4_Regression_Analysis/1_Regression.ipynb

{
 "metadata": {
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  },
  "orig_nbformat": 4,
  "kernelspec": {
   "name": "python3",
   "display_name": "Python 3.8.10 64-bit"
  },
  "interpreter": {
   "hash": "31f2aee4e71d21fbe5cf8b01ff0e069b9275f58929596ceb00d14d90e3e16cd6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2,
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Regression Analysis(회귀 분석)\n",
    "\n",
    "* In statistical modeling, regression analysis is a set of statistical processes for **estimating the relationships between a dependent variable** (often called the 'outcome' or 'response' variable) **and one or more independent variables** (often called 'predictors', 'covariates', 'explanatory variables' or 'features').\n",
    "\n",
    "from [wikipedia](https://en.wikipedia.org/wiki/Regression_analysis)\n",
    "\n",
    "* **Goal: Find most suitable linear/nonlinear equation for observed values.**\n",
    "\n",
    "## History\n",
    "* Francis Galton's 1875 illustration of the correlation between the heights of adults and their parents. The observation that adult children's heights tended to deviate less from the mean height than their parents suggested the concept of   \"regression toward the mean\", giving regression its name.\n",
    "![Francis Galton](https://upload.wikimedia.org/wikipedia/commons/b/b2/Galton%27s_correlation_diagram_1875.jpg)"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Linear Regression\n",
    "\n",
    "![](regression_analysis_sample.png)\n",
    "\n",
    "Linear Equation derived from linear regression analysis might be in following form : $$y = \\alpha + \\beta x$$\n",
    "\n",
    "Then, $y_i$, the arbitrary element of set $Y$ can be expressed as: $$y_i = \\alpha + \\beta x_i + \\epsilon_i$$\n",
    "\n",
    "$\\epsilon_i$ is error (the difference between $y$ (predicted value from equation) and $y_i$(observed value))\n",
    "\n",
    "Thus, the set of $y$, $Y$ can be expressed as: $$Y =  \\alpha + \\beta x + \\epsilon$$\n",
    "\n",
    "Then, the goal will be **Find the equation that has least error $\\epsilon$**, which can be rewritten as either 'minimize $\\sum \\lvert \\epsilon_i \\rvert$' or **'minimize $\\sum {\\epsilon_i}^2$'**\n",
    "\n",
    "($\\sum {\\epsilon_i}^2$ is preferred because it is easier mathmathically)"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Least Square Method: 최소제곱법 (for simple regression analysis, 단일변수 회귀분석을 위한 방법)\n",
    "## Find equation that has minimized SSE(Sums of Squared Error: $\\sum {\\epsilon_i}^2$)\n",
    "* SSE is cost function\n",
    "$$SSE=\\sum (\\epsilon_i)^2=\\Sigma(Y_i-\\alpha-\\beta x_i)^2$$\n",
    "\n",
    "Since SSE is expressed as quadrantic equation, mimimum value might be local minimum.\n",
    "Thus, Least Square Estimation for $\\alpha$,$\\beta$ would be:\n",
    "\n",
    "<br>\n",
    "\n",
    "$$\\frac{\\partial SSE}{\\partial \\alpha} = 2 \\sum(Y_i - \\alpha - \\beta x_i) (-1) = 0 \\quad \\cdots \\quad (1)$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$\\frac{\\partial SSE}{\\partial \\beta} = 2 \\sum(Y_i - \\alpha - \\beta x_i) (-x_i) = 0  \\quad \\cdots \\quad (2)$$\n",
    "\n",
    "$(1)$ can be rewritten as:\n",
    "\n",
    "<br>\n",
    "\n",
    "$$\\sum(Y_i - \\alpha - \\beta x_i)=0$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$\\sum Y_i = n \\alpha - \\beta \\sum x_i \\quad \\cdots \\quad (3)$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$\\overline{x} \\sum Y_i = \\alpha \\sum x_i - \\beta \\overline{x} \\sum x_i \\quad \\cdots \\quad (3)\\times\\overline{x}$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$\\overline{Y} = \\alpha + \\beta \\overline{x} \\quad \\cdots \\quad (3) \\div n$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$(\\because \\overline{x} = \\frac{1}{n} \\sum_{i=1}^{n} x_i)$$ \n",
    "\n",
    "<br>\n",
    "\n",
    "also, $(2)$ can be rewritten as:\n",
    "\n",
    "<br>\n",
    "\n",
    "$$\\sum(Y_i - \\alpha - \\beta x_i)(x_i)=0$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$\\sum x_i Y_i = \\alpha \\sum x_i + \\beta \\sum {x_i}^2 \\quad \\cdots \\quad (4)$$\n",
    "\n",
    "<br>\n",
    "\n",
    "Then, $(4)-(3)\\times\\overline{x}$ derives following:\n",
    "\n",
    "<br>\n",
    "\n",
    "$$\\sum (x_i Y_i - n\\overline{x}\\overline{Y}) = \\beta (\\sum {x_i}^2 - n {\\overline{x}}^2)$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$\\beta = \\frac{\\sum (x_i Y_i - n\\overline{x}\\overline{Y})}{\\sum {x_i}^2 - n {\\overline{x}}^2} = \\frac{\\sum (x_i-\\overline{x})(Y_i-\\overline{Y})}{\\sum({x_i-\\overline{x}})^2}$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$(\\because \\sum (x_i-\\overline{x})(Y_i-\\overline{Y})=\\sum (x_i Y_i - n\\overline{x}\\overline{Y})), \\sum {x_i}^2 - n {\\overline{x}}^2 = \\sum({x_i-\\overline{x}})^2)$$ \n",
    "\n",
    "<br>\n",
    "\n",
    "Thus, $\\alpha$ and $\\beta$ for minimized SSE would be\n",
    "\n",
    "<br>\n",
    "\n",
    "$$\\therefore \\quad \\hat{\\beta} = \\frac{\\sum (x_i-\\overline{x})(Y_i-\\overline{Y})}{\\sum({x_i-\\overline{x}})^2}, \\quad \\hat{\\alpha}=\\overline{Y} - \\hat{\\beta} \\overline{x}$$"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Multiple Regression Analysis\n",
    "\n",
    "$$Y_i = \\beta_0 + \\beta_1 x_{1i} + \\beta_2 x_{2i} + \\cdots + \\beta_k x_{ki} + \\epsilon_i, \\quad \\epsilon_i \\sim N(0,{\\sigma}^2), \\quad i=1,\\cdots,n$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$\n",
    "X = \n",
    "\\begin{pmatrix}\n",
    "1 & x_{11} & x_{21} & \\cdots & x_{k1} \\\\\n",
    "1 & x_{12} & x_{22} & \\cdots & x_{k2} \\\\\n",
    "\\vdots & \\vdots & \\vdots  & \\ddots & \\vdots  \\\\\n",
    "1 & x_{1n} & x_{2n} & \\cdots & x_{kn} \n",
    "\\end{pmatrix} ,\\quad\n",
    "\\beta = \\begin{pmatrix} \\beta_0 \\\\ \\beta_1 \\\\ \\vdots \\\\ \\beta_k \\end{pmatrix}, \\quad\n",
    "Y= \\begin{pmatrix} y_1 \\\\ y_2 \\\\ \\vdots \\\\ y_n \\end{pmatrix} = X \\beta + \\epsilon, \\quad\n",
    "$$\n",
    "\n",
    "<br>\n",
    "\n",
    "Find $\\beta$ for minimized SSE:\n",
    "\n",
    "<br>\n",
    "\n",
    "$$SSE = \\sum (\\epsilon_i)^2 = \\epsilon^T \\epsilon = (Y-X\\beta)^T(Y-X\\beta) = (Y^T-\\beta^TX^T)(Y-X\\beta)$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$=Y^T Y - Y^T X\\beta - \\beta^T X^T Y + \\beta^T X^T X\\beta$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$=Y^T Y - 2 \\beta^T X^T Y + \\beta^T X^T X\\beta \\quad (\\because (AB)^T = B^T A^T)$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$\\frac{\\partial SSE}{\\partial \\beta} = -2(X^T Y) -2(X^T X)\\hat{\\beta}=0$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$\\therefore \\quad \\hat{\\beta} = (X^T X)^{-1} X^T Y$$"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "source": [
    "# Assignment 1\n",
    "# for X = np.array([1,2,3]), Y = np.array([1,3,2])\n",
    "# find the linear regression equation and plot scatter and line. (use simple linear regression)\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "X = np.array([1,2,3])\n",
    "Y = np.array([1,3,2])\n",
    "n = len(X)\n",
    "\n",
    "Xbar = np.mean(X)\n",
    "Ybar = np.mean(Y)\n",
    "\n",
    "numerator = denominator = 0\n",
    "for i in range(n):\n",
    "    numerator += (X[i] - Xbar) * (Y[i] - Ybar)\n",
    "    denominator += (X[i] - Xbar)**2\n",
    "\n",
    "beta = numerator / denominator\n",
    "alpha = Ybar - beta*Xbar\n",
    "\n",
    "print(\"Alpha: %g / Beta: %g\"%(alpha, beta))\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "domain=np.linspace(0,4,10)\n",
    "plt.scatter(X,Y)\n",
    "plt.plot(domain,alpha+domain*beta)\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Alpha: 1 / Beta: 0.5\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
      "image/png": "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",
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<svg height=\"248.518125pt\" version=\"1.1\" viewBox=\"0 0 378.465625 248.518125\" width=\"378.465625pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n <metadata>\n  <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n   <cc:Work>\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n    <dc:date>2021-07-15T22:29:40.945452</dc:date>\n    <dc:format>image/svg+xml</dc:format>\n    <dc:creator>\n     <cc:Agent>\n      <dc:title>Matplotlib v3.4.2, https://matplotlib.org/</dc:title>\n     </cc:Agent>\n    </dc:creator>\n   </cc:Work>\n  </rdf:RDF>\n </metadata>\n <defs>\n  <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\n </defs>\n <g id=\"figure_1\">\n  <g id=\"patch_1\">\n   <path d=\"M 0 248.518125 \nL 378.465625 248.518125 \nL 378.465625 0 \nL 0 0 \nz\n\" style=\"fill:none;\"/>\n  </g>\n  <g id=\"axes_1\">\n   <g id=\"patch_2\">\n    <path d=\"M 36.465625 224.64 \nL 371.265625 224.64 \nL 371.265625 7.2 \nL 36.465625 7.2 \nz\n\" style=\"fill:#ffffff;\"/>\n   </g>\n   <g id=\"PathCollection_1\">\n    <defs>\n     <path d=\"M 0 3 \nC 0.795609 3 1.55874 2.683901 2.12132 2.12132 \nC 2.683901 1.55874 3 0.795609 3 0 \nC 3 -0.795609 2.683901 -1.55874 2.12132 -2.12132 \nC 1.55874 -2.683901 0.795609 -3 0 -3 \nC -0.795609 -3 -1.55874 -2.683901 -2.12132 -2.12132 \nC -2.683901 -1.55874 -3 -0.795609 -3 0 \nC -3 0.795609 -2.683901 1.55874 -2.12132 2.12132 \nC -1.55874 2.683901 -0.795609 3 0 3 \nz\n\" id=\"m9dd130b9c9\" style=\"stroke:#1f77b4;\"/>\n    </defs>\n    <g clip-path=\"url(#p162d49c381)\">\n     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"127.774716\" xlink:href=\"#m9dd130b9c9\" y=\"214.756364\"/>\n     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"203.865625\" xlink:href=\"#m9dd130b9c9\" y=\"17.083636\"/>\n     <use style=\"fill:#1f77b4;stroke:#1f77b4;\" x=\"279.956534\" xlink:href=\"#m9dd130b9c9\" y=\"115.92\"/>\n    </g>\n   </g>\n   <g id=\"matplotlib.axis_1\">\n    <g id=\"xtick_1\">\n     <g id=\"line2d_1\">\n      <defs>\n       <path d=\"M 0 0 \nL 0 3.5 \n\" id=\"m86efbc4d44\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n      </defs>\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"51.683807\" xlink:href=\"#m86efbc4d44\" y=\"224.64\"/>\n      </g>\n     </g>\n     <g id=\"text_1\">\n      <!-- 0.0 -->\n      <g transform=\"translate(43.732244 239.238437)scale(0.1 -0.1)\">\n       <defs>\n        <path d=\"M 2034 4250 \nQ 1547 4250 1301 3770 \nQ 1056 3291 1056 2328 \nQ 1056 1369 1301 889 \nQ 1547 409 2034 409 \nQ 2525 409 2770 889 \nQ 3016 1369 3016 2328 \nQ 3016 3291 2770 3770 \nQ 2525 4250 2034 4250 \nz\nM 2034 4750 \nQ 2819 4750 3233 4129 \nQ 3647 3509 3647 2328 \nQ 3647 1150 3233 529 \nQ 2819 -91 2034 -91 \nQ 1250 -91 836 529 \nQ 422 1150 422 2328 \nQ 422 3509 836 4129 \nQ 1250 4750 2034 4750 \nz\n\" id=\"DejaVuSans-30\" transform=\"scale(0.015625)\"/>\n        <path d=\"M 684 794 \nL 1344 794 \nL 1344 0 \nL 684 0 \nL 684 794 \nz\n\" id=\"DejaVuSans-2e\" transform=\"scale(0.015625)\"/>\n       </defs>\n       <use xlink:href=\"#DejaVuSans-30\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_2\">\n     <g id=\"line2d_2\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"89.729261\" xlink:href=\"#m86efbc4d44\" y=\"224.64\"/>\n      </g>\n     </g>\n     <g id=\"text_2\">\n      <!-- 0.5 -->\n      <g transform=\"translate(81.777699 239.238437)scale(0.1 -0.1)\">\n       <defs>\n        <path d=\"M 691 4666 \nL 3169 4666 \nL 3169 4134 \nL 1269 4134 \nL 1269 2991 \nQ 1406 3038 1543 3061 \nQ 1681 3084 1819 3084 \nQ 2600 3084 3056 2656 \nQ 3513 2228 3513 1497 \nQ 3513 744 3044 326 \nQ 2575 -91 1722 -91 \nQ 1428 -91 1123 -41 \nQ 819 9 494 109 \nL 494 744 \nQ 775 591 1075 516 \nQ 1375 441 1709 441 \nQ 2250 441 2565 725 \nQ 2881 1009 2881 1497 \nQ 2881 1984 2565 2268 \nQ 2250 2553 1709 2553 \nQ 1456 2553 1204 2497 \nQ 953 2441 691 2322 \nL 691 4666 \nz\n\" id=\"DejaVuSans-35\" transform=\"scale(0.015625)\"/>\n       </defs>\n       <use xlink:href=\"#DejaVuSans-30\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-35\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_3\">\n     <g id=\"line2d_3\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"127.774716\" xlink:href=\"#m86efbc4d44\" y=\"224.64\"/>\n      </g>\n     </g>\n     <g id=\"text_3\">\n      <!-- 1.0 -->\n      <g transform=\"translate(119.823153 239.238437)scale(0.1 -0.1)\">\n       <defs>\n        <path d=\"M 794 531 \nL 1825 531 \nL 1825 4091 \nL 703 3866 \nL 703 4441 \nL 1819 4666 \nL 2450 4666 \nL 2450 531 \nL 3481 531 \nL 3481 0 \nL 794 0 \nL 794 531 \nz\n\" id=\"DejaVuSans-31\" transform=\"scale(0.015625)\"/>\n       </defs>\n       <use xlink:href=\"#DejaVuSans-31\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_4\">\n     <g id=\"line2d_4\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"165.82017\" xlink:href=\"#m86efbc4d44\" y=\"224.64\"/>\n      </g>\n     </g>\n     <g id=\"text_4\">\n      <!-- 1.5 -->\n      <g transform=\"translate(157.868608 239.238437)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-31\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-35\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_5\">\n     <g id=\"line2d_5\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"203.865625\" xlink:href=\"#m86efbc4d44\" y=\"224.64\"/>\n      </g>\n     </g>\n     <g id=\"text_5\">\n      <!-- 2.0 -->\n      <g transform=\"translate(195.914063 239.238437)scale(0.1 -0.1)\">\n       <defs>\n        <path d=\"M 1228 531 \nL 3431 531 \nL 3431 0 \nL 469 0 \nL 469 531 \nQ 828 903 1448 1529 \nQ 2069 2156 2228 2338 \nQ 2531 2678 2651 2914 \nQ 2772 3150 2772 3378 \nQ 2772 3750 2511 3984 \nQ 2250 4219 1831 4219 \nQ 1534 4219 1204 4116 \nQ 875 4013 500 3803 \nL 500 4441 \nQ 881 4594 1212 4672 \nQ 1544 4750 1819 4750 \nQ 2544 4750 2975 4387 \nQ 3406 4025 3406 3419 \nQ 3406 3131 3298 2873 \nQ 3191 2616 2906 2266 \nQ 2828 2175 2409 1742 \nQ 1991 1309 1228 531 \nz\n\" id=\"DejaVuSans-32\" transform=\"scale(0.015625)\"/>\n       </defs>\n       <use xlink:href=\"#DejaVuSans-32\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_6\">\n     <g id=\"line2d_6\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"241.91108\" xlink:href=\"#m86efbc4d44\" y=\"224.64\"/>\n      </g>\n     </g>\n     <g id=\"text_6\">\n      <!-- 2.5 -->\n      <g transform=\"translate(233.959517 239.238437)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-32\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-35\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_7\">\n     <g id=\"line2d_7\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"279.956534\" xlink:href=\"#m86efbc4d44\" y=\"224.64\"/>\n      </g>\n     </g>\n     <g id=\"text_7\">\n      <!-- 3.0 -->\n      <g transform=\"translate(272.004972 239.238437)scale(0.1 -0.1)\">\n       <defs>\n        <path d=\"M 2597 2516 \nQ 3050 2419 3304 2112 \nQ 3559 1806 3559 1356 \nQ 3559 666 3084 287 \nQ 2609 -91 1734 -91 \nQ 1441 -91 1130 -33 \nQ 819 25 488 141 \nL 488 750 \nQ 750 597 1062 519 \nQ 1375 441 1716 441 \nQ 2309 441 2620 675 \nQ 2931 909 2931 1356 \nQ 2931 1769 2642 2001 \nQ 2353 2234 1838 2234 \nL 1294 2234 \nL 1294 2753 \nL 1863 2753 \nQ 2328 2753 2575 2939 \nQ 2822 3125 2822 3475 \nQ 2822 3834 2567 4026 \nQ 2313 4219 1838 4219 \nQ 1578 4219 1281 4162 \nQ 984 4106 628 3988 \nL 628 4550 \nQ 988 4650 1302 4700 \nQ 1616 4750 1894 4750 \nQ 2613 4750 3031 4423 \nQ 3450 4097 3450 3541 \nQ 3450 3153 3228 2886 \nQ 3006 2619 2597 2516 \nz\n\" id=\"DejaVuSans-33\" transform=\"scale(0.015625)\"/>\n       </defs>\n       <use xlink:href=\"#DejaVuSans-33\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_8\">\n     <g id=\"line2d_8\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"318.001989\" xlink:href=\"#m86efbc4d44\" y=\"224.64\"/>\n      </g>\n     </g>\n     <g id=\"text_8\">\n      <!-- 3.5 -->\n      <g transform=\"translate(310.050426 239.238437)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-33\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-35\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_9\">\n     <g id=\"line2d_9\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"356.047443\" xlink:href=\"#m86efbc4d44\" y=\"224.64\"/>\n      </g>\n     </g>\n     <g id=\"text_9\">\n      <!-- 4.0 -->\n      <g transform=\"translate(348.095881 239.238437)scale(0.1 -0.1)\">\n       <defs>\n        <path d=\"M 2419 4116 \nL 825 1625 \nL 2419 1625 \nL 2419 4116 \nz\nM 2253 4666 \nL 3047 4666 \nL 3047 1625 \nL 3713 1625 \nL 3713 1100 \nL 3047 1100 \nL 3047 0 \nL 2419 0 \nL 2419 1100 \nL 313 1100 \nL 313 1709 \nL 2253 4666 \nz\n\" id=\"DejaVuSans-34\" transform=\"scale(0.015625)\"/>\n       </defs>\n       <use xlink:href=\"#DejaVuSans-34\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\n      </g>\n     </g>\n    </g>\n   </g>\n   <g id=\"matplotlib.axis_2\">\n    <g id=\"ytick_1\">\n     <g id=\"line2d_10\">\n      <defs>\n       <path d=\"M 0 0 \nL -3.5 0 \n\" id=\"m5d7b767e42\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n      </defs>\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"36.465625\" xlink:href=\"#m5d7b767e42\" y=\"214.756364\"/>\n      </g>\n     </g>\n     <g id=\"text_10\">\n      <!-- 1.00 -->\n      <g transform=\"translate(7.2 218.555582)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-31\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-30\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_2\">\n     <g id=\"line2d_11\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"36.465625\" xlink:href=\"#m5d7b767e42\" y=\"190.047273\"/>\n      </g>\n     </g>\n     <g id=\"text_11\">\n      <!-- 1.25 -->\n      <g transform=\"translate(7.2 193.846491)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-31\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-32\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-35\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_3\">\n     <g id=\"line2d_12\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"36.465625\" xlink:href=\"#m5d7b767e42\" y=\"165.338182\"/>\n      </g>\n     </g>\n     <g id=\"text_12\">\n      <!-- 1.50 -->\n      <g transform=\"translate(7.2 169.137401)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-31\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-35\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-30\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_4\">\n     <g id=\"line2d_13\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"36.465625\" xlink:href=\"#m5d7b767e42\" y=\"140.629091\"/>\n      </g>\n     </g>\n     <g id=\"text_13\">\n      <!-- 1.75 -->\n      <g transform=\"translate(7.2 144.42831)scale(0.1 -0.1)\">\n       <defs>\n        <path d=\"M 525 4666 \nL 3525 4666 \nL 3525 4397 \nL 1831 0 \nL 1172 0 \nL 2766 4134 \nL 525 4134 \nL 525 4666 \nz\n\" id=\"DejaVuSans-37\" transform=\"scale(0.015625)\"/>\n       </defs>\n       <use xlink:href=\"#DejaVuSans-31\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-37\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-35\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_5\">\n     <g id=\"line2d_14\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"36.465625\" xlink:href=\"#m5d7b767e42\" y=\"115.92\"/>\n      </g>\n     </g>\n     <g id=\"text_14\">\n      <!-- 2.00 -->\n      <g transform=\"translate(7.2 119.719219)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-32\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-30\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_6\">\n     <g id=\"line2d_15\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"36.465625\" xlink:href=\"#m5d7b767e42\" y=\"91.210909\"/>\n      </g>\n     </g>\n     <g id=\"text_15\">\n      <!-- 2.25 -->\n      <g transform=\"translate(7.2 95.010128)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-32\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-32\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-35\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_7\">\n     <g id=\"line2d_16\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"36.465625\" xlink:href=\"#m5d7b767e42\" y=\"66.501818\"/>\n      </g>\n     </g>\n     <g id=\"text_16\">\n      <!-- 2.50 -->\n      <g transform=\"translate(7.2 70.301037)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-32\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-35\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-30\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_8\">\n     <g id=\"line2d_17\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"36.465625\" xlink:href=\"#m5d7b767e42\" y=\"41.792727\"/>\n      </g>\n     </g>\n     <g id=\"text_17\">\n      <!-- 2.75 -->\n      <g transform=\"translate(7.2 45.591946)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-32\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-37\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-35\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_9\">\n     <g id=\"line2d_18\">\n      <g>\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"36.465625\" xlink:href=\"#m5d7b767e42\" y=\"17.083636\"/>\n      </g>\n     </g>\n     <g id=\"text_18\">\n      <!-- 3.00 -->\n      <g transform=\"translate(7.2 20.882855)scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-33\"/>\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\n       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-30\"/>\n      </g>\n     </g>\n    </g>\n   </g>\n   <g id=\"line2d_19\">\n    <path clip-path=\"url(#p162d49c381)\" d=\"M 51.683807 214.756364 \nL 85.501989 192.792727 \nL 119.32017 170.829091 \nL 153.138352 148.865455 \nL 186.956534 126.901818 \nL 220.774716 104.938182 \nL 254.592898 82.974545 \nL 288.41108 61.010909 \nL 322.229261 39.047273 \nL 356.047443 17.083636 \n\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"patch_3\">\n    <path d=\"M 36.465625 224.64 \nL 36.465625 7.2 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"patch_4\">\n    <path d=\"M 371.265625 224.64 \nL 371.265625 7.2 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"patch_5\">\n    <path d=\"M 36.465625 224.64 \nL 371.265625 224.64 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"patch_6\">\n    <path d=\"M 36.465625 7.2 \nL 371.265625 7.2 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n   </g>\n  </g>\n </g>\n <defs>\n  <clipPath id=\"p162d49c381\">\n   <rect height=\"217.44\" width=\"334.8\" x=\"36.465625\" y=\"7.2\"/>\n  </clipPath>\n </defs>\n</svg>\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "source": [
    "# Assignment 2\n",
    "# for X = np.array([1,2,3]), Y = np.array([1,3,2])\n",
    "# find the linear regression equation. (use multiple linear regression)\n",
    "import numpy as np\n",
    "\n",
    "X = np.array([[1,1], [1,2], [1,3]])\n",
    "Y = np.array([1,3,2])\n",
    "\n",
    "tmp1 = np.linalg.inv(np.dot(X.T,X)) \n",
    "tmp2 = np.dot(X.T,Y)\n",
    "\n",
    "cof = np.dot(tmp1,tmp2)\n",
    "print(\"Alpha: %g / Beta: %g\" %(cof[0],cof[1]))"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Alpha: 1 / Beta: 0.5\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Logistic Regression\n",
    "* is a statistical model that in its basic form uses a logistic function to model a binary dependent variable, although many more complex extensions exist. \n",
    "* is estimating the parameters of a logistic model which has a dependent variable with two possible values, such as pass/fail\n",
    "\n",
    "from [wikipedia](https://en.wikipedia.org/wiki/Logistic_regression)\n",
    "\n",
    "* General type of regression is not suitable for binary model\n",
    "* Generally regression $\\hat{y}$'s range is $(-{\\infty},{\\infty})$, while desired range is only $\\{0,1\\}$\n",
    "\n",
    "## Implement Logistic Function\n",
    "\n",
    "$$Y=\\frac{1}{1+e^{-x}}$$\n",
    "\n",
    "<br>\n",
    "\n",
    "Sigmoid Function (one of Logistic Functions) $Y=\\frac{1}{1+e^{-x}}$ satisfies $0 < Y <1$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$\\widehat{Y}=\\frac{1}{1+exp(-X \\cdot \\hat{\\beta})}$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$\\frac{\\widehat{Y}}{1-\\widehat{Y}}=\\frac{1}{exp(-X \\cdot \\hat{\\beta})} = exp(X \\cdot \\hat{\\beta})$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$ln(\\frac{p}{1-p})= X \\cdot \\beta = \\beta_0 + \\beta_1 x_1 + \\cdots + \\beta_k x_k \\qquad p=Pr(Y=1)$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$ln(\\frac{p_i}{1-p_i})= X \\cdot \\beta \\qquad p_i=Pr(Y=1)$$\n",
    "\n",
    "<br>\n",
    "\n",
    "For given $\\hat{\\beta}$, $\\widehat{Y}$ can be estimated as follows: \n",
    "\n",
    "<br>\n",
    "\n",
    "$$\\widehat{Y}=\\frac{1}{1+exp(-X \\cdot \\hat{\\beta})} = \\frac{1}{1+exp(-X \\cdot \\hat{\\beta})} \\cdot \\frac{exp(X \\cdot \\hat{\\beta})}{exp(X \\cdot \\hat{\\beta})} = \\frac{exp(X \\cdot \\hat{\\beta})}{1+exp(X \\cdot \\hat{\\beta})}$$"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Cost minimizing (using Cost function (Loss Function))\n",
    "\n",
    "* Cost function decreases if it is correct, while increases if it is incorrect.\n",
    "* Cost function satisfies convexity(볼록성: 아래로 볼록한 함수)\n",
    "\n",
