.27,1118.51 2008.31,1118.59 2010.36,1118.67 2012.41,1118.75 2014.45,1118.83 \n",
       "  2016.5,1118.91 2018.54,1118.98 2020.59,1119.06 2022.63,1119.14 2024.68,1119.22 2026.72,1119.3 2028.77,1119.38 2030.81,1119.45 2032.86,1119.53 2034.9,1119.61 \n",
       "  2036.95,1119.69 2039,1119.76 2041.04,1119.84 2043.09,1119.92 2045.13,1119.99 2047.18,1120.07 2049.22,1120.14 2051.27,1120.22 2053.31,1120.29 2055.36,1120.37 \n",
       "  2057.4,1120.44 2059.45,1120.52 2061.49,1120.59 2063.54,1120.67 2065.59,1120.74 2067.63,1120.81 2069.68,1120.89 2071.72,1120.96 2073.77,1121.03 2075.81,1121.11 \n",
       "  2077.86,1121.18 2079.9,1121.25 2081.95,1121.32 2083.99,1121.4 2086.04,1121.47 2088.08,1121.54 2090.13,1121.61 2092.18,1121.68 2094.22,1121.75 2096.27,1121.82 \n",
       "  2098.31,1121.89 2100.36,1121.97 2102.4,1122.04 2104.45,1122.11 2106.49,1122.17 2108.54,1122.24 2110.58,1122.31 2112.63,1122.38 2114.68,1122.45 2116.72,1122.52 \n",
       "  2118.77,1122.59 2120.81,1122.66 2122.86,1122.73 2124.9,1122.79 2126.95,1122.86 2128.99,1122.93 2131.04,1123 2133.08,1123.06 2135.13,1123.13 2137.17,1123.2 \n",
       "  2139.22,1123.26 2141.27,1123.33 2143.31,1123.4 2145.36,1123.46 2147.4,1123.53 2149.45,1123.59 2151.49,1123.66 2153.54,1123.72 2155.58,1123.79 2157.63,1123.85 \n",
       "  2159.67,1123.92 2161.72,1123.98 2163.76,1124.05 2165.81,1124.11 2167.86,1124.18 2169.9,1124.24 2171.95,1124.3 2173.99,1124.37 2176.04,1124.43 2178.08,1124.49 \n",
       "  2180.13,1124.56 2182.17,1124.62 2184.22,1124.68 2186.26,1124.74 2188.31,1124.81 2190.35,1124.87 2192.4,1124.93 2194.45,1124.99 2196.49,1125.05 2198.54,1125.11 \n",
       "  2200.58,1125.17 2202.63,1125.23 2204.67,1125.3 2206.72,1125.36 2208.76,1125.42 2210.81,1125.48 2212.85,1125.54 2214.9,1125.6 2216.94,1125.66 2218.99,1125.72 \n",
       "  2221.04,1125.77 2223.08,1125.83 2225.13,1125.89 2227.17,1125.95 2229.22,1126.01 2231.26,1126.07 2233.31,1126.13 2235.35,1126.19 2237.4,1126.24 2239.44,1126.3 \n",
       "  2241.49,1126.36 2243.53,1126.42 2245.58,1126.47 2247.63,1126.53 2249.67,1126.59 2251.72,1126.64 2253.76,1126.7 2255.81,1126.76 2257.85,1126.81 2259.9,1126.87 \n",
       "  2261.94,1126.93 2263.99,1126.98 2266.03,1127.04 2268.08,1127.09 2270.12,1127.15 2272.17,1127.2 2274.22,1127.26 2276.26,1127.31 2278.31,1127.37 2280.35,1127.42 \n",
       "  2282.4,1127.48 2284.44,1127.53 2286.49,1127.58 2288.53,1127.64 2290.58,1127.69 2292.62,1127.75 2294.67,1127.8 2296.72,1127.85 2298.76,1127.91 2300.81,1127.96 \n",
       "  2302.85,1128.01 2304.9,1128.06 2306.94,1128.12 2308.99,1128.17 2311.03,1128.22 2313.08,1128.27 2315.12,1128.33 2317.17,1128.38 2319.21,1128.43 2321.26,1128.48 \n",
       "  \n",
       "  \"/>\n",
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       "  298.365,1391.11 300.41,1389.92 302.456,1388.73 304.501,1387.55 306.546,1386.38 308.592,1385.21 310.637,1384.04 312.683,1382.88 314.728,1381.72 316.773,1380.56 \n",
       "  318.819,1379.42 320.864,1378.27 322.91,1377.13 324.955,1376 327,1374.86 329.046,1373.74 331.091,1372.62 333.136,1371.5 335.182,1370.38 337.227,1369.27 \n",
       "  339.273,1368.17 341.318,1367.07 343.363,1365.97 345.409,1364.88 347.454,1363.79 349.5,1362.71 351.545,1361.63 353.59,1360.55 355.636,1359.48 357.681,1358.42 \n",
       "  359.727,1357.35 361.772,1356.29 363.817,1355.24 365.863,1354.19 367.908,1353.14 369.954,1352.1 371.999,1351.06 374.044,1350.03 376.09,1349 378.135,1347.97 \n",
       "  380.181,1346.95 382.226,1345.93 384.271,1344.91 386.317,1343.9 388.362,1342.89 390.408,1341.89 392.453,1340.89 394.498,1339.89 396.544,1338.9 398.589,1337.91 \n",
       "  400.635,1336.93 402.68,1335.95 404.725,1334.97 406.771,1334 408.816,1333.03 410.861,1332.06 412.907,1331.1 414.952,1330.14 416.998,1329.18 419.043,1328.23 \n",
       "  421.088,1327.28 423.134,1326.34 425.179,1325.4 427.225,1324.46 429.27,1323.53 431.315,1322.6 433.361,1321.67 435.406,1320.75 437.452,1319.83 439.497,1318.91 \n",
       "  441.542,1318 443.588,1317.09 445.633,1316.18 447.679,1315.28 449.724,1314.38 451.769,1313.48 453.815,1312.59 455.86,1311.7 457.906,1310.81 459.951,1309.93 \n",
       "  461.996,1309.05 464.042,1308.17 466.087,1307.3 468.133,1306.43 470.178,1305.56 472.223,1304.7 474.269,1303.84 476.314,1302.98 478.359,1302.12 480.405,1301.27 \n",
       "  482.45,1300.42 484.496,1299.58 486.541,1298.74 488.586,1297.9 490.632,1297.06 492.677,1296.23 494.723,1295.4 496.768,1294.57 498.813,1293.75 500.859,1292.93 \n",
       "  502.904,1292.11 504.95,1291.3 506.995,1290.49 509.04,1289.68 511.086,1288.87 513.131,1288.07 515.177,1287.27 517.222,1286.47 519.267,1285.68 521.313,1284.89 \n",
       "  523.358,1284.1 525.404,1283.31 527.449,1282.53 529.494,1281.75 531.54,1280.97 533.585,1280.2 535.631,1279.43 537.676,1278.66 539.721,1277.89 541.767,1277.13 \n",
       "  543.812,1276.37 545.858,1275.61 547.903,1274.85 549.948,1274.1 551.994,1273.35 554.039,1272.6 556.084,1271.86 558.13,1271.12 560.175,1270.38 562.221,1269.64 \n",
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       "  625.628,1248.06 627.673,1247.41 629.719,1246.75 631.764,1246.1 633.809,1245.45 635.855,1244.8 637.9,1244.15 639.946,1243.51 641.991,1242.87 644.036,1242.23 \n",
       "  646.082,1241.59 648.127,1240.96 650.173,1240.32 652.218,1239.69 654.263,1239.06 656.309,1238.44 658.354,1237.81 660.4,1237.19 662.445,1236.57 664.49,1235.95 \n",
       "  666.536,1235.34 668.581,1234.72 670.627,1234.11 672.672,1233.5 674.717,1232.9 676.763,1232.29 678.808,1231.69 680.854,1231.09 682.899,1230.49 684.944,1229.89 \n",
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       "  707.444,1223.46 709.489,1222.89 711.534,1222.32 713.58,1221.75 715.625,1221.19 717.671,1220.62 719.716,1220.06 721.761,1219.5 723.807,1218.94 725.852,1218.38 \n",
       "  727.898,1217.83 729.943,1217.27 731.988,1216.72 734.034,1216.17 736.079,1215.62 738.125,1215.08 740.17,1214.53 742.215,1213.99 744.261,1213.45 746.306,1212.91 \n",
       "  748.352,1212.38 750.397,1211.84 752.442,1211.31 754.488,1210.78 756.533,1210.25 758.579,1209.72 760.624,1209.19 762.669,1208.67 764.715,1208.15 766.76,1207.63 \n",
       "  768.805,1207.11 770.851,1206.59 772.896,1206.07 774.942,1205.56 776.987,1205.05 779.032,1204.54 781.078,1204.03 783.123,1203.52 785.169,1203.02 787.214,1202.52 \n",
       "  789.259,1202.01 791.305,1201.51 793.35,1201.02 795.396,1200.52 797.441,1200.02 799.486,1199.53 801.532,1199.04 803.577,1198.55 805.623,1198.06 807.668,1197.57 \n",
       "  809.713,1197.09 811.759,1196.6 813.804,1196.12 815.85,1195.64 817.895,1195.16 819.94,1194.69 821.986,1194.21 824.031,1193.74 826.077,1193.26 828.122,1192.79 \n",
       "  830.167,1192.32 832.213,1191.86 834.258,1191.39 836.304,1190.93 838.349,1190.46 840.394,1190 842.44,1189.54 844.485,1189.08 846.53,1188.62 848.576,1188.17 \n",
       "  850.621,1187.72 852.667,1187.26 854.712,1186.81 856.757,1186.36 858.803,1185.91 860.848,1185.47 862.894,1185.02 864.939,1184.58 866.984,1184.14 869.03,1183.7 \n",
       "  871.075,1183.26 873.121,1182.82 875.166,1182.38 877.211,1181.95 879.257,1181.51 881.302,1181.08 883.348,1180.65 885.393,1180.22 887.438,1179.79 889.484,1179.37 \n",
       "  891.529,1178.94 893.575,1178.52 895.62,1178.1 897.665,1177.68 899.711,1177.26 901.756,1176.84 903.802,1176.42 905.847,1176.01 907.892,1175.59 909.938,1175.18 \n",
       "  911.983,1174.77 914.029,1174.36 916.074,1173.95 918.119,1173.54 920.165,1173.14 922.21,1172.73 924.255,1172.33 926.301,1171.93 928.346,1171.53 930.392,1171.13 \n",
       "  932.437,1170.73 934.482,1170.33 936.528,1169.94 938.573,1169.54 940.619,1169.15 942.664,1168.76 944.709,1168.37 946.755,1167.98 948.8,1167.59 950.846,1167.2 \n",
       "  952.891,1166.82 954.936,1166.43 956.982,1166.05 959.027,1165.67 961.073,1165.29 963.118,1164.91 965.163,1164.53 967.209,1164.15 969.254,1163.78 971.3,1163.4 \n",
       "  973.345,1163.03 975.39,1162.66 977.436,1162.29 979.481,1161.92 981.527,1161.55 983.572,1161.18 985.617,1160.82 987.663,1160.45 989.708,1160.09 991.753,1159.73 \n",
       "  993.799,1159.37 995.844,1159 997.89,1158.65 999.935,1158.29 1001.98,1157.93 1004.03,1157.58 1006.07,1157.22 1008.12,1156.87 1010.16,1156.52 1012.21,1156.16 \n",
       "  1014.25,1155.81 1016.3,1155.47 1018.34,1155.12 1020.39,1154.77 1022.43,1154.43 1024.48,1154.08 1026.53,1153.74 1028.57,1153.4 1030.62,1153.06 1032.66,1152.72 \n",
       "  1034.71,1152.38 1036.75,1152.04 1038.8,1151.7 1040.84,1151.37 1042.89,1151.03 1044.93,1150.7 1046.98,1150.37 1049.02,1150.03 1051.07,1149.7 1053.12,1149.37 \n",
       "  1055.16,1149.05 1057.21,1148.72 1059.25,1148.39 1061.3,1148.07 1063.34,1147.74 1065.39,1147.42 1067.43,1147.1 1069.48,1146.78 1071.52,1146.46 1073.57,1146.14 \n",
       "  1075.61,1145.82 1077.66,1145.5 1079.71,1145.19 1081.75,1144.87 1083.8,1144.56 1085.84,1144.25 1087.89,1143.93 1089.93,1143.62 1091.98,1143.31 1094.02,1143 \n",
       "  1096.07,1142.7 1098.11,1142.39 1100.16,1142.08 1102.2,1141.78 1104.25,1141.47 1106.3,1141.17 1108.34,1140.87 1110.39,1140.57 1112.43,1140.27 1114.48,1139.97 \n",
       "  1116.52,1139.67 1118.57,1139.37 1120.61,1139.07 1122.66,1138.78 1124.7,1138.48 1126.75,1138.19 1128.79,1137.9 1130.84,1137.6 1132.89,1137.31 1134.93,1137.02 \n",
       "  1136.98,1136.73 1139.02,1136.45 1141.07,1136.16 1143.11,1135.87 1145.16,1135.59 1147.2,1135.3 1149.25,1135.02 1151.29,1134.73 1153.34,1134.45 1155.39,1134.17 \n",
       "  1157.43,1133.89 1159.48,1133.61 1161.52,1133.33 1163.57,1133.05 1165.61,1132.78 1167.66,1132.5 1169.7,1132.23 1171.75,1131.95 1173.79,1131.68 1175.84,1131.41 \n",
       "  1177.88,1131.14 1179.93,1130.86 1181.98,1130.59 1184.02,1130.33 1186.07,1130.06 1188.11,1129.79 1190.16,1129.52 1192.2,1129.26 1194.25,1128.99 1196.29,1128.73 \n",
       "  1198.34,1128.47 1200.38,1128.2 1202.43,1127.94 1204.47,1127.68 1206.52,1127.42 1208.57,1127.16 1210.61,1126.9 1212.66,1126.64 1214.7,1126.39 1216.75,1126.13 \n",
       "  1218.79,1125.88 1220.84,1125.62 1222.88,1125.37 1224.93,1125.12 1226.97,1124.86 1229.02,1124.61 1231.06,1124.36 1233.11,1124.11 1235.16,1123.86 1237.2,1123.62 \n",
       "  1239.25,1123.37 1241.29,1123.12 1243.34,1122.88 1245.38,1122.63 1247.43,1122.39 1249.47,1122.14 1251.52,1121.9 1253.56,1121.66 1255.61,1121.42 1257.65,1121.18 \n",
       "  1259.7,1120.94 1261.75,1120.7 1263.79,1120.46 1265.84,1120.22 1267.88,1119.98 1269.93,1119.75 1271.97,1119.51 1274.02,1119.28 1276.06,1119.04 1278.11,1118.81 \n",
       "  1280.15,1118.58 1282.2,1118.35 1284.24,1118.11 1286.29,1117.88 1288.34,1117.65 1290.38,1117.42 1292.43,1117.2 1294.47,1116.97 1296.52,1116.74 1298.56,1116.52 \n",
       "  1300.61,1116.29 1302.65,1116.07 1304.7,1115.84 1306.74,1115.62 1308.79,1115.39 1310.84,1115.17 1312.88,1114.95 1314.93,1114.73 1316.97,1114.51 1319.02,1114.29 \n",
       "  1321.06,1114.07 1323.11,1113.85 1325.15,1113.64 1327.2,1113.42 1329.24,1113.2 1331.29,1112.99 1333.33,1112.77 1335.38,1112.56 1337.43,1112.35 1339.47,1112.13 \n",
       "  1341.52,1111.92 1343.56,1111.71 1345.61,1111.5 1347.65,1111.29 1349.7,1111.08 1351.74,1110.87 1353.79,1110.66 1355.83,1110.46 1357.88,1110.25 1359.92,1110.04 \n",
       "  1361.97,1109.84 1364.02,1109.63 1366.06,1109.43 1368.11,1109.22 1370.15,1109.02 1372.2,1108.82 1374.24,1108.61 1376.29,1108.41 1378.33,1108.21 1380.38,1108.01 \n",
       "  1382.42,1107.81 1384.47,1107.61 1386.51,1107.42 1388.56,1107.22 1390.61,1107.02 1392.65,1106.82 1394.7,1106.63 1396.74,1106.43 1398.79,1106.24 1400.83,1106.04 \n",
       "  1402.88,1105.85 1404.92,1105.66 1406.97,1105.47 1409.01,1105.27 1411.06,1105.08 1413.1,1104.89 1415.15,1104.7 1417.2,1104.51 1419.24,1104.32 1421.29,1104.13 \n",
       "  1423.33,1103.95 1425.38,1103.76 1427.42,1103.57 1429.47,1103.39 1431.51,1103.2 1433.56,1103.02 1435.6,1102.83 1437.65,1102.65 1439.69,1102.47 1441.74,1102.28 \n",
       "  1443.79,1102.1 1445.83,1101.92 1447.88,1101.74 1449.92,1101.56 1451.97,1101.38 1454.01,1101.2 1456.06,1101.02 1458.1,1100.84 1460.15,1100.66 1462.19,1100.49 \n",
       "  1464.24,1100.31 1466.28,1100.13 1468.33,1099.96 1470.38,1099.78 1472.42,1099.61 1474.47,1099.43 1476.51,1099.26 1478.56,1099.09 1480.6,1098.91 1482.65,1098.74 \n",
       "  1484.69,1098.57 1486.74,1098.4 1488.78,1098.23 1490.83,1098.06 1492.88,1097.89 1494.92,1097.72 1496.97,1097.55 1499.01,1097.39 1501.06,1097.22 1503.1,1097.05 \n",
       "  1505.15,1096.88 1507.19,1096.72 1509.24,1096.55 1511.28,1096.39 1513.33,1096.22 1515.37,1096.06 1517.42,1095.9 1519.47,1095.73 1521.51,1095.57 1523.56,1095.41 \n",
       "  1525.6,1095.25 1527.65,1095.09 1529.69,1094.93 1531.74,1094.77 1533.78,1094.61 1535.83,1094.45 1537.87,1094.29 1539.92,1094.13 1541.96,1093.97 1544.01,1093.82 \n",
       "  1546.06,1093.66 1548.1,1093.5 1550.15,1093.35 1552.19,1093.19 1554.24,1093.04 1556.28,1092.88 1558.33,1092.73 1560.37,1092.58 1562.42,1092.42 1564.46,1092.27 \n",
       "  1566.51,1092.12 1568.55,1091.97 1570.6,1091.82 1572.65,1091.67 1574.69,1091.52 1576.74,1091.37 1578.78,1091.22 1580.83,1091.07 1582.87,1090.92 1584.92,1090.77 \n",
