08_Plate_Junctions.ipynb

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    "$\n",
    "\\newcommand{\\dd}{\\text{d}}\n",
    "\\newcommand{\\e}{\\operatorname{e}}\n",
    "\\newcommand{\\Fc}{\\underline F}\n",
    "\\newcommand{\\Hc}{\\underline H}\n",
    "\\newcommand{\\Xc}{\\underline X}\n",
    "\\newcommand{\\Yc}{\\underline Y}\n",
    "\\newcommand{\\Zc}{\\underline Z}\n",
    "\\newcommand{\\xic}{\\underline \\xi}\n",
    "\\newcommand{\\vc}{\\underline v}\n",
    "\\newcommand{\\pc}{\\underline p}\n",
    "\\newcommand{\\xiv}{\\pmb{\\xi}}\n",
    "\\newcommand{\\Psiv}{\\pmb{\\Psi}}\n",
    "\\newcommand{\\xivc}{\\underline \\xiv}\n",
    "\\newcommand{\\xv}{\\mathbf{x}}\n",
    "\\newcommand{\\jj}{\\operatorname{j}}\n",
    "$"
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    "# 8 Transmission over Plate Junctions\n",
    "## 8.1 Two Plates with different thickness\n",
    "![](tikzfig/plate_junction_L.svg)\n",
    "* wave transmission over any interface or junction can be studied in terms of the transmission coefficient\n",
    "\\begin{equation}\\label{eq:tau}\n",
    "\\tau = \\frac{P_T}{P_I}\n",
    "\\end{equation}\n",
    "where $P_T$ is the power transmitted and $P_I$ is the incident power\n",
    "* power in a wave\n",
    "\\begin{equation}\\label{eq:power}\n",
    "P = \\frac12\\Re(\\vc^*\\Fc) = \\frac12\\Re(\\vc^*\\Zc\\vc)\n",
    "\\end{equation}\n",
    "where $\\vc$ and $\\Zc$ can also be vector and matrix, respectively\n",
    "\n",
    "#### L-Waves\n",
    "* junction of two plates in the same plane\n",
    "* plane L-waves with wave front parallel to junction (perpendicular incidence)\n",
    "* three waves:\n",
    "  * incident wave on plate 1\n",
    "  * reflected wave on plate 1\n",
    "  * transmitted wave on plate 2\n",
    "* impedance is similar to beam:\n",
    "\\begin{equation}\\label{eq:ZLi}\n",
    "Z_{LI}=m'' c_{LI}\n",
    "\\end{equation}\n",
    "* junction at $x=0$:\n",
    "\\begin{gather}\n",
    "\\vc_1=\\vc_{1+}\\e^{-\\jj k_{L1} x} + \\vc_{1-}\\e^{\\jj k_{L1} x}\\\\\n",
    "\\vc_2=\\vc_{2+}\\e^{-\\jj k_{L2} x}\\\\\n",
    "\\Fc_1 = - \\left(\\Zc_{LI1}\\vc_{1+}\\e^{-\\jj k_{L1} x} - \\Zc_{LI1} \\vc_{1-}\\e^{\\jj k_{L1} x}\\right)\\\\\n",
    "\\Fc_2= \\Zc_{LI2}\\vc_{2+}\\e^{-\\jj k_{L2} x}\n",
    "\\end{gather}\n",
    "* at junction:\n",
    "  * velocities of all members are equal ($\\vc_1(0)=\\vc_2(0)$)\n",
    "  * sum of all forces must be zero"
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      "text/latex": [
       "$\\displaystyle \\frac{2 Z_{LI1} v_{1+}}{Z_{LI1} + Z_{LI2}}$"
      ],
      "text/plain": [
       "2*Z_LI1*v_1+/(Z_LI1 + Z_LI2)"
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     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{4.0 Z_{LI1} Z_{LI2}}{\\left(Z_{LI1} + Z_{LI2}\\right)^{2}}$"
      ],
      "text/plain": [
       "4.0*Z_LI1*Z_LI2/(Z_LI1 + Z_LI2)**2"
      ]
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   "source": [
    "import sympy as sy\n",
    "ZL1, ZL2 = sy.symbols('Z_LI1 Z_LI2',positive=True) \n",
    "v11, v12, v21 = sy.symbols('v_1+ v_1- v_2+')\n",
    "# v, F at the junction x=0\n",
    "v1 = v11 + v12\n",
    "F1 = -ZL1*v11 + ZL1*v12\n",
    "v2 = v21\n",
    "F2 = ZL2*v21\n",
    "# system of two equations, solve for unkown amplitude\n",
    "# transmitted and reflected waves\n",
    "sd = sy.solve([sy.Eq(v1,v2),sy.Eq(F1+F2,0)],v21,v12,dict=True)\n",
    "# amplitude of transmitted wave = ampl. at junction\n",
    "v = sd[0][v21]\n",
    "display(v)\n",
    "# transmitted and incident power\n",
    "PT = 1/2 * sy.re(v * ZL2 * sy.conjugate(v)) \n",
    "PI = 1/2 * sy.re(v11 * ZL1 * sy.conjugate(v11)) \n",
    "# transmission coefficient\n",
    "tau = sy.simplify(PT/PI)\n",
    "display(tau)"
   ]
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   "source": [
    "* the transmission coefficient depends on the impedances\n",
    "* sound reduction index\n",
    "\\begin{equation}\\label{eq:R}\n",
    "R = 10 \\lg \\frac{1}{\\tau}\\;\\text{dB}\n",
    "\\end{equation}\n",
    "* plot for different properties (ratio of thicknesses, ratio of wave speeds, ratio of densities) of both plates"
   ]
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       "interactive(children=(FloatSlider(value=1.0, description='cL_2', max=10.0, min=0.1), FloatSlider(value=1.0, de…"
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as pl\n",
    "import ipywidgets as ipw\n",
    "%matplotlib inline\n",
    "\n",
    "tau_ = sy.lambdify([ZL1,ZL2],tau)\n",
    "\n",
    "@ipw.interact(cL_2=(0.1,10),rho_2=(0.1,10))\n",
    "def plot_RL(cL_2=1.0,rho_2=1.0):\n",
    "    h2 = np.logspace(-1,1,20)\n",
    "    ZL2_ = cL_2 * rho_2 * h2\n",
    "    pl.semilogx(h2,-10*np.log10(tau_(1,ZL2_)))\n",
    "    pl.xlabel(r'$\\frac{h_2}{h_1}$')\n",
    "    pl.ylabel('R/dB')\n"
   ]
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   "source": [
    "* similar approach can be used for other wave types\n",
    "* will become very complicated for junctions with more than one wave type\n",
    "\n",
    "![](tikzfig/plate_junction_exploded.svg)\n",
    "\n",
    "* alternative approach to calculate $\\tau$:\n",
    "  1. use member-local coordinate system\n",
    "  2. get impedances for all members\n",
    "  3. use transform the coordinates to junction coordinates (global)\n",
    "  4. combine all impedances and velocities at plate edge of all members of the junction\n",
    "  5. find blocked forces / tractions acting on the junction through incident wave \n",
    "  6. compute velocities at junction\n",
    "  7. compute transmitted / reflected powers and transmission coefficients\n",
    "\n",
    "* for the L-wave this is extremely simple:\n",
    "  1. coordinate system: x>0\n",
    "  2. $Z_{LIi}$\n",
    "  3. only two possibilities: coordinate transform $K_i=1$ or $K_i=-1$, applied to both $Z$ and $\\vc$\n",
    "  4. $ \\sum_i K_i Z_{LIi} K_i$\n",
    "  5. $\\Fc_j = -2 Z_{LIj} \\vc_{j+}$ where the member $j$ carries the incident wave\n",
    "  6. solve $\\left(\\sum_i K_i Z_{LIi} K_i\\right)\\vc=K_i F_j$\n",
    "  7. use \\eqref{eq:power}"
   ]
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     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{2 Z_{LI1} v_{1+}}{Z_{LI1} + Z_{LI2}}$"
      ],
      "text/plain": [
       "2*Z_LI1*v_1+/(Z_LI1 + Z_LI2)"
      ]
     },
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     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{4.0 Z_{LI1} Z_{LI2}}{\\left(Z_{LI1} + Z_{LI2}\\right)^{2}}$"
      ],
      "text/plain": [
       "4.0*Z_LI1*Z_LI2/(Z_LI1 + Z_LI2)**2"
      ]
     },
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     "output_type": "display_data"
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   "source": [
    "# we start with step 4\n",
    "K1 = -1\n",
    "K2 = 1\n",
    "Zcomb = K1*ZL1*K1 + K2*ZL2*K2 # in this specific case, K has no effect \n",
    "Fj = -2*ZL1*v11\n",
    "v = sy.symbols(\"v\")\n",
    "v_ = sy.solve(sy.Eq(Zcomb*v,K1*Fj),v)[0]\n",
    "display(v_)\n",
    "# transmitted and incident power\n",
    "PT = 1/2 * sy.re(v_ * ZL2 * sy.conjugate(v_)) \n",
    "PI = 1/2 * sy.re(v11 * ZL1 * sy.conjugate(v11)) \n",
    "# transmission coefficient\n",
    "tau_ = sy.simplify(PT/PI)\n",
    "display(tau_)"
   ]
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   "source": [
    "* this is obviously the same result as above\n",
    "* now we can easily find the result in case of three or more plates (for the simple L-wave case this is not very realistic!)\n",
    "\n",
    "![](tikzfig/plate_junction_3L.svg)\n",
    "\n",
    "* example for three plates"
   ]
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    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{2 Z_{LI1} v_{1+}}{Z_{LI1} + Z_{LI2} + Z_{LI3}}$"
      ],
      "text/plain": [
       "2*Z_LI1*v_1+/(Z_LI1 + Z_LI2 + Z_LI3)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{4.0 Z_{LI1} Z_{LI2}}{\\left(Z_{LI1} + Z_{LI2} + Z_{LI3}\\right)^{2}}$"
      ],
      "text/plain": [
       "4.0*Z_LI1*Z_LI2/(Z_LI1 + Z_LI2 + Z_LI3)**2"
      ]
     },
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     "output_type": "display_data"
    }
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   "source": [
    "ZL3 = sy.symbols('Z_LI3',positive=True) \n",
    "K3 = 1\n",
    "Zcomb = K1*ZL1*K1 + K2*ZL2*K2 + K3*ZL3*K3\n",
    "v_ = sy.solve(sy.Eq(Zcomb*v,K1 * Fj),v)[0]\n",
    "display(v_)\n",
    "# transmitted and incident power\n",
    "PT = 1/2 * sy.re(v_ * ZL2 * sy.conjugate(v_)) \n",
    "PI = 1/2 * sy.re(v11 * ZL1 * sy.conjugate(v11)) \n",
    "# transmission coefficient\n",
    "tau_ = sy.simplify(PT/PI)\n",
    "display(tau_)"
   ]
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   "cell_type": "markdown",
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   "source": [
    "#### Bending Waves \n",
    "![](tikzfig/plate_junction_3B.svg)\n",
    "\n",
    "* step 1-7 can also be used here as follows (details are omitted because of the complicated expressions)\n",
    "  1. local coordinate system (same as for L-Waves)\n",
    "  2. as bending waves need $v_y$ and $w_z$ velocities and $F_y$ and $M_z$ forces / moments, the impedance is now a (2x2) matrix $\\mathbf{\\Zc_B}$\n",