    "For Bias $B$ and Weight $W$ ($\\beta$ in statistics), following Logistic function (Sigmoid) $H(X)$ and Cross Entropy function, Cost Function $Cost(W)$ is given.\n",
    "\n",
    "\n",
    "$$H(X)=\\frac{1}{1+exp(-WX)}$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$\n",
    "Cost(W)=\n",
    "    \\begin{cases} \n",
    "    \\sum -ln(H(X)) & \\,\\,\\,\\,\\,\\,\\,\\,\\,(y=1)\\\\\n",
    "    \\sum -ln(1-H(X)) & \\,\\,\\,\\,\\,\\,\\,\\,\\, (y=0)\n",
    "    \\end{cases}\n",
    "$$\n",
    "\n",
    "\n",
    "Cost Function can be rewritten in one line:\n",
    "\n",
    "$$Cost(W)=\\sum \\big[ -y_iln(H(X)) + (1-y_i) -ln(1-H(X)) \\big]$$\n",
    "\n",
    "### Convexity Check\n",
    "$$\n",
    "X = \\begin{pmatrix} 1 \\\\ 2 \\\\ 3 \\\\ 4 \\\\ 5 \\\\ 6 \\end{pmatrix} ,\\quad\n",
    "Y= \\begin{pmatrix} 0 \\\\ 0 \\\\ 0 \\\\ 1 \\\\ 1 \\\\ 1 \\end{pmatrix} ,\\quad\n",
    "XY = \\begin{pmatrix} 1 & 0 \\\\ 2 & 0 \\\\ 3 & 0 \\\\ 4 & 1 \\\\ 5 & 1 \\\\ 6 & 1 \\end{pmatrix}\n",
    "$$\n",
    "\n",
    "```a``` is the section $(-5,5)$ which equally divided into 100 and ```b``` is the section $(-2.5,2.5)$ which equally divided into 100.\n",
    "\n",
    "MeshGrid made in area (a,b)"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "source": [
    "# Convexity Check\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "def sigmoid(x):\n",
    "    return 1/(1+np.exp(-x))\n",
    "\n",
    "x = np.array([1,2,3,4,5,6])\n",
    "y = np.array([0,0,0,1,1,1])\n",
    "xy = np.array([[1,0],[2,0],[3,0],[4,1],[5,1],[6,1]])\n",
    "\n",
    "n = 100\n",
    "a = np.linspace(-5,5,n)\n",
    "b = np.linspace(-2.5,2.5,n)\n",
    "a,b = np.meshgrid(a,b)\n",
    "cost1 = np.zeros((n,n)) # cross entropy function\n",
    "\n",
    "for val in xy:\n",
    "    temp = -val[1]*np.log(sig(a+b*val[0])) - (1-val[1])*np.log(1-sig(a+b*val[0]))\n",
    "    cost1 += temp\n",
    "\n",
    "cost2 = np.zeros((n,n))\n",
    "for val in xy:\n",
    "    temp = (val[1]-sig(a+b*val[0]))**2 # error sums of square function\n",
    "    cost2 += temp\n",
    "\n",
    "ax = plt.axes(projection='3d')\n",
    "ax.contour3D(a,b,cost1,n,cmap='binary') # satisfies convexity\n",
    "#ax.contour3D(a,b,cost2,n,cmap='binary') # SSE failed convexity"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "<matplotlib.contour.QuadContourSet at 0x7f64fab37e80>"
      ]
     },
     "metadata": {},
     "execution_count": 13
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
      "image/png": "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",
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<svg height=\"238.039633pt\" version=\"1.1\" viewBox=\"0 0 247.0147 238.039633\" width=\"247.0147pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n <metadata>\n  <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n   <cc:Work>\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n    <dc:date>2021-07-15T17:07:46.870582</dc:date>\n    <dc:format>image/svg+xml</dc:format>\n    <dc:creator>\n     <cc:Agent>\n      <dc:title>Matplotlib v3.4.2, https://matplotlib.org/</dc:title>\n     </cc:Agent>\n    </dc:creator>\n   </cc:Work>\n  </rdf:RDF>\n </metadata>\n <defs>\n  <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\n </defs>\n <g id=\"figure_1\">\n  <g id=\"patch_1\">\n   <path d=\"M 0 238.039633 \nL 247.0147 238.039633 \nL 247.0147 0 \nL 0 0 \nz\n\" style=\"fill:none;\"/>\n  </g>\n  <g id=\"patch_2\">\n   <path d=\"M 7.2 224.64 \nL 224.64 224.64 \nL 224.64 7.2 \nL 7.2 7.2 \nz\n\" style=\"fill:#ffffff;\"/>\n  </g>\n  <g id=\"pane3d_1\">\n   <g id=\"patch_3\">\n    <path d=\"M 23.61822 171.026264 \nL 95.424009 110.837228 \nL 94.42584 24.033878 \nL 19.183773 78.942111 \n\" style=\"fill:#f2f2f2;opacity:0.5;stroke:#f2f2f2;stroke-linejoin:miter;\"/>\n   </g>\n  </g>\n  <g id=\"pane3d_2\">\n   <g id=\"patch_4\">\n    <path d=\"M 95.424009 110.837228 \nL 210.64668 144.32791 \nL 214.758571 54.534718 \nL 94.42584 24.033878 \n\" style=\"fill:#e6e6e6;opacity:0.5;stroke:#e6e6e6;stroke-linejoin:miter;\"/>\n   </g>\n  </g>\n  <g id=\"pane3d_3\">\n   <g id=\"patch_5\">\n    <path d=\"M 23.61822 171.026264 \nL 145.759879 210.91773 \nL 210.64668 144.32791 \nL 95.424009 110.837228 \n\" style=\"fill:#ececec;opacity:0.5;stroke:#ececec;stroke-linejoin:miter;\"/>\n   </g>\n  </g>\n  <g id=\"axis3d_1\">\n   <g id=\"line2d_1\">\n    <path d=\"M 23.61822 171.026264 \nL 145.759879 210.91773 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"Line3DCollection_1\">\n    <path d=\"M 41.240222 176.78161 \nL 112.110677 115.687384 \nL 111.821115 28.443073 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-width:0.8;\"/>\n    <path d=\"M 61.968862 183.551584 \nL 131.711859 121.384673 \nL 132.268249 33.625826 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-width:0.8;\"/>\n    <path d=\"M 83.079037 190.446167 \nL 151.643632 127.178053 \nL 153.075303 38.899807 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-width:0.8;\"/>\n    <path d=\"M 104.58138 197.468832 \nL 171.914432 133.069974 \nL 174.251863 44.267448 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-width:0.8;\"/>\n    <path d=\"M 126.48692 204.623182 \nL 192.532983 139.062973 \nL 195.807861 49.731265 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"xtick_1\">\n    <g id=\"line2d_2\">\n     <path d=\"M 41.857584 176.24941 \nL 40.002836 177.848305 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n    </g>\n    <g id=\"text_1\">\n     <!-- −4 -->\n     <g transform=\"translate(26.34637 200.190487)scale(0.1 -0.1)\">\n      <defs>\n       <path d=\"M 678 2272 \nL 4684 2272 \nL 4684 1741 \nL 678 1741 \nL 678 2272 \nz\n\" id=\"DejaVuSans-2212\" transform=\"scale(0.015625)\"/>\n       <path d=\"M 2419 4116 \nL 825 1625 \nL 2419 1625 \nL 2419 4116 \nz\nM 2253 4666 \nL 3047 4666 \nL 3047 1625 \nL 3713 1625 \nL 3713 1100 \nL 3047 1100 \nL 3047 0 \nL 2419 0 \nL 2419 1100 \nL 313 1100 \nL 313 1709 \nL 2253 4666 \nz\n\" id=\"DejaVuSans-34\" transform=\"scale(0.015625)\"/>\n      </defs>\n      <use xlink:href=\"#DejaVuSans-2212\"/>\n      <use x=\"83.789062\" xlink:href=\"#DejaVuSans-34\"/>\n     </g>\n    </g>\n   </g>\n   <g id=\"xtick_2\">\n    <g id=\"line2d_3\">\n     <path d=\"M 62.576855 183.009637 \nL 60.750231 184.637837 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n    </g>\n    <g id=\"text_2\">\n     <!-- −2 -->\n     <g transform=\"translate(47.101769 207.136553)scale(0.1 -0.1)\">\n      <defs>\n       <path d=\"M 1228 531 \nL 3431 531 \nL 3431 0 \nL 469 0 \nL 469 531 \nQ 828 903 1448 1529 \nQ 2069 2156 2228 2338 \nQ 2531 2678 2651 2914 \nQ 2772 3150 2772 3378 \nQ 2772 3750 2511 3984 \nQ 2250 4219 1831 4219 \nQ 1534 4219 1204 4116 \nQ 875 4013 500 3803 \nL 500 4441 \nQ 881 4594 1212 4672 \nQ 1544 4750 1819 4750 \nQ 2544 4750 2975 4387 \nQ 3406 4025 3406 3419 \nQ 3406 3131 3298 2873 \nQ 3191 2616 2906 2266 \nQ 2828 2175 2409 1742 \nQ 1991 1309 1228 531 \nz\n\" id=\"DejaVuSans-32\" transform=\"scale(0.015625)\"/>\n      </defs>\n      <use xlink:href=\"#DejaVuSans-2212\"/>\n      <use x=\"83.789062\" xlink:href=\"#DejaVuSans-32\"/>\n     </g>\n    </g>\n   </g>\n   <g id=\"xtick_3\">\n    <g id=\"line2d_4\">\n     <path d=\"M 83.67721 189.894202 \nL 81.880066 191.55252 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n    </g>\n    <g id=\"text_3\">\n     <!-- 0 -->\n     <g transform=\"translate(72.43082 214.211064)scale(0.1 -0.1)\">\n      <defs>\n       <path d=\"M 2034 4250 \nQ 1547 4250 1301 3770 \nQ 1056 3291 1056 2328 \nQ 1056 1369 1301 889 \nQ 1547 409 2034 409 \nQ 2525 409 2770 889 \nQ 3016 1369 3016 2328 \nQ 3016 3291 2770 3770 \nQ 2525 4250 2034 4250 \nz\nM 2034 4750 \nQ 2819 4750 3233 4129 \nQ 3647 3509 3647 2328 \nQ 3647 1150 3233 529 \nQ 2819 -91 2034 -91 \nQ 1250 -91 836 529 \nQ 422 1150 422 2328 \nQ 422 3509 836 4129 \nQ 1250 4750 2034 4750 \nz\n\" id=\"DejaVuSans-30\" transform=\"scale(0.015625)\"/>\n      </defs>\n      <use xlink:href=\"#DejaVuSans-30\"/>\n     </g>\n    </g>\n   </g>\n   <g id=\"xtick_4\">\n    <g id=\"line2d_5\">\n     <path d=\"M 105.169261 196.90657 \nL 103.403013 198.595849 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n    </g>\n    <g id=\"text_4\">\n     <!-- 2 -->\n     <g transform=\"translate(93.964579 221.417618)scale(0.1 -0.1)\">\n      <use xlink:href=\"#DejaVuSans-32\"/>\n     </g>\n    </g>\n   </g>\n   <g id=\"xtick_5\">\n    <g id=\"line2d_6\">\n     <path d=\"M 127.064016 204.05033 \nL 125.330145 205.771446 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n    </g>\n    <g id=\"text_5\">\n     <!-- 4 -->\n     <g transform=\"translate(115.904041 228.759946)scale(0.1 -0.1)\">\n      <use xlink:href=\"#DejaVuSans-34\"/>\n     </g>\n    </g>\n   </g>\n  </g>\n  <g id=\"axis3d_2\">\n   <g id=\"line2d_7\">\n    <path d=\"M 210.64668 144.32791 \nL 145.759879 210.91773 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"Line3DCollection_2\">\n    <path d=\"M 31.423843 70.009865 \nL 35.262198 161.266051 \nL 156.320859 200.079566 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-width:0.8;\"/>\n    <path d=\"M 45.164595 59.982491 \nL 48.350904 150.294838 \nL 168.174128 187.915196 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-width:0.8;\"/>\n    <path d=\"M 58.478537 50.266582 \nL 61.050371 139.649893 \nL 179.656664 176.131289 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-width:0.8;\"/>\n    <path d=\"M 71.385252 40.847849 \nL 73.377708 129.316875 \nL 190.785593 164.710271 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-width:0.8;\"/>\n    <path d=\"M 83.903142 31.712864 \nL 85.349035 119.282271 \nL 201.577001 153.635632 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"xtick_6\">\n    <g id=\"line2d_8\">\n     <path d=\"M 155.301111 199.752617 \nL 158.362971 200.734303 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n    </g>\n    <g id=\"text_6\">\n     <!-- −2 -->\n     <g transform=\"translate(161.732482 220.990124)scale(0.1 -0.1)\">\n      <use xlink:href=\"#DejaVuSans-2212\"/>\n      <use x=\"83.789062\" xlink:href=\"#DejaVuSans-32\"/>\n     </g>\n    </g>\n   </g>\n   <g id=\"xtick_7\">\n    <g id=\"line2d_9\">\n     <path d=\"M 167.165593 187.598551 \nL 170.193744 188.549286 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n    </g>\n    <g id=\"text_7\">\n     <!-- −1 -->\n     <g transform=\"translate(173.391009 208.605413)scale(0.1 -0.1)\">\n      <defs>\n       <path d=\"M 794 531 \nL 1825 531 \nL 1825 4091 \nL 703 3866 \nL 703 4441 \nL 1819 4666 \nL 2450 4666 \nL 2450 531 \nL 3481 531 \nL 3481 0 \nL 794 0 \nL 794 531 \nz\n\" id=\"DejaVuSans-31\" transform=\"scale(0.015625)\"/>\n      </defs>\n      <use xlink:href=\"#DejaVuSans-2212\"/>\n      <use x=\"83.789062\" xlink:href=\"#DejaVuSans-31\"/>\n     </g>\n    </g>\n   </g>\n   <g id=\"xtick_8\">\n    <g id=\"line2d_10\">\n     <path d=\"M 178.659145 175.824468 \nL 181.654182 176.745694 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n    </g>\n    <g id=\"text_8\">\n     <!-- 0 -->\n     <g transform=\"translate(188.87448 196.608328)scale(0.1 -0.1)\">\n      <use xlink:href=\"#DejaVuSans-30\"/>\n     </g>\n    </g>\n   </g>\n   <g id=\"xtick_9\">\n    <g id=\"line2d_11\">\n     <path d=\"M 189.798894 164.412824 \nL 192.761405 165.305893 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n    </g>\n    <g id=\"text_9\">\n     <!-- 1 -->\n     <g transform=\"translate(199.820077 184.980953)scale(0.1 -0.1)\">\n      <use xlink:href=\"#DejaVuSans-31\"/>\n     </g>\n    </g>\n   </g>\n   <g id=\"xtick_10\">\n    <g id=\"line2d_12\">\n     <path d=\"M 200.60093 153.347136 \nL 203.531495 154.213319 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n    </g>\n    <g id=\"text_10\">\n     <!-- 2 -->\n     <g transform=\"translate(210.433486 173.706457)scale(0.1 -0.1)\">\n      <use xlink:href=\"#DejaVuSans-32\"/>\n     </g>\n    </g>\n   </g>\n  </g>\n  <g id=\"axis3d_3\">\n   <g id=\"line2d_13\">\n    <path d=\"M 210.64668 144.32791 \nL 214.758571 54.534718 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"Line3DCollection_3\">\n    <path d=\"M 211.389122 128.114867 \nL 95.243468 95.1369 \nL 22.818642 154.422526 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-width:0.8;\"/>\n    <path d=\"M 212.141312 111.688969 \nL 95.060696 79.242656 \nL 22.008071 137.590496 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-width:0.8;\"/>\n    <path d=\"M 212.905831 94.993828 \nL 94.875074 63.100462 \nL 21.183702 120.471925 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-width:0.8;\"/>\n    <path d=\"M 213.682985 78.022768 \nL 94.686533 46.70447 \nL 20.345178 103.059432 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-width:0.8;\"/>\n    <path d=\"M 214.47309 60.768893 \nL 94.495005 30.048646 \nL 19.492132 85.345382 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-width:0.8;\"/>\n   </g>\n   <g id=\"xtick_11\">\n    <g id=\"line2d_14\">\n     <path d=\"M 210.413972 127.837986 \nL 213.341762 128.669292 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n    </g>\n    <g id=\"text_11\">\n     <!-- 10 -->\n     <g transform=\"translate(223.407241 133.149006)scale(0.1 -0.1)\">\n      <use xlink:href=\"#DejaVuSans-31\"/>\n      <use x=\"63.623047\" xlink:href=\"#DejaVuSans-30\"/>\n     </g>\n    </g>\n   </g>\n   <g id=\"xtick_12\">\n    <g id=\"line2d_15\">\n     <path d=\"M 211.157935 111.416448 \nL 214.110444 112.23467 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n    </g>\n    <g id=\"text_12\">\n     <!-- 20 -->\n     <g transform=\"translate(224.305488 116.763549)scale(0.1 -0.1)\">\n      <use xlink:href=\"#DejaVuSans-32\"/>\n      <use x=\"63.623047\" xlink:href=\"#DejaVuSans-30\"/>\n     </g>\n    </g>\n   </g>\n   <g id=\"xtick_13\">\n    <g id=\"line2d_16\">\n     <path d=\"M 211.914087 94.725846 \nL 214.891735 95.530443 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n    </g>\n    <g id=\"text_13\">\n     <!-- 30 -->\n     <g transform=\"translate(225.218404 100.110521)scale(0.1 -0.1)\">\n      <defs>\n       <path d=\"M 2597 2516 \nQ 3050 2419 3304 2112 \nQ 3559 1806 3559 1356 \nQ 3559 666 3084 287 \nQ 2609 -91 1734 -91 \nQ 1441 -91 1130 -33 \nQ 819 25 488 141 \nL 488 750 \nQ 750 597 1062 519 \nQ 1375 441 1716 441 \nQ 2309 441 2620 675 \nQ 2931 909 2931 1356 \nQ 2931 1769 2642 2001 \nQ 2353 2234 1838 2234 \nL 1294 2234 \nL 1294 2753 \nL 1863 2753 \nQ 2328 2753 2575 2939 \nQ 2822 3125 2822 3475 \nQ 2822 3834 2567 4026 \nQ 2313 4219 1838 4219 \nQ 1578 4219 1281 4162 \nQ 984 4106 628 3988 \nL 628 4550 \nQ 988 4650 1302 4700 \nQ 1616 4750 1894 4750 \nQ 2613 4750 3031 4423 \nQ 3450 4097 3450 3541 \nQ 3450 3153 3228 2886 \nQ 3006 2619 2597 2516 \nz\n\" id=\"DejaVuSans-33\" transform=\"scale(0.015625)\"/>\n      </defs>\n      <use xlink:href=\"#DejaVuSans-33\"/>\n      <use x=\"63.623047\" xlink:href=\"#DejaVuSans-30\"/>\n     </g>\n    </g>\n   </g>\n   <g id=\"xtick_14\">\n    <g id=\"line2d_17\">\n     <path d=\"M 212.682732 77.759514 \nL 215.68595 78.549922 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n    </g>\n    <g id=\"text_14\">\n     <!-- 40 -->\n     <g transform=\"translate(226.14635 83.183313)scale(0.1 -0.1)\">\n      <use xlink:href=\"#DejaVuSans-34\"/>\n      <use x=\"63.623047\" xlink:href=\"#DejaVuSans-30\"/>\n     </g>\n    </g>\n   </g>\n   <g id=\"xtick_15\">\n    <g id=\"line2d_18\">\n     <path d=\"M 213.46418 60.510563 \nL 216.49341 61.286194 \n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-width:0.8;\"/>\n    </g>\n    <g id=\"text_15\">\n     <!-- 50 -->\n     <g transform=\"translate(227.0897 65.975098)scale(0.1 -0.1)\">\n      <defs>\n       <path d=\"M 691 4666 \nL 3169 4666 \nL 3169 4134 \nL 1269 4134 \nL 1269 2991 \nQ 1406 3038 1543 3061 \nQ 1681 3084 1819 3084 \nQ 2600 3084 3056 2656 \nQ 3513 2228 3513 1497 \nQ 3513 744 3044 326 \nQ 2575 -91 1722 -91 \nQ 1428 -91 1123 -41 \nQ 819 9 494 109 \nL 494 744 \nQ 775 591 1075 516 \nQ 1375 441 1709 441 \nQ 2250 441 2565 725 \nQ 2881 1009 2881 1497 \nQ 2881 1984 2565 2268 \nQ 2250 2553 1709 2553 \nQ 1456 2553 1204 2497 \nQ 953 2441 691 2322 \nL 691 4666 \nz\n\" id=\"DejaVuSans-35\" transform=\"scale(0.015625)\"/>\n      </defs>\n      <use xlink:href=\"#DejaVuSans-35\"/>\n      <use x=\"63.623047\" xlink:href=\"#DejaVuSans-30\"/>\n     </g>\n    </g>\n   </g>\n  </g>\n  <g id=\"axes_1\">\n   <g id=\"Line3DCollection_4\"/>\n   <g id=\"Line3DCollection_5\"/>\n   <g id=\"Line3DCollection_6\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 89.273156 122.071038 \nL 89.730673 122.799573 \nL 89.734546 122.806883 \nL 90.170744 123.566519 \nL 90.207471 123.625625 \nL 90.586976 124.345621 \nL 90.642262 124.440839 \nL 90.976007 125.150442 \nL 91.024524 125.242056 \nL 91.3238 125.993081 \nL 91.338391 126.024509 \nL 91.538756 126.7747 \nL 91.53578 126.954499 \nL 91.575493 127.477579 \nL 91.339221 128.100344 \nL 90.042644 128.407429 \nL 89.862502 128.383607 \nL 88.825249 128.123516 \nL 87.869596 127.794819 \nL 87.53948 127.659229 \nL 86.978484 127.412351 \nL 86.12662 126.997837 \nL 85.284645 126.576306 \nL 84.447814 126.151803 \n\" style=\"fill:none;stroke:#fdfdfd;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_7\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 92.682174 118.234229 \nL 93.101614 118.773949 \nL 93.205935 118.912077 \nL 93.727902 119.593673 \nL 93.769222 119.647471 \nL 94.243793 120.282665 \nL 94.423444 120.518774 \nL 94.759518 120.974069 \nL 95.072984 121.390421 \nL 95.27504 121.667928 \nL 95.717156 122.262212 \nL 95.790326 122.364281 \nL 96.301509 123.066446 \nL 96.349876 123.132345 \nL 96.806029 123.77664 \nL 96.967491 123.999735 \nL 97.3088 124.490692 \nL 97.576264 124.866231 \nL 97.809517 125.208884 \nL 98.174872 125.731435 \nL 98.307808 125.931556 \nL 98.761738 126.594878 \nL 98.80321 126.659129 \nL 99.290452 127.396176 \nL 99.329654 127.454409 \nL 99.768051 128.144027 \nL 99.876531 128.309397 \nL 100.239152 128.900012 \nL 100.404923 129.160587 \nL 100.702219 129.665506 \nL 100.911626 130.007014 \nL 101.155164 130.442369 \nL 101.392663 130.847475 \nL 101.595071 131.233197 \nL 101.843043 131.680462 \nL 102.01771 132.041748 \nL 102.256402 132.504049 \nL 102.416691 132.87369 \nL 102.624494 133.315738 \nL 102.781852 133.73803 \nL 102.936443 134.112235 \nL 103.095953 134.650036 \nL 103.177601 134.889098 \nL 103.327188 135.637861 \nL 103.327772 135.640204 \nL 103.299893 136.339303 \nL 103.050762 136.973239 \nL 102.176274 137.420093 \nL 101.317659 137.401315 \nL 100.196861 137.189802 \nL 99.186893 136.882078 \nL 98.233654 136.525865 \nL 97.312733 136.142687 \nL 96.411579 135.7436 \nL 96.064684 135.579228 \nL 95.545495 135.315392 \nL 94.700119 134.870665 \nL 93.855461 134.426809 \nL 93.010812 133.984431 \nL 92.878377 133.91232 \nL 92.199986 133.514347 \nL 91.389136 133.045855 \nL 90.572086 132.584254 \nL 90.312738 132.435349 \nL 89.777938 132.104528 \nL 88.987761 131.622991 \nL 88.188457 131.150861 \nL 87.997123 131.036437 \nL 87.41263 130.660238 \nL 86.635231 130.172578 \nL 85.847493 129.695329 \nL 85.831133 129.685229 \nL 85.090233 129.193745 \nL 84.320738 128.704194 \nL 83.792846 128.375011 \nL 83.553341 128.214472 \nL 82.801479 127.713215 \nL 82.036822 127.224405 \n\" style=\"fill:none;stroke:#fafafa;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_8\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 95.051014 115.281817 \nL 95.49091 115.840693 \nL 95.578222 115.953036 \nL 96.103773 116.627862 \nL 96.168288 116.710792 \nL 96.626661 117.307166 \nL 96.838133 117.580398 \nL 97.149859 117.988445 \nL 97.505977 118.451134 \nL 97.673371 118.671707 \nL 98.171573 119.32293 \nL 98.197207 119.356952 \nL 98.716724 120.048152 \nL 98.826277 120.193246 \nL 99.235079 120.742637 \nL 99.475882 121.063785 \nL 99.753233 121.439603 \nL 100.121869 121.934982 \nL 100.271144 122.139096 \nL 100.76384 122.806724 \nL 100.788776 122.841163 \nL 101.301443 123.549845 \nL 101.393604 123.676591 \nL 101.812034 124.262686 \nL 102.016105 124.54604 \nL 102.321566 124.978831 \nL 102.632736 125.415483 \nL 102.829901 125.698415 \nL 103.242859 126.284729 \nL 103.336885 126.421588 \nL 103.842138 127.148699 \nL 103.845445 127.153474 \nL 104.339874 127.884794 \nL 104.43163 128.019084 \nL 104.835008 128.625642 \nL 105.008683 128.88371 \nL 105.327162 129.371596 \nL 105.575544 129.747034 \nL 105.815881 130.123079 \nL 106.130987 130.608687 \nL 106.300613 130.880603 \nL 106.673574 131.468234 \nL 106.780674 131.644798 \nL 107.201611 132.325165 \nL 107.255202 132.416454 \nL 107.713078 133.178868 \nL 107.723085 133.196588 \nL 108.179884 133.989153 \nL 108.202522 134.027703 \nL 108.625819 134.794019 \nL 108.669756 134.871599 \nL 109.059768 135.612241 \nL 109.11275 135.709934 \nL 109.478669 136.446599 \nL 109.527486 136.541485 \nL 109.878239 137.300975 \nL 109.908961 137.36473 \nL 110.250574 138.17766 \nL 110.251794 138.18141 \nL 110.533792 138.974669 \nL 110.569151 139.114901 \nL 110.751869 139.753678 \nL 110.810585 140.119309 \nL 110.88796 140.509556 \nL 110.917805 141.234911 \nL 110.91243 141.251859 \nL 110.73702 141.898124 \nL 110.242388 142.467802 \nL 109.238528 142.746734 \nL 108.870064 142.773019 \nL 107.964049 142.657003 \nL 106.877743 142.400115 \nL 105.862778 142.080731 \nL 104.891179 141.723987 \nL 103.947615 141.343647 \nL 103.495983 141.146637 \nL 103.037181 140.93533 \nL 102.154233 140.50416 \nL 101.277851 140.068681 \nL 100.40586 139.630828 \nL 99.748334 139.295168 \nL 99.545075 139.18463 \nL 98.711128 138.716431 \nL 97.873736 138.252837 \nL 97.03359 137.79322 \nL 96.903228 137.720045 \nL 96.220504 137.311565 \nL 95.406238 136.832565 \nL 94.586007 136.360364 \nL 94.398372 136.250776 \nL 93.78773 135.870709 \nL 92.989104 135.383002 \nL 92.182834 134.903542 \nL 92.077131 134.839829 \nL 91.400158 134.405325 \nL 90.612204 133.913321 \nL 89.885092 133.470641 \nL 89.818823 133.427629 \nL 89.048836 132.923466 \nL 88.268216 132.430098 \nL 87.794523 132.134744 \nL 87.49245 131.934215 \nL 86.727322 131.430886 \nL 85.951772 130.938116 \nL 85.766478 130.820336 \nL 85.192926 130.432749 \nL 84.430902 129.931752 \nL 83.797815 129.526407 \nL 83.664847 129.435828 \nL 82.916158 128.926818 \nL 82.156077 128.429119 \nL 81.881773 128.250867 \nL 81.407395 127.923424 \nL 80.65912 127.419042 \n\" style=\"fill:none;stroke:#f7f7f7;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_9\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 97.073024 112.626222 \nL 102.406304 119.62173 \nL 106.8957 125.873079 \nL 110.242282 130.87567 \nL 112.872013 135.167751 \nL 114.704906 138.551365 \nL 115.825696 141.030671 \nL 116.397389 142.761923 \nL 116.637718 144.153745 \nL 116.511897 145.150282 \nL 116.393912 145.528051 \nL 115.86035 146.092516 \nL 114.566506 146.427422 \nL 113.773542 146.374459 \nL 111.553033 145.880604 \nL 108.618331 144.791821 \nL 105.896515 143.524823 \nL 101.584018 141.244568 \nL 98.177254 139.292244 \nL 87.958151 132.887178 \nL 83.29759 129.829571 \nL 79.596391 127.344299 \nL 79.596391 127.344299 \n\" style=\"fill:none;stroke:#f4f4f4;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_10\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 99.71609 111.190253 \nL 105.112566 118.363405 \nL 109.699348 124.815142 \nL 113.228476 130.106984 \nL 116.550014 135.506098 \nL 118.815957 139.614157 \nL 120.055326 142.222499 \nL 120.917666 144.474493 \nL 121.312266 146.103916 \nL 121.336137 147.506234 \nL 121.111478 148.168162 \nL 120.610567 148.747559 \nL 119.34089 149.169137 \nL 118.01005 149.11273 \nL 115.756282 148.63016 \nL 113.74339 147.933066 \nL 109.98863 146.310035 \nL 106.165372 144.361076 \nL 99.739134 140.681599 \nL 93.304076 136.710821 \nL 83.238663 130.149995 \nL 78.718068 127.111093 \nL 78.718068 127.111093 \n\" style=\"fill:none;stroke:#f1f1f1;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_11\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 103.294439 111.286944 \nL 108.813002 118.81635 \nL 113.342715 125.379643 \nL 117.275091 131.469061 \nL 120.133434 136.229691 \nL 122.410912 140.368543 \nL 124.086186 143.866378 \nL 124.97608 146.1747 \nL 125.40236 147.760354 \nL 125.514362 149.257208 \nL 125.386586 149.952152 \nL 125.064793 150.589567 \nL 124.388066 151.120329 \nL 122.799101 151.419009 \nL 120.378247 151.07205 \nL 118.253797 150.456905 \nL 115.306576 149.324873 \nL 112.519388 148.060235 \nL 108.093208 145.785729 \nL 103.834306 143.402131 \nL 94.473494 137.680789 \nL 80.39984 128.459757 \nL 77.935572 126.794457 \nL 77.935572 126.794457 \n\" style=\"fill:none;stroke:#eeeeee;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_12\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 106.604255 111.302135 \nL 111.461019 118.071205 \nL 116.069776 124.875234 \nL 119.874846 130.850947 \nL 123.427839 136.836 \nL 126.193505 141.94989 \nL 127.94577 145.712509 \nL 128.730368 147.787047 \nL 129.19514 149.704604 \nL 129.290853 150.91244 \nL 129.184256 151.595365 \nL 128.90264 152.248498 \nL 128.334403 152.815733 \nL 127.225973 153.219538 \nL 126.761654 153.256431 \nL 125.394372 153.220678 \nL 124.177834 153.045854 \nL 121.995244 152.467619 \nL 118.966432 151.383749 \nL 115.191515 149.717136 \nL 111.59127 147.916455 \nL 107.25717 145.552388 \nL 100.068573 141.296156 \nL 90.227981 135.046069 \nL 81.752791 129.457693 \nL 