       "  1586.96,1090.63 1589.01,1090.48 1591.05,1090.33 1593.1,1090.19 1595.14,1090.04 1597.19,1089.89 1599.24,1089.75 1601.28,1089.61 1603.33,1089.46 1605.37,1089.32 \n",
       "  1607.42,1089.17 1609.46,1089.03 1611.51,1088.89 1613.55,1088.75 1615.6,1088.61 1617.64,1088.47 1619.69,1088.33 1621.73,1088.18 1623.78,1088.05 1625.83,1087.91 \n",
       "  1627.87,1087.77 1629.92,1087.63 1631.96,1087.49 1634.01,1087.35 1636.05,1087.22 1638.1,1087.08 1640.14,1086.94 1642.19,1086.81 1644.23,1086.67 1646.28,1086.54 \n",
       "  1648.33,1086.4 1650.37,1086.27 1652.42,1086.13 1654.46,1086 1656.51,1085.87 1658.55,1085.73 1660.6,1085.6 1662.64,1085.47 1664.69,1085.34 1666.73,1085.2 \n",
       "  1668.78,1085.07 1670.82,1084.94 1672.87,1084.81 1674.92,1084.68 1676.96,1084.55 1679.01,1084.43 1681.05,1084.3 1683.1,1084.17 1685.14,1084.04 1687.19,1083.91 \n",
       "  1689.23,1083.79 1691.28,1083.66 1693.32,1083.53 1695.37,1083.41 1697.41,1083.28 1699.46,1083.16 1701.51,1083.03 1703.55,1082.91 1705.6,1082.78 1707.64,1082.66 \n",
       "  1709.69,1082.54 1711.73,1082.41 1713.78,1082.29 1715.82,1082.17 1717.87,1082.05 1719.91,1081.93 1721.96,1081.8 1724,1081.68 1726.05,1081.56 1728.1,1081.44 \n",
       "  1730.14,1081.32 1732.19,1081.2 1734.23,1081.08 1736.28,1080.97 1738.32,1080.85 1740.37,1080.73 1742.41,1080.61 1744.46,1080.49 1746.5,1080.38 1748.55,1080.26 \n",
       "  1750.59,1080.15 1752.64,1080.03 1754.69,1079.91 1756.73,1079.8 1758.78,1079.68 1760.82,1079.57 1762.87,1079.45 1764.91,1079.34 1766.96,1079.23 1769,1079.11 \n",
       "  1771.05,1079 1773.09,1078.89 1775.14,1078.78 1777.18,1078.66 1779.23,1078.55 1781.28,1078.44 1783.32,1078.33 1785.37,1078.22 1787.41,1078.11 1789.46,1078 \n",
       "  1791.5,1077.89 1793.55,1077.78 1795.59,1077.67 1797.64,1077.56 1799.68,1077.46 1801.73,1077.35 1803.78,1077.24 1805.82,1077.13 1807.87,1077.03 1809.91,1076.92 \n",
       "  1811.96,1076.81 1814,1076.71 1816.05,1076.6 1818.09,1076.5 1820.14,1076.39 1822.18,1076.29 1824.23,1076.18 1826.27,1076.08 1828.32,1075.97 1830.37,1075.87 \n",
       "  1832.41,1075.77 1834.46,1075.66 1836.5,1075.56 1838.55,1075.46 1840.59,1075.36 1842.64,1075.25 1844.68,1075.15 1846.73,1075.05 1848.77,1074.95 1850.82,1074.85 \n",
       "  1852.86,1074.75 1854.91,1074.65 1856.96,1074.55 1859,1074.45 1861.05,1074.35 1863.09,1074.25 1865.14,1074.15 1867.18,1074.05 1869.23,1073.96 1871.27,1073.86 \n",
       "  1873.32,1073.76 1875.36,1073.66 1877.41,1073.57 1879.45,1073.47 1881.5,1073.37 1883.55,1073.28 1885.59,1073.18 1887.64,1073.09 1889.68,1072.99 1891.73,1072.9 \n",
       "  1893.77,1072.8 1895.82,1072.71 1897.86,1072.61 1899.91,1072.52 1901.95,1072.43 1904,1072.33 1906.04,1072.24 1908.09,1072.15 1910.14,1072.06 1912.18,1071.96 \n",
       "  1914.23,1071.87 1916.27,1071.78 1918.32,1071.69 1920.36,1071.6 1922.41,1071.51 1924.45,1071.42 1926.5,1071.33 1928.54,1071.24 1930.59,1071.15 1932.63,1071.06 \n",
       "  1934.68,1070.97 1936.73,1070.88 1938.77,1070.79 1940.82,1070.7 1942.86,1070.61 1944.91,1070.53 1946.95,1070.44 1949,1070.35 1951.04,1070.26 1953.09,1070.18 \n",
       "  1955.13,1070.09 1957.18,1070 1959.23,1069.92 1961.27,1069.83 1963.32,1069.75 1965.36,1069.66 1967.41,1069.58 1969.45,1069.49 1971.5,1069.41 1973.54,1069.32 \n",
       "  1975.59,1069.24 1977.63,1069.16 1979.68,1069.07 1981.72,1068.99 1983.77,1068.91 1985.82,1068.82 1987.86,1068.74 1989.91,1068.66 1991.95,1068.58 1994,1068.49 \n",
       "  1996.04,1068.41 1998.09,1068.33 2000.13,1068.25 2002.18,1068.17 2004.22,1068.09 2006.27,1068.01 2008.31,1067.93 2010.36,1067.85 2012.41,1067.77 2014.45,1067.69 \n",
       "  2016.5,1067.61 2018.54,1067.53 2020.59,1067.45 2022.63,1067.37 2024.68,1067.29 2026.72,1067.21 2028.77,1067.14 2030.81,1067.06 2032.86,1066.98 2034.9,1066.9 \n",
       "  2036.95,1066.83 2039,1066.75 2041.04,1066.67 2043.09,1066.6 2045.13,1066.52 2047.18,1066.45 2049.22,1066.37 2051.27,1066.29 2053.31,1066.22 2055.36,1066.14 \n",
       "  2057.4,1066.07 2059.45,1066 2061.49,1065.92 2063.54,1065.85 2065.59,1065.77 2067.63,1065.7 2069.68,1065.63 2071.72,1065.55 2073.77,1065.48 2075.81,1065.41 \n",
       "  2077.86,1065.33 2079.9,1065.26 2081.95,1065.19 2083.99,1065.12 2086.04,1065.05 2088.08,1064.97 2090.13,1064.9 2092.18,1064.83 2094.22,1064.76 2096.27,1064.69 \n",
       "  2098.31,1064.62 2100.36,1064.55 2102.4,1064.48 2104.45,1064.41 2106.49,1064.34 2108.54,1064.27 2110.58,1064.2 2112.63,1064.13 2114.68,1064.06 2116.72,1063.99 \n",
       "  2118.77,1063.92 2120.81,1063.86 2122.86,1063.79 2124.9,1063.72 2126.95,1063.65 2128.99,1063.58 2131.04,1063.52 2133.08,1063.45 2135.13,1063.38 2137.17,1063.32 \n",
       "  2139.22,1063.25 2141.27,1063.18 2143.31,1063.12 2145.36,1063.05 2147.4,1062.99 2149.45,1062.92 2151.49,1062.85 2153.54,1062.79 2155.58,1062.72 2157.63,1062.66 \n",
       "  2159.67,1062.59 2161.72,1062.53 2163.76,1062.47 2165.81,1062.4 2167.86,1062.34 2169.9,1062.27 2171.95,1062.21 2173.99,1062.15 2176.04,1062.08 2178.08,1062.02 \n",
       "  2180.13,1061.96 2182.17,1061.9 2184.22,1061.83 2186.26,1061.77 2188.31,1061.71 2190.35,1061.65 2192.4,1061.58 2194.45,1061.52 2196.49,1061.46 2198.54,1061.4 \n",
       "  2200.58,1061.34 2202.63,1061.28 2204.67,1061.22 2206.72,1061.16 2208.76,1061.1 2210.81,1061.04 2212.85,1060.98 2214.9,1060.92 2216.94,1060.86 2218.99,1060.8 \n",
       "  2221.04,1060.74 2223.08,1060.68 2225.13,1060.62 2227.17,1060.56 2229.22,1060.5 2231.26,1060.44 2233.31,1060.39 2235.35,1060.33 2237.4,1060.27 2239.44,1060.21 \n",
       "  2241.49,1060.15 2243.53,1060.1 2245.58,1060.04 2247.63,1059.98 2249.67,1059.93 2251.72,1059.87 2253.76,1059.81 2255.81,1059.76 2257.85,1059.7 2259.9,1059.64 \n",
       "  2261.94,1059.59 2263.99,1059.53 2266.03,1059.48 2268.08,1059.42 2270.12,1059.37 2272.17,1059.31 2274.22,1059.26 2276.26,1059.2 2278.31,1059.15 2280.35,1059.09 \n",
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   "source": [
    "tspan = (0.0,100.0)\n",
    "prob = ODEProblem(simpleODE2_rev!,u₀,tspan,p)\n",
    "sol = solve(prob)\n",
    "plot(sol,label=[\"a\",\"b\",\"c\"])\n",
    "title!(\"reversible ODE solver using DSL\")\n",
    "xlabel!(\"Time [s]\")\n",
    "ylabel!(\"Concentration [M]\")"
   ]
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   "cell_type": "markdown",
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   "source": [
    "At equilibrium, when $ \\frac{\\mathrm{d} c_{eq}}{\\mathrm{d} t}=0$, we have:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "k_2 \\cdot c_{eq}= k_1 \\cdot a_{eq}\\cdot b_{eq} \\tag{11}\\\\\n",
    "c_{eq}= \\frac{k_1 \\cdot a_{eq}\\cdot b_{eq}}{k_2} \\tag{12}\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "In addition, since  $ \\frac{\\mathrm{d} c}{\\mathrm{d} t}=-\\frac{\\mathrm{d} a}{\\mathrm{d} t} $ at any time, the condition $[a]+[c]=[a_o]$ is true at all time points. thererefore we can rewrite the equilibrium equation as:\n",
    "$\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "c_{eq}= \\frac{k_1 \\cdot (a_{0}-c_{eq})\\cdot b_{eq}}{k_2} \\tag{13}\\\\\n",
    "c_{eq}= \\frac{k_1 \\cdot a_{0}\\cdot b_{eq}}{k_2}-\\frac{k_1 \\cdot c_{eq}\\cdot b_{eq}}{k_2}  \\tag{14}\\\\\n",
    "c_{eq}+\\frac{k_1 \\cdot c_{eq}\\cdot b_{eq}}{k_2} = \\frac{k_1 \\cdot a_{0}\\cdot b_{eq}}{k_2} \\tag{15}\\\\\n",
    "c_{eq}(1+\\frac{k_1 \\cdot b_{eq}}{k_2}) = \\frac{k_1 \\cdot a_{0}\\cdot b_{eq}}{k_2} \\tag{16}\\\\\n",
    "c_{eq}(\\frac{k_2+k_1 \\cdot b_{eq}}{k_2}) = \\frac{k_1 \\cdot a_{0}\\cdot b_{eq}}{k_2} \\tag{17}\\\\\n",
    "c_{eq}= \\frac{k_1 \\cdot a_{0}\\cdot b_{eq}}{k_2+k_1 \\cdot b_{eq}} \\tag{18}\\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "so, divinding numerator and denoiminator by $k_1$\n",
    "$$\n",
    "\\begin{align}\n",
    "c_{eq}= \\frac{a_{0}\\cdot b_{eq}}{\\frac{k_2}{k_1}+\\cdot b_{eq}} \\tag{19}\\\\\n",
    "c_{eq}= \\frac{a_{0}\\cdot b_{eq}}{K_{eq}+\\cdot b_{eq}} \\tag{20}\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "\n",
    "where $K_{eq}$ is the equilibirum constant, defined as:\n",
    "\n",
    "\n",
    "\\begin{equation}\n",
    "K_{eq}=\\frac{k_2}{k_1} \\tag{21}\n",
    "\\end{equation}"
   ]
  },
  {
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       "  932.437,395.738 934.482,396.135 936.528,396.531 938.573,396.925 940.619,397.318 942.664,397.71 944.709,398.1 946.755,398.489 948.8,398.877 950.846,399.264 \n",
       "  952.891,399.649 954.936,400.034 956.982,400.416 959.027,400.798 961.073,401.179 963.118,401.558 965.163,401.936 967.209,402.313 969.254,402.688 971.3,403.063 \n",
       "  973.345,403.436 975.39,403.808 977.436,404.178 979.481,404.548 981.527,404.916 983.572,405.283 985.617,405.649 987.663,406.014 989.708,406.378 991.753,406.74 \n",
       "  993.799,407.102 995.844,407.462 997.89,407.821 999.935,408.179 1001.98,408.536 1004.03,408.891 1006.07,409.246 1008.12,409.599 1010.16,409.951 1012.21,410.302 \n",
       "  1014.25,410.652 1016.3,411.001 1018.34,411.348 1020.39,411.695 1022.43,412.04 1024.48,412.385 1026.53,412.728 1028.57,413.07 1030.62,413.411 1032.66,413.751 \n",
       "  1034.71,414.09 1036.75,414.428 1038.8,414.765 1040.84,415.1 1042.89,415.435 1044.93,415.768 1046.98,416.101 1049.02,416.432 1051.07,416.763 1053.12,417.092 \n",
       "  1055.16,417.42 1057.21,417.748 1059.25,418.074 1061.3,418.399 1063.34,418.723 1065.39,419.046 1067.43,419.368 1069.48,419.689 1071.52,420.009 1073.57,420.328 \n",
       "  1075.61,420.646 1077.66,420.963 1079.71,421.279 1081.75,421.594 1083.8,421.908 1085.84,422.221 1087.89,422.533 1089.93,422.844 1091.98,423.154 1094.02,423.463 \n",
       "  1096.07,423.772 1098.11,424.079 1100.16,424.385 1102.2,424.69 1104.25,424.994 1106.3,425.297 1108.34,425.6 1110.39,425.901 1112.43,426.201 1114.48,426.501 \n",
       "  1116.52,426.799 1118.57,427.097 1120.61,427.394 1122.66,427.689 1124.7,427.984 1126.75,428.278 1128.79,428.571 1130.84,428.863 1132.89,429.154 1134.93,429.444 \n",
       "  1136.98,429.733 1139.02,430.022 1141.07,430.309 1143.11,430.596 1145.16,430.881 1147.2,431.166 1149.25,431.45 1151.29,431.733 1153.34,432.015 1155.39,432.296 \n",
       "  1157.43,432.576 1159.48,432.856 1161.52,433.134 1163.57,433.412 1165.61,433.689 1167.66,433.965 1169.7,434.24 1171.75,434.514 1173.79,434.787 1175.84,435.06 \n",
       "  1177.88,435.331 1179.93,435.602 1181.98,435.872 1184.02,436.141 1186.07,436.41 1188.11,436.677 1190.16,436.944 1192.2,437.209 1194.25,437.474 1196.29,437.738 \n",
       "  1198.34,438.002 1200.38,438.264 1202.43,438.526 1204.47,438.787 1206.52,439.047 1208.57,439.306 1210.61,439.564 1212.66,439.822 1214.7,440.079 1216.75,440.335 \n",
       "  1218.79,440.59 1220.84,440.844 1222.88,441.098 1224.93,441.351 1226.97,441.603 1229.02,441.854 1231.06,442.105 1233.11,442.355 1235.16,442.603 1237.2,442.852 \n",
       "  1239.25,443.099 1241.29,443.346 1243.34,443.592 1245.38,443.837 1247.43,444.081 1249.47,444.325 1251.52,444.568 1253.56,444.81 1255.61,445.051 1257.65,445.292 \n",
       "  1259.7,445.532 1261.75,445.771 1263.79,446.009 1265.84,446.247 1267.88,446.484 1269.93,446.72 1271.97,446.955 1274.02,447.19 1276.06,447.424 1278.11,447.657 \n",
       "  1280.15,447.89 1282.2,448.122 1284.24,448.353 1286.29,448.583 1288.34,448.813 1290.38,449.042 1292.43,449.27 1294.47,449.498 1296.52,449.725 1298.56,449.951 \n",
       "  1300.61,450.177 1302.65,450.402 1304.7,450.626 1306.74,450.849 1308.79,451.072 1310.84,451.294 1312.88,451.515 1314.93,451.736 1316.97,451.956 1319.02,452.176 \n",
       "  1321.06,452.394 1323.11,452.612 1325.15,452.83 1327.2,453.046 1329.24,453.263 1331.29,453.478 1333.33,453.693 1335.38,453.907 1337.43,454.12 1339.47,454.333 \n",
       "  1341.52,454.545 1343.56,454.756 1345.61,454.967 1347.65,455.177 1349.7,455.387 1351.74,455.596 1353.79,455.804 1355.83,456.012 1357.88,456.219 1359.92,456.425 \n",
       "  1361.97,456.631 1364.02,456.836 1366.06,457.04 1368.11,457.244 1370.15,457.447 1372.2,457.65 1374.24,457.852 1376.29,458.053 1378.33,458.254 1380.38,458.454 \n",
       "  1382.42,458.654 1384.47,458.853 1386.51,459.051 1388.56,459.249 1390.61,459.446 1392.65,459.642 1394.7,459.838 1396.74,460.034 1398.79,460.228 1400.83,460.423 \n",
       "  1402.88,460.616 1404.92,460.809 1406.97,461.002 1409.01,461.193 1411.06,461.385 1413.1,461.575 1415.15,461.765 1417.2,461.955 1419.24,462.144 1421.29,462.332 \n",
       "  1423.33,462.52 1425.38,462.707 1427.42,462.894 1429.47,463.08 1431.51,463.265 1433.56,463.45 1435.6,463.635 1437.65,463.818 1439.69,464.002 1441.74,464.184 \n",
       "  1443.79,464.367 1445.83,464.548 1447.88,464.729 1449.92,464.91 1451.97,465.09 1454.01,465.269 1456.06,465.448 1458.1,465.626 1460.15,465.804 1462.19,465.981 \n",
       "  1464.24,466.158 1466.28,466.334 1468.33,466.51 1470.38,466.685 1472.42,466.86 1474.47,467.034 1476.51,467.207 1478.56,467.38 1480.6,467.553 1482.65,467.725 \n",
       "  1484.69,467.896 1486.74,468.067 1488.78,468.237 1490.83,468.407 1492.88,468.577 1494.92,468.746 1496.97,468.914 1499.01,469.082 1501.06,469.249 1503.1,469.416 \n",
       "  1505.15,469.582 1507.19,469.748 1509.24,469.914 1511.28,470.078 1513.33,470.243 1515.37,470.407 1517.42,470.57 1519.47,470.733 1521.51,470.895 1523.56,471.057 \n",
