diff --git a/Week 6/11 Parabolic PDEs: 1D Schrödinger Equation with Potential.ipynb b/Week 6/11 Parabolic PDEs: 1D Schrödinger Equation with Potential.ipynb index 4268513..5a147fc 100644 --- a/Week 6/11 Parabolic PDEs: 1D Schrödinger Equation with Potential.ipynb +++ b/Week 6/11 Parabolic PDEs: 1D Schrödinger Equation with Potential.ipynb @@ -89,7 +89,8 @@ }, "outputs": [], "source": [ - "import numpy as np" + "import numpy as np\n", + "from matplotlib import pyplot as plt" ] }, { @@ -142,28 +143,34 @@ }, "source": [ "The potential $V(x)$ is a scalar quantity, and will therefore only occur on the diagonal of the matrix $H$.\n", - "The second derivative operator will however be matrix valued, as $x$ is a vector, so that\n", + "The second derivative operator will however be matrix valued, and we will determine it by looking at the finite differences approximation.\n", "\n", "$$\n", - "\\partial^2/\\partial{}x^2 = \\begin{bmatrix} \\partial^2/\\partial{}x_1^2 & \\ldots & \\partial^2/\\partial{}x_1x_n \\\\ \\vdots & \\ddots & \\vdots \\\\ \\partial^2/\\partial{}x_nx_1 & \\ldots & \\partial^2/\\partial{}x_n^2 \\end{bmatrix},\n", + "\\frac{\\partial^2\\Psi}{\\partial{}x^2}(x_i) = \\frac{\\Psi(x_{i+1}) - 2\\Psi(x_i) + \\Psi(x_{i-1})}{h^2} - \\frac{h^2}{12} \\frac{\\partial^4\\Psi}{\\partial x^4}(x_i)\n", "$$\n", "\n", - "or more cleanly, that element $ij$ equals\n", + "For small $h$, we can ignore the latter term, which we will indeed do.\n", + "We can encode this in a tridiagonal matrix, as each step depends on the step before and after it and not on anything else.\n", + "\n", + "Our beautiful hamiltonian now has elements like\n", + "\n", "$$\n", - "(\\partial^2/\\partial{}x^2)_{ij} = \\partial^2/\\partial{}x_ix_j.\n", + "H_{ij} = \\frac{-\\hbar^2}{2m} \\left[ \\delta_{i,j-1} - 2\\delta_{ij} + \\delta_{i,j+1} \\right] + V(x) \\delta_{ij} = -\\left[ \\delta_{i,j-1} - 2\\delta_{ij} + \\delta_{i,j+1} \\right] + V(x) \\delta_{ij}\n", "$$\n", "\n", - "This leads to a hamiltonian matrix with elements\n", - "$$\n", - "H_{ij} = \\frac{-\\hbar^2}{2m}\\frac{\\partial^2}{\\partial{}x_ix_j} + V(x) \\delta_{ij} = -\\frac{\\partial^2}{\\partial{}x_ix_j} + V(x) \\delta_{ij},\n", - "$$\n", + "with $\\delta_{ij} = 1 \\iff i = j$, and using the approximations $\\hbar = 1$, $m = 0.5$.\n", "\n", - "with $\\delta_{ij} = 1 \\iff i = j$, and using the approximations $\\hbar = 1$, $m = 0.5$." + "\n", + "finite differences for second derivative to get a tridiagonal matrix (one lower and one higher than diagonal)\n", + "then plot eigenvalues\n", + "no time component -> not complex?\n", + "energy should be real\n", + "eigenvectors squared should be normalized" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": { "deletable": false, "nbgrader": { @@ -194,35 +201,50 @@ " A tuple of the eigenvalues E and eigenfunctions \\Psi of the hamiltonian H.\n", " \"\"\"\n", " \n", + " # TODO: Is n the dimensionality of Psi?\n", " n = len(x)\n", " h = x[1] - x[0]\n", " \n", " # In the stationary case, \n", - " H = -1/h**2*np.ones(n) + np.eye(n)*V(x)\n", + " H = 1/h**2*(np.eye(n, n, -1) - 2*np.eye(n) + np.eye(n, n, 1)) + np.eye(n)*V(x) \n", " \n", - " # TODO: I think H could be complex, so I used eigh instead of eig.\n", + " # In principle, the eigenvalues and eigenvectors could be complex, so\n", + " # we opt for eigh instead of eig.\n", " return np.linalg.eigh(H)" ] }, { "cell_type": "code", - "execution_count": 16, - "metadata": {}, + "execution_count": 3, + "metadata": { + "scrolled": true + }, "outputs": [ { "data": { "text/plain": [ - "array([[-2., -1., 0.],\n", - " [-1., -2., -1.],\n", - " [ 0., -1., -2.]])" + "[]" ] }, - "execution_count": 16, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" } ], "source": [ + "# TODO: Remove this cell.\n", "def stationary_hamiltonian(x, V, h, m): #construct the hamiltonian in tridiagonal matrix form for the stationary case (time-independent schrodinger equation) using the amount of x-steps m and the small x-parameter h (since hbar = 1 and m = 0.5 --> 2m = 1 all factors due to hbar or m will disappear)\n", " H = np.zeros((m,m))\n", " off_diag = -1/(h**2) * np.ones(m-1)\n", @@ -233,10 +255,12 @@ " return H\n", "\n", "V = lambda x: -x**2*0\n", - "x = np.array([1,2,3])\n", + "#x = np.array([1,2,3])\n", + "x = np.linspace(0, 1, 200)\n", "h = 1\n", "m = 3\n", - "stationary_hamiltonian(x, V(x), h, m)" + "E, Psi = SEQStat(x, V)\n", + "plt.plot(x, Psi[:, 3])" ] }, { @@ -263,7 +287,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 8, "metadata": { "deletable": false, "nbgrader": { @@ -281,36 +305,37 @@ "outputs": [ { "data": { + "image/png": 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q6+uZPXs2X/rSl3jiiSe46667WLly5ajnfOGFF/jFL36B0+mktraW0tJS5syZc9kxBw4coLS0lOXLlwMwMDDA0qVLRx3vvvvuA+C2227j3LlzN/ydBAcHs3nzZgBmz55NSEgIDoeD2bNnX3b7jRs3Eh8fP3KOvXv3YrfbOXz4MAsXLgSMFzdJScZzYVBQEPfff/8Nz+8pknwLIUSAO3qxjSe3lrI6J5HPr8/26rk+vz6b4ottfHNrCQWp0czNmOTV8wnhdTeYobYil8vFgQMHCA0Nveq6kJCQka+DgoJwOp3k5ORw5MgRXn31Vb72ta+xfv36q2aqz549y/e//33effddYmNj+ehHP0pfX99V42ut2bhxI7/73e9uGKc7FnccAHa7HZfLNXLMpedwOBwj76jZbLaR29tstpHbA1e966aUQmvNo48+yr/9279dFUdoaChBQZ4pwxsLq7caFEIIMQEt3QN85jeHSYwK4UcPFmKzebcUJMim+D8PFpIYFcJnf3uElu4Br55PiFvVwoUL2bVrF62trTidTl566aWR6zZt2sSPf/zjke+vN4MORglLeHg4Dz/8MI8//jhHjhwBICoqis7OTsCYPY+IiCAmJob6+npee21k4/HLjluyZAlFRUVUVFQARqmIe0Z+LKZNm0ZxcTEul4uLFy9y8ODBMd/Wbdu2bbS0tNDb28srr7zC8uXLWb9+PS+++CINDQ0AtLS0cP78+XGP7Qky8y2EEAHs6388QVPXAC9+ZimxPtqJMjYimP/48Hwe+Pl+vv7HE/zkb+b75LxCBJIra743b9480m4QIC0tja9+9assWrSIuLg4Zs6cSUxMDGAsgvz7v/975syZg9PpZNWqVfz85z+/5rmOHz/O448/js1mw+Fw8LOf/QyAT33qU2zevJnU1FR27tzJvHnzmDlzJhkZGSNlJaMd99xzz/GhD32I/v5+AJ566ilycnLG9HMvX76c6dOnk5+fT15eHvPnj//5Y9GiRdx///1UVVXx8MMPs2DBgpE4Nm3ahMvlwuFw8NOf/pSpU6ded6yXX36Zf/iHf6CxsZE777yTwsJC3njjjXHHdCl1K+1KtmDBAu2pHo1CCGF1x6vaufsne/mHdVl8aZNnV+uPxQ/ePMWPd1Twp8dWMDs9xufnF+JmlZWVkZeXZ3YYN9TV1UVkZCROp5MtW7bwsY99jC1btpgd1i1ntPuLUuqw1nrBaMdL2YkQQgSo775xkthwB59cNcOU839y1QwmhTv47hsnTTm/EIHum9/8JoWFhcyaNYvp06fzgQ98wOyQxBhI2YkQQgSgooom9pxu4mt35hEd6jAlhuhQB3+/Jotvv1rGvoomlmUlmBKHEIHq+9//vtkhiJsgM99CCBFgtNZ89/WTpMSE8vCS69czettHlk4lJSaU77xxilupzFEIIa5Fkm8hhAgwb5TUcbSqnS9syPHYLpY3K9QRxD9uyOboxTbeKKk3NRYhhLACSb6FECKAOIdcfO+NU2QmRnDf/DSzwwHg/vnpzEiM4PtvnsI55LrxDYQQIoBJ8i2EEAHkD0eqqWzs5vHbc7EHWeMp3h5k4/FNuVQ0dPGH96rNDkcIIUxljWdmIYQQE9Y3OMQPt5czN2MStxckmx3OZTbPSmZuegw/2lZO3+CQ2eEIYXlBQUEUFhaOfLh7fH/iE5+4bOt4b/rRj35ET0+Px47zheeee47HHnvMY+M9/vjjzJw5kzlz5rBlyxba2tomPKYk30IIESB+c+A8te19PLE596rtlc2mlOKJzTOpae/jNwfM2VVOCH8SFhZGcXHxyMeXv/xlAH75y1+Sn5/vkxj8MfmeqKGhyycHNm7cyIkTJzh27Bg5OTmjbk8/XpJ8CyFEAOjoG+SnOytYmZ3AskxrtvRblpXAyuwEfrqzgs6+QbPDEcIvrVmzBveGgc8++yw5OTksWrSIT37ykyMzvo2Njdx///0sXLiQhQsXUlRUBBh9wT/2sY+xZs0aZsyYwTPPPAMYW8DfeeedzJ07l1mzZvH888/zzDPPUFNTw9q1a1m7di0An/nMZ1iwYAEFBQV84xvfABj1uDfffJOlS5cyf/58HnjgAbq6ukb9OZ544gkWLVpETk4Oe/bsAa6eub7rrrt4++23AYiMjOTxxx+noKCADRs2cPDgwZGfZevWrSO3uXjxImvWrCE7O5snn3xy5PLf/OY3LFq0iMLCQj796U+PJNqRkZF86UtfYu7cuezfv/+yODdt2oTdbnTmXrJkCVVVVeP+m11J+nwLIUQA+OXuM7T2DPJPt880O5Trevz2XO75SRH/tfsMXzRh100hxus7B7/DyRbPbhQ1M24mTyx64rrHXLm9/Fe+8hUefPDBke9ramr4l3/5F44cOUJUVBTr1q1j7ty5AHz+85/nC1/4AitWrODChQvcfvvtlJWVAXDy5El27txJZ2cnubm5fOYzn+H1118nNTWVv/zlLwC0t7cTExPD008/zc6dO0lIMF7Qf/vb3yYuLo6hoSHWr1/PsWPH+NznPnfZcU1NTTz11FNs376diIgIvvOd7/D000/z9a9//aqf0el0cvDgQV599VWefPJJtm/fft3fSXd3N+vWreN73/seW7Zs4Wtf+xrbtm2jtLSURx99lHvuuQeAgwcPcuLECcLDw1m4cCF33nknERERPP/88xQVFeFwOPjsZz/Lb3/7Wx555BG6u7tZvHgxP/jBD657/l/96leX/Q1uliTfQgjh53oHhvj1/vNsLki2/Dbuc9IncXvBZH69/zyfXZtleitEIazKXXZyLQcPHmT16tXExcUB8MADD1BeXg7A9u3bL6sL7+joGJl9vvPOOwkJCSEkJISkpCTq6+uZPXs2X/rSl3jiiSe46667WLly5ajnfOGFF/jFL36B0+mktraW0tJS5syZc9kxBw4coLS0lOXLlwMwMDDA0qVLRx3vvvvuA+C2227j3LlzN/ydBAcHs3nzZgBmz55NSEgIDoeD2bNnX3b7jRs3Eh8fP3KOvXv3YrfbOXz4MAsXLgSMFzdJSUmAUV9///33X/fc3/72t7Hb7Xz4wx++YZw3Ism3EEL4uT8dq6G9d5CPLp9mdihj8tFl03mjpJ4/Ha3hgQUZZocjxHXdaIbailwuFwcOHCA0NPSq60JCQka+DgoKwul0kpOTw5EjR3j11Vf52te+xvr166+aqT579izf//73effdd4mNjeWjH/0ofX19V42vtWbjxo387ne/u2Gc7ljccQDY7XZcrvdbkl56DofDMbKexWazjdzeZrON3B64as2LUgqtNY8++uioNduhoaEEBV17IuC5557jz3/+M2+99ZZH1tNIzbcQQvi53xw4T3ZSJIunx5kdypgsmRFHVlKkLLwUYgIWLlzIrl27aG1txel08tJLL41ct2nTJn784x+PfH+9GXQwSljCw8N5+OGHefzxxzly5AgAUVFRdHZ2AsbseUREBDExMdTX1/Paa6+N3P7S45YsWUJRUREVFRWAUSrinpEfi2nTplFcXIzL5eLixYscPHhwzLd127ZtGy0tLfT29vLKK6+wfPly1q9fz4svvkhDQwMALS0tnD9/4+eg119/ne9+97ts3bqV8PDwcccyGpn5FkIIP3b0YhvHqtp58p4Cy3U4uRalFA8vnsI3/1TKsao25qRPMjskISznyprvzZs3j7QbBEhLS+OrX/0qixYtIi4ujpkzZxITY5SdPfPMM/z93/89c+bMwel0smrVKn7+859f81zHjx/n8ccfx2az4XA4+NnPfgbApz71KTZv3kxqaio7d+5k3rx5zJw5k4yMjJGyktGOe+655/jQhz5Ef38/AE899RQ5OTlj+rmXL1/O9OnTyc/PJy8vj/nz54/5d+a2aNEi7r//fqqqqnj44YdZsGDBSBybNm3C5XLhcDj46U9/ytSpU6871mOPPUZ/fz8bN24EjBcX1/tdjoXSWk9oAH+yYMEC7V4hLIQQgeDx/3eUvxyv5cBX1xMd6jA7nDHr6Btk8bff4u65KXz3g3PNDkeIy5SVlZGXl2d2GDfU1dVFZGQkTqeTLVu28LGPfYwtW7aYHdYtZ7T7i1LqsNZ6wWjHS9mJEEL4qbaeAbYereED89L8KvEGiA518IF5afyxuIb2Hmk7KMTN+OY3v0lhYSGzZs1i+vTpfOADHzA7JDEGUnYihBB+6sXDVfQ7XTy8+Ppvm1rVw0um8LuDF/h/hy/yiZUzzA5HCL/z/e9/3+wQxE2QmW8hhPBDLpfmt+9c4LapseSnRpsdzk0pSI1h/pRJ/PadC7hct04JpBDi1ibJtxBC+KGiyibONnXzkSX+Oevt9pGlUznb1M2+ymazQxHiMrfSmjhx827mfiLJtxBC+KH/2X+euIhg7pidbHYoE3LHrBTiIoL5nwPnzA5FiBGhoaE0NzdLAi6uS2tNc3PzqP3Ur0dqvoUQws/UtPWyvayeT6/OJMTu3ztEhjqC+OsFGfxidyW17b2kxISZHZIQpKenU1VVRWNjo9mhCIsLDQ0lPT19XLeR5FsIIfzM7w9eQAN/s2iK2aF4xIcXT+E/d1fyu4MX+eLGsfUCFsKbHA4H06dPNzsMEaCk7EQIIfzIgNPF7969yNrcJDLiPLPbmtky4sJZk5PI7w5eYHDIdeMbCCGEH5PkWwgh/MibpXU0dvb7/ULLK31k6VQaO/t5s6Te7FCEEMKrJPkWQgg/8psD58mIC2NVTqLZoXjU6pwk0mPDZOGlECLgSfIthBB+oqq1hwNnWnhwQQZBNmV2OB4VZFM8tDCDA2daqG7rNTscIYTwGkm+hRDCT/z5WC0A98