diff --git a/examples/pvtol-lqr-nested.ipynb b/examples/pvtol-lqr-nested.ipynb index bd55f8abb..9fff756ff 100644 --- a/examples/pvtol-lqr-nested.ipynb +++ b/examples/pvtol-lqr-nested.ipynb @@ -26,12 +26,29 @@ "\n", "The position and orientation of the center of mass of the aircraft is denoted by $(x,y,\\theta)$, $m$ is the mass of the vehicle, $J$ the moment of inertia, $g$ the gravitational constant and $c$ the damping coefficient. The forces generated by the main downward thruster and the maneuvering thrusters are modeled as a pair of forces $F_1$ and $F_2$ acting at a distance $r$ below the aircraft (determined by the geometry of the thrusters).\n", "\n", - "It is convenient to redefine the inputs so that the origin is an equilibrium point of the system with zero input. Letting $u_1 =\n", - "F_1$ and $u_2 = F_2 - mg$, the equations can be written in state space form as:\n", - "![PVTOL state space dynamics](http://www.cds.caltech.edu/~murray/wiki/images/2/21/Pvtol-statespace.png)\n", + "Letting $z=(x,y,\\theta, \\dot x, \\dot y, \\dot\\theta$), the equations can be written in state space form as:\n", + "$$\n", + "\\frac{dz}{dt} = \\begin{bmatrix}\n", + " z_4 \\\\\n", + " z_5 \\\\\n", + " z_6 \\\\\n", + " -\\frac{c}{m} z_4 \\\\\n", + " -g- \\frac{c}{m} z_5 \\\\\n", + " 0\n", + " \\end{bmatrix}\n", + " +\n", + " \\begin{bmatrix}\n", + " 0 \\\\\n", + " 0 \\\\\n", + " 0 \\\\\n", + " \\frac{1}{m} \\cos \\theta F_1 + \\frac{1}{m} \\sin \\theta F_2 \\\\\n", + " \\frac{1}{m} \\sin \\theta F_1 + \\frac{1}{m} \\cos \\theta F_2 \\\\\n", + " \\frac{r}{J} F_1\n", + " \\end{bmatrix}\n", + "$$\n", "\n", "## LQR state feedback controller\n", - "This section demonstrates the design of an LQR state feedback controller for the vectored thrust aircraft example. This example is pulled from Chapter 6 (State Feedback) of [Astrom and Murray](https://fbsbook.org). The python code listed here are contained the the file pvtol-lqr.py.\n", + "This section demonstrates the design of an LQR state feedback controller for the vectored thrust aircraft example. This example is pulled from Chapter 6 (Linear Systems, Example 6.4) and Chapter 7 (State Feedback, Example 7.9) of [Astrom and Murray](https://fbsbook.org). The python code listed here are contained the the file pvtol-lqr.py.\n", "\n", "To execute this example, we first import the libraries for SciPy, MATLAB plotting and the python-control package:" ] @@ -59,37 +76,39 @@ "cell_type": "code", "execution_count": 2, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "m = 4.000000\n", - "J = 0.047500\n", - "r = 0.250000\n", - "g = 9.800000\n", - "c = 0.050000\n" - ] - } - ], + "outputs": [], "source": [ "m = 4 # mass of aircraft\n", "J = 0.0475 # inertia around pitch axis\n", "r = 0.25 # distance to center of force\n", "g = 9.8 # gravitational constant\n", - "c = 0.05 # damping factor (estimated)\n", - "print(\"m = %f\" % m)\n", - "print(\"J = %f\" % J)\n", - "print(\"r = %f\" % r)\n", - "print(\"g = %f\" % g)\n", - "print(\"c = %f\" % c)" + "c = 0.05 # damping factor (estimated)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "The linearization of the dynamics near the equilibrium point $x_e = (0, 0, 0, 0, 0, 0)$, $u_e = (0, mg)$ are given by" + "Choosing equilibrium inputs to be $u_e = (0, mg)$, the dynamics of the system $\\frac{dz}{dt}$, and their linearization $A$ about equilibrium point $z_e = (0, 0, 0, 0, 0, 0)$ are given by\n", + "$$\n", + "\\frac{dz}{dt} = \\begin{bmatrix}\n", + " z_4 \\\\\n", + " z_5 \\\\\n", + " z_6 \\\\\n", + " -g \\sin z_3 -\\frac{c}{m} z_4 \\\\\n", + " g(\\cos z_3 - 1)- \\frac{c}{m} z_5 \\\\\n", + " 0\n", + " \\end{bmatrix}\n", + "\\qquad\n", + "A = \\begin{bmatrix}\n", + " 0 & 0 & 0 &1&0&0\\\\\n", + " 0&0&0&0&1&0 \\\\\n", + " 0&0&0&0&0&1 \\\\\n", + " 0&0&-g&-c/m&0&0 \\\\\n", + " 0&0&0&0&-c/m&0 \\\\\n", + " 0&0&0&0&0&0\n", + " \\end{bmatrix}\n", + "$$" ] }, { @@ -110,6 +129,8 @@ "outputs": [], "source": [ "# Dynamics matrix (use matrix type so that * works for multiplication)\n", + "# Note that we write A and B here in full generality in case we want\n", + "# to test different xe and ue.