       "  1525.6,471.218 1527.65,471.379 1529.69,471.54 1531.74,471.7 1533.78,471.859 1535.83,472.018 1537.87,472.177 1539.92,472.335 1541.96,472.492 1544.01,472.649 \n",
       "  1546.06,472.806 1548.1,472.962 1550.15,473.118 1552.19,473.273 1554.24,473.428 1556.28,473.582 1558.33,473.736 1560.37,473.889 1562.42,474.042 1564.46,474.194 \n",
       "  1566.51,474.346 1568.55,474.498 1570.6,474.649 1572.65,474.8 1574.69,474.95 1576.74,475.099 1578.78,475.249 1580.83,475.397 1582.87,475.546 1584.92,475.694 \n",
       "  1586.96,475.841 1589.01,475.988 1591.05,476.135 1593.1,476.281 1595.14,476.427 1597.19,476.572 1599.24,476.717 1601.28,476.861 1603.33,477.005 1605.37,477.149 \n",
       "  1607.42,477.292 1609.46,477.435 1611.51,477.577 1613.55,477.719 1615.6,477.86 1617.64,478.001 1619.69,478.142 1621.73,478.282 1623.78,478.422 1625.83,478.561 \n",
       "  1627.87,478.7 1629.92,478.838 1631.96,478.976 1634.01,479.114 1636.05,479.251 1638.1,479.388 1640.14,479.525 1642.19,479.661 1644.23,479.796 1646.28,479.932 \n",
       "  1648.33,480.066 1650.37,480.201 1652.42,480.335 1654.46,480.468 1656.51,480.602 1658.55,480.735 1660.6,480.867 1662.64,480.999 1664.69,481.131 1666.73,481.262 \n",
       "  1668.78,481.393 1670.82,481.523 1672.87,481.653 1674.92,481.783 1676.96,481.912 1679.01,482.041 1681.05,482.17 1683.1,482.298 1685.14,482.426 1687.19,482.553 \n",
       "  1689.23,482.68 1691.28,482.807 1693.32,482.933 1695.37,483.059 1697.41,483.185 1699.46,483.31 1701.51,483.435 1703.55,483.559 1705.6,483.683 1707.64,483.807 \n",
       "  1709.69,483.93 1711.73,484.053 1713.78,484.176 1715.82,484.298 1717.87,484.42 1719.91,484.542 1721.96,484.663 1724,484.783 1726.05,484.904 1728.1,485.024 \n",
       "  1730.14,485.144 1732.19,485.263 1734.23,485.382 1736.28,485.501 1738.32,485.619 1740.37,485.737 1742.41,485.855 1744.46,485.972 1746.5,486.089 1748.55,486.206 \n",
       "  1750.59,486.322 1752.64,486.438 1754.69,486.553 1756.73,486.668 1758.78,486.783 1760.82,486.898 1762.87,487.012 1764.91,487.126 1766.96,487.239 1769,487.353 \n",
       "  1771.05,487.466 1773.09,487.578 1775.14,487.69 1777.18,487.802 1779.23,487.914 1781.28,488.025 1783.32,488.136 1785.37,488.246 1787.41,488.357 1789.46,488.466 \n",
       "  1791.5,488.576 1793.55,488.685 1795.59,488.794 1797.64,488.903 1799.68,489.011 1801.73,489.119 1803.78,489.227 1805.82,489.334 1807.87,489.441 1809.91,489.548 \n",
       "  1811.96,489.654 1814,489.761 1816.05,489.866 1818.09,489.972 1820.14,490.077 1822.18,490.182 1824.23,490.286 1826.27,490.391 1828.32,490.495 1830.37,490.598 \n",
       "  1832.41,490.702 1834.46,490.805 1836.5,490.907 1838.55,491.01 1840.59,491.112 1842.64,491.214 1844.68,491.315 1846.73,491.416 1848.77,491.517 1850.82,491.618 \n",
       "  1852.86,491.718 1854.91,491.818 1856.96,491.918 1859,492.017 1861.05,492.117 1863.09,492.215 1865.14,492.314 1867.18,492.412 1869.23,492.51 1871.27,492.608 \n",
       "  1873.32,492.705 1875.36,492.802 1877.41,492.899 1879.45,492.996 1881.5,493.092 1883.55,493.188 1885.59,493.284 1887.64,493.379 1889.68,493.474 1891.73,493.569 \n",
       "  1893.77,493.664 1895.82,493.758 1897.86,493.852 1899.91,493.946 1901.95,494.039 1904,494.133 1906.04,494.226 1908.09,494.318 1910.14,494.411 1912.18,494.503 \n",
       "  1914.23,494.595 1916.27,494.686 1918.32,494.777 1920.36,494.868 1922.41,494.959 1924.45,495.05 1926.5,495.14 1928.54,495.23 1930.59,495.32 1932.63,495.409 \n",
       "  1934.68,495.498 1936.73,495.587 1938.77,495.676 1940.82,495.764 1942.86,495.852 1944.91,495.94 1946.95,496.028 1949,496.115 1951.04,496.202 1953.09,496.289 \n",
       "  1955.13,496.376 1957.18,496.462 1959.23,496.548 1961.27,496.634 1963.32,496.72 1965.36,496.805 1967.41,496.89 1969.45,496.975 1971.5,497.059 1973.54,497.144 \n",
       "  1975.59,497.228 1977.63,497.312 1979.68,497.395 1981.72,497.479 1983.77,497.562 1985.82,497.645 1987.86,497.727 1989.91,497.81 1991.95,497.892 1994,497.974 \n",
       "  1996.04,498.055 1998.09,498.137 2000.13,498.218 2002.18,498.299 2004.22,498.38 2006.27,498.46 2008.31,498.54 2010.36,498.62 2012.41,498.7 2014.45,498.78 \n",
       "  2016.5,498.859 2018.54,498.938 2020.59,499.017 2022.63,499.095 2024.68,499.174 2026.72,499.252 2028.77,499.33 2030.81,499.408 2032.86,499.485 2034.9,499.562 \n",
       "  2036.95,499.639 2039,499.716 2041.04,499.793 2043.09,499.869 2045.13,499.945 2047.18,500.021 2049.22,500.097 2051.27,500.172 2053.31,500.247 2055.36,500.322 \n",
       "  2057.4,500.397 2059.45,500.472 2061.49,500.546 2063.54,500.62 2065.59,500.694 2067.63,500.768 2069.68,500.841 2071.72,500.915 2073.77,500.988 2075.81,501.061 \n",
       "  2077.86,501.133 2079.9,501.206 2081.95,501.278 2083.99,501.35 2086.04,501.422 2088.08,501.493 2090.13,501.565 2092.18,501.636 2094.22,501.707 2096.27,501.778 \n",
       "  2098.31,501.848 2100.36,501.919 2102.4,501.989 2104.45,502.059 2106.49,502.129 2108.54,502.198 2110.58,502.267 2112.63,502.337 2114.68,502.405 2116.72,502.474 \n",
       "  2118.77,502.543 2120.81,502.611 2122.86,502.679 2124.9,502.747 2126.95,502.815 2128.99,502.882 2131.04,502.95 2133.08,503.017 2135.13,503.084 2137.17,503.151 \n",
       "  2139.22,503.217 2141.27,503.284 2143.31,503.35 2145.36,503.416 2147.4,503.482 2149.45,503.547 2151.49,503.613 2153.54,503.678 2155.58,503.743 2157.63,503.808 \n",
       "  2159.67,503.873 2161.72,503.937 2163.76,504.001 2165.81,504.066 2167.86,504.129 2169.9,504.193 2171.95,504.257 2173.99,504.32 2176.04,504.383 2178.08,504.446 \n",
       "  2180.13,504.509 2182.17,504.572 2184.22,504.634 2186.26,504.697 2188.31,504.759 2190.35,504.821 2192.4,504.882 2194.45,504.944 2196.49,505.005 2198.54,505.067 \n",
       "  2200.58,505.128 2202.63,505.188 2204.67,505.249 2206.72,505.31 2208.76,505.37 2210.81,505.43 2212.85,505.49 2214.9,505.55 2216.94,505.61 2218.99,505.669 \n",
       "  2221.04,505.728 2223.08,505.788 2225.13,505.847 2227.17,505.905 2229.22,505.964 2231.26,506.022 2233.31,506.081 2235.35,506.139 2237.4,506.197 2239.44,506.255 \n",
       "  2241.49,506.312 2243.53,506.37 2245.58,506.427 2247.63,506.484 2249.67,506.541 2251.72,506.598 2253.76,506.654 2255.81,506.711 2257.85,506.767 2259.9,506.823 \n",
       "  2261.94,506.879 2263.99,506.935 2266.03,506.991 2268.08,507.046 2270.12,507.101 2272.17,507.157 2274.22,507.212 2276.26,507.266 2278.31,507.321 2280.35,507.376 \n",
       "  2282.4,507.43 2284.44,507.484 2286.49,507.538 2288.53,507.592 2290.58,507.646 2292.62,507.7 2294.67,507.753 2296.72,507.806 2298.76,507.859 2300.81,507.912 \n",
       "  2302.85,507.965 2304.9,508.018 2306.94,508.07 2308.99,508.123 2311.03,508.175 2313.08,508.227 2315.12,508.279 2317.17,508.331 2319.21,508.382 2321.26,508.434 \n",
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       "  686.99,957.214 689.035,957.807 691.081,958.397 693.126,958.986 695.171,959.572 697.217,960.157 699.262,960.739 701.307,961.32 703.353,961.898 705.398,962.475 \n",
       "  707.444,963.049 709.489,963.622 711.534,964.192 713.58,964.761 715.625,965.328 717.671,965.892 719.716,966.455 721.761,967.016 723.807,967.575 725.852,968.132 \n",
       "  727.898,968.688 729.943,969.241 731.988,969.792 734.034,970.342 736.079,970.89 738.125,971.436 740.17,971.98 742.215,972.522 744.261,973.062 746.306,973.601 \n",
       "  748.352,974.137 750.397,974.672 752.442,975.205 754.488,975.737 756.533,976.266 758.579,976.794 760.624,977.32 762.669,977.844 764.715,978.366 766.76,978.887 \n",
       "  768.805,979.406 770.851,979.923 772.896,980.438 774.942,980.952 776.987,981.464 779.032,981.974 781.078,982.483 783.123,982.989 785.169,983.494 787.214,983.998 \n",
       "  789.259,984.5 791.305,985 793.35,985.498 795.396,985.995 797.441,986.49 799.486,986.983 801.532,987.475 803.577,987.965 805.623,988.453 807.668,988.94 \n",
       "  809.713,989.425 811.759,989.909 813.804,990.391 815.85,990.871 817.895,991.35 819.94,991.827 821.986,992.303 824.031,992.777 826.077,993.249 828.122,993.72 \n",
       "  830.167,994.19 832.213,994.657 834.258,995.124 836.304,995.588 838.349,996.051 840.394,996.513 842.44,996.973 844.485,997.431 846.53,997.888 848.576,998.344 \n",
       "  850.621,998.798 852.667,999.25 854.712,999.701 856.757,1000.15 858.803,1000.6 860.848,1001.05 862.894,1001.49 864.939,1001.93 866.984,1002.38 869.03,1002.82 \n",
       "  871.075,1003.26 873.121,1003.69 875.166,1004.13 877.211,1004.57 879.257,1005 881.302,1005.43 883.348,1005.86 885.393,1006.29 887.438,1006.72 889.484,1007.14 \n",
       "  891.529,1007.57 893.575,1007.99 895.62,1008.42 897.665,1008.84 899.711,1009.26 901.756,1009.67 903.802,1010.09 905.847,1010.51 907.892,1010.92 909.938,1011.33 \n",
       "  911.983,1011.74 914.029,1012.15 916.074,1012.56 918.119,1012.97 920.165,1013.38 922.21,1013.78 924.255,1014.18 926.301,1014.59 928.346,1014.99 930.392,1015.39 \n",
       "  932.437,1015.78 934.482,1016.18 936.528,1016.58 938.573,1016.97 940.619,1017.36 942.664,1017.76 944.709,1018.15 946.755,1018.54 948.8,1018.92 950.846,1019.31 \n",
       "  952.891,1019.7 954.936,1020.08 956.982,1020.46 959.027,1020.84 961.073,1021.22 963.118,1021.6 965.163,1021.98 967.209,1022.36 969.254,1022.73 971.3,1023.11 \n",
       "  973.345,1023.48 975.39,1023.85 977.436,1024.22 979.481,1024.59 981.527,1024.96 983.572,1025.33 985.617,1025.7 987.663,1026.06 989.708,1026.42 991.753,1026.79 \n",
       "  993.799,1027.15 995.844,1027.51 997.89,1027.87 999.935,1028.23 1001.98,1028.58 1004.03,1028.94 1006.07,1029.29 1008.12,1029.65 1010.16,1030 1012.21,1030.35 \n",
       "  1014.25,1030.7 1016.3,1031.05 1018.34,1031.39 1020.39,1031.74 1022.43,1032.09 1024.48,1032.43 1026.53,1032.77 1028.57,1033.12 1030.62,1033.46 1032.66,1033.8 \n",
       "  1034.71,1034.14 1036.75,1034.47 1038.8,1034.81 1040.84,1035.15 1042.89,1035.48 1044.93,1035.81 1046.98,1036.15 1049.02,1036.48 1051.07,1036.81 1053.12,1037.14 \n",
       "  1055.16,1037.47 1057.21,1037.79 1059.25,1038.12 1061.3,1038.45 1063.34,1038.77 1065.39,1039.09 1067.43,1039.41 1069.48,1039.74 1071.52,1040.06 1073.57,1040.37 \n",
       "  1075.61,1040.69 1077.66,1041.01 1079.71,1041.33 1081.75,1041.64 1083.8,1041.95 1085.84,1042.27 1087.89,1042.58 1089.93,1042.89 1091.98,1043.2 1094.02,1043.51 \n",
       "  1096.07,1043.82 1098.11,1044.13 1100.16,1044.43 1102.2,1044.74 1104.25,1045.04 1106.3,1045.34 1108.34,1045.65 1110.39,1045.95 1112.43,1046.25 1114.48,1046.55 \n",
       "  1116.52,1046.85 1118.57,1047.14 1120.61,1047.44 1122.66,1047.74 1124.7,1048.03 1126.75,1048.32 1128.79,1048.62 1130.84,1048.91 1132.89,1049.2 1134.93,1049.49 \n",
       "  1136.98,1049.78 1139.02,1050.07 1141.07,1050.36 1143.11,1050.64 1145.16,1050.93 1147.2,1051.21 1149.25,1051.5 1151.29,1051.78 1153.34,1052.06 1155.39,1052.34 \n",
       "  1157.43,1052.62 1159.48,1052.9 1161.52,1053.18 1163.57,1053.46 1165.61,1053.74 1167.66,1054.01 1169.7,1054.29 1171.75,1054.56 1173.79,1054.83 1175.84,1055.11 \n",
       "  1177.88,1055.38 1179.93,1055.65 1181.98,1055.92 1184.02,1056.19 1186.07,1056.46 1188.11,1056.72 1190.16,1056.99 1192.2,1057.26 1194.25,1057.52 1196.29,1057.78 \n",
       "  1198.34,1058.05 1200.38,1058.31 1202.43,1058.57 1204.47,1058.83 1206.52,1059.09 1208.57,1059.35 1210.61,1059.61 1212.66,1059.87 1214.7,1060.13 1216.75,1060.38 \n",
       "  1218.79,1060.64 1220.84,1060.89 1222.88,1061.14 1224.93,1061.4 1226.97,1061.65 1229.02,1061.9 1231.06,1062.15 1233.11,1062.4 1235.16,1062.65 1237.2,1062.9 \n",
       "  1239.25,1063.15 1241.29,1063.39 1243.34,1063.64 1245.38,1063.88 1247.43,1064.13 1249.47,1064.37 1251.52,1064.61 1253.56,1064.86 1255.61,1065.1 1257.65,1065.34 \n",
       "  1259.7,1065.58 1261.75,1065.82 1263.79,1066.06 1265.84,1066.29 1267.88,1066.53 1269.93,1066.77 1271.97,1067 1274.02,1067.24 1276.06,1067.47 1278.11,1067.7 \n",
       "  1280.15,1067.94 1282.2,1068.17 1284.24,1068.4 1286.29,1068.63 1288.34,1068.86 1290.38,1069.09 1292.43,1069.32 1294.47,1069.54 1296.52,1069.77 1298.56,1070 \n",
       "  1300.61,1070.22 1302.65,1070.45 1304.7,1070.67 1306.74,1070.9 1308.79,1071.12 1310.84,1071.34 1312.88,1071.56 1314.93,1071.78 1316.97,1072 1319.02,1072.22 \n",
       "  1321.06,1072.44 1323.11,1072.66 1325.15,1072.88 1327.2,1073.09 1329.24,1073.31 1331.29,1073.52 1333.33,1073.74 1335.38,1073.95 1337.43,1074.17 1339.47,1074.38 \n",
       "  1341.52,1074.59 1343.56,1074.8 1345.61,1075.01 1347.65,1075.22 1349.7,1075.43 1351.74,1075.64 1353.79,1075.85 1355.83,1076.06 1357.88,1076.27 1359.92,1076.47 \n",
       "  1361.97,1076.68 1364.02,1076.88 1366.06,1077.09 1368.11,1077.29 1370.15,1077.49 1372.2,1077.7 1374.24,1077.9 1376.29,1078.1 1378.33,1078.3 1380.38,1078.5 \n",
       "  1382.42,1078.7 1384.47,1078.9 1386.51,1079.1 1388.56,1079.3 1390.61,1079.49 1392.65,1079.69 1394.7,1079.88 1396.74,1080.08 1398.79,1080.27 1400.83,1080.47 \n",
       "  1402.88,1080.66 1404.92,1080.86 1406.97,1081.05 1409.01,1081.24 1411.06,1081.43 1413.1,1081.62 1415.15,1081.81 1417.2,1082 1419.24,1082.19 1421.29,1082.38 \n",