xNMzkS77h7bioAfz5aY3IkQgjhPZJ8CyGEn9haXENhxiSmxAfGQssrTY2PYG7GJLZK8i2ECGCSfAshhB+oaOiitLZjZHY4UN09J4WSmg4qG7vMDkUIIbxCkm8hhPADfzpag1Jw15wUs0PxqrvnpqKU8fMKIUQgkuRbCCEsTmvNn47VsGR6PJOjx7eNsb+ZHB3K4ulx/OlojWztLYQISJJ8CyGExZXUdHCmsTvgS07c7p6bSmVjN6W1HWaHIoQQHifJtxBCWNyfjtVgtynumJVsdig+ccesFOw2xZ+O1podihBCeJwk30IIYWEul+bPR2tZmZ1AbESw2eH4RFxEMCuyE6T0RAgRkCT5FkIICztyoZXqtl7uKbw1Sk7c7pmbSnVbL0cutJodihBCeJRPkm+l1Gal1CmlVIVS6sujXB+ilHp++Pp3lFLThi9fpJQqHv44qpTacsltzimljg9fd8gXP4cQQvjan47WEGK3sTH/1ig5cduYP5kQu01KT4QQAcfrybdSKgj4KXAHkA98SCmVf8VhHwdatdZZwA+B7wxffgJYoLUuBDYD/6mUsl9yu7Va60Kt9QJv/gxCCGEG55CLvxyvZX1eEpEh9hvfIIBEhTpYNzOJPx+rxTnkMjscIYTwGF/MfC8CKrTWZ7TWA8DvgXuvOOZe4NfDX78IrFdKKa11j9baOXx5KCDFf0KIW8aBMy00dQ1wzy3S5eRK98xNpamrn3fOtpgdihBCeIwvku804OIl31cNXzbqMcPJdjsQD6CUWqyUKgGOA393STKugTeVUoeVUp+61smVUp9SSh1SSh1qbGz0yA8khBC+sPVoNZEhdtbkJpkdiinWzjRm/LcWy4Y7QojAYfkFl1rrd7TWBcBC4CtKKfcOEyu01vMxyln+Xim16hq3/4XWeoHWekFiYqKPohZCiInpdw7x+ok6NhVMJtQRZHY4pgh1BLEpfzKvnahlwCmlJ0KIwOCL5LsayLjk+/Thy0Y9ZrimOwZovvQArXUZ0AXMGv6+evhzA/AyRnmLEEIEhN3lTXT0OW+ZjXWu5e65qXT0OdldLu9cCiECgy+S73eBbKXUdKVUMPAQsPWKY7YCjw5//UFgh9ZaD9/GDqCUmgrMBM4ppSKUUlHDl0cAmzAWZwohREDYerSG2HAHK7ISzA7FVCuyE5gU7mDrUSk9EUIEBq8vn9daO5VSjwFvAEHAr7TWJUqpbwGHtNZbgWeB/1FKVQAtGAk6wArgy0qpQcAFfFZr3aSUmgG8rJRy/wz/q7V+3ds/ixBC+ELvwBDbS+vZMj8NR5DlqwO9yhFk445ZKbzyXjW9A0OEBd+aJThCiMDhk95VWutXgVevuOzrl3zdBzwwyu3+B/ifUS4/A8z1fKRCCGG+vRVN9A4O8VezUswOxRLunJ3C7w5eoKiiiQ35k80ORwghJuTWnlIRQggL2l5aT1SoncUz4swOxRIWTY8jKsTO9rJ6s0MRQogJk+RbCCEsxOXSvHWynjW5Sbd8yYlbsN3G6txEtpc14HLJdg9CCP8mz+xCCGEhxVVtNHUNsCHv1uztfS0b8yfT1NXP0ao2s0MRQogJkeRbCCEsZHtpPXabYk2OJN+XWpOTRJBNSemJEMLvSfIthBAWsq20nkXT44gJd5gdiqXEhDtYNC2ObaWSfAsh/Jsk30IIYRHnmro53dDFhjzp6DGaDfmTKa/v4nxzt9mhCCHETZPkWwghLMJdUiHJ9+jcdfDbyxpMjkQIIW6eJN9CCGER28vqyZ0cxZT4cLNDsaSp8RHkTI5ku5SeCCH8mCTfQghhAW09A7x7rpUN+bLQ8no25E3m4LkW2nsGzQ5FCCFuiiTfQghhAW+famTIpaXk5AY25E9myKV5u1xKT4QQ/kmSbyGEsIBtZfUkRoUwN32S2aFYWmH6JBIiQ6TriRDCb0nyLYQQJhtwuth1qpENeUnYbMrscCzNZlNsyEti16lGBpwus8MRQohxk+RbCCFM9s7ZZrr6nVJyMkYb8ibT2e/k4NkWs0MRQohxk+RbCCFMtr20nlCHjeVZCWaH4heWZyUQ6rDJbpdCCL8kybcQQphIa8220npWZicS6ggyOxy/EBYcxIqsRLaV1qO1NjscIYQYF0m+hRDCRKW1HdS097FRSk7GZWN+EtVtvZTVdpodihBCjIsk30IIYaLtpQ0oBWtnSn/v8Vg3czJKIaUnQgi/I8m3EEKYaHtZPfMyJpEYFWJ2KH4lMSqEwoxJknwLIfyOJN9CCGGSuvY+jle3syFfSk5uxoa8yRyraqeuvc/sUIQQYswk+RZCCJO8fcrYpXGdlJzclPV5xu9tl+x2KYTwI5J8CyGESXafbiQ5OpTcyVFmh+KXcidHMTk6hN3lTWaHIoQQYybJtxBCmMA55GLP6SZW5SSglOxqeTOUUqzKTmTP6UacQ7LbpRDCP0jyLYQQJjha1UZnn5NVOYlmh+LXVuUk0tHn5GhVu9mhCCHEmEjyLYQQJth1qhGbghWyq+WErMhKwKZgV3mj2aEIIcSYSPIthBAm2HW6ibkZk5gUHmx2KH4tNiKYOemT2C3JtxDCT0jyLYQQPtbSPcCxqjZWS8mJR6zOSeRoVRut3QNmhyKEEDckybcQQvjY3oomtEaSbw9ZnZuI1sbvVQghrE6SbyGE8LFdpxqZFO5gTvoks0MJCHPTJxET5pC6byGEX5DkWwghfEhrze7TjazISiDIJi0GPSHIpliRncDu8ka01maHI4QQ1yXJtxBC+FBZbSeNnf3SYtDDVmcn0tDZz8m6TrNDEUKI65LkWwghfGj3aaM0Quq9Pcv9Yka6ngghrE6SbyGE8KFdpxqZmRzF5OhQs0MJKMkxoeROjpK6byGE5UnyLYQQPtLd7+TQ+RaZ9faS1bmJHDrXSne/0+xQhBDimiT5FkIIH9lf2czgkJZ6by9ZlZ3IwJCLA2eazQ5FCCGuSZJvIYTwkd2nGwlzBLFgWqzZoQSkBdNiCXMESd23EMLSJPkWQggf2VXeyNLMeELsQWaHEpBCHUEsmREndd9CCEuT5FsIIXzgXFM355t7pN7by1bnJHKuuYfzzd1mhyKEEKOS5FsIIXzA3WJQ6r29S1oOCiGsTpJvIYTwgd3ljUyJC2dafLjZoQS06QkRZMSFsau8yexQhBBiVJJ8CyGElw04XeyrbGZVTgJKyZby3qSUYlV2IvsrmxhwuswORwghruKT5FsptVkpdUopVaGU+vIo14copZ4fvv4dpdS04csXKaWKhz+OKqW2jHVMIYSwikPnW+gZGGJ1TpLZodwSVuck0j0wxKHzLWaHIoQQV/F68q2UCgJ+CtwB5AMfUkrlX3HYx4FWrXUW8EPgO8OXnwAWaK0Lgc3Afyql7GMcUwghLGHv6SaCbIqlmfFmh3JLWJoZT5BNUVQhpSdCCOvxxcz3IqBCa31Gaz0A/B6494pj7gV+Pfz1i8B6pZTSWvdord1blYUCehxjCiGEJRRVNjMvYxKRIXazQ7klRIU6KMyYRFGFbLYjhLAeXyTfacDFS76vGr5s1GOGk+12IB5AKbVYKVUCHAf+bvj6sYzJ8O0/pZQ6pJQ61Ngoq9+FEL7V3jPI8ao2lmUlmB3KLWV5ZjzHqtpo7x00OxQhhLiM5Rdcaq3f0VoXAAuBryilQsd5+19orRdorRckJkqLLyGEb+0/04xLwwpJvn1qeVYCLo1sNS+EsBxfJN/VQMYl36cPXzbqMUopOxADXPaMqbUuA7qAWWMcUwghTLevsokwRxCFGZPMDuWWMm+KsdX8Pqn7FkJYjC8KEN8FspVS0zES5IeAv7nimK3Ao8B+4IPADq21Hr7NRa21Uyk1FZgJnAPaxjCmECKQ9XfB6TfB2Q/adflHcCTk3wv2YLOjZG9FE4tnxBFst/wbjQEl2G5j0fQ49lol+XYOQOkfYaALlO3yD3sIZG+CkEizoxRC+IDXk+/hxPkx4A0gCPiV1rpEKfUt4JDWeivwLPA/SqkKoAUjmQZYAXxZKTUIuIDPaq2bAEYb09s/ixDCIrqb4Df3Q23xtY8p+QM88JyR2Jiktr2XM43d/M2iKabFcCtbkZXAt18to669j+SYcVUsepazH154FMpfu/YxqfPgwy9BhHTEESLQ+WTpvdb6VeDVKy77+iVf9wEPjHK7/wH+Z6xjCiFuAe1V8D9boO2CkVynFF4yi6iMz6Vb4fUn4PmPwF//NzjMSbzc3TaWZUq9txmWZRmJbFFFE/fflm5OEIN98MJHjHdp7vgu5N09/A6Nfv+dmtpiePnv4P9uho+8AjGj9g8QQgQI6XslhPAfzZXw3/dCXzt85GWYumz045b8nVFy8ucvwPMfhgd/a0oCvq+iifiIYGYmR/n83ALykqOJiwimqNKk5HuwF55/GCq2w10/ggV/O/pxcdMhIgn+90H41WZ45BWIz/RlpEIIH5IiRCGEf6g9Br+63UhoHv3TtRNvtwUfg3t+DBVvwe8eMm7nQ1pr9lY0sTQzHptNtpQ3g214Y6Oiiia01je+gScN9MDvPmTc/+75ybUTb7dpy+Gjf4bBbiMBrzvumziFED4nybcQwvrO74fn7oKgEPjY65BaOLbbzX8E7v0pnHnbmFUc6PFmlJepaOiiobNfWgyabEVWAvUd/VQ2dvnupAM98LsHjfvdB/4D5n9kbLdLLYS/fR2CguH/3gkXDngzSiGESST5FkJY29k9Ro13ZKKReCdkj+/28z4MW34O5/bA//41DHR7J84ruLc2Xy7Jt6mWD9fb+2y3y4Fu4352bi9s+U8oHGcjrsQc434emQj//QHj/i+ECCiSfAshrMvZD1sfMxag/e3rMCnjxrcZzdyHYMsvjIRo9/c8G+M17K1oZkpcOBlx4T45nxjdlPhwMuLCfNdycPf3hhPvX8DcB29ujEkZxv09Jg22/oPxOBBCBAxJvoUQ1nXgZ9B6Dv7qe8ZM4ETMeQBm3QcH/wu6vTsL6hxy8c6ZZpn1togVWQkcONOMc8jl3RN1N8M7v4BZ9xv3t4mITDS6o7SehXd+7pn4hBCWIMm3EMKauhpg9/chZzNkrvPMmKv+ySgL2P8Tz4x3Dceq2+nsd7I8S3o2W8GyzAQ6+5wcr2737on2/xgGe2D1P3lmvKz1kH077Pqe8XgQQgQESb6FENa041/A2Qubvu25MZNmDs9+/8Krs9/uLc2lv7c1LMs0XgTtq/TiOx6Xznon5npu3Nu/bTwOdjzluTGFEKaS5FsIYT21x+DI/8CiT0NClmfHHpn9/rFnx73E3oom8lOMHtPCfPGRIeSlRLP3tBfrvvc949lZb7eEbFj0KTjy38bjQgjh9yT5FkJYi9bw+lcgLNbziQy8P/v9jndmv3sHhjhyvo0V2TLrbSUrsuI5fL6V3oEhzw/e3WSsJfD0rLfb6n8yHg9vfNV4fAgh/Jok30IIayn7E5zfC+v+fxA2yTvnWPVPxiylF2a/3z3XwsCQa6TUQVjDsqwEBoZcHDrf4vnB93m41vtKYbGw9qtGu8yTf/bOOYQQPiPJtxDCOpz98ObXICkf5n/Ue+fx4ux3UUUTjiDFoulxHh1XTMyiaXE4gpTnWw56e9bb7ba/hcQ84/EhrQeF8GuSfAshrOPAf0Dbebj9XyHI7t1zeWn2u6iyiflTYgkP9nL8YlwiQuzMmxLLPk9vtuPtWW+3IDts/lej9eaBn3n3XEIIr5LkWwhhDZ31sPsHkPtXkLnW++fzwux3a/cAJTUd0t/bopZnJnCipp22ngHPDOirWW+3zHWQc4fRglNaDwrhtyT5FkJYw65/B2cfbPJhSzUPz37vP9OM1rKlvFWtyI5Ha9jvqZaDvpr1vtSmp4zHydv/5rtzCiE8SpJvIYT5eluh+HdQ+DcQn+m783p49ruooonIEDtz02M8EJzwtDnpk4gIDvJM3bevZ73dErKMx0nx74zHjRDC70jyLYQwX/HvjI1EFn7C9+d2z34f/MWEh9pf2cyi6XHYg+Sp1YocQTYWTY9j/xkPzHwf/IXvZ73dFn7CeLwc/b3vzy2EmDD5DyGEMJfWcOhZSF8EKXN8f/6kmTB9FZx4cUI9lOva+zjT1M3SGdJi0MqWZsZzprGb+o6+mx9Eazj+IsxY7dtZb7eUOZC+EN59Vvp+C+GHJPkWQpjr7C5oroCFHzcvhoItRgz1J256iP1njFKGpdLf29KWZRr1+BOq+647Di2Vxv3GLAs+Ds2n4exu82IQQtwUSb6FEOZ691kIi4P8D5gXQ97doIKg5OWbHmJ/ZTMxYQ7yU6I9GJjwtLyUaKJD7RNLvkteNu4vM+/2XGDjVbDF2Hzn0LPmxSCEuCmSfAshzNNRAyf/AvMeBkeoeXFEJBilJyUv3/Tb+Psqm1kyIw6bTXk4OOFJQTbFkhnx7Dtzk4sutTbuJzNWQ4SJ73I4Qo3HTdmfoaPWvDiEEOMmybcQwjxH/hu0Cxb8rdmRGDOJLWeg7ti4b3qxpYeq1l6p9/YTSzPjudjSy8WWnvHfuPYotJ41t+TEbcHHQA8ZjyMhhN+Q5FsIYY6hQTj8HGSth7gZZkczodITdwnDMunv7RdG6r5vputJyctgs8PMuzwc1U2ImwGZ643H0ZDT7GiEEGMkybcQwhynXoPOWmPhmBWEx8GMNXDiD+MuPdl/ppmEyGCykyK9E5vwqJzJkcRHBHNgvHXfWkPJH4z7SXicV2Ibt4Ufh84aKH/N7EiEEGMkybcQwhyHnoWYDMi53exI3lewBdrOQ817Y76J1pp9lU0smRGPUlLv7Q+UUizJjGdfZTN6PC+0ao5A2wVrlJy4Zd8O0enGwmUhhF+Q5FsI4XtNFXDmbbjtUbAFmR3N+/LuAptjXKUnZ5u6qe/olxaDfmbpjHjqOvo41zyOuu+Sl437x8w7vRfYeAXZ4baPwpmd0FxpdjRCiDGQ5FsI4XuHfmXUzc57xOxILhcWC5lroeSVMZee7HPXe2dKvbc/WTb8Ymlf5Ri7nmht3C8y1xn3EyuZ/4jxeDr0K7MjEUKMgSTfQgjfGuyF4t9C3j0QNdnsaK5WsAXaL0D1kTEdvv9MM8nRoUyLD/dyYMKTpidEMDk6ZOz9vqsPQ/tFa5WcuEVNNhYMv/cb4/ElhLA0u9kBCCF8a3BokG/s+wbbL2wnMSyR5Ijkyz7y4/IpSCjwXgAn/gB9bebuaHk9uX81XHryB0i/7bqHaq05UNnM6pxEqff2M0oplmUmsOd0I1rrG//9Sl6GoGDIvcM3AY7Xgo8bMZa8DIV/47XTlDSVUNpSSl133WUfjb2NbJiygSeXPYkjyOG18wsRCCT5FuIW0jPYwxfe/gL7avZx94y7GXANUNddxzu179DY24hLuwD4P2v/D+umrPNOEIf/LyTOhKnLvTP+RIVNMtoflrwCm56C6yRl5fVdNHcPsETqvf3S0hnxvPxeNacbusiZHHXtA12u4ZKT9cb9w4qmrYCEXKP0xEvJ91sX3uIfd/4jADZlG3nxnhefx1zbXP505k809zXzwzU/JNwh7wQJcS2SfAtxi2jvb+ezb32WE00n+Nayb7El+/K3z50uJw09DXzp7S/xlT1f4X/v/F8yJ2V6NoiWs1D1Lmz81nWTWtMVbIHy16HqEGQsvOZh+4frhZdJ8u2X3Itk91c2Xz/5rj4EHVWw/us+iuwmKAXzPgzbvg6t5yB2mkeHr2yr5Kt7vsqs+Fn8YM0PSApPwm67PIVYmLyQb+7/Jp/c9kn+Y/1/EBMS49EYhAgUUvMtxC2gvruej77+Ucqay3h69dNXJd4Adpud1MhUfrj2h4TaQ/n8zs/TMdDh2UBKXzE+W7Fu9lK5dxglBjfoerKvspmMuDDSY2WWzx9lxIWTHht240WXJS9DUIh1S07c8j9gfC55xaPDdgx08LkdnyPMHsYP1/6Q1MjUqxJvgC3ZW3h69dOUNZfx0dc/SkNPg0fjECJQSPItRIA733GeR19/lJquGn6+4eesn7r+uscnRyTzwzU/pLqzmid2P8GQa8hzwZz4A6QvhElTPDemN4TGQNYG48WCyzXqIUMuzTtnW1g2Q7qc+LNlmfEcONOCy3WN7jbukpOsDRAa7dPYxi12KqQtMNYreMiQa4gndj9BTXcNP1z7Q5Ijkq97/Pqp6/nZhp9R01XDI689woWOCx6LRYhAIcm3EAHsVMspHnntEXoGe/jV7b9iUcqiMd1u/uT5fGXxV9hbvZefFv/UM8E0V0LdMevPersVbIGOaqNMZhRltR209w5Kf28/tzQznvbeQUprr/EuT9VBYwdJf7rf1h71WM/vnxT/hL3Ve/nKoq8wL2nemG6zOGUxv7r9V/QM9vDIa49wquWUR2IRIlBI8i1EgBoYGuAfd/4jDpuD5+54btwdTB7IeYD7s+/nv47/F2+ce2PiAbln49xvjVtdzmaj1OAapSfuFnWSfPu3pcPvXBw4c42WgyMlJ5t9GNUEFHzA+DyOjaKu5fVzr/PL47/kgzkf5K9z/3p8YSQU8Nwdz2G32fnHnf/IwNDAhOMRIlBI8i1EgHr+1PNUdVXxrWXfYkbMjHHfXinFVxd/lbmJc/nnon+e+OxVySuQsQRi0iY2jq+ERsOM1VCxfdSr91U2MSMxgsnRoT4OTHhSckwoMxIiRjZLukrFduN+EHKdBZlWEpMOGYsnXPd9quUUXy/6OoWJhXxl0VduaowZMTN4ctmTVHVV8cKpFyYUjxCBRJJvIQJQx0AH/3nsP1mWuoxlactuepzgoGB+uOaHRDoi+fzOz9M10HVzAzWWQ/0JmHXfTcdiiumrofk0dNRcdvHgkIuDZ1tYOkNmvQPBksx4Dp5twTl0RX1/ezU0V8CMNabEddMK7oP649B0+qZu3jXQxed3fp4oRxRPr3ma4KDgmw5ledpylqYs5efHfu75BdxC+ClJvoUIQL88/ks6+jv44m1fnPBYieGJfHfVd6nuquaPlX+8uUFKXgaUsaulP5m+yvh8dvdlFx+vbqd7YEi2lA8QyzLj6ep3cry6/fIr3H939/3AX+TfC6ibLj15peIVqruq+e7q75IYnjjhcL644It09Hfw7PFnJzyWEIFAkm8hAkxNVw2/Lf0td2feTW5crkfGXJC8gDmJc/j9yd+j9TW6QlxPyR+MTXWiUzwSj89MngVhcVcl3+567yUz4syISnjYkuF3MPZfWfd9djeEx0OSF3d89YboFJi6zOguNE4u7eL5U88zN3Eut02+/g6vYzUzbiZ3Z97Nb0p/Q21XrUfGFMKfSfItRID5yXs/QSnFP8z7B4+O+1DuQ5zrOMeB2gPju2FDGTSefH8hmD+x2WD6SjizCy550bG/spncyVHER4aYGJzwlITIEHInR428qAKMv/fZXTBtpXE/8DcFW6CxzHj8jcOB2gOc6zjHQzMf8mg4jxU+BhjdU4S41fnkGUUptVkpdUopVaGU+vIo14copZ4fvv4dpdS04cs3KqUOK6WOD39ed8lt3h4es3j4I8kXP4sQVlbWXMafz