\n", "A = matrix(\n", " [[ 0, 0, 0, 1, 0, 0],\n", " [ 0, 0, 0, 0, 1, 0],\n", @@ -135,9 +156,9 @@ "metadata": {}, "source": [ "To compute a linear quadratic regulator for the system, we write the cost function as\n", - "\n", + "$$ J = \\int_0^\\infty (\\xi^T Q_\\xi \\xi + v^T Q_v v) dt,$$\n", "\n", - "where $z = z - z_e$ and $v = u - u_e$ represent the local coordinates around the desired equilibrium point $(z_e, u_e)$. We begin with diagonal matrices for the state and input costs:" + "where $\\xi = z - z_e$ and $v = u - u_e$ represent the local coordinates around the desired equilibrium point $(z_e, u_e)$. We begin with diagonal matrices for the state and input costs:" ] }, { @@ -155,13 +176,18 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This gives a control law of the form $v = -K z$, which can then be used to derive the control law in terms of the original variables:\n", + "This gives a control law of the form $v = -K \\xi$, which can then be used to derive the control law in terms of the original variables:\n", + "\n", + "\n", + " $$u = v + u_e = - K(z - z_d) + u_d.$$\n", + "where $u_e = (0, mg)$ and $z_d = (x_d, y_d, 0, 0, 0, 0)$\n", "\n", + "The way we setup the dynamics above, $A$ is already hardcoding $u_d$, so we don't need to include it as an external input. So we just need to cascade the $-K(z-z_d)$ controller with the PVTOL aircraft's dynamics to control it. For didactic purposes, we will cheat in two small ways:\n", "\n", - " $$u = v + u_d = - K(z - z_d) + u_d.$$\n", - "where $u_d = (0, mg)$ and $z_d = (x_d, y_d, 0, 0, 0, 0)$\n", + "- First, we will only interface our controller with the linearized dynamics. Using the nonlinear dynamics would require the `NonlinearIOSystem` functionalities, which we leave to another notebook to introduce.\n", + "2. Second, as written, our controller requires full state feedback ($K$ multiplies full state vectors $z$), which we do not have access to because our system, as written above, only returns $x$ and $y$ (because of $C$ matrix). Hence, we would need a state observer, such as a Kalman Filter, to track the state variables. Instead, we assume that we have access to the full state.\n", "\n", - "Since the `python-control` package only supports SISO systems, in order to compute the closed loop dynamics, we must extract the dynamics for the lateral and altitude dynamics as individual systems. In addition, we simulate the closed loop dynamics using the step command with $K x_d$ as the input vector (assumes that the \"input\" is unit size, with $xd$ corresponding to the desired steady state. The following code performs these operations:" + "The following code implements the closed loop system:" ] }, { @@ -170,44 +196,28 @@ "metadata": {}, "outputs": [], "source": [ - "xd = matrix([[1], [0], [0], [0], [0], [0]]) \n", - "yd = matrix([[0], [1], [0], [0], [0], [0]]) " - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [], - "source": [ - "# Indices for the parts of the state that we want\n", - "lat = (0,2,3,5)\n", - "alt = (1,4)\n", + "# Our input to the system will only be (x_d, y_d), so we need to\n", + "# multiply it by this matrix to turn it into z_d.