    "  3. as the angle $\\vartheta$ between the global plane and the individual plate  is arbitrary, the coordinate transformation $\\mathbf{K}$ is now also a matrix, connecting local $v_y$ and $w_z$ to global $v_x$, $v_y$ and $w_z$, depending on $\\vartheta$\n",
    "  4. $\\sum_i \\mathbf{K_i \\Zc_{Bi}K_i^T}$\n",
    "  5. $\\mathbf{F_j}=\\mathbf{\\Zc_{BFj}}\\vc_{j+}$ where $\\mathbf{\\Zc_{BFj}}$ is a (2x1) vector giving both blocked force and moment at the junction\n",
    "  6. solve $\\left(\\sum_i \\mathbf{K_i \\Zc_{Bi}K_i^T}\\right)\\mathbf{\\vc}=\\mathbf{K_j F_j}$\n",
    "  7. use \\eqref{eq:power}\n",
    "  \n",
    "* to demonstrate this, we use the special python package `transmission` implementing this unified approach with high-level object-oriented control\n",
    "* two plate example, as before\n",
    "* first, we define the properties of the member plates (we use typical values for steel)"
   ]
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   "cell_type": "code",
   "execution_count": 5,
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     "text": [
      "B'= 153.84615384615387\n",
      "kB= 31.62892453951373\n"
     ]
    }
   ],
   "source": [
    "from transmission import *\n",
    "# define material\n",
    "mat1 = ElasticMaterial(dens=7800.,elas=2.1e11,poisson=0.3)\n",
    "# define plate section properties for isotropic plate 1\n",
    "sec1 = IsoPlateSec(mat=mat1,thick=2e-3)\n",
    "# bending stiffness\n",
    "print(\"B'=\",sec1.B1())\n",
    "# wave number at 500 Hz\n",
    "print(\"kB=\",sec1.kb4(2*np.pi*500)**0.25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* now we define the plate members and their orientation"
   ]
  },
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   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# same for plate 2 (same material, but different thickness)\n",
    "sec2 = IsoPlateSec(mat=mat1,thick=1e-3)\n",
    "# define the connection of the plates\n",
    "# two plates\n",
    "pl01 = InfPlate(sec=sec1,theta=180)\n",
    "pl02 = InfPlate(sec=sec2,theta=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* finally we define the connection and compute $\\tau$"
   ]
  },
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   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.93585115]\n"
     ]
    }
   ],
   "source": [
    "# connection\n",
    "conn = ContLineConnect()\n",
    "conn.add_member(pl01)\n",
    "conn.add_member(pl02)\n",
    "# calculate transmission for a single frequency\n",
    "fr = 500\n",
    "om = 2*np.pi*fr \n",
    "conn.get_trans(fr,pl01,2,pl02) # workaraound for bug in transmission :-(\n",
    "k = np.array((1e-5,))*sec1.kb4(om)**0.25 # wave number along junction, \n",
    "                                         # see text below    \n",
    "tau = conn.calck(om,k,pl01,2) # compute transmission coefficients\n",
    "print(tau[pl02][2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* it is possible to do a parametric study and plot the sound reduction index as function of the thickness ratio (as shown above for L-waves)"
   ]
  },
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Hj9doS3656TgAAEOaXZbebzmw9uYg2zvlVBQVm4mNCNW1A9wnKjP9AwDBa+3B4yqurFdCVJiu7JtuOo4xFBUb8kz/zN9aqKZmTlQGgGDkebN6/eBOCg8N3pfr4P0vt7Er+qQpKTpMpVX1WnPguOk4AAAfq2ts1ofbiyQF35b5Z6Ko2FBYiFNTh7g39eFEZQAIPp/sLlZlfZOyEiI1uluy6ThGUVRsalrL9fKLtxeptqHZcBoAgC95pn1uGtZZTmfwnJR8NhQVmxrZNUnZSVGqbmjW0l2cqAwAwaK8plHL95RIkqYND+5pH4miYlsOh0M3DWVLfQAINou2F6qh2aW+GXHqlxlvOo5xRovKr371KzkcjtNumZmZJiPZyrTh7umf5XtKdLK6wXAaAIAvtG6Zz2iKJBuMqAwcOFCFhYWtt23btpmOZBt9MuLUv1O8mlyWFmzjRGUACHSF5bX6/NAJSWodVQ92xotKaGioMjMzW29paWmmI9mK57K091tOzwQABK73NxfIsqQx3ZKVnRRtOo4tGC8q+/btU1ZWlrp376677rpLBw8ePOdj6+vrVVFRcdot0N00LEsOh7Tu8Anln6wxHQcA0IHmtbwpZdrnS0aLyiWXXKJXXnlFixcv1t///ncVFRXpsssu0/HjZ9/kbPbs2UpISGi95eTk+Dix73VKiNIl3d3X0HvOfAAABJ69xyq1q7BCYSEOTR3cyXQc2zBaVKZMmaJbb71VgwcP1jXXXKMFCxZIkv7xj3+c9fGzZs1SeXl56y0vL8+XcY3x7Kny3hcUFQAIVJ69Uyb0SVdidLjhNPZhfOrnVDExMRo8eLD27dt31j+PiIhQfHz8abdgMGVQJ4WHOLWnpW0DAAKLy2XpvZZpH/ZOOZ2tikp9fb127dqlTp0Y8jpVQnSYruzrXmTMlvoAEHg25Z7U0bJaxYSHaGK/DNNxbMVoUfmv//ovrVixQocOHdLnn3+u2267TRUVFZoxY4bJWLbk2VPlg80Fcrksw2kAAN7keRM6eVCmosJDDKexF6NFJT8/X9OnT1ffvn11yy23KDw8XGvXrlXXrl1NxrKlq/ulKy4iVAXldVp3+ITpOAAAL2lsdmnBVvdeWZ41ifhSqMlv/sYbb5j89n4lMixE1w3K1Nsb8/Xe5gJd2iPFdCQAgBes3FuikzWNSo2N0GU9+X/7mWy1RgXn55n+WbitUA1NLsNpAADe4Nk75cahnRQawsvymfiJ+JFLe6QoPS5C5bWNWr6n2HQcAEA7VdU3acnOIklM+5wLRcWPhDhPPVGZPVUAwN99tKNIdY0udU+N0ZDsBNNxbImi4mc80z9Ldx1TZV2j4TQAgPZo3TJ/WJYcDofhNPZEUfEzA7Pi1SMtRvVNLn24vch0HADARSqprNfqfSWSpJuZ9jknioqfcTgcX26pz/QPAPitBVsL5LKkodkJ6p4aYzqObVFU/NDNw9zrVNYcKFVxRZ3hNACAi/HltA+jKedDUfFDXVNiNLxLolyW9EHLJkEAAP9xuLRam/PK5HRINwzl2Jjzoaj4qS+nfzj7BwD8jWfqflyvVKXHRRpOY28UFT81dUgnhTgd2ppfroMlVabjAAAukGVZrW8y2Tvl61FU/FRqbITG906V9OU8JwDA/rYdLdfB0mpFhjk1eVCm6Ti2R1HxY6dO/1gWJyoDgD+Y94X7zeU1/TMUG2H0yD2/QFHxY9cOyFBUWIiOHK/R5rwy03EAAF+j2WXpg61c7dMWFBU/FhMRqmsHZEhiTxUA8AdrDpSqpLJeidFhmtAnzXQcv0BR8XPThrv3VJm/tUBNzZyoDAB25nlTef3gTgoP5SX4QvBT8nPje6cpOSZcpVUN+vTAcdNxAADnUNfY3Hr0CVf7XDiKip8LC3Fq6mD3ZkHvfcGeKgBgVx/vKlZVfZM6J0ZpVNck03H8BkUlAHimfxbvKFJtQ7PhNACAs5nXsnfKTcOy5HRyUvKFoqgEgBFdkpSTHKXqhmYt2XXMdBwAwBnKahq0fE+xJKZ92oqiEgAcDoduHur+xZ/H9A8A2M7CbUVqbLbULzNOfTPjTMfxKxSVADFtuLuorNhbomOcqAwAtvLmhjxJ0jeGM5rSVhSVANErPVajuiap2WXpnY35puMAAFrsKqzQlrwyhTodumVEtuk4foeiEkDuGtNFkvTG+ly5XGypDwB28OZ692jKtQMylBYXYTiN/6GoBJCpgzspLiJUeSdqtYY9VQDAuLrGZr27yT3K7XkzibahqASQqPAQ3dxyqfIb63MNpwEAfLi9SBV17r1TLu+VajqOX6KoBJi7Rrsb+0c7julEdYPhNAAQ3Oasc79pvGNUjkLYO+WiUFQCzKDOCRrcOUENza7W4UYAgO8dLKnS54dOyOmQbh/FItqLRVEJQHeOzpHkbvKWxaJaADDBs4h2Qp80ZSVGGU7jvygqAejmYVmKCgvRgZJqbTxy0nQcAAg6DU0u/YtFtF5BUQlAcZFhumGI+6DCOevyDKcBgODz8a5jKq1qUFpchK7ul246jl+jqASou8a4p38WbCtQeW2j4TQAEFzmtEz73DYyW2EhvNS2Bz+9ADWiS5J6p8eqrtGl97cUmI4DAEEj/2SNVu0rkSTd1bJmEBePohKgHA7HlzvVrmNPFQDwlbc25MuypMt6pqhrSozpOH6PohLAbhneWeEhTu0oqNC2/HLTcQAg4DW7LL3dcgAhi2i9g6ISwJJiwjV5UKYkdqoFAF9YubdEheV1SowO06QBGabjBATbFJXZs2fL4XDoBz/4gekoAWV6y/zoe5sLVNPQZDgNAAQ2z060twzPVmRYiOE0gcEWRWX9+vV67rnnNGTIENNRAs6lPVLUNSVaVfVNmr+10HQcAAhYxRV1+nh3saQvr7xE+xkvKlVVVbr77rv197//XUlJSabjBByn06E7RrmfMCyqBYCO8/bGfDW7LI3okqg+GXGm4wQM40Xl4Ycf1tSpU3XNNdd87WPr6+tVUVFx2g1f7/aR2QpxOrQpt0x7j1WajgMAAcflsvQWi2g7hNGi8sYbb2jTpk2aPXv2BT1+9uzZSkhIaL3l5DC0diHS4yM1sWVnxDfYqRYAvG7tweM6crxGcRGhrTuDwzuMFZW8vDz9x3/8h1599VVFRkZe0OfMmjVL5eXlrbe8PF50L9T0lob/7hf5qmtsNpwGAAKLZyfam4ZlKTo81HCawGKsqGzcuFHFxcUaOXKkQkNDFRoaqhUrVuipp55SaGiompu/+mIaERGh+Pj40264MFf0SVOnhEiV1TTqo53HTMcBgIBxsrpBi7cXSZLuGs20j7cZKyoTJ07Utm3btHnz5tbbqFGjdPfdd2vz5s0KCeGyLm8KcTp0O4tqAcDr3v3iqBqaXRqYFa/B2Qmm4wQcY+NTcXFxGjRo0Gn3xcTEKCUl5Sv3wzvuGJWt//tkn9YcOK4jx6vZ2hkA2smyrNY3fyyi7RgXNaKyb98+/etf/9KhQ4ckSQsWLNAVV1yh0aNH6/HHH5dlWV4NCe/ITorW+N5pkqQ317O+BwDaa1NumfYVVykyzKmbh2WZjhOQ2jyiMnfuXN1xxx1yOp1yOBx67rnn9OCDD+qqq65SfHy8fvWrXyk0NFQ//vGP2xxm+fLlbf4ctM300TlaubdEb2/M1w+v7cPx4wDQDp7RlKmDsxQfGWY4TWBq86vU448/rh/96Eeqq6vTM888o5kzZ+p3v/udFi1apPnz5+svf/mLXn755Q6ICm+Y2D9DqbHhKqms1yctOygCANqusq6xdcfv6exE22HaXFT27Nmj++67Tw6HQzNmzFBDQ8Npm7VNmjRJR44c8WpIeE94qFO3jsiWxKJaAGiP9zYXqLaxWb3SYzWyKzurd5Q2F5Xq6mrFxbm3BnY6nYqKilJ0dHTrn0dFRam+vt57CeF1d7YcVLhib4kKymoNpwEA/+RZ63fX6Bw5HA7DaQJXm4uKw+E47S/kzI9hfz3SYnVJ92S5LOntDfmm4wCA39l+tFzbjpYrPMSpW1pGqdEx2ryY1rIs9enTp7WcVFVVafjw4XI6na1/DvubPqaLPj90Qm9tyNMjV/dSiJOyCQAX6o317qnzSQMzlBwTbjhNYGtzUXnppZc6Igd87LpBmYp/L1RHy2q1en+pJvRJMx0JAPxCbUOz3vuiQBI70fpCm4vKjBkzOiIHfCwyLES3jMjWy2sO6411uRQVALhAC7YVqrK+STnJUbqsZ4rpOAGPTTSCmGdR7ZKdx1RSyQJoALgQrTvRju4iJ9PmHa5NIypJSUkXvHD2xIkTFxUIvtO/U7yG5iRqS16Z3t2Ur4cm9DQdCQBsbX9xpTYcOakQp0O3jWQRrS+0qag8+eSTrf9+/Phx/fa3v9XkyZM1duxYSdJnn32mxYsX6xe/+IVXQ6LjTB+doy15ZXpzfZ4evKIHV3ABwHm8sc59SfJVfdOVER9pOE1wcFgXeZnOrbfeqquuukqPPPLIafc//fTTWrp0qebNm+eNfOdVUVGhhIQElZeXKz4+vsO/XyCqrm/SmMeXqrqhWW88eKku7cF8KwCcTX1Tsy594mOdrGnUCzNGaWL/DNOR/FZbXr8veo3K4sWLdd11133l/smTJ2vp0qUX+2XhYzERobqp5SAtdqoFgHP7aMcxnaxpVGZ8JBcg+NBFF5WUlBTNnTv3K/fPmzdPKSm8K/cnd7ZcXrdwe5HKaxoNpwEAe/LsRHv7qGyFcqCrz7T58mSPX//61/rud7+r5cuXt65RWbt2rT788EM9//zzXguIjjc0O0H9MuO0u6hSc7/I173jupuOBAC2knu8Rqv3l8rhkO4YxQGEvnTRlfDee+/VmjVrlJiYqHfffVf/+te/lJCQoE8//VT33nuvFyOiozkcDk0f4x5VeWN9HrsLA8AZ3tzgnhq/vFeqcpKjv+bR8KY2j6h89NFHuuqqqxQWFqZLLrlEr732Wkfkgo9NG9ZZTyzcpd1FldqSX65hOYmmIwGALTQ1u1rPRWMnWt9r84jKzJkzlZaWpjvvvFOvv/66ysrKOiAWfC0hOkzXD+4kiUW1AHCqZXtKVFxZr5SYcF07gCt9fK3NReXgwYNauXKlBg8erCeffFKZmZmaOHGinnrqKR0+fLgDIsJX7mrZqfb9LQWqqm8ynAYA7MHz5u3WkdkKD2URra9d1E98yJAh+vnPf65169bp4MGDuv322/Xhhx+qf//+Gjp0qB577DFt2LDB21nRwcZ0T1aP1BjVNDRr/pYC03EAwLii8jot21MsiUW0prS7GmZlZWnmzJlauHChSktL9dhjj2n16tWaMmWKnnjiCW9khI84HI7W83/mtFyGBwDB7O0NeXJZ0phuyeqVHms6TlDy6hhWZWWlli9frs8++0zHjh3TAw884M0vDx+4dWS2wkIc2pJXpl2FFabjAIAxLpelNze437TdNYbRFFPaXFTKysp09913Ky0tTVlZWXrqqafkcrn02GOPqUePHlq7dq1efPFFOZ1OpaWxc5+/SY2NaF0sxqJaAMFs9f5S5Z+sVVxkaOvFBvC9NheVn/70p1q5cqVmzJih5ORk/fCHP9QNN9yg1atXa9GiRVq/fr2mT5/eEVnhI56daud+cVR1jc2G0wCAGZ6daL8xvLMiw0IMpwlebS4qCxYs0EsvvaQ//vGPev/992VZlvr06aNPPvlEEyZM6IiM8LHxvVLVOTFKFXVNWrS90HQcAPC541X1+mhnkST2TjGtzUWloKBAAwYMkCT16NFDkZGRuv/++70eDOY4nacsql3HoloAwedfm/LV2GxpaHaCBmSd/3RfdKw2FxWXy6WwsLDWj0NCQhQTE+PVUDDv9lHZcjqkdYdO6GBJlek4AOAzlmXpjZZpnzsZTTGuzVvoW5ale++9VxEREZKkuro6zZw58ytl5d133/VOQhjRKSFKV/ZN1ye7i/Xm+jzNur6/6UgA4BPrD5/UwZJqRYeH6KZhWabjBL02F5UZM2ac9vG3vvUtr4WBvdw1Okef7C7WOxvz9Z+T+rIjI4Cg4Lni8cYhWYqNaPPLJLyszX8DL730UkfkgA1d1S9daXERKqms18e7jmkKl+cBCHDltY1asM19EcGd7J1iC7xFxjmFhTh1+8hsSexUCyA4vLf5qOqbXOqbEafhnCJvCxQVnJfn6p9V+0qUd6LGcBoA6DiWZbVe6XjXmBw5HA7DiSBRVPA1uqbEaFyvFFmW9M+1R0zHAYAOs+7QCe0qrFB4qFPfGN7ZdBy0oKjga3338u6SpNc/z1VFXaPhNADQMZ5beVCSdNvIbCVGhxtOAw+KCr7WlX3S1Ts9VlX1TZrzOef/AAg8+45V6uPdxXI4pAfG9zAdB6egqOBrOZ0OPXiF+4n74qeH1NDkMpwIALzLM5oyeUCmuqeyiamdGC0qzzzzjIYMGaL4+HjFx8dr7NixWrRokclIOIebh3VWRnyEjlXU673NR03HAQCvOVZRp3kt/197cAKjKXZjtKhkZ2frd7/7nTZs2KANGzbo6quv1s0336wdO3aYjIWzCA916jvj3GtVnlt5UC6XZTgRAHjHi58eUmOzpdHdkjSiS5LpODiD0aJy44036vrrr1efPn3Up08fPf7444qNjdXatWtNxsI5fPOSLoqNCNW+4iot31tsOg4AtFtlXaNeX+tee/fQFT0Np8HZ2GaNSnNzs9544w1VV1dr7NixpuPgLOIjw/TNS9wHdP1txUHDaQCg/easy1VlfZN6psXo6n7ppuPgLIwXlW3btik2NlYRERGaOXOm5s6dqwEDBpz1sfX19aqoqDjtBt/6zrhuCgtxaN2hE/oi96TpOABw0RqaXHpx9WFJ7tEUp5MN3uzIeFHp27evNm/erLVr1+rf/u3fNGPGDO3cufOsj509e7YSEhJabzk5nMPga50SonTTUPdGSJ5V8gDgj97fUqCiijqlx0Xo5uGckmxXDsuybLUq8pprrlHPnj317LPPfuXP6uvrVV9f3/pxRUWFcnJyVF5ervj4eF/GDGp7iio1+cmVcjikZf95pbpxKR8AP2NZliY/uVJ7j1Xpx9f1079dyfoUX6qoqFBCQsIFvX4bH1E5k2VZp5WRU0VERLReyuy5wff6Zsbpqr5psizp76sYVQHgf5bvKdHeY1WKCQ9pXXsHezJaVH76059q1apVOnz4sLZt26af/exnWr58ue6++26TsXABHprgfvfxzsZ8lVadvVgCgF09u/KAJPfVjAlRYYbT4HyMFpVjx47pnnvuUd++fTVx4kR9/vnn+vDDD3XttdeajIULcEn3ZA3NTlB9k0uvrDlsOg4AXLAteWVae/CEQp2O1v2hYF+hJr/5Cy+8YPLbox0cDocemtBT//7aJr2y9ohmXtlT0eFGf50A4IJ4LgS4aViWshKjDKfB17HdGhX4j8kDM9U1JVplNY16a32e6TgA8LWOHK/Wou2FktR6hhnsjaKCixbidOj+llNGn199SE3NHFYIwN6eX3VILku6sm+a+mVyQYY/oKigXW4fma3kmHDln6zVwu1FpuMAwDkdr6rX2xvdo7+MpvgPigraJTIsRN8e21WS9NzKA7LZtjwA0OqVz46ortGlwZ0TNLZHiuk4uEAUFbTbt8d2U2SYU9uPVmjNgeOm4wDAV9Q2NOuVzw5Lkh6a0EMOB9vl+wuKCtotOSZcd4xyH2fwLNvqA7Chtzfm6WRNo3KSo3TdwEzTcdAGFBV4xf2X95DTIa3cW6JdhRwWCcA+mppden7VIUnSA+N7KDSElz5/wt8WvKJLSrSmDO4kicMKAdjLhzuKlHuiRknRYbp9JIfZ+huKCrzmoZZV9B9sKdDRslrDaQDAfX6c583Tt8d2U1R4iOFEaCuKCrxmSHaixvZIUZPL0ourD5mOAwBae/CEtuaXKyLU2XqFIvwLRQVe9dAE96jKG+tyVV7TaDgNgGDnOXzwjlE5SomNMJwGF4OiAq+a0CdN/TLjVN3QrFc/P2I6DoAgtruoQsv3lMjpkO4fz+GD/oqiAq9yOBytOz6+vOaw6hqbDScCEKw8a1OmDOqkrikxhtPgYlFU4HU3Ds1Sp4RIlVTWa94XR03HARCECstr9f7mAklsl+/vKCrwurAQp757uXuY9blVB+Vysa0+AN96cfUhNbksXdojWUNzEk3HQTtQVNAh7hrTRXGRoTpYUq2lu46ZjgMgiJTXNmrOOvfhgw9d0dNwGrQXRQUdIjYiVHdf4jmskA3gAPjO65/nqqq+SX0yYnVl3zTTcdBOFBV0mO+M66bwEKc2HDmpjUdOmI4DIAjUNzXrpU/d+zg9eEVPDh8MABQVdJiM+EhNG54lSXp2BaMqADree5sLVFxZr8z4SN00NMt0HHgBRQUdyrPafsmuYzpQUmU4DYBA5nJ9uV3+fZd3U3goL3GBgL9FdKhe6XG6pn+6LEt6fhWjKgA6zrI9xdpfXKW4iFBNH9PFdBx4CUUFHe6hCe5V9//aeFTFlXWG0wAIVJ4p5m9e2kVxkWGG08BbKCrocKO6Jml4l0Q1NLv0jzWHTccBEIA25Z7UusMnFBbi0H3j2C4/kFBU0OEcDkfrXgb//OyIquqbDCcCEGieaxlNmTasszLiIw2ngTdRVOAT1w7IUPfUGFXUNenN9Xmm4wAIIIdKq7V4Z5EktssPRBQV+ESI06EHxrv/B/Li6kNqbHYZTgQgUPx91UFZljSxX7p6Z8SZjgMvo6jAZ24Z0VmpseE6WlarBVsLTccBEABKKuv1zsZ8SYymBCqKCnwmMixE917WTZL07MqDsiwOKwTQPq98dlgNTS4Ny0nUmO7JpuOgA1BU4FPfurSrosNDtKuwQqv2lZqOA8CP1TQ06Z9rj0iSHrqiB9vlByiKCnwqMTpcd47OkcRhhQDa5631eSqraVS3lGhNGphpOg46CEUFPvfdy7srxOnQ6v2l2n603HQcAH6oqdml51e7Dx+8f3wPhTgZTQlUFBX4XHZStKYO7iSJURUAF2fh9iLln6xVSky4bhuZbToOOhBFBUZ4Vucv2FaovBM1htMA8CeWZenZFQckSTMu66bIsBDDidCRKCowYlDnBF3eK1XNLksvtAzfAsCFWHPguHYUVCgqLET3XNrVdBx0MIoKjHlogntUZc66XOWfZFQFwNezLEt/+miPJOmOUdlKigk3nAgdjaICYy7vlapLuiervsml3y3abToOAD/w/pYCbcotU3R4iP79ql6m48AHjBaV2bNna/To0YqLi1N6erqmTZumPXv2mIwEH3I4HHrsxgFyOKT5Wwu17tAJ05EA2FhNQ5NmL3S/qXn4ql4cPhgkjBaVFStW6OGHH9batWu1ZMkSNTU1adKkSaqurjYZCz40MCtBd7Xsq/Kb+TvkcrFbLYCz+9uKgyqqqFN2UpS+e3l303HgI6Emv/mHH3542scvvfSS0tPTtXHjRl1xxRWGUsHX/nNSX83fUqjtRyv0zsZ83dFSXADAI/9kTeuVPj+7vj9X+gQRW61RKS93b/6VnHz28xrq6+tVUVFx2g3+LzU2Qt+f2FuS9IfFu1VZ12g4EQC7+d2i3apvcumS7sm6bhC70AYT2xQVy7L06KOP6vLLL9egQYPO+pjZs2crISGh9ZaTwzvvQDHjsm7qnhqj0qoGPb1sv+k4AGxk3aETmr+1UA6HWta1sQttMLFNUXnkkUe0detWzZkz55yPmTVrlsrLy1tveXl5PkyIjhQe6tTPp/aXJL24+pAOl7JOCYDkcln6zfwdkqS7RnfRwKwEw4nga7YoKt/73vf0/vvva9myZcrOPvdWyBEREYqPjz/thsBxdb90je+dqsZmS48v3GU6DgAbeGdjvrYfrVBcRKj+c1If03FggNGiYlmWHnnkEb377rv65JNP1L07q7iDmcPh0GM3DFCI06ElO49p9b5S05EAGFRZ16g/LHZvWfH9ib2VGhthOBFMMFpUHn74Yb366qt6/fXXFRcXp6KiIhUVFam2ttZkLBjUOyOudUvs38zfoaZml+FEAEx5etl+lVbVq3tqjGZc1s10HBhitKg888wzKi8v15VXXqlOnTq13t58802TsWDYD67prcToMO09VqU563JNxwFgwOHSar20+rAk6edT+ys81BYrFWCA8amfs93uvfdek7FgWGJ0uB691j0X/f+W7FVZTYPhRAB87fGFu9TQ7NIVfdJ0db9003FgEBUVtvTNMV3UJyNWJ2sa9eTSfabjAPChT/eXasnOYwpxOvSLqf25HDnIUVRgS6EhTv3ihgGSpH+uPaL9xZWGEwHwhaZml37zwU5J0j2XdlXvjDjDiWAaRQW2Nb53mq7pn6Fml6XfzN8ly+IcICDQzVmXqz3HKpUYHaYfXNPbdBzYAEUFtvazqf0VFuLQyr0lWran2HQcAB2orKZB/2/JXknSo9f2UWJ0uOFEsAOKCmyte2qM7hvn3l/nt/N3qaGJy5WBQPXk0n06WdOoPhmx+uaYLqbjwCYoKrC9R67updTYcB0srdYrnx02HQdAB9hfXKl/rj0iSXrshoEKDeHlCW78JsD24iLD9F+T+kqS/vzxPh2vqjecCIA3WZZ7HVqzy9I1/TN0ee9U05FgIxQV+IXbR+VoYFa8Kuua9KeWOWwAgWHZnmKt3FuisBBH6+GkgAdFBX4hxOnQL28cKEl6Y12udhZUGE4EwBsamlz67Xz3IaT3jeuubqkxhhPBbigq8Btjuidr6uBOclnuc4C4XBnwf698dlgHS6uVGhuuR67uZToObIiiAr/ykyn9FBHq1NqDJ7R4R5HpOADa4XhVvf78sXvn6f+e3FdxkWGGE8GOKCrwKznJ0Xrwih6SpN8u2KW6xmbDiQBcrD8t2avKuiYNzIrXbSNzTMeBTVFU4Hf+7cqeyoyPVP7JWr2w+pDpOAAuws6CCr3Rcjr6L28cqBAn5/ng7Cgq8DvR4aH68RT35cp/WbZfxyrqDCcC0Bbuy5F3yGVJU4d00pjuyaYjwcYoKvBLNw/trGE5iappaNYfPtxjOg6ANli8o0hrD55QRKhTs6b0Mx0HNkdRgV9yOh365Y3u05X/tSlfW/LKzAYCcEHqGpv12wXuy5EfuqKHspOiDSeC3VFU4LeGd0nSLcM7S5J+/QGXKwP+4IXVh5R/slaZ8ZGaeWVP03HgBygq8Gs/uq6fosJCtCm3TO9vKTAdB8B5HKuo01+W7Zck/XhKX0WHhxpOBH9AUYFfy0yI1MNXud+V/W7RbtU0NBlOBOBc/vDhHtU0NGt4l0TdPLSz6TjwExQV+L37x/dQ58QoFZbX6dkVB03HAXAWW/LK9K9N+ZLclyM7uRwZF4iiAr8XGRain7UcZPa3FQd0tKzWcCIAp7IsS7/+YIck6ZYR7iv2gAtFUUFAmDIoU2O6J6u+yaXfLdptOg6AU7y/pUCbcssUHR6iH1/H5choG4oKAoLD4dBjNwyQwyF9sKVA6w+fMB0JgKSahqbWNw//fmVPZcRHGk4Ef0NRQcAY1DlBd412nxfymw92yuXicmXAtL+tOKjC8jplJ0Xp/vE9TMeBH6KoIKD856S+iosI1baj5XqnZeEeADOOltXq2RUHJEk/vb6/IsNCDCeCP6KoIKCkxkboexN7SXJfCllZ12g4ERC8Zi/cpfoml8Z0T9aUQZmm48BPUVQQcO69rLu6p8aotKpev3yfHWsBExZuK9T8rYVyOKRf3jhADgeXI+PiUFQQcMJDnXriG4MV4nTo3U1H9Y81h01HAoLKnqJK/dfbWyRJD47voYFZCYYTwZ9RVBCQxvZMaT2V9X8W7NLag8cNJwKCQ3lNox785wbVNDRrXK8U/ffkvqYjwc9RVBCwvnt5d00blqVml6WHX9vERnBAB2t2WfreG1/oyPEadU6M0v9NH6HQEF5m0D78BiFgORwOzb5liAZ0itfx6gbN/OdG1TU2m44FBKw/frRHK/eWKDLMqee+PVLJMeGmIyEAUFQQ0KLCQ/TsPSOVFB2mbUfL9dO521hcC3SABVsL9cxy96XIv791COtS4DUUFQS8nORo/eWbI1hcC3SQPUWV+u933ItnHxjfXTcP42RkeA9FBUHhsl6pLK4FOsCZi2c5ywfeRlFB0GBxLeBdpy6ezU6K0tMsnkUHMPobtXLlSt14443KysqSw+HQvHnzTMZBgGNxLeBdpy6effaekUpi8Sw6gNGiUl1draFDh+rpp582GQNBhMW1gHeweBa+Emrym0+ZMkVTpkwxGQFByLO49p4X1+ndTUc1pHOC7h3X3XQswG/sLqpo3XmWxbPoaH41mVhfX6+KiorTbsDFYHEtcHHKaxr10D83qraRxbPwDb8qKrNnz1ZCQkLrLScnx3Qk+DEW1wJtw+JZmOBXv2GzZs1SeXl56y0vL890JPgxFtcCbXPazrP3jGLxLHzCr4pKRESE4uPjT7sB7cHiWuDCnLp49g+3DdWALP7/C9/wq6ICdAR2rgXO79TFsw9e0UM3Dc0ynAjBxGhRqaqq0ubNm7V582ZJ0qFDh7R582bl5uaajIUgxOJa4OzOXDz7o8l9TUdCkDFaVDZs2KDhw4dr+PDhkqRHH31Uw4cP12OPPWYyFoIUi2uB07F4FnZgdB+VK6+8kvUAsA3P4tq9x6q0s7BCM/+5UW/PHKvIsBDT0QAjWDwLO6AaA6dgcS3gxuJZ2AVFBTjDmYtrX2ZxLYIMi2dhJxQV4CxOXVz7WxbXIoiU1TTowVfci2cv75XK4lkYR1EBzoHFtQg2zS5L339js3JPuBfP/t/04SyehXH8BgLn4FlcOzCLnWsRHFg8CzuiqADnERUeor99i8W1CHwsnoVdUVSAr8HiWgQ6Fs/CzigqwAVgcS0CFYtnYXcUFeACnbq49oFXNuiT3cdMRwLaJe9Ejb71wufKPVGjnGQWz8Ke+I0ELpBnce3obkmqrGvSfS9v0P9bslfNLtaswP8s31OsG59ere1HK5QUHaZnv8XiWdgTRQVog6jwEL12/6WaMbarJOmpj/fpOy+v18nqBsPJgAvjcln681L3721ZTaOGZido/vfHs3gWtkVRAdooPNSpX988SE/eOUyRYU6t3FuiG/5vtbbll5uOBpxXeU2jvvuP9fr/lu6VZUnfvKSL3po5Vp0To0xHA86JogJcpGnDO2vuv49Tt5RoHS2r1a1/W6M31uWajgWc1faj5brh6VVatqdEEaFO/e9tQ/TENwYrIpRDN2FvFBWgHfp3itd7j1yuawdkqKHJpZ+8u00/emcLG8PBVt7akKdbn1mjvBO1ykmO0rv/fpluH5VjOhZwQSgqQDslRIXp2W+N1H9P7iunQ3prQ75u+9sa5Z2oMR0NQa6+qVmz3t2mH72zVfVNLl3dL13zHxmvgVkJpqMBF4yiAniB0+nQw1f10iv3XaLkmHBtP1qhG59ereV7ik1HQ5A6WlarO/72measy5XDIT16bR89/+1RSogOMx0NaBOKCuBFl/dO1fzvXa6hOYkqq2nUd15erz8v3ScXlzDDh1btK9ENT63SlvxyJUaH6eXvjNH3J/aW0+kwHQ1oM4oK4GVZiVF666FLdfclXWRZ0v+3dK+++4/1KqvhEmZ0LJfL0tOf7NO3X1ynkzWNGtw5QR88crkm9EkzHQ24aBQVoANEhIbo8W8M1h9vH6qIUKeW7Slp2VyLS5jRMcprG/XgPzfojx+5Lz2+a3SO3p45VjnJ0aajAe1CUQE60G0js/Xuv1+mnOQo5Z2o1a3PrNFbG/JMx0KA2VlQoZueXq2lu4oVHurU728drN/dOkSRYVx6DP9HUQE62MCsBM1/ZLyu7peu+iaXfvTOVs16d5vqm7iEGe337qZ83fLMpzpyvEadE6P0r5mX6c7RXUzHAryGogL4QEJ0mJ7/9ij957V95HBIc9bl6o6/faajZbWmo8FP1Tc16+fztunRt7aortGlCX3SNP97l2twNpceI7BQVAAfcTod+t7E3nr5O2OUGB2mLfnluuGpVVq1r8R0NPiZwvJa3fnsWr261r0T8n9M7K0X7x3NoYIISBQVwMcm9EnTB49crsGdE3SyplHffnGdnv6ES5hxYdbsL9UNT63W5rwyxUeG6qV7R+uH1/ZRCJceI0BRVAADcpKj9fbMsbprdI4sS/rjR3v14D83qLy20XQ02JRlWXpm+QF964XPdby6QQM6xWv+98brqn7ppqMBHcphWZbfvo2rqKhQQkKCysvLFR/PEeXwT2+uz9Uv3tuhhiaXuqZEa9aUfprYP0NhIbyPgNu2/HL9+eO9WrrLvdPxbSOz9dtpg7iqB36rLa/fFBXABrbll+vfXtuo/JPuxbVpcRG6fWS27hrdRV1S2AcjGFXWNer9LQWasy5X249WSJLCQ5z61U0DNX1MjhwOpnrgvygqgB8qq2nQsysP6u0NeSqt+nIX2/G9UzV9TBdd0z9D4aGMsgQyy7K0Nb9cc9bl6v0tBappcF/CHh7i1HWDMvXQhB4cKIiAQFEB/FhDk0sf7zqm19flatW+0tb7U2PDddvIHN01OkfdUmMMJoS3VdQ16r3NBZrzea52Fla03t8jLUbfHNNFt4zIVjJX9CCAUFSAAJF7vEZvbsjVWxvyVVJZ33r/uF4pmj6miyYNyGSUxU9ZlqXNeWWasy5XH2wpVG1jy+hJqFPXD8rU9DFdNKZ7MlM8CEgUFSDANDa79PGuYs1Zl6uV+0rkedamxITrtpHZumtMF3VnlMUvlNc26r3NR/X657naXVTZen+v9FhNH9NFtwzvzH4oCHgUFSCA5Z2o0Vsb8vTWhjwdq/hylGVsjxRNv6SLJg/MUEQoV4PYiWVZ2pTrHj2Zv7VAdY0uSVJEqFNTB3fS9Eu6aFTXJEZPEDQoKkAQaGp2admeEs1Zl6tle4pbR1mSosNaR1l6psWaDRnkymsa9e4X+ZqzLld7j1W13t8nI1bfHNNF3xierYToMIMJATMoKkCQOVpWq7fW5+nN9Xkqqqhrvf+S7smaPqaLrhuUyZ4bPmJZljYcOak5n+dqwbZC1Te5R08iw5y6YUiWpo/pohFdEhk9QVCjqABBqqnZpRV73aMsn+wulmdX/sToME0akKE+GXHqkRajnmmxyk6KZtv1drIsSyVV9TpYUt1yq9LyvSXaX/zl6Em/zDh985IuunlYZyVEMXoCSH5WVP7617/qf//3f1VYWKiBAwfqySef1Pjx4y/ocykqwLkVltfqrfX5enN9rgrK677y5+EhTnVNiW4tLj3SYt3/nhrLdMQZ6hqbdeR4jQ6WVOlgabUOFFfpQKm7mFTWNX3l8VFhIbpxaCdNH9NFw3IYPQHO5DdF5c0339Q999yjv/71