       "  1423.33,1082.57 1425.38,1082.75 1427.42,1082.94 1429.47,1083.13 1431.51,1083.31 1433.56,1083.5 1435.6,1083.68 1437.65,1083.86 1439.69,1084.05 1441.74,1084.23 \n",
       "  1443.79,1084.41 1445.83,1084.59 1447.88,1084.78 1449.92,1084.96 1451.97,1085.14 1454.01,1085.32 1456.06,1085.49 1458.1,1085.67 1460.15,1085.85 1462.19,1086.03 \n",
       "  1464.24,1086.2 1466.28,1086.38 1468.33,1086.56 1470.38,1086.73 1472.42,1086.91 1474.47,1087.08 1476.51,1087.25 1478.56,1087.43 1480.6,1087.6 1482.65,1087.77 \n",
       "  1484.69,1087.94 1486.74,1088.11 1488.78,1088.28 1490.83,1088.45 1492.88,1088.62 1494.92,1088.79 1496.97,1088.96 1499.01,1089.13 1501.06,1089.3 1503.1,1089.46 \n",
       "  1505.15,1089.63 1507.19,1089.79 1509.24,1089.96 1511.28,1090.12 1513.33,1090.29 1515.37,1090.45 1517.42,1090.62 1519.47,1090.78 1521.51,1090.94 1523.56,1091.1 \n",
       "  1525.6,1091.26 1527.65,1091.43 1529.69,1091.59 1531.74,1091.75 1533.78,1091.91 1535.83,1092.06 1537.87,1092.22 1539.92,1092.38 1541.96,1092.54 1544.01,1092.7 \n",
       "  1546.06,1092.85 1548.1,1093.01 1550.15,1093.16 1552.19,1093.32 1554.24,1093.47 1556.28,1093.63 1558.33,1093.78 1560.37,1093.94 1562.42,1094.09 1564.46,1094.24 \n",
       "  1566.51,1094.39 1568.55,1094.54 1570.6,1094.7 1572.65,1094.85 1574.69,1095 1576.74,1095.15 1578.78,1095.3 1580.83,1095.44 1582.87,1095.59 1584.92,1095.74 \n",
       "  1586.96,1095.89 1589.01,1096.03 1591.05,1096.18 1593.1,1096.33 1595.14,1096.47 1597.19,1096.62 1599.24,1096.76 1601.28,1096.91 1603.33,1097.05 1605.37,1097.2 \n",
       "  1607.42,1097.34 1609.46,1097.48 1611.51,1097.62 1613.55,1097.77 1615.6,1097.91 1617.64,1098.05 1619.69,1098.19 1621.73,1098.33 1623.78,1098.47 1625.83,1098.61 \n",
       "  1627.87,1098.75 1629.92,1098.88 1631.96,1099.02 1634.01,1099.16 1636.05,1099.3 1638.1,1099.43 1640.14,1099.57 1642.19,1099.71 1644.23,1099.84 1646.28,1099.98 \n",
       "  1648.33,1100.11 1650.37,1100.25 1652.42,1100.38 1654.46,1100.51 1656.51,1100.65 1658.55,1100.78 1660.6,1100.91 1662.64,1101.05 1664.69,1101.18 1666.73,1101.31 \n",
       "  1668.78,1101.44 1670.82,1101.57 1672.87,1101.7 1674.92,1101.83 1676.96,1101.96 1679.01,1102.09 1681.05,1102.22 1683.1,1102.34 1685.14,1102.47 1687.19,1102.6 \n",
       "  1689.23,1102.73 1691.28,1102.85 1693.32,1102.98 1695.37,1103.11 1697.41,1103.23 1699.46,1103.36 1701.51,1103.48 1703.55,1103.61 1705.6,1103.73 1707.64,1103.85 \n",
       "  1709.69,1103.98 1711.73,1104.1 1713.78,1104.22 1715.82,1104.34 1717.87,1104.47 1719.91,1104.59 1721.96,1104.71 1724,1104.83 1726.05,1104.95 1728.1,1105.07 \n",
       "  1730.14,1105.19 1732.19,1105.31 1734.23,1105.43 1736.28,1105.55 1738.32,1105.67 1740.37,1105.78 1742.41,1105.9 1744.46,1106.02 1746.5,1106.14 1748.55,1106.25 \n",
       "  1750.59,1106.37 1752.64,1106.48 1754.69,1106.6 1756.73,1106.71 1758.78,1106.83 1760.82,1106.94 1762.87,1107.06 1764.91,1107.17 1766.96,1107.29 1769,1107.4 \n",
       "  1771.05,1107.51 1773.09,1107.62 1775.14,1107.74 1777.18,1107.85 1779.23,1107.96 1781.28,1108.07 1783.32,1108.18 1785.37,1108.29 1787.41,1108.4 1789.46,1108.51 \n",
       "  1791.5,1108.62 1793.55,1108.73 1795.59,1108.84 1797.64,1108.95 1799.68,1109.06 1801.73,1109.17 1803.78,1109.27 1805.82,1109.38 1807.87,1109.49 1809.91,1109.59 \n",
       "  1811.96,1109.7 1814,1109.81 1816.05,1109.91 1818.09,1110.02 1820.14,1110.12 1822.18,1110.23 1824.23,1110.33 1826.27,1110.44 1828.32,1110.54 1830.37,1110.64 \n",
       "  1832.41,1110.75 1834.46,1110.85 1836.5,1110.95 1838.55,1111.06 1840.59,1111.16 1842.64,1111.26 1844.68,1111.36 1846.73,1111.46 1848.77,1111.56 1850.82,1111.66 \n",
       "  1852.86,1111.76 1854.91,1111.86 1856.96,1111.96 1859,1112.06 1861.05,1112.16 1863.09,1112.26 1865.14,1112.36 1867.18,1112.46 1869.23,1112.56 1871.27,1112.65 \n",
       "  1873.32,1112.75 1875.36,1112.85 1877.41,1112.95 1879.45,1113.04 1881.5,1113.14 1883.55,1113.23 1885.59,1113.33 1887.64,1113.43 1889.68,1113.52 1891.73,1113.62 \n",
       "  1893.77,1113.71 1895.82,1113.8 1897.86,1113.9 1899.91,1113.99 1901.95,1114.09 1904,1114.18 1906.04,1114.27 1908.09,1114.36 1910.14,1114.46 1912.18,1114.55 \n",
       "  1914.23,1114.64 1916.27,1114.73 1918.32,1114.82 1920.36,1114.91 1922.41,1115.01 1924.45,1115.1 1926.5,1115.19 1928.54,1115.28 1930.59,1115.37 1932.63,1115.46 \n",
       "  1934.68,1115.54 1936.73,1115.63 1938.77,1115.72 1940.82,1115.81 1942.86,1115.9 1944.91,1115.99 1946.95,1116.07 1949,1116.16 1951.04,1116.25 1953.09,1116.34 \n",
       "  1955.13,1116.42 1957.18,1116.51 1959.23,1116.59 1961.27,1116.68 1963.32,1116.77 1965.36,1116.85 1967.41,1116.94 1969.45,1117.02 1971.5,1117.11 1973.54,1117.19 \n",
       "  1975.59,1117.27 1977.63,1117.36 1979.68,1117.44 1981.72,1117.53 1983.77,1117.61 1985.82,1117.69 1987.86,1117.77 1989.91,1117.86 1991.95,1117.94 1994,1118.02 \n",
       "  1996.04,1118.1 1998.09,1118.18 2000.13,1118.26 2002.18,1118.35 2004.22,1118.43 2006.27,1118.51 2008.31,1118.59 2010.36,1118.67 2012.41,1118.75 2014.45,1118.83 \n",
       "  2016.5,1118.91 2018.54,1118.98 2020.59,1119.06 2022.63,1119.14 2024.68,1119.22 2026.72,1119.3 2028.77,1119.38 2030.81,1119.45 2032.86,1119.53 2034.9,1119.61 \n",
       "  2036.95,1119.69 2039,1119.76 2041.04,1119.84 2043.09,1119.92 2045.13,1119.99 2047.18,1120.07 2049.22,1120.14 2051.27,1120.22 2053.31,1120.29 2055.36,1120.37 \n",
       "  2057.4,1120.44 2059.45,1120.52 2061.49,1120.59 2063.54,1120.67 2065.59,1120.74 2067.63,1120.81 2069.68,1120.89 2071.72,1120.96 2073.77,1121.03 2075.81,1121.11 \n",
       "  2077.86,1121.18 2079.9,1121.25 2081.95,1121.32 2083.99,1121.4 2086.04,1121.47 2088.08,1121.54 2090.13,1121.61 2092.18,1121.68 2094.22,1121.75 2096.27,1121.82 \n",
       "  2098.31,1121.89 2100.36,1121.97 2102.4,1122.04 2104.45,1122.11 2106.49,1122.17 2108.54,1122.24 2110.58,1122.31 2112.63,1122.38 2114.68,1122.45 2116.72,1122.52 \n",
       "  2118.77,1122.59 2120.81,1122.66 2122.86,1122.73 2124.9,1122.79 2126.95,1122.86 2128.99,1122.93 2131.04,1123 2133.08,1123.06 2135.13,1123.13 2137.17,1123.2 \n",
       "  2139.22,1123.26 2141.27,1123.33 2143.31,1123.4 2145.36,1123.46 2147.4,1123.53 2149.45,1123.59 2151.49,1123.66 2153.54,1123.72 2155.58,1123.79 2157.63,1123.85 \n",
       "  2159.67,1123.92 2161.72,1123.98 2163.76,1124.05 2165.81,1124.11 2167.86,1124.18 2169.9,1124.24 2171.95,1124.3 2173.99,1124.37 2176.04,1124.43 2178.08,1124.49 \n",
       "  2180.13,1124.56 2182.17,1124.62 2184.22,1124.68 2186.26,1124.74 2188.31,1124.81 2190.35,1124.87 2192.4,1124.93 2194.45,1124.99 2196.49,1125.05 2198.54,1125.11 \n",
       "  2200.58,1125.17 2202.63,1125.23 2204.67,1125.3 2206.72,1125.36 2208.76,1125.42 2210.81,1125.48 2212.85,1125.54 2214.9,1125.6 2216.94,1125.66 2218.99,1125.72 \n",
       "  2221.04,1125.77 2223.08,1125.83 2225.13,1125.89 2227.17,1125.95 2229.22,1126.01 2231.26,1126.07 2233.31,1126.13 2235.35,1126.19 2237.4,1126.24 2239.44,1126.3 \n",
       "  2241.49,1126.36 2243.53,1126.42 2245.58,1126.47 2247.63,1126.53 2249.67,1126.59 2251.72,1126.64 2253.76,1126.7 2255.81,1126.76 2257.85,1126.81 2259.9,1126.87 \n",
       "  2261.94,1126.93 2263.99,1126.98 2266.03,1127.04 2268.08,1127.09 2270.12,1127.15 2272.17,1127.2 2274.22,1127.26 2276.26,1127.31 2278.31,1127.37 2280.35,1127.42 \n",
       "  2282.4,1127.48 2284.44,1127.53 2286.49,1127.58 2288.53,1127.64 2290.58,1127.69 2292.62,1127.75 2294.67,1127.8 2296.72,1127.85 2298.76,1127.91 2300.81,1127.96 \n",
       "  2302.85,1128.01 2304.9,1128.06 2306.94,1128.12 2308.99,1128.17 2311.03,1128.22 2313.08,1128.27 2315.12,1128.33 2317.17,1128.38 2319.21,1128.43 2321.26,1128.48 \n",
       "  \n",
       "  \"/>\n",
       "<polyline clip-path=\"url(#clip5302)\" style=\"stroke:#3da44d; stroke-width:12; stroke-opacity:1; fill:none\" points=\"\n",
       "  277.911,1403.28 279.956,1402.04 282.002,1400.81 284.047,1399.58 286.092,1398.35 288.138,1397.13 290.183,1395.92 292.229,1394.71 294.274,1393.51 296.319,1392.31 \n",
       "  298.365,1391.11 300.41,1389.92 302.456,1388.73 304.501,1387.55 306.546,1386.38 308.592,1385.21 310.637,1384.04 312.683,1382.88 314.728,1381.72 316.773,1380.56 \n",
       "  318.819,1379.42 320.864,1378.27 322.91,1377.13 324.955,1376 327,1374.86 329.046,1373.74 331.091,1372.62 333.136,1371.5 335.182,1370.38 337.227,1369.27 \n",
       "  339.273,1368.17 341.318,1367.07 343.363,1365.97 345.409,1364.88 347.454,1363.79 349.5,1362.71 351.545,1361.63 353.59,1360.55 355.636,1359.48 357.681,1358.42 \n",
       "  359.727,1357.35 361.772,1356.29 363.817,1355.24 365.863,1354.19 367.908,1353.14 369.954,1352.1 371.999,1351.06 374.044,1350.03 376.09,1349 378.135,1347.97 \n",
       "  380.181,1346.95 382.226,1345.93 384.271,1344.91 386.317,1343.9 388.362,1342.89 390.408,1341.89 392.453,1340.89 394.498,1339.89 396.544,1338.9 398.589,1337.91 \n",
       "  400.635,1336.93 402.68,1335.95 404.725,1334.97 406.771,1334 408.816,1333.03 410.861,1332.06 412.907,1331.1 414.952,1330.14 416.998,1329.18 419.043,1328.23 \n",
       "  421.088,1327.28 423.134,1326.34 425.179,1325.4 427.225,1324.46 429.27,1323.53 431.315,1322.6 433.361,1321.67 435.406,1320.75 437.452,1319.83 439.497,1318.91 \n",
       "  441.542,1318 443.588,1317.09 445.633,1316.18 447.679,1315.28 449.724,1314.38 451.769,1313.48 453.815,1312.59 455.86,1311.7 457.906,1310.81 459.951,1309.93 \n",
       "  461.996,1309.05 464.042,1308.17 466.087,1307.3 468.133,1306.43 470.178,1305.56 472.223,1304.7 474.269,1303.84 476.314,1302.98 478.359,1302.12 480.405,1301.27 \n",
       "  482.45,1300.42 484.496,1299.58 486.541,1298.74 488.586,1297.9 490.632,1297.06 492.677,1296.23 494.723,1295.4 496.768,1294.57 498.813,1293.75 500.859,1292.93 \n",
       "  502.904,1292.11 504.95,1291.3 506.995,1290.49 509.04,1289.68 511.086,1288.87 513.131,1288.07 515.177,1287.27 517.222,1286.47 519.267,1285.68 521.313,1284.89 \n",
       "  523.358,1284.1 525.404,1283.31 527.449,1282.53 529.494,1281.75 531.54,1280.97 533.585,1280.2 535.631,1279.43 537.676,1278.66 539.721,1277.89 541.767,1277.13 \n",
       "  543.812,1276.37 545.858,1275.61 547.903,1274.85 549.948,1274.1 551.994,1273.35 554.039,1272.6 556.084,1271.86 558.13,1271.12 560.175,1270.38 562.221,1269.64 \n",
       "  564.266,1268.91 566.311,1268.18 568.357,1267.45 570.402,1266.72 572.448,1266 574.493,1265.28 576.538,1264.56 578.584,1263.85 580.629,1263.13 582.675,1262.42 \n",
       "  584.72,1261.71 586.765,1261.01 588.811,1260.3 590.856,1259.6 592.902,1258.91 594.947,1258.21 596.992,1257.52 599.038,1256.83 601.083,1256.14 603.129,1255.45 \n",
       "  605.174,1254.77 607.219,1254.09 609.265,1253.41 611.31,1252.73 613.356,1252.06 615.401,1251.39 617.446,1250.72 619.492,1250.05 621.537,1249.39 623.582,1248.72 \n",
       "  625.628,1248.06 627.673,1247.41 629.719,1246.75 631.764,1246.1 633.809,1245.45 635.855,1244.8 637.9,1244.15 639.946,1243.51 641.991,1242.87 644.036,1242.23 \n",
       "  646.082,1241.59 648.127,1240.96 650.173,1240.32 652.218,1239.69 654.263,1239.06 656.309,1238.44 658.354,1237.81 660.4,1237.19 662.445,1236.57 664.49,1235.95 \n",
       "  666.536,1235.34 668.581,1234.72 670.627,1234.11 672.672,1233.5 674.717,1232.9 676.763,1232.29 678.808,1231.69 680.854,1231.09 682.899,1230.49 684.944,1229.89 \n",
       "  686.99,1229.3 689.035,1228.71 691.081,1228.12 693.126,1227.53 695.171,1226.94 697.217,1226.36 699.262,1225.77 701.307,1225.19 703.353,1224.62 705.398,1224.04 \n",
       "  707.444,1223.46 709.489,1222.89 711.534,1222.32 713.58,1221.75 715.625,1221.19 717.671,1220.62 719.716,1220.06 721.761,1219.5 723.807,1218.94 725.852,1218.38 \n",
       "  727.898,1217.83 729.943,1217.27 731.988,1216.72 734.034,1216.17 736.079,1215.62 738.125,1215.08 740.17,1214.53 742.215,1213.99 744.261,1213.45 746.306,1212.91 \n",
       "  748.352,1212.38 750.397,1211.84 752.442,1211.31 754.488,1210.78 756.533,1210.25 758.579,1209.72 760.624,1209.19 762.669,1208.67 764.715,1208.15 766.76,1207.63 \n",
       "  768.805,1207.11 770.851,1206.59 772.896,1206.07 774.942,1205.56 776.987,1205.05 779.032,1204.54 781.078,1204.03 783.123,1203.52 785.169,1203.02 787.214,1202.52 \n",
       "  789.259,1202.01 791.305,1201.51 793.35,1201.02 795.396,1200.52 797.441,1200.02 799.486,1199.53 801.532,1199.04 803.577,1198.55 805.623,1198.06 807.668,1197.57 \n",
       "  809.713,1197.09 811.759,1196.6 813.804,1196.12 815.85,1195.64 817.895,1195.16 819.94,1194.69 821.986,1194.21 824.031,1193.74 826.077,1193.26 828.122,1192.79 \n",
       "  830.167,1192.32 832.213,1191.86 834.258,1191.39 836.304,1190.93 838.349,1190.46 840.394,1190 842.44,1189.54 844.485,1189.08 846.53,1188.62 848.576,1188.17 \n",
       "  850.621,1187.72 852.667,1187.26 854.712,1186.81 856.757,1186.36 858.803,1185.91 860.848,1185.47 862.894,1185.02 864.939,1184.58 866.984,1184.14 869.03,1183.7 \n",
       "  871.075,1183.26 873.121,1182.82 875.166,1182.38 877.211,1181.95 879.257,1181.51 881.302,1181.08 883.348,1180.65 885.393,1180.22 887.438,1179.79 889.484,1179.37 \n",
       "  891.529,1178.94 893.575,1178.52 895.62,1178.1 897.665,1177.68 899.711,1177.26 901.756,1176.84 903.802,1176.42 905.847,1176.01 907.892,1175.59 909.938,1175.18 \n",