/yZh/MevmE/3vG6fdrtxIXG8fuTvx/fDU/8AZRt+K1wPzR9lbG7YcsZAPqdQxw63yJdTgLM0sx4Dp1rZcA5XPfdcsZoNelvJSduefcYj7txlp78/uTviQuNY9PUTR4NJyUyhYfzH+ZPlX/iZMtJj44thL/xevKtlAoCfgrcAeQDH1JK5V9x2MeBVq11FvBD4DvDlzcBd2utZwOPAv9zxe0+rLUuHP6QrbTELU1rzQ8O/4CYkBg+PvvjHh8/OCiY+7Lv4+2qt8f+1rHWxj//aSsg0k9fH09fY3weLj05erGdvkGXJN8BZsmMeHoHhzha1WZccHaX8dnfFlu6RU02Sr1KXr7sXZvrqe2qZVfVLu7Pvn9Ciyyv5eOzP05MSAxPH3ra42ML4U98MfO9CKjQWp/RWg8AvweunAK7F/j18NcvAuuVUkpr/Z7W2t1moAQIU0rJ+7xCjKKopoh3at/h7+b+HVHB3mmL9tc5Rq/f/1f+/8Z2g/oTRreQAj/rcnKp+EyISh1JxvZXNqMULJkuyXcgWTIjDqXer+fnzC6IToO48bfptIxZ90FTOdSXjOnwF8qNdoAP5DzglXCig6P59JxPs792P0XVRV45hxD+wBfJdxpw8ZLvq4YvG/UYrbUTaAeu/M92P3BEa91/yWX/d7jk5J+VUsqzYQvhP4ZcQ/zg0A/IiMoYSZC9ISUyhdXpq3np9Etj2zSj5GVQQf7X5eRSShmlB2f3gMvF/jNN5KdEExPuMDsy4UGTwoPJS442km+XC87tMf7u/vyvJe8e4/E3htKT/qF+Xip/iTXpa0iJ9N7C6AdzHyQ9Mp0fHP4BQ64hr51HCCvzi1UkSqkCjFKUT19y8YeHy1FWDn985Bq3/ZRS6pBS6lBjY6P3gxXCBFsrt1LRVsHn538eR5B3k8KHZj5ES1/LjXe91Nqo956xGiL8fJZ4xmroaaK/5gRHLrSNdMcQgWXJjHiOXGilv+Y49DQbfd79WUSC8QKi5A83LD1589ybtPa3enyh5ZUcQQ4+f9vnOd16mj+d+ZNXzyWEVfki+a4GMi75Pn34slGPUUrZgRigefj7dOBl4BGtdaX7Blrr6uHPncD/YpS3XEVr/Qut9QKt9YLExIn3KxXCapwuJ/9x9D+YkzDH44ukRrMkZQnToqfx+1M3WHhZexRazxpdF/zdtJUA1BS/wYDTJZvrBKilmfH0O13UFg+/sJy+0tyAPKFgi7F4tO7YdQ/7/cnfMy16GktSlng9pNun3s6chDn8R/F/yOy3uCX5Ivl+F8hWSk1XSgUDDwFbrzhmK8aCSoAPAju01lopNQn4C/BlrfVIgZhSyq6UShj+2gHcBZzw7o8hhDUVVRdR113H3876W3xRfWVTNh7MfZBjjccobS699oElfwCbHWbe5fWYvG5SBsTNwFW5C5uCRdLfOyAtmh6HTYGrchfEZRpbtfu7vLuNx+F1en6XNJdwrOkYD818yCfPIUopPjrro9R211JUI7Xf4tbj9eR7uIb7MeANoAx4QWtdopT6llLKXQj6LBCvlKoAvgi42xE+BmQBX7+ipWAI8IZS6hhQjDFz/l/e/lmEsKIXT79IfGg8qzN89xb5PVn3EGYPu3bbQXeXkxlrITxAEtXpq0lpO8yc1EiiQ6XeOxDFhDmYnRJJctsRo9QoEITHGR1brtP15Pcnf0+YPYx7Mn23NmNN+hriQuN4sfxFn51TCKvwSc231vpVrXWO1jpTa/3t4cu+rrXeOvx1n9b6Aa11ltZ6kdb6zPDlT2mtIy5pJ1iotW7QWndrrW/TWs/RWhdorT+vtZb3rsQtp6GngT1Ve7g3614cNt8lhNHB0dw5405ePfsq7f3tVx9QfwLaLkC+Hy+0vMJAxgrCdQ9bJktX00C2JbmBcN3DwJQVZofiOfn3Qtv5UbuetPW18drZ17hrxl1e65I0GkeQg3uz7mV31W4ae2Q9lri1+MWCSyHE6P5Y8UeG9BD3Zfu+ld9DuQ/RP9TPKxWvXH3lqdeNzzmbfRqTNx0Jmg3ASvt1Sm2E31sVZCSo79lmmxyJB2Xfbnwuf+2qq16peIX+oX6vL7QczX1Z9zGkh/hj5R99fm4hzCTJtxB+yqVdvHT6JRYmL2Rq9FSfnz83Lpf5SfN5/tTzuLTr8ivLX4e02/x3Y51R7KnRlLmmMKXjkNmhCC+a0nGIUtdU9lSPbWMavxA1GVLnQ/nlHYpc2sXzp55nftJ8cmJzfB7WtJhpLJi8gJfKX7r6OUSIACbJtxB+6mDdQaq7qrk/+37TYnho5kNc7LzIgZoD71/Y1QDVhyHnDtPi8ob9lc2cjpiPveogDPaZHY7whsFe7FUHOR0xj/1nms2OxrNy74CqQ9D1fonHgZoDVHVV8aGZHzItrPtz7qeqq4p36941LQYhfE2SbyH81EvlLxEdHM2GqRtMi2HdlHWE2cPYeXHn+xeWvwFoyA2ckpPufifHqtoZnLISnH1QddDskIQ3XDwIQ/0MTFnJ0YttdPc7zY7Ic3I2AxpOvz/7vePiDsLsYaybss60sDZO3Uh0cDQvlb9kWgxC+Jok30L4oda+Vt668BZ3Z95NSFCIaXGEBIWwOHkxe6r3oN2dFMpfh+h0mDzLtLg87d1zLThdmpS564wdA8/uNjsk4Q1nd4MKInXOOpwuzaHzrWZH5DnJs43H5Smj7ltrzd7qvSxOWUxwULBpYYUEhXDXjLvYfmE7rX0B9PsW4jok+RbCD22t3Mqga9DUkhO3FWkrqO6q5lzHOaMco3KHMevtz9tyX2H/mWYcQYp5WVMhdR6c2WV2SMIbzu6CtPnMy56CI0gZW80HCqUg53ao3AmDfZztOEt1VzUr08zfSOj+nPsZdA3yp0rZ8VLcGiT5FsLPaK35w+k/MCdxDtmx2WaHw4p0oyXbnqo9cG4PDPYEVJcTgAOVzRRmTCIsOMjo/1x9GPo7zQ5LeFJfB1QfgemrCQ+2Mzd9UuDVfedshsFuOLfXeLxivHg2W05sDnMS5vCH0394/x00IQKYJN9C+JnixmLOtJ+xxKw3QFpkGjNiZrCneo9RcuKIGNmOPRB09A1yvLr9/S3lp68CPQTn95kbmPCs8/uMv+v0VYCx1fyJ6nY6+wZNDsyDpq8CRziUv86e6j1kxmSSGplqdlQA3Jd9H5XtlRxtPGp2KEJ4nSTfQviZF8tfJNwezuZp1pldXpm2ksP1h+k59TpkrgVHqNkhecy7Z1twaViSOZx8ZyyGoBCp+w40Z3cbf9eMxQAsnRHPkEvz7rkWkwPzIEcozFhLT/nrHK4/zMp067xIvmP6HYTbw2XHS3FLkORbCD/SMdDBm+fe5K9m/BXhjnCzwxmxMn0lg65B3nE2B1zJyf7KZoLtNuZPiTUucIRBxiKjPlgEjnO7jb/r8AvH+VNjCQ6yBVbdN0DuZg4MNuF0OS1R7+0W7gjnjul38Ma5N+gckJIuEdgk+RbCj7x25jX6hvr4YPYHzQ7lMvOT5hOu7OwNC4XsTWaH41H7zzQzf8okQh1B7184ZamxVfdAt3mBCc/p7zL+nlOXjVwU6ghi3pQArPvO3sTesFDClZ15SfPMjuYyH8z5IH1Dfbx29uqdOIUIJJJ8C+FHXjr9ErmxueTH55sdymUcQQ6WDNnYExWDDqBdLdt7Bimt7WCJu97bLX0haBfUvGdOYMKzat4z/p7pCy+7eMmMeEpqOmjvDZy6bx05mT1RMSwdCsIR5DA7nMsUxBeQE5sjpSci4EnyLYSfqGyrpKyljC3ZW1BWa+PX1cCKllpqlYvKtkqzo/GYd842ozXvL7Z0S19gfK6SXfkCgvvvmHbbZRcvzYxHazh4NnDqvivaKqhTLla01Bq70VqIUor7su+jrKUsoJ5HhLiSJN9C+Ik3z7+JQrFx6kazQ7la+Rus7DG2XN9bvdfkYDxn/5lmQuw2CqdMuvyK8DiIm2Fs1y38X9UhiMs0/q6XmDdlEiH2wKr7dj8+V/T0wuk3TY7mau7nt23nt5kciRDeI8m3EH5i+/ntFCYVkhRuwbKO8tdJjkgha1KW0XIwQOyvbGbBtFhC7EFXX5m+0Jgxlb7E/k1r4+94RckJQIg9iNumxrKvssmEwLxjT/UesidlkxyRPLLbpZUkhSdRmFjI9vPbzQ5FCK+R5FsIP3C+4zzlreXWnPV272qZczsr01dypOEIXQNdZkc1Yc1d/Zys62RZZsLoB6QvhK56aL/o28CEZ7VdgO6G90uJrrAsM56TdZ20dA/4ODDP6xro4r3694wWg5fsdmk1G6du5FTrKS50XDA7FCG8QpJvIfyA+y3YDVM2mBzJKNy7Wubewcq0lThdTt6pfcfsqCbswBmjzndpZvzoB4zUfUvpiV+rHv77jTLzDbB0+MXXgQDoenKg9gBOPdxiMOeOkd0urWbDVON5TkpPRKCS5FsIP7D9/HZmxc8iJTLF7FCuduq1kV0tC5MKiXREBkTpyf4zTUQEBzE7LWb0AybPAnuoJN/+ruoQ2MNgcsGoV89JjyE8OCgg6r73VO8h0hHJ3KS5l+x2ab3Sk9TIVAriC6T0RAQsSb6FsLjqrmpKmkvYOM2CJSdaQ/kbI7taOmwOlqYuZU/1HrSf10Lvq2xm0fQ4HEHXeJoMckDqPOl44u+q3jX+jtdou+cIsrFoepzf131rrdlbtZelqUtx2Bwju11S/oYl1y1snLqRE80nqOmqMTsUITxOkm8hLM49+7NxigWT7/oS6Kgy6keHrUhbQUNPA+Wt5SYGNjH1HX2caey+dr23W/oCqD0Kzn7fBCY8y9lv/P2uUe/ttiwznsrGbuo7rFcfPVblreU09DZcvqtlzu3GmoWGUvMCuwb3+haZ/RaBSJJvISxu2/ltzIybSUZ0htmhXK1i+B9j1vsvDFakrQD8u+Wgu8TgmvXebukLYagf6k74ICrhcXXHYWjgmvXebssCoO7bXQq2PG35+xdmDz9uK6yX4E6JnkJubK7UfYuAJMm3EBZW313P0caj1lxoCcY/7cmzIPr9WvSk8CRyY3P9uu57X2UTMWEO8lOir39gmmy249fcf7cbzHznpUQTHWpnX4UfJ99Ve5gZN/PyVqXRqZBUYMnkG4yFl8WNxTT0WGszICEmSpJvISzsrQtvAViz3ru/Ey4cgKz1V121Mn0lxQ3FdAx0mBDYxO2rbGbJjDhsthvsJBqTBlGpknz7q6p3ITrNSEKvI8imWDIjnn1n/LPuu2Ogg6ONRy8vOXHLWg/n90O/9dqDbpq6CXj/eVCIQCHJtxAWtu38NjJjMpkRM8PsUK52dg+4BiHr6ln5lWkrGdJDHKg5YEJgE3OxpYeq1t4b13u7pS94v12d8C9Vh2446+22LDOeiy29XGzp8XJQnre/Zj9Desjo732lrA3G4/ic9d6pmjFpBjNiZkjpiQg4knwLYVFNvU0caThizVlvMN6qdkRAxpKrrpqTOIcIR4Rf9vsec723W/pCaD0HXY3eC0p4XlcDtJ2/Yb23m7vf934/rPs+WHuQCEcEsxNmX33llCXG49iipScbp27kcP1hmnv97/cuxLVI8i2ERe24sAOXdlmz3ltrqNgGM1aDPfiqq+02O3MS5nC08agJwU3MvsomEiKDyU6KHNsN3MmbzH77l6rrb65zpZzJkcRHBPtlv+/ixmLmJs7FbrNffaU9xOj5fXqbZVsOurSLHRd3mB2KEB4jybcQFrX9/HamRE0hJzbH7FCu1lxpbMs9Sr23W2FSIafbTvvVVvNaa/ZVNrM0MwGlblDv7ZYyF2x2qfv2N1XvGn+3lLljOlwpxdLMePZVNvlVD/uugS5Ot56mMLHw2gdlrTfeBWg547O4xionNoeMqAxpOSgCiiTfQlhQW18bB+sOsnHqxrEngb7kfos68zrJd2IhLu3ieNNxHwU1cWeaumno7GfpjDGWnAAEhxsdXyT59i9V70LybHCEjfkmSzPjqe/o52xTtxcD86xjTcfQaGNXy2txr9uwYOmJUoqNUzdysPYg7f3tZocjhEdI8i2EBe28uJMhPTSy0YTlVGyH+CyIm37NQ2YnzkahKG4s9l1cE7RvuKRg2Vjrvd3SF0L1EXANeSEq4XGuIePvNcaSEzf3Itx9flR6crThKArFnIQ51z4objrEZVoy+Qaj9MSpney8uNPsUITwCEm+hbCg7Re2kxqRSn58vtmhXG2wF87tHbXLyaWigqPIis3iaIP/1H3vr2wiNSaUqfHh47th+gIY6ILGk94JTHhWQxkMdr/fp32MpsWHkxIT6ld138WNxWTHZhMZfIM1DFkbjA5Gg9bbxbMgvoCUiBQpPREBQ5JvISymc6CTfTX72DB1gzVLTs7vA2fvDZNvMEpPjjYexaVdPghsYlwuzf7x1nu7uWdQq2TRpV9wL44dY5tBN3fd9/4zzbhc1q/7HnINcazx2PXrvd2yNhiP6wv7vB7XeCml2DB1A/tq9tE50Gl2OEJMmCTfQlhMUXURTpeT9VOuXU9tqoq3ICgEpi6/4aGFSYV0DXZR2Vbpg8Am5lR9J609g2NvMXipuBkQFit13/6i6l0IizP+buO0dEY8Ld0DlDdYPwmsbK+ka7CLwqTCGx88bbnxuK6w5oY2G6ZsYNA1SFFNkdmhCDFhknwLYTG7q3YTExLD3MSxdWHwuYptxj/q4BuXZrhn3Pyh7nvfePt7X0opY/ZbZr79Q9Uh4+91E+8sue8f/rDVfHFDMcDYZr6DI2DqMqPloAXNSZxDdHA0e6qstxmQEOMlybcQFjLkGmJv9V5WpK0gyBZkdjhXaz0PTeWQNbaFoBlRGcSFxo0kAVa2v7KJafHhpE0ae/eLy6QvNGq++6Qjg6X1thl/p3EutnRLjw1nany4Xyy6PNp4lLjQONKj0sd2g+yN0HTKaCNqMXabnRVpK9hbvdcvytiEuB5JvoWwkBPNJ2jtb2VV2iqzQxld5fBb0mOo9wajVnNu4lzLb7bjHHLxzpmWm5v1dktfAGiji4awrprhv884670vtXRGPO+cbWbI4nXfxQ3FFCYWjn0Nw0jLQWuWnqxKX0VLXwsnmk6YHYoQEyLJtxAWsrtqNzZlY3najeupTVHxFsRMgYTsMd+kMKmQ8x3naelr8WJgE1NS00Fnv3NkC/GbknYboKT0xOqqDgEK0ubf9BBLM+Pp7HNSUmPddzmae5u50HlhbPXebgk5EJNh2ZaDK9JWYFM2dlftNjsUISZEkm8hLGRP1R4KEwuJCYkxO5SrOQfgzC5jN7xx1Mq6602t3HJwpN57PJvrXCk0BhJzZdGl1VW9C4kzjb/XTRqp+7Zw6Yn73aZxJd9KGY/vM7tgaNA7gU2Aey2MJN/C30nyLYRF1HfXU9ZSxsr0lWaHMrqqgzDQOeaSE7f8+HzsNrulF13uq2wiZ3IkiVEhExsobYHRxs6Pth+/pWg9vNjytgkNkxQVSnZSpKWT7+LGYuw2+/j3CsjaYDzOLx70TmATtCp9FWUtZTT0NJgdihA3TZJvISxiT7Wxin91+mqTI7mGiu1gs8P08dWjh9pDyY/Lt+yiywGni0PnWic26+2WNh96mqH94sTHEp7XdgF6WyD15ktO3JZmxvPu2RYGnNZc/He04Sj58fmEBI3zBeX0Vcbj3KKlJ6vSjecf6Xoi/NkNk2+l1CPDH/cppQp9EJMQt6TdVbtJiUgha1KW2aGMrmI7ZCyB0Ohx33Ru0lxKmksYtOBb2e9daKV3cIjlWROo93ZLKTQ+11q3xOaW5v67pBZOeKjlWQn0Dg5RfLFtwmN52uDQICeaToytxeCVQmMgY7Flk+/sSdkkRyRL6Ynwa2OZ+V47/PEg8GulVLFSalzLxJVSm5VSp5RSFUqpL49yfYhS6vnh699RSk0bvnyjUuqwUur48Od1l9zmtuHLK5RSzyhLbgUoxNgMDA1woPYAq9JXWXNXy846qDtu1IPehMLEQvqH+jnZYr3t14sqmrApWOyJme/J+aCCJPm2qtqjxt8nqWDCQy2ZEY9Nwd6KJg8E5lllLWUMuAbGV+99qaz1UHcMOus9GpcnKKVYlbaK/bX7GRgaMDscIW6K/UYHaK3/9tLvlVJ3Aq8opeZqrW9Y8KaUCgJ+CmwEqoB3lVJbtdallxz2caBVa52llHoI+A5Gst8E3K21rlFKzQLeANKGb/Mz4JPAO8CrwGbgtRvFI4QVHao7RK+zd+QtVcup3GF8vtnkezgJKG4sZnbibA8F5Rl7K5qYkz6JmDDHxAdzhBmL+fw4+e4a6OL5U8/T4+y56rpwezgP5j5IZHCkCZF5QO1RSMoDR+iEh4oJczA7fRJFFU18cWOOB4LzHHeJ101v1JW1Ad76lvG4L/yQ5wLzkFXpq3ih/AUO1R9iWeoys8MRYtxumHwrpb44ysVtwHeUUqVa66dvMMQioEJrfWZ4vN8D9wKXJt/3At8c/vpF4CdKKaW1fu+SY0qAMKVUCBAHRGutDwyP+d/AB5DkW/ipXVW7CAkKYWHyzW384XWVOyAiESbfXOKcFJ5EakQqxQ3FfCT/Ix4O7uZ19g1ytKqdz6zO9NygKXONt+y1vqkdFM32nXe/wysVr2BTV78x6tIuznec51vLv2VCZBOkNdQWQ/Ymjw25Iiuen+86Q2ffIFGhHnjx5iHFjcWkRaaRFJ50cwNMng3hCZZNvhelLCIkKITdVbsl+RZ+aSxlJ1GjfNiAcGAs0x9pwKWrj6p4f/b6qmO01k6gHbjyPeD7gSNa6/7h46tuMKYQfkFrze6q3SxOWUyY/SZ3V/Qml8v4J5y5Dmw3v0Z7btJcihuK0RbqBPLOmRaGXNoz9d5uqYXQ3WCU6viZQ3WHeKXiFT4+6+McfeToVR8fm/UxXq54mcP1h80Odfw6a6G78f26fA9YnpXAkEtz8Kx1ethrrTnacPTmZ73BeJxnrjMe9y7rLSgNs4exKHkRu6t2W+r5RIixuuF/Uq31k5d+APuAGODzWmufTH8opQowSlE+fRO3/ZRS6pBS6lBjY6PngxNigs52nKWqq8q6u1rWHTM6eGSuu/Gx11GYWEhDbwN13dZJSvdWNBHqsDF/6iTPDZoynPT4WenJ4NAgTx14irTIND49d/Sn2k/P+TSpEak8deApSy6evS733yNlAknpFeZPiSXEbrNU3Xdtdy0NvQ03X+/tlrkOepqg/rhH4vK0VemruNh5kXMd58wORYhxG0u3k18Nf/xOKfUe8DTwQa31WDPZaiDjku/Thy8b9RillB0juW8e/j4deBl4RGtdecnx6TcYEwCt9S+01gu01gsSExPHGLIQvuNumWX5eu8Zayc0jDsZsNJW80UVTSycFkeIPchzg06eBSi/S75/XfprKtsr+erir17zHZhwRzhfXfxVKtoq+O/S//ZxhBNUexRQkDzLY0OGOoJYND2OIgsl3yOb69xMp5NLZQ4/3t2Pf4txP19K1xPhj8byHvKu4Y+XMBZGztFa7x/HOd4FspVS05VSwcBDwNYrjtkKPDr89QeBHVprrZSaBPwF+LLWush9sNa6FuhQSi0Z7nLyCPDHccQkhGXsrtpN1qQsUiJTzA5ldJU7jBrQqMkTGiYnNocwe5hlNttp6OjjdEMXKzxZcgIQEgkJ2X6VfFd1VvGfR/+TjVM33vBF4OqM1WyYsoGfH/051V2jznlYU+1RY/v04AiPDrs8K4Hy+i4aOvs8Ou7NKm4oJsweRnZs9sQGiko2XkhWvOWZwDwsNTKVrElZ0u9b+KWxlJ38evjjRa31ET3OAqvhGu7HMDqVlAEvaK1LlFLfUkrdM3zYs0C8UqoC+CLgbkf4GJAFfH24xWGxUsq9guSzwC+BCqASWWwp/FDnQCdH6o9Yd9a7vwsuHHh/FmwC7DY7sxNmW2aznaJKY7bSo/XebilzjcV9fkBrzb++86/YlI1/WvhPY7rNE4uewKZs/Os7/+o/Nbc1xR4tOXFzv3jbV2GN3S6LG4uZkzAHu+2G/RRuLHOt8fgf6J74WF6wMn0lh+sP0zXQZXYoQoyLT3a41Fq/qrXO0Vpnaq2/PXzZ17XWW4e/7tNaP6C1ztJaL3J3RtFaP6W1jtBaF17y0TB83SGt9azhMR8b74sCIaxgX80+nNpp3V0tz+0F1+BNtxi80tzEuZxsOUnP4NVt7Hxt7+lmYsMd5KeMf9OgG0ophI5q6LL+OpO3LrzFnuo9PDbvMZIjksd0m+SIZP6+8O/ZXbWbHResWZZwma4G6KzxyOY6V8pPiWZSuMMSdd89gz2cajnF3CQPvcjIXG88/s/t9cx4HrY6fTVO7WRfzT6zQxFiXGR7eSFMtLtqN9HB0cxJnGN2KKOr3AH2MGNnSw8oTCpkSA9R0lzikfFultaaooomlmUmYLN5oR2ge4a1ztqlJ92D3fzbwX9jZtxMPjRzfC3l/ibvb8iNzeXfDv4b3YPWnBkdUXvM+OyFmW+bTbEsM56iiibT3wUoaS5hSA9NvN7bbcpS4/Fv0brvuYlziQ6Olrpv4Xck+RbCJC7tYm/1XpanLffMW8TeUPkWTFvhkU1J4P1NP8xedHmmqZu6jj7vlJwAJA/3Q7d43fdPi39KY08j/7zkn8d9H7Tb7Hx96ddp6GngP4r/w0sReoi7BCjZOxs8Lc9KoLa9j7NN5r4IcZd0eezFvCMUpi23bN233WZneepy9lTvwaWt1xJRiGuR5FsIk5Q0ldDS12Ldeu/W89BcMeEWg5eKCYlhesx005Nvd3cKjy+2dAubBLHTLZ18n2w5yW/Lfstf5/71TSdrcxLn8EDOA/y27LecbDnp4Qg9qPYoxM2A0BivDO++H5nd9eRY4zGmx0wnJsSDP2fmOmg+DW0XPDemB61MX0lLXwulzaU3PlgIi5DkWwiT7K3ei0KxPHW52aGM7sxO47OH6r3d8uPzKWsu8+iY47X3dBPpsWFMiQ/33klS5hqL/Czqf8v+l3B7OJ+b/7kJjfO5+Z8j1B7K707+zkOReUFtsVdKTtymxIWTNinM9Lrv0pZSCuILPDto5vDjv3KnZ8f1kBVpK1Ao9lRL1xPhPyT5FsIke2v2MjthNrGhsWaHMrqKtyA6zWjP5kF5cXnU99TT3GtOd4ghl2b/mWbvzXq7pRZC23nobfXueW7CoGuQHRd3sDpjNdHBE1twGhMSw+r01ey4sAOny+mhCD2op8WYtfXgzpZXUkqxIiuB/ZXNDLnMqftu6m2ioaeBvLg8zw6cmAtRqUYJmgXFhsYyK2EWRdVFNz5YCIuQ5FsIE7T1tXGi6QTL0yw66z3khLO7jLeclWcXJObH5wOYVqZwvLqdzj6n9+q93UZ2ujzm3fPchEN1h2jvb2fjlI0eGW/j1I209bdxqP6QR8bzqDrvLba81PLsBDr6nJyobvfqea7F/XjKi/dw8q0UZK2DM2+Da8izY3vI8rTlHG86Tnu/Ob97IcZLkm8hTHCg9gAu7bJu8l1zBPraPVrv7TYzbiYAZS3mlJ6463KXZcZ790TJ1t1mfvv57YTZwzx2/1uetpwwexjbz2/3yHge5YVt5Ufjvj+ZVXriLuVyP748KnOd8XxQfcTzY3vA8tTluLSL/bXj2f9PCPNI8i2ECYpqiogOjmZWvOe2uvaoyh2AghlrPD50VHAUU6KmmLZAau/pJvJSoomPDPHuiSLiISbDcpvtDLmG2H5hOyvTVhJq90wXmzB7GCvSVrD9/HaGrDY7WlMMMVMgPM6rp0mIDGFmcpRpiy7LWsqYGj2VqOAozw8+Yy2gLNtycFbCLKKDo9lXLf2+hX+Q5FsIH9NaU1RdxLLUZQTZgswOZ3QVb0HafK8lLHnxeaYsuuwdGOLw+VZWZHl51tstZa7lZr7fa3iPlr4WNk71TMmJ28apG2nua6a4sdij405Y7VFI8U0f/RVZCRw630rfoO9fgJQ2l3q+3tstPA5S51m27ttus7M0dSlF1UWm91oXYiwk+RbCx8pby2nsbbRuyUlvG1Qf8krJiVteXB5VXVU+r9E8dL6FgSGX9+u93VIKjXaNfR2+Od8YbL+wnZCgEFamr/TouKvSVxFsC7ZW6UlfB7RUemVny9Esz05gwOni0DnfLrJt72+nuqva8/Xel8pcB1WHjOcHC1qeupyG3gZOt502OxQhbkiSbyF8rKjGWJW/LHWZyZFcw9ndoF3vtxjzAneS4OtFl3srmnAEKRZN924Jwgh3nXH9Cd+c7wZc2sX289tZlrqMCEeER8eOcESwLG0Z285vs86GJ3XHjc9e7HRyqUXT4nAEKZ/XfbvXT3ht5huMlqN6CM5Zs6Wf+/lUup4IfyDJtxA+VlRdRE5sDknhSWaHMrrKtyA4CtIXeO0U7iTB16Un+yqamTcllvBgH+0ommKtRZfHm45T31Pv8ZITt41TN1LfU8+JJmu82PDVYku3iBA78zJi2Vfp4+S72QfJd/pC43nBortdTo6YTHZstiTfwi9I8i2ED3UPdnOk4Yh1S060hoodMGM1BDm8dprY0FhSIlIobfHdosvW7gFO1LSzPNNHJScAUZMhMtkym+1sP78du83O6ozVXhl/dfpq7MpundKT2mKISoFI373QXZ6VwPHqdlq7B3x2zrLmMlIjUpkUOsl7JwlywPRVxotzi9ZVr0hdweGGw/QM9pgdihDXJcm3ED50sPYgTpeTFakrzA5ldM2V0H4BMtd6/VR5cb5ddLm3ogmtYWWOD5NvsMyiS601285vY0nKkglvrHMtMSExLE5dzLbz26yx8K32qM9mvd1WZCegNRT5cPa7rKXMu/XebplrjQ2LWs54/1w3YXnacpwuJwfrDpodihDXJcm3ED5UVFNEmD2MeUnzzA5ldO5WYl5cbOmWF5/H+Y7zdA92e/1cALvLG4kJczA3fZJPzjcitRCaTsGAubNxZS1lVHdVe63kxG3jlI1UdVWZtonSiIFuaCr3Wb2329z0GKJD7ewub/TJ+boGujjXcc67JSdu7ucFi5aezEuaR5g9jL3Ve80ORYjrkuRbCB/RWrO3ei+LUxbj8GJJx4RUbIfY6RA3w+unyo/PR6M51XLK6+fSWrP7dCMrshIIsnl2x84bSplrLGCtL/Htea+w/fx2glQQazO8+67G2ilrsSkb285v8+p5bqi+xPi9+3jm2x5kY0V2ArvLm3wy+3+q1Xj8+GTmOz4TYqdZtuVgcFAwi5MXS923sDxJvoXwkQudF6juqrZuyYmz3+hkkOW9LieXGll06YOdLsvru6jv6GeVr0tO4JJFl8W+P/cwd8nJguQFxIbGevVccaFxLJy8kO0XTK779vFiy0utyk6krqOP0w1dXj+Xu3QrPz7f6+cCjC5IZ/eA03c17eOxPG05VV1VXOi4YHYoQlyTJN9C+Ij7rdBlaRZtMXjhAAz2QNYGn5wuMTyRhLAEn+x06S4BWJWT6PVzXSU6DcLjTU2+K9sqOddxjo1TvFty4rZh6gbOtp+lsq3SJ+cbVU0xhCdAdKrPT+2+n/mi9KSspYzEMOOx5BNZG2CwGy4e8M35xsm9mF1KT4SVSfIthI8UVRcxLXoaGVEZZocyusq3wOaAaZ7dfOV68uPzfTLzvau8keykSFJiwrx+rqsoZfqiy23nt6FQrJ/qm3c11k9Zj0Lx5vk3fXK+UbkXWyoflxkBqZPCyEqKZJcPku/S5lLfzXoDTF8JNrtl674zojKYGj11ZD8FIaxIkm8hfKB/qJ936961botBMP6ZTlkCIZE+O2VeXB5n2s7Q5+zz2jl6B4Y4eK6F1WbMerulFEJDmVHaY4JtF7YxL2mez2ZHE8MTmZc0z7yWg4N90Fjms50tR7M6J5F3zrbQO+C9reZ7nb2caT/jm3pvt5AoyFhi2eQbjN0u3617l/4hcx5vQtyIJN9C+MDh+sP0DfWxPNWiyXdnnbELow+6nFwqLz6PIT1EeWu5185x4GwzA06XOSUnbilzwOWEBt/1NXc7136O062nvd7l5Eobpm6gvLWc8x3nfXpewEi8XU5InuP7cw9blZPIgNPFO2ebvXaO8tZyXNrlm04nl8paB/XHobPet+cdo+Vpy+l19nKk/ojZoQgxKkm+hfCBouoigm3BLEj23q6RE+JuMeijem+3/Djj7XJv9vveXd5IiN3muy3lR+NOAut8v/Oje+Hjhqm+/dtumGKcz5SuJ+5t5ZNn+/7cwxZPjyPEbmN3uff6fft8saWb+3nC/bxhMQsmLyDYFixdT4RlSfIthA8UVRdx2+TbCLObUHM8FhVvQUQSTJ7l09MmRyQzKWSSV+u+d5c3snhGPKGOIK+d44Zip4Mj4v2k0If21+wnLy6P5Ihkn543JTKFmXEzOVBjwsK8uuMQHGn83k0S6ghi0fQ4dp/2Xt13WUsZsSGxTA6f7LVzjGrybIhItGzLwXBHOPMnz5e6b2FZknwL4WW1XbVUtldat97bNWTMYGWuA5tvnxKUUuTF5Xmt40l1Wy+Vjd2syjahxeClbDZInmWU9vjQ4NAgxxqPcdvk23x6XrfbJt/GsaZjDLoGfXviuhPGC0kf35+vtDonkYqGLmraer0yflmzsbOl8vWiUpvNeL6o3AEul2/PPUYr0lZQ0VZBXXed2aEIcRVJvoXwMvfsy4o0i/b3ri2G3haf9fe+Ul58HqfbTjM45PkEzd3qzdTFlm6TZxkzsj7cdr20pZS+oT7TdlSdlzSPXmevV8uKruJyGb/nZN++izMab7YcHBga4HTbad/Xe7tlroeeZlNbaF6Pe32NlJ4IK5LkWwgv21ezj+SIZGbEeH/XyJtSMVy3OcO7Ox9eS158Hk6Xk4q2Co+Pvbu8kZSYULKSfNfB5ZqSZ0N/B7T5bgGie8HZ/MnzfXbOS7ln3H268K3tPAx0mlrv7ZadFElydKhXSk8q2ipwupy+7XRyKffibIuWnmROymRy+GQpPRGWJMm3EF406Bpkf81+lqcu9/1bw2NV+ZbRCi/SnNnhkUWXHq77dg652FvRxKrsRGv87k1YdHmk/ghTo6f6bgOWKySEJTAlagqHGw777qTu0h4LJN9KKVblJLD3dBPOIc+WZ4wstozz8WJLt8hEo496hTUXXSqlWJG2ggM1B3C6nGaHI8RlJPkWwouONx6na7DLuiUnfe1w8aBpJScA6VHpRDoiPV73fbSqjc4+p7ktBi+VlAfK5rNFly7t4r3G95ifZM6st9v8yfMpbijGpX1UG1x33Pg9J5mUlF5hVU4iHX1Ojla1e3TcspYyohxRpEele3TccclcDxffMZ5HLGh52nI6Bzs53uT7hc5CXI8k30J40d7qvQSpIBanLDY7lNGd2QV6yPgnahKbsjEzbqbH64J3lTdhU7Aiy+TFlm7B4RCf5bPk+0zbGdr7200rOXGbnzSftv42zraf9c0J645DfDY4rNFZaEVWAjbl+brv0uZSZsbPNPddnaz1xvPH2d3mxXAdi1MWE6SCZKt5YTmSfAvhRUU1RcxNnEtUcJTZoYyu8i0IjoKMRaaGkR+fz6nWUx59e3h3eSNzMyYRE+7w2JgTljzb2JzEB440GHXWtyWZ0+nEzV33fbjeR6UndScsUXLiNik8mDnpkzxa9z3oGuRUyynzSk7c0hcZLR0tuttldHA0cxPnyqJLYTmSfAvhJc29zZQ2l1q35ERro15zxmoIMjdBzYvPo3+o32Ozo209AxyramNVtkVKTtySZ0PbBeht8/qpDtcfJiEswdyyBCAjKoP40PiRFwNe1dsK7RcslXyDUXpy9GIb7T2e6ehztv0sA64B8xZbutmDYfpq40W8D7v4jMfytOWUNJfQ3Ou9nUaFGC9JvoXwkn01+wBYlrbM5Eiuoem0kaj4eEv50Xh60eXeiiZcGuvUe7tNHk4KfdDv+0jDEeYnzTd9salSivmT5/um44l7MasF2gxeanVOAi5t3C89wV2iZXryDcZW820XoNnz3Yo8wd1ycH/tfpMjEeJ9knwL4SVFNUXEhcaZ14f3RtwtwkxcbOk2NXoqYfYwj9V97y5vJDrUztz0GI+M5zHuGVkv133XdNVQ111ner23222Tb6O2u5barlrvnmhkW/k53j3POM1Nn0RUqN1jdd9lLWWE2cOYGjXVI+NNiHu9iEVLT/Li84gNiZXSE2EpknwL4QUu7WJf9T6WpS7Dpiz6MKt4C+IyIXaa2ZEQZAsiNzbXIx1PtNbsKm9kRXYC9iCL/e6jJkNEktfbDY7Ue5u0s+WV3B1XvF56Un8CIidDZJJ3zzNO9iAbK7IS2FXeiPZAeUZZcxm5sbkE2YI8EN0ExU2HuBmW7fdtUzaWpS1jX80+33XcEeIGLPafSYjAUNZcRmt/q3W3lB/sg3N7LTHr7ZYbl0t5a/mEk5Py+i7qO/qtV+/tljwL6o559RRH6o8Q6Ygke1K2V88zVjmxOUQ6Ir1felJ3zNhJ1IJW5SRS19HH6YauCY2jteZU6ylmxs30UGQekLneeD4Z7DM7klEtT11OS1+Lx/cSEOJmSfIthBfsrd6LQrEs1aL13hf2gbMXsjaYHcmInNgcuga7qOmumdA4O081ALA616rJ92xoPAlDnll8N5oj9UcoTCq0xswoxjsbc5Pmenfm2zkADSctt9jSbfXw+oOdJxsmNE51VzXdg93kxOV4IizPyNoAgz1wwZp11e7nYSk9EVYhybcQXrCvZh/58fnEhcaZHcroKt6CoGCYZp1OLLlxuQCcajk1oXF2lDWQnxJNSow1+jxfJXkODA1AU7lXhm/ra6OyvdIyJSdutyXdRkVbBW19bd45QVM5uAYtm3ynTgojLyWatyaYfJ9qNR4fubG5ngjLM6atAJvDsqUn8WHx5MfnS/ItLEOSbyE8rGOgg6ONR61bcgJQsR2mLIXgCLMjGZE9KRuForz15pPStp4BDl9oZX2etWp+L+PlRZfu2eV5SfO8Mv7NcsfzXsN73jmBRRdbXmr9zCQOn2+dUMvB8tZyFIqsSVkejGyCQiJh6jI4vd3sSK5peepyjjYepXOg0+xQhJDkWwhPe6f2HYb0kHX7e7eeN8oecm43O5LLhDvCyYjKmFDyvau8kSGXZu1MCyffcZlgD/Ve8l1/BIfNwawEa9U+z06cjcPm8F7pSd1xsIdBfKZ3xveAtTOTGHJpdk1gw53ylnKmRE8h3BHuwcg8IHsTNJYZbQctaEXaCob0EO/UvmN2KEJI8i2EpxVVFxHliGJ2gjXf/ub0m8bn7E3mxjGK3LjcCZWd7DjZQHxEMHPTJ3kuKE8LskNSvteS7/ca3mN2wmxCgkK8Mv7NCgkKYVbCLO8l3/XHYXI+WKTOfTSFGZOIiwhmR1n9TY9xqvUUObEWqvd2cz+fuJ9fLGZ24mwiHZGy1bywBJ8k30qpzUqpU0qpCqXUl0e5PkQp9fzw9e8opaYNXx6vlNqplOpSSv3kitu8PTxm8fCHhae6xK1Ca83e6r0sSV2C3WY3O5zRnd5mtBeMt9Db1sOyY7O52HmRnsGecd/WOeRiV3kja3KTCLKZu7HMDSXPNpJvD+8K2DPYQ2lzqWX6e19pftJ8SptK6XX2enZgrY3fp0Xrvd2CbIo1uYm8PfwOzXj1DPZwsfOiNZPvhGyYNNV4frEgh83BkpQlFNUUeaTdoxAT4fXkWykVBPwUuAPIBz6klMq/4rCPA61a6yzgh8B3hi/vA/4Z+P+uMfyHtdaFwx8TW8UihAdUtlVS31M/squa5Qz2wtndkH07mLzz4WhyY3PRaE63nR73bd+72EZbzyDrrFxy4pY8G3pboGNinV2udLzpOE7tHOmrbTXzJ8/HqZ0cb/TwrH9HtbG1vEXbDF5q3cwk2noGee9C67hv6y7JstRiSzeljFK2M7us23IwbTl13XWcaT9jdijiFueLme9FQIXW+ozWegD4PXDvFcfcC/x6+OsXgfVKKaW17tZa78VIwoWwvKIaYzW9ZRdbnisyWgxasOQEJtbx5K2yBuw2xcqcBE+H5XleWnR5pP4ICkVhUqFHx/WUwqRCFIrDDYc9O7AfLLZ0W5mdiN2mbqrryUjyHWfB5BuM5xVnL5y3ZmmHe1JESk+E2XyRfKcBFy/5vmr4slGP0Vo7gXYgfgxj/9/hkpN/VsqC03jilrO3ei9Zk7JIjkg2O5TRnX7TWJQ2zZovDlIjUol0RN7UosudJxtYND2O6FCHFyLzsMkFxud6zybfhxsOkxObQ1RwlEfH9ZTo4GiyY7M9v9lO3QlAGTXfFhcT5mDhtLib6vdd3lpOlCOKlIgUL0TmAdNWGIuJLVp6khKZQmZMprQcFKbz5wWXH9ZazwZWDn98ZLSDlFKfUkodUkodamy8+RXmQtxIz2APh+sPW7fkRGs4/QZMXwUOa/bAVkqRE5sz7uT7YksPp+o7/aPkBCAkytiS24Mz34OuQY41HrNsvbfb/KT5HG08itPl9NygdceM32eINV90XGndzCRO1nVS1Tq+tQ2nWk6RHZuNZeeaHGHG84tFF12C8a7kofpDN7WuRAhP8UXyXQ1kXPJ9+vBlox6jlLIDMUDz9QbVWlcPf+4E/hejvGW0436htV6gtV6QmGjRHe9EQDhUf4hB16B1S06aK6D1HGRvNDuS63In3y7tGvNt3Lta+k3yDUZ9sgeT71Mtp+h19lo++b5t8m30OnsnvJnSZeqOQ7L1673d1g33oR/P7LdLuyhvLbduyYlb9iZoOQNNFWZHMqrlacsZdA1yqP6Q2aGIW5gvku93gWyl1HSlVDDwELD1imO2Ao8Of/1BYIe+znJkpZRdKZUw/LUDuAs44fHIhRiHvdV7CbOHWTf5sXCLwUvlxOXQPdhNTdfYFyO+VdbA9IQIZiRGejEyD0ueAy1nod8zm34crjfqqG9LstbOlldyPz7c8U5Yfye0nrV8p5NLzUiIYFp8+Ljqvqu7qulx9liz08ml3C/uLTr7fdvk2wgNCpXSE2EqryffwzXcjwFvAGXAC1rrEqXUt5RS9wwf9iwQr5SqAL4IjLQjVEqdA54GPqqUqhrulBICvKGUOgYUY8yc/5e3fxYhrkVrzZ6qPSxMXmi5/sojTr8JiTMhdqrZkVyXu5ODexvtG+kZcLL/TLN/zXrDcLKoob7UI8MdqT9CRlQGieHWfocvKTyJ9Mh0z/X7ri8xPvvBYks3pRTrZk5mX2UzPQNjK78pb7Fwp5NLxU6DhFzLJt8hQSEsTF7Inuo90nJQmMYnNd9a61e11jla60yt9beHL/u61nrr8Nd9WusHtNZZWutFWuszl9x2mtY6TmsdqbVO11qXDndBuU1rPUdrXaC1/rzWesgXP4sQoznXcY6qripWpa0yO5TR9XcZnU4sXnICkDUpy9hmvmVsdd9FFc0MOF1+mHwPl0nUHfPIcMebjjM3ca5HxvK2wqRCz7UbdJfu+EGbwUutm5nEgNPFvorrVliOONV6ythWPtZ6/fmvkr0RzhcZzzsWtCp9FRc7L3K+47zZoYhblD8vuBTCMnZX7QZgZfpKkyO5hrO7wDVo+ZITMLaZnxI9ZcyLLnecrCcyxM7CaXFejszDotMgLBbqJ14x19DTQGNvo+W2lL+WgvgCGnobaOjxwPYMdcchLA6iUyc+lg8tmh5HRHDQmEtPylvLmRo9lTC7NRdLXyZ7EwwNGHsKWJD7edr9vC2Er0nyLYQH7KneQ9akLFIjLZoAnH4TgqMgY4nZkYxJTmzOmMpOtNbsONnAqpwEgu1+9nSm1Ps7XU5QSZNRelEQXzDhsXyhIMGIs7TZAyU37p0trdoB5BqC7TZW5SSy82TDmMofTrVYdFv50UxZCsGRli09SYtMIzMmkz3Ve8wORdyi/Oy/lRDW0z3YzeH6w9ad9dba6LubuQbswWZHMya5sblc7LxI92D3dY8rqemgvqOftbl+VnLiNnm2UbM8NLG2eyXNJdiUzfqdMIblxuZiUzZKmksmNtCQExpK/Wqx5aXWzkyirqOP0tqO6x7XNdBFVVeV3/x9sQfDjDXG845F66pXpa/iUP2hGz7HCOENknwLMUH7a/bjdDlZmWbR5Luh1Nh+2w9KTtzcM3ynW6+/zfyOkw0oBWv8NflOng3OPmipnNAwJc0lZE7K9I+SBIzSohkxM0Zm7G9ac4Xx+/PX5Hv4fruj7PqlJxVtRts+v5n5BuP5pqMKGsrMjmRUK9NX4nQ5OVBzwOxQxC1Ikm8hJmhP9R6iHFGW3dKb8jeMz1nWX2zp5p7hu1Hd946TDcxNn0RilEU7zNyIB7aZ11pT2lzqNyUnbgXxBZQ0l0ys44S7Xt7PFlu6JUaFMDdjEjtOXT/5dvdEt3ynk0uNtBx8w9w4rqEwqZBIR6SUnghTSPItxAS4WwwuTV2Kw2bRbc1PbzPasEVbdEvqUaREpBDliLruRiyNnf0crWrzvy4nl0rIgaDgCSXfdd11tPS1+F/ynVBAS18L9T31Nz9I3THj95foR0npFdblJlF8sY2mrv5rHnOq9RRRwVEkRyT7MLIJik41XlxadKt5h83B0tSl7KmSloPC9yT5FmICTracpLG3kVXpFm0x2NsKF9/xq5ITMPogZ8dmX3fme+epBrT2s10tr2QPNnqvTyD5dtdN+13yPRzvhEpP6o5DUh4EWfSF7xisz0tC6+vvdlneWk5ObI51t5W/luxNcOEA9LaZHcmoVqWvoqG3Ycx7CgjhKZJ8CzEB7lZVK9JWmBzJNVTuBD3kd8k3GKUn19tm/s2SelJjQilIjfZxZB42wY4nJc0l2JWdnDg/qgfGqF+2K/vNL7rUGmqPGYtW/VhBajQpMaG8WTr6OwAj28r7U8mJW/Ym4/nnzE6zIxmV+3lbWg4KX5PkW4gJ2FO9h1nxs4gPizc7lNGd3mb0kk5fYHYk45Ybm0uPs4fqzuqrruvud7L7dCO3z0r2v9nAKyXPhu4G6Ly58ouSphKyY7Otu7PqNYTaQ8mKzbr55LurHnqa/HaxpZtSitsLktld3kh3/9Vdb6o6q+h19vpPp5NLpS2A0ElQbs2WgwlhCRTEF7CnSuq+hW9J8i3ETWrta+VY4zHrlpy4hozFTlkbwBZkdjTj5u7sMFrpydunGhlwuthc4Ec1sNfiTh7rxz/7rbWmpLlkpG+2v5nQosu64cWWfp58A2yelUy/08Wu8sarrnPf//2q04lbkN14/jn9pvF8ZEGr0ldxrOkYbX1tZocibiGSfAtxk4pqitBo6/b3vvgO9DRD7l+ZHclNyYo1tpkfrR7z9ZI64iOCWeBvu1qOxt2p4yZKT6o6q+gY6PC7em+3goQC2vvbqeqqGv+N644Zn5P9s9PJpRZOiyM+IpjXT9Rddd2p1lPYlI3MSZkmROYBM//KeIfi4kGzIxnVyrSVuLSLopois0MRtxBJvoW4SburdhMXGkd+fL7ZoYzu5F/A5jBmnvxQmD2MqdFTr+p40jc4xI6yejYVTCbI5uclJwBhk2DSlJtKvv11saXbyKLLmyk9qTsOk6ZCaIyHo/K9IJtiY/5kdpxsoN95+QzxqZZTTIma4jc93K+StdF4Hjr1F7MjGVVBQgFxoXFS9y18SpJvIW7CkGuIouoiVqStwKYs+DDS2ki+Z6yGUP9dkJgTm3NV2cm+yia6B4a4PRBKTtyS59x08h1sCyZrUpYXgvK+7EnZOGwOSptuYpt597byAeL2Wcl09TvZV9F82eXlreX+We/tFhoN01cZz0cWbOlnUzZWpK2gqKaIIYuWxojAY8GsQQjrO9Z0jI6BDuvWezeehNazflty4pYbl0tVVxVdA10jl71+oo6oEDvLMhNMjMzDJs+CptMwML6trkuaS8iNy8Xhp632HEEOcmNzxz/zPdBt7G4ZQMn3ssx4okLsl5WedA10Ud1V7Z+dTi4186+g5Qw0WrOl38r0lbT3t3O86ea7DgkxHpJ8C3ETdlftJkgFsSx1mdmhjO7k8Fu8fp58j2wz32ZsM+8ccrGttJ71eUkE2wPo6St5NqDHtRW3S7sobS61btnTGBUkFFDaXHrNlpKjqi8FdEAl3yH2INblJbGtrB7nkPG78OvFlpdyPw9ZtPRkWeoyglSQlJ4Inwmg/15C+M6eqj3MS5pHVHCU2aGM7tSrkDrfr3a1HI17xq+8xUhCDp5robVnMLBKTuCSbeaPjfkm5zvO0z3Y7bf13m4F8QV0DXZxoePC2G80stgycJJvgNsLkmnpHuDdc63A+8m3X5edgLHbZeo8OPmq2ZGMKjo4msKkQtlqXviMJN9CjFNddx2nWk9Zt+SkoxaqDxtv9fq55IhkooKjRjqevHGijhC7jdW5iSZH5mGTpkBIzPvt88ZgZLGln7YZdHPP3I+r9KT+hLHQMibDS1GZY3VOIiF2G2+UGKUnp1pPER0czeTwySZH5gG5d0L1Iei8uqOLFaxKX8XJlpPUd99cv30hxkOSbyHGaW/1XsBoUWVJp4Znl3LvNDcOD1BKkRObw6nWU7hcmjdK6lmdk0h4sN3s0DxLqXHvdFnSVEJoUCgzYmZ4MTDvy5yUSUhQyPiS77rjxiJVf99g6QoRIXZW5STyRkkdWmvKW/x0W/nRuCcDTllz9tv9fO5+fhfCmyT5FmKcdlftJjUi1bp9d0+9CrHTISnP7Eg8Ijc2l9OtpymuaqWuo4/NswKs5MQteTbUl4x5M5LS5lJmxs3EbvPvFyJ2m52ZcTMpaRpj8u0aMn5PAVZy4ra5IJna9j6KL7Zyuu20/5ecuCXlQ+w0y5aeZE3KIiUiReq+hU9I8i3EOPQ6e9lfs59V6ausORvV3wlnd8PMOwNmVjA3LpdeZy8vHT2K3aZYPzMA3oIfTfIsGOyGlrM3PHTINURZS5nfl5y4FcQXUNZSNrZWby1nYLDn/c2JAsz6vCTsNsWLx44a28r7e6cTN6WMd+PO7jKepyxGKcWq9FXsr91Pn7PP7HBEgJPkW4hxOFBzgL6hPtZNWWd2KKOr2A5DA37f5eRS7k4PO84eZWlmPDHh/tlW74bGsejyTPsZep29fr/Y0q0goYBeZy9n22/8wiNQF1u6TQoPZmlmPDvPHAUCoNPJpWb+lfH8VPGW2ZGMat2UdfQ6ezlQe8DsUESAk+RbiHHYcXEHUY4oFiQvMDuU0Z18FcLiIGOx2ZF4TOakTGzYaB44F7glJwCJM8FmH1Pdt7/vbHmlce10WXfc2DExcaaXozLP7QXJNA2cxYYfbys/mowlEBZr2brvhZMXEuWIYseFHWaHIgKcJN9CjNGQa4hdF3exKmMVDpsFZ1+HBuH0G5CzGYL8uw74UmH2MKLsKQSF1rIxP0BLTgDsIUZCWX/jjiclTSWE28OZGj3VB4F537ToaYTZw8aYfJ8wfk/2YO8HZpJN+ZMJCq0j2p5CqD3U7HA8J8huPD+Vv248X1mMI8jByvSV7KraJbtdCq+S5FuIMSpuLKa1v5W1GWvNDmV054ugrz0gWgxeaaBnMmERDSRFBVAiMpoxdjxxb64TZAvyQVDeF2QLIj8+f+wz3wFacuKWFB1KWEQ9/T0B+E5P7l8Zz1Pn95kdyajWTllLS18LRxuPmh2KCGCSfAsxRjsu7MBhc7AibYXZoYzu5KtgD4VMi9aj36Tzzd20tSUyaGu6bJv5gJQ8GzproavxmocMugY52XIyYEpO3AriCzjVcopB13VmRLsaoKsu4JPvzoFOBm3NtLUlcKG5x+xwPCtzHQSFWLb0ZEXqChw2h5SeCK+S5FuIMdBas+PCDpakLCHCEWF2OFfT2vhnNmMtBFswvgl4o6SOoX5jBtC9zXzAcnfwqL/27HdlWyUDroGA6XTiVhBfQP9QP2fazlz7IPe7AsmB2enE7XSrcT8f6k/h9ZJak6PxsJBIyFxrTBZobXY0V4kMjmRxymJ2XNyBtmB8IjBI8i3EGJxuO01VV5V1u5zUHYf2iwFZcvKno7XkTDI6PpxqOWVyNF420vHk2sm3ux92wM18J4xh0aX79xKgbQbd3Du65kzK4c/HAiz5BqP0pP3CmNY3mGHdlHVc7LxIRVuF2aGIACXJtxBjsPPCThSKNRlrzA5ldKdeBZSxmCmAVDZ2cby6nfvmFBAVHEV5a7nZIXlXeBxEp18/+W4uIcoRRUZUYG2tnhGVQZQj6vqb7dQdN7aUD4/zXWAmKG8tJzo4mvvm5HOsqp0zjQFWbpV7B6Asu+HOmvQ1AOy8uNPcQETAkuRbiDHYcXEHcxLnkBCWYHYoozv5Z8hYBJFJZkfiUVuLa1AK7ilMIzc2d2RGMKDdYNFlSXMJ+Qn51tzkaQJsynbjRZe3wGJLgPKWcnLjcrl7bhpKwdajNWaH5FmRSZC+0HjesqDE8ETmJM6Rum/hNZJ8C3EDdd11lDaXWrfkpLnSSEpm3mV2JB6ltWbr0RqWzohncnQoObE5nG49jUu7zA7Nu5JnQ9NpGOy96qrBoUHKW8vJj883ITDvy4/P51TrKQZHa0M32AvNpwM++XZpF6fbTpMTm0NyTChLpseztbgm8OqP8+42NkxqrjQ7klGty1hHSXMJdd11ZociApAk30LcgHv2Y12GRZPvkpeNzwVbzI3Dw45Xt3O2qZt7C1OB97eZr+qsMjkyL0ueDXoIGsquuqqirQKnyxnQybfT5aSyfZSErKEUtCvgk++LnRcv21b+3sJUzjR1c6K6w+TIPKzgA8bn0lfMjOKa3JMtUnoivEGSbyFuYMfFHUyPmc60mGlmhzK6klcgfRFMCqwa4D8W1xAcZGNzQQrASDIS8KUn7k4eo5SelLUYCXl+XGAm33nxeQCUNV/9wuOWWWw5vKg4J85YZHzHrBQcQYo/FlebGZbnTZpilJ64Jw8sZnrMdKZFT5PSE+EVknwLcR3t/e0crjts3VnvptNGW7oAm/Uecmn+dLSGNbmJxIQbu4lmTsrEpmyBv+hy0jQIjho1+S5tLiXSEUl6VLrv4/KBjKgMIhwRlDaXXn1l3XEIiYZJgbGr57WUt5ZjUzYyY4xt5WPCHazJTeJPx2oYcgVY6UnBFuPv2mTNriLrpqzjUN0hOgYC7F0HYTpJvoW4jj3Ve3Bqp3XrvUdKTj5gahie9s6ZZho6+7m3MG3kslB7KFOjpwZ+u0GbzZj9vsbM98y4mdhUYD5125SNmXEzR2b4L1N33Jj1tgXmz+52qvUU06KnXbat/L2FqdR39PPO2WYTI/OC/A8Yny06+71uyjqc2smeqj1mhyICTGA/iwkxQTsu7CAxLJFZCRZ9q/vEH2DKUohONTsSj/pjcQ0RwUGsz7u8e0tObE7gz3yDUddcfwJc7y8udbqclLeUj5RmBKq8uDxOtZxiyDX0/oUuF9SdCPh6bzA22MmJzbnssvUzJxMRHMTW4gDrehKTBhlLoOQPZkcyqtkJs0kIS5DSE+FxknwLcQ39Q/3srd7Lmow11pxpbCiDxjIouM/sSDyq3znEqydquX1WMqGOoMuuy43Npbqr+tbYZn6gC1rPjlx0rv0cfUN95MUFePIdn0ffUB/nOs69f2HrWRjsDvjku3Ogk+quanLjci+7PCw4iNsLknn1eC39zqFr3NpPzbrPWEzbcNLsSK5iUzbWZKxhb/VeBoYGzA5HBBALZhRCWMM7te/Q6+y1eMmJgvx7zI7Eo94+1Uhnn/OykhM3d1IS8LPfo+x06S7FCPjke/jnu6zue2Rb+cBOvt336ytnvgHuKUylo8/JrlONvg7Lu/LuAZR1S08y1tHj7OGd2nfMDkUEEEm+hbiGHRd2EOGIYFHyIrNDuZrWxj+raSsgKtnsaDxqa3EN8RHBLM+Mv+o6d1IS8Ml3Yh7Y7EYf5GGlzaWEBoVat+uOh0yPmU5IUMjldd+1R43fR+JM8wLzgesl38uzEoiLCOaPgbbhTnQKTF1uPJ9ZsJf54pTFhNvD2XFRSk+E50jyLcQohlxD7Ly4kxVpKwgOCjY7nKvVl0BTecAttOzqd7K9rJ4756RgD7r66Wly+GSig6MDv92gI9RIwGuKRy4qaykjJy4Hu81uXlw+YLfZyY3NvbzdYG0xJOUZv5cAdqrlFDEhMUwOn3zVdY4gG3fOTuGtsnq6+p0mROdFBR+AplNG+YnFBAcFszJ9JTsv7Lx8HYIQEyDJtxCjOFR/iJa+FjZN3WR2KKMreRmUDfLuNTsSj3qzpI5+p2tkY50rKaVunUWXKXONpFNrXNrFyZaTAV9y4pYXn8fJlpPGbqZaGy9CUuaaHZbXuRdbKqVGvf7ewlT6Bl1sKw2wXRfz7zWezyxaerJx6kaa+5o5XH/Y7FBEgPBJ8q2U2qyUOqWUqlBKfXmU60OUUs8PX/+OUmra8OXxSqmdSqkupdRPrrjNbUqp48O3eUZd69lKiJvw2tnXCLeHszJ9pdmhXG2k5GQlRCaaHY1H/bG4hvTYMOZPib3mMblxubfGNvOphdDTDB3VXOy8SPdgd8DubHmlvLg8uga7jN1M26ugtwVSCs0Oy6uGXEOcbjs9spnUaOZPiSVtUhh/DLSuJ5FJRgmdRUtPVqWvIswexmvnXjM7FBEgvJ58K6WCgJ8CdwD5wIeUUlf+B/k40Kq1zgJ+CHxn+PI+4J+B/2+UoX8GfBLIHv7Y7Pnoxa1o0DXI9gvbWZOxhjB7mNnhXK3uGLRUGl0CAkhTVz97K5q4Z27qNWf+wOh4cktsM+9ONmuKR0owbqWZb4DSllJj9h8gdZ55AflAVVcVvc7eUeu93Ww2xT2Fqew53URzV78Po/OBgvuguWLU/vZmC7OHsSZjDdvOb2PQNWh2OCIA+GLmexFQobU+o7UeAH4PXPle+b3Ar4e/fhFYr5RSWuturfVejCR8hFIqBYjWWh/QWmvgv4EPePOHELeOAzUHaO9v547pd5gdyuhKXgYVBDPvNjsSj3r1eC1DLj1ql5NLuZOTgK/7Tp5l/J1riyltKcVus5M1KcvsqHwia1IWdpvdeNFRU2z8HiYXmB2WV125rfy13FuYypBL8+rxWl+E5Tt59xh/Z4uWntwx7Q7a+9ul64nwCF8k32nAxUu+rxq+bNRjtNZOoB24utXB5cdfOu012phC3JTXz71OVHAUy1KXmR3K1bQ2NtaZsQYirvcQ8T8vHalmZnIUuclR1z3Ovc18wO906QgzunsMz3xnT8rGEeQwOyqfCA4KJntStpF8jyy2tOC7UB50qvUUNmW74QusmcnR5E6O4sUj1T6KzEci4mHGamPDHQuWnixPW06UI4rXzkrpiZi4gF9wqZT6lFLqkFLqUGNjgPVHFR7XP9TPWxfeYv2U9dbsclLzHrSdh4ItZkfiUWW1HRy92MYDCzJueKx7m/lbZdGlrjWS71ul3tstLz6PspYy9C2y2LK8tZxp0dMICQq54bEPLEjn6MU2TtZ1+CAyHyrYAq3n3i81spDgoGDWTVnHjgs76B8KsJIf4XO+SL6rgUv/o6YPXzbqMUopOxADNN9gzPQbjAmA1voXWusFWusFiYmBtThNeN7e6r10D3ZzxzSrlpz8weh3PPNOsyPxqOffvUhwkI0t88b2BlZubO6tkXynFlLb30L7QPstU+/tlheXR1t/G3X9rQG/2BKgvKX8uostL3Xf/HSCg2w8/+7FGx/sT2beZTy/nbDmdvN3TL+DrsEuiqqLzA5F+DlfJN/vAtlKqelKqWDgIWDrFcdsBR4d/vqDwI7hWu5Raa1rgQ6l1JLhLiePAH/0fOjiVvP62deJDYllUYpVN9b5I2Sug/A4s6PxmL7BIV5+r5rbZyUTFzG2dxtyYnOo7qqmc6DTy9GZLKWQsmDjd+JehHirGFl0GRJsdH4JYJ0DndR019yw3tstLiKYTQWTefm9avoGA6j3dHgczFgLJa9YsvRkUcoiYkNief3s62aHIvyc15Pv4Rrux4A3gDLgBa11iVLqW0op977YzwLxSqkK4IvASDtCpdQ54Gngo0qpqks6pXwW+CVQAVQCUoglJqRnsIddVbvYOHWjNTcyOb8P2i/ArPvNjsSj3iipo713kIcW3rjkxM29zfzp1tPeCssakmdRGhJCEOq6XTACUU5sDjYUZSEhMHmW2eF41fV2tryWhxZOoa1nkDdKAqzn96z7jee5C/vNjuQqDpuDDVM38HbV2/QM9pgdjvBjPqn51lq/qrXO0Vpnaq2/PXzZ17XWW4e/7tNaP6C1ztJaL9Jan7nkttO01nFa60itdbrWunT48kNa61nDYz52vZlyIcZid9Vuep29bJ5u0a6Vxf8LwVGQF1hdTn5/8CIZcWEsnTH2BaS3zDbzwRGURU5iOsGE2gN7d8crhdnDmIGDsshYCA43Oxyvct+Px1p2ArAsM5702LDAKz3JvweCI6H4t2ZHMqo7pt9Br7OX3dW7zQ5F+LGAX3ApxFi9dvY1ksKSmJ803+xQrtbfZbTgKvgABEeYHY3HnGvqZv+ZZh5ckIHNNvZ9sm6ZbeaBMkcQ+X235ixbXl8vZY7A/zfl3lY+KTxpzLex2RQPLshgX2Uz55u7vRidjwVHGM9zJa/AgPV+rvlJ80kMS5TSEzEhgf+sJsQYdA50sqd6D5umbSLIFmR2OFcr2wqD3VD4YbMj8agXDv3/27vz+Kiq+/H/rzNL9j