rxo3bpyeffZZPf/889q5c6e6dOnytZ9PUQG+XrPL0sp9Jdp05KQOlFTpYEm1DpVWt05JnE1qbLh6pMaqZ3qMeqS6C0yPtFjlJEUpNEC39rcsSyWV9TpQUq2DpVU6UOz+58GSauWfrNG5zox0OKTspCj3zystVv06xem6QZmKj6TsAefiN0Xlkksu0YgRI/TMM8+03te/f39NmzZNs2fP/trPp6gAF6fZZamgrLa1uJz6wnzqlURnCgtxqGtKjHqkxqhneqx6pMaoR1qM4iPDFBkWoogwpyJCQxQZ5lR4iNMWIwlNzS7VNblU19isusZm1Te5VNvQrNwT7hGSAy1TNgdLqlVZ/9XREY+4iNBTRp/cxa1nWqy6pkSz/gdoo7a8fof6KNNXNDQ0aOPGjfrJT35y2v2TJk3SmjVrDKUCgkOI06Gc5GjlJEfryr6n/1llXaMOlX655uJASbUOlFS1jsLsL65yr8HYeey838PhcF9+GxkWosiW8uIpMRFhIe5i0/rnztM/bnms0+loLRf1LUWjrtGl+ib3P+uamlXf8s+6Rvdj6k8pJXVNLjWfayjkLJwOKTspWj1bikiPtJjWkaW02AhbFC8g2BgrKqWlpWpublZGRsZp92dkZKioqOisn1NfX6/6+i/f7VVUVJz1cQAuXlxkmIZkJ2pIduJp97tclgrKa08bgThQUqUjx2tU3dDUWiI8LEvuMtHoktTo2/+IcwgPdbaWoazEKPX0jJC0jBB1TYlmDxrAZowVFY8z36FYlnXOdy2zZ8/Wr3/9a1/EAnAGp9Oh7KRoZSdFa0KftLM+xrIsNTS7zjK6ccooSGPzV0ZCzhw18Xxes6WzjrZ4Pj7nyEyYs2UU58s/iwh1yslVToDfMVZUUlNTFRIS8pXRk+Li4q+MsnjMmjVLjz76aOvHFRUVysnJ6dCcAC6cw+FQRGiIe1SCS3EBeIGx5fvh4eEaOXKklixZctr9S5Ys0WWXXXbWz4mIiFB8fPxpNwAAELiMTv08+uijuueeezRq1CiNHTtWzz33nHJzczVz5kyTsQAAgE0YLSp33nmnjh8/rt/85jcqLCzUoEGDtHDhQnXt2tVkLAAAYBPGd6ZtD/ZRAQDA/7Tl9Tswt5gEAAABgaICAABsi6ICAABsi6ICAABsi6ICAABsi6ICAABsi6ICAABsi6ICAABsi6ICAABsy+gW+u3l2VS3oqLCcBIAAHChPK/bF7I5vl8XlcrKSklSTk6O4SQAAKCtKisrlZCQcN7H+PVZPy6XSwUFBbr66qu1YcOGC/qc0aNHa/369V/7uIqKCuXk5CgvL49zhFpc6M/OBF9n66jv562v256vczGf29bPuZDH8xz8Kjs/ByWeh978Oh39PDT9WmhZliorK5WVlSWn8/yrUPx6RMXpdCo7O1uhoaEX/AMMCQlp0w87Pj6e/0m2aOvPzpd8na2jvp+3vm57vs7FfG5bP6ctj+c5+CU7Pwclnofe/Dod/Ty0w2vh142keATEYtqHH364Qx6L09n5Z+frbB31/bz1ddvzdS7mc9v6OXb+XbIzu//ceB567+t09PPQ7r9Lp/LrqZ+O1JYjqAF4H89BwDw7PA8DYkSlI0REROiXv/ylIiIiTEcBghLPQcA8OzwPGVEBAAC2xYgKAACwLYoKAACwLYoKAACwLYoKAACwLYoKAACwLYqKF3zjG99QUlKSbrvtNtNRgKAwf/589e3bV71799bzzz9vOg4QlHz12sflyV6wbNkyVVVV6R//+Ifeeecd03GAgNbU1KQBAwZo2bJlio+P14gRI/T5558rOTnZdDQgqPjqtY8RFS+46qqrFBcXZzoGEBTWrVungQMHqnPnzoqLi9P111+vxYsXm44FBB1fvfYFfFFZuXKlbrzxRmVlZcnhcGjevHlfecxf//pXde/eXZGRkRo5cqRWrVrl+6BAkGjvc7KgoECdO3du/Tg7O1tHjx71RXQgYPjTa2PAF5Xq6moNHTpUTz/99Fn//M0339QPfvAD/exnP9MXX3yh8ePHa8qUKcrNzW19zMiRIzVo0KCv3AoKCnz1nwEEjPY+J882W+1wODo0MxBovPHa6DNWEJFkzZ0797T7xowZY82cOfO0+/r162f95Cc/adPXXrZsmXXrrbe2NyIQVC7mOfnpp59a06ZNa/2z73//+9Zrr73W4VmBQNWe10ZfvPYF/IjK+TQ0NGjjxo2aNGnSafdPmjRJa9asMZQKCF4X8pwcM2aMtm/frqNHj6qyslILFy7U5MmTTcQFApLdXhtDff4dbaS0tFTNzc3KyMg47f6MjAwVFRVd8NeZPHmyNm3apOrqamVnZ2vu3LkaPXq0t+MCAe9CnpOhoaH605/+pKuuukoul0s/+tGPlJKSYiIuEJAu9LXRV699QV1UPM6c37Ysq01z3lxxAHjX1z0nb7rpJt10002+jgUEla97HvrqtS+op35SU1MVEhLyldGT4uLirzRJAB2P5yRgnt2eh0FdVMLDwzVy5EgtWbLktPuXLFmiyy67zFAqIHjxnATMs9vzMOCnfqqqqrR///7Wjw8dOqTNmzcrOTlZXbp00aOPPqp77rlHo0aN0tixY/Xcc88pNzdXM2fONJgaCFw8JwHz/Op52KHXFNnAsmXLLElfuc2YMaP1MX/5y1+srl27WuHh4daIESOsFStWmAsMBDiek4B5/vQ85KwfAABgW0G9RgUAANgbRQUAANgWRQUAANgWRQUAANgWRQUAANgWRQUAANgWRQUAANgWRQUAANgWRQUAANgWRQUAANgWRQWAbcybN08//OEPTccAYCMUFQC2sXXrVg0dOtR0DAA2QlEBYBtbt27V3r17NXbsWHXt2lU7d+40HQmAYRQVALaxdetW9erVS5999pkeeOABffDBB6YjATCMogLAFmpqauRyuXTfffdJksLDw5WYmKiPP/5Y999/v6ZNm6ZPPvnEcEoAvkZRAWAL27dv16hRo077eODAgZo4caKef/55vfzyy3rnnXcMJgRgAkUFgC1s3bpVgwcPbv1427ZtGjRoUOvHs2fP1v33328iGgCDKCoAbGHbtm2tRaWpqUlVVVVKTEyUJP3qV7/SxIkTNWLECIMJAZjgsCzLMh0CAM7ltdde0x/+8AeNHTtWI0aM0IMPPmg6EgAfoqgAAADbYuoHAADYFkUFAADYVqjpAAAgSQ6Ho02PZ9YaCA6MqACwBcuyNHfuXP3gBz+QZVlfewMQHCgqAGyDQwkBnImiAsA2OJQQwJkoKgBsg0MJAZyJxbQAbOFshxImJCQYTgXANEZUANjCuQ4l/OKLL3TnnXfq5z//ucF0AEyhqACwhXMdSjh8+HD9/ve/N5gMgEkUFQC2cL5DCQEEL9aoALCFP//5z63/Hhoaqn379hlMA8AuGFEBYGuHDh3Sz372My1atEivvvqq6TgAfIzTkwEAgG0xogIAAGyLogIAAGyLogIAAGyLogIAAGyLogIAAGyLogIAAGyLogIAAGyLogIAAGyLogIAAGyLogIAAGyLogIAAGyLogIAAGzr/wf2+25tErmyvwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@np.vectorize\n",
    "def tau_B(h2):\n",
    "    sec2.thick = h2*sec1.thick\n",
    "    tau = conn.calck(om,k,pl01,2)\n",
    "    return tau[pl02][2][0]\n",
    "\n",
    "h2 = np.logspace(-1,1,21)\n",
    "pl.semilogx(h2,-10*np.log10(tau_B(h2)))\n",
    "pl.xlabel(r'$\\frac{h_2}{h_1}$')\n",
    "pl.ylabel('R/dB')\n",
    "#reset the thickness for further use\n",
    "sec2.thick = sec1.thick"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8.2 Arbitrary Junctions\n",
    "\n",
    "* we can also handle arbitrary angles $\\theta$ for the orientation  the plates\n",
    "* transfer of energy may occur from one wave type to another (e.g. bending waves to L-waves)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ERKqmkkXzZE1mRFHEI488gnXr1iEpKQnx8fFNPiYvLw/p6emIiIhohwivDZtMRESkahZ17Jot65iZBQsW4PPPP8cXX3wBX19fZGVlISsrC+Xl5QCAkpISPPHEE9izZw8uXryIpKQkTJ8+HSEhIbj11lvlDL1ZOJuJiIhUyVaZYZupYStWrAAAjBs3rtbtK1euxLx586DVanHs2DGsWrUKhYWFiIiIwPjx47FmzRr4+vrKEHHzCNzPgIiI1Mw2Zkbhi+bJ3mZqjKenJzZt2tRO0bQ+bmdARESqZuF2BlSFhRkiIlIllbSZmMy0IXuXidOZiIhIjVTSZmIy05bYZSIiIjVjm4lsWJghIiJVsm1noGVlxmXZtjNgLkNERKpkZmXG5XEyExERqZo9mWFlxuWxzURERKpkGzPTwGym1zedQr/ETfjP1vq3GGovTGbaUPWaecxmiIhIZawWwGqWLjfQZiosM8FQYYZV5m/tTGaIiIioLluLCWiwzVRcISU7vh7y7lvNZKYNcddsIiJSLUuNZKaBNlNxhQkA4Ofh1h4RNYjJTBsSuNAMERGplW3BPAiAtv5khZUZIiIiUi7bVgY6fYPTc6uTGVZmnFZ1m4l9JiIiUhmLbSuDhvdlsrWZWJlxYmwyERGRapkbn5YNVFdm/DxZmXF6rMsQEZHq2BfMqz+ZsVhFFBs5Zsb5VfWZ2GUiIiLVsTSezJRUJTIAkxmnxjYTERGplm0AcBPTst11Guh12vaKql5MZtoBVwAmIiLVsU3NbmLBPD+ZqzIAk5k2xUXziIhItSyN75itlGnZAJOZNsVF84iISLXss5kaqswoY1o2wGSmXbAwQ0REqtPEbKbqNhMrM06NbSYiIlKtJmYzsTLjIthkIiIi1Wpi0TyDQvZlApjMtBOWZoiISGXMjQ8ANtgrM2wzOTW2mYiISLUsjk3NZmXGyQkN7DJKRESkeE0umsep2S6FlRkiIlIdc+O7ZnMAsIvhCsBERKQ6tsoMp2YTERGRKlkcWzSP2xk4OQ4AJiIi1bK3mRqYzVTOMTMugdsZEBGRajXZZuKYGZfCwgwREamObWp2PW0mi1VEaaUFAJMZp8c2ExERqVYji+aVVA3+BdhmcnpsMhERkWrZk5m6lRnb6r96nQbuOvlTCfkjcAGcmk1ERKpTXiCdewTUucs+LdtT/qoMwGSmTdkXAGYuQ0REalOaI517d6hzl5IG/wJMZtoUZzMREZEqWcxAWb502Se0zt0GBW1lADCZaRcszBARkaqU5UH66yUAnkF17lbSgnkAk5k2VT2biekMERGpSOkV6dwrGNDWTViUtGM2wGSGiIiIrmYbL1NPiwmoMWZGzzaTy2BdhoiIVKWkqjLjHVLv3azMuBChqs/ELhMREamKrc3kXX9lhgOAXQjnMhERkSo52Gby82RlxmWwMENERKrSRJuJlRkXwtlMRESkSk20mbhongthm4mIiFSpkdV/AQ4AdkmsyxARkaqU5krnPg0lM7ZF89hmcnqCwNoMERGpjCg60GZiZcb1sDRDRERqUVEIWCqly/W0mcwWK8oqLQA4ANgl2AcAM5shIiK1sLWY9H6Am0edu0uMZvtlVmYALFu2DEOHDoWvry9CQ0MxY8YMnD59utYxoigiMTERkZGR8PT0xLhx45CcnCxTxM3DJhMREalOSeODfw3lUjLj6aaFm1YZNRFZo9ixYwcWLFiAvXv3YsuWLTCbzZg8eTJKS0vtx7z22mt44403sHz5cuzfvx/h4eGYNGkSiouLZYy8eTgzm4iIVKOJmUwGhU3LBgBZI9m4cWOt6ytXrkRoaCgOHjyIMWPGQBRFvPnmm3juuecwc+ZMAMCnn36KsLAwfPHFF/jrX/8qR9iO43YGRESkNk3OZFLW4F9AYWNmioqKAABBQUEAgJSUFGRlZWHy5Mn2Y/R6PcaOHYvdu3fX+zOMRiMMBkOtk1zYZiIiItVpos1UvWCeMgb/AgpKZkRRxOLFi3H99dejT58+AICsrCwAQFhYWK1jw8LC7PddbdmyZfD397efoqOj2zZwB3AAMBERqYbKpmUDCkpmFi5ciKNHj+LLL7+sc9/V67WIotjgGi7PPPMMioqK7Kf09PQ2idcR1dsZyBYCERFR89iSGZUsmAfIPGbG5pFHHsEPP/yAnTt3omPHjvbbw8PDAUgVmoiICPvtOTk5dao1Nnq9Hnq9vm0DdpDARhMREalNk20mqTKjlB2zAZkrM6IoYuHChVi7di22bduG+Pj4WvfHx8cjPDwcW7Zssd9WWVmJHTt2YNSoUe0dbouxMENERKrRRJvJoMAxM7KmVQsWLMAXX3yB//3vf/D19bWPg/H394enpycEQcCiRYuwdOlSdO3aFV27dsXSpUvh5eWFu+66S87QHcI2ExERqY49mWliNpNeOZUZWSNZsWIFAGDcuHG1bl+5ciXmzZsHAHjyySdRXl6Ohx9+GAUFBRg+fDg2b94MX1/fdo62+dhkIiIiVaksAypLpMsqmpotaySiAyULQRCQmJiIxMTEtg+ozbA0Q0REKmCrymj10nYG9VBim0kxs5mcEdtMRESkKjVbTA3MGlZiZYbJTBvibCYiIlKVJqZlA1w0z2WxMENERKpgn5Zd/0wmgFOzXY+9zcR0hoiIVKCJTSaB6jEzSlo0j8kMERERSZrYZNJksaLCZAXAMTMuwzZihnUZIiJSBQdX/wUAHwWtM8Nkpg01tH8UERGRIjW5yaTUYvJy10KnVU4KoZxInBiHzBARkSo0ucmk8qZlA0xm2hTbTEREpCpNtJmUuGAewGSmTbHLREREqmExA+X50uUG20xV07JZmXE9nJpNRESKV1Y1k0nQAF5B9R5S3WZiZcZlsDJDRESqYWsxeQUDGm29hxjKbW0mVmZcBrczICIi1WhiJhPAyoxLY5eJiIgUz57MhDR4SLF99V9WZlyGfddszmciIiKls7WZfBypzDCZISIiIqVxpM1k5NRsl8U2ExERKZ5DbSZWZlyObTsDJjNERKR49tV/G67MGOzrzLAy4zI4l4mIiFSjidV/AaCYU7NdFwcAExGR4tnbTA0nMwZOzXY99tlMzGWIiEjJRNGhNlNxBSszLoeL5hERkSqUFwBWqeoCr/oHAFearTCarQA4ZsYlsTBDRESKZqvK6P0BN496D7FVZQDAh5UZ12Hfm4nZDBERKZm9xdTI4N+q8TLe7lpoNcrqPDCZISIicnWOzGSyTcv2VFaLCWAy06aqCzMszRARkYKV5krnjc5kUubgX4DJTJsSlFWFIyIiql+pI5UZZW5lADCZaRecmk1ERIrmwCaTBoVuZQAwmWljVdsZyBwFERFRoxxoMxUrdME8gMlMm2KbiYiIVKFZbSZWZlySyD4TEREpmQNtJqXumA0wmWlTXGaGiIhUwaE2k1SZUdrqvwCTmTYlsM9ERERKV1kKmEqly41NzS6vWmeGlRnXxC4TEREplm31X50HoPdt8LBiI6dmuyS2mYiISPFKqpIZ7w6NzlzhmBkXxS4TEREpngMzmQBOzSb2mYiISKnsm0w2PJMJ4NRsl2WrzDCVISIixbK3mUIaPYwrALsoAewzERGRwtnbTA1XZipMFlSarQC4a7bLYpeJiIgUq7TGAOAG2MbLCALg487KjGuxt5mYzRARkUKVND1mxjZexsddB41GeV0HJjNtSHlvNxER0VWaUZlR4ngZgMlMu2CbiYiIFMuhTSaVOy0baGEyc/bsWXz33XdISUkBAKxfvx5jxozB0KFD8corr3BjxSq27Qz4z0FERIpkMQHlBdJlB9pMSq3MNDuqdevW4c4774RGo4EgCHj//ffxl7/8BePHj4efnx8SExOh0+nw1FNPtUW8RERE1FpsG0wKGsAzqMHDnK7N9Morr+DJJ59ERUUFVqxYgfnz5+PVV1/Fzz//jJ9++glvv/02PvnkkzYIVX24nQERESmarcXkFQJoGk4JDLYdsxU4LRtoQTJz+vRp3HfffRAEAXPnzkVlZSUmTpxov3/y5MlITU1t1SDVitsZEBGRojkwkwlQ9oJ5QAuSmdLSUvj6SrtqajQaeHp6wsvLy36/p6cnjEZj60WoYl7uWgCAodwkcyRERET1KHVs9d/qMTNOUpkRBME+sLW+61QtNtgbAHC5qBxGs0XmaIiIiK7iwOq/gPLHzDQ7KlEU0a1bN3sCU1JSgoEDB0JT1WvjTKZqwd7u8HbXorTSgvT8cnQJ9ZE7JCIiomrN3mRSmZWZZiczK1eubIs4nJIgCIgN9saJTANS80qZzBARkbI4uMmkrTLj5yyVmblz57bak+/cuROvv/46Dh48iMzMTKxbtw4zZsyw3z9v3jx8+umntR4zfPhw7N27t9ViaGtxIV44kWnAxbwyuUMhIiKqzUnaTLKuAFxaWor+/ftj+fLlDR4zZcoUZGZm2k8bNmxoxwivnW3cTGpeqcyREBERXcWBrQwAJ2szBQYGOjzYNz8/v8ljEhISkJCQ0Ogxer0e4eHhDj2nEsUFSzO9WJkhIiLFsU/NbjyZMdjbTE6QzLz55pv2y3l5eXj55Zdx4403YuTIkQCAPXv2YNOmTXjhhRdaLcCkpCSEhoYiICAAY8eOxSuvvILQ0IbLYUajsdbUcIPB0GqxtAQrM0REpEhWK1BWtQJwI20mURSdazuDmuNlbrvtNvz973/HwoUL7bc9+uijWL58ObZu3YrHH3/8moNLSEjAHXfcgdjYWKSkpOCFF17AhAkTcPDgQej1+nofs2zZMixZsuSan7u1xFUlMxkF5TBZrHDTcm9PIiJSgIpCwCpVXBobAGw0W2GySDOVlZrMtPgv66ZNmzBlypQ6t994443YunXrNQVlM2vWLEydOhV9+vTB9OnT8fPPP+PMmTNYv359g4955plnUFRUZD+lp6e3SiwtFeqrh4ebBhariEsF5bLGQkREZFdSNfjXwx/Q1V8gAKq3MhAEwNvdyZKZ4OBgrFu3rs7t33//PYKDg68pqIZEREQgNjYWZ8+ebfAYvV4PPz+/Wic5aTQCYoOk6sxFtpqIiEgp7IN/HZvJ5KPXQaNR5iK5LU6xlixZgvvvvx9JSUn2MTN79+7Fxo0b8eGHH7ZagDXl5eUhPT0dERERbfLz20pssBdOZxcjlYOAiYhIKezTspuayaTswb/ANSQz8+bNQ8+ePfHWW29h7dq1EEURvXr1wm+//Ybhw4c79DNKSkpw7tw5+/WUlBQcOXIEQUFBCAoKQmJiIm677TZERETg4sWLePbZZxESEoJbb721pWHLIi6ElRkiIlIYB2cyKX3wL9CCZGbz5s0YP3483NzcMHz4cKxevbrFT37gwAGMHz/efn3x4sUApIHGK1aswLFjx7Bq1SoUFhYiIiIC48ePx5o1a+wbXapFbNX0bFZmiIhIMRxeY8YJKzPz589Hfn4+brzxRtxyyy246aabEBAQ0KInHzduXKN7OW3atKlFP1dpbDOaWJkhIiLFcHD1X0O58iszzR4AfOHCBezcuRN9+/bFm2++ifDwcNxwww146623cPHixTYIUf1slZmM/HJYrNyIk4iIFKC0ao2ZJttMyt7KAGjhbKZ+/frh+eefx759+3DhwgXccccd2LhxI3r27In+/fvjxRdfxIEDB1o7VtWK8PeEu1aDSosVmUWcnk1ERApQ4ugAYGVvZQC0wt5MkZGRmD9/PjZs2IDc3Fy8+OKL+PXXX5GQkIClS5e2Royqp9UIiA7yBMBxM0REpBCOtplUUJlp1ciKi4uRlJSEPXv2oLS0FHl5ea3541UtNtgb56+U4mJeKa7r0vhW60RERG3O1mZqZPVfoGabyYkqM4WFhbj77rvRoUMHREZG4q233oLVasWLL76ITp06Ye/evfj444+h0WjQoUPjpStXwhlNRESkGMYSwFT198inqUXzlD8AuNmRPfvss9i5cyfmzp2LjRs34vHHH8fGjRtRUVGBn3/+GWPHjm2LOFXPPqMplzOaiIhIZrYWk84TcPdp9FD71GxP5VZmmp3MrF+/HitXrsTEiRPx8MMPo0uXLujWrVutHbWpLlZmiIhIMewtpg7SpkuNMKigMtPsNtPly5fRq1cvAECnTp3g4eGBBx54oNUDcza2ykxqfimsnJ5NRERyss1kamJaNlBz0TzlJjPNjsxqtcLNrbrUpNVq4e3t3apBOaOoQE9oNQIqTFbkFBsR7u8hd0hELsdqFVFQVomcYiOKyk0oNZpRYjSj1GhBqdGM0kpz1W3SdZPF2uTP1GoE+Oh18NHr4K3Xwdej+rJP1WU/DzeE+uoR4OUGoYlvwUTtwsFNJgF1TM1udjIjiiLmzZsHvV7aLryiogLz58+vk9CsXbu2dSJ0Em5aDToGeiI1rwwX80qZzBC1MrPFikuF5biYV4bsogpkGyqQU2y0n+cYKnClxAiTRb7KqF6nQYS/B8L8PBDh74Fwf0+E++kR7u+JCH8PxIV4w1/B4xLIidiTmcZnMomiqIpF85od2dy5c2td/9Of/tRqwTi72GBvpOaVITWvFCM6BcsdDpHqiKKIbIMRF3JLcDG3DCm5JUjJLcWF3FKk55c5nKgEebsjwMtNqqC4V1VR9Nqqc+m6t14Hd91Vnfh6tl8xWUR7hafEXukxo7ii+nJRuQkFZSYYzVZczCvDxUbGzoX56dE11BddQn3QNcwHXUN90TXUB4He7s36tyJqlL3N1HhlpsJkhblqaIRTVWZWrlzZFnG4hLhgL+wEGv1FRkQSo9mCs9klSL5chOOXDEi+XIRTWcUoq7Q0+Bi9ToO4YG9EBHggzNcDoX56hPp5INRXj1BfPcL8PBDio6+bpLSDCpMFOQYjsgwVyCwqR1ZRBbIMFfbzy4XlyDYY7adfz+XWenyIjx5dQ33QK9IPg2MDMSgmkBVeajmHN5mUWkwaAfB217Z1VC2m3JqRE4q1DQLmhpNEtVSYLEi+bKhKXIqQfNmAM9nF9VZatBoB0YGeiA/xRnyID+I7eCM+2BvxHbwR4ecBjUaZY1I83LSICfZCTNXMxvoUV5hwLqcEZ3NKcDa7uOq8BJcKy5FbYkRuiRF7LuTho19TAACR/h4YWJXYDIoJQO9If1kSNVIhB5MZQ40F85Q83ovJTDuKq/oldjGXlRlybUXlJhxMzce+lALsv5iPoxmF9SYu/p5u6BPlh96R/ugd6YfekX6ICfJ22j/Yvh5uGBgTiIExgbVuLzWacf5KCU5nFeOPjEIcSi3EqSwDLhdV4PLRTKw/mgkAcNdp0DfKH8PigzC2WwcMjg2Em9Y5/63oGjnYZlLDtGyAyUy7slVm0vLLIIqiorNcotaUbajAvpR87L+Yj30p+TidXVxn+EmIjx79OtqSFn/0ifJDVIAn/58A8Nbr0K9jAPp1DMAdQ6IBSAnOH+mFOJRWgENp0nlhmQkHUwtwMLUAK5LOw0evw3VdgjGueyjGde+ACH9PmV8JKUapo5tMKn8rA4DJTLuKDvKEIAAlRjPySisR4qOXOySiNlFhsmDvhTwknb6CnWeu4EI9K1/Hh3hjaFwghsYFYVh8EGKCvJi4NIO3XodRXUIwqmqvN1EUkZJbioOpBfjtXC52ns1FfmklNiVnY1NyNgCge5gvxnXvgLHdO2BIbJDTVrioCaW5QEWRdNk/utFD1bCVAcBkpl3pdVpE+nviUmE5UvNKmcyQ07D9IU06fQU7zlzB3gt5MJqr12gRBKBnuB+GxUuJy5C4QIT6cvBqaxIEAZ06+KBTBx/cMSQaVquIY5eKkHT6CpLO5OBIeiFOZxfjdHYx3tt5Ab56HSb3DsfNAyJxXedg6NiOch3Zx6XzwHhA7+BWBkxmqKa4EC9pLYzcMgyODZI7HKIWqzBZsPt8Lrafkv5YpueX17o/wt9DqgJ064CRnUO4fko702gE9I8OQP/oADw2sSsKSiux8+wV7KhKOPNKK/HdoQx8dygDwd7umNovAjf3j8SgmEDFDqKmVpKdLJ2H92nyUDUsmAcwmWl3MUHe+A15nNFEqlReacGOMznYcCwL207loMRott/nphXsA0/HdQ9F11Afto0UJNDbHbcMiMItA6JgtYo4mFaA/x25hA3HspBXWolVe1Kxak8qogI8Ma2/lNj0ivDje+iMsqoqM2GOJDPKXzAPYDLT7uwzmrjWDKlEidGMbadysPF4JrafuoJyU/U6L+F+HpjYKxTjuoViZOdgeOv5K0UNNBoBQ+OCMDQuCC9N743fzuXihyOXsSk5C5cKy/Hejgt4b8cFdAn1weyh0bhjcDT8vZT9zZyawdZmCuvd5KHVbSZlv//8zdPOuNYMqUGJ0YzNyVnYcCwLO89eQWWN8S8dAz2R0CccCX0jMKBjAFsSKuem1VTNdgpFhcmCbady8MORy9h2Ogfnckrw8vqT+Ofm07i5fyTuHRmHPlH+codM18JiAq6cki47UJkxlHMAMNUjLoSVGVImi1XE7vO5WHvoEjYez6pVgYkP8ZYSmD4R6BPF1oOz8nDT4qa+EbipbwQMFSb8+MdlfLYnFaeyivH1gQx8fSADA6IDcM+IWEztFwEPN+WuCEsNyDsHWCoBdx8gILbJww2cmk31iQmSkpmichMKyyoR4MX9VkheZ7OL8e2hDHx/+BKyDUb77fEh3pjePxI39Q1H9zBfJjAuxs/DDXcPj8Vdw2JwMLUAn+1NxYZjmTiSXogj6YV4ef0J3Dk0Gn8aHovooIZXNSaFsQ3+DesNaJqewcap2VQvL3cdwvz0yDYYcTGvDAOYzJAM8kqM+OGPy1h76BKOXSqy3+7v6Yab+0di5qAoDIgOYAJDEAQBQ+KCMCQuCM9P7YWvD6Rj9d5UXC6qwHs7LuD9nRdwY69wLJzQhS0oNcg6Jp07MF4G4ABgakRssDeyDUak5pViQHSA3OGQixBFEXvO5+Hz31OxOTnbvhOuTiNgfI9Q3DYoCuN7hEKvY+uA6tfBV48F47tg/tjO2HYqB5/tTcXOM1ewMTkLG5OzML57Byyc0BWDYwOb/mEkj5qVGQcUGzk1mxoQF+yFfSn53KOJ2kVRmQnfHsrA6t9TceFK9cDzfh39MXNgFKb3j0QwF3CkZtBqBEzqFYZJvcJwNrsY7ySdx/+OXML201ew/fQVjOocjIUTumBkp2BW95TGnsz0dehwLppHDeKMJmoPf6QX4vO9qfjx6GVUmKTZSN7uWtw6KAp3D49Fzwg/mSMkZ9A1zBf/njUAj93QFe/uOI/vDmVg9/k87D6fh0ExAXhkQleM696BSY0SlOUDxZely2G9mjxcFEXuzUQNi6tKZi4ymaFWVl5pkWag7E2tNRamR7gv/jQiFjMGRsGHa8FQG4gL8cart/XDIzd0xfs7zuPL/ek4lFaIP3+yH70j/bBoYjdM7BnKpEZO9m0M4gC9b5OHl1VaYKlqR/t5Kvv3hrKjc1KxVQvnpeWzzUSt40qxEZ/tuYjP9qaioEzqcbtrNZjaLwJ/GhGDQTGB/CNC7SIqwBNLbumDBeO74INdF/D53jQkXzbgwVUHMDw+CM9N7Yl+HQPkDtM1NWPlX6C6xaTVCPBU+DR8JjMysCUzuSWVKK4wKb58R8p1LqcYH+5KwdrDl+wL20UHeeJPw2Nxx5BoBHlzthzJI9TPA89N7YWHxnXB+zsv4OPfUvB7Sj5uXv4bbh0YhSdu7I6oAE+5w3QtzR38W2NattK/DDGZkYGvhxtCfNyRW1KJ1LwyTmekZhFFEXsv5OODXRew7VSO/faBMQH4y+hOmNw7HFquyksKEeTtjqcTeuCekbH456bTWHf4EtYdvoQNxzJx//XxeGhcZ36hay/ZzavMGFQyLRtgMiOb2GBvJjPULCaLFRuOZeKDXRdw/JIBACAIwOReYfjLmE7chZ0ULSrAE/+eNQB/vi4OL68/iX0p+Xgn6TzW7E/HokndMGdoNHTaphdxoxaymIGck9Ll5lZm9MpPNpnMyCQ22AsHUws4CJiaVGm24tuDGXgn6RwyCsoBAB5uGtwxOBr3XR+P+BBvmSMkcly/jgFY85cR2HIiG6/+fAoXckvxwvfH8clvKXh+ai+M7xEqd4jOKf88YDECbt5AYLxDD1HLgnkAkxnZxAZxejY1rsJkwTcH0rEi6TwuF1UAAIK93TF3VBz+NCKW42FItQRBwOTe4RjfIxRf/J6GN7eewfkrpfjzJ/txU99wJE7vjVA/D7nDdC72lX97ObSNAQDVTMsGmMzIhhtOUkMqTBZ8uS8N7+44b98rKcxPj/ljO2POsBhu7kdOw02rwdxRcbh1UBSWbzuHj35NwYZjWdh1JhdPJfTAXcNiuCt7a2nm4F8AMFS1mZQ+LRtgMiMbLpxHVyuvtGD176l4b+cFXCmWkpgIfw88NK4z7hwSzSSGnJafhxuevaknZgyIwjNrj+KPjCI8//1xrDt8Cctm9kW3sKbXRKEm2JMZxwb/AtVjZvxYmaGGxFVNz842GFFWaYaXO98KV1VeacFney/i/Z0XkFtSCUAaLPnw+M64fXBH7pVELqNXpB/WPnwdVu25iH9uOo2DqQWY+tYuzB/bGQvGd2FCfy2aOZMJ4JgZckCAlzv8Pd1QVG5CWn4ZeoRzaXlXY7ZY8fWBDPznlzP2dlJ0kCcWjOuCmYM6wl3HmR3kerQaAX++Lh439g7Hi/9LxtaT2fjvtnP46Wgmlt7aFyM7B8sdovqU5QOGS9JlB7YxsGEyQw6JC/bCHxlFuJjLZMaViKKIn49n4Z+bTuNCrtRmjArwxGMTu+LWgVFw4/RUIkQGeOKDewdjU3IWXvxfMlJySzHng724Y3BHvDC9lypaH4phazEFxAAeji8FUr1onvL/rZnMyCg22Bt/ZBRx3IwL+e1cLv6x8RSOZkj7JgV5u2Ph+C64e0QM20lEVxEEAVP6RGBUlxC8tvEUPt+bhm8OShtZ/nvWAAyL59pKDmnBeBkA9q1R1JA4MpmRkW3cDGc0Ob9jGUX4x8ZT+PVcLgBp9+oHRnfCA6PjVfGth0hOfh5ueHlGX8wYEIXFX/+BtPwyzH5/DxaM74JHb+jKamZTWjBexmIVcTJTWpyza5hPW0TVqpjMyIgzmpxfWl4Z/rHpFNYfzQQAuGkF3D08FgsndEGIj17m6IjUZUhcEDY8Nhov/S8Z3x3KwH+3ncPOs7l4c9YALh7ZGHsy4/i07DPZxSirtMBXr0OXDkxmqBG2tWZSWZlxOiVGM5ZvO4ePf01BpcUKQQBuHRCFxyd1Q3SQl9zhEamWj16Hf93ZH+N7dMCza4/hj/RCTH1rF16a3gt3DolW/IaI7c5qqbGNgeOVmcNphQCAftH+qljrh8mMjGyVmctF5TCaLRwz4QSsVhHfHszAa5tOI7dEmqF0fZcQPDe1J3pGcJA3UWuZ1i8Sg2ICsfjrI9h7IR9PfXcM209dwbKZfRHI1bGr5Z0HzBWAmxcQ5Ng2BgBwJL0AADAwOrCtImtVTGZkFOztDh+9DiVGM9Lzy9ElVPmlPGrYvpR8/P2nZPsmkHHBXnh+ai/c0DOU3xaJ2kBkgCdWPzACH+y6gH9tPo2NyVk4nF6Af90xANd3DZE7PGWwtZhCewIax78w2yozA6IDWj+mNsBRUzISBAGxwbZWE8fNqFV6fhkWfHEId763B8cvGeCr1+G5m3pi8+NjMbFXGBMZojak1QiYP7Yz1j18HTp18Ea2wYg/ffQ7/rnpNCxWUe7w5NeCmUyGChPOXSkBAAyICWiDoFofkxmZxVW1mjijSX3KKs341+bTuOGNHVh/NBOCAMwZFoPt/zcOD47pxEXviNpRnyh/rH9kNO4aHgMAWL79HP78yX4UllXKHJnMWjCT6Wh6EURRWsRTLRMV2GaSGSsz6iOKIjafyMaSH5Ltu1mP6BSEF6f1Rq9IjoshkounuxZLb+2LYXFBeHrtUew8cwXTl/+Kd/80GL0jHV8szqm0YIPJw2nqGi8DMJmRHSsz6pKeX4bEH5Lxy6kcANLKvS9M64kbe4eznUSkEDMGRqFbmC/mf34QafllmPnObiyb2RczB3WUO7T2VV4AFKVLl5uRzBxJLwSgnvEyAJMZ2cWwMqMKlWYrPth1Af/ddhYVJivctAIeHN0Jj0zoCk93zkIjUppekX74ceH1eGzNYSSdvoLFX/+BP9IL8dzUXq7TAs4+IZ37RwOeAQ49RBRFHK5KZgaqZLwMIPOYmZ07d2L69OmIjIyEIAj4/vvva90viiISExMRGRkJT09PjBs3DsnJyfIE20ZslZmMgnKUGs0yR0P12XM+Dze9tQuvbzqNCpMVIzoF4efHRuPJKT2YyBApmL+XGz6eOxSP3tAVAPDpnlTc9cFe5BgqZI6snbRg8G96fjnySyvhrtWoqm0uazJTWlqK/v37Y/ny5fXe/9prr+GNN97A8uXLsX//foSHh2PSpEkoLi5u50jbTpifHjFBXrBYRew6e0XucKiG3BIjFq85gjkf7MW5nBIEe7vjjTv748sHR6BLqK/c4RGRAzQaAYsndcOH9w6Br4cOB1ILMPW/v+LAxXy5Q2t72cek8+aMl6laX6ZXpJ+q1j6TNZlJSEjAyy+/jJkzZ9a5TxRFvPnmm3juuecwc+ZM9OnTB59++inKysrwxRdfyBBt2xAEAZN7hQEANp/IljkaAqSF7774PQ0T/pmEtYcvQRCAu4fHYNvfxmHmoI4cG0OkQhN7heGHhdeje5gvrhQbMfv9vfh8b6rcYbWtFg3+LQSgrhYToOCp2SkpKcjKysLkyZPtt+n1eowdOxa7d++WMbLWN7l3OADgl5M5MFusMkfj2i7mluKuD/fi2XXHYKgwo0+UH9Y9fB1eubUv/L24ISSRmsWHeGPdglGY3j8SZquI578/jlfWn4DVGdejsVqqx8yE93X4YYdVOPgXUPAA4KysLABAWFhYrdvDwsKQmtpwNm00GmE0Gu3XDQZD2wTYigbHBiLI2x35pZXYdzEfozpz5cr2ZrZY8fFvKfjX5jMwmq3wdNPiiRu7Y96oOGhVsC8JETnGy12Ht2YPQPcwH/xz8xl8sCsF6fnl+PesAc41Bi4/BTCXAzoPIKiTQw+pMFlw4nIRAGBQjHqmZQMKrszYXF3SF0Wx0TL/smXL4O/vbz9FR0e3dYjXTKsRcEOPUADA5mS2mtrbqSwDbluxG0s3nILRbMV1XYKxadEY3H99PBMZIickCAIWTuiK/8weAHetBhuTszD7g724Umxs+sFq0YJtDE5kGmCyiAj2dkfHQM82DK71KTaZCQ+XWi+2Co1NTk5OnWpNTc888wyKiorsp/T09DaNs7XYWk1bTmRDFJ2w5KlARrMFb2w5g2lv/Yo/Morg66HDa7f1w+f3D7dPmSci53XLgCisfnA4Arzc8Ed6IW595zeczXaSCSYtWPm35ngZtY0NVGwyEx8fj/DwcGzZssV+W2VlJXbs2IFRo0Y1+Di9Xg8/P79aJzUY3TUEnm5aXCosx4lM5bfG1O5wWgGm//dXvPXLWZitIib1CsPWxWNx59Bo1f0nJqKWGxoXhHUPX4e4YC9kFJRj5ord2H0uV+6wrl0LpmWrcbE8G1mTmZKSEhw5cgRHjhwBIA36PXLkCNLS0iAIAhYtWoSlS5di3bp1OH78OObNmwcvLy/cddddcobdJjzctBjTTRorw1ZT26kwWfDyTycwc8VunMkuQYiPO96+axDev2cwwvw85A6PiGQQH+KNtQ9fhyGxgSiuMOPej/fh24MZcod1bbKqKjPhzanMVG1joLLxMoDMycyBAwcwcOBADBw4EACwePFiDBw4EC+++CIA4Mknn8SiRYvw8MMPY8iQIbh06RI2b94MX1/nXONjUi+p1cQp2m3jSHohbnprFz78NQWiCMwcGIUtj4/F1H4RrMYQubggb3d8/sBw+0ynJ775A29sPq3Otn9FEVCUJl0O7eXQQ64UG5FRUA5BAPp1VN8+VrLOZho3blyjHxRBEJCYmIjExMT2C0pGN/QIhUYATmYakJ5fhuggjttoDZVmK/677SzeSToPi1VEqK8er97WFxN6NDz2iohcj4ebFv+ZNQAxQZ54e/t5vLXtHNILyvHa7f3gplXsqIy6bFOy/aIAryCHHmJrMXUN9YGvh/qWoVDRu+P8Ar3dMSxe+uCxOtM6TmYacMvbv+G/287BYhVxc/9IbH58DBMZIqqXRiPg/27sgX/c1hc6jYB1hy/hr58dRHmlRe