       "  911.983,1174.77 914.029,1174.36 916.074,1173.95 918.119,1173.54 920.165,1173.14 922.21,1172.73 924.255,1172.33 926.301,1171.93 928.346,1171.53 930.392,1171.13 \n",
       "  932.437,1170.73 934.482,1170.33 936.528,1169.94 938.573,1169.54 940.619,1169.15 942.664,1168.76 944.709,1168.37 946.755,1167.98 948.8,1167.59 950.846,1167.2 \n",
       "  952.891,1166.82 954.936,1166.43 956.982,1166.05 959.027,1165.67 961.073,1165.29 963.118,1164.91 965.163,1164.53 967.209,1164.15 969.254,1163.78 971.3,1163.4 \n",
       "  973.345,1163.03 975.39,1162.66 977.436,1162.29 979.481,1161.92 981.527,1161.55 983.572,1161.18 985.617,1160.82 987.663,1160.45 989.708,1160.09 991.753,1159.73 \n",
       "  993.799,1159.37 995.844,1159 997.89,1158.65 999.935,1158.29 1001.98,1157.93 1004.03,1157.58 1006.07,1157.22 1008.12,1156.87 1010.16,1156.52 1012.21,1156.16 \n",
       "  1014.25,1155.81 1016.3,1155.47 1018.34,1155.12 1020.39,1154.77 1022.43,1154.43 1024.48,1154.08 1026.53,1153.74 1028.57,1153.4 1030.62,1153.06 1032.66,1152.72 \n",
       "  1034.71,1152.38 1036.75,1152.04 1038.8,1151.7 1040.84,1151.37 1042.89,1151.03 1044.93,1150.7 1046.98,1150.37 1049.02,1150.03 1051.07,1149.7 1053.12,1149.37 \n",
       "  1055.16,1149.05 1057.21,1148.72 1059.25,1148.39 1061.3,1148.07 1063.34,1147.74 1065.39,1147.42 1067.43,1147.1 1069.48,1146.78 1071.52,1146.46 1073.57,1146.14 \n",
       "  1075.61,1145.82 1077.66,1145.5 1079.71,1145.19 1081.75,1144.87 1083.8,1144.56 1085.84,1144.25 1087.89,1143.93 1089.93,1143.62 1091.98,1143.31 1094.02,1143 \n",
       "  1096.07,1142.7 1098.11,1142.39 1100.16,1142.08 1102.2,1141.78 1104.25,1141.47 1106.3,1141.17 1108.34,1140.87 1110.39,1140.57 1112.43,1140.27 1114.48,1139.97 \n",
       "  1116.52,1139.67 1118.57,1139.37 1120.61,1139.07 1122.66,1138.78 1124.7,1138.48 1126.75,1138.19 1128.79,1137.9 1130.84,1137.6 1132.89,1137.31 1134.93,1137.02 \n",
       "  1136.98,1136.73 1139.02,1136.45 1141.07,1136.16 1143.11,1135.87 1145.16,1135.59 1147.2,1135.3 1149.25,1135.02 1151.29,1134.73 1153.34,1134.45 1155.39,1134.17 \n",
       "  1157.43,1133.89 1159.48,1133.61 1161.52,1133.33 1163.57,1133.05 1165.61,1132.78 1167.66,1132.5 1169.7,1132.23 1171.75,1131.95 1173.79,1131.68 1175.84,1131.41 \n",
       "  1177.88,1131.14 1179.93,1130.86 1181.98,1130.59 1184.02,1130.33 1186.07,1130.06 1188.11,1129.79 1190.16,1129.52 1192.2,1129.26 1194.25,1128.99 1196.29,1128.73 \n",
       "  1198.34,1128.47 1200.38,1128.2 1202.43,1127.94 1204.47,1127.68 1206.52,1127.42 1208.57,1127.16 1210.61,1126.9 1212.66,1126.64 1214.7,1126.39 1216.75,1126.13 \n",
       "  1218.79,1125.88 1220.84,1125.62 1222.88,1125.37 1224.93,1125.12 1226.97,1124.86 1229.02,1124.61 1231.06,1124.36 1233.11,1124.11 1235.16,1123.86 1237.2,1123.62 \n",
       "  1239.25,1123.37 1241.29,1123.12 1243.34,1122.88 1245.38,1122.63 1247.43,1122.39 1249.47,1122.14 1251.52,1121.9 1253.56,1121.66 1255.61,1121.42 1257.65,1121.18 \n",
       "  1259.7,1120.94 1261.75,1120.7 1263.79,1120.46 1265.84,1120.22 1267.88,1119.98 1269.93,1119.75 1271.97,1119.51 1274.02,1119.28 1276.06,1119.04 1278.11,1118.81 \n",
       "  1280.15,1118.58 1282.2,1118.35 1284.24,1118.11 1286.29,1117.88 1288.34,1117.65 1290.38,1117.42 1292.43,1117.2 1294.47,1116.97 1296.52,1116.74 1298.56,1116.52 \n",
       "  1300.61,1116.29 1302.65,1116.07 1304.7,1115.84 1306.74,1115.62 1308.79,1115.39 1310.84,1115.17 1312.88,1114.95 1314.93,1114.73 1316.97,1114.51 1319.02,1114.29 \n",
       "  1321.06,1114.07 1323.11,1113.85 1325.15,1113.64 1327.2,1113.42 1329.24,1113.2 1331.29,1112.99 1333.33,1112.77 1335.38,1112.56 1337.43,1112.35 1339.47,1112.13 \n",
       "  1341.52,1111.92 1343.56,1111.71 1345.61,1111.5 1347.65,1111.29 1349.7,1111.08 1351.74,1110.87 1353.79,1110.66 1355.83,1110.46 1357.88,1110.25 1359.92,1110.04 \n",
       "  1361.97,1109.84 1364.02,1109.63 1366.06,1109.43 1368.11,1109.22 1370.15,1109.02 1372.2,1108.82 1374.24,1108.61 1376.29,1108.41 1378.33,1108.21 1380.38,1108.01 \n",
       "  1382.42,1107.81 1384.47,1107.61 1386.51,1107.42 1388.56,1107.22 1390.61,1107.02 1392.65,1106.82 1394.7,1106.63 1396.74,1106.43 1398.79,1106.24 1400.83,1106.04 \n",
       "  1402.88,1105.85 1404.92,1105.66 1406.97,1105.47 1409.01,1105.27 1411.06,1105.08 1413.1,1104.89 1415.15,1104.7 1417.2,1104.51 1419.24,1104.32 1421.29,1104.13 \n",
       "  1423.33,1103.95 1425.38,1103.76 1427.42,1103.57 1429.47,1103.39 1431.51,1103.2 1433.56,1103.02 1435.6,1102.83 1437.65,1102.65 1439.69,1102.47 1441.74,1102.28 \n",
       "  1443.79,1102.1 1445.83,1101.92 1447.88,1101.74 1449.92,1101.56 1451.97,1101.38 1454.01,1101.2 1456.06,1101.02 1458.1,1100.84 1460.15,1100.66 1462.19,1100.49 \n",
       "  1464.24,1100.31 1466.28,1100.13 1468.33,1099.96 1470.38,1099.78 1472.42,1099.61 1474.47,1099.43 1476.51,1099.26 1478.56,1099.09 1480.6,1098.91 1482.65,1098.74 \n",
       "  1484.69,1098.57 1486.74,1098.4 1488.78,1098.23 1490.83,1098.06 1492.88,1097.89 1494.92,1097.72 1496.97,1097.55 1499.01,1097.39 1501.06,1097.22 1503.1,1097.05 \n",
       "  1505.15,1096.88 1507.19,1096.72 1509.24,1096.55 1511.28,1096.39 1513.33,1096.22 1515.37,1096.06 1517.42,1095.9 1519.47,1095.73 1521.51,1095.57 1523.56,1095.41 \n",
       "  1525.6,1095.25 1527.65,1095.09 1529.69,1094.93 1531.74,1094.77 1533.78,1094.61 1535.83,1094.45 1537.87,1094.29 1539.92,1094.13 1541.96,1093.97 1544.01,1093.82 \n",
       "  1546.06,1093.66 1548.1,1093.5 1550.15,1093.35 1552.19,1093.19 1554.24,1093.04 1556.28,1092.88 1558.33,1092.73 1560.37,1092.58 1562.42,1092.42 1564.46,1092.27 \n",
       "  1566.51,1092.12 1568.55,1091.97 1570.6,1091.82 1572.65,1091.67 1574.69,1091.52 1576.74,1091.37 1578.78,1091.22 1580.83,1091.07 1582.87,1090.92 1584.92,1090.77 \n",
       "  1586.96,1090.63 1589.01,1090.48 1591.05,1090.33 1593.1,1090.19 1595.14,1090.04 1597.19,1089.89 1599.24,1089.75 1601.28,1089.61 1603.33,1089.46 1605.37,1089.32 \n",
       "  1607.42,1089.17 1609.46,1089.03 1611.51,1088.89 1613.55,1088.75 1615.6,1088.61 1617.64,1088.47 1619.69,1088.33 1621.73,1088.18 1623.78,1088.05 1625.83,1087.91 \n",
       "  1627.87,1087.77 1629.92,1087.63 1631.96,1087.49 1634.01,1087.35 1636.05,1087.22 1638.1,1087.08 1640.14,1086.94 1642.19,1086.81 1644.23,1086.67 1646.28,1086.54 \n",
       "  1648.33,1086.4 1650.37,1086.27 1652.42,1086.13 1654.46,1086 1656.51,1085.87 1658.55,1085.73 1660.6,1085.6 1662.64,1085.47 1664.69,1085.34 1666.73,1085.2 \n",
       "  1668.78,1085.07 1670.82,1084.94 1672.87,1084.81 1674.92,1084.68 1676.96,1084.55 1679.01,1084.43 1681.05,1084.3 1683.1,1084.17 1685.14,1084.04 1687.19,1083.91 \n",
       "  1689.23,1083.79 1691.28,1083.66 1693.32,1083.53 1695.37,1083.41 1697.41,1083.28 1699.46,1083.16 1701.51,1083.03 1703.55,1082.91 1705.6,1082.78 1707.64,1082.66 \n",
       "  1709.69,1082.54 1711.73,1082.41 1713.78,1082.29 1715.82,1082.17 1717.87,1082.05 1719.91,1081.93 1721.96,1081.8 1724,1081.68 1726.05,1081.56 1728.1,1081.44 \n",
       "  1730.14,1081.32 1732.19,1081.2 1734.23,1081.08 1736.28,1080.97 1738.32,1080.85 1740.37,1080.73 1742.41,1080.61 1744.46,1080.49 1746.5,1080.38 1748.55,1080.26 \n",
       "  1750.59,1080.15 1752.64,1080.03 1754.69,1079.91 1756.73,1079.8 1758.78,1079.68 1760.82,1079.57 1762.87,1079.45 1764.91,1079.34 1766.96,1079.23 1769,1079.11 \n",
       "  1771.05,1079 1773.09,1078.89 1775.14,1078.78 1777.18,1078.66 1779.23,1078.55 1781.28,1078.44 1783.32,1078.33 1785.37,1078.22 1787.41,1078.11 1789.46,1078 \n",
       "  1791.5,1077.89 1793.55,1077.78 1795.59,1077.67 1797.64,1077.56 1799.68,1077.46 1801.73,1077.35 1803.78,1077.24 1805.82,1077.13 1807.87,1077.03 1809.91,1076.92 \n",
       "  1811.96,1076.81 1814,1076.71 1816.05,1076.6 1818.09,1076.5 1820.14,1076.39 1822.18,1076.29 1824.23,1076.18 1826.27,1076.08 1828.32,1075.97 1830.37,1075.87 \n",
       "  1832.41,1075.77 1834.46,1075.66 1836.5,1075.56 1838.55,1075.46 1840.59,1075.36 1842.64,1075.25 1844.68,1075.15 1846.73,1075.05 1848.77,1074.95 1850.82,1074.85 \n",
       "  1852.86,1074.75 1854.91,1074.65 1856.96,1074.55 1859,1074.45 1861.05,1074.35 1863.09,1074.25 1865.14,1074.15 1867.18,1074.05 1869.23,1073.96 1871.27,1073.86 \n",
       "  1873.32,1073.76 1875.36,1073.66 1877.41,1073.57 1879.45,1073.47 1881.5,1073.37 1883.55,1073.28 1885.59,1073.18 1887.64,1073.09 1889.68,1072.99 1891.73,1072.9 \n",
       "  1893.77,1072.8 1895.82,1072.71 1897.86,1072.61 1899.91,1072.52 1901.95,1072.43 1904,1072.33 1906.04,1072.24 1908.09,1072.15 1910.14,1072.06 1912.18,1071.96 \n",
       "  1914.23,1071.87 1916.27,1071.78 1918.32,1071.69 1920.36,1071.6 1922.41,1071.51 1924.45,1071.42 1926.5,1071.33 1928.54,1071.24 1930.59,1071.15 1932.63,1071.06 \n",
       "  1934.68,1070.97 1936.73,1070.88 1938.77,1070.79 1940.82,1070.7 1942.86,1070.61 1944.91,1070.53 1946.95,1070.44 1949,1070.35 1951.04,1070.26 1953.09,1070.18 \n",
       "  1955.13,1070.09 1957.18,1070 1959.23,1069.92 1961.27,1069.83 1963.32,1069.75 1965.36,1069.66 1967.41,1069.58 1969.45,1069.49 1971.5,1069.41 1973.54,1069.32 \n",
       "  1975.59,1069.24 1977.63,1069.16 1979.68,1069.07 1981.72,1068.99 1983.77,1068.91 1985.82,1068.82 1987.86,1068.74 1989.91,1068.66 1991.95,1068.58 1994,1068.49 \n",
       "  1996.04,1068.41 1998.09,1068.33 2000.13,1068.25 2002.18,1068.17 2004.22,1068.09 2006.27,1068.01 2008.31,1067.93 2010.36,1067.85 2012.41,1067.77 2014.45,1067.69 \n",
       "  2016.5,1067.61 2018.54,1067.53 2020.59,1067.45 2022.63,1067.37 2024.68,1067.29 2026.72,1067.21 2028.77,1067.14 2030.81,1067.06 2032.86,1066.98 2034.9,1066.9 \n",
       "  2036.95,1066.83 2039,1066.75 2041.04,1066.67 2043.09,1066.6 2045.13,1066.52 2047.18,1066.45 2049.22,1066.37 2051.27,1066.29 2053.31,1066.22 2055.36,1066.14 \n",
       "  2057.4,1066.07 2059.45,1066 2061.49,1065.92 2063.54,1065.85 2065.59,1065.77 2067.63,1065.7 2069.68,1065.63 2071.72,1065.55 2073.77,1065.48 2075.81,1065.41 \n",
       "  2077.86,1065.33 2079.9,1065.26 2081.95,1065.19 2083.99,1065.12 2086.04,1065.05 2088.08,1064.97 2090.13,1064.9 2092.18,1064.83 2094.22,1064.76 2096.27,1064.69 \n",
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   "source": [
    "B=sol4[2,:]\n",
    "c_eq=B*u₀[1]./(B.+(k2/k1))\n",
    "plot(sol4,label=[\"a\",\"b\",\"c\"])\n",
    "plot!(sol4.t,c_eq,label=\"C_eq\")\n",
    "title!(\"Reversible ODE solver using DSL and Equilibrium solution\")\n",
    "xlabel!(\"Time [s]\")\n",
    "ylabel!(\"Concentration [M]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. A practical case\n",
    "\n",
    "Now we will solve the more complex reaction\n",
    "\n",
    "$$ NaCO_3 + CaCl_2  \\overset{k_1}{\\underset{k_2}{\\longleftrightarrow}}  CaCO_3 + 2 NaCl \\tag{22}$$\n",
    "\n",
    "\n",
    "\n",
    "with forward and reverse kinetic constants `k1` and `k2`, respectively. We decompose the reversible reaction into two reactions:\n",
    "$$\\begin{align} \n",
    " NaCO_3 + CaCl_2  &\\overset{k_1}{\\longrightarrow}  CaCO_3 + 2 NaCl \\tag{23}\\\\\n",
    " CaCO_3 + 2 NaCl &\\overset{k_2}{\\longrightarrow} NaCO_3 + CaCl_2 \\tag{24}\n",
    " \\end{align}\n",
    "$$\n",
    "\n",
    "\n",
    "The system consists of four species $X_s=1…4$ and two reactions $k_j=1…2$. Renaming the reactants for simplicity ($a = NaCO_3$, $b  =CaCl_2$, $c  = CaCo_3$, $d = NaCl)$, we obtain\n",
    "\n",
    "$$\\begin{align} \n",
    " a + b  &\\overset{k_1}{\\longrightarrow}  c + 2 d \\tag{25}\\\\\n",
    " c + 2 d &\\overset{k_2}{\\longrightarrow} a + b \\tag{26}\n",
    " \\end{align}\n",
    "$$\n",
    "\n",
    "For this system, the stoichiometrix matrices are:\n",
    "$$\n",
    "A=\\begin{bmatrix}\n",
    " 1& 1 & 0 & 0  \\tag{27}\\\\ \n",
    " 0 & 0 &1   &2  \n",
    "\\end{bmatrix} $$\n",
    "\n",
    "$$\n",
    "B=\\begin{bmatrix}\n",
    "0 & 0 &1   &2 \\tag{28}\\\\ \n",
    "1 & 1 &0   &0  \n",
    "\\end{bmatrix}\n",
    "\\\\\n",
    "$$\n",
    "The forward reaction is of order 2, the backward reaction is of order 3. Therefore, the units of $k_1 = s^{-1} M^{-1}$, and the units of $k_2 = s^{-1} M^{-2}$\n",
    "\n",
    "Based on Mass Action Kinetics, the system of differential equations consists in the following four coupled ODEs:\n",
    "\n",
    "$$\\begin{align}        \n",
    "            \\frac{ da }{dt} &= - k_1 \\cdot a \\cdot b + k_2 \\cdot c \\cdot d^2  \\tag{29}\\\\ \n",
    "            \\frac{ db }{dt} &= - k_1 \\cdot a \\cdot b + k_2 \\cdot c \\cdot d^2   \\tag{30}  \\\\\n",
    "             \\frac{ dc }{dt} &=  k_1 \\cdot a \\cdot b - k_2 \\cdot c \\cdot d^2  \\tag{31}  \\\\\n",
    "              \\frac{ dd }{dt} &= 2 k_1 \\cdot a  \\cdot b - 2 k_2 \\cdot c \\cdot d^2   \\tag{32}  \\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Next, we solve the equations numerically:"
   ]
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  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(::abetterway{getfield(Main, Symbol(\"##19#23\")),getfield(Main, Symbol(\"##20#24\")),getfield(Main, Symbol(\"##21#25\")),Nothing,Nothing,getfield(Main, Symbol(\"##22#26\")),Expr,Expr}) (generic function with 2 methods)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simpleODE3! = @ode_def abetterway begin\n",