77.221417 126.417781 \nL 77.221417 126.417781 \n\" style=\"fill:none;stroke:#ebebeb;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_13\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 109.707418 111.254033 \nL 114.421377 117.981663 \nL 118.899869 124.747426 \nL 123.157236 131.588853 \nL 126.925928 138.085963 \nL 129.364227 142.644415 \nL 131.311772 146.772235 \nL 132.051176 148.675098 \nL 132.63662 150.735109 \nL 132.791409 151.704742 \nL 132.694802 153.155386 \nL 132.403903 153.809136 \nL 131.839781 154.381013 \nL 130.790317 154.806083 \nL 129.58041 154.892868 \nL 128.253401 154.814002 \nL 125.95755 154.32504 \nL 122.813673 153.321667 \nL 119.866508 152.148692 \nL 115.22344 149.977177 \nL 109.931578 147.170201 \nL 104.844541 144.239672 \nL 99.090452 140.738334 \nL 87.232696 133.107751 \nL 78.063538 127.008247 \nL 76.556065 125.997665 \nL 76.556065 125.997665 \n\" style=\"fill:none;stroke:#e8e8e8;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_14\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 112.642417 111.153995 \nL 117.222515 117.842491 \nL 121.175359 123.928516 \nL 125.729347 131.349041 \nL 129.742181 138.320979 \nL 132.47436 143.440281 \nL 134.429097 147.540753 \nL 135.417128 150.038578 \nL 135.946652 151.916903 \nL 136.146464 153.21457 \nL 136.02084 154.494112 \nL 135.992716 154.654726 \nL 135.657595 155.298404 \nL 135.041031 155.857628 \nL 133.930247 156.26721 \nL 132.634653 156.344095 \nL 131.30703 156.260195 \nL 128.981586 155.785709 \nL 125.787355 154.807803 \nL 122.357084 153.481914 \nL 118.063674 151.525349 \nL 113.56273 149.225528 \nL 107.523535 145.839054 \nL 100.070272 141.33113 \nL 91.286377 135.726915 \nL 79.704907 128.079309 \nL 75.925722 125.545813 \nL 75.925722 125.545813 \n\" style=\"fill:none;stroke:#e5e5e5;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_15\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 115.438463 111.01064 \nL 119.892495 117.662034 \nL 124.147777 124.361392 \nL 128.750649 132.011511 \nL 133.071314 139.638988 \nL 136.204407 145.630975 \nL 137.834162 149.172984 \nL 138.730311 151.525728 \nL 139.188881 153.192945 \nL 139.371147 154.688715 \nL 139.189987 155.864596 \nL 139.126185 156.107948 \nL 138.721062 156.73365 \nL 138.005085 157.265833 \nL 136.723791 157.626505 \nL 135.863718 157.664193 \nL 133.980031 157.540904 \nL 132.119701 157.173012 \nL 128.860866 156.234497 \nL 124.963907 154.784994 \nL 121.932563 153.461838 \nL 117.309793 151.226379 \nL 112.801421 148.835606 \nL 106.037029 144.931792 \nL 99.452438 140.888822 \nL 89.430166 134.447446 \nL 75.320712 125.070426 \nL 75.320712 125.070426 \n\" style=\"fill:none;stroke:#e2e2e2;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_16\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 118.118375 110.830701 \nL 122.987675 118.279042 \nL 127.683739 125.870862 \nL 132.597794 134.249914 \nL 136.863506 141.945447 \nL 139.78729 147.683785 \nL 141.053653 150.497527 \nL 141.969942 152.994457 \nL 142.376809 154.605813 \nL 142.492465 156.135335 \nL 142.385905 156.852456 \nL 142.12133 157.522936 \nL 141.614741 158.121015 \nL 140.743505 158.609034 \nL 139.213176 158.896677 \nL 136.558133 158.713305 \nL 134.215268 158.231251 \nL 130.965836 157.266659 \nL 127.894427 156.146802 \nL 123.039682 154.063519 \nL 118.313035 151.76228 \nL 111.980142 148.341666 \nL 105.421496 144.491689 \nL 98.049553 139.912369 \nL 89.013502 134.071938 \nL 74.734256 124.577245 \nL 74.734256 124.577245 \n\" style=\"fill:none;stroke:#dfdfdf;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_17\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 120.697112 110.618615 \nL 124.934309 117.205503 \nL 129.523425 124.689717 \nL 134.64985 133.458714 \nL 139.344625 141.901415 \nL 142.344671 147.688469 \nL 144.280712 151.955878 \nL 145.151446 154.449422 \nL 145.501071 156.050332 \nL 145.521526 157.557772 \nL 145.340073 158.255479 \nL 144.972911 158.898033 \nL 144.327262 159.456949 \nL 142.795718 159.950409 \nL 141.260686 160.048291 \nL 138.712984 159.746829 \nL 136.384739 159.239962 \nL 133.12866 158.264388 \nL 129.042497 156.74198 \nL 124.188262 154.635683 \nL 118.640779 151.904245 \nL 113.319857 149.026229 \nL 106.493382 145.044205 \nL 99.086544 140.456671 \nL 87.184341 132.742021 \nL 74.161568 124.070317 \nL 74.161568 124.070317 \n\" style=\"fill:none;stroke:#dcdcdc;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_18\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 123.190452 110.37903 \nL 127.855239 117.774858 \nL 133.336243 126.910738 \nL 138.74527 136.339855 \nL 143.441538 144.940881 \nL 145.985319 149.994657 \nL 147.471866 153.407182 \nL 148.284497 155.893549 \nL 148.559821 157.556824 \nL 148.567165 158.234304 \nL 148.408591 159.076853 \nL 148.185245 159.629152 \nL 147.686768 160.234958 \nL 146.592264 160.822521 \nL 144.855061 161.110706 \nL 142.878197 161.046193 \nL 140.933821 160.737925 \nL 137.508014 159.899432 \nL 134.297419 158.867344 \nL 130.221185 157.317558 \nL 126.320148 155.627749 \nL 121.626066 153.382321 \nL 116.20868 150.544901 \nL 109.278383 146.592746 \nL 102.598086 142.529984 \nL 93.709519 136.868191 \nL 81.211558 128.640401 \nL 73.599226 123.552536 \nL 73.599226 123.552536 \n\" style=\"fill:none;stroke:#d9d9d9;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_19\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 125.610262 110.115447 \nL 130.182977 117.474217 \nL 135.728629 126.802217 \nL 141.896422 137.613716 \nL 146.609961 146.276915 \nL 149.18833 151.439444 \nL 150.634972 154.853822 \nL 151.231179 156.754864 \nL 151.50829 158.122572 \nL 151.499173 159.631542 \nL 151.298655 160.328701 \nL 150.909137 160.969687 \nL 150.244725 161.528105 \nL 149.165006 161.960788 \nL 147.356194 162.171356 \nL 145.696876 162.076751 \nL 143.20241 161.703629 \nL 139.7792 160.845853 \nL 136.545897 159.817861 \nL 132.432328 158.279405 \nL 127.076867 155.968066 \nL 121.889673 153.455455 \nL 115.596799 150.106787 \nL 108.697708 146.119222 \nL 102.035133 142.034325 \nL 92.362193 135.839366 \nL 79.126646 127.093929 \nL 73.044724 123.026014 \nL 73.044724 123.026014 \n\" style=\"fill:none;stroke:#d6d6d6;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_20\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 127.969359 109.83162 \nL 132.470357 117.168125 \nL 137.898068 126.357151 \nL 144.614028 138.146555 \nL 149.339813 146.800687 \nL 152.070653 152.226285 \nL 153.466406 155.453608 \nL 154.262444 157.95066 \nL 154.507904 159.537385 \nL 154.489007 160.290156 \nL 154.276964 161.158372 \nL 154.03719 161.674226 \nL 153.493509 162.271472 \nL 152.616875 162.771014 \nL 150.799992 163.130522 \nL 148.747127 163.117116 \nL 146.747786 162.852713 \nL 143.211266 162.083801 \nL 139.901342 161.107664 \nL 135.705055 159.618053 \nL 130.69253 157.569032 \nL 124.951608 154.905946 \nL 119.443278 152.087816 \nL 114.129028 149.154588 \nL 107.285841 145.124044 \nL 98.222697 139.46177 \nL 85.531812 131.18276 \nL 72.496193 122.492327 \nL 72.496193 122.492327 \n\" style=\"fill:none;stroke:#d3d3d3;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_21\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 130.273899 109.52938 \nL 135.804612 118.670964 \nL 142.906671 130.880521 \nL 150.098217 143.692624 \nL 153.449112 149.976207 \nL 155.558443 154.329512 \nL 156.864541 157.658911 \nL 157.171217 158.759163 \nL 157.425107 160.170667 \nL 157.385099 161.362261 \nL 157.350287 161.670198 \nL 157.100847 162.357714 \nL 156.649808 162.985179 \nL 155.913617 163.526889 \nL 154.735262 163.947828 \nL 152.884777 164.137448 \nL 150.366598 163.962544 \nL 147.898893 163.542481 \nL 144.442814 162.682545 \nL 140.094541 161.303427 \nL 135.518511 159.587789 \nL 130.970316 157.65744 \nL 126.181495 155.424023 \nL 120.641765 152.607759 \nL 114.42026 149.180112 \nL 107.206249 144.915893 \nL 98.489156 139.460192 \nL 87.336883 132.198567 \nL 71.952402 121.952511 \nL 71.952402 121.952511 \n\" style=\"fill:none;stroke:#d0d0d0;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_22\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 132.535351 109.212061 \nL 138.420564 119.025003 \nL 146.133792 132.346176 \nL 153.387395 145.278365 \nL 157.093311 152.292354 \nL 158.874285 156.11844 \nL 159.730132 158.340205 \nL 160.25207 160.398602 \nL 160.377474 161.575433 \nL 160.124194 163.027502 \nL 159.749061 163.680055 \nL 159.122103 164.257111 \nL 158.135783 164.725569 \nL 156.605224 165.028533 \nL 154.051618 165.018851 \nL 151.519424 164.670053 \nL 147.956728 163.893261 \nL 144.600105 162.927292 \nL 140.324725 161.465554 \nL 135.209668 159.452778 \nL 130.295125 157.289827 \nL 124.615387 154.545391 \nL 119.144571 151.669741 \nL 112.981484 148.194908 \nL 106.177784 144.115716 \nL 97.140458 138.414697 \nL 84.456959 130.109117 \nL 71.4127 121.40712 \nL 71.4127 121.40712 \n\" style=\"fill:none;stroke:#cdcdcd;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_23\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 161.301384 165.514591 \nL 160.106544 165.851064 \nL 157.892881 165.994981 \nL 155.211492 165.759922 \nL 152.738049 165.323949 \nL 149.241007 164.469735 \nL 144.820023 163.113573 \nL 139.55476 161.198763 \nL 134.511609 159.110418 \nL 128.689643 156.441303 \nL 123.085386 153.63029 \nL 116.784828 150.211721 \nL 109.848802 146.172234 \nL 102.06993 141.374377 \nL 91.337774 134.456527 \nL 74.673353 123.400723 \nL 70.875173 120.857745 \nL 70.875173 120.857745 \n\" style=\"fill:none;stroke:#cbcbcb;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 134.761029 108.881798 \nL 140.577531 118.632463 \nL 149.144839 133.444944 \nL 156.586608 146.695389 \nL 159.855505 152.857358 \nL 161.647236 156.637657 \nL 162.562389 158.93954 \nL 163.102678 160.875662 \nL 163.291865 162.20689 \nL 163.266299 162.964772 \nL 163.084012 163.756021 \nL 163.084012 163.756021 \n\" style=\"fill:none;stroke:#cbcbcb;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_24\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 158.985292 166.801494 \nL 157.688829 166.63562 \nL 154.007901 165.93813 \nL 150.544577 165.037317 \nL 146.139967 163.646914 \nL 140.877642 161.706301 \nL 135.814865 159.61364 \nL 129.966231 156.942085 \nL 124.328992 154.134311 \nL 117.987804 150.721232 \nL 111.462144 146.957563 \nL 104.157641 142.498119 \nL 94.462 136.301768 \nL 80.286028 126.952299 \nL 70.339235 120.304873 \nL 70.339235 120.304873 \n\" style=\"fill:none;stroke:#c8c8c8;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 136.957259 108.540431 \nL 137.044026 108.683874 \nL 137.441123 109.343705 \nL 137.512052 109.461287 \nL 137.924528 110.148436 \nL 137.980345 110.241213 \nL 138.407535 110.954644 \nL 138.448937 111.023638 \nL 138.890204 111.762353 \nL 138.917857 111.808549 \nL 139.372595 112.571583 \nL 139.387136 112.595933 \nL 139.854762 113.382354 \nL 139.856801 113.385777 \nL 140.32686 114.17809 \nL 140.336651 114.194656 \nL 140.797359 114.972841 \nL 140.818415 115.008536 \nL 141.26833 115.770017 \nL 141.300127 115.824022 \nL 141.739799 116.569607 \nL 141.781835 116.64113 \nL 142.21179 117.371602 \nL 142.263584 117.459879 \nL 142.684328 118.175992 \nL 142.745418 118.280287 \nL 143.157437 118.982769 \nL 143.22738 119.102371 \nL 143.631138 119.791927 \nL 143.709508 119.926147 \nL 144.105454 120.603458 \nL 144.191842 120.751631 \nL 144.580405 121.417357 \nL 144.674418 121.578839 \nL 145.056012 122.233618 \nL 145.157268 122.407786 \nL 145.532292 123.052238 \nL 145.640426 123.238486 \nL 146.009263 123.873212 \nL 146.12392 124.070954 \nL 146.486943 124.69654 \nL 146.607779 124.905203 \nL 146.965347 125.522218 \nL 147.092028 125.741244 \nL 147.44449 126.350248 \nL 147.57669 126.579092 \nL 147.924384 127.180629 \nL 148.061785 127.418756 \nL 148.405041 128.013364 \nL 148.547331 128.260247 \nL 148.886472 128.848458 \nL 149.033342 129.103576 \nL 149.368685 129.685913 \nL 149.51983 129.948752 \nL 149.851687 130.525738 \nL 150.006803 130.795781 \nL 150.335483 131.367941 \nL 150.494265 131.644672 \nL 150.820077 132.212532 \nL 150.982216 132.495429 \nL 151.305468 133.059524 \nL 151.470652 133.348057 \nL 151.791654 133.908934 \nL 151.959561 134.202559 \nL 152.27863 134.76078 \nL 152.448927 135.058936 \nL 152.766385 135.615084 \nL 152.938726 135.917185 \nL 153.254907 136.471873 \nL 153.428926 136.777305 \nL 153.744177 137.331178 \nL 153.919486 137.639287 \nL 154.234171 138.193036 \nL 154.410353 138.503122 \nL 154.724857 139.057492 \nL 154.90146 139.368796 \nL 155.216196 139.924596 \nL 155.392727 140.236291 \nL 155.70814 140.794411 \nL 155.884052 141.105583 \nL 156.200627 141.667009 \nL 156.375316 141.976642 \nL 156.693584 142.542476 \nL 156.866371 142.849429 \nL 157.18692 143.420916 \nL 157.357039 143.723896 \nL 157.680523 144.30245 \nL 157.847106 144.599986 \nL 158.174259 145.187227 \nL 158.336314 145.477627 \nL 158.667961 146.075422 \nL 158.82435 146.35673 \nL 159.161427 146.967251 \nL 159.310841 147.237188 \nL 159.65441 147.862972 \nL 159.795335 148.118871 \nL 160.146604 148.762901 \nL 160.277287 149.00162 \nL 160.637633 149.667425 \nL 160.75604 149.885243 \nL 161.127032 150.57702 \nL 161.230803 150.769503 \nL 161.614221 151.492277 \nL 161.700615 151.654116 \nL 162.098475 152.413933 \nL 162.164316 152.538735 \nL 162.578877 153.342915 \nL 162.620499 153.422937 \nL 163.054262 154.280401 \nL 163.067457 154.306208 \nL 163.502808 155.187828 \nL 163.522143 155.228866 \nL 163.923927 156.067002 \nL 163.980015 156.190824 \nL 164.32783 156.942821 \nL 164.4253 157.168879 \nL 164.710648 157.814108 \nL 164.853707 158.167335 \nL 165.067651 158.679418 \nL 165.259215 159.192235 \nL 165.393059 159.536986 \nL 165.633168 160.25226 \n\" style=\"fill:none;stroke:#c8c8c8;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_25\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 157.699106 167.067853 \nL 154.157446 166.222998 \nL 149.662402 164.89141 \nL 144.296645 163.012584 \nL 139.145543 160.965273 \nL 133.191935 158.345165 \nL 127.454184 155.582824 \nL 121.909486 152.703961 \nL 115.657102 149.228155 \nL 108.723905 145.125583 \nL 99.601551 139.421855 \nL 88.35671 132.103902 \nL 69.804409 119.7489 \nL 69.804409 119.7489 \n\" style=\"fill:none;stroke:#c5c5c5;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 139.129592 108.189569 \nL 139.16012 108.240257 \nL 139.610771 108.991848 \nL 139.628163 109.020794 \nL 140.091736 109.795652 \nL 140.096595 109.803757 \nL 140.56543 110.589148 \nL 140.572465 110.60098 \nL 141.034703 111.37695 \nL 141.053049 111.407861 \nL 141.504451 112.167141 \nL 141.533592 112.216331 \nL 141.9747 112.959711 \nL 142.014142 113.026407 \nL 142.445476 113.754651 \nL 142.494747 113.838109 \nL 142.916804 114.551949 \nL 142.975452 114.651454 \nL 143.388707 115.351599 \nL 143.456301 115.466459 \nL 143.86121 116.153591 \nL 143.937334 116.283141 \nL 144.334335 116.957917 \nL 144.418592 117.101517 \nL 144.808104 117.764571 \nL 144.900113 117.921602 \nL 145.282538 118.573546 \nL 145.381933 118.743413 \nL 145.757657 119.384837 \nL 145.864089 119.566965 \nL 146.23348 120.198438 \nL 146.346611 120.392272 \nL 146.710026 121.014345 \nL 146.829533 121.219348 \nL 147.187313 121.832555 \nL 147.312883 122.048209 \nL 147.665358 122.653065 \nL 147.796689 122.878866 \nL 148.144177 123.475873 \nL 148.280977 123.711333 \nL 148.623785 124.300977 \nL 148.765772 124.545623 \nL 149.104196 125.128378 \nL 149.251095 125.381747 \nL 149.585422 125.958076 \nL 149.736967 126.219717 \nL 150.067477 126.790072 \nL 150.223406 127.059544 \nL 150.550371 127.62437 \nL 150.710427 127.901237 \nL 151.034114 128.460974 \nL 151.198043 128.744806 \nL 151.518713 129.299888 \nL 151.686266 129.590261 \nL 152.004177 130.141118 \nL 152.175103 130.437609 \nL 152.490509 130.984674 \nL 152.664559 131.286857 \nL 152.977715 131.830564 \nL 153.154635 132.138011 \nL 153.465794 132.678801 \nL 153.645327 132.991077 \nL 153.954747 133.529398 \nL 154.13663 133.846058 \nL 154.444569 134.382373 \nL 154.628529 134.702956 \nL 154.935255 135.237743 \nL 155.121007 135.561771 \nL 155.426794 136.095533 \nL 155.614039 136.422503 \nL 155.919173 136.955768 \nL 156.107591 137.285147 \nL 156.412374 137.81848 \nL 156.601623 138.149697 \nL 156.906371 138.683707 \nL 157.09608 139.016144 \nL 157.401136 139.55149 \nL 157.590899 139.884473 \nL 157.896629 140.421881 \nL 158.085998 140.754666 \nL 158.392803 141.294941 \nL 158.581281 141.626702 \nL 158.889599 142.170738 \nL 159.076628 142.50055 \nL 159.386947 143.049359 \nL 159.571896 143.376173 \nL 159.884758 143.930902 \nL 160.066912 144.253526 \nL 160.382926 144.815486 \nL 160.561468 145.132552 \nL 160.881321 145.703255 \nL 161.055311 146.01318 \nL 161.379783 146.594379 \nL 161.54814 146.895327 \nL 161.878118 147.489065 \nL 162.03959 147.778888 \nL 162.376088 148.387563 \nL 162.529221 148.663737 \nL 162.8734 149.290179 \nL 163.016504 149.549719 \nL 163.369695 150.197285 \nL 163.5008 150.436648 \nL 163.864525 151.109341 \nL 163.981338 151.324294 \nL 164.357335 152.026915 \nL 164.457183 152.21238 \nL 164.847432 152.950717 \nL 164.927207 153.10057 \nL 165.333938 153.881637 \nL 165.390039 153.988453 \nL 165.815744 154.820805 \nL 165.844019 154.875527 \nL 166.287068 155.761167 \nL 166.291224 155.769861 \nL 166.71624 156.644479 \nL 166.756739 156.732437 \nL 167.128814 157.524637 \nL 167.210444 157.710428 \n\" style=\"fill:none;stroke:#c5c5c5;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_26\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 156.652365 167.09442 \nL 152.119927 165.775546 \nL 146.708909 163.910009 \nL 141.504376 161.882876 \nL 135.48637 159.286138 \nL 129.682241 156.548004 \nL 123.155057 153.205092 \nL 116.389877 149.46655 \nL 109.915571 145.655013 \nL 101.532669 140.453481 \nL 90.207324 133.119932 \nL 72.310731 121.225722 \nL 69.270304 119.19015 \nL 69.270304 119.19015 \n\" style=\"fill:none;stroke:#c2c2c2;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 141.282689 107.830561 \nL 141.737089 108.590275 \nL 141.761999 108.63207 \nL 142.206084 109.375941 \nL 142.241323 109.435169 \nL 142.675607 110.163946 \nL 142.720707 110.239875 \nL 143.145683 110.954277 \nL 143.200197 111.046206 \nL 143.616336 111.746927 \nL 143.679838 111.854179 \nL 144.087589 112.541887 \nL 144.159673 112.663812 \nL 144.559466 113.339148 \nL 144.639741 113.475122 \nL 145.03199 114.138703 \nL 145.120082 114.288124 \nL 145.505182 114.940544 \nL 145.600735 115.102834 \nL 145.979062 115.744665 \nL 146.081735 115.919268 \nL 146.453652 116.551061 \nL 146.563116 116.737441 \nL 146.92897 117.359726 \nL 147.044913 117.557368 \nL 147.405035 118.170656 \nL 147.527157 118.379063 \nL 147.881866 118.983846 \nL 148.009877 119.202539 \nL 148.35948 119.799293 \nL 148.493103 120.027812 \nL 148.837893 120.616995 \nL 148.976862 120.854893 \nL 149.317121 121.436949 \nL 149.461179 121.683796 \nL 149.79718 122.259153 \nL 149.946078 122.514533 \nL 150.278083 123.083608 \nL 150.431583 123.347117 \nL 150.759845 123.910313 \nL 150.917714 124.181558 \nL 151.242477 124.739269 \nL 151.40449 125.017868 \nL 151.725993 125.570478 \nL 151.891929 125.856059 \nL 152.210402 126.403941 \nL 152.380048 126.69614 \nL 152.695715 127.239662 \nL 152.868859 127.53812 \nL 153.181941 128.077646 \nL 153.358376 128.38201 \nL 153.669087 128.917898 \nL 153.848608 129.227818 \nL 154.157161 129.760424 \nL 154.339562 130.075552 \nL 154.646168 130.605232 \nL 154.831243 130.92522 \nL 155.136111 131.452331 \nL 155.323654 131.776827 \nL 155.626994 132.301732 \nL 155.816792 132.630379 \nL 156.118815 133.153448 \nL 156.310653 133.485881 \nL 156.611575 134.007493 \nL 156.805228 134.343336 \nL 157.105267 134.863884 \nL 157.300503 135.202746 \nL 157.599887 135.722642 \nL 157.796458 136.064112 \nL 158.095422 136.583789 \nL 158.293068 136.927431 \nL 158.59186 137.447351 \nL 158.790299 137.792699 \nL 159.089182 138.313362 \nL 159.28811 138.659912 \nL 159.587364 139.181856 \nL 159.786448 139.529058 \nL 160.086377 140.052876 \nL 160.285248 140.400125 \nL 160.586183 140.926472 \nL 160.784433 141.273096 \nL 161.086737 141.802703 \nL 161.283906 142.147948 \nL 161.587982 142.681637 \nL 161.783552 143.024654 \nL 162.089849 143.563358 \nL 162.283231 143.903176 \nL 162.592253 144.447961 \nL 162.782775 144.783471 \nL 163.095091 145.335563 \nL 163.281979 145.665484 \nL 163.598239 146.226302 \nL 163.7806 146.549147 \nL 164.101542 147.120345 \nL 164.278342 147.434379 \nL 164.604813 148.017891 \nL 164.77485 148.321077 \nL 165.107823 148.919183 \nL 165.269696 149.209118 \nL 165.61029 149.824517 \nL 165.762365 150.098354 \nL 166.111868 150.734254 \nL 166.252232 150.988601 \nL 166.612126 151.648839 \nL 166.738545 151.879638 \nL 167.110532 152.568821 \nL 167.220394 152.771193 \nL 167.606417 153.494885 \nL 167.696677 153.662939 \nL 168.098942 154.427891 \nL 168.166057 154.554476 \nL 168.587041 155.368927 \n\" style=\"fill:none;stroke:#c2c2c2;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_27\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 155.734779 166.990364 \nL 151.305222 165.562992 \nL 145.96994 163.615518 \nL 139.811728 161.095204 \nL 133.60488 158.296764 \nL 127.199144 155.149703 \nL 120.766023 151.737711 \nL 113.678591 147.70533 \nL 105.963733 143.035914 \nL 96.101242 136.763575 \nL 82.585358 127.875352 \nL 68.736888 118.628646 \nL 68.736888 118.628646 \n\" style=\"fill:none;stroke:#bfbfbf;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 143.420668 107.464593 \nL 143.840903 108.167974 \nL 143.899051 108.265595 \nL 144.31088 108.956011 \nL 144.377629 109.068237 \nL 144.78148 109.746318 \nL 144.856445 109.872536 \nL 145.252726 110.538889 \nL 145.335538 110.678509 \nL 145.724639 111.333716 \nL 145.814947 111.486172 \nL 146.197241 112.130792 \nL 146.294708 112.295539 \nL 146.670552 112.930112 \nL 146.774857 113.106627 \nL 147.144593 113.731668 \nL 147.255428 113.91945 \nL 147.619381 114.535456 \nL 147.736453 114.734023 \nL 148.094937 115.341471 \nL 148.217964 115.550359 \nL 148.571278 116.14971 \nL 148.699991 116.368474 \nL 149.048421 116.960169 \nL 149.182562 117.188379 \nL 149.526383 117.772844 \nL 149.665705 118.010089 \nL 150.005181 118.587733 \nL 150.149445 118.833616 \nL 150.484828 119.404835 \nL 150.633808 119.658974 \nL 150.965342 120.224148 \nL 151.118818 120.486173 \nL 151.446734 121.045671 \nL 151.604495 121.315227 \nL 151.92902 121.869405 \nL 152.090862 122.146146 \nL 152.412211 122.695349 \nL 152.577937 122.978943 \nL 152.89632 123.523505 \nL 153.06574 123.813628 \nL 153.381359 124.353875 \nL 153.554287 124.650211 \nL 153.867337 125.18646 \nL 154.043594 125.488704 \nL 154.354266 126.021265 \nL 154.533675 126.329116 \nL 154.842155 126.858292 \nL 155.024542 127.171455 \nL 155.331011 127.697547 \nL 155.516207 128.015732 \nL 155.820842 128.539035 \nL 156.008677 128.861955 \nL 156.311655 129.382762 \nL 156.501961 129.710132 \nL 156.803455 130.228737 \nL 156.996064 130.56027 \nL 157.296246 131.076969 \nL 157.490987 131.412377 \nL 157.790031 131.927466 \nL 157.986731 132.266457 \nL 158.284812 132.780241 \nL 158.483293 133.122516 \nL 158.780587 133.635307 \nL 158.980666 133.980558 \nL 159.277355 134.49268 \nL 159.47884 134.840587 \nL 159.775111 135.352376 \nL 159.9778 135.702603 \nL 160.273848 136.214417 \nL 160.477526 136.566608 \nL 160.773554 137.078824 \nL 160.977991 137.4326 \nL 161.274218 137.945626 \nL 161.479162 138.300574 \nL 161.775819 138.814853 \nL 161.980998 139.170525 \nL 162.278336 139.686541 \nL 162.483447 140.042444 \nL 162.781738 140.560732 \nL 162.986446 140.916317 \nL 163.285991 141.437474 \nL 163.489918 141.79213 \nL 163.791049 142.316826 \nL 163.993769 142.669858 \nL 164.296857 143.198855 \nL 164.497887 143.549477 \nL 164.80335 144.083641 \nL 165.002135 144.430949 \nL 165.310445 144.971279 \nL 165.506348 145.314234 \nL 165.818042 145.86188 \nL 166.010329 146.199276 \nL 166.326021 146.755581 \nL 166.513837 147.086012 \nL 166.834233 147.652543 \nL 167.016587 147.97436 \nL 167.342498 148.55296 \nL 167.518231 148.864223 \nL 167.850593 149.45707 \nL 168.018351 149.75548 \nL 168.358247 150.365158 \nL 168.516443 150.647985 \nL 168.865125 151.277576 \nL 169.011899 151.541561 \nL 169.370811 152.194755 \nL 169.503983 152.435991 \nL 169.874792 153.117228 \n\" style=\"fill:none;stroke:#bfbfbf;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_28\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 154.888735 166.812647 \nL 149.466991 164.910619 \nL 143.204208 162.443399 \nL 137.169038 159.816988 \nL 130.38077 156.591512 \nL 123.838784 153.222699 \nL 117.521796 149.735475 \nL 110.544834 145.640549 \nL 102.124028 140.420733 \nL 91.547456 133.586808 \nL 74.309266 122.150716 \nL 68.203532 118.064905 \nL 68.203532 118.064905 \n\" style=\"fill:none;stroke:#bcbcbc;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 145.547305 107.092749 \nL 145.941382 107.752384 \nL 146.025428 107.893427 \nL 146.412684 108.542519 \nL 146.503905 108.695789 \nL 146.884694 109.334867 \nL 146.982771 109.499852 \nL 147.357432 110.129423 \nL 147.46206 110.305631 \nL 147.830915 110.926182 \nL 147.941806 111.113139 \nL 148.305165 111.725139 \nL 148.422041 111.922392 \nL 148.780198 112.526289 \nL 148.902794 112.733402 \nL 149.256032 113.329627 \nL 149.384096 113.546184 \nL 149.732685 114.135152 \nL 149.865974 114.360752 \nL 150.210173 114.94286 \nL 150.348456 115.177117 \nL 150.688512 115.752747 \nL 150.831568 115.995293 \nL 151.167717 116.564814 \nL 151.315333 116.815292 \nL 151.647803 117.379057 \nL 151.799776 117.637127 \nL 152.128784 118.195475 \nL 152.284919 118.46081 \nL 152.610675 119.01407 \nL 152.770784 119.286351 \nL 153.093488 119.834839 \nL 153.257391 120.113764 \nL 153.577235 120.657785 \nL 153.744759 120.943058 \nL 154.061929 121.482907 \nL 154.232907 121.774246 \nL 154.547582 122.310207 \nL 154.721851 122.607336 \nL 155.034204 123.139688 \nL 155.211609 123.442341 \nL 155.521806 123.971352 \nL 155.702193 124.27927 \nL 156.010398 124.805202 \nL 156.193619 125.118132 \nL 156.499988 125.641243 \nL 156.685899 125.958938 \nL 156.990585 126.479477 \nL 157.179044 126.801696 \nL 157.482197 127.319911 \nL 157.673064 127.646415 \nL 157.974831 128.16255 \nL 158.167968 128.493104 \nL 158.468493 129.007401 \nL 158.663761 129.341771 \nL 158.963189 129.854472 \nL 159.16045 130.192423 \nL 159.458922 130.70377 \nL 159.658036 131.045066 \nL 159.955697 131.555307 \nL 160.156522 131.899708 \nL 160.453515 132.409091 \nL 160.655905 132.756354 \nL 160.952376 133.265136 \nL 161.156181 133.615009 \nL 161.45228 134.123456 \nL 161.657342 134.475677 \nL 161.953224 134.984066 \nL 162.159377 135.33836 \nL 162.455204 135.846984 \nL 162.662271 136.203061 \nL 162.95821 136.71223 \nL 163.166004 137.069779 \nL 163.462234 137.579828 \nL 163.670548 137.938513 \nL 163.967261 138.449804 \nL 164.175871 138.809259 \nL 164.473274 139.32219 \nL 164.681931 139.682012 \nL 164.980249 140.197019 \nL 165.188678 140.556763 \nL 165.48816 141.074335 \nL 165.69605 141.4335 \nL 165.99697 141.954185 \nL 166.203972 142.312206 \nL 166.506637 142.836624 \nL 166.712353 143.192861 \nL 167.017107 143.721721 \nL 167.221081 144.075438 \nL 167.528316 144.609552 \nL 167.730025 144.959903 \nL 168.040185 145.50021 \nL 168.239022 145.846216 \nL 168.552617 146.393805 \nL 168.747881 146.734324 \nL 169.065495 147.290469 \nL 169.256366 147.624163 \nL 169.578675 148.19036 \nL 169.764198 148.515656 \nL 170.091983 149.093667 \nL 170.271038 149.408706 \nL 170.605203 150.000621 \nL 170.776477 150.303197 \nL 171.118072 150.911501 \n\" style=\"fill:none;stroke:#bcbcbc;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_29\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 154.098972 166.576486 \nL 148.743899 164.601049 \nL 142.537219 162.070848 \nL 135.562571 158.940403 \nL 128.841581 155.655985 \nL 122.356701 152.239752 \nL 115.206911 148.205623 \nL 107.452442 143.54839 \nL 98.303155 137.770087 \nL 85.457349 129.361951 \nL 67.669969 117.499143 \nL 67.669969 117.499143 \n\" style=\"fill:none;stroke:#b9b9b9;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 147.665481 106.715853 \nL 148.04002 107.342237 \nL 148.143915 107.516363 \nL 148.512948 108.134233 \nL 148.622837 108.318596 \nL 148.986656 108.928395 \nL 149.102277 109.122566 \nL 149.461162 109.724718 \nL 149.582265 109.928288 \nL 149.936485 110.523199 \nL 150.062831 110.735774 \nL 150.412639 111.323833 \nL 150.544 111.545038 \nL 150.889642 112.126619 \nL 151.025801 112.356092 \nL 151.367509 112.931554 \nL 151.508257 113.168949 \nL 151.846255 113.738636 \nL 151.991393 113.983621 \nL 152.325895 114.547864 \nL 152.475232 114.80012 \nL 152.806442 115.359237 \nL 152.959798 115.618459 \nL 153.287912 116.172753 \nL 153.44511 116.438648 \nL 153.770316 116.988414 \nL 153.93119 117.260699 \nL 154.253667 117.806219 \nL 154.418057 118.084624 \nL 154.737978 118.626169 \nL 154.905729 118.910433 \nL 155.22326 119.448265 \nL 155.394225 119.738137 \nL 155.709525 120.272508 \nL 155.883561 120.567747 \nL 156.196784 121.098901 \nL 156.373752 121.399273 \nL 156.685046 121.927447 \nL 156.864815 122.232725 \nL 157.174322 122.758147 \nL 157.356763 123.068113 \nL 157.664621 123.591006 \nL 157.849609 123.905446 \nL 158.155952 124.426027 \nL 158.343365 124.744734 \nL 158.648324 125.263215 \nL 158.838043 125.585987 \nL 159.141744 126.102574 \nL 159.333653 126.429213 \nL 159.636219 126.94411 \nL 159.830204 127.27442 \nL 160.131757 127.78783 \nL 160.327703 128.121617 \nL 160.628363 128.633739 \nL 160.826157 128.970812 \nL 161.126043 129.481846 \nL 161.32557 129.822013 \nL 161.6248 130.332158 \nL 161.825948 130.675226 \nL 162.12464 131.184685 \nL 162.32729 131.530459 \nL 162.625563 132.039437 \nL 162.829597 132.387717 \nL 163.127572 132.896426 \nL 163.332865 133.247005 \nL 163.630667 133.755664 \nL 163.837091 134.108329 \nL 164.134846 134.617166 \nL 164.342264 134.971691 \nL 164.640106 135.480947 \nL 164.848374 135.837096 \nL 165.146442 136.347025 \nL 165.355405 136.704545 \nL 165.653847 137.215422 \nL 165.863336 137.574037 \nL 166.16231 138.086159 \nL 166.372141 138.445572 \nL 166.671817 138.959265 \nL 166.881786 139.319146 \nL 167.182353 139.834768 \nL 167.392233 140.194753 \nL 167.693893 140.712705 \nL 167.903431 141.072386 \nL 168.206412 141.593115 \nL 168.415319 141.952033 \nL 168.719874 142.476047 \nL 168.927824 142.833677 \nL 169.234239 143.361555 \nL 169.440857 143.7173 \nL 169.749454 144.249705 \nL 169.954309 144.602874 \nL 170.265458 145.140572 \nL 170.468052 145.490369 \nL 170.782172 146.034247 \nL 170.981927 146.379743 \nL 171.299505 146.930839 \nL 171.495746 147.270946 \nL 171.817341 147.830476 \nL 172.00928 148.163915 \nL 172.335542 148.733311 \n\" style=\"fill:none;stroke:#b9b9b9;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_30\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 33.251277 80.095035 \nL 32.472376 79.583116 \n\" style=\"fill:none;stroke:#020202;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_31\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 153.348447 166.298757 \nL 147.006052 163.842072 \nL 140.881461 161.234447 \nL 133.981502 158.036492 \nL 127.32258 154.698735 \nL 119.987748 150.738059 \nL 112.891849 146.63959 \nL 104.394521 141.435575 \nL 94.471067 135.07592 \nL 78.66129 124.634076 \nL 67.136049 116.931477 \nL 67.136049 116.931477 \n\" style=\"fill:none;stroke:#b6b6b6;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 149.777616 106.334595 \nL 150.138094 106.93645 \nL 150.256843 107.135068 \nL 150.612904 107.730107 \nL 150.736672 107.937297 \nL 151.088558 108.525888 \nL 151.21713 108.741295 \nL 151.565073 109.323791 \nL 151.698242 109.547076 \nL 152.042463 110.123813 \nL 152.180033 110.35465 \nL 152.520743 110.925954 \nL 152.662526 111.16403 \nL 152.999928 111.730211 \nL 153.145745 111.975229 \nL 153.480031 112.536584 \nL 153.629711 112.788257 \nL 153.961065 113.345072 \nL 154.114444 113.603126 \nL 154.443045 114.155676 \nL 154.599966 114.419847 \nL 154.925981 114.968395 \nL 155.086295 115.238432 \nL 155.409887 115.78323 \nL 155.573451 116.058891 \nL 155.894774 116.600182 \nL 156.06145 116.881235 \nL 156.380654 117.419253 \nL 156.550309 117.705474 \nL 156.867536 118.240444 \nL 157.040045 118.531619 \nL 157.355433 119.063757 \nL 157.530673 119.35968 \nL 157.844353 119.889196 \nL 158.022209 120.189667 \nL 158.334308 120.716762 \nL 158.514665 121.02159 \nL 158.825305 121.546459 \nL 159.008055 121.855458 \nL 159.317355 122.378291 \nL 159.502392 122.691281 \nL 159.810465 123.212262 \nL 159.997687 123.529069 \nL 160.304645 124.048376 \nL 160.493951 124.36883 \nL 160.799901 124.886638 \nL 160.991194 125.210573 \nL 161.296242 125.727054 \nL 161.489426 126.054306 \nL 161.793673 126.569629 \nL 161.988654 126.900039 \nL 162.292201 127.414369 \nL 162.488887 127.74778 \nL 162.791833 128.261282 \nL 162.990129 128.597536 \nL 163.292573 129.110375 \nL 163.492386 129.449315 \nL 163.794425 129.961656 \nL 163.995662 130.303125 \nL 164.297395 130.815134 \nL 164.499959 131.158971 \nL 164.801483 131.67082 \nL 165.005278 132.016861 \nL 165.306694 132.528722 \nL 165.511617 132.8768 \nL 165.813027 133.388855 \nL 166.018973 133.738795 \nL 166.320483 134.251229 \nL 166.527339 134.602848 \nL 166.829059 135.115861 \nL 167.036708 135.468964 \nL 167.338754 135.982766 \nL 167.547067 136.337147 \nL 167.84956 136.851963 \nL 168.0584 137.207397 \nL 168.361472 137.723471 \nL 168.570687 138.079715 \nL 168.874478 138.597314 \nL 169.083902 138.954099 \nL 169.388567 139.473518 \nL 169.598012 139.830547 \nL 169.90372 140.352114 \nL 170.112978 140.709054 \nL 170.419916 141.233136 \nL 170.628752 141.589611 \nL 170.937129 142.116624 \nL 171.145274 142.472207 \nL 171.455326 143.002625 \nL 171.662472 143.356828 \nL 171.974467 143.891192 \nL 172.180259 144.243454 \nL 172.4945 144.78239 \nL 172.698529 145.13206 \nL 173.015366 145.676294 \nL 173.217157 146.022614 \nL 173.53699 146.572991 \n\" style=\"fill:none;stroke:#b6b6b6;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_32\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 35.415945 81.774515 \nL 34.650339 81.27115 \nL 33.864477 80.754461 \nL 33.450212 80.482087 \nL 33.079874 80.238594 \n\" style=\"fill:none;stroke:#050505;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_33\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 37.582532 83.455428 \nL 36.830212 82.96062 \nL 36.042257 82.442367 \nL 35.611541 82.159073 \nL 35.255566 81.924938 \nL 34.470134 81.408331 \nL 33.685958 80.892545 \n\" style=\"fill:none;stroke:#080808;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_34\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 39.751066 85.137783 \nL 39.012003 84.651523 \nL 38.221949 84.131706 \nL 37.774783 83.837487 \nL 37.433164 83.612714 \nL 36.645643 83.094547 \nL 35.859384 82.577202 \nL 35.806514 82.542414 \nL 35.074383 82.060678 \nL 34.290636 81.544974 \n\" style=\"fill:none;stroke:#0b0b0b;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_35\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 41.921581 86.82159 \nL 41.195722 86.343855 \nL 40.403563 85.822474 \nL 39.939967 85.517338 \nL 39.612678 85.301919 \nL 38.823062 84.782191 \nL 38.034713 84.263288 \nL 37.966421 84.218336 \nL 37.247627 83.745207 \nL 36.461799 83.227948 \nL 36.000878 82.924548 \nL 35.677228 82.711508 \nL 34.89391 82.195886 \n\" style=\"fill:none;stroke:#0e0e0e;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_36\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 152.626573 165.98994 \nL 146.336839 163.47297 \nL 139.255509 160.365949 \nL 132.42174 157.109347 \nL 125.81999 153.723459 \nL 118.538569 149.720869 \nL 111.512429 145.605482 \nL 103.028777 140.362973 \nL 92.245443 133.407959 \nL 75.029414 121.99814 \nL 66.601646 116.362006 \nL 66.601646 116.362006 \n\" style=\"fill:none;stroke:#b3b3b3;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 151.885735 105.949548 \nL 152.236683 106.534107 \nL 152.366162 106.750094 \nL 152.713596 107.329252 \nL 152.847287 107.552425 \nL 153.191409 108.126488 \nL 153.329135 108.356552 \nL 153.670135 108.925813 \nL 153.811727 109.162487 \nL 154.149789 109.727226 \nL 154.295085 109.970241 \nL 154.630383 110.530728 \nL 154.779228 110.779827 \nL 155.11193 111.336317 \nL 155.264178 111.591253 \nL 155.594443 112.143995 \nL 155.749951 112.404532 \nL 156.077932 112.953763 \nL 156.236567 113.219675 \nL 156.562411 113.765621 \nL 156.724044 114.036691 \nL 157.047889 114.57957 \nL 157.212397 114.855591 \nL 157.534378 115.395613 \nL 157.701643 115.676386 \nL 158.021889 116.213751 \nL 158.191797 116.499085 \nL 158.51043 117.033987 \nL 158.682874 117.323699 \nL 159.000013 117.856324 \nL 159.174889 118.150237 \nL 159.490647 118.680764 \nL 159.667855 118.978709 \nL 159.982341 119.507312 \nL 160.161784 119.809124 \nL 160.475104 120.335969 \nL 160.656689 120.641492 \nL 160.968944 121.166741 \nL 161.152583 121.475823 \nL 161.46387 121.999632 \nL 161.649475 122.312125 \nL 161.959889 122.834646 \nL 162.147377 123.150407 \nL 162.45701 123.671788 \nL 162.646298 123.990678 \nL 162.955239 124.511064 \nL 163.146247 124.832948 \nL 163.454583 125.352479 \nL 163.647234 125.677223 \nL 163.955049 126.19604 \nL 164.149264 126.523513 \nL 164.456643 127.041753 \nL 164.652346 127.371826 \nL 164.959371 127.889625 \nL 165.156485 128.22217 \nL 165.463237 128.739663 \nL 165.661686 129.074551 \nL 165.968246 129.591876 \nL 166.167953 129.928979 \nL 166.474402 130.446273 \nL 166.675289 130.785459 \nL 166.981709 131.302862 \nL 167.183695 131.643998 \nL 167.490169 132.161654 \nL 167.693172 132.504604 \nL 167.999784 133.022661 \nL 168.203716 133.36728 \nL 168.510555 133.885893 \nL 168.715324 134.232033 \nL 169.022481 134.751365 \nL 169.22799 135.098868 \nL 169.53556 135.619092 \nL 169.741706 135.967787 \nL 170.049789 136.489089 \nL 170.256458 136.838794 \nL 170.565164 137.361375 \nL 170.772231 137.711891 \nL 171.081676 138.23597 \nL 171.289004 138.587078 \nL 171.599316 139.112897 \nL 171.806753 139.464354 \nL 172.118071 139.992182 \nL 172.325445 140.343717 \nL 172.637925 140.873856 \nL 172.845043 141.225161 \nL 173.158857 141.757952 \nL 173.365497 142.108678 \nL 173.680841 142.644509 \nL 173.886751 142.994259 \nL 174.203844 143.533574 \nL 174.408735 143.881889 \nL 174.727829 144.4252 \n\" style=\"fill:none;stroke:#b3b3b3;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_37\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 44.094118 88.506862 \nL 43.381381 88.037611 \nL 42.58711 87.514665 \nL 42.107126 87.198637 \nL 41.794118 86.992549 \nL 41.002401 86.47126 \nL 40.211955 85.950798 \nL 40.128264 85.895691 \nL 39.422777 85.43116 \nL 38.634864 84.912345 \nL 38.157461 84.597986 \nL 37.848212 84.394353 \nL 37.062817 83.87718 \nL 36.278676 83.360826 \nL 36.194626 83.305479 \nL 35.495786 82.845288 \n\" style=\"fill:none;stroke:#111111;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_38\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 46.268729 90.193617 \nL 45.568994 89.732782 \nL 44.772602 89.208274 \nL 44.276303 88.881398 \nL 43.977495 88.684596 \nL 43.183669 88.161748 \nL 42.39112 87.639727 \nL 42.292078 87.57449 \nL 41.599845 87.118533 \nL 40.809839 86.598163 \nL 40.315975 86.272853 \nL 40.021099 86.078617 \nL 39.233622 85.559893 \nL 38.447404 85.041989 \nL 38.347896 84.976439 \nL 37.662441 84.524904 \nL 36.87873 84.008636 \nL 36.387771 83.685213 \nL 36.096268 83.493184 \n\" style=\"fill:none;stroke:#141414;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_39\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 48.445473 91.881872 \nL 47.758577 91.42936 \nL 46.960055 90.903291 \nL 46.447547 90.565636 \nL 46.162825 90.378054 \nL 45.366882 89.853647 \nL 44.572222 89.33007 \nL 44.457904 89.254747 \nL 43.778841 88.807319 \nL 42.986736 88.285396 \nL 42.476455 87.94916 \nL 42.195901 87.764297 \nL 41.406336 87.244021 \nL 40.618033 86.724568 \nL 40.503091 86.648825 \nL 39.830992 86.205935 \nL 39.045208 85.688122 \nL 38.537737 85.353704 \nL 38.260677 85.171125 \nL 37.477397 84.654945 \nL 36.695363 84.139579 \n\" style=\"fill:none;stroke:#171717;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_40\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 151.927992 165.655372 \nL 145.683417 163.085773 \nL 138.640456 159.932872 \nL 131.834637 156.64175 \nL 125.253954 153.228965 \nL 117.98987 149.203027 \nL 110.054344 144.511917 \nL 101.66787 139.284243 \nL 90.243906 131.878774 \nL 70.647296 118.855805 \nL 66.066766 115.790721 \nL 66.066766 115.790721 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 153.991525 105.561188 \nL 154.336696 106.134435 \nL 154.473492 106.3619 \nL 154.815901 106.930925 \nL 154.956242 107.164419 \nL 155.296053 107.729476 \nL 155.439792 107.968759 \nL 155.777166 108.53009 \nL 155.924164 108.774929 \nL 156.25925 109.332767 \nL 156.409375 109.58294 \nL 156.742318 110.137508 \nL 156.895442 110.392803 \nL 157.226382 110.944314 \nL 157.382384 111.204527 \nL 157.711451 111.753186 \nL 157.870215 112.018124 \nL 158.197537 112.564126 \nL 158.358953 112.833603 \nL 158.68465 113.377137 \nL 158.848611 113.650974 \nL 159.1728 114.192221 \nL 159.339206 114.470248 \nL 159.661997 115.009379 \nL 159.83075 115.291433 \nL 160.15225 115.828616 \nL 160.323258 116.114539 \nL 160.643568 116.649935 \nL 160.816743 116.939577 \nL 161.135961 117.473338 \nL 161.311216 117.766554 \nL 161.629437 118.29883 \nL 161.806691 118.595482 \nL 162.124005 119.126414 \nL 162.303178 119.426368 \nL 162.619672 119.956095 \nL 162.800688 120.259222 \nL 163.116446 120.787878 \nL 163.299232 121.094052 \nL 163.614335 121.621767 \nL 163.79882 121.930869 \nL 164.113347 122.457767 \nL 164.299462 122.769679 \nL 164.613489 123.295885 \nL 164.801166 123.610493 \nL 165.114766 124.136124 \nL 165.30394 124.453318 \nL 165.617187 124.978493 \nL 165.807793 125.298163 \nL 166.120756 125.822996 \nL 166.312731 126.145036 \nL 166.62548 126.669641 \nL 166.818761 126.993945 \nL 167.131365 127.518434 \nL 167.325889 127.844898 \nL 167.638414 128.369384 \nL 167.834119 128.697903 \nL 168.146634 129.222499 \nL 168.343457 129.552966 \nL 168.656028 130.077786 \nL 168.853904 130.410096 \nL 169.166599 130.935256 \nL 169.365463 131.2693 \nL 169.678352 131.794918 \nL 169.878135 132.130583 \nL 170.191287 132.656781 \nL 170.391919 132.993952 \nL 170.705408 133.520859 \nL 170.906812 133.859412 \nL 171.220713 134.387163 \nL 171.422811 134.72697 \nL 171.737203 135.255707 \nL 171.939909 135.596629 \nL 172.254876 136.126505 \nL 172.458097 136.468394 \nL 172.773729 136.999574 \nL 172.977363 137.342267 \nL 173.293756 137.874932 \nL 173.497691 138.21825 \nL 173.814951 138.752599 \nL 174.019061 139.096343 \nL 174.337304 139.632599 \nL 174.541449 139.976548 \nL 174.860802 140.514957 \nL 175.064824 140.858859 \nL 175.38543 141.399702 \nL 175.589147 141.743274 \nL 175.911168 142.286869 \n\" style=\"fill:none;stroke:#b0b0b0;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_41\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 50.624424 93.57165 \nL 49.950148 93.127332 \nL 49.149487 92.599707 \nL 48.620919 92.251371 \nL 48.350123 92.072913 \nL 47.552054 91.54695 \nL 46.755274 91.021818 \nL 46.625792 90.936477 \nL 45.95978 90.497513 \nL 45.165566 89.974036 \nL 44.638941 89.626919 \nL 44.37263 89.451386 \nL 43.580968 88.92956 \nL 42.790575 88.408558 \nL 42.660246 88.322646 \nL 42.001449 87.888377 \nL 41.213585 87.369018 \nL 40.689624 87.023616 \nL 40.426979 86.850478 \nL 39.641629 86.332755 \nL 38.85753 85.815849 \nL 38.72698 85.729784 \nL 38.07468 85.299757 \nL 37.293075 84.784478 \n\" style=\"fill:none;stroke:#1a1a1a;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_42\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 52.805671 95.262979 \nL 52.143732 94.826684 \nL 51.340918 94.297506 \nL 50.796493 93.938625 \nL 50.53941 93.76916 \nL 49.739205 93.241644 \nL 48.940294 92.71496 \nL 48.795803 92.619699 \nL 48.142676 92.189104 \nL 47.346346 91.664076 \nL 46.803484 91.306148 \nL 46.5513 91.139876 \nL 45.757533 90.616501 \nL 44.965042 90.093951 \nL 44.819403 89.997917 \nL 44.173823 89.572224 \nL 43.383872 89.05132 \nL 42.843465 88.69496 \nL 42.595184 88.531236 \nL 41.807758 88.011972 \nL 41.021588 87.493525 \nL 40.875569 87.397229 \nL 40.236672 86.975895 \nL 39.453005 86.45908 \nL 38.915634 86.104686 \nL 38.670585 85.943078 \nL 37.889408 85.427887 \n\" style=\"fill:none;stroke:#1d1d1d;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_43\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 54.989324 96.955892 \nL 54.339354 96.527396 \nL 53.534375 95.996672 \nL 52.974358 95.627426 \nL 52.73071 95.466779 \nL 51.928355 94.937716 \nL 51.127303 94.409484 \nL 50.968011 94.304436 \nL 50.327551 93.882079 \nL 49.529094 93.355504 \nL 48.970144 92.986866 \nL 48.731927 92.829757 \nL 47.936047 92.304836 \nL 47.141448 91.78074 \nL 46.980612 91.674653 \nL 46.348128 91.257469 \nL 45.556082 90.735021 \nL 44.999303 90.367749 \nL 44.765305 90.213395 \nL 43.975795 89.692589 \nL 43.187547 89.172603 \nL 43.026107 89.066103 \nL 42.400558 88.653435 \nL 41.614824 88.135083 \nL 41.060935 87.769672 \nL 40.830341 87.617546 \nL 40.047107 87.100823 \nL 39.265117 86.584912 \nL 39.103696 86.478414 \nL 38.484368 86.069811 \n\" style=\"fill:none;stroke:#202020;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_44\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 57.175516 98.650431 \nL 56.537049 98.229445 \nL 55.729888 97.697183 \nL 55.154623 97.317807 \nL 54.92405 97.16575 \nL 54.119532 96.635146 \nL 53.316325 96.105372 \nL 53.142505 95.990716 \nL 52.514427 95.576425 \nL 51.71383 95.048307 \nL 51.138996 94.669094 \nL 50.914532 94.521017 \nL 50.116528 93.994553 \nL 49.319811 93.468915 \nL 49.143933 93.352873 \nL 48.524381 92.944101 \nL 47.73023 92.420112 \nL 47.157188 92.041998 \nL 46.937355 91.896945 \nL 46.145754 91.3746 \nL 45.355419 90.853076 \nL 45.178637 90.736417 \nL 44.56635 90.33237 \nL 43.778542 89.812483 \nL 43.208181 89.436083 \nL 42.99199 89.293412 \nL 42.206691 88.775155 \nL 41.422642 88.257714 \nL 41.24572 88.140949 \nL 40.63984 87.741083 \nL 39.85828 87.225264 \nL 39.291174 86.850975 \nL 39.077959 86.710254 \n\" style=\"fill:none;stroke:#232323;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_45\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 151.248602 165.29913 \nL 144.027994 162.234708 \nL 137.051803 159.021553 \nL 130.302837 155.681665 \nL 122.855467 151.727363 \nL 115.671506 147.651004 \nL 107.868996 142.957401 \nL 98.386684 136.965683 \nL 85.724469 128.680005 \nL 65.531178 115.217806 \nL 65.531178 115.217806 \n\" style=\"fill:none;stroke:#adadad;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 156.096389 105.169909 \nL 156.4389 105.736789 \nL 156.580184 105.970862 \nL 156.920556 106.534501 \nL 157.064831 106.773644 \nL 157.403201 107.334252 \nL 157.550348 107.578265 \nL 157.886847 108.136044 \nL 158.03675 108.384736 \nL 158.371504 108.939878 \nL 158.524053 109.193067 \nL 158.857183 109.745757 \nL 159.012274 110.003268 \nL 159.343893 110.553681 \nL 159.501427 110.815348 \nL 159.831644 111.363655 \nL 159.991526 111.629317 \nL 160.320447 112.17568 \nL 160.482585 112.445185 \nL 160.81031 112.98976 \nL 160.974617 113.262962 \nL 161.301242 113.805897 \nL 161.467636 114.082655 \nL 161.793253 114.624095 \nL 161.961653 114.904276 \nL 162.28635 115.444358 \nL 162.456682 115.727833 \nL 162.780543 116.26669 \nL 162.952732 116.553335 \nL 163.275839 117.091094 \nL 163.449816 117.380791 \nL 163.772247 117.917575 \nL 163.947943 118.210211 \nL 164.269773 118.746138 \nL 164.447125 119.041602 \nL 164.768427 119.576787 \nL 164.947372 119.874975 \nL 165.268214 120.409528 \nL 165.448691 120.710337 \nL 165.769142 121.244365 \nL 165.951094 121.547697 \nL 166.271218 122.081305 \nL 166.454587 122.387064 \nL 166.774449 122.920353 \nL 166.95918 123.228446 \nL 167.278841 123.761515 \nL 167.464881 124.071851 \nL 167.784399 124.604798 \nL 167.971695 124.917289 \nL 168.291131 125.450208 \nL 168.479631 125.764766 \nL 168.799042 126.297752 \nL 168.988694 126.614291 \nL 169.308137 127.147437 \nL 169.49889 127.465871 \nL 169.818421 127.999271 \nL 170.010223 128.319516 \nL 170.329898 128.853262 \nL 170.522699 129.175231 \nL 170.842574 129.709418 \nL 171.03632 130.033024 \nL 171.356452 130.567749 \nL 171.551089 130.892903 \nL 171.871535 131.428263 \nL 172.067008 131.754874 \nL 172.387826 132.290971 \nL 172.584077 132.618944 \nL 172.905328 133.155883 \nL 173.102294 133.485119 \nL 173.424041 134.023012 \nL 173.621658 134.353405 \nL 173.943967 134.892369 \nL 174.142164 135.223806 \nL 174.465104 135.763968 \nL 174.663805 136.096328 \nL 174.987451 136.637825 \nL 175.186573 136.970975 \nL 175.511005 137.513955 \nL 175.710455 137.847749 \nL 176.03576 138.392377 \nL 176.235437 138.726653 \nL 176.561711 139.273111 \nL 176.761498 139.607687 \nL 177.088848 140.15618 \n\" style=\"fill:none;stroke:#adadad;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_46\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 59.364408 100.346643 \nL 58.736854 99.932802 \nL 57.927494 99.399012 \nL 57.337421 99.009808 \nL 57.119466 98.866049 \nL 56.312768 98.333912 \nL 55.50739 97.802604 \nL 55.319395 97.678573 \nL 54.70333 97.272122 \nL 53.900581 96.742467 \nL 53.31013 96.352861 \nL 53.099138 96.21364 \nL 52.298997 95.685637 \nL 51.500152 95.158461 \nL 51.309441 95.0326 \nL 50.7026 94.632109 \nL 49.906335 94.106582 \nL 49.317181 93.717728 \nL 49.111352 93.581878 \nL 48.31765 93.057995 \nL 47.52522 92.534935 \nL 47.33321 92.408189 \nL 46.734063 92.012694 \nL 45.944171 91.491272 \nL 45.357413 91.10393 \nL 45.155542 90.970668 \nL 44.368173 90.45088 \nL 43.582058 89.931908 \nL 43.389684 89.804904 \nL 42.797195 89.413749 \nL 42.01358 88.896402 \nL 41.429931 88.511066 \nL 41.231209 88.379866 \nL 40.450079 87.86414 \nL 39.670187 87.349222 \n\" style=\"fill:none;stroke:#262626;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_47\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 61.556197 102.044588 \nL 60.938819 101.637431 \nL 60.127236 101.102126 \nL 59.522915 100.703479 \nL 59.316997 100.567645 \nL 58.5081 100.033987 \nL 57.700533 99.501155 \nL 57.498813 99.368046 \nL 56.894295 98.969146 \nL 56.089377 98.437962 \nL 55.483654 98.0382 \nL 55.285774 97.907605 \nL 54.483483 97.378071 \nL 53.682495 96.849363 \nL 53.477227 96.713861 \nL 52.882809 96.321478 \nL 52.084417 95.794417 \nL 51.479355 95.394961 \nL 51.287316 95.26818 \nL 50.491502 94.742764 \nL 49.696967 94.21817 \nL 49.489885 94.081437 \nL 48.903712 93.694396 \nL 48.111729 93.171443 \nL 47.508682 92.773231 \nL 47.321014 92.649308 \nL 46.531566 92.127989 \nL 45.743377 91.607488 \nL 45.53563 91.470292 \nL 44.956446 91.087801 \nL 44.170769 90.568928 \nL 43.570623 90.172572 \nL 43.386341 90.050867 \nL 42.603159 