7QHNeiwb/q2ym7JiYzCjO5l21WU1YTR1JjzBYr3kk6h5uX/4qTmQYEernh7bsG4a05AxHg5S53eESkcLOGxuCDe4fAw02DbadycO/Hv6Oo3CR3WI6xJzMt2ClbZSv/2jCZUZhJVVsb7EvJR0FppczRqNOFKyW44709eG3jaZgsIib2DMPmqrExRESOGt8jFJ/dPxy+Hjrsv1iA2e+rZC2aZg7+tVhF/KHCnbJrYjKjMNFBXugZ4QerCPxyKkfucFTFahXxyW8puOmtXTicVghfvQ7/vKM/Prh3MDr46uUOj4hUaGhcENb8ZSRCfPQ4mWnAHe/uRnp+mdxhNcxqBXKqxsw42GY6l1OC0koLvN216KrSTXSZzCiQfePJZLaaHJVtqMDclfuQ+OMJVJisuL5LCDY9Pga3D+bGkER0bXpF+uHb+SPRMdATF/PKcPu7u3FGqYvr5Z4BTGWAVg8EdXboIbbxMv06Bqh21XMmMwo0ubeUzOw8e0Vdg85ksvF4Fqa8uRO7zuZCr9Ngyc29seq+YYgMUNdy3ESkXHEh3vjuoVHoFuaDbIMRd763x54EKMrJH6XzuOsArWMTlm0r/6p1vAzAZEaRekX4ISrAExUmK351hpUo20ip0Ywnv/0D8z8/iIIyE/pE+WH9o9dj7qg4aFT67YKIlCvMzwNf/3UkBsYEoLDMhLs//B27zl6RO6zajn8nnfe5zeGH2Ab/DlThyr82TGYUSBAE+0BgtprqdyitADe9tQtfH8iAIAAPjeuMtQ9dhy4q7fcSkToEeLnj8/uHY3TXEJRVWnDfJ/ux4Vim3GFJck4CV04CGjegx1SHHlJcYcKZHKllxsoMtTpbq2nryWyYLVaZo1EOs8WKN7eewR3v7kFqXhki/T3w5YMj8NSUHnDX8eNMRG3PW6/Dh3OHYGrfCJgsIhZ+cUgZ2x8cXyudd7kB8HRsvZhjGUUQRSAqwBOhvurd0kXWFYCpYcPiguDv6YaCMhMOphZgeKdguUOSXWpeKRatOWLv797cPxL/b0Yf+Huqb7VKIlI3vU6Lt+YMhK+HDl/tT8cT3/yB8koz7hkZJ09AoggkVyUzvWc6/LDDKp+SbcOvsgql02pwQ49QAFwNWBRFfHMgHTf9p3rK9X9mD8BbcwYykSEi2Wg1ApbN7Is/XxcHAHjhf8l4f+d5eYLJOgrknQN0HkD3BIcfZh/8q+LxMgCTGUWztZq2nMhW52ZnraCozISFXxzG/317FKWVFgyLC8LPi0bjlgFRcodGRARBEPDitF5YMF6aBr10wym8ufVM+//OtrWYuk4CPPwceogoijiSrt6dsmtim0nBxnTrAL1Og7T8MpzOLkaPcMc+oM5i74U8LF5zBJeLKqDTCHh8UjfMH9tZtesgEJFzEgRpPycvdx1e33Qab249i/JKC55O6NE+61y1sMWUUVCO3JJKuGkF9I5U998XVmYUzMtdh9FdQwAAm5Ndp9Vksljx+qZTmPPBXlwuqkBcsBe+e2gUFozvwkSGiBRrwfgueGFaLwDAezsv4KUfkmG1tkOF5tIhoDANcPMCut3o8MNs42V6RfjBw03bRsG1DyYzCmefou0iG09ezC3F7St24+3t5yGKwJ1DOmL9o6PRX+X9XCJyDfdfH49lM/tCEIBVe1Lx1HdHYWnrhMZWlemeALh7O/ww26J/ah8vA7DNpHg39AyDIBzD8UsGXCosR5STrmoriiK+OZiBxB+SUVZpgZ+HDstm9uPmkESkOnOGxcDDTYMnvjmKbw5moNxkwb9nDYCbtg3qB1Zr9XiZZrSYgBqL5al8vAzAyozihfjoMSRW+qBtddJZTbZBvk9+exRllRaM6BSEjYvGMJEhItW6dWBHLJ8zEG5aAT8dzcRDnx9ChakNtqdJ/x0ovgzo/YAuEx1+mNFsQfIlAwDnqMwwmVGByb3CAThnq2nX2Su48c2dWH8sEzqNgCendMfqB0ZwXyUiUr2EvhF4/54h0Os02HoyG/NW7kNxhal1n8TeYroJcHN80buTmcWotFgR6OWG2GCv1o1JBkxmVMA2bmbvhXzklRhljqZ1VJgsSPwhGfd8tA9ZhgrEV23i9vA4DvIlIucxvkcoPvnzMPjoddh7IR+z39+LK8Wt9HvcagFO/E+63Kd5Laaa42XaZcZVG2MyowJxId7oHekHi1XEi/9LVv2aM8cyijD1rV34ZPdFAMA9I2Kx/tHrOciXiJzSyM7B+OovIxDi447kywbc/u5upOWVXfsPTv0NKMkGPAKATuOb9VDbYnnOMF4GYDKjGktv7QudRsD6Y5nK2AOkBcwWK5ZvO4tb3/kN56+UooOvHp/8eSj+34w+8HLnWHQicl59ovzx7fxRiA7yRGpeGW57dzdOZhqu7YfadsjuOR3QuTv8MJPFigMX8wGofxsDGyYzKtE/OgCPT+oGAEj8IRkXc0tljqh5LuaW4s739uCfm8/AbBVxU99wbF40BuO6h8odGhFRu4gL8cZ380ehR7gvrhQbced7e7AvJb9lP8xiAk78IF1uZovptY2ncLmoAr4eOlZmqP3NH9sZw+ODUFppwWNrjsCkgt20RVHEF7+n4aa3duFQ1b5K/57VH2/fNQiB3o5/kyAicgahfh5Y89eRGBYXhOIKM+756HdsaclM1ZQdQHk+4BUCxI1x+GFbTmTjg10pAIDXb+8PH71zVMWZzKiIViPg37MGwM9Dhz/SC/HWL2flDqlR6fllmLdyP55dd6x6yvXjY3DrwI5OMeCMiKgl/D3dsOr+YZjYMwxGsxV//ewAvt6f3rwfcnyddN7rFkDrWEKSnl+Gv319BABw33XxmNInvHnPqWBMZlQmMsATy2b2AwC8vf1cy0uUbchkseK9Hecx6d87sOPMFbhrNXh+ak988cAIp130j4ioOTzctHj3T4Nwx+COsIrAk98dxbs7zjs2wcNsBE79KF12sMVUabZi4ZeHYagwo390AJ5O6HEN0SsPkxkVmtovArdX/Qd4fM0RFJW38roF1+BIeiFuXv4blv18ChUmK0Z0kna5fmB0J2g45ZqIyE6n1eC12/th/lhpx+1Xfz6Fv339BwxNrUVzfhtQUQT4hAMxIx16rmU/n8Qf6YXw93TD23cNhLvOuf78O9ercSGJN/dGbLAXLhWW4/nvj8s+Xbu4woSX/ncct77zG05mGhDg5YbXb++HLx8cgc4dfGSNjYhIqQRBwNMJPfD81J7QCMDaw5eQ8OYu/H4hr+EH2bcvmAFomt4g8udjmVj520UAwBt39kfHQPUvknc1JjMq5aPX4T+zB0KrEfDjH5ex7vAl2WLZeDwLE9/YgU/3pEIUgZkDo/DL4rG4Y0g0x8YQETnggdGd8PVfRyImSPqSOvuDvVj280kYzVdtgWAqB05vkC47sBdTal4pnvz2KADgr2M64YaeYa0duiIwmVGxAdEBeHxiVwDAi/9Lbp1FmJrhcmE5Hlx1APM/P4hsgxGxwV74/P7heGPWAAT76Ns1FiIitRsSF4QNj43GnUM6QhSB93ZcwIy3d+NMdnH1QWe3AJUlgH800HFooz+vwmTBgi8OodhoxuDYQDxxY/c2fgXyYTKjcg+N64JhcUEoMZrx2JrD7TJdOz2/DM9/fwzj/pmELSeyodMIWDi+CzYtGoPru4a0+fMTETkrH70Or93eH+/dMxhB3u44mWnAtP/+io9+TYHVKlbvxdR7BqBp/E/4K+tP4vglAwK93LD8roFts2u3Qgii3IMt2pjBYIC/vz+Kiorg5+cndzht4lJhOaa8uRPFFWY8ekNXLK5aXK+1nc4qxoqkc/jxaCYsVuljMyw+CC/P6INuYb5t8pxERK4qp7gCT317FNtPXwEATOjkhY9y5kAwlwMPbgeiBjX42B//uIxHvjwMAPjkz0NVuUBpc/5+O8dqOS4uKsATS2/ti0e+PIzl286ipMKMOcOi0bWVEoxDaQV4Z/t5bD1ZvbDTmG4d8PA4aRE/joshImp9ob4e+HjeUKz+PQ0vrz+B8NQfIbiVI88tEp8c90Jo2kWE+nkg1FePMD8PdPDVw02rwYUrJXj6O2mczILxnVWZyDQXKzNO5OnvjuKrGgsvDYkNxJxhMbipbwQ83Zse8V6TKIrYdTYX7ySdw94L0lo2ggAk9AnHQ2O7oG9H/1aNnYiIGnYxPQ1BH18HP9GAv5vuwceWhHqPC/Z2h0UUUVhmwvD4IKx+YDh0Km0vNefvN5MZJ2K1ithx9gq+/D0Nv5zKsbeCfD10mDkwCrOHxaBnRN1/A1EUcbmoAmeyi3E2uxhnsktwNKMQZ7JLAAA6jYBbB0Zh/rjOnGZNRCSHHxcBB1fC4NcVn/X9DFmlFmQbKpBTbERO1bnZWv3nPMTHHesfHY0wPw/5Yr5GTGZqcKVkpqYcQwW+OZiBL/elIaOg3H77gOgA3Da4I4wmC85UJS7nckpQYjTX+RkebhrMGRaDB0d3QiRX7iUikselQ8AHEwCIwLwNQNx1dQ6xWkUUlFUi22BETnEFuof7IsJf3b+3mczU4KrJjI3VKuK387n4cl8aNidn18rca9JpBMSHeKNbmC+6hvmgW5gvRnQKRhA3gyQiko/VCnx4A3D5ENBvFjDzfbkjajccAEx2Go2A0V07YHTXDrhSbMR3hzKw7WQOgn3c0TXMF92qEpe4YG+nW96aiEj1Dq+SEhm9HzDp/8kdjWIxmXEhHXz1mD+2s30fECIiUrCyfGBronR5/LOAr3Ou3tsa+FWciIhIiX5ZApQXAKG9gaEPyh2NojGZISIiUppLB4GDn0qXp/4T0LKR0hgmM0REREpitQDr/wZABPrNBmJHyR2R4jGZISIiUpJDq4DLh6sG/f5d7mhUgckMERGRUpTmSWNlAGD8cxz06yAmM0REREphG/Qb1gcY+oDc0agGkxkiIiIlyDggtZgA4CYO+m0OJjNERERyqznot/8cIHak3BGpCpMZIiIiuf32JpB5hIN+W4jJDBERkZz2vAP8UpXATHwJ8AmVNx4VYjJDREQkl70rgE3PSJdHPwEMuV/eeFSKyQwREZEc9r4LbHxaujz6b8CE5wFBkDcmlWIyQ0RE1N5+fw/Y+JR0+frFwIQXmMhcA0UnM4mJiRAEodYpPDxc7rCIiIha7vf3gZ+flC5f/zhww4tMZK6R4iex9+7dG1u3brVf12q1MkZDRER0DfZ9APz8f9Ll6xYBN7zERKYVKD6Z0el0rMYQEZH67fsA2PCEdPm6x4CJiUxkWomi20wAcPbsWURGRiI+Ph6zZ8/GhQsXGj3eaDTCYDDUOhEREclq/4fVicyoR4GJS5jItCJFJzPDhw/HqlWrsGnTJnzwwQfIysrCqFGjkJeX1+Bjli1bBn9/f/spOjq6HSMmIiKqwWoBdr1RtbovgFGPSIviMZFpVYIoiqLcQTiqtLQUnTt3xpNPPonFixfXe4zRaITRaLRfNxgMiI6ORlFREfz8/NorVCIicnVZx4EfHgEuH5Kuj1wITH6ZiYyDDAYD/P39Hfr7rfgxMzV5e3ujb9++OHv2bIPH6PV66PX6doyKiIioBlMFsPN1aYsCqxnQ+wOT/w4MmstEpo2oKpkxGo04efIkRo8eLXcoREREdV38DfjxUSDvnHS9xzRpB2y/CHnjcnKKTmaeeOIJTJ8+HTExMcjJycHLL78Mg8GAuXPnyh0aERFRtYoiYGsicOBj6bpPmJTE9LpZ1rBchaKTmYyMDMyZMwe5ubno0KEDRowYgb179yI2Nlbu0IiIiCSn1ksDfIszpeuD5kqDfD0DZA3LlSg6mfnqq6/kDoGIiKguUQQu/grs/i9wdpN0W1AnYPp/gPgx8sbmghSdzBARESmKqRw4+rW0t1JOsnSboAWuexQY+xTg5ilvfC6KyQwREVFTijKkhe8OfgKUF0i3uXkB/WcDw+cDHbrLGp6rYzJDzWO1ADkngIz9QMYBoCQHgCiVXBs61+kB33DAN0IaFOcbUXUKB3xCAa2bvK+JiKg+ogik7QV+fxc4+SMgWqTb/WOAYQ8Cg+4BPAPljZEAMJmhppTmViUu+4H0fcClQ4CptBWfQAC8O0jTFgPjpJ5zzZNPOKBR9ELVRORMrFYg8zBwZhNw8qfqVhIAxI2WqjDdEwANNz1WEiYzVFfBRWDXv4CUXUBBSt373X2BjoOBjkOlBARC1UJQDZybyoGSLKD4qlNJlrSgVGmOdMr8o+5z6TyAwPiq5KbqPLgLENwZ8I1kokNE166yDLiQBJz5GTizWfrdZKPzAPrNAob/FQjrLVuI1DgmM1TNWCztIbLnbcBSvSUEQroD0UOl5KXjMKk33BrfSqxWoCxPms5ouATkpwD5F6QEKv8CUJAKmCuAKyel09V0nlXJTScgqLOU4AR3qarohHGlTSJqmOEycGYjcHojkLJD+l1j4+4DdJ4gVWC6TQG8guSLkxzCZIakpOLoV8DWJdXfSOLHShuidRzadmslaDSATwfpFNGv7v0WE1CULiU2tkQn7zyQf16qHpnLpRJwzTKwjc6zqm0VX1XZqXHuHw3o3NvmNRGR8pgqgKyj0jg/23i/orTax/jHAN2nSMlL3PXSWD9SDSYzri59H/DzU9UboQXGAze+AnS/Sf7KhtateuzM1SxmoDC1OsHJOyclOXnnpQTIXN5wRUfQAH4dgYBoKbEJiAYCYqouxwD+HfmLjEitrFag8CKQcbB6vF/WMcBquupAAeg4REpeuicAob3k/51HLcZkxlUVXQK2vgQc+0a67u4LjHkCGPGQOv6Qa3VVbaXOQNdJte8zV1ZVdFKkllXBxerL+SlSolOUVvebWU0+4VJS4xcB+EVJs6/8IqWT7TLXkyCSj8Uk/X++cgrIPQ1cOSOd554FTGV1j/fuAEQNkRKYjkOAyEGAR+M7MZN6MJlxNeZKaSfXX/9d9R9eAAbeDUx4EfANkzu61qFzr050riaKQEm2NB6nKB0oTKs+L0yXLpvKpHZbSRZwqZHn8QyUBiH7hFafvEOl8To+HaRz71DAK5gDlYlaosJQ9f8zvfr/aUGKlLjkn5cmENRH6w6E96sa51eVvATEsvLixJjMuBKzEfj6XmnQGwDEjASmLAMiB8obV3sShKo1b8IBDK97vyhKg5IL06RFsoozpYGCV5+byqSFs8oL6h+zU+s5tdIAQq/gqlPNy8GAV4h07hkojU/yCAA8/KXqE5EzslqAsnzpi0VJNlB6RTo3XK5KXKq+XFQUNv5z3LyBDt2kSQr28x7SeDn+/3EpfLddRc1ERucB3Lwc6Hs7v6lcTRAA7xDpFDWo/mNEUdoh15bY2H4Rl+RIp9Kc6stledJCW6VXpFNzuPtWJzeeAVKC4xEglcb1foDet+qyb9V1v+rr7t7SjAyuhUFtTRSByhIpsS/Lr0ryq87LCqqv1/x/UppbvQBdUzwDa4xniwYCY4GQrlLS4hfF32EEgMmMa7g6kblrDdBpnNxRqZcgSMmFZwAQ2rPxYy1moCxXSmpKq87L8qRf+vbLuUBpnvQttLwQqCyWHltZLJ2K0lseq85TSmz0PlJyY0ty3L2kb7VuVfe7eVadbJe9pGN0eulnuHlI5zq9dL/Oo/rEFpq6WC3S2k/mCqCyVKoyVpZJCYmprPZtplKp1WMsrjoZqs8ralxuqN3TKEGqSPqEVbdpfcOrEpfYqgH6HaXknKgJTGacHRMZeWl1NdpaDrKYpMpPeWF1glNRKH3DrSiq/UelwlD/Zdu3XnO5dCrLbf3XZqN1rz7p9DXO9dL4Jfu5O6Bxk2apad2qHuNWdZu79G+lcQM0OumkrTrXuEkVJtvttsuCRrosaGufa7TSfQ2eBOkcVd/oay30iBqXa37jF6vOxNrXbbeJVulk28LDdr3WZYuUSFgt1Zft51YpIbCapfe/scuWSumyxSidm41Vt1VW32eukKYjm2ucTBXSZ6FFiYcjnwO91EL1DKx9st3m3aE6cfEOlaqf3MqEWgmTGWdmNgJfz61OZOZ8xURGDbRu1a2ulhBF6b2vLK2q7pRWnUoAY0n1ZVO59A3cVCZdrqxx2VRadV71B9BsrP42b66o/QfR9keU1EfnWV2lc/eqqsh5V1Xrqqpzev+qVmbNtqZv7ds9A6WKHVs+JBMmM87Knsj8XJ3IdB4vd1TUHgRBagu5eQDewW3zHBazlOSYKqQKga06UOvcKM2eM1dUVRVMVYmPuToBsta4bKmqQFht1QhL7cqE/XR1RcN23Vx9W62KyNUnsbpyVWtjVNS4XKMSU7NiY/v3rXkdqBqbJNSu/NjPq6pAGm39lSRBK7XqBG11pUpT87KudtVK61ZdAbOf6rnN1hp086jdFnSrahfqPDimipwGkxlnxESG2ppWB2h9OZ6BiBSBI/ecjbnyqkTmSyYyRETk1JjMOBNzZdVg35qJzAS5oyIiImpTTGachSgCPyysTmRmf8FEhoiIXAKTGWdx4CPg6BppEOHs1UCXG+SOiIiIqF0wmXEGlw4CG5+RLk9MBLpMlDUcIiKi9sRkRu3K8qUBv5ZKoOd0YNQjckdERETUrpjMqJnVCqx9UFruPqgTcMvbXLSKiIhcDpMZNdv5OnBuq7Qw1p2fSRsREhERuRgmM2p17hcgaZl0edobQHgfeeMhIiKSCZMZNSrKAL57AIAIDJoLDLhL7oiIiIhkw2RGbWwr/JbnAxH9gYTX5I6IiIhIVkxm1Gbz88ClA4BHAHDnKmkTOSIiIhfGZEZNjn0L7HtPujzzfSAwTtZwiIiIlIDJjFrknAJ+eFS6PPpvQLcb5Y2HiIhIIZjMqIGxGPj6HsBUCsSPAcY/J3dEREREisFkRulEEfj+YSD3DOAbCdz2MaDRyh0VERGRYjCZUbrf/gOc/AHQuEkDfn06yB0RERGRojCZUbILScAvS6TLN70GRA+VNRwiIiIlYjKjVIVpwDd/BkQrMOBPwOA/yx0RERGRIjGZUSJTBbDmnqqF8QYAU//JDSSJiIgawGRGaUQR2PA3IPMI4BkEzPoMcPOUOyoiIiLFYjKjNAc/AQ5/Dgga4PaPgIAYuSMiIiJSNCYzSpJxANjwf9LlCS8AnSfIGw8REZEKMJlRipIcaZyM1QT0mAZc/7jcEREREakCkxklsJiBb+8Dii8DId2AGSs44JeIiMhBTGbkJorAlheBi7sAdx9g1ueAh5/cUREREakGkxk5Wa3ApueAvW9L12e8A3ToLm9MREREKqOTOwCXZTYC3z8EHP9Oun7jUqDXLfLGREREpEJMZuRQYQDW3A2k7JT2XJrxDtDvTrmjIiIiUiUmM+2tOAtYfTuQdaxqjMxnnIJNRER0DZjMtKfcc8Dnt0r7Lnl3AO7+FogcIHdUREREqsZkpr1kHAC+uBMoywOCOgF/+k46JyIiomvCZKY9nNkMfDMXMJUBkQOBu74BfDrIHRUREZFTYDLTlqxW4PBnwE+PA6IF6HwDcOcqQO8jd2REREROQxXrzLzzzjuIj4+Hh4cHBg8ejF27dskdUsMsJuD8duCnxcAbPYEfH5USmX6zgbvWMJEhIiJqZYqvzKxZswaLFi3CO++8g+uuuw7vvfceEhIScOLECcTEKGRHaVM5cH4bcPJH4PTPQEVh9X16P2DEw8C4p7lFARERURsQRFEU5Q6iMcOHD8egQYOwYsUK+209e/bEjBkzsGzZsiYfbzAY4O/vj6KiIvj5teI2ARVF0liYUz8CZ7dI42FsvEKAHlOBntOB+DGATt96z0tEROQCmvP3W9GVmcrKShw8eBBPP/10rdsnT56M3bt31/sYo9EIo9Fov15UVARA+kdpVRuflcbD2PhFAd2mAN0SgOihgEYr3V5mBGCs90cQERFR/Wx/tx2puSg6mcnNzYXFYkFYWFit28PCwpCVlVXvY5YtW4YlS5bUuT06OrpNYqx2qur0Zhs/DxERkesoLi6Gv79/o8coOpmxEa4aayKKYp3bbJ555hksXrzYft1qtSI/Px/BwcENPqalDAYDoqOjkZ6e3rotLBXga+drd6XX7qqvG+Br52uX77WLooji4mJERkY2eayik5mQkBBotdo6VZicnJw61RobvV4Pvb72GJWAgIC2ChEA4Ofn53IfdBu+dr52V+Kqrxvga+drl0dTFRkbRU/Ndnd3x+DBg7Fly5Zat2/ZsgWjRo2SKSoiIiJSEkVXZgBg8eLFuOeeezBkyBCMHDkS77//PtLS0jB//ny5QyMiIiIFUHwyM2vWLOTl5eHvf/87MjMz0adPH2zYsAGxsbFyhwa9Xo+XXnqpTlvLFfC187W7Eld93QBfO1+7Ol674teZISIiImqMosfMEBERETWFyQwRERGpGpMZIiIiUjUmM0RERKRqTGZa6J133kF8fDw8PDwwePBg7Nq1S+6QWt2yZcswdOhQ+Pr6IjQ0FDNmzMDp06drHTNv3jwIglDrNGLECJkibj2JiYl1Xld4eLj9flEUkZiYiMjISHh6emLcuHFITk6WMeLWExcXV+e1C4KABQsWAHCu93znzp2YPn06IiMjIQgCvv/++1r3O/I+G41GPPLIIwgJCYG3tzduvvlmZGRktOOraJnGXrvJZMJTTz2Fvn37wtvbG5GRkbj33ntx+fLlWj9j3LhxdT4Ls2fPbudX0nxNve+OfMad8X0HUO//fUEQ8Prrr9uPUeL7zmSmBdasWYNFixbhueeew+HDhzF69GgkJCQgLS1N7tBa1Y4dO7BgwQLs3bsXW7ZsgdlsxuTJk1FaWlrruClTpiAzM9N+2rBhg0wRt67evXvXel3Hjh2z3/faa6/hjTfewPLly7F//36Eh4dj0qRJKC4uljHi1rF///5ar9u2aOUdd9xhP8ZZ3vPS0lL0798fy5cvr/d+R97nRYsWYd26dfjqq6/w66+/oqSkBNOmTYPFYmmvl9Eijb32srIyHDp0CC+88AIOHTqEtWvX4syZM7j55pvrHPvggw/W+iy899577RH+NWnqfQea/ow74/sOoNZrzszMxMcffwxBEHDbbbfVOk5x77tIzTZs2DBx/vz5tW7r0aOH+PTTT8sUUfvIyckRAYg7duyw3zZ37lzxlltukS+oNvLSSy+J/fv3r/c+q9UqhoeHi6+++qr9toqKCtHf319899132ynC9vPYY4+JnTt3Fq1WqyiKzvueAxDXrVtnv+7I+1xYWCi6ubmJX331lf2YS5cuiRqNRty4cWO7xX6trn7t9dm3b58IQExNTbXfNnbsWPGxxx5r2+DaWH2vvanPuCu977fccos4YcKEWrcp8X1nZaaZKisrcfDgQUyePLnW7ZMnT8bu3btliqp9FBUVAQCCgoJq3Z6UlITQ0FB069YNDz74IHJycuQIr9WdPXsWkZGRiI+Px+zZs3HhwgUAQEpKCrKysmp9BvR6PcaOHet0n4HKykp8/vnnuO+++2pt1Oqs73lNjrzPBw8ehMlkqnVMZGQk+vTp43SfhaKiIgiCUGevu9WrVyMkJAS9e/fGE0884RTVSaDxz7irvO/Z2dlYv3497r///jr3Ke19V/wKwEqTm5sLi8VSZ6PLsLCwOhtiOhNRFLF48WJcf/316NOnj/32hIQE3HHHHYiNjUVKSgpeeOEFTJgwAQcPHlTNypH1GT58OFatWoVu3bohOzsbL7/8MkaNGoXk5GT7+1zfZyA1NVWOcNvM999/j8LCQsybN89+m7O+51dz5H3OysqCu7s7AgMD6xzjTL8PKioq8PTTT+Ouu+6qteng3Xffjfj4eISHh+P48eN45pln8Mcff9TZT09tmvqMu8r7/umnn8LX1xczZ86sdbsS33cmMy1U81sqIP2xv/o2Z7Jw4UIcPXoUv/76a63bZ82aZb/cp08fDBkyBLGxsVi/fn2d/wBqkpCQYL/ct29fjBw5Ep07d8ann35qHwjoCp+Bjz76CAkJCYiMjLTf5qzveUNa8j4702fBZDJh9uzZsFqteOedd2rd9+CDD9ov9+nTB127dsWQIUNw6NAhDBo0qL1DbTUt/Yw70/sOAB9//DHuvvtueHh41Lpdie8720zNFBISAq1WWyf7zsnJqfMNzlk88sgj+OGHH7B9+3Z07Nix0WMjIiIQGxuLs2fPtlN07cPb2xt9+/bF2bNn7bOanP0zkJqaiq1bt+KBBx5o9Dhnfc8deZ/Dw8NRWVmJgoKCBo9RM5PJhDvvvBMpKSnYsmVLrapMfQYNGgQ3Nzen+yxc/Rl39vcdAHbt2oXTp083+f8fUMb7zmSmmdzd3TF48OA65bQtW7Zg1KhRMkXVNkRRxMKFC7F27Vps27YN8fHxTT4mLy8P6enpiIiIaIcI24/RaMTJkycRERFhL6/W/AxUVlZix44dTvUZWLlyJUJDQzF16tRGj3PW99yR93nw4MFwc3OrdUxmZiaOHz+u+s+CLZE5e/Ystm7diuDg4CYfk5ycDJPJ5HSfhas/4878vtt89NFHGDx4MPr379/ksYp432UcfKxaX331lejm5iZ+9NFH4okTJ8RFixaJ3t7e4sWLF+UOrVU99NBDor+/v5iUlCRmZmbaT2VlZaIoimJxcbH4t7/9Tdy9e7eYkpIibt++XRw5cqQYFRUlGgwGmaO/Nn/729/EpKQk8cKFC+LevXvFadOmib6+vvb3+NVXXxX9/f3FtWvXiseOHRPnzJkjRkREqP5121gsFjEmJkZ86qmnat3ubO95cXGxePjwYfHw4cMiAPGNN94QDx8+bJ+x48j7PH/+fLFjx47i1q1bxUOHDokTJkwQ+/fvL5rNZrlelkMae+0mk0m8+eabxY4dO4pHjhyp9f/faDSKoiiK586dE5csWSLu379fTElJEdevXy/26NFDHDhwoKpfu6OfcWd8322KiopELy8vccWKFXUer9T3nclMC7399ttibGys6O7uLg4aNKjWdGVnAaDe08qVK0VRFMWysjJx8uTJYocOHUQ3NzcxJiZGnDt3rpiWliZv4K1g1qxZYkREhOjm5iZGRkaKM2fOFJOTk+33W61W8aWXXhLDw8NFvV4vjhkzRjx27JiMEbeuTZs2iQDE06dP17rd2d7z7du31/sZnzt3riiKjr3P5eXl4sKFC8WgoCDR09NTnDZtmir+PRp77SkpKQ3+/9++fbsoiqKYlpYmjhkzRgwKChLd3d3Fzp07i48++qiYl5cn7wtzQGOv3dHPuDO+7zbvvfee6OnpKRYWFtZ5vFLfd0EURbFNSz9EREREbYhjZoiIiEjVmMwQERGRqjGZISIiIlVjMkNERESqxmSGiIiIVI3JDBEREakakxkiIiJSNSYzREREpGpMZohItc6dO4cpU6bA19cXw4YNQ1pamtwhEZEMmMwQkSoVFxdj0qRJ6NOnDw4dOoTAwEAsWrRI7rCISAY6uQMgImqJdevWQRAEvP766xAEAfPnz8e9994rd1hEJANWZohIlc6cOQN/f38IggAA8Pb2RllZmcxREZEcmMwQkSp16dIFR44cwXfffQeTyYTU1FSEhobKHRYRyYBtJiJSleTkZAwfPhxHjx7F/fffj7vvvhsmkwlarRbjx4+XOzwikgErM0SkKsnJyfD29kanTp3w4YcfoqSkBGlpaejZsyfGjRsnd3hEJAMmM0SkKnl5eQgLC7Nf1+l08PDwwIkTJ3DbbbfJGBkRyYXJDBGpiq+vL7Kzs2vdtmTJEkydOhXdunWTKSoikhPHzBCRqowfPx6FhYVYunQp7rvvPqxevRrffvstfv/9d7lDIyKZsDJDRKoSFRWFlStXYsWKFejUqRO2b9+OXbt2ITo6Wu7QiEgmgiiKotxBEBEREbUUKzNERESkakxmiIiISNWYzBAREZGqMZkhIiIiVWMyQ0RERKrGZIaIiIhUjckMERERqRqTGSIiIlI1JjNERESkakxmiIiISNWYzBAREZGqMZkhIiIiVfv/F/qbxWeVQgwAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@np.vectorize\n",
    "def tau_B2(theta):#\n",
    "    pl02.theta = theta\n",
    "    tau = conn.calck(om,k,pl01,2)\n",
    "    return (tau[pl02][0][0],tau[pl02][2][0])\n",
    "\n",
    "theta = np.linspace(0,179,50)\n",
    "pl.plot(theta,-10*np.log10(tau_B2(theta)[0]),label=\"B->L\")\n",
    "pl.plot(theta,-10*np.log10(tau_B2(theta)[1]),label=\"B->B\")\n",
    "pl.legend()\n",
    "pl.xlabel(r'$\\vartheta$')\n",
    "pl.ylabel('R/dB')\n",
    "pl.ylim(0,30);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](tikzfig/plate_junction_incidence.svg)\n",
    "\n",
    "* so far we had only perpendicular incidence ($\\varphi=\\pi/2$)\n",
    "* any other angles will result in **periodicity** along junction (wave impedances !)\n",
    "* the dependency an the angle of incidence $\\varphi$ can be very complicated"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl02.theta = 90\n",
    "sec2.thick = 2e-3\n",
    "phi = np.linspace(1e-5,np.pi/2,500)\n",
    "kk = np.cos(phi)*sec1.kb4(om)**0.25\n",
    "tau = conn.calck(om,kk,pl01,2)\n",
    "pl.plot(180*phi/np.pi,-10*np.log10(tau[pl02][2]))\n",
    "pl.xlabel(r'$\\varphi$')\n",
    "pl.ylabel('R/dB')\n",
    "pl.ylim(0,30);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* note the pole near 87° \n",
    "* often we are interested in a diffuse incidence (with same probability from every angle)\n",
    "* integration is necessary:\n",
    "\\begin{equation}\\label{eq:diffuse}\n",
    "\\overline\\tau = \\int_0^{\\pi/2}\\tau(\\varphi)sin(\\varphi)d\\varphi=\\int_0^1 \\tau(k_z)d \\frac{k_z}{k_B}\n",
    "\\end{equation}\n",
    "* example of connection between two different plates:\n",
    "![trex1.png](trex1.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 L -> 1 ('L', 'T', 'B') : [ 3.14  4.95 33.28] dB\n",
      "1 L -> 2 ('L', 'T', 'B') : [11.43  9.52 19.76] dB\n",
      "1 T -> 1 ('L', 'T', 'B') : [ 7.22  3.44 28.11] dB\n",
      "1 T -> 2 ('L', 'T', 'B') : [11.52  5.57 20.65] dB\n",
      "1 B -> 1 ('L', 'T', 'B') : [50.59 43.13  0.54] dB\n",
      "1 B -> 2 ('L', 'T', 'B') : [26.88 24.87  9.52] dB\n",
      "2 L -> 1 ('L', 'T', 'B') : [11.98  9.79 10.13] dB\n",
      "2 L -> 2 ('L', 'T', 'B') : [ 1.59 14.7  21.17] dB\n",
      "2 T -> 1 ('L', 'T', 'B') : [12.19  5.97 10.25] dB\n",
      "2 T -> 2 ('L', 'T', 'B') : [16.84  2.49 20.56] dB\n",
      "2 B -> 1 ('L', 'T', 'B') : [38.84 37.45 11.3 ] dB\n",
      "2 B -> 2 ('L', 'T', 'B') : [39.71 36.99  0.34] dB\n"
     ]
    }
   ],
   "source": [
    "mat1=ElasticMaterial(dens=8000.,elas=2e11,poisson=0.3)\n",
    "sec1=IsoPlateSec(mat=mat1,thick=2e-3)\n",
    "mat2=ElasticMaterial(dens=5000.,elas=1e11,poisson=0.25)\n",
    "sec2=IsoPlateSec(mat=mat2,thick=1e-3)\n",
    "node=CNode() # default coordinates: (0,0)\n",
    "pl01=InfPlate(sec=sec1,theta=180)\n",
    "pl02=InfPlate(sec=sec2,theta=90)\n",
    "conn=ContLineConnect()\n",
    "conn.add_member(pl01)\n",
    "conn.add_member(pl02)\n",
    "# calculate transmission for a single frequency\n",
    "fr=500\n",
    "# print result table\n",
    "wavetypes=(\"L\",\"T\",\"B\")\n",
    "for x1 in range(2):\n",
    "    for wt in range(3):\n",
    "        for x2 in range(2):\n",
    "            frpl=conn.members[x1] # source member\n",
    "            topl=conn.members[x2] # receiver member\n",
    "            tau=conn.get_trans(fr,frpl,wt,topl)\n",
    "            print(x1+1,wavetypes[wt],\"->\",x2+1,wavetypes,\":\",\\\n",
    "                    array2string(-10*log10(tau),precision=2),\"dB\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* example of a connection with an extra stiffener beam along the connection (steel, dimensions in mm)\n",
    "![trex2.png](trex2.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# define steel material\n",
    "steel=ElasticMaterial(dens=7800,elas=2.1e11,poisson=0.3)\n",
    "# plate and beam section\n",
    "sec1=IsoPlateSec(mat=steel,thick=0.02)\n",
    "sec2=RectBeamSec(mat=steel,leny=0.23,lenz=0.037)\n",
    "# assemble connetion\n",
    "node1=CNode()\n",
    "pl1=InfPlate(sec=sec1,node=node1,theta=0,y0=0.037/2) #shift by half  \n",
    "pl2=InfPlate(sec=sec1,node=node1,theta=180,y0=-0.037/2) # beam width\n",
    "b1=ConnBeam(sec=sec2,node=node1,theta=0)\n",
    "conn=ContLineConnect()\n",
    "conn.add_member(pl1)\n",
    "conn.add_member(pl2)\n",
    "conn.add_member(b1)\n",
    "# calculate tau for some sixth octave center frequencies\n",
    "# and plot tau for bending waves from 1 to 2\n",
    "fr1 = 10**np.arange(2.1,4.,0.05)    \n",