0hGwmQQIAQwhpQkFYFVBZFsG5oxX35tlZt/VXtYq21rbX6sYvVtm6tO2pVxAUEAZFVCHtIWEIge8i+b7Oc3x83wyKokMzMvTM5z8djHkkmM/e+k0nufc+57/M+pZgEXDnxzEtOQFtmfkTMCA7U+/fId017DbXSRmZbM7T4WXnBd2muJLOtmRppo6bdvztVHWjQJlue7ULNV+akYBLa/5FfGXc9dLdC/tenh+nPbDJz8ZCLWVe2jtbuVr3DUXyUSr4VBVhTugab02bskpOYdBh0rt6RuI3N4eTdbWVMHxlPYuTZl1QMjx7OwUb/Xma+oL5nZcuubm2xmf6kcieZ3d3A8d+DP3I4HRQ2Fvaqpj8pMpgLR8Tzbm4Zdocf/R8MmgLRaYYtPZk1ZBbdzm7WlK7ROxTFR6nkW1HQSk6SQ5MZEzdG71BOVX8YjqyDcdfBWY6MGdmafdXUtHRxzaRBvXq+a5n54uZiN0dmHPl1+QCM7LYZsvexR1XsZGSXtpR3QZ3/Jt8lLSXfuaz8t7lmUirVLV2s2e9HVweE0Ea/j6zT+n4bzNgBY0kOTVYL7ii9ppJvpd9r6Gxgc8VmLkm75Kwv+3rFrsWAgLEL9Y7Erd7eWkp8eCAXjuhd/33XojP76ve5MyxDKagrYEjEEEJjh0HlLr3D8a7KXYTFZjA4YrBfj3y73lj0dhGlC0fGMyA8kLe3lrgzLP2NvRYQPcc/YxFCcMmQS9hUsYnGzka9w1F8kEq+lX7v85LPsUu7MRfWcTph15vacvKRKd/5cF9R1dTJmv3VXDkxBYu5d4eh9Kh0rCarX4+KFtQXaIvrJI3rl2UnJI8jMybT71/jAFMA6VHpvXq+1WziyokprN5XTVVTp5uj01FUqrbc/M43teOgwcxKm4Vd2vm85HO9Q1F8kEq+lX7vs8OfMSRiCCNjRuodyqmK10Njid9NtHw3txSn1C6Z95bVZGV49PBjpRn+pqGzgcq2Sm2xmeRx0FIBrdV6h+UdLUehpRKSxpEZm0lFW4XfjjDm1+UzPHo4VpO119u4JicVp4T/bfPDiZeNxVBsvBUlM2MyGRwxmOVHVNcT5eyp5Fvp16rbq9l6dCuXDDFoycnONyEwAjIv1TsSt3E6JW/nljJ1aCyDY/vWNjEzNpP8+nz8sc3/scmWsZnHl1fvL6Pfrvr2npFv8M9Jl1JKCuoK+rx66ZC4UKakx/J2bilOpx/9L4y8VDv+7XxT70hOIYRg1pBZbK3aSnV7P3lTrLiNSr6Vfm3poaU4pZN5Q+d994O9rasF8j+E0VeANVjvaNxm46E6yho6+jTq7TIqdhQt3S2Ut5a7ITJjcZVaaGUnPROB+0vdd+UuQEBitl8n32WtZbTYWnpd732iayenUlrfwaaiOjdEZhABIZC1QDsOdhmvrd9lQy/DKZ0sPWS8loiKsankW+m3pJR8cPADJiZMZFBE7zpueNTeJWBr97uSk8VbS4gMtnJJVmKftzUqRkta/DExK6gvYGDYQCIDIyEwHGKH9Z+OJxU7tZ83MJyooCiSQ5P9su772BusPo58A1ySlUhksJW3tvjZxMtx12trHOQv0TuSUwyOGMyE+AksKVzil1ffFM9RybfSb+UezaWkpYQrMq7QO5TT2/kmxGZAyiS9I3GbqqZOludV8YMJKQRZ+76Y0bDoYViExS/rvgvqCo6N+gL9a9Jlz2RLl8zYTL98g5Vfl49FWMiIyujztoKsZq6YMJDleVUcbfajiZepk7U3YgYsPQG4IuMKipuL2XZ0m96hKD5EJd9Kv/XBwQ8Is4Zx0eCL9A7lVHWHoGSj3/X2fnXTERxSctPUIW7ZXqA5kKFRQ/1uVLSlu4WSlpKTJwEnj4PmMmir1S0ur2itgeby43XuaKU3xc3FfreiYEF9AcOihxFgDnDL9m6aOgSHlLy66YhbtmcIQmjHweINUF+kdzSnuGjwRYRaQ/mg8AO9Q1F8iEq+lX6ppbuFlcUrmZ02m2CLAeupd70FwtTT69Y/dHQ7eHNLCRePSmBQbIjbtjsqdhQF9QV+ddnXNZKfFZd1/E5XMurvpSeuuvYTRr5dNdH+dIXDNdnSHfXeLoNjQ7koM4E3viqho9vhtu3qbuxC7Xi48y29IzlFiDWE2WmzWXFkhd+9OVQ8RyXfSr+07PAyOh2dLBi2QO9QTuV0aieZodMhIlnvaNzmve1lNLbbuHVa7/oZf5PM2EzqO+s52n7UrdvVU15tHgCjY0cfv9M16dLfS08qd2gfE7OP3TU6Tvs95NXl6RGRR1S1VdHQ1XByaZEb3DotjcZ2G+/vKHPrdnUVkQzpF2qDEgbs+b1g2AI6HZ0sO6JWvFTOjEq+lX7pg4MfMCxq2LGTuqEcWq2VF4y7Tu9I3MbplLy84TDZAyOZNCTardt2JS/+NCq6t24vKWEpRAVFHb8zKBJi0v1/5LtiJ8QM1X7eHtFB0QwMG3jsTYk/yK/X/l7dMdnyRJPTYhg9MIKX1x/2r7aD46+HplLt+Ggw2XHZDIsaxgcHVemJcmZU8q30OwcaDpBXl8cVGVcYs7f3V/+CsAQYeZnekbjN2gM1FNW0ceu0NLf/zkfEjMAkTH41IS+vNu/0bwyTxkGFn7cbrNx1UsmJy+i40eyt3ev9eDykoK4AkzAxPHq4W7crhODWaWkcqmlj7cEat25bVyMv046LW/6tdySnEEKwYNgC9tTu4WDDQb3DUXyASr6VfueDgx9gMVm4NN2AC9fUHYLClZBzK1jcMwnLCF5af5jEiCDmZCe5fdvBlmDSI9P9ZtJlbUctlW2Vp0++k8dBUwm013s9Lq9oq9NGN0+YbOkyOnY0FW0V1HX4Rx/rgvoC0iPTPTLnZG52MgkRgby8/rDbt60bSwDk3AIHV2jHSYO5bOhlWEwWNfFSOSMq+Vb6lW5HNx8Xfcz01OlEB7m3/MEttjwPJitMvEnvSNymoLKZ9YW1LJo6mACLZw45mTGZflN24hrdzYrNOvWb/j7p8oSVLb/ONfl0b51/jH7n1+W7dbLliQIsJhZNGcK6g7Xsq2r2yD50MfFm7fi45QW9IzlFdFA0F6ZeyMeHPsbmsOkdjmJwKvlW+pU1pWto7GpkQYYBJ1p2tcCON7QVLcMT9I7GbV5ef5hgq5nrJntuIaPM2ExqOmqoaff9y+x5dXmYhOn0iZm/T7p0Jd+JY0751qjYUQiEX9R917TXUNtR6/bJlie6/pxBBFlN/jX6HZ6grXi543XteGkwC4YtoKGrgTWla/QORTE4lXwr/coHBz8gMTSRKUlT9A7lVDvfgu4WmHyn3pG4TU1LFx/urOAHEwcSFeK5Mhp/WoI8rzaP9Mh0QqynaccYHK1Nuiz30wU9yrdrky2Do075Vqg1lPTIdL9Ivl1/p+6ebHmiqJAAfjAhhSU7K6ht7fLYfrzunDu14+SuxXpHcoqpyVNJCEng/cL39Q5FMTiVfCv9RlVbFRsrNnL50Msxm/q+uqJbOZ3aRKKBOZAyUe9o3Ob1zcV0O5zcfF6aR/fjSmJ8ve5bSsne2r3f3oUnZTKUbgE/6msOaD9P6VfaiobfYHTcaPbW7fX5nu75dfkIxMmLKHnALdPS6LY7eX1zsUf341UpOTBwInz1b8O1HTSbzFw+7HI2lm+kqq1K73AUA1PJt9JvLClcgkQyf9h8vUM5VdFqqCvURnX8RKfNweubi5k+Mp6hA8I8uq9QayhDIob4fN13RVsFDV0NJ/f3/rrUydBWDQ1HvBaXVzQchraa70y+6zvrqWyr9GJg7pdfl8/giMGEWkM9up+hA8K4cMQAXt9cTKfNjxbdmXwn1B2EIuOVd8wfNh+J5MPCD/UORTEwlXwr/YJTOllSuIRzEs8hJTxF73BO9dW/tTZao+brHYnbLN1ZQV1bN7dN8+yot0tmTKbPl53sqd0D8O0j36nnaB/LtnohIi8q7fl5XD/fabh+L67fk68qqC/waMnJiW77Xjq1rd0s3VXhlf15RdZ8CI3XjpsGkxqeyuTEyXxQ+AFOaayRecU4VPKt9AubKzZT3lpuzImWdYe09lk5t/hNe0EpJS+tP8zIxHCmDI31yj4zYzOpbKukobPBK/vzhL21e7GarN/e+zk+EwLCtRINf1L6lfZzDfjmUozh0cOxmCw+3e+7vrOeqrYqRsV4ptPJ100dGsvIxHBeXn/Y58t1jrEEGrrt4IKMBZS3lrO5YrPeoSgGpZJvpV94teBV4oLjuGjwRXqHcqotL/S0F7xZ70jcZkX+UfYfbeGO76d7bSEjV3cQXx79zqvNY0T0CKxm6zc/yGTW5gWUbvFeYN5QtkWr5/2W+RgB5gBGRI/w6WXm99XtA/BYm8GvE0Jw+/fS2VfVwsr8o17Zp1fk3Kz9rWx9Ue9ITnHx4IuJDYrltYLX9A5FMSiVfCt+r7ChkA3lG1g4ciEBZoONLHe1aG2zshb4TXtBp1Pyl5UHSIsLZd7YZK/t1zV5zVfrvh1OB/l1+cf6WX+rlMlwNA+6Wj0fmDd0tcDRvd9a7+0yOm40+XX5PntJ37Ws/MhYz062PNHl45JJiwvlL58f9J8l58MTT2g7aKz/gwBzAAtHLmR9+XoONRpvZF7Rn0q+Fb/3esHrBJmDuGr4VXqHcqpdi7W2WX400fKzvVXsq2rh3hkZWMzeO8REBkYyMGygz3Y8OdJ8hHZ7O9lx2d/94NRzQDr9p+Vg+Tbt5znD5LvN1saRpiOej8sD8uvySQlLISIgwmv7tJhN3DNjGAWVzazI96MuHJPvhK5m2PWW3pGc4uoRVxNoDuS1fDX6rZxKJd+KX6vrqOOjQx9x2dDLjLeipdOpTRgaOFG73O4HnE7JXz8/yNABoVzmxVFvl1Gxo3y27MTVv/pbJ1u6uNpRlvlJ6YlrsuXA7/4/cHWC8dXSk4I67022PNG8sQNJHxDKX1b60eh3Sg4kT9BWBjZY28HooGguG3oZHx36iPrOer3DUQxGJd+KX3tn/zt0O7v54agf6h3KqQ6t0tpl+dGiOp/mVbL/aAv3zhyO2eSdWu8TjYodRWlLKc3dvrekdl5tHiGWEIZEDPnuBwdHaxMT/aXuu/QrGJB52sV1vi4tMo1gS7BPLrbT1NVEWWuZ1+q9T2Q2Ce6dkcH+oy0sy/OT0W8htKuGtQfg0Gq9oznFDZk30O3s5u39b+sdimIwKvlW/FaXo4vF+xfz/ZTvkx6Zrnc4J5MS1v4ZIlK0ukU/4OgZ9c6ID2NudpIuMbhWunRNavMlebV5jIoddeYLQKVO1toNGmzE76w5ndrPcQYlJ6AtZDIqdpRPJt/76nsmW3qp08nXXTommWHxYfz18wM4/GX0O+sK7Tj65Z8Nt/BUelQ63xv4PRbvW0yXw49WGVX6TCXfit/6tOhT6jvrWTRqkd6hnKpojVYy8L2f+k17wY93V1BY3cq9MzN0GfWG45Mufa30xOawsb9h/5mVnLikTIaOBm1xJl9WdxA6G884+Qat9GRf/T5sDpvn4vIA13wEb062PJFr9PtgdSuf7PHthYqOsQTAtPu0qydFX+gdzSkWZS2ivrOeT4s+1TsUxUBU8q34JSklr+a/yojoEUxOPPOTuldICV88AeHJMP4GvaNxC4dT8rdVBxmREM6c0fqMegPEBseSEJLgcx1PDjQcwOa0nVmnExfXYjS+3u/bFf+3LK7zdaPjRmNz2jjQeMBDQXlGfn0+iaGJxATF6BbD3OwkhieE8Td/Gv2esEg7nq59wnCj3+cknsPw6OG8mv+q//RZV/pMJd+KX9pUsYnCxkIWZS3yWp/pM3b4SyjdDNN+qi0W4QeW7iqnqKaN+2ZmYNJp1NvFFyddukoozqjTiUvsMAiK8v1Jl6VbtBr22GFn/BTXFQJfW2ynoK5At5ITF5NJcN/M4RyqaeMjf1n10hKojX6XbIIj6/SO5iRCCBaNWkRhYyGbKjfpHY5iECr5VvzSq/naojqzh8zWO5RTrX0CwpO00Ro/YHc4+fuqQjKTIrgkK1HvcMiMzeRI0xHabG16h3LG8uryiA6MJjn0LDrEmExaqYavT7os3aKV0JzFm+SBYQOJCozyqbrvNlsbxc3FunQ6+bpZWYmMTAzn76sOYnf4+JwBlwk3QliidlXRYGanzSY2KJZX81/VOxTFIFTyrfidgw0H2VChLarzrSsF6uHwOijeAOfdB9YgvaNxiyU7Kzhca4xRb9Ams0mkT/X7zqvNIysu6+yv0qRMhpp90NHokbg8rqMBavdD6qSzepoQgqy4LJ9qN5hfl49E6tLp5Otco99FtW18uNNPRr+tQdrod/F6OLJe72hO4lp0Z0P5BgobfHyOhuIWKvlW/I6hF9VZ+wSEJcDEG/WOxC1sDifPrD5IVnIEF48yxgqd2QO00o2dNTv1DeQMtdvaKWoqOrvJli6uSYplue4NyltccZ9FvbfL6NjRHGo8RLut3c1Becauml3AWZYWedAlWQlkJUfw99UHsfnL6PfEmyA0Hr74k96RnMK16M7rBa/rHYpiACr5VvxKXUcdHx/6mHlD5xlvUZ0jG7R6xPPuBWuw3tG4xeubiymua+f+i4cbprY+JiiGIRFD2FG9Q+9QzohrqXTX4jFnZeBEECbfnXRZ+hUIs7ZQylkaHTcap3T6TH3/9qPbSYtMM8xxSQjBzy4aTnFdO29sLtY7HPewBmvH1yProHij3tGcJDoomnlD56lFdxRAJd+Kn3k1/1VsTpsxF9VZ+4Q2KjPxZr0jcYva1i6eXnmA7w8fwIUj4vUO5yQTEiaws3onTmn8Eb29ddqkwbPqdOISGAYJWb476bJ0ixZ/YNhZP9V1pcAX6r6d0snOmp1MiD/7NxmeNH1kPN/LiOPplQeoa/WTPtQ5t0DoAO14azA/HPVDbE4br+5Vtd/9nUq+Fb9R21HLmwVvMid9DmmRaXqHc7KSzXB4LZx3DwSE6B2NWzz12X46uh385tJRhhn1dhkfP57m7mYONx3WO5TvlFebR2JoInHBcb3bQOo5WvmG0+HewDzN6YDybb0qOQGIC44jISTBJzqeFDUW0dLdwvj48XqHchIhBI9cNor2bgdPrdivdzjuERACU+/Ren6XGOuKUHpkOrPTZvPmvjep7ajVOxxFRyr5VvzG87ufx+6086OxP9I7lFN98ScIidNGZfzA7rJG3s4t5ebzhjAs/uxHLT3NleRsr96ucyTfLa82r291wCmTobsVqn2j/OKY6nwt7rNYXOfrsuOyfWLSpevv0GjJN8Cw+HBumjqExVtL2VPWpHc47jHpVgiJhbXGq/3+8bgf0+3o5oXdL+gdiqIjryTfQohZQoj9QohCIcRDp/l+oBDi7Z7vfyWEGHLC937Rc/9+IcQlJ9x/RAixRwixUwjho7ONFHcpby3n3QPvsiBjAYMiBukdzslKt2grWk79CQSE6h1Nnzmdkt8u3UtsaCD3zMjQO5zTGhQ+iJigGHZW79Q7lG/V2NlIWWsZWbG9KDlxcSWvvlb3fWxxnd4n31lxWZS2lNLUZeykcWf1TmKDYkkNT9U7lNO6Z2YGsaEBPLI0zz8WggkI1Y63h1YbrhXnoIhBLMhYwDsH3qGi1U86zShnzePJtxDCDDwLzAZGAQuFEF/vtXQr0CClHAb8BXii57mjgGuBLGAW8FzP9lwulFKOk1LmePjHUAzunzv/iQkTd4y5Q+9QTiYlrPi1Nuo96Ta9o3GLJTvL2V7SyIOzRhAeZLBWjj2EEIyPH8/2o8Ye+d5duxvoYweM6CFajavBkozvVLpFmwMRNbjXmxgTNwY43knEqLZXb2d8/HjDlWe5RARZeWDWSLaXNLJkZ7ne4bjHpNu14+6Khw236uWdY+7EhIl/7vqn3qEoOvHGyPdkoFBKWSSl7AYWA5d/7TGXA6/0fP4/YIbQjlKXA4ullF1SysNAYc/2FOWYosYiPir6iGtHXktiqP6LvJxkz7vaCN/MR3o1qcxoWrvsPL5sH2NTo/jBhBS9w/lW4+PHU9ZaRk17jd6hfKOtVVuxmqzH2iP2ihA9dd8+mHynnt3iOl+XPSAbi8lCbpVxL35Wt1dT3lpuyJKTE105IYWxKZE8/uk+WrvseofTd4FhMOM32mrCe/6ndzQnSQxN5JqR17D00FKKmor0DkfRgTeS74FA6Qlfl/Xcd9rHSCntQBMQ+x3PlcAKIcQ2IYTBhjsVb/rHzn8QZA7i1uxb9Q7lZF2tsPI3kDQOxhmw+0ovPLP6IDUtXTw6L8sQC+p8G1eyY+SWg7lVuWTHZRNs6WPryZRJUF8ErcZ9o3GS1mpoONynkhOAYEsw2XHZ5B41bvLt+vszevJtMgl+Oy+L6pYu/rHaTxaCGf9DSBqrHYe7jbXi7W3ZtxFkDuLZHc/qHYqiA1+ecDlNSjkBrZzlx0KI75/uQUKIO4QQuUKI3JoaHzkxKWdsb91eVhavZFHWImKCYvQO52Trn4aWSpj9Z20pcB9XVNPKy+sPc9XEFMalRukdznfKjMkkyBxk2OS7tbuV/Pp8chLdUDXn6hjiK6PfrhKZXnY6OVFOQg75dfm02YyVXLnsrN5JkDmIkbEj9Q7lO40fFM2VE1N4aX0Rh2uN+fs8KyazdvxtqYB1T+sdzUligmK4YdQNrCheQX5dvt7hKF7mjYygHDhxlklKz32nfYwQwgJEAnXf9lwppetjNfAB31COIqV8XkqZI6XMGTBgQJ9/GMVYntnxDJGBkSwatUjvUE5WXwQbn4Ex18CgvicYRvDYx/kEWcw8MMv4SQSA1WxldNxowybfO6p34JROchLckHwnjwOT1Xfqvsu2aPEmjevzpnISc3BIh2Ff5+3V28kekI3VZMz5EV/3wKwRBFrMPPaxnySEg86F7Ku143G9sVqP3ph1IxEBETyz4xm9Q1G8zBvJ91YgQwiRJoQIQJtAufRrj1kKuNbbvhJYLbUp10uBa3u6oaQBGcAWIUSoECIcQAgRClwMGL/flOJW245uY0P5Bm4dfSvhAeF6h3Oyz36tJRczH9U7ErdYnlfFmv013DszgwHhgXqHc8bGx49nX/0+Qy5Bnns0F4vJwtgBY/u+MWuwdnndYKv6faPiTdobBmtQnzc1bsA4LMKYdd/ttnb21+83fMnJieLDg7h3Rgar91WzPK9K73Dc46JHwWTRJr8bSHhAOLdm38r68vWGnxyuuJfHk++eGu67gc+AAuAdKeVeIcTvhBDzeh72EhArhCgEfgY81PPcvcA7QD6wHPixlNIBJADrhRC7gC3AJ1LK5Z7+WRTjkFLy9+1/Z0DwAK4dea3e4Zzs0GrY/wl8//+DiCS9o+mz2tYufvXBHkYPjODGqUP0DuesjI8fj0M62FO7R+9QTpFblcvo2NGEWN206FL6BVCeCx0N7tmep3Q0aHGmX+CWzYVYQ8iKy2Lr0a1u2Z477a7djUM6fCr5BrjpvCFkJUfwqw/2UOsPK19GJMP374d9H8OhNXpHc5KFIxcSFxzH37b/zT/aPCpnxCuFqFLKT6WUw6WUQ6WUf+i57zdSyqU9n3dKKa+SUg6TUk6WUhad8Nw/9DxvhJRyWc99RVLKsT23LNc2lf5jffl6tldv544xd/R9spo7OWyw7CGIToMpP9Y7mj6TUvKL9/fQ0mXn6avHYTX7Vu362PixCIThShLabe3srdvLpMRJ7tvosJkgnVC01n3b9ISiL7Q4h8102yYnJU4ivzbfcFc4dlTvQCDcc3XDi6xmE3+5ZhwtXXZ+8f4e/0gKz/2x1pZz+UPacdoggi3B3DHmDrZXb2dDxQa9w1G8xLfOpIoCdDm6eGLrE6SGp/KDjB/oHc7Jtr4Itfvhkj+CxXfKM77J/7aVsTL/KA9cMoLhCQYr7TkDEQERDIseZrjke0f1DhzS4Z56b5eUHAiMgEOr3LdNTyhcBYGRMNB9P3tOQg52aTfcoko7ju4gIzrDeGVxZ2B4Qjg/v3gEK/OP8t52P+j9bQ3Sjss1+2DrS3pHc5IrM64kNTyVJ7Y8QZfDD640KN9JJd+Kz3lh9wsUNxfz63N/jdVsoElMbbWw5nEYOgNGzNY7mj4ra2jn0Y/yOScthlvOS9M7nF6bED+BXTW7cDgdeodyTO7RXCzCwrj4ce7bqNkK6edD4WrDLSpyjJRaWVb6+WC2uG2z4+PHYxZmQ7UctDvt7KrZ5XMlJye6ZVoak9NieHTpXsoajHVVoVdGzIGh02HNH7XjtUFYzVZ+fc6vOdJ8hBf3vKh3OIoXqORb8SlFjUW8lPcSc9PnMjV5qt7hnGzFw2Brg1l/6tPCIUbgdEr+v3e1VQOfumqs4Xt6f5tx8eNos7VxsPGg3qEcs7VqK6PiRrmv3ttl6AxoLoOa/e7drrvU7IPmchg2w62bDbGGkBWbxdYq49R9H2w4SLu93aeTb7NJ8H9XjcUpJT9/dzdOp0Hf1J0pIbTjs61N6/1tIFMHTmVO2hxe3POiWninH1DJt+IznNLJo5seJcQSws9zfq53OCcr+Ah2vQnn3QcDhusdTZ+9vOEwm4vq+c1lo0iNcXOC6GUT4icAxllsp93Wzt7avUxKcGO9t4srqTVq6UlhT1xD3Zt8g9ZyMK8uzzB1366/N9ffn69KjQnhkcuy2FRUx382HtE7nL4bMEI7Tu98Awo+1juakzww6QFCLCH8btPvcEqn3uEoHqSSb8VnLClcwvbq7dyfcz+xwbF6h3Ncy1H46F6tZ/EFD+kdTZ8dPNrCnz/bz8zMBK6aaOwl5M9EUmgS8SHx7DhqjOR7Z81O7NLunsV1vi5qEMQNP57kGs2hVRA3AqJSv/uxZyknIedYqYcR7KjeQUJIAklhvt/x6KqcFGZmxvPE8n0cPNqidzh9d/6DWmvOj+7Rjt8GERscy88m/oxtR7fxYeGHeoejeJBKvhWfUNdRx//l/h8TEyayYNgCvcM5Tkr48Mfa0sVXPK/V3fowm8PJT9/ZSVighcevyEb4ePkMgBCCCfET2FFjjOQ7tyoXszB7rhxh6Awo3gC2Ds9sv7e62+HIBreXnLgYqe5bSsn26u0+P+rtIoTg8SvGEBZo4Wfv7MLm8PFRWUsAXPGCdtxeereh5kgsyFjAhPgJPJX7FHUddXqHo3iISr4Vn/Bk7pO029v5zbm/MVZCmPsSFK6Eix7TLmf6uCc/209eeTN/XJDtU4vpfJdx8eOoaquisrVS71DIPZrLqNhRhFpDPbODYTPA3qkl4EZSvBEcXR4pOQEICwgjMybTEIvtVLZVUt1e7d4JtTobEB7IH+aPZk95E09+ZtA5BWdjwAi46HdwcAXkvqx3NMeYhIlHpjxCu72dp3Kf0jscxUNU8q0Y3saKjXxS9Am3Zd9GelS63uEcV3tQW8ly6HSYdJve0fTZ+9vLeP7LIhZNGcys0Yl6h+NWRqn77rB3sKd2j2dKTlwGnwfmQK3riZEcWgWWIBhynsd2MSlxEntq99Bh13fU/1i9d4J/jHy7zM5O4oZzB/P8l0V8sKNM73D6btLtkH6htvJlbaHe0RyTHpXOraNv5eOij9lY4SOr1ipnRSXfiqF12jt5bNNjDIkYwm3ZBkpwHTZ4/w6td+zlz4HJt/+VdpY28tD7e5iSHsvDl47SOxy3y4jOIMQSwvZqfZdw3lWzC7vT7t7+3l8XEAKDpxpv0mXhKi0uq+cWxcpJzMHmtLG7ZrfH9nEmdlTvINQaSkZUhq5xeMJvLhvFuekxPPjeHnaWNuodTt+YTDD/OTAHwPu3G2rxndvH3M7giMH8fvPv6bR36h2O4ma+nTEofu+5Xc9R1lrGw+c+TKDZQGUQXz4JFdvh0r/6/BLyR5s7uePVXOLDA3n2+gk+t4rlmbCYLIwdMFb3RVhyq3IxCZPna4GHzdDa+jUZZHSysVRbfMpDJScu4+PHYxIm3eu+d1TvYOyAsZhNZl3j8ASr2cRz108kPjyQO1/L5WizjyeGEclw2V+14/mXxinzCDQH8vC5D1PaUspzu57TOxzFzfzvLKv4jS/LvuQ/ef/hyuFXMjlpst7hHFe6VTtIj7kWsubrHU2fdNoc3PHaNlq77Lx4Yw4xoQF6h+Qx4+PHc6DhAC3d+nVr2Fq1lcyYTMICwjy7I9fS7UbpeuIahXfjkvKnEx4QzsiYkbr2+27ubuZgw0G/qvf+upjQAF5YlENLp507XttGp804C1j1StYCGHONNqhSpv+cAZdzks7hBxk/4D95/2Fd2Tq9w1HcSCXfiiGVt5bzi3W/YGTMSB6c9KDe4RzXWgP/u0UbLZnzZ72j6RMpJb98fw+7Sht5+upxjEyM0DskjxqfMB6J1K0VXae9kz21e5iU6IH+3l83YCSEJxun9KRwFUQM9Mqk5EkJk9hTs0e3Zbp31+xGIv2m08k3yUyK4Omrx7GrtJFffrAHaaCOIb0y50ntuP6/m7XjvEE8NPkhRkSP4Bfrf0FFa4Xe4ShuopJvxXC6Hd3c/8X9SCl5+vynCbIE6R2SxtYJi6+Dthq4+hUIitQ7oj55cd1h3t9Rzk9nDve7CZanMyZuDIHmQNaXr9dl/7trdmNz2jxb7+0iBAybDoe+AIfd8/v7Ng47FK3VJiZ7oVNRTmIO3c5u3eq+15WtI9AcSHZcti7796ZZoxO5b2YG728v56X1h/UOp2+CIrXjemu1dpy3GaOcJsgSxNMXPI3D6eD+L+6n29Gtd0iKG6jkWzGcP2/9M3vr9vLYtMdIjXD/Yhy94urnXbYFrvg3DJyod0R9smZfNY8vK2BOdiI/mT5M73C8IsQawpSkKawuWa3LKF3uUa3ee3yCl5YbHzYTupqgfJt39vdNynO1ODxccuIyIWECAqFLy0EpJatLVzMleQohVt9eGfZM3TM9g9mjE/njpwWs2Vetdzh9M3AiLPi3dpz/8MeG6f89KGIQvz/v9+TV5fHk1if1DkdxA5V8K4bySdEnvL3/bW7OupkZgzw7OeusfPEnyPsfzHgERl2udzR9sqGwlrte30ZmUgRPXTUWk8lAfdM9bMbgGVS2VZJfn+/1fW+t2sqI6BFEBHipvCf9AhAm/UtPCldpcaSf75XdRQREaHXfR71f951fl09VWxUzB3nnjYYRmEyCp64aS2ZSBHe9vo2NhbV6h9Q3WfNhxm+04/3aJ/SO5pgZg2dwU9ZNLN6/mE+LPtU7HKWPVPKtGMahxkM8uulRJsRP4CcTfqJ3OMftfgfW/gnG/RCm/VTvaPpk06E6bn1lK2lxobx26zmEBFj0DsmrLki5ALMws6rYuwlpl6OL3TW7vVPv7RIcrY3kFX7uvX2eTuHnMDBHi8dLchJz2F2z2+t136tKVmEWZi5IvcCr+9VbaKCFV2+ZzJDYUG55ZSubi3x8ZcZpP4Ox18EXj8Pud/WO5ph7JtzDhPgJ/HbTbylqLNI7HKUPVPKtGEK7rZ2fffEzgi3BPHn+k1hNBlmmvWSzdvlx8DS49C9eqVn1lC2H67nlv1tJjQ7h9dvO8evOJt8kKiiKiQkTWV3i3QVodtfsptvZ7Z167xMNmwnl26G93rv7dWmrg4odXis5cclJyKHL0cWemj1e3e+qklXkJOQQGejb80F6IzYskDduP4fU6BBu+e9WthzW6W/OHYSAy/6mLVj14Y+g5Cu9IwLAarLy5PlPEmwJ5qdf/JR2W7veISm9pJJvRXcOp4OHNzzMkeYjPPn9J4kPidc7JE39YW3iTWQqXPMaWHw3Wd1WXM9N/9lCclQQb95+LnFhBuqZ7mXTB03nUNMhjjQd8do+15SuwWqyMjHRy3MFhs4AJBSt8e5+XYrWaPsf5t0SspzEHCwmC2tKvfdzH246TFFTEdMHTffaPo0mricBT4wM4ub/bGFbsQ8n4JYAuOZ1iEzRzgMNR/SOCID4kHie+P4THGk+wsMbHsYpnXqHpPSCSr4VXUkpeWzzY6woXsFPJ/zUOP28myvhjavA6YDr3oGQGL0j6rUdJQ3c+PJWEiOCeOv2cxkQ3n8Tb+DYXIJVJd4pPXE4HSw/vJxpA6d5r97bZeAECIrSr9934Sqt3CTZS5NMe0QERDBt4DSWH16Ow+mdHtSuv6f+nHwDxIdrx5n4iCBufHkrO0oa9A6p90JitOO/066dD1qq9I4IgHOTzuW+CfexongFj21+zPfbPPZDKvlWdCOl5M9b/8x7B9/j9uzbuWn0TXqHpGksgf/MhpZKWLgY4ny3G8iu0kYWvbSF2LAA3uw5IfZ3iaGJZMVmea30JPdoLjUdNcxJn+OV/Z3EZIahF8LBFd5fOtth0/abfqEWh5fNTZtLdUc12456p9vL6pLVjI4dTWKo/7ft/C4JEUG8ebtW2rbo5S3s8uVl6OMyYOFb0FwBL8/Szg8GcPPom7kt+zb+d+B/PJn7pErAfYxKvhXdPLvzWV4veJ3rM6/nJ+MNMsGythBeng0d9bDoQxg8Re+Ieu2zvVUsfGEzUaFW3rz9XBIjVeLtMmPQDHbX7uZo21GP72vZ4WWEWEI4P8U73T5OMeZarTf9/mXe3e/+T6G9FsZe69399jg/9XyCLcF8etjznSGq2qrYU7uHGYMN1KFJZ0mRwbx1x7lEhVhZ+MJmVuw1xqhxrwyeCjcs0c4LL8+GukN6RwTAPePv4bqR1/Fa/mtqCXofo5JvRRcv7XmJf+/+N1dkXMEDkx5AGGEi49F8bcTb3gk3fQIpXp4c5yZSSp77opC7Xt9GRnwY7901lYFRwXqHZSiu0pPVpZ4d/e52dLOieAXTB00n2KLTazBsprba5fZXvLvfba9oq1p6ebKlS7AlmOmDprOyeKXHFyZxXUXp7yUnXzcwKpj37ppKRnwYd76+jX9+cch3R2hTJ8GNH4O9QxsBP+r9dqVfJ4TgwckPsmDYAv6161+8nPey3iEpZ0gl34rXvbXvLf66/a/MTpvNb879DSZhgD/D8u3w3zna5fGbP4VE31ydrtPm4P53dvHn5fu5dEwyb985RZWanEZ6VDpDIoZ4vO57ffl6WrpbmJOmQ8mJi9kCE27Q6q8bir2zz4ZiOLQaxt+gS8mJy5y0OTR3N7OhfINH97O6ZDVpkWmkR6Z7dD++KD4iiLfvnMLc7CSeWL6P+9/dRZfdO3X4bpc0Bm5epvWt/+8crZOPzkzCxCNTHmH2kNn8ZdtfWLxvsd4hKWfAAFmP0p8sKVzCH7/6IxemXsgfpv0Bs44n5mOKN8Er8yAwXDuwDhihd0S9UtPSxXUvbOb9HeX87KLh/P3acQRZDfD7NagZg2aQW5VLU1eTx/ax7PAyogOjOTf5XI/t44yMv0H7uON17+xvx2tau7bxP/TO/r7BlOQpRAVGseyw50puGjsbyT2aa6xFwQwmyGrmmYXj+enM4by/vZzrXviK2lbv9mB3mwEj4JZlEBCunTdKNusdEWaTmT987w9ckHoBf/jqDywpXKJ3SMp3UMm34hVSSp7f/TwPb3iYqclTeer8p4zRy3vXYnhtAYQnwM3LISZN74h6paCymfnPbiC/spnnrp/APTMyjFHKY2AzBs3AIR2sLVvrke232dr4ovQLLh5ysf5/61GpWvnHjtfAYffsvhx2LckfNlPbr46sJisXD76YNaVrPNYTeW3ZWhzSoZLv7yCE4N6ZGTx73QT2VjRx+T82UFDZrHdYvROTriXgYfHw6nztPKIzq8nKU+c/xZSkKTy84WFe2P2C75b49AMq+VY8rtPeyYNfPsgzO55hbvpc/j797wSYde6ZbeuApT+BD+7U2rHdvAwiB+obUy84nZIX1xUx/9kNOJySd++cypzsJL3D8glZcVnEh8R7bLXL1SWr6XR06ltycqKJN2kdfApXenY/B1do+5l4k2f3c4bmpM+h09Hpsfr+VSWrSAhJICs2yyPb9zdzxyTx7p1TsTudzH92Ay+tP4zT6YNJYmSKdt4YOEE7jyy9B2yduoYUaA7kmRk959kdf+fBdQ/Sadc3JuX0VPKteFR1ezU3Lb+J5UeWc++Ee3l82uMEmnXuM113CF66CLa/qi0Xv2ipNoLhY0rq2rn2hc38/pMCvpcRx9KfnEd2Sv9bWa+3TMLE9NTpbKzYSIe9w+3bX3Z4GUmhSYyLH+f2bffK8EsgLAG2/dez+9n2XwhLhIxLPLufMzQ+fjyJoYkeKT1pt7WzsWIj0wdNV1eazkJ2SiQf/WQa04bF8djH+Vz7wmZK6nxwtcaweO38cd592oTml2ZCvb7LvgeaA3l82uPcO+Felh1exs3Lb6a6vVrXmJRTqeRb8Zi82jwWfryQoqYi/nrhX7kt+zb9T1D5S+H5C6CxFBa+DTN/q01I8yFSSl7fXMysv31JQUUzT101lhcW5RAfriZWnq2Zg2fS6ehkY/lGt263vrOejRUbmZU2yxgTigHMVq0G++AKaCr3zD6ayrSR9fE/NMz/lUmYmD1kNhvLN9LQ6d4FXzZWbKTL0cXMQfp0dPFl8eFBvHhjDk9eOYaCimZm/e1LXt9c7HulEmYLXPSodj5pLIV/n6+dZ3QkhOC27Nv424V/41DTIRZ+vJC9tXt1jUk5mUHOCoq/WXZ4GTctvwmLycJrs1/TvwWXrROW/xLeuQFih8GdX8KIWfrG1AsVjR0senkLv16Sx8TB0Xz20+9z5cQU/d/U+KiJCROJDIx0e9eTlUdW4pAO5qbNdet2+2z8DSCdnpt4ueN1bfsTbvDM9ntpTvoc7NLOymL3ltysKllFVGAUExImuHW7/YUQgqtyUvnsp99n4uBofr0kj0Uvb6Gi0f1XojxuxCztvBI7VDvPLP+l7mUo0wdN57XZr2ExWbhx+Y0enXisnB2VfCtu1dDZwC/W/YIHvnyArNgs3rr0LUbE6Nw95MBn8Ny5sPlZmHwH3LIcogfrG9NZau+28/dVB7no6bVsK27gDwtG8+otk0lW/bv7xGKycH7K+XxR9gU2p/tWgPz08KcMjRzK8OjhbtumW8SkaStO7ngN3L3sutMB21+DodMheoh7t91HI6JHkB6Z7tYFd2xOG2vL1nJ+yvlYTMYY5fdVyVHBvHrLZH4/fzTbihu4+C9f8syqg7R3e3hysLtFD4ZbPtPOM5uf1c47B1boGtKImBG8OfdNsmKzeODLB/jlul+6/QqQcvZU8q24hZSST4s+5fIll7P88HLuHHMnL178IjFBMfoF1XAE3loIb14NJou2QtmcJ8Gic835WbA7nLzxVTHnP/kFT688wLSMOJbf+32uP2ewGu12kxmDZtDS3UJuVa5btlfZWsn26u3MTpttzNdo4o3QVKr14XanwlXQXAYTbnTvdt1ACMHstNlsO7qNqjb3rLS4tWorLd0tqsuJmwgh+OG5g1l+7/c5b1gs/7fyABc8+QVvflWC3eHUO7wzZwnUzjM3LNHOO29eBW9d570e+6cRGxzLixe/yB1j7mDZ4WXM/3A+nxZ96nslPn5EJd9Kn1W1VXH36rt5cN2DpISn8PZlb3P3+LuxmnVqr2brhC+egGfPgaK1MPNR+H8bYeiF+sTTC1JKludVcfFfv+RXH+QxOCaE9/7fFP59Qw6DYkP0Ds+vTE2eSoglhHcPvOuW7S07ol3aNUyXk68bMRdC4tw/8XL7KxA6AEYY8+d2vR7uuvT+7v53CbGEMCV5ilu2p2gGxYbw7xtyeO//TWFQTAi//GAPl/z1Sz7bW+VbyeLQC7XzzszfQtEaeHYyrP2zbqUoVrOVn4z/CYsvXUxyaDIPrnuQn6z+idvejCpnRyXfSq85nA4W71vM/A/ns7VqKz/P+TmvzX5Nv0vtDpvWb/W5c+GLP8KI2XD3Vph2H1h0bm14hhxOyYq9Vfzgnxu56/VtCOD5Gyby7l1TmDhYx6sIfizIEsRNo29iZfFKtlZt7fP2lh1expi4MaRG6Nvj+htZAmDcdbB/GbS46cTbUqVtb9x1hv1fGxQxiOy4bLck31urtvJ5yefcPPpmgixqorMnTBwcw7t3TeH5GyYCcOdr27jyX5tYsbcKh6+0JrQEaB217t4Kw2fBmj9o56ddb2vnKx2MiBnB63Ne5+c5P+eryq+Y/+F8Fu9bjMPdZWjKtxI+9U6yj3JycmRurnsuLfdndqedT4o+4YU9L1DcXMy5SefyyJRHSAlP0Seg7jat1nTTP7TL6fGj4JI/+tRId1O7jXdyS3ll0xHKGjpIjgzinhkZXDkxBYtZvUf2tA57B/OWzCMqMIrFcxf3euXVQ42HmP/hfB6c9CA/HKXv6o7fqrYQ/jERZvwGvnd/37f35VOw+jH4yXZtwplBvZb/Gn/e+mc+vPxD0qN6txS8w+ngmo+vobm7maXzl6rk2wvsDifvbivjmVUHqWjqJCU6mBunDOHqnFQiQwywWNuZOrQGPvslVOdDZCpMuVubnBwQqks4pS2l/G7T79hcuZkhEUO4fcztzEmbo+YwuIkQYpuUMue031PJt3KmbA4bHxV9xAu7X6CstYyRMSO5a8xd+vW4bauDLc9rt456GDRF67eacTGYfCNhPXi0hf9uPML728vpsDk4Jy2Gm88bwszMBJV0e9myw8t44MsHeHTqo1yRcUWvtvHopkd5/+D7fH7l5wwIGeDmCN3sv5dCYzHcndu3eRD2LvhHjjbJ8saP3BaeJ9S01zDzfzO5IuMKHpnySK+28d6B9/jtpt/y5PefZFaa73VM8mV2h5OV+Uf5z8YjbDlcT7DVzBUTBnLT1CFkJITrHd6ZcTq1dp8b/golmyA4RpugOfkOCI31ejhSSlaXrOZfu//Fvvp9pISlcMeYO7h06KX6r8zr41Ty3UMl373Tae9k6aGlvLTnJSraKsiKzeKusXdxfsr53k+6nQ44sg52vwt73wdbu1Zjet59MOgc78bSS2UN7Xy6p5JPdleyq6yJAIuJ+eOSuWlqGqOSI/QOr9+SUrJo2SJKWkr4ZMEnhAWEndXz15au5e7Vd7No1CJ+PunnHorSjQ5+Dm/8ACbdBnP/r/fb+fhnkPsSXP8eZBi/3/WTW5/k1fxX+cf0f3B+6vln9dzW7lbmfjCXwRGDeWXWK8acUNtP7K1o4pWNR1iys4Juu5OxKZHMHZPEnOwkUqJ9ZF5MyWZY/1c4sAysITD6Csi+GoZMg15efestKSVry9byr13/Ym/dXpJDk7k1+1bmDZ2nru70kkq+e6jk+8xJKdlRvYOlh5by2ZHPaLW1MiZuDHeNvYtpA6d596QjJVTugj3vQt572tLVAeGQNV+7bBc/0nux9FJFYwef7qnk492V7CxtBGBMSiSXjkniyompxIQas062v8mrzWPhJwu5efTN/Gziz874ebUdtfxg6Q8YEDyAN+e+SYDZR17PFb+Gjc/AFS/CmKvO/vm734H3b4ep98DFj7k/Pg/odnSz8JOF1HbU8t6894gLjjvj5z6d+zT/2fsfFs9dTFacWk7eCOrbuvnftlI+3l3J7rImAMYPimJutpaI+0Q71uoC2PQs7F0C3S0QngSjfwBjrobEMeDF862UkvXl6/nXrn+xu3Y3YdYwLhlyCfOGzmN8/Hj1hvMsqOS7h0q+v1t5azlLDy3lo0MfUdpSSrAlmIsGX8T8YfPJScjx3j+evRvKtmqzxPOXQu1+MFkh4yLtgDR8FliNe1Bt67Kz5XA9Gwpr2XiojvzKZgCykiOYOyaJS7OTVdcSg/rV+l+x7PAyPrz8wzOaNOmUTn606kfkVuXy9qVvMzTKuDXPp3DY4ZXLoHIn3L4a4jPP/LnVBfDCdEgery2xbZAVLc9EYUMh135yLZMSJ/HcjOfO6LhW0lzC5R9ezty0ufx+2u+9EKVytorr2vik56ri3grtmDsqKYLzhsUydWgck9NiCA008N+prUObuLznXTi4Epw2iBsBo+Zp/flTJnltQrOUktyjuSwpXMLK4pV02DtIDU/lsqGXMW/oPAaGDfRKHL5MJd89VPJ9KpvDxs6anWyq2MTGio3srduLQDA5cTLzhs1j5qCZhFi9kCRKCTX7tAkpRWvgyAawtYEwabXc2VfCqPkQYsyOHw1t3eRVNLH1SAMbC2vZWdqI3SkJMJuYODiaaRlxzMlOIi1On4k1ypmrbq/m0g8uZUrSFP42/W/f+fg3Ct7gT1v+xK/O+RXXjrzWCxG6WUsV/Ot7EBQJd6yBwDOone1qgecvhM4muGsdhCd6Pk43e2vfW/zxqz/y0OSHuD7z+u98/D2r7+Gryq/4eMHHxq/nVzhc28aneypZf7CWbcUNdDucWEyCcalRTB0Wx6Qh0YxOjiTaqFcd2+shfwns+Z9WGy6dYA3VSlKGXqgl4wNGeGVUvN3WzsrilSw9tJQtVVsAyIrNYmryVKYkT2HcgHH6tRY2MJV891DJt9ap5FDjIXKP5rKpYhNbqrbQYe/ALMyMHTCW76V8j7lpc0kKS/JcEFJCczlU7ISKHdqoW8VOaK/Vvh8z9PjBZcg0CI7yXCxnSUpJbWs3BZXN7ClvIq+8iT3lTZQ1aMshmwRkp0QxdWgs5w2NI2dINEFW79buKX33wu4X+PuOv/PixS9yTtI3zyU40HCAhR8v5Nzkc/nH9H/47iXZw+vg1Xkw6nK48j/ffkKXEt69CQo+ghuXav+jPkhKyY9X/ZivKr9i8aWLyYjO+MbHbq7czO0rbufeCfdyW/ZtXoxScYdOm4PcIw1sOFTLxsJa9pQ34epWmBIdTPbASEYPjCR7YCSZSRHEhQUY63+5o1Gb61T0hTZAVX9Iuz8kDpLHaVefksZpn0cM9GhCXtFawaeHP2Vd2Tp21ezCIR0EW4KZnDiZKclTyEnIYWjUUNUxBQMk30KIWcDfADPwopTyT1/7fiDwKjARqAOukVIe6fneL4BbAQdwj5TyszPZ5un0t+Tb5rRR1FhEfl0+e+v2UlBXwP6G/XQ5ugAYFD6IKclTmJo8lUmJkwgPcPNscacDGku0A0XdIagr1G6Vu48n2sIMA0ZqB4/UyVrSHTXIvXGcJSklDe02Kho7KK5rp6imlaLatmMfWzqPL3k8KCaE7BTtoJ09MJLslEgigtQIgK/rcnRx+ZLLCbWG8s6l75y29WCnvZOFnyykobOB9+a9R2yw9zsVuNX6v8Dnv4VZT8C5d33z4zb/E5Y/pC1eNe0+b0XnEXUddVyx9ApigmJYfOliAs2ndn2xO+1c/fHVtNva+XD+h6d9jOJbmjpsxwZO9pQ3saesiZL69mPfDw+ykD4gjPS4UO02IIzBsSEkRwUTHWLVPzFvLNGS8NIt2gBWzT6QPX26Q+IgaQzEDuu5DdUGtKIGuX0SZ0t3C1urtrKxYiMbKzZS2lIKQKA5kBHRI8iMzSQrNotRsaNIj0rvd91TdE2+hRBm4ABwEVAGbAUWSinzT3jMj4AxUsq7hBDXAguklNcIIUYBbwGTgWTgc8C1gsu3bvN0/C35llLSamulpr2GstYySppLKGnRbqXNpVS0VmCXWqIYag0lMyaTUbGjyIzNZOyAsaSG92ERkO52aK/TkujmSmipgOaK4583lWttzBzdx58TEK4dCBJGa+/Qk8ZB4miv1W7bHU4a2m3UtXVR39pNbVs39a1d1LV1U9nUSWVTBxWN2sdO28nLGSdFBpE+IJT0uDDS4kIZkRjO6ORI3+oxq5yVFUdWcP/a+7l6+NWcn3o+w6OHkxCScOzE+6ctf+KNgjf458x/Mm2gb47+nkRKWHyd1gbt5mXam+GvK/kK/jsHMi6Ba9/w6kQwT1lXto4frfoRP8z8IQ9OfhDQjq1H249yoOEAa0vX8s6Bd3j6gqe5aPBFOkereEpTu428iib2V7VwuLaNotpWimraqGw6eUXKIKuJ5MhgkqKCSIoMJikyiNjQAGLCAokLDSAmLIDY0ECiQ6zeaxdr64CqvONXkY/ugboibfKmizkAogZD5EAIT4aIJIhIPv55SByExEJA78tMS1tK2VWzi/y6fArqCiioL6DN1gaARVhIDksmNSKVQeGDtFvEIFLCUhgQMoAwa5j+b2rcTO/kewrwWynlJT1f/wJASvn4CY/5rOcxm4QQFqAKGAA8dOJjXY/redq3bvN0jJp8SynpdHTSYe+g095Ju62d5u7m47cu7WNTVxO1HbXUdtRS01FDTXsNnY6TDwyh1lAGhQ9icMRgUsNTGRaZzqioYQwKjsfkdICjS0uI7V1amz5bR8+tXVv2trtVu3W1nHBr1mo72xu0ftrtdWA/zRK5wqzVfkYka7O1Y9KPv/OOHaYtPX2afy4pJU4JNoez5yZP+rzb7qTL7qDTpn3ssjnpsjvptDlo77bT3u2grdtBh+vzLjstnXaaO23axw4bzZ12Wrvsp8aMVioSHx5EUlSQdlCNDCIpKpjkyCAGxYaQFhdKSIC6hNbfSCm5f+39rCxeeey+8IBwMqIyGBg2kI+KPuL6zOt5aPJDOkbpZh2N8Pz52v994phTv1+1GwIj4I4vDFUO1lePf/U4b+57k8vSL6O8tZyDDQdpsR1PXC4efDFPnf+U3yUHyndr77ZzuLaNkrp2Kpo6qWzsoLKpk4qmDiobO6lu6eSbFtwMC7QQEWQhIthKeJCFiCDtY2ighZAAM8EBFkIDzIQEmAkJsBBkNRNoMRFoNRFoMRPU8zHAYsJqFljNpp7b8c9NgtP/XUoJbTXHrzjXHYL6Iq1bWHOFNtdDnmZVS0uQloQHx0BItDYXJDBCmwviugWEaTdrkNYi0RrccwvR1gwwB4A5EKfJTElHNfmNhRQ2FWmDgz2DhK6k3CXIHMSAkAEMCB5AXHAcccFxRAZGEhEQQURghPax5xZiDSHIEkSwJZggc5Bh/y/1Tr6vBGZJKW/r+foG4Bwp5d0nPCav5zFlPV8fAs5BS7Q3Sylf77n/JcC1NvC3bvN09Ei+f/PaQvI692EH7ELiQGIXaDckXULSdYZvjkOcEO2AGIck1iGJc0Ks3Umsw8lAu53BNjuxDjsW7JilAzMOTDi/e8On4UTQIUJoFyF0iBDaTCG0iAiaRQTNpgiaRThNIoImIqgV0dSa4qgnAjtmnFLidEocUuJ0glNKHE557KPrZj/hozsEW3sOYoHmYwe5iCArEcHWY1/H9oxKxIQGEBcWQGxYIJHBVswmY/7zKvpr7m6msKGQgw0HOdh4kAMNBzjYcJDU8FRenf2q//XArcqDFb/Srm59XUAIXPwH7YqVH+m0d7Jo2SJKW0rJiM5gePRwMqIyyIjOYFj0MCICVP995fQcTklTh4261i5qW7upb+umrq2LutbuY4NA2gCQ7djX7V0O2rrtp1xh7S2LSWA2iWMfXTeTOP7RZAKzEJh6vrbgIIZm4py1xMkGImkmUjYTIVuIcDYTIZsJl82EOtsJlu2ESO2jid6dr52YcGDGIczYsVBntlBstVBusVBnNlFnMVFrgjqzoN4saDBD+xnmRoFOCJQCCwKLBIsEMwKLFFiA7KCRPHrDW72Kuy++Lfn2++E8IcQdwB0AgwZ5v5bY5LAT7HRikQKzpOeP4/gfRYCEQGkiQAoCnYJAKQiQgmBpJsRp0m7STKDTjAkTTmHCiQknZiTi2NddwkKB1YzDasEhzCf9kduFFbuwYhNW7FixCws2EUCXCKRbBB373GYKpEsE0SFC6TYFIUwCgej5PWrvrgUce6et5avaxwghiDKd+JgT/ukF2ucmgVmccJAwuw4WJsxCYLUIAswmLCaB1aK9qw/oeXfvGgHQRgSOjwoEB5gJDbAQbDVjUgm04gERARFMSJjAhIQJx+5zDVoYdcSlTxJHw6IP9Y7Cq4IsQbx96duAn76miseYTYKY0ABiQgPISDi75zqdkg6bloh3dJ9wddfu7LnCq91nczjpdl0NtjuxO6X2tV0b5HI4tfscjuODWg7XIJhTu7J84iCYpOeKszOSTplCiQTQHue6Eu16jGt8ViKRTkmAs5Ng2Uag7MTq7CJQdmGV3QTIzmOfW6QdCzas0obFdTthUFD7aMeMgwSbnSSbE5N0IpCYegYNTdKJEyddJgftwkG7yUm7yUmHcNAtXAOXsudzJ92CY4OcdiGxA46ez02O01/11pM3ku9y4MTi4pSe+073mLKespNItImX3/bc79omAFLK54HnQRv57t2P0Hu/veldb+9SURQPUwma/1GvqeJtJpMgNNBi7N7jikd4YzbAViBDCJEmhAgArgWWfu0xS4Ebez6/ElgttaGlpcC1QohAIUQakAFsOcNtKoqiKIqiKIqhePztlpTSLoS4G/gMrS3gy1LKvUKI3wG5UsqlwEvAa0KIQqAeLZmm53HvAPloVxR+LKU2Q+B02/T0z6IoiqIoiqIofaEW2VEURVEURVEUN/q2CZdeakKpKIqiKIqiKIpKvhVFURRFURTFS1TyrSiKoiiKoiheopJvRVEURVEURfESlXwriqIoiqIoipeo5FtRFEVRFEVRvEQl34qiKIqiKIriJSr5VhRFURRFURQvUcm3oiiKoiiKoniJSr4VRVEURVEUxUtU8q0oiqIoiqIoXqKSb0VRFEVRFEXxEpV8K4qiKIqiKIqXqORbURRFURRFUbxEJd+KoiiKoiiK4iVCSql3DF4jhKgBivWOo5+IA2r1DkLxOPU69w/qdfZ/6jXuH9Tr7D2DpZQDTveNfpV8K94jhMiVUuboHYfiWep17h/U6+z/1GvcP6jX2RhU2YmiKIqiKIqieIlKvhVFURRFURTFS1TyrXjK83oHoHiFep37B/U6+z/1GvcP6nU2AFXzrSiKoiiKoiheoka+FUVRFEVRFMVLVPKteJwQ4n4hhBRCxOkdi+JeQognhRD7hBC7hRAfCCGi9I5JcR8hxCwhxH4hRKEQ4iG941HcTwiRKoRYI4TIF0LsFULcq3dMimcIIcxCiB1CiI/1jqW/U8m34lFCiFTgYqBE71gUj1gJjJZSjgEOAL/QOR7FTYQQZuBZYDYwClgohBilb1SKB9iB+6WUo4BzgR+r19lv3QsU6B2EopJvxfP+AjwAqMkFfkhKuUJKae/5cjOQomc8iltNBgqllEVSym5gMXC5zjEpbialrJRSbu/5vAUtORuob1SKuwkhUoC5wIt6x6Ko5FvxICHE5UC5lHKX3rEoXnELsEzvIBS3GQiUnvB1GSop82tCiCHAeOArnUNR3O+vaANhTp3jUACL3gEovk0I8TmQeJpv/Qr4JVrJieLDvu01llJ+2POYX6Fdvn7Dm7EpiuIeQogw4D3gPills97xKO4jhLgUqJZSbhNCXKBzOAoq+Vb6SEo583T3CyGygTRglxACtHKE7UKIyVLKKi+GqPTRN73GLkKIm4BLgRlS9S71J+VA6glfp/Tcp/gZIYQVLfF+Q0r5vt7xKG53HjBPCDEHCAIihBCvSyl/qHNc/Zbq8614hRDiCJAjpazVOxbFfYQQs4CngfOllDV6x6O4jxDCgjaJdgZa0r0VuE5KuVfXwBS3EtroyCtAvZTyPp3DUTysZ+T7/5NSXqpzKP2aqvlWFKUv/gGEAyuFEDuFEP/SOyDFPXom0t4NfIY2Ce8dlXj7pfOAG4DpPf/DO3tGSBVF8RA18q0oiqIoiqIoXqJGvhVFURRFURTFS1TyrSiKoiiKoiheopJvRVEURVEURfESlXwriqIoiqIoipeo5FtRFEVRFEVRvEQl34qiKIqiKIriJSr5VhRFURRFURQvUcm3oiiKcgohxBohxEU9n/9eCPGM3jEpiqL4A4veASiKoiiG9AjwOyFEPDAemKdzPIqiKH5BrXCpKIqinJYQYi0QBlwgpWzROx5FURR/oMpOFEVRlFMIIbKBJKBbJd6Koijuo5JvRVEU5SRCiCTgDeByoFUIMUvnkBRFUfyGSr4VRVGUY4QQIcD7wP1SygLgMbT6b0VRFMUNVM23oiiKoiiKoniJGvlWFEVRFEVRFC9RybeiKIqiKIqieIlKvhVFURRFURTFS1TyrSiKoiiKoiheopJvRVEURVEURfESlXwriqIoiqIoipeo5FtRFEVRFEVRvEQl34qiKIqiKIriJf8/+JZLgqrHPgoAAAAASUVORK5CYII=\n", "text/plain": [ - "array([-5. , -4.8989899 , -4.7979798 , -4.6969697 , -4.5959596 ,\n", - " -4.49494949, -4.39393939, -4.29292929, -4.19191919, -4.09090909,\n", - " -3.98989899, -3.88888889, -3.78787879, -3.68686869, -3.58585859,\n", - " -3.48484848, -3.38383838, -3.28282828, -3.18181818, -3.08080808,\n", - " -2.97979798, -2.87878788, -2.77777778, -2.67676768, -2.57575758,\n", - " -2.47474747, -2.37373737, -2.27272727, -2.17171717, -2.07070707,\n", - " -1.96969697, -1.86868687, -1.76767677, -1.66666667, -1.56565657,\n", - " -1.46464646, -1.36363636, -1.26262626, -1.16161616, -1.06060606,\n", - " -0.95959596, -0.85858586, -0.75757576, -0.65656566, -0.55555556,\n", - " -0.45454545, -0.35353535, -0.25252525, -0.15151515, -0.05050505,\n", - " 0.05050505, 0.15151515, 0.25252525, 0.35353535, 0.45454545,\n", - " 0.55555556, 0.65656566, 0.75757576, 0.85858586, 0.95959596,\n", - " 1.06060606, 1.16161616, 1.26262626, 1.36363636, 1.46464646,\n", - " 1.56565657, 1.66666667, 1.76767677, 1.86868687, 1.96969697,\n", - " 2.07070707, 2.17171717, 2.27272727, 2.37373737, 2.47474747,\n", - " 2.57575758, 2.67676768, 2.77777778, 2.87878788, 2.97979798,\n", - " 3.08080808, 3.18181818, 3.28282828, 3.38383838, 3.48484848,\n", - " 3.58585859, 3.68686869, 3.78787879, 3.88888889, 3.98989899,\n", - " 4.09090909, 4.19191919, 4.29292929, 4.39393939, 4.49494949,\n", - " 4.5959596 , 4.6969697 , 4.7979798 , 4.8989899 , 5. ])" + "
" ] }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" } ], "source": [ - "x = np.linspace(-5, 5, 100)\n" + "V = lambda x: 0.25*x**2\n", + "x = np.linspace(-5, 5, 100)\n", + "the_first_few = 3\n", + "\n", + "E, Psi = SEQStat(x, V)\n", + "\n", + "# TODO: The plot is unreadable.\n", + "plt.figure(figsize=(12,8))\n", + "\n", + "for i in range(the_first_few):\n", + " # TODO: Add Psi**2 for density?\n", + " # TODO: Confirm normalization?\n", + " #plt.plot(x, Psi[:, i]**2, label=\"Eigenstate number \" + str(i))\n", + " plt.plot(x, Psi[:, i], label=\"Eigenstate number \" + str(i))\n", + "plt.xlabel(\"$x$\")\n", + "plt.ylabel(\"$\\Psi$\")\n", + "plt.legend()\n", + "\n", + "plt.show()" ] }, { @@ -540,7 +565,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "metadata": { "deletable": false, "nbgrader": { @@ -557,8 +582,12 @@ }, "outputs": [], "source": [ - "# YOUR CODE HERE\n", - "raise NotImplementedError()" + "def V(x):\n", + " if -4.0 < x < -3.5 or -2.5 < x < -2.0 or -1.0 < x < -0.5:\n", + " return 15.\n", + " if 0.5 < x < 1.0 or 2.0 < x < 2.5 or 3.5 < x < 4.0:\n", + " return 15.\n", + " return 0" ] } ],