89.533617 \nL 41.82122 89.017177 \nL 41.613569 88.880028 \nL 41.04052 88.501544 \nL 40.261055 87.986719 \n\" style=\"fill:none;stroke:#292929;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_48\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 63.751123 103.74434 \nL 63.142999 103.343286 \nL 62.329167 102.806484 \nL 61.7113 102.39888 \nL 61.516693 102.270501 \nL 60.705574 101.735334 \nL 59.895796 101.200991 \nL 59.680923 101.059185 \nL 59.08736 100.667467 \nL 58.280255 100.134766 \nL 57.659702 99.725151 \nL 57.474474 99.602888 \nL 56.670016 99.071831 \nL 55.86687 98.541598 \nL 55.647399 98.396691 \nL 55.065036 98.012187 \nL 54.264504 97.483599 \nL 53.643802 97.073725 \nL 53.46527 96.955834 \nL 52.667332 96.42889 \nL 51.870682 95.902768 \nL 51.648738 95.756184 \nL 51.075317 95.377465 \nL 50.281232 94.852983 \nL 49.66205 94.444003 \nL 49.488422 94.32932 \nL 48.696885 93.806473 \nL 47.906613 93.284445 \nL 47.683609 93.137129 \nL 47.117607 92.763232 \nL 46.329859 92.242834 \nL 45.713292 91.835508 \nL 45.543366 91.723249 \nL 44.758126 91.204477 \nL 43.974133 90.686515 \nL 43.751 90.539094 \nL 43.191385 90.169363 \nL 42.409877 89.653019 \nL 41.796636 89.247841 \nL 41.629606 89.137482 \nL 40.85057 88.62275 \n\" style=\"fill:none;stroke:#2c2c2c;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_49\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 150.585917 164.923705 \nL 143.403726 161.812516 \nL 136.456322 158.563332 \nL 129.729517 155.194899 \nL 122.300821 151.215408 \nL 114.93082 147.002541 \nL 107.336841 142.410929 \nL 97.308344 136.050673 \nL 83.609958 127.060803 \nL 64.994781 114.643336 \nL 64.994781 114.643336 \n\" style=\"fill:none;stroke:#aaaaaa;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 158.201493 104.776035 \nL 158.543933 105.340627 \nL 158.687356 105.577292 \nL 159.028176 106.13946 \nL 159.174131 106.380396 \nL 159.513446 106.940314 \nL 159.661833 107.185357 \nL 159.999751 107.743191 \nL 160.150476 107.992185 \nL 160.487101 108.548094 \nL 160.640073 108.800888 \nL 160.975505 109.355026 \nL 161.13064 109.611476 \nL 161.464973 110.16399 \nL 161.622188 110.42396 \nL 161.955513 110.974988 \nL 162.11473 111.238347 \nL 162.447135 111.788025 \nL 162.608279 112.054647 \nL 162.939846 112.603103 \nL 163.102846 112.872869 \nL 163.433655 113.420228 \nL 163.598442 113.693023 \nL 163.928569 114.239402 \nL 164.09508 114.515117 \nL 164.424598 115.060631 \nL 164.592768 115.339159 \nL 164.921749 115.883919 \nL 165.091518 116.165159 \nL 165.420028 116.709269 \nL 165.59134 116.993126 \nL 165.919444 117.536689 \nL 166.092243 117.823068 \nL 166.420004 118.366181 \nL 166.594236 118.654994 \nL 166.921714 119.197752 \nL 167.097329 119.488912 \nL 167.424582 120.031407 \nL 167.60153 120.324831 \nL 167.928614 120.867153 \nL 168.106847 121.16276 \nL 168.433816 121.704993 \nL 168.613288 122.002706 \nL 168.940196 122.544936 \nL 169.120861 122.844678 \nL 169.447758 123.386987 \nL 169.629573 123.688684 \nL 169.95651 124.231153 \nL 170.139431 124.534733 \nL 170.466457 125.07744 \nL 170.650441 125.382832 \nL 170.977603 125.925856 \nL 171.162609 126.232989 \nL 171.489955 126.776407 \nL 171.675941 127.085212 \nL 172.003518 127.629103 \nL 172.190441 127.93951 \nL 172.518296 128.483949 \nL 172.706114 128.795889 \nL 173.034293 129.340956 \nL 173.222964 129.654357 \nL 173.551515 130.200132 \nL 173.740993 130.514922 \nL 174.069963 131.061485 \nL 174.260204 131.377589 \nL 174.589643 131.925026 \nL 174.780598 132.242367 \nL 175.110555 132.790764 \nL 175.302174 133.109262 \nL 175.632703 133.658712 \nL 175.824933 133.978279 \nL 176.156087 134.52888 \nL 176.348871 134.849426 \nL 176.680709 135.401281 \nL 176.873983 135.722706 \nL 177.206567 136.275929 \nL 177.400264 136.598124 \nL 177.73366 137.152839 \nL 177.927704 137.475685 \nL 178.261985 138.032028 \n\" style=\"fill:none;stroke:#aaaaaa;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_50\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 65.94948 105.445987 \nL 65.349463 105.050313 \nL 64.533352 104.512034 \nL 63.902818 104.096083 \nL 63.718613 103.974568 \nL 62.905245 103.437912 \nL 62.093232 102.902074 \nL 61.865921 102.75205 \nL 61.282573 102.367049 \nL 60.473258 101.832843 \nL 59.838436 101.413765 \nL 59.665279 101.299458 \nL 58.858635 100.766888 \nL 58.053313 100.235142 \nL 57.820091 100.081131 \nL 57.249313 99.704214 \nL 56.446625 99.174107 \nL 55.81063 98.754053 \nL 55.645244 98.644822 \nL 54.845168 98.116355 \nL 54.046387 97.588711 \nL 53.80986 97.432458 \nL 53.248901 97.061885 \nL 52.452702 96.535878 \nL 51.817591 96.116271 \nL 51.657785 96.010691 \nL 50.864149 95.486321 \nL 50.071785 94.962769 \nL 49.833682 94.805435 \nL 49.280693 94.440033 \nL 48.490866 93.918112 \nL 47.857989 93.499889 \nL 47.7023 93.397005 \nL 46.914992 92.876712 \nL 46.128938 92.35723 \nL 45.890404 92.199585 \nL 45.344134 91.83856 \nL 44.560576 91.320698 \nL 43.930815 90.904473 \nL 43.778261 90.803646 \nL 42.997185 90.287399 \nL 42.217344 89.771958 \nL 41.979137 89.61451 \nL 41.438735 89.257321 \n\" style=\"fill:none;stroke:#2f2f2f;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_51\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 68.151625 107.149636 \nL 67.558294 106.758445 \nL 66.739866 106.218716 \nL 66.097763 105.795177 \nL 65.922828 105.679791 \nL 65.10718 105.141667 \nL 64.2929 104.604354 \nL 64.05405 104.446714 \nL 63.479992 104.067848 \nL 62.668441 103.532154 \nL 62.020054 103.104101 \nL 61.858239 102.997276 \nL 61.049386 102.463209 \nL 60.241866 101.929961 \nL 59.995467 101.767229 \nL 59.43568 101.397528 \nL 58.630817 100.865913 \nL 57.979974 100.435987 \nL 57.827271 100.335117 \nL 57.025041 99.805137 \nL 56.224115 99.275978 \nL 55.97336 99.110293 \nL 55.424492 98.747635 \nL 54.626166 98.220111 \nL 53.975396 97.790063 \nL 53.829129 97.693406 \nL 53.033382 97.167517 \nL 52.238914 96.642446 \nL 51.985924 96.475232 \nL 51.445725 96.11819 \nL 50.653808 95.59475 \nL 50.004776 95.165735 \nL 49.863158 95.072125 \nL 49.073775 94.550312 \nL 48.28565 94.029314 \nL 48.031832 93.861517 \nL 47.498782 93.509126 \nL 46.713166 92.989749 \nL 46.066963 92.562526 \nL 45.928798 92.471182 \nL 45.145676 91.953421 \nL 44.363793 91.436469 \nL 44.110077 91.268716 \nL 43.583149 90.920321 \nL 42.803737 90.404978 \nL 42.161071 89.980041 \nL 42.025556 89.890437 \n\" style=\"fill:none;stroke:#323232;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_52\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 70.357994 108.855419 \nL 69.769593 108.467598 \nL 68.948804 107.926452 \nL 68.29649 107.496269 \nL 68.129426 107.386099 \nL 67.311458 106.846533 \nL 66.494877 106.307772 \nL 66.245601 106.143265 \nL 65.679685 105.769807 \nL 64.865867 105.232647 \nL 64.204798 104.796232 \nL 64.053414 104.696296 \nL 63.242324 104.160749 \nL 62.432581 103.626016 \nL 62.173723 103.455045 \nL 61.624185 103.092092 \nL 60.817125 102.558983 \nL 60.151997 102.119575 \nL 60.011394 102.026689 \nL 59.206989 101.495206 \nL 58.4039 100.964543 \nL 58.139373 100.78973 \nL 57.602124 100.434693 \nL 56.801653 99.90566 \nL 56.135574 99.465411 \nL 56.002482 99.377444 \nL 55.204609 98.850042 \nL 54.408024 98.323458 \nL 54.140427 98.14655 \nL 53.612725 97.797688 \nL 52.818707 97.272734 \nL 52.153727 96.833068 \nL 52.025963 96.748594 \nL 51.234492 96.225267 \nL 50.444287 95.702754 \nL 50.175346 95.524911 \nL 49.655346 95.181052 \nL 48.867663 94.660162 \nL 48.205131 94.222017 \nL 48.081234 94.140082 \nL 47.296056 93.62081 \nL 46.512124 93.102347 \nL 46.242981 92.924339 \nL 45.729436 92.584689 \nL 44.947987 92.067838 \nL 44.28878 91.631827 \nL 44.167773 91.55179 \nL 43.388791 91.036545 \nL 42.611037 90.522101 \n\" style=\"fill:none;stroke:#343434;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_53\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 149.936811 164.532192 \nL 142.788369 161.379017 \nL 134.89541 157.618744 \nL 128.219298 154.208212 \nL 120.840095 150.190326 \nL 113.712048 146.064343 \nL 105.956137 141.332159 \nL 95.96068 134.957413 \nL 80.711291 124.916658 \nL 64.457522 114.067349 \nL 64.457522 114.067349 \n\" style=\"fill:none;stroke:#a7a7a7;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 160.307804 104.379833 \nL 160.65233 104.945501 \nL 160.795937 105.181447 \nL 161.139277 105.74537 \nL 161.285032 105.984923 \nL 161.627282 106.547246 \nL 161.775104 106.790271 \nL 162.116352 107.351131 \nL 162.266164 107.5975 \nL 162.606498 108.15703 \nL 162.758225 108.406618 \nL 163.097727 108.964945 \nL 163.251299 109.217636 \nL 163.590047 109.774881 \nL 163.745397 110.030562 \nL 164.083467 110.58684 \nL 164.24053 110.845405 \nL 164.577994 111.400828 \nL 164.73671 111.662173 \nL 165.073638 112.216848 \nL 165.233947 112.480875 \nL 165.570404 113.034905 \nL 165.732251 113.301521 \nL 166.068301 113.855004 \nL 166.231631 114.124118 \nL 166.567335 114.677149 \nL 166.732098 114.948675 \nL 167.067515 115.501346 \nL 167.233661 115.775202 \nL 167.568847 116.327599 \nL 167.736329 116.603706 \nL 168.071337 117.155914 \nL 168.24011 117.434195 \nL 168.574993 117.986296 \nL 168.745013 118.266679 \nL 169.079822 118.818751 \nL 169.251047 119.101165 \nL 169.585829 119.653285 \nL 169.758218 119.937663 \nL 170.093021 120.489904 \nL 170.266536 120.77618 \nL 170.601404 121.328614 \nL 170.776006 121.616724 \nL 171.110984 122.169422 \nL 171.286637 122.459304 \nL 171.621768 123.012334 \nL 171.798435 123.303927 \nL 172.13376 123.857357 \nL 172.311406 124.150603 \nL 172.646967 124.704497 \nL 172.825556 124.999338 \nL 173.161393 125.553762 \nL 173.340892 125.850141 \nL 173.677044 126.40516 \nL 173.857419 126.70302 \nL 174.193925 127.258698 \nL 174.375141 127.557982 \nL 174.712041 128.114384 \nL 174.894063 128.415036 \nL 175.231397 128.972227 \nL 175.414189 129.274188 \nL 175.751995 129.832234 \nL 175.935523 130.135446 \nL 176.273841 130.694416 \nL 176.458066 130.998818 \nL 176.796938 131.55878 \nL 176.981822 131.86431 \nL 177.321289 132.425339 \nL 177.50679 132.731929 \nL 177.846896 133.2941 \nL 178.032971 133.601681 \nL 178.373762 134.165077 \nL 178.560364 134.473574 \nL 178.901888 135.03828 \nL 179.088965 135.347613 \nL 179.431274 135.913723 \n\" style=\"fill:none;stroke:#a7a7a7;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_54\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 72.569117 110.563496 \nL 71.983478 110.177671 \nL 71.160276 109.635148 \nL 70.499438 109.199492 \nL 70.338508 109.093404 \nL 69.518176 108.552432 \nL 68.699251 108.012253 \nL 68.440935 107.841813 \nL 67.881736 107.472859 \nL 67.065614 106.934259 \nL 66.392961 106.490247 \nL 66.250874 106.39646 \nL 65.437516 105.859455 \nL 64.62552 105.323257 \nL 64.355104 105.144654 \nL 63.814886 104.787862 \nL 63.005603 104.253275 \nL 62.326897 103.804878 \nL 62.197661 103.719498 \nL 61.39106 103.186528 \nL 60.585785 102.654373 \nL 60.308062 102.470818 \nL 59.781836 102.123027 \nL 58.979203 101.592496 \nL 58.298262 101.142358 \nL 58.177879 101.062779 \nL 57.377864 100.533874 \nL 56.579145 100.005784 \nL 56.297301 99.81942 \nL 55.781722 99.478508 \nL 54.985589 98.952045 \nL 54.304935 98.501917 \nL 54.190737 98.426397 \nL 53.397168 97.90156 \nL 52.604871 97.377538 \nL 52.321021 97.189789 \nL 51.813845 96.854326 \nL 51.024084 96.331926 \nL 50.34538 95.882965 \nL 50.235584 95.810336 \nL 49.448343 95.289555 \nL 48.662352 94.769583 \nL 48.377901 94.581397 \nL 47.877612 94.250418 \nL 47.094117 93.73206 \nL 46.418449 93.285027 \nL 46.311862 93.214507 \nL 45.530846 92.697757 \nL 44.751063 92.181811 \nL 44.466938 91.993813 \nL 43.97251 91.666665 \nL 43.195184 91.15232 \n\" style=\"fill:none;stroke:#373737;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_55\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 74.785642 112.274063 \nL 74.200094 111.888543 \nL 73.374417 111.344692 \nL 72.707138 110.905007 \nL 72.550201 110.801602 \nL 71.727451 110.259266 \nL 70.90613 109.717708 \nL 70.640487 109.542488 \nL 70.086245 109.17692 \nL 69.267775 108.636913 \nL 68.584902 108.186254 \nL 68.450707 108.097696 \nL 67.635043 107.559261 \nL 66.820757 107.021624 \nL 66.539902 106.836144 \nL 66.007852 106.484781 \nL 65.196315 105.948737 \nL 64.504916 105.49197 \nL 64.386133 105.413498 \nL 63.577308 104.879058 \nL 62.769822 104.345427 \nL 62.479626 104.153619 \nL 61.963676 103.812602 \nL 61.158858 103.280585 \nL 60.463621 102.820952 \nL 60.355361 102.74938 \nL 59.553184 102.218982 \nL 58.752314 101.689398 \nL 58.456681 101.493886 \nL 57.95275 101.160624 \nL 57.154485 100.632662 \nL 56.45851 100.172317 \nL 56.357511 100.105513 \nL 55.561828 99.579173 \nL 54.767426 99.053647 \nL 54.46895 98.85618 \nL 53.974303 98.528931 \nL 53.182453 98.005025 \nL 52.487786 97.545394 \nL 52.39187 97.481931 \nL 51.602554 96.959644 \nL 50.814495 96.438168 \nL 50.5149 96.239908 \nL 50.027694 95.917498 \nL 49.242143 95.397635 \nL 48.55013 94.939658 \nL 48.457839 94.878579 \nL 47.67478 94.360327 \nL 46.892959 93.842879 \nL 46.593384 93.644598 \nL 46.112375 93.326232 \nL 45.333023 92.810388 \nL 44.644541 92.354678 \nL 44.554899 92.295343 \nL 43.778001 91.781097 \n\" style=\"fill:none;stroke:#3a3a3a;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_56\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 77.008355 113.987356 \nL 76.419616 113.600063 \nL 75.591388 113.054945 \nL 74.920239 112.613008 \nL 74.764655 112.510566 \nL 73.939421 111.966916 \nL 73.115644 111.424027 \nL 72.844792 111.245452 \nL 72.293333 110.881889 \nL 71.472462 110.340516 \nL 70.78106 109.884386 \nL 70.653017 109.799918 \nL 69.835 109.260086 \nL 69.018383 108.721043 \nL 68.728479 108.529624 \nL 68.203168 108.18278 \nL 67.389338 107.645307 \nL 66.686351 107.180939 \nL 66.576882 107.10863 \nL 65.765801 106.572742 \nL 64.956074 106.037657 \nL 64.65431 105.838205 \nL 64.147703 105.50337 \nL 63.340674 104.969886 \nL 62.631853 104.501255 \nL 62.534978 104.437209 \nL 61.730617 103.905332 \nL 60.927574 103.374267 \nL 60.618732 103.169997 \nL 60.125849 102.844007 \nL 59.325433 102.314556 \nL 58.614587 101.844308 \nL 58.526318 101.785916 \nL 57.728506 101.258082 \nL 56.931982 100.73106 \nL 56.619244 100.524118 \nL 56.136748 100.204847 \nL 55.342794 99.679443 \nL 54.632442 99.209332 \nL 54.550116 99.154849 \nL 53.758713 98.631062 \nL 52.968575 98.108085 \nL 52.654053 97.899897 \nL 52.1797 97.585915 \nL 51.392084 97.064552 \nL 50.683885 96.595738 \nL 50.605721 96.543996 \nL 49.82061 96.024243 \nL 49.036743 95.505296 \nL 48.72184 95.29681 \nL 48.254119 94.987151 \nL 47.472732 94.469809 \nL 46.767773 94.003054 \nL 46.692579 93.953268 \nL 45.913659 93.437526 \nL 45.135963 92.922583 \nL 44.821606 92.714429 \nL 44.359492 92.408437 \n\" style=\"fill:none;stroke:#3d3d3d;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_57\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 79.238216 115.703667 \nL 78.642251 115.312051 \nL 77.811384 114.765739 \nL 77.13953 114.323734 \nL 76.98205 114.220138 \nL 76.154255 113.675238 \nL 75.32795 113.131076 \nL 75.054497 112.9509 \nL 74.503145 112.587641 \nL 73.679811 112.044952 \nL 72.981969 111.584804 \nL 72.857929 111.503019 \nL 72.037507 110.961834 \nL 71.218506 110.421422 \nL 70.921274 110.225226 \nL 70.400933 109.881776 \nL 69.584767 109.342907 \nL 68.871562 108.871896 \nL 68.769995 108.804822 \nL 67.956621 108.267514 \nL 67.144617 107.731001 \nL 66.832409 107.524667 \nL 66.333986 107.195276 \nL 65.524715 106.660345 \nL 64.8032 106.183341 \nL 64.716791 106.126216 \nL 63.910219 105.592879 \nL 63.104977 105.060349 \nL 62.783655 104.847814 \nL 62.301067 104.528618 \nL 61.498478 103.997692 \nL 60.773332 103.517941 \nL 60.697202 103.467574 \nL 59.89724 102.938257 \nL 59.098577 102.409751 \nL 58.77204 102.193644 \nL 58.301213 101.882049 \nL 57.505141 101.355155 \nL 56.77946 100.874814 \nL 56.710352 100.82907 \nL 55.916847 100.30379 \nL 55.124616 99.779319 \nL 54.795454 99.561392 \nL 54.333656 99.255654 \nL 53.543962 98.732795 \nL 52.819791 98.253293 \nL 52.755529 98.210743 \nL 51.968355 97.689494 \nL 51.182432 97.169051 \nL 50.852367 96.950469 \nL 50.397758 96.649411 \nL 49.614328 96.130574 \nL 48.89301 95.652853 \nL 48.832138 95.612539 \nL 48.051186 95.095303 \nL 47.271465 94.578868 \nL 46.941637 94.360404 \nL 46.492974 94.06323 \nL 45.715708 93.54839 \nL 44.998119 93.073068 \nL 44.939662 93.034346 \n\" style=\"fill:none;stroke:#404040;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_58\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 149.29878 164.127069 \nL 142.180668 160.935442 \nL 134.313911 157.14088 \nL 126.720487 153.208211 \nL 119.389099 149.153943 \nL 111.430175 144.476056 \nL 102.478164 138.920702 \nL 91.640797 131.917302 \nL 74.697492 120.691821 \nL 63.919354 113.489876 \nL 63.919354 113.489876 \n\" style=\"fill:none;stroke:#a4a4a4;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 162.416123 103.981521 \nL 162.764537 104.551035 \nL 162.906695 104.783535 \nL 163.254287 105.351871 \nL 163.398274 105.587424 \nL 163.745122 106.154703 \nL 163.89087 106.393199 \nL 164.237049 106.959533 \nL 164.384496 107.200866 \nL 164.730078 107.766367 \nL 164.879163 108.010437 \nL 165.224215 108.575207 \nL 165.37488 108.821918 \nL 165.719469 109.38606 \nL 165.871658 109.635318 \nL 166.215846 110.198928 \nL 166.369508 110.450647 \nL 166.713355 111.013817 \nL 166.868438 111.267912 \nL 167.212002 111.830731 \nL 167.368459 112.087123 \nL 167.711795 112.649675 \nL 167.869579 112.908287 \nL 168.212741 113.470655 \nL 168.371808 113.731413 \nL 168.714846 114.293676 \nL 168.875154 114.55651 \nL 169.218116 115.118743 \nL 169.379625 115.383585 \nL 169.72256 115.945862 \nL 169.885231 116.212648 \nL 170.228182 116.775037 \nL 170.391978 117.043706 \nL 170.73499 117.606277 \nL 170.899876 117.876767 \nL 171.24299 118.439585 \nL 171.40893 118.711841 \nL 171.752188 119.274969 \nL 171.919149 119.548934 \nL 172.262589 120.112434 \nL 172.43054 120.388055 \nL 172.774201 120.951988 \nL 172.94311 121.229213 \nL 173.287028 121.793636 \nL 173.456865 122.072416 \nL 173.801076 122.637386 \nL 173.971812 122.917671 \nL 174.316351 123.483245 \nL 174.487957 123.764986 \nL 174.832859 124.331219 \nL 175.005306 124.61437 \nL 175.350604 125.181316 \nL 175.523864 125.46583 \nL 175.869592 126.033544 \nL 176.043637 126.319375 \nL 176.389827 126.887909 \nL 176.564629 127.175011 \nL 176.911316 127.744421 \nL 177.086846 128.032748 \nL 177.434061 128.603087 \nL 177.610292 128.892592 \nL 177.958068 129.463916 \nL 178.134969 129.754551 \nL 178.483341 130.326917 \nL 178.660882 130.618632 \nL 179.009883 131.192098 \nL 179.188032 131.484843 \nL 179.537698 132.05947 \nL 179.716421 132.35319 \nL 180.066789 132.929042 \nL 180.246051 133.223681 \nL 180.597158 133.800826 \n\" style=\"fill:none;stroke:#a4a4a4;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_59\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 81.476389 117.423347 \nL 80.868247 117.024288 \nL 80.034635 116.476871 \nL 79.365975 116.037477 \nL 79.202602 115.930131 \nL 78.372154 115.384057 \nL 77.543235 114.838693 \nL 77.270395 114.659073 \nL 76.715856 114.294027 \nL 75.889983 113.750081 \nL 75.188279 113.287705 \nL 75.065596 113.20687 \nL 74.242702 112.664383 \nL 73.421257 112.122652 \nL 73.118821 111.923113 \nL 72.601269 111.581666 \nL 71.782715 111.041441 \nL 71.060989 110.564972 \nL 70.965578 110.501987 \nL 70.149863 109.963293 \nL 69.335539 109.425383 \nL 69.014286 109.213114 \nL 68.52261 108.888249 \nL 67.711059 108.3519 \nL 66.977961 107.867299 \nL 66.900873 107.816343 \nL 66.092057 107.281569 \nL 65.284586 106.747594 \nL 64.951694 106.527412 \nL 64.478462 106.214412 \nL 63.673675 105.682029 \nL 62.934946 105.193276 \nL 62.870212 105.150448 \nL 62.068078 104.619663 \nL 61.267254 104.089684 \nL 60.927502 103.864809 \nL 60.467741 103.560507 \nL 59.66953 103.032134 \nL 58.928976 102.541881 \nL 58.872612 102.504568 \nL 58.07699 101.977803 \nL 57.282649 101.451846 \nL 56.939215 101.224427 \nL 56.489589 100.926693 \nL 55.697805 100.402345 \nL 54.957941 99.91235 \nL 54.907287 99.878804 \nL 54.118038 99.356064 \nL 53.330047 98.83413 \nL 52.985042 98.605599 \nL 52.543312 98.312999 \nL 51.757829 97.79267 \nL 51.020315 97.304096 \nL 50.973591 97.273144 \nL 50.190599 96.754417 \nL 49.408844 96.236492 \nL 49.063671 96.0078 \nL 48.628324 95.719365 \nL 47.849036 95.203037 \nL 47.114958 94.716649 \nL 47.070973 94.687506 \nL 46.294136 94.172769 \nL 45.518518 93.658827 \n\" style=\"fill:none;stroke:#434343;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_60\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 83.724289 119.146824 \nL 83.097899 118.736513 \nL 82.261418 118.188098 \nL 81.600743 117.754591 \nL 81.426568 117.640317 \nL 80.593359 117.093161 \nL 79.761723 116.546682 \nL 79.493447 116.37026 \nL 78.931675 116.000864 \nL 78.103175 115.455736 \nL 77.400785 114.993329 \nL 77.276198 114.911315 \nL 76.450755 114.367589 \nL 75.626794 113.824596 \nL 75.321773 113.623482 \nL 74.804324 113.282325 \nL 73.983319 112.740794 \nL 73.255168 112.260331 \nL 73.163757 112.200017 \nL 72.345648 111.65998 \nL 71.528953 111.120713 \nL 71.200382 110.90368 \nL 70.713677 110.582206 \nL 69.899802 110.044471 \nL 69.156498 109.553239 \nL 69.087312 109.507517 \nL 68.276213 108.971334 \nL 67.466477 108.43594 \nL 67.123149 108.208879 \nL 66.658106 107.901331 \nL 65.851089 107.367512 \nL 65.099675 106.870388 \nL 65.04541 106.834489 \nL 64.241077 106.302254 \nL 63.438066 105.77082 \nL 63.085834 105.537675 \nL 62.636379 105.240182 \nL 61.836007 104.710344 \nL 61.081156 104.210583 \nL 61.03694 104.18131 \nL 60.23918 103.653072 \nL 59.442712 103.125639 \nL 59.085473 102.889045 \nL 58.647535 102.599008 \nL 57.853642 102.07318 \nL 57.098449 101.572945 \nL 57.061026 101.548157 \nL 56.269688 101.023933 \nL 55.479615 100.500514 \nL 55.119961 100.262228 \nL 54.690807 99.977897 \nL 53.903258 99.456082 \nL 53.149766 98.956807 \nL 53.116961 98.93507 \nL 52.331918 98.414857 \nL 51.548118 97.895445 \nL 51.18777 97.656636 \nL 50.76556 97.376832 \nL 49.98424 96.859017 \nL 49.233794 96.361647 \nL 49.204152 96.342001 \nL 48.425296 95.82578 \nL 47.647664 95.310355 \nL 47.287763 95.0718 \nL 46.871254 94.795724 \nL 46.096063 94.281886 \n\" style=\"fill:none;stroke:#464646;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_61\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 85.983626 120.874617 \nL 85.331557 120.448414 \nL 84.492059 119.899127 \nL 83.845259 119.475506 \nL 83.654255 119.350426 \nL 82.818156 118.802298 \nL 81.983681 118.254807 \nL 81.724824 118.084817 \nL 81.150852 117.707932 \nL 80.319619 117.161711 \nL 79.620454 116.701967 \nL 79.489953 116.616164 \nL 78.66187 116.071275 \nL 77.835306 115.527092 \nL 77.530925 115.326572 \nL 77.010273 114.983602 \nL 76.186741 114.440826 \nL 75.454755 113.958169 \nL 75.364684 113.898782 \nL 74.544115 113.357454 \nL 73.724988 112.816878 \nL 73.391235 112.596526 \nL 72.907309 112.277043 \nL 72.091057 111.737963 \nL 71.339254 111.241295 \nL 71.276213 111.19965 \nL 70.462787 110.662092 \nL 69.650742 110.125313 \nL 69.298383 109.892328 \nL 68.840084 109.589305 \nL 68.030799 109.054077 \nL 67.267817 108.549368 \nL 67.22287 108.519637 \nL 66.416304 107.985975 \nL 65.611076 107.453107 \nL 65.247283 107.212316 \nL 64.807187 106.921028 \nL 64.004628 106.389742 \nL 63.236204 105.880983 \nL 63.203386 105.859255 \nL 62.403466 105.329559 \nL 61.604848 104.800665 \nL 61.234397 104.555297 \nL 60.807533 104.272568 \nL 60.011514 103.74527 \nL 59.241452 103.235119 \nL 59.216781 103.218775 \nL 58.423337 102.693077 \nL 57.631166 102.168182 \nL 57.257237 101.920392 \nL 56.84027 101.644087 \nL 56.050641 101.120792 \nL 55.281457 100.611014 \nL 55.262273 100.5983 \nL 54.475166 100.076605 \nL 53.68931 99.555711 \nL 53.314014 99.306937 \nL 52.904703 99.035616 \nL 52.121341 98.51632 \nL 51.354694 98.008082 \nL 51.339217 97.997822 \nL 50.558332 97.480119 \nL 49.778677 96.963213 \nL 49.403418 96.714409 \nL 49.000251 96.447102 \nL 48.223048 95.931784 \nL 47.460027 95.425854 \nL 47.447065 95.41726 \nL 46.672301 94.903526 \n\" style=\"fill:none;stroke:#494949;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_62\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 148.670288 163.709863 \nL 141.579584 160.482809 \nL 133.488518 156.530411 \nL 126.161608 152.698294 \nL 118.843779 148.624155 \nL 110.895126 143.929528 \nL 102.364496 138.625456 \nL 90.83269 131.164527 \nL 71.443258 118.300084 \nL 63.380289 112.910902 \nL 63.380289 112.910902 \n\" style=\"fill:none;stroke:#a1a1a1;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 164.527116 103.58128 \nL 164.880929 104.156922 \nL 165.02027 104.383729 \nL 165.373565 104.958666 \nL 165.514467 105.188066 \nL 165.86731 105.762398 \nL 166.00972 105.994299 \nL 166.362172 106.568121 \nL 166.506037 106.802436 \nL 166.858159 107.375839 \nL 167.003428 107.612487 \nL 167.355277 108.185558 \nL 167.501904 108.424459 \nL 167.853534 108.997282 \nL 168.001473 109.238362 \nL 168.352936 109.811015 \nL 168.502144 110.054202 \nL 168.853491 110.626764 \nL 169.003926 110.871989 \nL 169.355205 111.444533 \nL 169.506827 111.691731 \nL 169.858085 112.264328 \nL 170.010857 112.513436 \nL 170.362137 113.086154 \nL 170.516023 113.337112 \nL 170.867367 113.910017 \nL 171.022333 114.162768 \nL 171.373783 114.735923 \nL 171.529796 114.990411 \nL 171.88139 115.563877 \nL 172.038418 115.82005 \nL 