    "  da = -k1 * a * b + k2 * c * d^2\n",
    "  db = -k1 * a * b + k2 * c * d^2\n",
    "  dc = k1 * a * b - k2 * c * d^2\n",
    "  dd = 2 * k1 * a * b - 2 * k2 * c * d^2\n",
    "    end k1 k2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "k1=2.3e0;  # units 1/(Ms)\n",
    "k2=2.5e0;  # units 1/(M M s)\n",
    "\n",
    "p = (k1,k2)\n",
    "\n",
    "a₀=0.02; # units (M)\n",
    "b₀=0.01; # units (M)\n",
    "c₀=0; # units (M)\n",
    "d₀=0; # units (M)\n",
    "\n",
    "u₀=[a₀,b₀,c₀,d₀];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
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       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:66px; text-anchor:middle;\" transform=\"rotate(0, 1299.59, 1590.4)\" x=\"1299.59\" y=\"1590.4\">Time [s]</text>\n",
       "</g>\n",
       "<g clip-path=\"url(#clip5700)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:66px; text-anchor:middle;\" transform=\"rotate(-90, 57.6, 783.233)\" x=\"57.6\" y=\"783.233\">Concentration [M]</text>\n",
       "</g>\n",
       "<polyline clip-path=\"url(#clip5702)\" style=\"stroke:#009af9; stroke-width:12; stroke-opacity:1; fill:none\" points=\"\n",
       "  277.911,163.187 279.956,166.032 282.002,168.858 284.047,171.664 286.092,174.452 288.138,177.22 290.183,179.969 292.229,182.7 294.274,185.413 296.319,188.107 \n",
       "  298.365,190.783 300.41,193.442 302.456,196.082 304.501,198.706 306.546,201.311 308.592,203.9 310.637,206.471 312.683,209.026 314.728,211.564 316.773,214.085 \n",
       "  318.819,216.59 320.864,219.079 322.91,221.552 324.955,224.008 327,226.449 329.046,228.874 331.091,231.284 333.136,233.678 335.182,236.057 337.227,238.421 \n",
       "  339.273,240.769 341.318,243.103 343.363,245.423 345.409,247.728 347.454,250.018 349.5,252.294 351.545,254.556 353.59,256.804 355.636,259.037 357.681,261.257 \n",
       "  359.727,263.464 361.772,265.657 363.817,267.836 365.863,270.002 367.908,272.155 369.954,274.294 371.999,276.421 374.044,278.535 376.09,280.636 378.135,282.724 \n",
       "  380.181,284.8 382.226,286.863 384.271,288.914 386.317,290.953 388.362,292.98 390.408,294.995 392.453,296.997 394.498,298.988 396.544,300.967 398.589,302.935 \n",
       "  400.635,304.89 402.68,306.835 404.725,308.768 406.771,310.69 408.816,312.6 410.861,314.5 412.907,316.389 414.952,318.266 416.998,320.133 419.043,321.989 \n",
       "  421.088,323.835 423.134,325.67 425.179,327.494 427.225,329.308 429.27,331.112 431.315,332.905 433.361,334.689 435.406,336.462 437.452,338.226 439.497,339.979 \n",
       "  441.542,341.723 443.588,343.457 445.633,345.181 447.679,346.896 449.724,348.601 451.769,350.297 453.815,351.983 455.86,353.66 457.906,355.328 459.951,356.986 \n",
       "  461.996,358.636 464.042,360.277 466.087,361.908 468.133,363.531 470.178,365.145 472.223,366.75 474.269,368.346 476.314,369.934 478.359,371.513 480.405,373.084 \n",
       "  482.45,374.646 484.496,376.2 486.541,377.746 488.586,379.283 490.632,380.813 492.677,382.334 494.723,383.847 496.768,385.352 498.813,386.849 500.859,388.338 \n",
       "  502.904,389.82 504.95,391.293 506.995,392.759 509.04,394.217 511.086,395.668 513.131,397.111 515.177,398.546 517.222,399.974 519.267,401.395 521.313,402.808 \n",
       "  523.358,404.214 525.404,405.613 527.449,407.004 529.494,408.389 531.54,409.766 533.585,411.136 535.631,412.5 537.676,413.856 539.721,415.206 541.767,416.548 \n",
       "  543.812,417.884 545.858,419.213 547.903,420.535 549.948,421.851 551.994,423.16 554.039,424.463 556.084,425.759 558.13,427.048 560.175,428.331 562.221,429.608 \n",
       "  564.266,430.878 566.311,432.142 568.357,433.4 570.402,434.652 572.448,435.897 574.493,437.136 576.538,438.369 578.584,439.597 580.629,440.818 582.675,442.033 \n",
       "  584.72,443.242 586.765,444.445 588.811,445.643 590.856,446.835 592.902,448.02 594.947,449.201 596.992,450.375 599.038,451.544 601.083,452.707 603.129,453.864 \n",
       "  605.174,455.016 607.219,456.163 609.265,457.304 611.31,458.439 613.356,459.569 615.401,460.694 617.446,461.813 619.492,462.928 621.537,464.036 623.582,465.14 \n",
       "  625.628,466.238 627.673,467.331 629.719,468.419 631.764,469.502 633.809,470.58 635.855,471.653 637.9,472.721 639.946,473.783 641.991,474.841 644.036,475.894 \n",
       "  646.082,476.942 648.127,477.985 650.173,479.023 652.218,480.057 654.263,481.086 656.309,482.109 658.354,483.129 660.4,484.143 662.445,485.153 664.49,486.158 \n",
       "  666.536,487.159 668.581,488.155 670.627,489.146 672.672,490.133 674.717,491.116 676.763,492.094 678.808,493.067 680.854,494.036 682.899,495.001 684.944,495.961 \n",
       "  686.99,496.917 689.035,497.869 691.081,498.816 693.126,499.76 695.171,500.698 697.217,501.633 699.262,502.564 701.307,503.49 703.353,504.412 705.398,505.33 \n",
       "  707.444,506.245 709.489,507.154 711.534,508.06 713.58,508.962 715.625,509.86 717.671,510.754 719.716,511.644 721.761,512.53 723.807,513.413 725.852,514.291 \n",
       "  727.898,515.166 729.943,516.036 731.988,516.903 734.034,517.766 736.079,518.625 738.125,519.481 740.17,520.333 742.215,521.181 744.261,522.026 746.306,522.866 \n",
       "  748.352,523.704 750.397,524.537 752.442,525.367 754.488,526.194 756.533,527.016 758.579,527.836 760.624,528.652 762.669,529.464 764.715,530.273 766.76,531.078 \n",
       "  768.805,531.88 770.851,532.679 772.896,533.474 774.942,534.266 776.987,535.054 779.032,535.839 781.078,536.621 783.123,537.399 785.169,538.174 787.214,538.946 \n",
       "  789.259,539.715 791.305,540.48 793.35,541.242 795.396,542.001 797.441,542.757 799.486,543.51 801.532,544.259 803.577,545.005 805.623,545.748 807.668,546.488 \n",
       "  809.713,547.225 811.759,547.959 813.804,548.69 815.85,549.418 817.895,550.143 819.94,550.865 821.986,551.584 824.031,552.3 826.077,553.013 828.122,553.723 \n",
       "  830.167,554.43 832.213,555.134 834.258,555.835 836.304,556.534 838.349,557.229 840.394,557.922 842.44,558.612 844.485,559.299 846.53,559.983 848.576,560.664 \n",
       "  850.621,561.343 852.667,562.019 854.712,562.692 856.757,563.363 858.803,564.03 860.848,564.695 862.894,565.358 864.939,566.017 866.984,566.674 869.03,567.328 \n",
       "  871.075,567.98 873.121,568.629 875.166,569.276 877.211,569.919 879.257,570.561 881.302,571.199 883.348,571.835 885.393,572.469 887.438,573.1 889.484,573.729 \n",
       "  891.529,574.355 893.575,574.978 895.62,575.599 897.665,576.218 899.711,576.834 901.756,577.448 903.802,578.059 905.847,578.668 907.892,579.274 909.938,579.878 \n",
       "  911.983,580.48 914.029,581.079 916.074,581.676 918.119,582.271 920.165,582.863 922.21,583.453 924.255,584.04 926.301,584.626 928.346,585.209 930.392,585.789 \n",
       "  932.437,586.368 934.482,586.944 936.528,587.518 938.573,588.09 940.619,588.659 942.664,589.227 944.709,589.792 946.755,590.355 948.8,590.916 950.846,591.474 \n",
       "  952.891,592.031 954.936,592.585 956.982,593.137 959.027,593.687 961.073,594.235 963.118,594.781 965.163,595.325 967.209,595.866 969.254,596.406 971.3,596.943 \n",
       "  973.345,597.479 975.39,598.012 977.436,598.544 979.481,599.073 981.527,599.6 983.572,600.126 985.617,600.649 987.663,601.17 989.708,601.69 991.753,602.207 \n",
       "  993.799,602.722 995.844,603.236 997.89,603.748 999.935,604.257 1001.98,604.765 1004.03,605.271 1006.07,605.775 1008.12,606.277 1010.16,606.777 1012.21,607.275 \n",
       "  1014.25,607.771 1016.3,608.266 1018.34,608.758 1020.39,609.249 1022.43,609.738 1024.48,610.225 1026.53,610.711 1028.57,611.194 1030.62,611.676 1032.66,612.156 \n",
       "  1034.71,612.634 1036.75,613.11 1038.8,613.585 1040.84,614.057 1042.89,614.528 1044.93,614.998 1046.98,615.465 1049.02,615.931 1051.07,616.395 1053.12,616.858 \n",
       "  1055.16,617.318 1057.21,617.777 1059.25,618.235 1061.3,618.69 1063.34,619.144 1065.39,619.597 1067.43,620.047 1069.48,620.496 1071.52,620.944 1073.57,621.389 \n",
       "  1075.61,621.833 1077.66,622.276 1079.71,622.717 1081.75,623.156 1083.8,623.593 1085.84,624.029 1087.89,624.464 1089.93,624.897 1091.98,625.328 1094.02,625.758 \n",
       "  1096.07,626.186 1098.11,626.612 1100.16,627.037 1102.2,627.461 1104.25,627.883 1106.3,628.303 1108.34,628.722 1110.39,629.14 1112.43,629.555 1114.48,629.97 \n",
       "  1116.52,630.383 1118.57,630.794 1120.61,631.204 1122.66,631.612 1124.7,632.019 1126.75,632.425 1128.79,632.829 1130.84,633.231 1132.89,633.633 1134.93,634.032 \n",
       "  1136.98,634.431 1139.02,634.827 1141.07,635.223 1143.11,635.617 1145.16,636.009 1147.2,636.401 1149.25,636.79 1151.29,637.179 1153.34,637.566 1155.39,637.951 \n",
       "  1157.43,638.336 1159.48,638.719 1161.52,639.1 1163.57,639.48 1165.61,639.859 1167.66,640.237 1169.7,640.613 1171.75,640.988 1173.79,641.361 1175.84,641.734 \n",
       "  1177.88,642.104 1179.93,642.474 1181.98,642.842 1184.02,643.209 1186.07,643.575 1188.11,643.939 1190.16,644.302 1192.2,644.664 1194.25,645.025 1196.29,645.384 \n",
       "  1198.34,645.742 1200.38,646.099 1202.43,646.455 1204.47,646.809 1206.52,647.162 1208.57,647.514 1210.61,647.864 1212.66,648.214 1214.7,648.562 1216.75,648.909 \n",
       "  1218.79,649.255 1220.84,649.599 1222.88,649.943 1224.93,650.285 1226.97,650.626 1229.02,650.966 1231.06,651.304 1233.11,651.642 1235.16,651.978 1237.2,652.313 \n",
       "  1239.25,652.647 1241.29,652.98 1243.34,653.312 1245.38,653.642 1247.43,653.972 1249.47,654.3 1251.52,654.627 1253.56,654.953 1255.61,655.278 1257.65,655.602 \n",
       "  1259.7,655.924 1261.75,656.246 1263.79,656.566 1265.84,656.886 1267.88,657.204 1269.93,657.521 1271.97,657.837 1274.02,658.152 1276.06,658.466 1278.11,658.779 \n",
       "  1280.15,659.091 1282.2,659.402 1284.24,659.711 1286.29,660.02 1288.34,660.328 1290.38,660.634 1292.43,660.94 1294.47,661.244 1296.52,661.548 1298.56,661.85 \n",
       "  1300.61,662.151 1302.65,662.452 1304.7,662.751 1306.74,663.049 1308.79,663.347 1310.84,663.643 1312.88,663.938 1314.93,664.233 1316.97,664.526 1319.02,664.818 \n",
       "  1321.06,665.11 1323.11,665.4 1325.15,665.689 1327.2,665.978 1329.24,666.265 1331.29,666.552 1333.33,666.837 1335.38,667.122 1337.43,667.405 1339.47,667.688 \n",
       "  1341.52,667.97 1343.56,668.25 1345.61,668.53 1347.65,668.809 1349.7,669.087 1351.74,669.364 1353.79,669.64 1355.83,669.916 1357.88,670.19 1359.92,670.463 \n",
       "  1361.97,670.736 1364.02,671.007 1366.06,671.278 1368.11,671.547 1370.15,671.816 1372.2,672.084 1374.24,672.351 1376.29,672.618 1378.33,672.883 1380.38,673.147 \n",
       "  1382.42,673.411 1384.47,673.673 1386.51,673.935 1388.56,674.196 1390.61,674.456 1392.65,674.715 1394.7,674.974 1396.74,675.231 1398.79,675.488 1400.83,675.744 \n",
       "  1402.88,675.998 1404.92,676.253 1406.97,676.506 1409.01,676.758 1411.06,677.01 1413.1,677.261 1415.15,677.51 1417.2,677.76 1419.24,678.008 1421.29,678.255 \n",
       "  1423.33,678.502 1425.38,678.748 1427.42,678.993 1429.47,679.237 1431.51,679.481 1433.56,679.723 1435.6,679.965 1437.65,680.206 1439.69,680.446 1441.74,680.686 \n",
       "  1443.79,680.924 1445.83,681.162 1447.88,681.399 1449.92,681.636 1451.97,681.871 1454.01,682.106 1456.06,682.34 1458.1,682.573 1460.15,682.806 1462.19,683.038 \n",
       "  1464.24,683.269 1466.28,683.499 1468.33,683.728 1470.38,683.957 1472.42,684.185 1474.47,684.412 1476.51,684.639 1478.56,684.865 1480.6,685.09 1482.65,685.314 \n",
       "  1484.69,685.538 1486.74,685.761 1488.78,685.983 1490.83,686.204 1492.88,686.425 1494.92,686.645 1496.97,686.864 1499.01,687.083 1501.06,687.301 1503.1,687.518 \n",
       "  1505.15,687.734 1507.19,687.95 1509.24,688.165 1511.28,688.38 1513.33,688.593 1515.37,688.806 1517.42,689.019 1519.47,689.23 1521.51,689.441 1523.56,689.651 \n",
       "  1525.6,689.861 1527.65,690.07 1529.69,690.278 1531.74,690.486 1533.78,690.693 1535.83,690.899 1537.87,691.105 1539.92,691.31 1541.96,691.514 1544.01,691.717 \n",
       "  1546.06,691.92 1548.1,692.123 1550.15,692.325 1552.19,692.526 1554.24,692.726 1556.28,692.926 1558.33,693.125 1560.37,693.323 1562.42,693.521 1564.46,693.718 \n",
       "  1566.51,693.915 1568.55,694.111 1570.6,694.306 1572.65,694.501 1574.69,694.695 1576.74,694.889 1578.78,695.082 1580.83,695.274 1582.87,695.466 1584.92,695.657 \n",
       "  1586.96,695.847 1589.01,696.037 1591.05,696.226 1593.1,696.415 1595.14,696.603 1597.19,696.791 1599.24,696.977 1601.28,697.164 1603.33,697.349 1605.37,697.535 \n",
       "  1607.42,697.719 1609.46,697.903 1611.51,698.086 1613.55,698.269 1615.6,698.452 1617.64,698.633 1619.69,698.814 1621.73,698.995 1623.78,699.175 1625.83,699.354 \n",
       "  1627.87,699.533 1629.92,699.711 1631.96,699.889 1634.01,700.066 1636.05,700.243 1638.1,700.419 1640.14,700.594 1642.19,700.769 1644.23,700.943 1646.28,701.117 \n",
       "  1648.33,701.291 1650.37,701.463 1652.42,701.635 1654.46,701.807 1656.51,701.978 1658.55,702.149 1660.6,702.319 1662.64,702.489 1664.69,702.658 1666.73,702.826 \n",
       "  1668.78,702.994 1670.82,703.161 1672.87,703.328 1674.92,703.495 1676.96,703.661 1679.01,703.826 1681.05,703.991 1683.1,704.155 1685.14,704.319 1687.19,704.482 \n",