    "tau1 = np.vectorize(lambda fr: conn.get_trans(fr,pl1,2,pl2)[2])(fr1)\n",
    "pl.semilogx(fr1,-10*np.log10(tau1))\n",
    "pl.xlabel(r'$f$/Hz')\n",
    "pl.ylabel('R/dB');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* example of connection with realistic `I`-Beam (steel, plates 2 mm, flanges 4 mm, Beam 10 cm x 15 cm)\n",
    "![trex3.png](trex3.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#material and plate section parameters\n",
    "mat1=ElasticMaterial(dens=7800,elas=2e11,poisson=0.3)\n",
    "sec1=IsoPlateSec(mat=mat1,thick=2e-3) #for the plates\n",
    "sec2=IsoPlateSec(mat=mat1,thick=4e-3) #for the flanges\n",
    "#in this case we need 6 nodes\n",
    "node1=CNode(y=-0.05,z=0)\n",
    "node2=CNode(y=0,z=0)\n",
    "node3=CNode(y=0.05,z=0)\n",
    "node4=CNode(y=-0.05,z=0.15)\n",
    "node5=CNode(y=0.0,z=0.15)\n",
    "node6=CNode(y=0.05,z=0.15)\n",
    "#two plate members with given section and connection angle\n",
    "pl01=InfPlate(sec=sec1,node=node1,theta=180)\n",
    "pl02=InfPlate(sec=sec1,node=node3,theta=0)\n",
    "#five strip plates for the flange\n",
    "sp03=StripPlate(sec=sec2,node1=node1,node2=node2)\n",
    "sp05=StripPlate(sec=sec2,node1=node2,node2=node3)\n",
    "sp06=StripPlate(sec=sec2,node1=node2,node2=node5)\n",
    "sp07=StripPlate(sec=sec2,node1=node4,node2=node5)\n",
    "sp08=StripPlate(sec=sec2,node1=node5,node2=node6)\n",
    "#connection type is continuous line\n",
    "conn=ContLineConnect()\n",
    "#add the members\n",
    "conn.add_member(pl01)\n",
    "conn.add_member(pl02)\n",
    "conn.add_member(sp03)\n",
    "conn.add_member(sp05)\n",
    "conn.add_member(sp06)\n",
    "conn.add_member(sp07)\n",
    "conn.add_member(sp08)\n",
    "#calculate the transmission coeff.s for all frequencies\n",
    "fr1 = 10**np.arange(2.1,4.,0.05)    \n",
    "for fr in fr1:\n",
    "    conn.calculate(fr,100) \n",
    "    # gausspoints defaults to 50, we take 100 for improved accuracy\n",
    "# calculate tau for some sixth octave center frequencies\n",
    "# and plot tau for bending waves from 1 to 2\n",
    "tau1 = np.vectorize(lambda fr: conn.get_trans(fr,pl01,2,pl02)[2])(fr1)\n",
    "pl.semilogx(fr1,-10*np.log10(tau1))\n",
    "pl.xlabel(r'$f$/Hz')\n",
    "pl.ylabel('R/dB');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### ----------------------------------------\n",
    "* wave transmission over junctions is a complex phenomenon\n",
    "* transmission loss due to a jump in thickness is small\n",
    "* energy can also be transmitted from one wave type to another\n",
    "* all junctions can be analyzed using the same generic approach\n",
    "* next topic: damping"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### License\n",
    "\n",
    "This notebook is an [Open Educational Resource](https://en.wikipedia.org/wiki/Open_educational_resources). Feel free to use it for your own purposes. The text and the images are licensed under [Creative Commons Attribution 4.0](https://creativecommons.org/licenses/by/4.0/), and any code under the [MIT license](https://opensource.org/licenses/MIT). Please attribute the work as follows: Ennes Sarradj, Structure-borne sound lecture notes, 2019."
   ]
  },
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   "cell_type": "code",
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    "# this is just for custom formatting\n",
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       "outputs": [
        {
         "data": {
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\n",
          "text/plain": "<Figure size 432x288 with 1 Axes>"
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ]
      }
     },
     "67e21a66526e4fe88662ee0d4e570f6e": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_4539a17df68645a7a756ced05e715ea9",
       "outputs": [
        {
         "data": {
          "image/png": 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6HCh2JSx4jXXv4oFZwyKwOjEXJ4urmv8GIuowR3PL8e2RfDwwJgqB3u6q49gcC94GHr4mBu4mAxZxEBmRTb2yMRWdPVwwZ6z+bubREix4G/D3csMDY6KxPrkAh3PKVMchcgrfZ5Rgd3oJHro6Bj7u+hwH3BwWvI3MGRuNrp6ueHl9KgeREWlMSomXN6Qi1Ncddw2PUB1HGRa8jXi5mfDwNTHYl3kWu9I5TphIS+uOFuBIbjn+MCEW7i76HQfcHBa8Dd05LBzdOnfCy+tTYbVyF0+khQaLFYs2pSE2yAu3DNb3OODmsOBtyM1kxKPXx+JYfgXWHslTHYdIl9Yk5iKrpBoLJsbBaND/QLErYcHb2LQBYYgL9sZrm06g3sxxwkQd6Xy9BW9sOYGEiM64rneg6jjKXbHgL952b7YQYqq4YKEQ4lshxGIhhHOMY+tgBsOFQWSnS2uw6sBp1XGIdOUfe7NQVFmHhTc4xzjg5jS3g18J4HoA9+HCuN9wAEsAVAL4UMtgeja+VwCGRnXBm1szUF1nVh2HSBfKaurx7o6TuDYuEFdFdlEdxy40V/B9pJSzANwKoJeU8iEp5QYp5ZMAumsfT59+HidcUlWHD/ZkqY5DpAvv7jiJqjozFkzqpTqK3Wiu4OsBQEppBnD5q4K8k0U7DInojAl9grBsVyZKq+tVxyFyaPnl5/Hh3mzcPDAMccE+quPYjeYKvpsQ4k0hxFuXfP7zr8NskE/XHpvYCzX1Zry9neOEidrjjc3pkBL4g5ONA26OqZmvL7jk88TLvnb5r6mVegZ5Y/rgbvh43yncOyoS3Tp7qI5E5HAyiiqx5mAOZo+MRPcu/Dt0qSsWvJTyI1sFcVZ/mBCLr5PysGhjGt64Y5DqOEQO56X1qfBwNeHhq51vHHBzrljwQoi1AJp8y6WUcmqHJ3IyoX6dMHdMNJZsz8CdwyIwNIqv/hO11PbUImw5XoSFk+LQ1ctNdRy709w5+EUAXgOQBeA8gBUXP6oAJGsbzXk8eHUPhPq64+mvk2G28M1PRC1RZ7bg2bUpiPb3xP2jo1THsUtXLHgp5U4p5U4Ag6SUt0sp1178uBPAaNtE1D8PVxOenNIHqQWV+GQ/3/xE1BLv7c5C9tka/HVqPFxNfFN+Y1r6byVACPGfiflCiCgAAdpEck439A3GqJiuWLQxDWer6lTHIbJreWXnsWRbBibGB2FsLKuoKS0t+D8A2CGE2CGE2AFgO4BHNEvlhIQQ+Ouv4lFTb8ErG3jnJ6IreWHdcVilxJM39lEdxa41N4smBACklBsA9MSFUn8EF97Vukn7eM6lZ5A37h0ViX8n5vDOT0RN2JtRgu+O5OPB8TG8LLIZze3gPxBC/CCEeAnACAApUsokKSXPIWjkd9f2RKC3G57+Opkz44ku02Cx4plvUtC9SyfMG+ec91ltjeZeZL0BwHhcGDR2M4AfhBBfCCHmCiHCtY/nfLzdXfDE5N44kluO1Yk5quMQ2ZWP9mYjvagKT0+Jd+o7NbVUs+fgpZS1FweMPSKlTADwKC5cP79ECLFf84ROaNrAUFwV2Rkvb0hFWQ3n1BABQFFFLd7Yko7xvQI4672FWn1tkZQyC8AyAKvBSyU1IYTAs1P7ovx8A17ffEJ1HCK78NL6VNSbrXjmV/Gc9d5Czb3I6iOE+LMQYokQ4vqLN/34LYBMADOklNxeaqRPqA/uHh6Bf/5wCil55arjECl1ILsUX/x0BnPGRiHK31N1HIfR3A7+YwC9ABwF8ACATbgwG36alHKaxtmc3h8n9IKfhyue+ToFUvIFV3JOFqvE01+nIMTXHQ9x3kyrNFfw0VLKX0splwGYCSABwBQp5WHNkxF8PVywcFIvJJ46h68On1Edh0iJT348heP5FXjyxj7wcG1uAC5dqrmCb/j5EymlBUCWlLJS20h0qRlDumNAdz/837pUVNY2NP8NRDpytqoOr25Mw8geXTG5X7DqOA6nuYIfIISouPhRCaD/z58LISpsEdDZGQwCz02NR0lVHRZvSVcdh8imFm1KQ029Bc9O5QurbdHcdfBGKaXPxQ9vKaXpks+veF8sIUR3IcR2IcRxIUSKEIKjDdpoQHc/3HFVd/xjbzZOFPIHKHIOSTllWHUgB78eGYmeQd6q4zgkLUewmQE8KqXsDWA4gIeEEBwc0UYLJsbBy82Ev37DF1xJ/6xWiae/SUFXTzc8cl1P1XEclmYFL6XMl1Ieuvh5JYDj4H1c26yLpyv+dH0s9p48i3VHC1THIdLUZwdzkZRThicmx8Hb3UV1HIdlkyHKQohIAIMA/NjI1+YKIRKFEInFxcW2iOOw7hwWgT4hPvjbd8dQU29WHYdIE+U1DXh5QyoSIjrj5kHcE7aH5gUvhPAC8DmA30sp/+eFWSnlcillgpQyISCAc52vxGgQeG5aPPLLa/H29gzVcYg08fctJ3Cuph7PTuMLq+2lacELIVxwodz/JaX8Qsu1nEVCZBfcMigMK3ZlIaukWnUcog51PL8CK/dl467hEYgP9VUdx+FpVvDiwv963wdwXEr5ulbrOKPHJ8fB1WTAs2v5givph5QSz3ydAj8PV/xxQqzqOLqg5Q5+FIC7AVwjhDh88WOyhus5jUBvd/z+up7YkVaMrceLVMch6hDfJOVhf3YpHpt4YUQHtZ9m7/uVUu4BwBNoGpk9MhL/PpCDZ79Nweie/pyNTQ6tqs6MF747jgHdfHFbQnfVcXSDtyJ3UC5GA56dGo+c0vNYtjNTdRyidnlzazqKKuvw7LS+MBi4L+woLHgHNjLGHzf2D8E7OzKQU1qjOg5Rm2QUVeKDPVm4PaE7Bnb3Ux1HV1jwDu4vk3vDIASe/jqZL7iSw7FaJZ74MhkerkY8NqmX6ji6w4J3cKF+nfDYpF7YnlbMe7iSw/nH3mzszyrFk1P6oKuXm+o4usOC14HZIyIxIrornlt7jKdqyGFkFFXhlQ2puK53IGYM6aY6ji6x4HXAYBB4dUZ/CCGw4LMkWK08VUP2zWyx4tHVh+HhasT/3dKP71jVCAteJ7p19sDTU/rgh8xSfLg3W3Ucoit6d8dJJOWW42839UOgt7vqOLrFgteRGQndcG1cIF7ekIqMoirVcYgalXymHIu3pmPqgFDc2D9EdRxdY8HriBACL97SD51cjXh0TRLMFqvqSES/UGe24NHVSeji6YrnpsWrjqN7LHidCfRxx99u6ouknDIs3XlSdRyiX/j75nSkFVbi5en9OY7ABljwOjSlfyim9A/B4q3pSMkrVx2HCABw8FQplu86iZlDu+PquEDVcZwCC16nnp/WF34ernh0dRLqzBbVccjJ1dSb8ejqJIT6dcJfbuSdO22FBa9TnT1d8fL0fkgtqMQbW9JVxyEn99L6VJwqrcGiGQPg5abZjEO6DAtex66JC8LtCd2xbOdJHDx1TnUcclJ70kuwct8p3DcqCsOju6qO41RY8Dr35JTeCPHthD+tSeJ9XMnmKmobsOCzJPQI8MSCiZw1Y2sseJ3zdnfBqzP6I6ukGq9sSFMdh5zMs98cQ1FlHV6/bSDvWaAAC94JjOzhj3tHReLDvdn4PqNEdRxyEptSCvD5oVw8NL4HBnAMsBIseCexcFIcogM8sWBNEipqG1THIZ07W1WHJ748ivhQHzx8TU/VcZwWC95JuLsY8dqMASioqMXza4+pjkM6JqXEk18lo+K8Ga/fNhCuJtaMKvw370QGhXfGg+NjsOZgLrYcK1Qdh3Tqm6Q8rE8uwB+vj0WvYG/VcZwaC97J/O7anugd4oPHvziK0up61XFIZwrKa/HUV8kYEtEZc8ZEq47j9FjwTsbVZMDrtw1A+fl6PPUVb/NHHUdKiYWfH0GDReK1GQNg5M2zlWPBO6HeIT74w4RYfHc0H2uP5KuOQzrx6f4c7DxRjCcmxyHS31N1HAIL3mnNHRONQeF+eOqrZBRW1KqOQw7u9Nka/O27Yxgd449ZwyJUx6GLWPBOymQ04PXbBqLObMHCz4/wVA21mcUq8ac1STAKgVdu7Q8DT83YDRa8E4vy98Sfb+iNHWnF+GT/adVxyEG9tzsT+7NL8czUeIT6dVIdhy7Bgndydw+PwJie/nj2m2McSEattie9BK9sTMOk+GBMHxymOg5dhgXv5AwGgbdmDkKInzvmfXwQ+eXnVUciB5FdUo2HPjmEmAAvLLptAITgqRl7w4In+Hm44r17ElDbYMHclQdxvp43CKErq6xtwAMrE2EQwHuzEzjj3U6x4AkA0DPIG4vvGIjkvHI8xhdd6QosVolHVh1Gdkk13pk1BN27eKiORE1gwdN/XNs7CI9NjMPapDy8s4M37KbGLdqUhm2pRXhmajxG9OANPOwZf66iX5g/LhqpBRVYtCkNsUHemNAnSHUksiNfHz6Dd3ecxKxh4bh7OK93t3ea7eCFEB8IIYqEEMlarUEdTwiBl6f3R78wX/x+1U84UVipOhLZiaScMjz22REMi+qCZ34VrzoOtYCWp2g+BDBJw+cnjbi7GLH87gR4uJnwwEeJOMehZE6vqKIWcz9ORIC3G96ZNZgjgB2EZv+VpJS7AJRq9fykrWBfdyy/ewgKKmrx4L8OocFiVR2JFKltsGDOxwdRWWvGinsS0NXLTXUkaiH+b5iaNCi8M168uR/2ZZ7F89/yJiHOSEqJJ744iqScMrx+20D0DvFRHYlaQfmLrEKIuQDmAkB4eLjiNHS56UO6Ia2wEst3ZaJXsDcHSTmZFbsz8cVPZ/DHCbGY1DdYdRxqJeU7eCnlcillgpQyISAgQHUcasTCSXEYFxuAZ75OwY+ZZ1XHIRvZnlqEF9en4sZ+IfjtNTGq41AbKC94sn9Gg8CbMwchvKsHfvOvQ8gprVEdiTSWUVSF3336E3oH++DVGf05hsBBaXmZ5KcA9gHoJYTIFULcr9VapD3fTi54754ENFismLMyEdV1ZtWRSCPlNQ2YszIRriYDVsxOgIer8jO51EZaXkUzU0o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          "text/plain": "<Figure size 432x288 with 1 Axes>"
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\n",
          "text/plain": "<Figure size 432x288 with 1 Axes>"
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
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 },
 "nbformat": 4,
 "nbformat_minor": 2
}