172.390195 116.393885 \nL 172.548207 116.651693 \nL 172.900204 117.225954 \nL 173.05917 117.485348 \nL 173.411421 118.060091 \nL 173.571315 118.321024 \nL 173.923855 118.8963 \nL 174.084648 119.158728 \nL 174.437509 119.734589 \nL 174.599176 119.998468 \nL 174.952391 120.574965 \nL 175.114905 120.840252 \nL 175.468505 121.417435 \nL 175.631843 121.684089 \nL 175.985858 122.262005 \nL 176.149994 122.529987 \nL 176.504454 123.108682 \nL 176.669366 123.377953 \nL 177.024299 123.957474 \nL 177.189963 124.227995 \nL 177.545398 124.808387 \nL 177.711791 125.080122 \nL 178.067756 125.661431 \nL 178.234856 125.934341 \nL 178.591379 126.516612 \nL 178.759162 126.79066 \nL 179.116271 127.373938 \nL 179.284715 127.649087 \nL 179.642437 128.233418 \nL 179.811517 128.509629 \nL 180.169881 129.09506 \nL 180.339574 129.372294 \nL 180.698607 129.958873 \nL 180.868889 130.23709 \nL 181.22862 130.824866 \nL 181.399464 131.104025 \nL 181.759924 131.693047 \n\" style=\"fill:none;stroke:#a1a1a1;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_63\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 88.256474 122.607354 \nL 87.569632 122.159619 \nL 86.726944 121.609613 \nL 86.101246 121.200746 \nL 85.886026 121.060131 \nL 85.046884 120.511164 \nL 84.209428 119.962785 \nL 83.965948 119.803173 \nL 83.373684 119.414968 \nL 82.539592 118.867761 \nL 81.848462 118.413978 \nL 81.707121 118.321186 \nL 80.876287 117.775227 \nL 80.047017 117.229941 \nL 79.747246 117.032678 \nL 79.219326 116.685311 \nL 78.393178 116.141365 \nL 77.660549 115.658729 \nL 77.568543 115.598123 \nL 76.745437 115.055568 \nL 75.923804 114.513742 \nL 75.587503 114.291853 \nL 75.103654 113.972633 \nL 74.284963 113.432259 \nL 73.526769 112.931631 \nL 73.467705 112.892634 \nL 72.651896 112.353743 \nL 71.837492 111.815618 \nL 71.477842 111.577892 \nL 71.024499 111.278249 \nL 70.212901 110.741645 \nL 69.439739 110.230327 \nL 69.402679 110.205819 \nL 68.593842 109.670758 \nL 67.786361 109.136482 \nL 67.412149 108.888824 \nL 66.980237 108.602986 \nL 66.175459 108.070275 \nL 65.394367 107.553156 \nL 65.372012 107.538356 \nL 64.569904 107.00722 \nL 63.769111 106.476881 \nL 63.386191 106.223245 \nL 62.969635 105.947333 \nL 62.171467 105.41858 \nL 61.387118 104.898923 \nL 61.374595 104.890627 \nL 60.579025 104.363465 \nL 59.784739 103.837104 \nL 59.397008 103.580134 \nL 58.991737 103.311541 \nL 58.200012 102.786776 \nL 57.415502 102.266752 \nL 57.409556 102.262811 \nL 56.620372 101.739642 \nL 55.832446 101.217273 \nL 55.442497 100.958732 \nL 55.045777 100.695702 \nL 54.260361 100.174928 \nL 53.477735 99.655978 \nL 53.47619 99.654954 \nL 52.693265 99.135773 \nL 51.911577 98.61739 \nL 51.521135 98.358452 \nL 51.131124 98.099801 \nL 50.351902 97.583007 \nL 49.573904 97.067007 \nL 49.572507 97.06608 \nL 48.797132 96.551797 \nL 48.021577 96.03738 \nL 47.631785 95.778827 \nL 47.247238 95.523753 \n\" style=\"fill:none;stroke:#4c4c4c;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_64\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 90.545326 124.345795 \nL 89.812601 123.869693 \nL 88.966525 123.319146 \nL 88.370796 122.930946 \nL 88.122305 122.769049 \nL 87.279944 122.219398 \nL 86.439338 121.670278 \nL 86.218542 121.525852 \nL 85.600524 121.121656 \nL 84.763425 120.573591 \nL 84.086242 120.129794 \nL 83.928011 120.026109 \nL 83.094297 119.479191 \nL 82.262199 118.932906 \nL 81.971914 118.742155 \nL 81.431737 118.387232 \nL 80.602866 117.842206 \nL 79.873521 117.362305 \nL 79.775553 117.297849 \nL 78.949817 116.754143 \nL 78.125592 116.211139 \nL 77.789985 115.989901 \nL 77.30289 115.668824 \nL 76.481683 115.127216 \nL 75.719703 114.624446 \nL 75.661942 114.586336 \nL 74.843684 114.046166 \nL 74.026859 113.506742 \nL 73.662068 113.265736 \nL 73.211474 112.968057 \nL 72.39751 112.430119 \nL 71.615887 111.9134 \nL 71.584945 111.892945 \nL 70.773792 111.35652 \nL 69.964014 110.820869 \nL 69.580801 110.56731 \nL 69.155613 110.285986 \nL 68.348579 109.751876 \nL 67.555949 109.227193 \nL 67.542893 109.218551 \nL 66.738564 108.685998 \nL 65.935566 108.154235 \nL 65.541105 107.892963 \nL 65.133899 107.623256 \nL 64.333555 107.093066 \nL 63.535653 106.564421 \nL 63.53452 106.56367 \nL 62.736801 106.03506 \nL 61.940377 105.507248 \nL 61.539445 105.241504 \nL 61.145248 104.980228 \nL 60.351409 104.454003 \nL 59.558847 103.928577 \nL 59.552044 103.924066 \nL 58.767568 103.403942 \nL 57.977556 102.880107 \nL 57.573336 102.612056 \nL 57.188811 102.357067 \nL 56.401327 101.834823 \nL 55.615095 101.313378 \nL 55.603016 101.305366 \nL 54.830119 100.792725 \nL 54.046386 100.27287 \nL 53.640993 100.003954 \nL 53.263895 99.753809 \nL 52.482642 99.235541 \nL 51.702621 98.718069 \nL 51.687048 98.707737 \nL 50.923831 98.201387 \nL 50.146265 97.685498 \nL 49.741106 97.416678 \nL 49.36992 97.1704 \nL 48.594793 96.656091 \nL 47.820878 96.142572 \n\" style=\"fill:none;stroke:#4f4f4f;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_65\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 92.853178 126.090851 \nL 92.061022 125.578125 \nL 91.211326 125.027244 \nL 90.656432 124.666871 \nL 90.363588 124.476726 \nL 89.517801 123.926576 \nL 88.673851 123.376889 \nL 88.484691 123.253486 \nL 87.831785 122.827621 \nL 86.991507 122.278852 \nL 86.335531 121.849942 \nL 86.152986 121.730603 \nL 85.31624 121.18286 \nL 84.48117 120.6357 \nL 84.206359 120.455437 \nL 83.647804 120.089098 \nL 82.816084 119.543099 \nL 82.094859 119.069257 \nL 81.985975 118.997729 \nL 81.157499 118.452965 \nL 80.330579 117.90887 \nL 79.999657 117.690967 \nL 79.505229 117.365428 \nL 78.681417 116.822662 \nL 77.918861 116.319983 \nL 77.859107 116.280596 \nL 77.038323 115.73921 \nL 76.219004 115.198549 \nL 75.851723 114.95606 \nL 75.401158 114.658601 \nL 74.584766 114.119381 \nL 73.796806 113.598751 \nL 73.769798 113.580907 \nL 72.956273 113.04316 \nL 72.144146 112.506174 \nL 71.753688 112.24791 \nL 71.333422 111.96994 \nL 70.524086 111.434466 \nL 69.721317 110.903206 \nL 69.716118 110.899766 \nL 68.90953 110.365824 \nL 68.104289 109.832664 \nL 67.699442 109.564546 \nL 67.300398 109.300279 \nL 66.497847 108.768673 \nL 65.696619 108.237856 \nL 65.687313 108.231689 \nL 64.896723 107.707816 \nL 64.098135 107.178569 \nL 63.684755 106.904566 \nL 63.300856 106.650109 \nL 62.504879 106.122439 \nL 61.71019 105.595564 \nL 61.691253 105.583006 \nL 60.916797 105.069476 \nL 60.12468 104.544185 \nL 59.70667 104.266952 \nL 59.33384 104.019686 \nL 58.544272 103.495981 \nL 57.755964 102.973073 \nL 57.730652 102.956281 \nL 56.968921 102.450955 \nL 56.18313 101.929634 \nL 55.763088 101.650944 \nL 55.398588 101.409107 \nL 54.615293 100.889372 \nL 53.833236 100.370432 \nL 53.803729 100.350851 \nL 53.052418 99.852281 \nL 52.27283 99.334924 \nL 51.852486 99.055958 \nL 51.49447 98.818358 \nL 50.717335 98.302581 \nL 49.941417 97.787595 \nL 49.909177 97.766196 \nL 49.166718 97.273395 \nL 48.393229 96.759984 \n\" style=\"fill:none;stroke:#525252;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_66\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 148.050056 163.281842 \nL 140.984251 160.021967 \nL 133.163178 156.165716 \nL 125.605255 152.183488 \nL 118.299672 148.090776 \nL 110.36047 143.380221 \nL 101.836349 138.064682 \nL 90.303969 130.593515 \nL 70.521689 117.464103 \nL 62.84022 112.330506 \nL 62.84022 112.330506 \n\" style=\"fill:none;stroke:#9e9e9e;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 166.641335 103.179255 \nL 167.001815 103.762903 \nL 167.13719 103.982169 \nL 167.497409 104.565509 \nL 167.634122 104.786981 \nL 167.994135 105.370095 \nL 168.132141 105.593699 \nL 168.491999 106.176667 \nL 168.631255 106.402332 \nL 168.991009 106.985229 \nL 169.131473 107.212888 \nL 169.49117 107.795787 \nL 169.632804 108.025375 \nL 169.99249 108.608345 \nL 170.135257 108.839801 \nL 170.494975 109.422908 \nL 170.638839 109.656174 \nL 170.998632 110.239483 \nL 171.143559 110.474503 \nL 171.503466 111.058076 \nL 171.649424 111.294795 \nL 172.009485 111.87869 \nL 172.156443 112.117058 \nL 172.516694 112.701334 \nL 172.664623 112.941302 \nL 173.0251 113.526011 \nL 173.17397 113.767533 \nL 173.534708 114.352729 \nL 173.684493 114.59576 \nL 174.045525 115.181494 \nL 174.196199 115.42599 \nL 174.557556 116.012312 \nL 174.709095 116.258233 \nL 175.070808 116.84519 \nL 175.223186 117.092495 \nL 175.585285 117.680133 \nL 175.738481 117.928785 \nL 176.100994 118.517148 \nL 176.254985 118.767112 \nL 176.617941 119.356243 \nL 176.772705 119.607482 \nL 177.136131 120.197424 \nL 177.291647 120.449904 \nL 177.655569 121.040699 \nL 177.811818 121.294386 \nL 178.17626 121.886073 \nL 178.333223 122.140935 \nL 178.698212 122.733555 \nL 178.855867 122.989561 \nL 179.221427 123.583151 \nL 179.379757 123.84027 \nL 179.745912 124.43487 \nL 179.904899 124.693071 \nL 180.271672 125.288719 \nL 180.431296 125.547971 \nL 180.798712 126.144705 \nL 180.958954 126.404979 \nL 181.327037 127.002838 \nL 181.487878 127.264102 \nL 181.85665 127.863124 \nL 182.018073 128.125348 \nL 182.387558 128.725572 \nL 182.549542 128.988725 \nL 182.919765 129.590191 \n\" style=\"fill:none;stroke:#9e9e9e;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_67\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 95.183694 127.843637 \nL 95.171158 127.835583 \nL 94.315527 127.284326 \nL 93.461949 126.733351 \nL 92.961189 126.409446 \nL 92.610448 126.182635 \nL 91.760999 125.6322 \nL 90.913478 125.082149 \nL 90.766912 124.986842 \nL 90.067951 124.532423 \nL 89.224292 123.983128 \nL 88.598436 123.575063 \nL 88.382478 123.434281 \nL 87.542521 122.885869 \nL 86.70431 122.337984 \nL 86.452318 122.173052 \nL 85.867882 121.790591 \nL 85.033166 121.243748 \nL 84.326004 120.780021 \nL 84.200122 120.697484 \nL 83.368776 120.151775 \nL 82.539038 119.606695 \nL 82.217707 119.39541 \nL 81.710926 119.062222 \nL 80.884401 118.518388 \nL 80.125223 118.01854 \nL 80.059424 117.975221 \nL 79.23602 117.432697 \nL 78.414118 116.89087 \nL 78.047615 116.649108 \nL 77.593731 116.349727 \nL 76.774834 115.809286 \nL 75.983161 115.286582 \nL 75.957393 115.269569 \nL 75.14143 114.730554 \nL 74.326893 114.192282 \nL 73.931356 113.930789 \nL 73.513787 113.654743 \nL 72.702097 113.117946 \nL 71.891796 112.581909 \nL 71.890924 112.581332 \nL 71.082903 112.046614 \nL 70.275376 111.51209 \nL 69.861574 111.238105 \nL 69.469219 110.978329 \nL 68.664423 110.445335 \nL 67.860966 109.913122 \nL 67.8424 109.90082 \nL 67.058861 109.381676 \nL 66.258078 108.851015 \nL 65.83319 108.569397 \nL 65.45862 108.321135 \nL 64.660478 107.792037 \nL 63.863638 107.26373 \nL 63.833337 107.243637 \nL 63.068106 106.736204 \nL 62.273863 106.209471 \nL 61.842674 105.923474 \nL 61.480908 105.683526 \nL 60.689235 105.158372 \nL 59.898834 104.634011 \nL 59.860785 104.608766 \nL 59.109707 104.110438 \nL 58.321841 103.58766 \nL 57.88754 103.299459 \nL 57.535234 103.065673 \nL 56.749882 102.544478 \nL 55.965776 102.024076 \nL 55.922647 101.99545 \nL 55.182918 101.504463 \nL 54.401296 100.985643 \nL 53.966005 100.696692 \nL 53.62091 100.467614 \nL 52.841755 99.950373 \nL 52.063824 99.433924 \nL 52.017404 99.403105 \nL 51.287119 98.918261 \nL 50.51163 98.403387 \nL 50.076761 98.11465 \nL 49.737356 97.889299 \nL 48.964293 97.375996 \n\" style=\"fill:none;stroke:#555555;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_68\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 97.541677 129.605617 \nL 97.436758 129.538601 \nL 96.576833 128.987626 \nL 95.719079 128.436828 \nL 95.288703 128.15978 \nL 94.86354 127.886168 \nL 94.010159 127.335694 \nL 93.15881 126.785513 \nL 93.068229 126.726839 \nL 92.309583 126.235547 \nL 91.462311 125.685936 \nL 90.877502 125.30593 \nL 90.616986 125.136685 \nL 89.773611 124.58779 \nL 88.932063 124.039353 \nL 88.711895 123.89564 \nL 88.092391 123.491331 \nL 87.254503 122.943798 \nL 86.568708 122.49513 \nL 86.418362 122.396784 \nL 85.583993 121.850264 \nL 84.751291 121.304323 \nL 84.445576 121.103668 \nL 83.920284 120.758936 \nL 83.090919 120.214143 \nL 82.339984 119.720479 \nL 82.263155 119.669977 \nL 81.437021 119.126408 \nL 80.612434 118.583503 \nL 80.250726 118.345178 \nL 79.789408 118.041247 \nL 78.967915 117.499659 \nL 78.175765 116.977138 \nL 78.147916 116.95877 \nL 77.329437 116.418551 \nL 76.512415 115.879053 \nL 76.114476 115.61615 \nL 75.696859 115.340264 \nL 74.882751 114.802196 \nL 74.070058 114.26487 \nL 74.065323 114.261738 \nL 73.258803 113.728266 \nL 72.448938 113.192417 \nL 72.027956 112.913777 \nL 71.640468 112.657317 \nL 70.833381 112.12297 \nL 70.027654 111.589393 \nL 70.001287 111.571926 \nL 69.223299 111.056569 \nL 68.420285 110.524522 \nL 67.985059 110.236089 \nL 67.618613 109.993246 \nL 66.818275 109.462743 \nL 66.019253 108.933025 \nL 65.97855 108.906035 \nL 65.221555 108.40408 \nL 64.425159 107.875922 \nL 63.981556 107.581684 \nL 63.630065 107.348547 \nL 62.836266 106.821957 \nL 62.043748 106.296158 \nL 61.993588 106.262875 \nL 61.252518 105.771142 \nL 60.462559 105.246918 \nL 60.01449 104.949543 \nL 59.673869 104.723482 \nL 58.886443 104.200835 \nL 58.100272 103.678981 \nL 58.043922 103.641572 \nL 57.315358 103.157912 \nL 56.531689 102.637636 \nL 56.081762 102.338909 \nL 55.749264 102.118149 \nL 54.968077 101.599451 \nL 54.188122 101.081543 \nL 54.127771 101.041466 \nL 53.4094 100.56442 \nL 52.6319 100.048087 \nL 52.18185 99.749197 \nL 51.855622 99.532541 \nL 51.080562 99.017779 \nL 50.306712 98.503805 \nL 50.243827 98.462036 \nL 49.534074 97.990612 \n\" style=\"fill:none;stroke:#585858;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_69\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 99.931932 131.378263 \nL 99.710291 131.237648 \nL 98.845739 130.68727 \nL 97.983483 130.136953 \nL 97.6433 129.919194 \nL 97.123601 129.586633 \nL 96.265987 129.036399 \nL 95.41052 128.486355 \nL 95.392261 128.474582 \nL 94.557322 127.936396 \nL 93.706173 127.38671 \nL 93.175796 127.043479 \nL 92.85709 126.837281 \nL 92.010058 126.288119 \nL 91.164946 125.739336 \nL 90.987631 125.623972 \nL 90.321819 125.190873 \nL 89.480557 124.642831 \nL 88.825097 124.215229 \nL 88.641128 124.095235 \nL 87.803556 123.548063 \nL 86.967722 123.001411 \nL 86.68502 122.816273 \nL 86.133661 122.455249 \nL 85.301308 121.909627 \nL 84.564601 121.426241 \nL 84.470616 121.364582 \nL 83.641621 120.820082 \nL 82.814225 120.276205 \nL 82.462256 120.044635 \nL 81.988447 119.732932 \nL 81.16425 119.19029 \nL 80.375607 118.670721 \nL 80.341592 118.648313 \nL 79.520503 118.106969 \nL 78.700909 117.566318 \nL 78.303861 117.30424 \nL 77.882821 117.026347 \nL 77.066217 116.48707 \nL 76.251061 115.948514 \nL 76.245181 115.944627 \nL 75.437378 115.410653 \nL 74.625113 114.87353 \nL 74.199141 114.591732 \nL 73.814272 114.337136 \nL 73.004841 113.801478 \nL 72.196791 113.266576 \nL 72.164431 113.245146 \nL 71.390141 112.73241 \nL 70.584852 112.19901 \nL 70.140738 111.904758 \nL 69.780925 111.666368 \nL 68.978353 111.134489 \nL 68.177112 110.603386 \nL 68.127202 110.570294 \nL 67.377216 110.073045 \nL 66.578636 109.543484 \nL 66.123573 109.241661 \nL 65.781373 109.0147 \nL 64.98542 108.486692 \nL 64.190761 107.959472 \nL 64.129275 107.918671 \nL 63.397404 107.433027 \nL 62.605329 106.907371 \nL 62.144115 106.601249 \nL 61.814534 106.382499 \nL 61.025016 105.858412 \nL 60.236762 105.335116 \nL 60.167699 105.289262 \nL 59.449776 104.812602 \nL 58.664043 104.290878 \nL 58.199878 103.982647 \nL 57.879563 103.769942 \nL 57.096331 103.249792 \nL 56.314337 102.730433 \nL 56.240377 102.681308 \nL 55.533586 102.211857 \nL 54.754064 101.69407 \nL 54.289079 101.385193 \nL 53.97577 101.17707 \nL 53.198701 100.660854 \nL 52.42285 100.145425 \nL 52.345788 100.094227 \nL 51.648217 99.630778 \nL 50.874794 99.116916 \nL 50.41041 98.808367 \nL 50.102579 98.603836 \n\" style=\"fill:none;stroke:#5b5b5b;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_70\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 147.437018 162.844067 \nL 139.404798 159.07476 \nL 131.636863 155.174454 \nL 124.125752 151.155981 \nL 116.861336 147.033826 \nL 108.961222 142.29826 \nL 99.634 136.431563 \nL 86.546382 127.894122 \nL 62.299114 111.748709 \nL 62.299114 111.748709 \n\" style=\"fill:none;stroke:#9b9b9b;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 168.759237 102.775567 \nL 169.127456 103.368767 \nL 169.257896 103.57897 \nL 169.626071 104.172195 \nL 169.75766 104.38428 \nL 170.125838 104.977599 \nL 170.258539 105.191506 \nL 170.626762 105.784985 \nL 170.76054 106.000656 \nL 171.12885 106.594356 \nL 171.263671 106.811736 \nL 171.632109 107.40572 \nL 171.767941 107.624757 \nL 172.136545 108.219082 \nL 172.273358 108.439724 \nL 172.642163 109.034446 \nL 172.779928 109.256648 \nL 173.148971 109.85182 \nL 173.287659 110.075534 \nL 173.656974 110.671209 \nL 173.796559 110.896392 \nL 174.166177 111.492619 \nL 174.306635 111.71923 \nL 174.676588 112.316055 \nL 174.817893 112.544054 \nL 175.188212 113.141526 \nL 175.330342 113.370874 \nL 175.701054 113.969035 \nL 175.843987 114.199698 \nL 176.215121 114.798591 \nL 176.358835 115.030532 \nL 176.730418 115.630199 \nL 176.874893 115.863386 \nL 177.246951 116.463867 \nL 177.392167 116.698266 \nL 177.764725 117.2996 \nL 177.910663 117.535182 \nL 178.283747 118.137406 \nL 178.430389 118.37414 \nL 178.80402 118.977291 \nL 178.951349 119.21515 \nL 179.325552 119.819264 \nL 179.473551 120.058218 \nL 179.848347 120.663329 \nL 179.996999 120.903353 \nL 180.37241 121.509496 \nL 180.5217 121.750563 \nL 180.897748 122.357771 \nL 181.047659 122.599855 \nL 181.424364 123.208162 \nL 181.574882 123.451238 \nL 181.952265 124.060676 \nL 182.103374 124.30472 \nL 182.481455 124.915321 \nL 182.63314 125.160308 \nL 183.01194 125.772105 \nL 183.164185 126.01801 \nL 183.543724 126.631036 \nL 183.696514 126.877835 \nL 184.076812 127.492122 \n\" style=\"fill:none;stroke:#9b9b9b;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_71\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 102.360472 133.163417 \nL 101.992654 132.931861 \nL 101.123113 132.382422 \nL 100.256003 131.832921 \nL 100.030094 131.689252 \nL 99.391448 131.283251 \nL 98.529269 130.733569 \nL 97.743892 130.23156 \nL 97.66938 130.183948 \nL 96.811894 129.63429 \nL 95.956571 129.084804 \nL 95.496999 128.788831 \nL 95.103451 128.535452 \nL 94.252492 127.986271 \nL 93.403555 127.437379 \nL 93.282583 127.358981 \nL 92.556732 126.888695 \nL 91.711863 126.340356 \nL 91.097746 125.941103 \nL 90.868928 125.792375 \nL 90.027944 125.244736 \nL 89.188779 124.697551 \nL 88.938161 124.533872 \nL 88.351481 124.150776 \nL 87.515963 123.60448 \nL 86.800844 123.136366 \nL 86.682181 123.058701 \nL 85.85017 122.513405 \nL 85.019819 121.968683 \nL 84.683663 121.747919 \nL 84.191153 121.424511 \nL 83.364125 120.880925 \nL 82.583895 120.367695 \nL 82.538688 120.337962 \nL 81.714878 119.795587 \nL 80.892607 119.253872 \nL 80.500506 118.995361 \nL 80.07189 118.7128 \nL 79.2527 118.17239 \nL 78.434993 117.632675 \nL 78.431316 117.630246 \nL 77.618805 117.093623 \nL 76.804065 116.555286 \nL 76.375806 116.272172 \nL 75.990783 116.017655 \nL 75.178943 115.480738 \nL 74.368511 114.944558 \nL 74.332388 114.920648 \nL 73.55951 114.409095 \nL 72.751893 113.874382 \nL 72.300687 113.575542 \nL 71.945662 113.340413 \nL 71.14081 112.807192 \nL 70.337308 112.274735 \nL 70.279672 112.236529 \nL 69.535174 111.743028 \nL 68.734373 111.212091 \nL 68.269038 110.9035 \nL 67.934906 110.681922 \nL 67.136767 110.152521 \nL 66.339937 109.6239 \nL 66.268102 109.576233 \nL 65.544425 109.096046 \nL 64.750208 108.568976 \nL 64.276628 108.254642 \nL 63.957284 108.042684 \nL 63.16565 107.517172 \nL 62.375291 106.992447 \nL 62.294153 106.938571 \nL 61.586212 106.4685 \nL 60.798397 105.94534 \nL 60.320498 105.627951 \nL 60.011844 105.422965 \nL 59.22655 104.901373 \nL 58.442502 104.380571 \nL 58.355343 104.322669 \nL 57.659706 103.860549 \nL 56.878147 103.341316 \nL 56.398549 103.022668 \nL 56.097825 102.822867 \nL 55.318736 102.305202 \nL 54.540871 101.788325 \nL 54.44989 101.727865 \nL 53.764232 101.272228 \nL 52.98881 100.756916 \nL 52.509257 100.438211 \nL 52.214602 100.242387 \nL 51.441605 99.728639 \nL 50.669812 99.215673 \n\" style=\"fill:none;stroke:#5e5e5e;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_72\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 104.834252 134.963214 \nL 104.284795 134.620313 \nL 103.409888 134.072178 \nL 102.537551 133.523852 \nL 102.455071 133.471789 \nL 101.667973 132.975169 \nL 100.80087 132.426379 \nL 100.128194 131.999324 \nL 99.936225 131.877496 \nL 99.074109 131.328462 \nL 98.214282 130.779483 \nL 97.845499 130.543327 \nL 97.356819 130.230496 \nL 96.501627 129.681579 \nL 95.648573 129.132847 \nL 95.600419 129.101786 \nL 94.797782 128.584193 \nL 93.949038 128.0358 \nL 93.389759 127.673698 \nL 93.102348 127.487661 \nL 92.257712 126.939775 \nL 91.414986 126.392263 \nL 91.207571 126.257247 \nL 90.574238 125.845066 \nL 89.735352 125.298279 \nL 89.050862 124.851505 \nL 88.898288 124.751936 \nL 88.063081 124.206004 \nL 87.229602 123.660588 \nL 86.916719 123.455571 \nL 86.397889 123.115656 \nL 85.567881 122.571257 \nL 84.802101 122.068509 \nL 84.739523 122.027431 \nL 83.91286 121.48414 \nL 83.087788 120.941467 \nL 82.705624 120.689881 \nL 82.264326 120.399394 \nL 81.442441 119.857943 \nL 80.62473 119.318899 \nL 80.622083 119.317155 \nL 79.803294 118.77699 \nL 78.985991 118.237514 \nL 78.558775 117.955349 \nL 78.170185 117.698713 \nL 77.35586 117.1606 \nL 76.542973 116.623203 \nL 76.505838 116.598639 \nL 75.731554 116.086495 \nL 74.921546 115.55052 \nL 74.465468 115.248612 \nL 74.112953 115.01527 \nL 73.305766 114.480749 \nL 72.499953 113.94698 \nL 72.436424 113.904881 \nL 71.695533 113.413942 \nL 70.892467 112.881663 \nL 70.418334 112.567316 \nL 70.090755 112.35014 \nL 69.290392 111.819373 \nL 68.491354 111.289378 \nL 68.410386 111.235658 \nL 67.693654 110.760139 \nL 66.897263 110.231677 \nL 66.41229 109.909801 \nL 66.102181 109.703986 \nL 65.308404 109.177067 \nL 64.515913 108.650931 \nL 64.423503 108.589568 \nL 63.724718 108.125566 \nL 62.934798 107.600984 \nL 62.443803 107.274875 \nL 62.146151 107.077183 \nL 61.358775 106.554162 \nL 60.572655 106.031927 \nL 60.472819 105.965595 \nL 59.787797 105.510469 \nL 59.004186 104.989798 \nL 58.510383 104.661662 \nL 58.221819 104.46991 \nL 57.440696 103.950804 \nL 56.660803 103.432484 \nL 56.556235 103.362982 \nL 55.882146 102.914943 \nL 55.104711 102.398187 \nL 54.610247 102.0695 \nL 54.328499 101.882213 \nL 53.553505 101.36702 \nL 52.779721 100.852609 \nL 52.67223 100.781145 \nL 52.00715 100.338976 \nL 51.235781 99.826124 \n\" style=\"fill:none;stroke:#616161;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_73\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 146.83027 162.39743 \nL 138.821402 158.595974 \nL 131.07164 154.669758 \nL 123.57433 150.630586 \nL 116.320453 146.491693 \nL 108.427821 141.742207 \nL 99.104455 135.864254 \nL 86.015323 127.318057 \nL 61.756948 111.165521 \nL 61.756948 111.165521 \n\" style=\"fill:none;stroke:#999999;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 170.881204 102.370313 \nL 171.25807 102.974339 \nL 171.382753 103.174225 \nL 171.759761 103.778557 \nL 171.885433 103.980053 \nL 172.26262 104.584748 \nL 172.389251 104.787804 \nL 172.766655 105.392917 \nL 172.894216 105.597487 \nL 173.271871 106.203071 \nL 173.400335 106.409109 \nL 173.778275 107.015215 \nL 173.907615 107.222679 \nL 174.285872 107.829355 \nL 174.416064 108.038204 \nL 174.794669 108.645497 \nL 174.925688 108.855691 \nL 175.304671 109.463647 \nL 175.436494 109.675149 \nL 175.815884 110.283811 \nL 175.94849 110.496586 \nL 176.328313 111.105995 \nL 176.461682 111.32001 \nL 176.841965 111.930206 \nL 176.976076 112.145428 \nL 177.356845 112.75645 \nL 177.49168 112.972848 \nL 177.87296 113.584734 \nL 178.008499 113.802278 \nL 178.390313 114.415064 \nL 178.526541 114.633727 \nL 178.908911 115.247447 \nL 179.045811 115.467201 \nL 179.42876 116.08189 \nL 179.566315 116.302709 \nL 179.949865 116.9184 \nL 180.088059 117.140258 \nL 180.47223 117.756983 \nL 180.611051 117.979857 \nL 180.995863 118.597647 \nL 181.135294 118.821514 \nL 181.520768 119.440399 \nL 181.660796 119.665236 \nL 182.04695 120.285246 \nL 182.187562 120.511031 \nL 182.574415 121.132195 \nL 182.715598 121.358907 \nL 183.103167 121.981254 \nL 183.244908 122.208873 \nL 183.633213 122.832431 \nL 183.775499 123.060936 \nL 184.164557 123.685733 \nL 184.307376 123.915103 \nL 184.697204 124.541167 \nL 184.840544 124.771384 \nL 185.23116 125.398742 \n\" style=\"fill:none;stroke:#999999;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_74\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 107.361201 136.780097 \nL 106.587695 136.30203 \nL 105.707036 135.75558 \nL 104.926293 135.269274 \nL 104.82912 135.208775 \nL 103.954126 134.661459 \nL 103.08172 134.113927 \nL 102.551174 133.779718 \nL 102.211964 133.566126 \nL 101.344852 133.018063 \nL 100.480164 132.469931 \nL 100.226496 132.30856 \nL 99.618024 131.921623 \nL 98.758263 131.373286 \nL 97.945865 130.853829 \nL 97.900778 130.825009 \nL 97.045705 130.276675 \nL 96.192785 129.728506 \nL 95.704867 129.414151 \nL 95.34206 129.180468 \nL 94.493497 128.632586 \nL 93.646949 128.084986 \nL 93.496349 127.987343 \nL 92.802507 