       "  1689.23,704.645 1691.28,704.807 1693.32,704.969 1695.37,705.13 1697.41,705.291 1699.46,705.451 1701.51,705.611 1703.55,705.77 1705.6,705.929 1707.64,706.088 \n",
       "  1709.69,706.245 1711.73,706.403 1713.78,706.56 1715.82,706.716 1717.87,706.872 1719.91,707.027 1721.96,707.182 1724,707.337 1726.05,707.491 1728.1,707.644 \n",
       "  1730.14,707.797 1732.19,707.95 1734.23,708.102 1736.28,708.253 1738.32,708.405 1740.37,708.555 1742.41,708.705 1744.46,708.855 1746.5,709.004 1748.55,709.153 \n",
       "  1750.59,709.302 1752.64,709.45 1754.69,709.597 1756.73,709.744 1758.78,709.891 1760.82,710.037 1762.87,710.182 1764.91,710.328 1766.96,710.472 1769,710.617 \n",
       "  1771.05,710.76 1773.09,710.904 1775.14,711.047 1777.18,711.189 1779.23,711.331 1781.28,711.473 1783.32,711.614 1785.37,711.755 1787.41,711.896 1789.46,712.035 \n",
       "  1791.5,712.175 1793.55,712.314 1795.59,712.453 1797.64,712.591 1799.68,712.729 1801.73,712.866 1803.78,713.003 1805.82,713.14 1807.87,713.276 1809.91,713.411 \n",
       "  1811.96,713.547 1814,713.682 1816.05,713.816 1818.09,713.95 1820.14,714.084 1822.18,714.217 1824.23,714.35 1826.27,714.482 1828.32,714.614 1830.37,714.746 \n",
       "  1832.41,714.877 1834.46,715.008 1836.5,715.138 1838.55,715.268 1840.59,715.398 1842.64,715.527 1844.68,715.656 1846.73,715.784 1848.77,715.913 1850.82,716.04 \n",
       "  1852.86,716.167 1854.91,716.294 1856.96,716.421 1859,716.547 1861.05,716.673 1863.09,716.798 1865.14,716.923 1867.18,717.048 1869.23,717.172 1871.27,717.296 \n",
       "  1873.32,717.419 1875.36,717.542 1877.41,717.665 1879.45,717.787 1881.5,717.909 1883.55,718.031 1885.59,718.152 1887.64,718.273 1889.68,718.393 1891.73,718.513 \n",
       "  1893.77,718.633 1895.82,718.753 1897.86,718.872 1899.91,718.99 1901.95,719.109 1904,719.227 1906.04,719.344 1908.09,719.462 1910.14,719.578 1912.18,719.695 \n",
       "  1914.23,719.811 1916.27,719.927 1918.32,720.043 1920.36,720.158 1922.41,720.272 1924.45,720.387 1926.5,720.501 1928.54,720.615 1930.59,720.728 1932.63,720.841 \n",
       "  1934.68,720.954 1936.73,721.067 1938.77,721.179 1940.82,721.29 1942.86,721.402 1944.91,721.513 1946.95,721.624 1949,721.734 1951.04,721.844 1953.09,721.954 \n",
       "  1955.13,722.063 1957.18,722.172 1959.23,722.281 1961.27,722.389 1963.32,722.497 1965.36,722.605 1967.41,722.713 1969.45,722.82 1971.5,722.927 1973.54,723.033 \n",
       "  1975.59,723.139 1977.63,723.245 1979.68,723.351 1981.72,723.456 1983.77,723.561 1985.82,723.666 1987.86,723.77 1989.91,723.874 1991.95,723.977 1994,724.081 \n",
       "  1996.04,724.184 1998.09,724.287 2000.13,724.389 2002.18,724.491 2004.22,724.593 2006.27,724.695 2008.31,724.796 2010.36,724.897 2012.41,724.997 2014.45,725.098 \n",
       "  2016.5,725.198 2018.54,725.297 2020.59,725.397 2022.63,725.496 2024.68,725.595 2026.72,725.693 2028.77,725.792 2030.81,725.89 2032.86,725.987 2034.9,726.085 \n",
       "  2036.95,726.182 2039,726.279 2041.04,726.375 2043.09,726.471 2045.13,726.567 2047.18,726.663 2049.22,726.758 2051.27,726.854 2053.31,726.948 2055.36,727.043 \n",
       "  2057.4,727.137 2059.45,727.231 2061.49,727.325 2063.54,727.418 2065.59,727.512 2067.63,727.604 2069.68,727.697 2071.72,727.789 2073.77,727.881 2075.81,727.973 \n",
       "  2077.86,728.065 2079.9,728.156 2081.95,728.247 2083.99,728.338 2086.04,728.428 2088.08,728.518 2090.13,728.608 2092.18,728.698 2094.22,728.787 2096.27,728.876 \n",
       "  2098.31,728.965 2100.36,729.054 2102.4,729.142 2104.45,729.23 2106.49,729.318 2108.54,729.406 2110.58,729.493 2112.63,729.58 2114.68,729.667 2116.72,729.753 \n",
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       "  1730.14,1327.84 1732.19,1328 1734.23,1328.15 1736.28,1328.3 1738.32,1328.45 1740.37,1328.6 1742.41,1328.75 1744.46,1328.9 1746.5,1329.05 1748.55,1329.2 \n",
       "  1750.59,1329.35 1752.64,1329.5 1754.69,1329.64 1756.73,1329.79 1758.78,1329.94 1760.82,1330.08 1762.87,1330.23 1764.91,1330.37 1766.96,1330.52 1769,1330.66 \n",
       "  1771.05,1330.81 1773.09,1330.95 1775.14,1331.09 1777.18,1331.24 1779.23,1331.38 1781.28,1331.52 1783.32,1331.66 1785.37,1331.8 1787.41,1331.94 1789.46,1332.08 \n",
       "  1791.5,1332.22 1793.55,1332.36 1795.59,1332.5 1797.64,1332.64 1799.68,1332.78 1801.73,1332.91 1803.78,1333.05 1805.82,1333.19 1807.87,1333.32 1809.91,1333.46 \n",
       "  1811.96,1333.59 1814,1333.73 1816.05,1333.86 1818.09,1334 1820.14,1334.13 1822.18,1334.26 1824.23,1334.4 1826.27,1334.53 1828.32,1334.66 1830.37,1334.79 \n",
       "  1832.41,1334.92 1834.46,1335.05 1836.5,1335.18 1838.55,1335.31 1840.59,1335.44 1842.64,1335.57 1844.68,1335.7 1846.73,1335.83 1848.77,1335.96 1850.82,1336.09 \n",
       "  1852.86,1336.21 1854.91,1336.34 1856.96,1336.47 1859,1336.59 1861.05,1336.72 1863.09,1336.84 1865.14,1336.97 1867.18,1337.09 1869.23,1337.22 1871.27,1337.34 \n",
       "  1873.32,1337.47 1875.36,1337.59 1877.41,1337.71 1879.45,1337.83 1881.5,1337.96 1883.55,1338.08 1885.59,1338.2 1887.64,1338.32 1889.68,1338.44 1891.73,1338.56 \n",
       "  1893.77,1338.68 1895.82,1338.8 1897.86,1338.92 1899.91,1339.04 1901.95,1339.16 1904,1339.27 1906.04,1339.39 1908.09,1339.51 1910.14,1339.62 1912.18,1339.74 \n",
       "  1914.23,1339.86 1916.27,1339.97 1918.32,1340.09 1920.36,1340.2 1922.41,1340.32 1924.45,1340.43 1926.5,1340.55 1928.54,1340.66 1930.59,1340.77 1932.63,1340.89 \n",
       "  1934.68,1341 1936.73,1341.11 1938.77,1341.22 1940.82,1341.34 1942.86,1341.45 1944.91,1341.56 1946.95,1341.67 1949,1341.78 1951.04,1341.89 1953.09,1342 \n",
       "  1955.13,1342.11 1957.18,1342.22 1959.23,1342.33 1961.27,1342.44 1963.32,1342.54 1965.36,1342.65 1967.41,1342.76 1969.45,1342.87 1971.5,1342.97 1973.54,1343.08 \n",
       "  1975.59,1343.19 1977.63,1343.29 1979.68,1343.4 1981.72,1343.5 1983.77,1343.61 1985.82,1343.71 1987.86,1343.82 1989.91,1343.92 1991.95,1344.02 1994,1344.13 \n",
       "  1996.04,1344.23 1998.09,1344.33 2000.13,1344.44 2002.18,1344.54 2004.22,1344.64 2006.27,1344.74 2008.31,1344.84 2010.36,1344.94 2012.41,1345.04 2014.45,1345.14 \n",
       "  2016.5,1345.24 2018.54,1345.34 2020.59,1345.44 2022.63,1345.54 2024.68,1345.64 2026.72,1345.74 2028.77,1345.84 2030.81,1345.94 2032.86,1346.03 2034.9,1346.13 \n",
       "  2036.95,1346.23 2039,1346.33 2041.04,1346.42 2043.09,1346.52 2045.13,1346.61 2047.18,1346.71 2049.22,1346.8 2051.27,1346.9 2053.31,1346.99 2055.36,1347.09 \n",
       "  2057.4,1347.18 2059.45,1347.28 2061.49,1347.37 2063.54,1347.46 2065.59,1347.56 2067.63,1347.65 2069.68,1347.74 2071.72,1347.84 2073.77,1347.93 2075.81,1348.02 \n",
       "  2077.86,1348.11 2079.9,1348.2 2081.95,1348.29 2083.99,1348.38 2086.04,1348.47 2088.08,1348.56 2090.13,1348.65 2092.18,1348.74 2094.22,1348.83 2096.27,1348.92 \n",
       "  2098.31,1349.01 2100.36,1349.1 2102.4,1349.19 2104.45,1349.28 2106.49,1349.36 2108.54,1349.45 2110.58,1349.54 2112.63,1349.63 2114.68,1349.71 2116.72,1349.8 \n",
       "  2118.77,1349.89 2120.81,1349.97 2122.86,1350.06 2124.9,1350.14 2126.95,1350.23 2128.99,1350.31 2131.04,1350.4 2133.08,1350.48 2135.13,1350.57 2137.17,1350.65 \n",
       "  2139.22,1350.73 2141.27,1350.82 2143.31,1350.9 2145.36,1350.98 2147.4,1351.07 2149.45,1351.15 2151.49,1351.23 2153.54,1351.31 2155.58,1351.4 2157.63,1351.48 \n",
       "  2159.67,1351.56 2161.72,1351.64 2163.76,1351.72 2165.81,1351.8 2167.86,1351.88 2169.9,1351.96 2171.95,1352.04 2173.99,1352.12 2176.04,1352.2 2178.08,1352.28 \n",
       "  2180.13,1352.36 2182.17,1352.44 2184.22,1352.52 2186.26,1352.59 2188.31,1352.67 2190.35,1352.75 2192.4,1352.83 2194.45,1352.91 2196.49,1352.98 2198.54,1353.06 \n",
       "  2200.58,1353.14 2202.63,1353.21 2204.67,1353.29 2206.72,1353.37 2208.76,1353.44 2210.81,1353.52 2212.85,1353.59 2214.9,1353.67 2216.94,1353.74 2218.99,1353.82 \n",
       "  2221.04,1353.89 2223.08,1353.97 2225.13,1354.04 2227.17,1354.11 2229.22,1354.19 2231.26,1354.26 2233.31,1354.33 2235.35,1354.41 2237.4,1354.48 2239.44,1354.55 \n",
       "  2241.49,1354.62 2243.53,1354.7 2245.58,1354.77 2247.63,1354.84 2249.67,1354.91 2251.72,1354.98 2253.76,1355.05 2255.81,1355.12 2257.85,1355.2 2259.9,1355.27 \n",
       "  2261.94,1355.34 2263.99,1355.41 2266.03,1355.48 2268.08,1355.55 2270.12,1355.62 2272.17,1355.68 2274.22,1355.75 2276.26,1355.82 2278.31,1355.89 2280.35,1355.96 \n",
       "  2282.4,1356.03 2284.44,1356.1 2286.49,1356.16 2288.53,1356.23 2290.58,1356.3 2292.62,1356.37 2294.67,1356.43 2296.72,1356.5 2298.76,1356.57 2300.81,1356.63 \n",
       "  2302.85,1356.7 2304.9,1356.77 2306.94,1356.83 2308.99,1356.9 2311.03,1356.96 2313.08,1357.03 2315.12,1357.09 2317.17,1357.16 2319.21,1357.22 2321.26,1357.29 \n",
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       "  298.365,1375.68 300.41,1373.03 302.456,1370.38 304.501,1367.76 306.546,1365.16 308.592,1362.57 310.637,1360 312.683,1357.44 314.728,1354.9 316.773,1352.38 \n",
       "  318.819,1349.88 320.864,1347.39 322.91,1344.92 324.955,1342.46 327,1340.02 329.046,1337.59 331.091,1335.18 333.136,1332.79 335.182,1330.41 337.227,1328.05 \n",
       "  339.273,1325.7 341.318,1323.36 343.363,1321.04 345.409,1318.74 347.454,1316.45 349.5,1314.17 351.545,1311.91 353.59,1309.66 355.636,1307.43 357.681,1305.21 \n",
       "  359.727,1303 361.772,1300.81 363.817,1298.63 365.863,1296.46 367.908,1294.31 369.954,1292.17 371.999,1290.05 374.044,1287.93 376.09,1285.83 378.135,1283.74 \n",
       "  380.181,1281.67 382.226,1279.6 384.271,1277.55 386.317,1275.51 388.362,1273.49 390.408,1271.47 392.453,1269.47 394.498,1267.48 396.544,1265.5 398.589,1263.53 \n",
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       "  1280.15,907.376 1282.2,907.065 1284.24,906.755 1286.29,906.447 1288.34,906.139 1290.38,905.833 1292.43,905.527 1294.47,905.223 1296.52,904.919 1298.56,904.617 \n",
       "  1300.61,904.315 1302.65,904.015 1304.7,903.716 1306.74,903.417 1308.79,903.12 1310.84,902.824 1312.88,902.528 1314.93,902.234 1316.97,901.941 1319.02,901.649 \n",
       "  1321.06,901.357 1323.11,901.067 1325.15,900.777 1327.2,900.489 1329.24,900.202 1331.29,899.915 1333.33,899.63 1335.38,899.345 1337.43,899.061 1339.47,898.779 \n",
       "  1341.52,898.497 1343.56,898.216 1345.61,897.937 1347.65,897.658 1349.7,897.38 1351.74,897.103 1353.79,896.827 1355.83,896.551 1357.88,896.277 1359.92,896.004 \n",
       "  1361.97,895.731 1364.02,895.46 1366.06,895.189 1368.11,894.919 1370.15,894.651 1372.2,894.383 1374.24,894.116 1376.29,893.849 1378.33,893.584 1380.38,893.32 \n",
       "  1382.42,893.056 1384.47,892.793 1386.51,892.532 1388.56,892.271 1390.61,892.011 1392.65,891.752 1394.7,891.493 1396.74,891.236 1398.79,890.979 1400.83,890.723 \n",
       "  1402.88,890.468 1404.92,890.214 1406.97,889.961 1409.01,889.709 1411.06,889.457 1413.1,889.206 1415.15,888.956 1417.2,888.707 1419.24,888.459 1421.29,888.212 \n",
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       "  1546.06,874.546 1548.1,874.344 1550.15,874.142 1552.19,873.941 1554.24,873.741 1556.28,873.541 1558.33,873.342 1560.37,873.143 1562.42,872.946 1564.46,872.748 \n",
       "  1566.51,872.552 1568.55,872.356 1570.6,872.16 1572.65,871.966 1574.69,871.772 1576.74,871.578 1578.78,871.385 1580.83,871.193 1582.87,871.001 1584.92,870.81 \n",
       "  1586.96,870.62 1589.01,870.43 1591.05,870.24 1593.1,870.052 1595.14,869.864 1597.19,869.676 1599.24,869.489 1601.28,869.303 1603.33,869.117 1605.37,868.932 \n",
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       "  1627.87,866.934 1629.92,866.756 1631.96,866.578 1634.01,866.401 1636.05,866.224 1638.1,866.048 1640.14,865.873 1642.19,865.698 1644.23,865.523 1646.28,865.35 \n",
       "  1648.33,865.176 1650.37,865.004 1652.42,864.831 1654.46,864.66 1656.51,864.489 1658.55,864.318 1660.6,864.148 1662.64,863.978 1664.69,863.809 1666.73,863.641 \n",
       "  1668.78,863.473 1670.82,863.305 1672.87,863.139 1674.92,862.972 1676.96,862.806 1679.01,862.641 1681.05,862.476 1683.1,862.312 1685.14,862.148 1687.19,861.985 \n",
       "  1689.23,861.822 1691.28,861.66 1693.32,861.498 1695.37,861.337 1697.41,861.176 1699.46,861.015 1701.51,860.856 1703.55,860.696 1705.6,860.538 1707.64,860.379 \n",
       "  1709.69,860.221 1711.73,860.064 1713.78,859.907 1715.82,859.751 1717.87,859.595 1719.91,859.44 1721.96,859.285 1724,859.13 1726.05,858.976 1728.1,858.823 \n",
       "  1730.14,858.67 1732.19,858.517 1734.23,858.365 1736.28,858.213 1738.32,858.062 1740.37,857.912 1742.41,857.761 1744.46,857.612 1746.5,857.462 1748.55,857.314 \n",
       "  1750.59,857.165 1752.64,857.017 1754.69,856.87 1756.73,856.723 1758.78,856.576 1760.82,856.43 1762.87,856.285 1764.91,856.139 1766.96,855.995 1769,855.85 \n",
       "  1771.05,855.706 1773.09,855.563 1775.14,855.42 1777.18,855.277 1779.23,855.135 1781.28,854.994 1783.32,854.852 1785.37,854.712 1787.41,854.571 1789.46,854.431 \n",
       "  1791.5,854.292 1793.55,854.153 1795.59,854.014 1797.64,853.876 1799.68,853.738 1801.73,853.601 1803.78,853.464 1805.82,853.327 1807.87,853.191 1809.91,853.055 \n",
       "  1811.96,852.92 1814,852.785 1816.05,852.651 1818.09,852.517 1820.14,852.383 1822.18,852.25 1824.23,852.117 1826.27,851.985 1828.32,851.853 1830.37,851.721 \n",
       "  1832.41,851.59 1834.46,851.459 1836.5,851.329 1838.55,851.198 1840.59,851.069 1842.64,850.94 1844.68,850.811 1846.73,850.682 1848.77,850.554 1850.82,850.427 \n",
       "  1852.86,850.299 1854.91,850.173 1856.96,850.046 1859,849.92 1861.05,849.794 1863.09,849.669 1865.14,849.544 1867.18,849.419 1869.23,849.295 1871.27,849.171 \n",
       "  1873.32,849.048 1875.36,848.925 1877.41,848.802 1879.45,848.68 1881.5,848.558 1883.55,848.436 1885.59,848.315 1887.64,848.194 1889.68,848.074 1891.73,847.953 \n",
       "  1893.77,847.834 1895.82,847.714 1897.86,847.595 1899.91,847.476 1901.95,847.358 1904,847.24 1906.04,847.123 1908.09,847.005 1910.14,846.888 1912.18,846.772 \n",
       "  1914.23,846.656 1916.27,846.54 1918.32,846.424 1920.36,846.309 1922.41,846.194 1924.45,846.08 1926.5,845.966 1928.54,845.852 1930.59,845.739 1932.63,845.626 \n",
       "  1934.68,845.513 1936.73,845.4 1938.77,845.288 1940.82,845.177 1942.86,845.065 1944.91,844.954 1946.95,844.843 1949,844.733 1951.04,844.623 1953.09,844.513 \n",
       "  1955.13,844.404 1957.18,844.295 1959.23,844.186 1961.27,844.077 1963.32,843.969 1965.36,843.862 1967.41,843.754 1969.45,843.647 1971.5,843.54 1973.54,843.434 \n",
       "  1975.59,843.327 1977.63,843.222 1979.68,843.116 1981.72,843.011 1983.77,842.906 1985.82,842.801 1987.86,842.697 1989.91,842.593 1991.95,842.489 1994,842.386 \n",
       "  1996.04,842.283 1998.09,842.18 2000.13,842.078 2002.18,841.976 2004.22,841.874 2006.27,841.772 2008.31,841.671 2010.36,841.57 2012.41,841.469 2014.45,841.369 \n",
       "  2016.5,841.269 2018.54,841.169 2020.59,841.07 2022.63,840.971 2024.68,840.872 2026.72,840.773 2028.77,840.675 2030.81,840.577 2032.86,840.479 2034.9,840.382 \n",
       "  2036.95,840.285 2039,840.188 2041.04,840.092 2043.09,839.995 2045.13,839.899 2047.18,839.804 2049.22,839.708 2051.27,839.613 2053.31,839.518 2055.36,839.424 \n",
       "  2057.4,839.33 2059.45,839.236 2061.49,839.142 2063.54,839.048 2065.59,838.955 2067.63,838.862 2069.68,838.77 2071.72,838.678 2073.77,838.585 2075.81,838.494 \n",
       "  2077.86,838.402 2079.9,838.311 2081.95,838.22 2083.99,838.129 2086.04,838.039 2088.08,837.949 2090.13,837.859 2092.18,837.769 2094.22,837.68 2096.27,837.591 \n",
       "  2098.31,837.502 2100.36,837.413 2102.4,837.325 2104.45,837.237 2106.49,837.149 2108.54,837.061 2110.58,836.974 2112.63,836.887 2114.68,836.8 2116.72,836.714 \n",
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       "  2139.22,835.779 2141.27,835.695 2143.31,835.612 2145.36,835.529 2147.4,835.446 2149.45,835.363 2151.49,835.281 2153.54,835.199 2155.58,835.117 2157.63,835.036 \n",
       "  2159.67,834.954 2161.72,834.873 2163.76,834.792 2165.81,834.712 2167.86,834.631 2169.9,834.551 2171.95,834.471 2173.99,834.392 2176.04,834.312 2178.08,834.233 \n",
       "  2180.13,834.154 2182.17,834.075 2184.22,833.997 2186.26,833.918 2188.31,833.84 2190.35,833.763 2192.4,833.685 2194.45,833.608 2196.49,833.53 2198.54,833.454 \n",
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       "  1177.88,445.445 1179.93,444.706 1181.98,443.969 1184.02,443.235 1186.07,442.504 1188.11,441.775 1190.16,441.049 1192.2,440.325 1194.25,439.604 1196.29,438.886 \n",
       "  1198.34,438.169 1200.38,437.456 1202.43,436.745 1204.47,436.036 1206.52,435.33 1208.57,434.626 1210.61,433.925 1212.66,433.226 1214.7,432.53 1216.75,431.836 \n",
       "  1218.79,431.144 1220.84,430.455 1222.88,429.769 1224.93,429.084 1226.97,428.402 1229.02,427.723 1231.06,427.045 1233.11,426.37 1235.16,425.698 1237.2,425.028 \n",
       "  1239.25,424.36 1241.29,423.694 1243.34,423.031 1245.38,422.37 1247.43,421.711 1249.47,421.054 1251.52,420.4 1253.56,419.748 1255.61,419.098 1257.65,418.451 \n",
       "  1259.7,417.805 1261.75,417.162 1263.79,416.521 1265.84,415.882 1267.88,415.246 1269.93,414.612 1271.97,413.979 1274.02,413.349 1276.06,412.721 1278.11,412.096 \n",
       "  1280.15,411.472 1282.2,410.85 1284.24,410.231 1286.29,409.614 1288.34,408.999 1290.38,408.386 1292.43,407.775 1294.47,407.166 1296.52,406.559 1298.56,405.954 \n",
       "  1300.61,405.351 1302.65,404.75 1304.7,404.152 1306.74,403.555 1308.79,402.96 1310.84,402.368 1312.88,401.777 1314.93,401.189 1316.97,400.602 1319.02,400.017 \n",
       "  1321.06,399.435 1323.11,398.854 1325.15,398.275 1327.2,397.698 1329.24,397.123 1331.29,396.55 1333.33,395.979 1335.38,395.41 1337.43,394.843 1339.47,394.278 \n",
       "  1341.52,393.714 1343.56,393.153 1345.61,392.593 1347.65,392.035 1349.7,391.48 1351.74,390.925 1353.79,390.373 1355.83,389.823 1357.88,389.274 1359.92,388.728 \n",
       "  1361.97,388.183 1364.02,387.64 1366.06,387.098 1368.11,386.559 1370.15,386.021 1372.2,385.485 1374.24,384.951 1376.29,384.419 1378.33,383.888 1380.38,383.359 \n",
       "  1382.42,382.832 1384.47,382.307 1386.51,381.784 1388.56,381.262 1390.61,380.742 1392.65,380.223 1394.7,379.707 1396.74,379.192 1398.79,378.678 1400.83,378.167 \n",
       "  1402.88,377.657 1404.92,377.149 1406.97,376.642 1409.01,376.137 1411.06,375.634 1413.1,375.133 1415.15,374.633 1417.2,374.135 1419.24,373.638 1421.29,373.143 \n",
       "  1423.33,372.65 1425.38,372.158 1427.42,371.668 1429.47,371.18 1431.51,370.693 1433.56,370.208 1435.6,369.724 1437.65,369.242 1439.69,368.761 1441.74,368.282 \n",
       "  1443.79,367.805 1445.83,367.329 1447.88,366.855 1449.92,366.382 1451.97,365.911 1454.01,365.442 1456.06,364.974 1458.1,364.507 1460.15,364.042 1462.19,363.579 \n",
       "  1464.24,363.117 1466.28,362.656 1468.33,362.197 1470.38,361.74 1472.42,361.284 1474.47,360.829 1476.51,360.376 1478.56,359.924 1480.6,359.474 1482.65,359.026 \n",
       "  1484.69,358.578 1486.74,358.133 1488.78,357.688 1490.83,357.246 1492.88,356.804 1494.92,356.364 1496.97,355.926 1499.01,355.488 1501.06,355.053 1503.1,354.618 \n",
       "  1505.15,354.185 1507.19,353.754 1509.24,353.324 1511.28,352.895 1513.33,352.467 1515.37,352.041 1517.42,351.617 1519.47,351.194 1521.51,350.772 1523.56,350.351 \n",
       "  1525.6,349.932 1527.65,349.514 1529.69,349.097 1531.74,348.682 1533.78,348.268 1535.83,347.856 1537.87,347.445 1539.92,347.035 1541.96,346.626 1544.01,346.219 \n",
       "  1546.06,345.813 1548.1,345.408 1550.15,345.005 1552.19,344.603 1554.24,344.202 1556.28,343.802 1558.33,343.404 1560.37,343.007 1562.42,342.611 1564.46,342.217 \n",
       "  1566.51,341.824 1568.55,341.432 1570.6,341.041 1572.65,340.651 1574.69,340.263 1576.74,339.876 1578.78,339.49 1580.83,339.106 1582.87,338.722 1584.92,338.34 \n",
       "  1586.96,337.959 1589.01,337.58 1591.05,337.201 1593.1,336.824 1595.14,336.448 1597.19,336.073 1599.24,335.699 1601.28,335.326 1603.33,334.955 1605.37,334.585 \n",
       "  1607.42,334.216 1609.46,333.848 1611.51,333.481 1613.55,333.115 1615.6,332.751 1617.64,332.388 1619.69,332.025 1621.73,331.664 1623.78,331.304 1625.83,330.946 \n",
       "  1627.87,330.588 1629.92,330.232 1631.96,329.876 1634.01,329.522 1636.05,329.169 1638.1,328.817 1640.14,328.466 1642.19,328.116 1644.23,327.767 1646.28,327.419 \n",
       "  1648.33,327.073 1650.37,326.727 1652.42,326.383 1654.46,326.04 1656.51,325.697 1658.55,325.356 1660.6,325.016 1662.64,324.677 1664.69,324.339 1666.73,324.002 \n",
       "  1668.78,323.666 1670.82,323.331 1672.87,322.997 1674.92,322.665 1676.96,322.333 1679.01,322.002 1681.05,321.672 1683.1,321.344 1685.14,321.016 1687.19,320.69 \n",
       "  1689.23,320.364 1691.28,320.039 1693.32,319.716 1695.37,319.393 1697.41,319.072 1699.46,318.751 1701.51,318.432 1703.55,318.113 1705.6,317.795 1707.64,317.479 \n",
       "  1709.69,317.163 1711.73,316.848 1713.78,316.535 1715.82,316.222 1717.87,315.91 1719.91,315.599 1721.96,315.289 1724,314.981 1726.05,314.673 1728.1,314.366 \n",
       "  1730.14,314.06 1732.19,313.754 1734.23,313.45 1736.28,313.147 1738.32,312.845 1740.37,312.543 1742.41,312.243 1744.46,311.944 1746.5,311.645 1748.55,311.347 \n",
       "  1750.59,311.051 1752.64,310.755 1754.69,310.46 1756.73,310.166 1758.78,309.873 1760.82,309.581 1762.87,309.289 1764.91,308.999 1766.96,308.709 1769,308.421 \n",
       "  1771.05,308.133 1773.09,307.846 1775.14,307.56 1777.18,307.275 1779.23,306.991 1781.28,306.708 1783.32,306.425 1785.37,306.144 1787.41,305.863 1789.46,305.583 \n",
       "  1791.5,305.304 1793.55,305.026 1795.59,304.748 1797.64,304.472 1799.68,304.196 1801.73,303.922 1803.78,303.648 1805.82,303.375 1807.87,303.102 1809.91,302.831 \n",
       "  1811.96,302.56 1814,302.291 1816.05,302.022 1818.09,301.754 1820.14,301.486 1822.18,301.22 1824.23,300.954 1826.27,300.689 1828.32,300.425 1830.37,300.162 \n",
       "  1832.41,299.9 1834.46,299.638 1836.5,299.377 1838.55,299.117 1840.59,298.858 1842.64,298.599 1844.68,298.342 1846.73,298.085 1848.77,297.829 1850.82,297.574 \n",
       "  1852.86,297.319 1854.91,297.065 1856.96,296.812 1859,296.56 1861.05,296.309 1863.09,296.058 1865.14,295.808 1867.18,295.559 1869.23,295.31 1871.27,295.063 \n",
       "  1873.32,294.816 1875.36,294.57 1877.41,294.324 1879.45,294.079 1881.5,293.836 1883.55,293.592 1885.59,293.35 1887.64,293.108 1889.68,292.867 1891.73,292.627 \n",
       "  1893.77,292.387 1895.82,292.149 1897.86,291.911 1899.91,291.673 1901.95,291.437 1904,291.201 1906.04,290.965 1908.09,290.731 1910.14,290.497 1912.18,290.264 \n",
       "  1914.23,290.032 1916.27,289.8 1918.32,289.569 1920.36,289.339 1922.41,289.109 1924.45,288.88 1926.5,288.652 1928.54,288.424 1930.59,288.197 1932.63,287.971 \n",
       "  1934.68,287.746 1936.73,287.521 1938.77,287.297 1940.82,287.073 1942.86,286.85 1944.91,286.628 1946.95,286.407 1949,286.186 1951.04,285.966 1953.09,285.746 \n",
       "  1955.13,285.528 1957.18,285.309 1959.23,285.092 1961.27,284.875 1963.32,284.659 1965.36,284.443 1967.41,284.228 1969.45,284.014 1971.5,283.801 1973.54,283.588 \n",
       "  1975.59,283.375 1977.63,283.163 1979.68,282.952 1981.72,282.742 1983.77,282.532 1985.82,282.323 1987.86,282.114 1989.91,281.906 1991.95,281.699 1994,281.492 \n",
       "  1996.04,281.286 1998.09,281.081 2000.13,280.876 2002.18,280.671 2004.22,280.468 2006.27,280.265 2008.31,280.062 2010.36,279.86 2012.41,279.659 2014.45,279.458 \n",
       "  2016.5,279.258 2018.54,279.059 2020.59,278.86 2022.63,278.662 2024.68,278.464 2026.72,278.267 2028.77,278.07 2030.81,277.874 2032.86,277.679 2034.9,277.484 \n",
       "  2036.95,277.29 2039,277.097 2041.04,276.903 2043.09,276.711 2045.13,276.519 2047.18,276.328 2049.22,276.137 2051.27,275.947 2053.31,275.757 2055.36,275.568 \n",
       "  2057.4,275.379 2059.45,275.191 2061.49,275.004 2063.54,274.817 2065.59,274.631 2067.63,274.445 2069.68,274.26 2071.72,274.075 2073.77,273.891 2075.81,273.708 \n",
       "  2077.86,273.524 2079.9,273.342 2081.95,273.16 2083.99,272.979 2086.04,272.798 2088.08,272.617 2090.13,272.438 2092.18,272.258 2094.22,272.079 2096.27,271.901 \n",
       "  2098.31,271.724 2100.36,271.546 2102.4,271.37 2104.45,271.194 2106.49,271.018 2108.54,270.843 2110.58,270.668 2112.63,270.494 2114.68,270.321 2116.72,270.148 \n",
       "  2118.77,269.975 2120.81,269.803 2122.86,269.631 2124.9,269.46 2126.95,269.29 2128.99,269.12 2131.04,268.95 2133.08,268.781 2135.13,268.613 2137.17,268.445 \n",
       "  2139.22,268.277 2141.27,268.11 2143.31,267.944 2145.36,267.778 2147.4,267.612 2149.45,267.447 2151.49,267.282 2153.54,267.118 2155.58,266.955 2157.63,266.792 \n",
       "  2159.67,266.629 2161.72,266.467 2163.76,266.305 2165.81,266.144 2167.86,265.983 2169.9,265.823 2171.95,265.663 2173.99,265.503 2176.04,265.345 2178.08,265.186 \n",
       "  2180.13,265.028 2182.17,264.871 2184.22,264.714 2186.26,264.557 2188.31,264.401 2190.35,264.245 2192.4,264.09 2194.45,263.935 2196.49,263.781 2198.54,263.627 \n",
       "  2200.58,263.474 2202.63,263.321 2204.67,263.168 2206.72,263.016 2208.76,262.865 2210.81,262.713 2212.85,262.563 2214.9,262.412 2216.94,262.263 2218.99,262.113 \n",
       "  2221.04,261.964 2223.08,261.816 2225.13,261.668 2227.17,261.52 2229.22,261.373 2231.26,261.226 2233.31,261.079 2235.35,260.934 2237.4,260.788 2239.44,260.643 \n",
       "  2241.49,260.498 2243.53,260.354 2245.58,260.21 2247.63,260.067 2249.67,259.924 2251.72,259.781 2253.76,259.639 2255.81,259.497 2257.85,259.356 2259.9,259.215 \n",
       "  2261.94,259.074 2263.99,258.934 2266.03,258.794 2268.08,258.655 2270.12,258.516 2272.17,258.378 2274.22,258.24 2276.26,258.102 2278.31,257.965 2280.35,257.828 \n",
       "  2282.4,257.691 2284.44,257.555 2286.49,257.42 2288.53,257.284 2290.58,257.149 2292.62,257.015 2294.67,256.881 2296.72,256.747 2298.76,256.614 2300.81,256.481 \n",
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      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tspan = (0.0,100.0)\n",
    "prob = ODEProblem(simpleODE3!,u₀,tspan,p)\n",
    "sol = solve(prob)\n",
    "plot(sol,label=[\"a\",\"b\",\"c\",\"d\"])\n",
    "title!(\"reversible ODE solver using DSL\")\n",
    "xlabel!(\"Time [s]\")\n",
    "ylabel!(\"Concentration [M]\")"
   ]
  }
 ],
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