127.537589 \nL 91.960017 126.990525 \nL 91.317263 126.572454 \nL 91.11945 126.443816 \nL 90.280836 125.897437 \nL 89.444031 125.351506 \nL 89.163576 125.168245 \nL 88.609086 124.80598 \nL 87.775919 124.260923 \nL 87.032017 123.773707 \nL 86.944476 123.716381 \nL 86.114804 123.172309 \nL 85.286783 122.628807 \nL 84.92069 122.388247 \nL 84.460439 122.085851 \nL 83.635731 121.54347 \nL 82.826656 121.010961 \nL 82.812602 121.001712 \nL 81.9911 120.46053 \nL 81.171127 119.920004 \nL 80.749058 119.641569 \nL 80.3527 119.380117 \nL 79.535797 118.840885 \nL 78.720369 118.302342 \nL 78.68561 118.279369 \nL 77.906452 117.764456 \nL 77.093979 117.22728 \nL 76.635766 116.924176 \nL 76.282954 116.690806 \nL 75.473368 116.155038 \nL 74.665181 115.620003 \nL 74.598021 115.575521 \nL 73.858419 115.08568 \nL 73.053035 114.552101 \nL 72.571927 114.233252 \nL 72.249029 114.019262 \nL 71.446396 113.487164 \nL 70.645107 112.955827 \nL 70.556512 112.897061 \nL 69.845178 112.425234 \nL 69.046576 111.895407 \nL 68.55142 111.566823 \nL 68.2493 111.366342 \nL 67.453348 110.83804 \nL 66.658696 110.310514 \nL 66.55601 110.242331 \nL 65.865356 109.78375 \nL 65.073304 109.257765 \nL 64.570009 108.923485 \nL 64.282538 108.732555 \nL 63.493057 108.208118 \nL 62.704842 107.684465 \nL 62.592984 107.610141 \nL 61.917902 107.161584 \nL 61.132218 106.639487 \nL 60.624731 106.302219 \nL 60.34779 106.11817 \nL 59.564615 105.597632 \nL 58.782679 105.077878 \nL 58.664949 104.999615 \nL 58.001987 104.558902 \nL 57.222527 104.040709 \nL 56.713483 103.702266 \nL 56.444297 103.523297 \nL 55.667293 103.006663 \nL 54.891506 102.490813 \nL 54.770119 102.410093 \nL 54.11694 101.97574 \nL 53.343582 101.461447 \nL 52.834739 101.123043 \nL 52.571433 100.947933 \nL 51.800489 100.435195 \n\" style=\"fill:none;stroke:#646464;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_75\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 109.952544 138.617509 \nL 109.792004 138.519907 \nL 108.902337 137.976015 \nL 108.015546 137.431634 \nL 107.452444 137.084375 \nL 107.131723 136.886684 \nL 106.250897 136.341143 \nL 105.372797 135.795252 \nL 105.019949 135.574928 \nL 104.497567 135.248888 \nL 103.625075 134.702169 \nL 102.755146 134.155249 \nL 102.646096 134.086402 \nL 101.887974 133.607961 \nL 101.023279 133.06055 \nL 100.324519 132.616823 \nL 100.161032 132.513043 \nL 99.301323 131.965361 \nL 98.443895 131.417729 \nL 98.047532 131.163828 \nL 97.588823 130.870082 \nL 96.736025 130.32249 \nL 95.885358 129.775076 \nL 95.808216 129.725296 \nL 95.036948 129.227731 \nL 94.190584 128.680637 \nL 93.603194 128.300172 \nL 93.346263 128.133793 \nL 92.503998 127.587187 \nL 91.663636 127.04095 \nL 91.426838 126.886734 \nL 90.825244 126.495022 \nL 89.988712 125.949493 \nL 89.275823 125.483953 \nL 89.153991 125.404406 \nL 88.321128 124.859716 \nL 87.489986 124.315538 \nL 87.147502 124.091006 \nL 86.6606 123.771839 \nL 85.832917 123.228662 \nL 85.038581 122.706882 \nL 85.006873 122.686057 \nL 84.182524 122.143974 \nL 83.359758 121.602506 \nL 82.947881 121.331204 \nL 82.538592 121.061633 \nL 81.719002 120.521374 \nL 80.90093 119.981772 \nL 80.872715 119.963146 \nL 80.084421 119.442788 \nL 79.269392 118.904487 \nL 78.81242 118.602487 \nL 78.455852 118.366857 \nL 77.643788 117.829905 \nL 76.833156 117.293667 \nL 76.765155 117.248658 \nL 76.023984 116.758112 \nL 75.216218 116.223284 \nL 74.730389 115.90148 \nL 74.409859 115.689176 \nL 73.6049 115.155791 \nL 72.801308 114.623152 \nL 72.706951 114.560586 \nL 71.999103 114.09124 \nL 71.198245 113.560083 \nL 70.694408 113.225827 \nL 70.398735 113.029676 \nL 69.600568 112.500019 \nL 68.803718 111.97113 \nL 68.691997 111.896959 \nL 68.008199 111.442993 \nL 67.213983 110.915626 \nL 66.699384 110.573863 \nL 66.421069 110.389028 \nL 65.629455 109.863195 \nL 64.839119 109.338141 \nL 64.716061 109.256373 \nL 64.050073 108.813853 \nL 63.262295 108.290344 \nL 62.741777 107.944396 \nL 62.475783 107.767612 \nL 61.690536 107.245654 \nL 60.906537 106.724478 \nL 60.776183 106.637812 \nL 60.123795 106.204075 \nL 59.342292 105.684454 \nL 58.819092 105.336548 \nL 58.562028 105.165613 \nL 57.783 104.647547 \nL 57.005197 104.130265 \nL 56.870259 104.040516 \nL 56.228622 103.613757 \nL 55.453263 103.098029 \nL 54.929542 102.749657 \nL 54.67912 102.58308 \nL 53.906189 102.068906 \nL 53.134461 101.555512 \nL 52.996764 101.463903 \nL 52.36394 101.042891 \n\" style=\"fill:none;stroke:#666666;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_76\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 146.229047 161.942691 \nL 138.241675 158.11102 \nL 130.508721 154.160304 \nL 122.521244 149.819727 \nL 114.890673 145.421439 \nL 106.574839 140.364881 \nL 96.911078 134.222205 \nL 82.278388 124.61916 \nL 61.213704 110.580951 \nL 61.213704 110.580951 \n\" style=\"fill:none;stroke:#969696;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 173.007554 101.963573 \nL 173.393842 102.579473 \nL 173.512067 102.76801 \nL 173.898654 103.384454 \nL 174.017733 103.574371 \nL 174.404653 104.191407 \nL 174.52456 104.382663 \nL 174.911843 105.000337 \nL 175.032555 105.192894 \nL 175.42023 105.81125 \nL 175.541725 106.005071 \nL 175.929821 106.624153 \nL 176.052077 106.819203 \nL 176.440621 107.43905 \nL 176.563617 107.635296 \nL 176.952635 108.25595 \nL 177.076352 108.45336 \nL 177.465869 109.074857 \nL 177.590289 109.273401 \nL 177.98033 109.895779 \nL 178.105433 110.095428 \nL 178.496022 110.718721 \nL 178.621793 110.919448 \nL 179.012951 111.54369 \nL 179.139373 111.745469 \nL 179.531122 112.370694 \nL 179.65818 112.573498 \nL 180.050541 113.199737 \nL 180.178221 113.403544 \nL 180.571214 114.030829 \nL 180.6995 114.235615 \nL 181.093146 114.863974 \nL 181.222025 115.069718 \nL 181.616342 115.699181 \nL 181.745802 115.90586 \nL 182.140808 116.536456 \nL 182.270835 116.744051 \nL 182.666548 117.375806 \nL 182.797132 117.584298 \nL 183.193569 118.217238 \nL 183.324697 118.426608 \nL 183.721876 119.060761 \nL 183.853536 119.27099 \nL 184.251473 119.90638 \nL 184.383655 120.117451 \nL 184.782366 120.754104 \nL 184.91506 120.965999 \nL 185.314561 121.60394 \nL 185.447756 121.816643 \nL 185.848062 122.455896 \nL 185.981748 122.66939 \nL 186.382875 123.309979 \n\" style=\"fill:none;stroke:#969696;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_77\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 112.618878 140.478729 \nL 112.125963 140.1826 \nL 111.229683 139.641273 \nL 110.336395 139.099336 \nL 110.041856 138.919672 \nL 109.446329 138.556589 \nL 108.559289 138.01321 \nL 107.675107 137.46935 \nL 107.542675 137.387464 \nL 106.794041 136.924785 \nL 105.915773 136.379798 \nL 105.112253 135.87929 \nL 105.040237 135.834452 \nL 104.167641 135.288563 \nL 103.297627 134.74245 \nL 102.742318 134.39259 \nL 102.430256 134.196061 \nL 101.56554 133.649387 \nL 100.703241 133.102635 \nL 100.423054 132.924351 \nL 99.843483 132.555699 \nL 98.98611 132.008717 \nL 98.147756 131.472508 \nL 98.130999 131.461794 \nL 97.278311 130.914791 \nL 96.427768 130.367947 \nL 95.91245 130.035819 \nL 95.579409 129.82123 \nL 94.733217 129.274652 \nL 93.889032 128.72835 \nL 93.709652 128.611998 \nL 93.046947 128.182244 \nL 92.206812 127.63646 \nL 91.536163 127.200051 \nL 91.36859 127.091029 \nL 90.532323 126.545912 \nL 89.697857 126.001238 \nL 89.38824 125.798822 \nL 88.865242 125.456963 \nL 88.034405 124.913148 \nL 87.262321 124.407217 \nL 87.20528 124.369844 \nL 86.377928 123.826998 \nL 85.552218 123.284718 \nL 85.156742 123.024709 \nL 84.728177 122.742978 \nL 83.905769 122.201805 \nL 83.084931 121.66125 \nL 83.068386 121.650344 \nL 82.265716 121.121264 \nL 81.448025 120.581927 \nL 80.996451 120.283856 \nL 80.631871 120.043226 \nL 79.817237 119.505169 \nL 79.004071 118.967799 \nL 78.938668 118.924548 \nL 78.192409 118.431079 \nL 77.382185 117.895064 \nL 76.894418 117.572212 \nL 76.573402 117.359745 \nL 75.766053 116.825125 \nL 74.960097 116.291235 \nL 74.862279 116.226407 \nL 74.155558 115.75805 \nL 73.352391 115.225604 \nL 72.84173 114.886956 \nL 72.550595 114.693894 \nL 71.750167 114.162918 \nL 70.951075 113.632699 \nL 70.831858 113.55357 \nL 70.153337 113.103219 \nL 69.35692 112.574499 \nL 68.832254 112.226108 \nL 68.561822 112.046538 \nL 67.768042 111.519333 \nL 66.975554 110.9929 \nL 66.842319 110.904375 \nL 66.184373 110.467225 \nL 65.394473 109.942323 \nL 64.861744 109.588261 \nL 64.605852 109.418192 \nL 63.81851 108.894829 \nL 63.032427 108.372245 \nL 62.890124 108.277629 \nL 62.247612 107.85043 \nL 61.464048 107.329392 \nL 60.927229 106.972393 \nL 60.681732 106.809132 \nL 59.900663 106.289645 \nL 59.120826 105.770938 \nL 58.972779 105.672455 \nL 58.342227 105.253004 \nL 57.564854 104.735849 \nL 57.026601 104.377747 \nL 56.788702 104.219472 \nL 56.013772 103.703868 \nL 55.240052 103.189043 \nL 55.088495 103.088192 \nL 54.467546 102.674991 \nL 53.696242 102.161715 \nL 53.158331 101.803737 \nL 52.926139 101.649214 \n\" style=\"fill:none;stroke:#696969;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_78\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 115.369758 142.366738 \nL 114.473855 141.835248 \nL 113.570642 141.296833 \nL 112.70529 140.778491 \nL 112.670538 140.757685 \nL 111.773912 140.217478 \nL 110.88029 139.676641 \nL 110.130648 139.220799 \nL 109.989713 139.135141 \nL 109.102404 138.592785 \nL 108.217968 138.049926 \nL 107.634499 137.690152 \nL 107.336497 137.506486 \nL 106.458042 136.962424 \nL 105.58231 136.418001 \nL 105.206565 136.183374 \nL 104.709445 135.873092 \nL 103.839329 135.327805 \nL 102.971771 134.782307 \nL 102.837678 134.697637 \nL 102.10697 134.236428 \nL 101.24465 133.690408 \nL 100.521106 133.230853 \nL 100.384766 133.144289 \nL 99.527433 132.597971 \nL 98.672373 132.051695 \nL 98.249574 131.780783 \nL 97.819662 131.505399 \nL 96.96923 130.959139 \nL 96.120922 130.413051 \nL 96.015806 130.345195 \nL 95.274866 129.867023 \nL 94.430855 129.321233 \nL 93.816238 128.922979 \nL 93.588877 128.775691 \nL 92.74896 128.23037 \nL 91.910937 127.685412 \nL 91.645552 127.512503 \nL 91.074877 127.140757 \nL 90.240677 126.59649 \nL 89.50009 126.112638 \nL 89.408275 126.052662 \nL 88.577736 125.509217 \nL 87.748908 124.96628 \nL 87.377467 124.722641 \nL 86.921829 124.423816 \nL 86.096451 123.881863 \nL 85.274131 123.341422 \nL 85.2727 123.340481 \nL 84.450647 122.799609 \nL 83.630167 122.259346 \nL 83.189109 121.968663 \nL 82.81128 121.719674 \nL 81.993966 121.180607 \nL 81.178162 120.642193 \nL 81.119588 120.603503 \nL 80.363914 120.10439 \nL 79.551142 119.567263 \nL 79.064864 119.245707 \nL 78.739851 119.030803 \nL 77.930033 118.495014 \nL 77.121638 117.959933 \nL 77.023198 117.894738 \nL 76.314697 117.42553 \nL 75.509157 116.891848 \nL 74.993968 116.550388 \nL 74.705015 116.358882 \nL 73.902271 115.826631 \nL 73.100885 115.295123 \nL 72.976073 115.212311 \nL 72.300879 114.764336 \nL 71.502215 114.234298 \nL 70.969017 113.88034 \nL 70.704891 113.705007 \nL 69.908905 113.176459 \nL 69.114229 112.648674 \nL 68.972087 112.554245 \nL 68.320878 112.121636 \nL 67.528824 111.595364 \nL 66.984906 111.233896 \nL 66.738064 111.069856 \nL 65.948599 110.545108 \nL 65.160405 110.021134 \nL 65.006998 109.919134 \nL 64.373493 109.497922 \nL 63.587844 108.975484 \nL 63.038083 108.609859 \nL 62.803454 108.453818 \nL 62.020324 107.932921 \nL 61.238434 107.412803 \nL 61.077835 107.305958 \nL 60.457795 106.893453 \nL 59.678389 106.37488 \nL 59.126047 106.007351 \nL 58.900214 105.857083 \nL 58.12327 105.340056 \nL 57.347543 104.823809 \nL 57.182489 104.713956 \nL 56.573039 104.308332 \nL 55.799744 103.793631 \nL 55.247005 103.425709 \nL 55.027658 103.279704 \nL 54.256779 102.766548 \nL 53.487095 102.254167 \n\" style=\"fill:none;stroke:#6c6c6c;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_79\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 145.632696 161.480494 \nL 137.665185 157.62032 \nL 129.947811 153.646371 \nL 122.387428 149.519276 \nL 114.351508 144.871956 \nL 105.643317 139.553515 \nL 95.207224 132.888844 \nL 80.150087 122.981034 \nL 60.669387 109.994988 \nL 60.669387 109.994988 \n\" style=\"fill:none;stroke:#939393;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 175.138552 101.55541 \nL 175.534925 102.184049 \nL 175.646092 102.360387 \nL 176.042902 102.989772 \nL 176.154807 103.167293 \nL 176.55208 103.797466 \nL 176.664702 103.976138 \nL 177.062465 104.607137 \nL 177.175784 104.786928 \nL 177.574062 105.418791 \nL 177.68806 105.599672 \nL 178.086877 106.232434 \nL 178.201537 106.414376 \nL 178.600915 107.048073 \nL 178.71622 107.23105 \nL 179.116183 107.865714 \nL 179.232116 108.049699 \nL 179.632685 108.685364 \nL 179.749231 108.870332 \nL 180.150427 109.507029 \nL 180.267572 109.692958 \nL 180.669414 110.330715 \nL 180.787144 110.517582 \nL 181.189652 111.156431 \nL 181.307954 111.344214 \nL 181.711146 111.984181 \nL 181.830007 112.172861 \nL 182.233901 112.813973 \nL 182.35331 113.00353 \nL 182.757924 113.645815 \nL 182.877868 113.83623 \nL 183.283218 114.479713 \nL 183.403687 114.670968 \nL 183.80979 115.315673 \nL 183.930773 115.507752 \nL 184.337645 116.153704 \nL 184.459132 116.34659 \nL 184.866788 116.993813 \nL 184.988769 117.187489 \nL 185.397225 117.836006 \nL 185.51969 118.030458 \nL 185.92896 118.680292 \nL 186.0519 118.875505 \nL 186.461999 119.526677 \nL 186.585406 119.722637 \nL 186.996347 120.375169 \nL 187.120211 120.571863 \nL 187.532009 121.225776 \n\" style=\"fill:none;stroke:#939393;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_80\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 118.225733 144.287855 \nL 117.750094 144.011313 \nL 116.836485 143.476951 \nL 115.926054 142.941769 \nL 115.459825 142.666084 \nL 115.019033 142.405563 \nL 114.11539 141.868367 \nL 113.21485 141.330433 \nL 112.795551 141.078539 \nL 112.317634 140.791568 \nL 111.423658 140.251854 \nL 110.532676 139.711512 \nL 110.221213 139.521584 \nL 109.644925 139.170336 \nL 108.760216 138.628499 \nL 107.878364 138.086168 \nL 107.725672 137.991768 \nL 106.999636 137.543109 \nL 106.123715 136.999607 \nL 105.299285 136.486104 \nL 105.250515 136.45574 \nL 104.380278 135.911297 \nL 103.512618 135.36662 \nL 102.934153 135.002141 \nL 102.647594 134.821659 \nL 101.785238 134.276387 \nL 100.925292 133.73103 \nL 100.619984 133.536724 \nL 100.067885 133.185479 \nL 99.212868 132.639862 \nL 98.360101 132.094302 \nL 98.349837 132.087713 \nL 97.509765 131.548641 \nL 96.66157 131.003131 \nL 96.119912 130.653917 \nL 95.815549 130.457743 \nL 94.971701 129.912476 \nL 94.129852 129.367481 \nL 93.922641 129.233025 \nL 93.290097 128.822672 \nL 92.452293 128.278173 \nL 91.754579 127.823967 \nL 91.61639 127.734025 \nL 90.782447 127.190174 \nL 89.950297 126.646761 \nL 89.612274 126.425674 \nL 89.119991 126.103742 \nL 88.291461 125.561171 \nL 87.491863 125.03696 \nL 87.464632 125.019111 \nL 86.639579 124.477493 \nL 85.81616 123.936436 \nL 85.391918 123.657371 \nL 84.994401 123.395915 \nL 84.174275 122.855951 \nL 83.355709 122.3166 \nL 83.30917 122.285904 \nL 82.538762 121.777811 \nL 81.723334 121.239664 \nL 81.242771 120.922281 \nL 80.909434 120.702149 \nL 80.097052 120.165269 \nL 79.28613 119.629071 \nL 79.190567 119.565839 \nL 78.476707 119.093518 \nL 77.668716 118.558662 \nL 77.151833 118.216338 \nL 76.862158 118.024499 \nL 76.05703 117.491027 \nL 75.253287 116.958281 \nL 75.12523 116.87336 \nL 74.450956 116.426234 \nL 73.649991 115.89492 \nL 73.11016 115.536707 \nL 72.850389 115.364338 \nL 72.052152 114.834483 \nL 71.255242 114.305381 \nL 71.105769 114.206107 \nL 70.459681 113.777012 \nL 69.665434 113.249398 \nL 69.111597 112.881404 \nL 68.872499 112.722539 \nL 68.080877 112.19643 \nL 67.29054 111.671088 \nL 67.127083 111.562413 \nL 66.501503 111.1465 \nL 65.713742 110.622679 \nL 65.151883 110.249016 \nL 64.927252 110.099626 \nL 64.142036 109.577335 \nL 63.358072 109.055819 \nL 63.185621 108.941082 \nL 62.57537 108.535067 \nL 61.793912 108.015088 \nL 61.228039 107.63852 \nL 61.013695 107.495882 \nL 60.23472 106.977444 \nL 59.456969 106.459783 \nL 59.278879 106.341236 \nL 58.680451 105.942889 \nL 57.905152 105.42677 \nL 57.337948 105.049156 \nL 57.131068 104.911425 \nL 56.3582 104.396848 \nL 55.586534 103.883047 \nL 55.405062 103.762209 \nL 54.816076 103.370014 \nL 54.046815 102.857753 \n\" style=\"fill:none;stroke:#6f6f6f;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 201.128411 96.558059 \nL 201.129497 96.559672 \n\" style=\"fill:none;stroke:#6f6f6f;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_81\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 121.196454 146.24514 \nL 121.06006 146.167494 \nL 120.135706 145.637622 \nL 119.214577 145.106859 \nL 118.31377 144.585082 \nL 118.296692 144.575194 \nL 117.382561 144.042172 \nL 116.471616 143.508311 \nL 115.563854 142.97362 \nL 115.547219 142.963755 \nL 114.659748 142.437678 \nL 113.758765 141.900971 \nL 112.883434 141.376999 \nL 112.860893 141.363513 \nL 111.966538 140.824945 \nL 111.075192 140.285729 \nL 110.311085 139.821289 \nL 110.186889 139.745836 \nL 109.301885 139.205044 \nL 108.419754 138.663735 \nL 107.818278 138.292943 \nL 107.540586 138.121832 \nL 106.664457 137.579271 \nL 105.791047 137.036339 \nL 105.394412 136.788683 \nL 104.920504 136.492906 \nL 104.052724 135.949069 \nL 103.187497 135.405012 \nL 103.030084 135.30561 \nL 102.325029 134.860557 \nL 101.465048 134.315943 \nL 100.718188 133.84152 \nL 100.60749 133.771227 \nL 99.7525 133.226285 \nL 98.899776 132.681379 \nL 98.45183 132.394288 \nL 98.049393 132.136443 \nL 97.201298 131.591525 \nL 96.355318 131.046774 \nL 96.223369 130.961571 \nL 95.511588 130.502071 \nL 94.669903 129.957594 \nL 94.029051 129.542199 \nL 93.83024 129.413361 \nL 92.992645 128.869331 \nL 92.156936 128.325659 \nL 91.863859 128.134631 \nL 91.323183 127.782283 \nL 90.49129 127.239283 \nL 89.723794 126.737635 \nL 89.661185 126.696719 \nL 88.832946 126.154523 \nL 88.00641 125.612829 \nL 87.606734 125.350545 \nL 87.181616 125.071603 \nL 86.358522 124.530879 \nL 85.537048 123.99072 \nL 85.508945 123.972218 \nL 84.717266 123.451062 \nL 83.899053 122.912007 \nL 83.42941 122.602321 \nL 83.082425 122.373538 \nL 82.267368 121.835663 \nL 81.453813 121.298438 \nL 81.365435 121.240029 \nL 80.64181 120.761817 \nL 79.831277 120.225865 \nL 79.316195 119.88507 \nL 79.022216 119.690576 \nL 78.214626 119.155949 \nL 77.408452 118.622026 \nL 77.280047 118.536935 \nL 76.603726 118.088775 \nL 75.800395 117.556238 \nL 75.256277 117.19539 \nL 74.998455 117.024414 \nL 74.197909 116.493297 \nL 73.398713 115.962919 \nL 73.243857 115.86011 \nL 72.600892 115.433256 \nL 71.804407 114.904336 \nL 71.242226 114.530908 \nL 71.009253 114.37616 \nL 70.215435 113.848719 \nL 69.422918 113.322038 \nL 69.250719 113.207569 \nL 68.63172 112.796098 \nL 67.841814 112.270919 \nL 67.268913 111.889949 \nL 67.053194 111.746501 \nL 66.265864 111.222835 \nL 65.479798 110.69994 \nL 65.296369 110.577901 \nL 64.695008 110.177802 \nL 63.911475 109.656433 \nL 63.332774 109.271313 \nL 63.129193 109.135833 \nL 62.348166 108.615995 \nL 61.568373 108.096932 \nL 61.377828 107.970081 \nL 60.789824 107.578633 \nL 60.012502 107.061106 \nL 59.431298 106.674119 \nL 59.236404 106.544351 \nL 58.461532 106.028362 \nL 57.687869 105.513148 \nL 57.492974 105.383348 \nL 56.915423 104.9987 \nL 56.144181 104.485023 \nL 55.562683 104.097701 \nL 55.37414 103.972117 \nL 54.6053 103.459976 \n\" style=\"fill:none;stroke:#727272;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 198.931058 96.981186 \nL 199.464882 97.778168 \nL 199.474501 97.792528 \nL 200.009572 98.591379 \n\" style=\"fill:none;stroke:#727272;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_82\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 145.040657 161.011394 \nL 137.091553 157.124241 \nL 129.388647 153.128208 \nL 121.927438 149.032381 \nL 113.812606 144.319754 \nL 105.110377 138.988279 \nL 95.02066 132.537925 \nL 78.819035 121.87037 \nL 60.123944 109.407667 \nL 60.123944 109.407667 \n\" style=\"fill:none;stroke:#909090;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 177.274419 101.145877 \nL 177.681452 101.787968 \nL 177.785043 101.951404 \nL 178.192631 102.594415 \nL 178.296859 102.758867 \nL 178.705025 103.402833 \nL 178.809874 103.568275 \nL 179.21864 104.213229 \nL 179.324093 104.379634 \nL 179.733481 105.025609 \nL 179.839524 105.192953 \nL 180.249554 105.839979 \nL 180.356172 106.00824 \nL 180.766864 106.656345 \nL 180.874044 106.825501 \nL 181.285417 107.474715 \nL 181.393145 107.644744 \nL 181.805218 108.295095 \nL 181.913482 108.465977 \nL 182.326271 109.117491 \nL 182.435059 109.289208 \nL 182.848584 109.941911 \nL 182.957885 110.114444 \nL 183.37216 110.768362 \nL 183.481963 110.941694 \nL 183.897006 111.596849 \nL 184.0073 111.770964 \nL 184.423126 112.427381 \nL 184.533902 112.602262 \nL 184.950526 113.259964 \nL 185.061774 113.435597 \nL 185.479211 114.094606 \nL 185.590923 114.270976 \nL 186.009186 114.931313 \nL 186.121353 115.108406 \nL 186.540457 115.770093 \nL 186.65307 115.947897 \nL 187.073028 116.610953 \nL 187.18608 116.789454 \nL 187.606906 117.453901 \nL 187.720388 117.633087 \nL 188.142095 118.298943 \nL 188.256 118.478803 \nL 188.6786 119.146088 \n\" style=\"fill:none;stroke:#909090;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_83\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 124.305072 148.245761 \nL 123.469767 147.777015 \nL 122.537652 147.251063 \nL 121.608798 146.724163 \nL 121.291609 146.543027 \nL 120.683612 146.195952 \nL 119.761871 145.666638 \nL 118.843371 145.136413 \nL 118.407347 144.88312 \nL 117.928409 144.605015 \nL 117.016921 144.072507 \nL 116.108625 143.53915 \nL 115.639561 143.262055 \nL 115.203765 143.004729 \nL 114.302313 142.469275 \nL 113.403972 141.933061 \nL 112.975592 141.675884 \nL 112.508975 141.395883 \nL 111.617241 140.857817 \nL 110.728504 140.319107 \nL 110.403133 140.120783 \nL 109.843014 139.779534 \nL 108.960582 139.23927 \nL 108.081007 138.698496 \nL 107.910589 138.593161 \nL 107.204569 138.15697 \nL 106.330948 137.614977 \nL 105.48773 137.089852 \nL 105.460038 137.072614 \nL 104.592118 136.529636 \nL 103.72677 135.986415 \nL 103.126971 135.608496 \nL 102.864051 135.442901 \nL 102.004017 134.899048 \nL 101.146388 134.355102 \nL 100.817541 134.145791 \nL 100.291295 133.81095 \nL 99.438599 133.266713 \nL 98.588147 132.722525 \nL 98.552378 132.69956 \nL 97.740128 132.178222 \nL 96.894249 131.634057 \nL 96.327454 131.268541 \nL 96.050535 131.090008 \nL 95.209003 130.546061 \nL 94.369462 130.00238 \nL 94.135492 129.850511 \nL 93.53201 129.458877 \nL 92.696511 128.91567 \nL 91.972671 128.444284 \nL 91.8629 128.372811 \nL 91.031257 127.830232 \nL 90.201398 127.288087 \nL 89.835821 127.048876 \nL 89.373376 126.746329 \nL 88.547132 126.205006 \nL 87.722575 125.664192 \nL 87.720779 125.663012 \nL 86.8998 125.123806 \nL 86.07865 124.583976 \nL 85.626336 124.2863 \nL 85.259153 124.044677 \nL 84.441287 123.505923 \nL 83.624974 122.967779 \nL 83.549082 122.917697 \nL 82.810276 122.430189 \nL 81.997091 121.893234 \nL 81.488118 121.556908 \nL 81.185426 121.356906 \nL 80.375279 120.821204 \nL 79.566582 120.286179 \nL 79.441401 120.203303 \nL 78.75938 119.751793 \nL 77.953604 119.218098 \nL 77.408098 118.85661 \nL 77.149254 118.685091 \nL 76.346332 118.152767 \nL 75.544786 117.621164 \nL 75.386954 117.516437 \nL 74.744647 117.090255 \nL 73.945868 116.560073 \nL 73.377292 116.18256 \nL 73.148444 116.030618 \nL 72.352382 115.501883 \nL 71.55764 114.973897 \nL 71.378318 114.854727 \nL 70.764239 114.446639 \nL 69.972149 113.92013 \nL 69.389516 113.532763 \nL 69.181361 113.394373 \nL 68.391884 112.869357 \nL 67.603684 112.345107 \nL 67.410368 112.216499 \nL 66.816777 111.821603 \nL 66.031141 111.298863 \nL 65.44049 110.905802 \nL 65.246768 110.776887 \nL 64.463665 110.255665 \nL 63.681806 109.735216 \nL 63.479535 109.600553 \nL 62.901204 109.215525 \nL 62.121839 108.696603 \nL 61.52722 108.30065 \nL 61.343708 108.17845 \nL 60.566814 107.661059 \nL 59.791138 107.144441 \nL 59.583305 107.006005 \nL 59.016688 106.628587 \nL 58.243451 106.113502 \nL 57.647579 105.716541 \nL 57.471421 105.599187 \nL 56.700603 105.085636 \nL 55.93098 104.572856 \nL 55.719872 104.432191 \nL 55.162559 104.06084 \n\" style=\"fill:none;stroke:#757575;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 196.73965 97.403118 \nL 197.259598 98.183701 \nL 197.27969 98.213865 \nL 197.800836 98.996255 \nL 197.821045 99.026596 \nL 198.343397 99.810803 \nL 198.363721 99.841317 \nL 198.887286 100.627354 \n\" style=\"fill:none;stroke:#757575;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_84\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 127.575737 150.297227 \nL 126.839969 149.893399 \nL 125.896626 149.372615 \nL 124.956557 148.850841 \nL 124.40835 148.544633 \nL 124.02006 148.32781 \nL 123.087225 147.803446 \nL 122.157659 147.278117 \nL 121.387185 146.840185 \nL 121.231483 146.751716 \nL 120.309096 146.223887 \nL 119.389957 145.695131 \nL 118.498585 145.179593 \nL 118.474089 145.165431 \nL 117.562028 144.634308 \nL 116.653167 144.102317 \nL 115.747505 143.569466 \nL 115.729399 143.558738 \nL 114.845546 143.035305 \nL 113.946722 142.500353 \nL 113.065288 141.973164 \nL 113.051013 141.96463 \nL 112.158867 141.427742 \nL 111.269732 140.890187 \nL 110.49437 140.419171 \nL 110.383643 140.351938 \nL 109.500887 139.812743 \nL 108.621006 139.273015 \nL 108.004217 138.892914 \nL 107.744088 138.732678 \nL 106.870235 138.191647 \nL 105.999099 137.650231 \nL 105.58386 137.391002 \nL 105.130833 137.108298 \nL 104.265344 136.565934 \nL 103.402405 136.023338 \nL 103.223636 135.910452 \nL 102.54223 135.480327 \nL 101.684548 134.937138 \nL 100.916046 134.448943 \nL 100.829279 134.393842 \nL 99.976595 133.850291 \nL 99.126172 133.306767 \nL 98.654545 133.004451 \nL 98.278083 132.763207 \nL 97.432291 132.219644 \nL 96.588608 131.676239 \nL 96.431124 131.574522 \nL 95.747173 131.132873 \nL 94.907785 130.589718 \nL 94.241829 130.157925 \nL 94.070408 130.046803 \nL 93.235108 129.504072 \nL 92.401685 128.961694 \nL 92.081935 128.753204 \nL 91.570213 128.419603 \nL 90.740603 127.877876 \nL 89.947093 127.359024 \nL 89.912768 127.336584 \nL 89.086807 126.79564 \nL 88.26254 126.255195 \nL 87.835446 125.974796 \nL 87.440008 125.715213 \nL 86.619176 125.175719 \nL 85.799955 124.636787 \nL 85.743074 124.59932 \nL 84.982425 124.098347 \nL 84.166458 123.560502 \nL 83.668903 123.232248 \nL 83.352068 123.023239 \nL 82.539249 122.486559 \nL 81.727924 121.950524 \nL 81.610368 121.87279 \nL 80.918146 121.415087 \nL 80.109834 120.880311 \nL 79.566514 120.520638 \nL 79.302986 120.346195 \nL 78.497607 119.81273 \nL 77.693635 119.279966 \nL 77.535796 119.175311 \nL 76.891107 118.747867 \nL 76.089968 118.216476 \nL 75.517407 117.836547 \nL 75.290213 117.685794 \nL 74.491849 117.155811 \nL 73.694828 116.626562 \nL 73.51039 116.504041 \nL 72.899175 116.098023 \nL 72.104853 115.570221 \nL 71.514113 115.177587 \nL 71.311855 115.043159 \nL 70.520189 114.516825 \nL 69.729817 113.991246 \nL 69.527967 113.856985 \nL 68.940758 113.466404 \nL 68.152985 112.942317 \nL 67.551478 112.542077 \nL 67.36649 112.418987 \nL 66.581282 111.896402 \nL 65.79733 111.374585 \nL 65.584245 111.232725 \nL 65.014649 110.85352 \nL 64.233218 110.333218 \nL 63.625918 109.92881 \nL 63.453031 109.813682 \nL 62.674095 109.294902 \nL 61.896385 108.776893 \nL 61.676224 108.630232 \nL 61.119913 108.259643 \nL 60.344662 107.743161 \nL 59.734907 107.336901 \nL 59.570628 107.227447 \nL 58.797815 106.712493 \nL 58.026205 106.19831 \nL 57.801774 106.048742 \nL 57.255805 105.684889 \nL 56.486603 105.172235 \nL 55.876634 104.765683 \nL 55.718595 104.660348 \n\" style=\"fill:none;stroke:#787878;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 194.554138 97.823855 \nL 195.060427 98.588158 \nL 195.090798 98.634008 \nL 195.598233 99.400052 \nL 195.628762 99.44614 \nL 196.137352 100.213938 \nL 196.168034 100.260259 \nL 196.677787 101.029822 \nL 196.70862 101.07637 \nL 197.219545 101.847711 \nL 197.250525 101.894483 \nL 197.76263 102.667614 \n\" style=\"fill:none;stroke:#787878;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_85\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 144.452443 160.535869 \nL 136.520446 156.623103 \nL 128.479828 152.416658 \nL 120.465703 147.972249 \nL 112.390615 143.233722 \nL 103.723069 137.883494 \nL 92.837344 130.885708 \nL 75.112982 119.179359 \nL 59.577364 108.81899 \nL 59.577364 108.81899 \n\" style=\"fill:none;stroke:#8d8d8d;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 179.415344 100.735016 \nL 179.833535 101.391147 \nL 179.929099 101.541101 \nL 180.347949 102.198304 \nL 180.444063 102.34913 \nL 180.863591 103.007433 \nL 180.960243 103.159109 \nL 181.380469 103.818541 \nL 181.477644 103.971046 \nL 181.898585 104.631634 \nL 181.996272 104.784948 \nL 182.417947 105.446718 \nL 182.516133 105.600823 \nL 182.938559 106.263801 \nL 183.037234 106.418679 \nL 183.460427 107.082889 \nL 183.559579 107.238523 \nL 183.983555 107.903989 \nL 184.083175 108.060362 \nL 184.50795 108.727108 \nL 184.608027 108.884205 \nL 185.033615 109.552253 \nL 185.134142 109.710059 \nL 185.560558 110.37943 \nL 185.661524 110.537932 \nL 186.088782 111.208647 \nL 186.190179 111.36783 \nL 186.618293 112.03991 \nL 186.720113 112.199763 \nL 187.149096 112.873228 \nL 187.251333 113.033738 \nL 187.681197 113.708607 \nL 187.783842 113.869762 \nL 188.214601 114.546054 \nL 188.317646 114.707843 \nL 188.749312 115.385577 \nL 188.852752 115.54799 \nL 189.285336 116.227183 \nL 189.389165 116.390209 \nL 189.822679 117.07088 \n\" style=\"fill:none;stroke:#8d8d8d;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_86\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 131.037156 152.408478 \nL 130.247666 151.984943 \nL 129.292838 151.469712 \nL 128.341299 150.953444 \nL 127.690469 150.598121 \nL 127.393304 150.43591 \nL 126.449112 149.916878 \nL 125.508204 149.396834 \nL 124.570601 148.875766 \nL 124.511294 148.842555 \nL 123.636958 148.353077 \nL 122.706637 147.829363 \nL 121.77961 147.304654 \nL 121.486608 147.137655 \nL 120.856326 146.778545 \nL 119.936511 146.251296 \nL 119.019961 145.723097 \nL 118.595619 145.476964 \nL 118.107001 145.193661 \nL 117.197544 144.66307 \nL 116.291297 144.1316 \nL 115.824487 143.856153 \nL 115.388521 143.599017 \nL 114.489183 143.065357 \nL 113.592967 142.530913 \nL 113.15967 142.271001 \nL 112.700119 141.995466 \nL 111.81056 141.459093 \nL 110.924005 140.922055 \nL 110.588176 140.717475 \nL 110.040713 140.384122 \nL 109.1605 139.845466 \nL 108.283147 139.306284 \nL 108.097897 139.191823 \nL 107.408946 138.76632 \nL 106.537573 138.225865 \nL 105.677996 137.690692 \nL 105.668903 137.685033 \nL 104.803253 137.143545 \nL 103.940172 136.601803 \nL 103.321124 136.211794 \nL 103.079715 136.059759 \nL 102.221962 135.517345 \nL 101.366609 134.974829 \nL 101.016032 134.751678 \nL 100.513791 134.432094 \nL 99.66338 133.889252 \nL 98.815207 133.346451 \nL 98.755517 133.308123 \nL 97.96947 132.80352 \nL 97.125874 132.260713 \nL 96.535315 131.879796 \nL 96.284435 131.718016 \nL 95.445187 131.1754 \nL 94.607923 130.633043 \nL 94.34842 130.464553 \nL 93.772746 130.090855 \nL 92.939523 129.548949 \nL 92.190631 129.061093 \nL 92.108177 129.007389 \nL 91.278807 128.466088 \nL 90.451214 127.925217 \nL 90.059056 127.668516 \nL 89.625451 127.384726 \nL 88.801468 126.844657 \nL 87.979164 126.305092 \nL 87.94932 126.28548 \nL 87.15864 125.765945 \nL 86.339736 125.227346 \nL 85.860141 124.911574 \nL 85.522478 124.689273 \nL 84.706853 124.151734 \nL 83.892771 123.614799 \nL 83.788258 123.545796 \nL 83.080301 123.078411 \nL 82.26934 122.54265 \nL 81.732614 122.187806 \nL 81.459891 122.007512 \nL 80.651958 121.472989 \nL 79.845469 120.93914 \nL 79.691285 120.837007 \nL 79.040469 120.405922 \nL 78.236892 119.873388 \nL 77.663321 119.493095 \nL 77.434731 119.341539 \nL 76.633997 118.810363 \nL 75.834631 118.279904 \nL 75.647553 118.1557 \nL 75.036667 117.750133 \nL 74.240058 117.221082 \nL 73.643221 116.824576 \nL 73.444796 116.692756 \nL 72.650893 116.165141 \nL 71.858302 115.638271 \nL 71.649595 115.499488 \nL 71.067048 115.112122 \nL 70.277098 114.586718 \nL 69.666096 114.180245 \nL 69.488444 114.062062 \nL 68.701096 113.53814 \nL 67.915018 113.014979 \nL 67.692254 112.866688 \nL 67.130228 112.49256 \nL 66.346703 111.970898 \nL 65.72764 111.558675 \nL 65.564433 111.449998 \nL 64.78343 110.929845 \nL 64.003662 110.410461 \nL 63.771941 110.256093 \nL 63.225146 109.89183 \nL 62.447862 109.373963 \nL 61.824841 108.958834 \nL 61.671803 108.856862 \nL 60.896979 108.340516 \nL 60.123364 107.82494 \nL 59.886125 107.666816 \nL 59.350969 107.310123 \nL 58.579781 106.796071 \nL 57.955559 106.379955 \nL 57.809794 106.282785 \nL 57.041014 105.770257 \nL 56.273421 105.258497 \n\" style=\"fill:none;stroke:#7b7b7b;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 192.374472 98.243393 \nL 192.867329 98.991555 \nL 192.907775 99.052955 \nL 193.401724 99.802788 \nL 193.44237 99.864491 \nL 193.937421 100.616008 \nL 193.978261 100.678008 \nL 194.474423 101.431223 \nL 194.515454 101.493514 \nL 195.012736 102.24844 \nL 195.053955 102.311016 \nL 195.552366 103.067666 \nL 195.593768 103.130522 \nL 196.093316 103.888909 \nL 196.134899 103.952039 \nL 196.635593 104.712175 \n\" style=\"fill:none;stroke:#7b7b7b;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_87\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 143.867634 160.054331 \nL 135.446435 155.857874 \nL 127.332101 151.568366 \nL 119.009787 146.904461 \nL 110.972814 142.141831 \nL 101.489965 136.235387 \nL 89.023296 128.157167 \nL 67.516845 113.892335 \nL 59.029634 108.228959 \nL 59.029634 108.228959 \n\" style=\"fill:none;stroke:#8a8a8a;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 181.561483 100.322859 \nL 181.99127 100.993518 \nL 182.078412 101.129511 \nL 182.50895 101.801373 \nL 182.596566 101.938112 \nL 183.027871 102.611202 \nL 183.115951 102.74867 \nL 183.54804 103.423011 \nL 183.636573 103.56119 \nL 184.069461 104.236807 \nL 184.158436 104.375682 \nL 184.59214 105.052597 \nL 184.681548 105.192152 \nL 185.116081 105.870387 \nL 185.205913 106.010609 \nL 185.641291 106.690185 \nL 185.731538 106.831058 \nL 186.167774 107.511997 \nL 186.258427 107.65351 \nL 186.695535 108.33583 \nL 186.786587 108.477969 \nL 187.22458 109.161692 \nL 187.316023 109.304446 \nL 187.754914 109.989589 \nL 187.846741 110.132946 \nL 188.286542 110.819529 \nL 188.378746 110.963478 \nL 188.819469 111.651518 \nL 188.912043 111.796049 \nL 189.3537 112.485565 \nL 189.446639 112.630668 \nL 189.889241 113.321675 \nL 189.982538 113.467341 \nL 190.426097 114.159858 \nL 190.519747 114.306077 \nL 190.964272 115.000119 \n\" style=\"fill:none;stroke:#8a8a8a;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_88\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 134.731915 154.592728 \nL 134.664419 154.557651 \nL 133.694473 154.049528 \nL 132.72783 153.540313 \nL 131.764508 153.029996 \nL 131.172044 152.714068 \nL 130.804843 152.518272 \nL 129.849002 152.004991 \nL 128.896466 151.490646 \nL 127.947256 150.975223 \nL 127.807979 150.899016 \nL 127.002042 150.45811 \nL 126.060241 149.939853 \nL 125.121757 149.420547 \nL 124.621309 149.141775 \nL 124.186944 148.899874 \nL 123.255823 148.377822 \nL 122.328005 147.854756 \nL 121.587264 147.434651 \nL 121.40364 147.330543 \nL 120.483112 146.804841 \nL 119.565856 146.278171 \nL 118.690699 145.772895 \nL 118.651909 145.750507 \nL 117.741823 145.221353 \nL 116.834956 144.691299 \nL 115.931305 144.160351 \nL 115.917178 144.151991 \nL 115.031415 143.628025 \nL 114.134669 143.094884 \nL 113.251594 142.567245 \nL 113.241049 142.560947 \nL 112.351039 142.025785 \nL 111.464047 141.489936 \nL 110.681123 141.014667 \nL 110.580106 140.953372 \nL 109.699537 140.415813 \nL 108.821844 139.877705 \nL 108.192837 139.490257 \nL 107.947121 139.338968 \nL 107.075489 138.799497 \nL 106.206573 138.259629 \nL 105.775356 137.990498 \nL 105.340534 137.719224 \nL 104.477289 137.178357 \nL 103.616591 136.637249 \nL 103.418719 136.512313 \nL 102.758664 136.095704 \nL 101.903239 135.55396 \nL 101.115018 135.053256 \nL 101.050216 135.012106 \nL 100.199801 134.469962 \nL 99.35164 133.927839 \nL 98.858019 133.611396 \nL 98.505809 133.38567 \nL 97.662286 132.843475 \nL 96.820865 132.301433 \nL 96.639335 132.184162 \nL 95.981693 131.759415 \nL 95.144569 131.217593 \nL 94.454808 130.770261 \nL 94.309447 130.676009 \nL 93.476413 130.134586 \nL 92.645247 129.593511 \nL 92.299991 129.368321 \nL 91.816029 129.052715 \nL 90.988675 128.512268 \nL 90.170179 127.976896 \nL 90.163083 127.972256 \nL 89.339374 127.432571 \nL 88.517352 126.893381 \nL 88.063779 126.595479 \nL 87.697057 126.354648 \nL 86.878464 125.81639 \nL 86.061475 125.278689 \nL 85.976676 125.222809 \nL 85.246173 124.74147 \nL 84.432431 124.20484 \nL 83.907736 123.85852 \nL 83.620258 123.668786 \nL 82.809657 123.133304 \nL 82.000541 122.598463 \nL 81.854524 122.501861 \nL 81.192969 122.064211 \nL 80.386857 121.530614 \nL 79.815948 121.152483 \nL 79.582202 120.997672 \nL 78.779016 120.465372 \nL 77.977229 119.933768 \nL 77.790567 119.809934 \nL 77.176881 119.402822 \nL 76.377918 118.872578 \nL 75.77747 118.473923 \nL 75.58033 118.343039 \nL 74.784132 117.814189 \nL 73.989268 117.286071 \nL 73.775775 117.144168 \nL 73.195768 116.758656 \nL 72.403593 116.231972 \nL 71.78478 115.820439 \nL 71.612734 115.706024 \nL 70.823206 115.180795 \nL 70.034963 114.65632 \nL 69.803927 114.502554 \nL 69.248028 114.132575 \nL 68.462373 113.609579 \nL 67.832691 113.190337 \nL 67.677988 113.087336 \nL 66.894888 112.565832 \nL 66.113036 112.045092 \nL 65.87071 111.883665 \nL 65.332449 111.525098 \nL 64.553107 111.005863 \nL 63.917596 110.582405 \nL 63.775001 110.48739 \nL 62.998143 109.969666 \nL 62.222503 109.45271 \nL 61.973105 109.286468 \nL 61.448095 108.936508 \nL 60.674903 108.421069 \nL 60.036951 107.995753 \nL 59.902919 107.906394 \nL 59.132154 107.392473 \nL 58.362583 106.879321 \nL 58.108964 106.710193 \nL 57.594217 106.366925 \nL 56.827044 105.855291 \n\" style=\"fill:none;stroke:#7e7e7e;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 190.200593 98.661728 \nL 190.680261 99.393914 \nL 190.730563 99.470701 \nL 191.211267 100.204482 \nL 191.261813 100.281643 \nL 191.743562 101.017033 \nL 191.794348 101.094561 \nL 192.277152 101.831576 \nL 192.328172 101.909464 \nL 192.812041 102.648118 \nL 192.863292 102.726358 \nL 193.348236 103.466665 \nL 193.399712 103.54525 \nL 193.88574 104.287225 \nL 193.937438 104.36615 \nL 194.42456 105.109805 \nL 194.476475 105.189062 \nL 194.964699 105.934412 \nL 195.016828 106.013997 \nL 195.506164 106.761053 \n\" style=\"fill:none;stroke:#7e7e7e;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_89\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 143.285962 159.567047 \nL 134.41397 155.10452 \nL 125.840296 150.521561 \nL 117.560185 145.828634 \nL 109.55956 141.043811 \nL 100.110462 135.121256 \nL 87.672416 127.037692 \nL 64.352634 111.555633 \nL 58.480747 107.637573 \nL 58.480747 107.637573 \n\" style=\"fill:none;stroke:#878787;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 183.712971 99.909433 \nL 184.154741 100.595025 \nL 184.233112 100.716658 \nL 184.675715 101.403568 \nL 184.754493 101.525838 \nL 185.197943 102.214087 \nL 185.277119 102.336979 \nL 185.72143 103.026589 \nL 185.800996 103.150089 \nL 186.246182 103.84108 \nL 186.326129 103.965176 \nL 186.772204 104.657567 \nL 186.852525 104.782246 \nL 187.299501 105.476057 \nL 187.380187 105.601308 \nL 187.828078 106.296558 \nL 187.909123 106.422368 \nL 188.357941 107.119076 \nL 188.439338 107.245435 \nL 188.889094 107.943618 \nL 188.970836 108.070516 \nL 189.421542 108.770191 \nL 189.503624 108.897619 \nL 189.955292 109.598802 \nL 190.037706 109.726751 \nL 190.490347 110.42946 \nL 190.573089 110.557919 \nL 191.026713 111.26217 \nL 191.109778 111.391133 \nL 191.564396 112.096941 \nL 191.647778 112.226399 \nL 192.1034 112.933779 \n\" style=\"fill:none;stroke:#878787;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_90\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 138.724588 156.869967 \nL 130.405959 152.536894 \nL 121.691634 147.73193 \nL 113.348593 142.864172 \nL 105.013794 137.752973 \nL 94.012376 130.718593 \nL 77.718633 119.993855 \nL 57.379468 106.450734 \nL 57.379468 106.450734 \n\" style=\"fill:none;stroke:#818181;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 188.032434 99.078853 \nL 188.499176 99.795259 \nL 188.559099 99.88724 \nL 189.026814 100.605157 \nL 189.08703 100.697591 \nL 189.55573 101.417037 \nL 189.616234 101.509913 \nL 190.085929 102.230904 \nL 190.146715 102.324215 \nL 190.617417 103.046767 \nL 190.678478 103.140503 \nL 191.150198 103.864632 \nL 191.21153 103.958785 \nL 191.684277 104.684506 \nL 191.745875 104.779069 \nL 192.219661 105.506397 \nL 192.281519 105.601361 \nL 192.756352 106.330311 \nL 192.818467 106.425671 \nL 193.294358 107.156256 \nL 193.356725 107.252004 \nL 193.833682 107.984239 \nL 193.896297 108.080369 \nL 194.374331 108.814267 \n\" style=\"fill:none;stroke:#818181;stroke-width:1.5;\"/>\n   </g>\n   <g id=\"Line3DCollection_91\">\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 142.707214 159.074228 \nL 133.850584 154.587034 \nL 125.288476 149.98424 \nL 117.017192 145.275107 \nL 108.384774 140.0852 \nL 99.576276 134.544557 \nL 86.321666 125.916422 \nL 61.003264 109.094848 \nL 57.930699 107.044828 \nL 57.930699 107.044828 \n\" style=\"fill:none;stroke:#848484;stroke-width:1.5;\"/>\n    <path clip-path=\"url(#p8c51fab2ad)\" d=\"M 185.869922 99.494759 \nL 186.324022 100.195618 \nL 186.393309 100.302563 \nL 186.848315 101.004842 \nL 186.91795 101.112326 \nL 187.373875 101.816044 \nL 187.44385 101.924056 \nL 187.900707 102.629232 \nL 187.971015 102.73776 \nL 188.428815 103.444411 \nL 188.499449 103.553446 \nL 188.958205 104.26159 \nL 189.029158 104.37112 \nL 189.488881 105.080774 \nL 189.560148 105.190791 \nL 190.02085 105.901972 \nL 190.092425 106.012466 \nL 190.554116 106.72519 \nL 190.625992 106.836152 \nL 191.088684 107.550436 \nL 191.160857 107.661858 \nL 191.624559 108.377716 \nL 191.697024 108.48959 \nL 192.161747 109.207037 \nL 192.234499 109.319357 \nL 192.700253 110.038408 \nL 192.773287 110.151166 \nL 193.240081 110.871836 \n\" style=\"fill:none;stroke:#848484;stroke-width:1.5;\"/>\n   </g>\n  </g>\n </g>\n <defs>\n  <clipPath id=\"p8c51fab2ad\">\n   <rect height=\"217.44\" width=\"217.44\" x=\"7.2\" y=\"7.2\"/>\n  </clipPath>\n </defs>\n</svg>\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Cross Entropy Function is known as **Maximum Likelihood Function for Logistic Regression**. (Maximum Likelihood Function: 최대 가능도 함수; 가장 그럴싸 하다)\n",
    "\n",
    "\n",
    "## Derivation of MLF for Multiple Logistic Regression\n",
    "\n",
    "Cross Entropy 함수는 Logistic Regression의 Maximum Likelihood 함수다.\n",
    "최대 가능도 함수(Maximum Likelihood function)에 대해 알아보자.\n",
    "\n",
    "$Y_i = \\frac{1}{ 1+exp( - {\\beta}_0 - {\\beta}_1 x_i + \\epsilon ) }$의 식에서 $Y_i$는 0 혹은 1의 값을 갖는 확률변수다.\n",
    "\n",
    "그러므로 $Y_i \\sim Bernoulli(p_i)$이다. 여기서, $p_i=Pr(Y_i = 1)$ 이고 확률질량함수(P.M.F.)는 아래와 같다.\n",
    "\n",
    "$$f(y)= P(Y=y) = {p_i}^y (1 - p_i  )^{1-y}$$\n",
    "\n",
    "\n",
    "만약, $Y_i|X_i = [y_1 , y_2 , \\cdots , y_n ]$ 이 관측되었다면 이렇게 관측될 확률은 아래와 같다.\n",
    "\n",
    "\n",
    "$$\\prod_{i=1}^{n} {p_i}^{y_i}(1-p_i)^{1-y_i}$$\n",
    "\n",
    "\n",
    "이 수식을 미지 모수 $p_i$에 대한 최대 가능도 함수라고 한다.\n",
    "위 수식에서 $y_i$ 는 주어진 값이고 미지수는 오직 $p_i$ 뿐이다.\n",
    "\n",
    "이 함수를 최대화 하는 $p_i$ 가 가장 관측값을 잘 설명하는 값이라고 생각하는 것이 MLE 추정(Maximum Likelihood\n",
    "Estimation)이다.\n",
    "\n",
    "$p_i$ 는 $y_i$ 에 대한 추정값으로 $p_i>0.5$ $\\rightarrow$ $y_i =1$ 아니면 $y_i=0$이 되므로 아래와 같은 식이 성립한다.\n",
    "\n",
    "\n",
    "$$p_i=\\frac{1}{1+exp(-\\hat{\\beta_0}-\\hat{\\beta_1}x_i)}, \\quad L(p_i)=\\prod_{i=1}^{n} {p_i}^{y_i}(1-p_i)^{1-y_i}$$\n",
    "\n",
    "\n",
    "이 식을 최대화 하는 $\\beta_0$, $\\beta_1$이 우리가 구하고자 하는 미지수이고 이를 MLE(Maximum Likelihood Estimator)라고\n",
    "한다. Likelihood 함수에 로그를 취하면, 아래와 같다.\n",
    "\n",
    "\n",
    "$$ln L(\\beta_0,\\beta_1) = \\sum_{i=1}^{n} \\Big[ y_i ln\\frac{1}{1+exp(-\\hat{\\beta_0}-\\hat{\\beta_1}x_i)} + (1-y_i)ln(1-\\frac{1}{1+exp(-\\hat{\\beta_0}-\\hat{\\beta_1}x_i)}) \\Big]$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$= \\sum_{i=1}^{n} \\Big[ y_i lnp_i + (1-y_i)ln(1-p_i) \\Big]$$\n",
    "\n",
    "\n",
    "이 식에 “-1”을 곱한 식이 Cross Entropy 함수다.\n",
    "최대가능도 함수를 최대화하는 것이나 Cross Entropy 함수를 최소화하는 것이나 같은 것이다.\n",
    "이 함수를 최소화하는 $\\beta_0$, $\\beta_1$ 를 구하면 MLE가 된다."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Gradient Descent Algorithm:  경사하강법\n",
    "\n",
    "$$w:=w-\\eta \\nabla Q_{i}(w)$$\n",
    "\n",
    "which can be rewritten to:\n",
    "\n",
    "$$B := B - \\eta \\frac{\\partial}{\\partial B} Cost(W,B)$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$W := W - \\eta \\frac{\\partial}{\\partial W} Cost(W,B)$$\n",
    "\n",
    "$B$: Bias<br>\n",
    "$W$: Weight<br>\n",
    "$Q(W)$: Cost Function<br>\n",
    "$Cost(W,B)$: Cost Function<br>\n",
    "$\\eta$: learning rate\n"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Assignment 3\n",
    "* For following Cost Function (Cross Entropy Function), derive partial derivative function for bias $b$ and weight $w$\n",
    "$ Cost(w,b) = -\\sum \\Big[ y_i ln(S(wx_i+b)) +(1-y_i)ln(1-S(wx_i+b)) \\Big]$\n",
    "\n",
    "$pf)$\n",
    "\n",
    "$$S(wx_i+b) = \\frac{1}{1+exp(-wx_i-b)}$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$\\frac{\\partial}{\\partial b} S(wx_i+b) = \\frac{exp(-wx_i-b)}{1+exp(-wx_i-b)} = S(wx_i+b)(1-S(wx_i+b))$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$\\frac{\\partial}{\\partial w} S(wx_i+b) = \\frac{exp(-wx_i-b)x_i}{1+exp(-wx_i-b)} = S(wx_i+b)(1-S(wx_i+b))x_i$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$Thus,$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$ \\frac {\\partial }{\\partial b} y_i ln(S(wx_i+b)) = y_i(1-S(wx_i+b))$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$ \\frac {\\partial }{\\partial b} (1-y_i)ln(1-S(wx_i+b)) =-(1- y_i)S(wx_i+b))$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$ \\frac {\\partial }{\\partial w} y_i ln(S(wx_i+b)) = y_i(1-S(wx_i+b))x_i$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$ \\frac {\\partial }{\\partial w} (1-y_i)ln(1-S(wx_i+b)) =-(1- y_i)S(wx_i+b))x_i$$\n",
    "\n",
    "<br>\n",
    "\n",
    "$In \\  conclusion,$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$ \\frac {\\partial }{\\partial b}Cost(w,b) =  -\\sum \\Big[y_i - S(wx_i+b)\\Big] $$\n",
    "\n",
    "<br>\n",
    "\n",
    "$$ \\frac {\\partial }{\\partial w}Cost(w,b) =  -\\sum \\Big[y_i - S(wx_i+b)\\Big] x_i$$"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "source": [
    "# Assignment 4\n",
    "\n",
    "# For x = np.array([1,2,3,4,5,6]) and y = np.array([0,0,0,1,1,1]) \n",
    "# Find bias b and weight w using Gradient Descent Algorithm\n",
    "\n",
    "def sigmoid(x):\n",
    "    return 1/(1+np.exp(-x))\n",
    "\n",
    "def deriv(bw): # derivatives: 도함수 / bw=[bias, weight]\n",
    "    partial_b = (-1) * np.sum(y - sigmoid(bw[0] + bw[1]*x)) \n",
    "    partial_w = (-1) * np.sum((y - sigmoid(bw[0] + bw[1]*x))*x)\n",
    "    return np.array([partial_b, partial_w])\n",
    "\n",
    "x = np.array([1,2,3,4,5,6])\n",
    "y = np.array([0,0,0,1,1,1])\n",
    "bw = np.array([0.5,0.5]) # random initial value\n",
    "\n",
    "np.set_printoptions(suppress=True, precision=3)\n",
    "alpha = 0.1 # learning rate\n",
    "for i in range(2001):\n",
    "    bw = bw - alpha * deriv(bw)\n",
    "    if i % 100 == 0: \n",
    "        print(\"%d of 2000 | Bias: %g, Weight: %g\" %(i,cof[0],cof[1]))\n",
    "        yhat = sigmoid(bw[0] + bw[1]*x)\n",
    "        print(yhat)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "0 of 2000 | Bias: -15.3545, Weight: 4.43019\n",
      "[0.585 0.602 0.619 0.635 0.652 0.668]\n",
      "100 of 2000 | Bias: -15.3545, Weight: 4.43019\n",
      "[0.045 0.155 0.414 0.731 0.913 0.976]\n",
      "200 of 2000 | Bias: -15.3545, Weight: 4.43019\n",
      "[0.013 0.076 0.341 0.764 0.953 0.992]\n",
      "300 of 2000 | Bias: -15.3545, Weight: 4.43019\n",
      "[0.006 0.046 0.298 0.787 0.97  0.996]\n",
      "400 of 2000 | Bias: -15.3545, Weight: 4.43019\n",
      "[0.003 0.031 0.268 0.806 0.979 0.998]\n",
      "500 of 2000 | Bias: -15.3545, Weight: 4.43019\n",
      "[0.002 0.022 0.244 0.821 0.985 0.999]\n",
      "600 of 2000 | Bias: -15.3545, Weight: 4.43019\n",
      "[0.001 0.017 0.226 0.833 0.988 0.999]\n",
      "700 of 2000 | Bias: -15.3545, Weight: 4.43019\n",
      "[0.001 0.013 0.21  0.844 0.991 1.   ]\n",
      "800 of 2000 | Bias: -15.3545, Weight: 4.43019\n",
      "[0.    0.01  0.196 0.853 0.993 1.   ]\n",
      "900 of 2000 | Bias: -15.3545, Weight: 4.43019\n",
      "[0.    0.008 0.185 0.862 0.994 1.   ]\n",
      "1000 of 2000 | Bias: -15.3545, Weight: 4.43019\n",
      "[0.    0.007 0.174 0.869 0.995 1.   ]\n",
      "1100 of 2000 | Bias: -15.3545, Weight: 4.43019\n",
      "[0.    0.006 0.165 0.875 0.996 1.   ]\n",
      "1200 of 2000 | Bias: -15.3545, Weight: 4.43019\n",
      "[0.    0.005 0.157 0.881 0.997 1.   ]\n",
      "1300 of 2000 | Bias: -15.3545, Weight: 4.43019\n",
      "[0.    0.004 0.15  0.887 0.997 1.   ]\n",
      "1400 of 2000 | Bias: -15.3545, Weight: 4.43019\n",
      "[0.    0.003 0.143 0.892 0.998 1.   ]\n",
      "1500 of 2000 | Bias: -15.3545, Weight: 4.43019\n",
      "[0.    0.003 0.137 0.896 0.998 1.   ]\n",
      "1600 of 2000 | Bias: -15.3545, Weight: 4.43019\n",
      "[0.    0.003 0.131 0.9   0.998 1.   ]\n",
      "1700 of 2000 | Bias: -15.3545, Weight: 4.43019\n",
      "[0.    0.002 0.126 0.904 0.998 1.   ]\n",
      "1800 of 2000 | Bias: -15.3545, Weight: 4.43019\n",
      "[0.    0.002 0.121 0.908 0.999 1.   ]\n",
      "1900 of 2000 | Bias: -15.3545, Weight: 4.43019\n",
      "[0.    0.002 0.117 0.911 0.999 1.   ]\n",
      "2000 of 2000 | Bias: -15.3545, Weight: 4.43019\n",
      "[0.    0.002 0.113 0.914 0.999 1.   ]\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Normalization\n",
    "\n",
    "Cost함수에서 Weight와 X를 곱하는 연산이 수행될때, X와 W의 Scale 조화가 필요하다. X의 Scale에 따라 W의 Scale을 조절하기는 힘드므로, X를 평균 0, 분산 1로 표준화하거나, 또는 0~1 범위로 압축하는 Scaling을 사용한다.\n",
    "\n",
    "$$Z_i=\\frac{X_i-\\overline{X}}{S_X}$$\n",
    "$$Z_i=\\frac{X_i-X_{min}}{X_{max}-X_{min}}$$"
   ],
   "metadata": {}
  }
 ]
}