\n", + "Xd = matrix([[1,0,0,0,0,0],\n", + " [0,1,0,0,0,0]]).T\n", "\n", - "# Decoupled dynamics\n", - "Ax = (A[lat, :])[:, lat] #! not sure why I have to do it this way\n", - "Bx, Cx, Dx = B[lat, 0], C[0, lat], D[0, 0]\n", - " \n", - "Ay = (A[alt, :])[:, alt] #! not sure why I have to do it this way\n", - "By, Cy, Dy = B[alt, 1], C[1, alt], D[1, 1]\n", + "# Closed loop dynamics\n", + "H = ss(A-B*K,B*K*Xd,C,D)\n", "\n", "# Step response for the first input\n", - "H1ax = ss(Ax - Bx*K1a[0,lat], Bx*K1a[0,lat]*xd[lat,:], Cx, Dx)\n", - "(Tx, Yx) = step(H1ax, T=linspace(0,10,100))\n", - "\n", + "x,t = step(H,input=0,output=0,T=linspace(0,10,100))\n", "# Step response for the second input\n", - "H1ay = ss(Ay - By*K1a[1,alt], By*K1a[1,alt]*yd[alt,:], Cy, Dy)\n", - "(Ty, Yy) = step(H1ay, T=linspace(0,10,100))" + "y,t = step(H,input=1,output=1,T=linspace(0,10,100))" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 7, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -219,7 +229,7 @@ } ], "source": [ - "plot(Yx.T, Tx, '-', Yy.T, Ty, '--')\n", + "plot(t,x,'-',t,y,'--')\n", "plot([0, 10], [1, 1], 'k-')\n", "ylabel('Position')\n", "xlabel('Time (s)')\n", @@ -237,36 +247,36 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# Look at different input weightings\n", "Qu1a = diag([1, 1])\n", "K1a, X, E = lqr(A, B, Qx1, Qu1a)\n", - "H1ax = ss(Ax - Bx*K1a[0,lat], Bx*K1a[0,lat]*xd[lat,:], Cx, Dx)\n", + "H1ax = H = ss(A-B*K1a,B*K1a*Xd,C,D)\n", "\n", "Qu1b = (40**2)*diag([1, 1])\n", "K1b, X, E = lqr(A, B, Qx1, Qu1b)\n", - "H1bx = ss(Ax - Bx*K1b[0,lat], Bx*K1b[0,lat]*xd[lat,:],Cx, Dx)\n", + "H1bx = H = ss(A-B*K1b,B*K1b*Xd,C,D)\n", "\n", "Qu1c = (200**2)*diag([1, 1])\n", "K1c, X, E = lqr(A, B, Qx1, Qu1c)\n", - "H1cx = ss(Ax - Bx*K1c[0,lat], Bx*K1c[0,lat]*xd[lat,:],Cx, Dx)\n", + "H1cx = ss(A-B*K1c,B*K1c*Xd,C,D)\n", "\n", - "[T1, Y1] = step(H1ax, T=linspace(0,10,100))\n", - "[T2, Y2] = step(H1bx, T=linspace(0,10,100))\n", - "[T3, Y3] = step(H1cx, T=linspace(0,10,100))" + "[Y1, T1] = step(H1ax, T=linspace(0,10,100), input=0,output=0)\n", + "[Y2, T2] = step(H1bx, T=linspace(0,10,100), input=0,output=0)\n", + "[Y3, T3] = step(H1cx, T=linspace(0,10,100), input=0,output=0)" ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 9, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -278,9 +288,7 @@ } ], "source": [ - "plot(Y1.T, T1, 'b-')\n", - "plot(Y2.T, T2, 'r-')\n", - "plot(Y3.T, T3, 'g-')\n", + "plot(T1, Y1.T, 'b-', T2, Y2.T, 'r-', T3, Y3.T, 'g-')\n", "plot([0 ,10], [1, 1], 'k-')\n", "title('Step Response for Inputs')\n", "ylabel('Position')\n", @@ -311,7 +319,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 10, "metadata": {}, "outputs": [], "source": [ @@ -323,31 +331,14 @@ "cell_type": "code", "execution_count": 12, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "m = 4.000000\n", - "J = 0.047500\n", - "r = 0.250000\n", - "g = 9.800000\n", - "c = 0.050000\n" - ] - } - ], + "outputs": [], "source": [ "# System parameters\n", "m = 4 # mass of aircraft\n", "J = 0.0475 # inertia around pitch axis\n", "r = 0.25 # distance to center of force\n", "g = 9.8 # gravitational constant\n", - "c = 0.05 # damping factor (estimated)\n", - "print(\"m = %f\" % m)\n", - "print(\"J = %f\" % J)\n", - "print(\"r = %f\" % r)\n", - "print(\"g = %f\" % g)\n", - "print(\"c = %f\" % c)" + "c = 0.05 # damping factor (estimated)" ] }, { @@ -443,7 +434,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -478,7 +469,7 @@ "outputs": [ { "data": { - "image/png": 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gg0sGdAi0qoYRcPwNrJ+jqj8+daCq00XkET+vaRhBgYgwIrs9I7Lb87sr+/P6p/nsi+rIjKK9/PbjNTz4yRq6JzpYq5sY3yedfpnxgVbZMM46/jqRAyLyIDAJV/fWLcBBv7UyjCBDROieFMadOf24/7K+fLn3GDOK9jJl6WaeyCvmibxiMhOj6RNfQ036Psb2SAm0yoZxVvDXidwE/B7XMF+AeW6ZYbRaRIR+mQn0y0xgWMRu+g8fw5ziUvK/3M+cL/cy581lRIQJ3ROENbUbGdcrlVpLDGm0Uvwd4nsI+GUz6WIYIUl6QjQ3nNOZG87pzKz8AmI6D2L+plJmrNjGk7M38LdZG4gJh/NLlnFujxTCjjkt27DRavDLiYhIAe7Z6nVR1Yv8ua5hhCoRDuG8Xqmc1yuVsTH7GHzOuSzcfID3561h3Z6jzFy3D4C/Lp9F93gnm8K2MKpbMv0zEwgPs5UZjNDD3+6s++rsRwPXATV+XtMwWg3JsZFcObgjcYc2kJOTQ8nh47wxbQFlUenMXbeLP051zc2NjQxjWJf2DM9uz8js9gztkkSCzU0xQgB/u7MKzxAtEJG5/lzTMFozWe3bMa5TBDk5Q5gz5zB9h41h8daDLN12iOXbj/Bc/kacCiLQp0M8I7LbM7RzEsO6tKd7aqwtB2wEHf52Z9Wdue4ARgAZfmnU+D0vA54BwoBXVfWxlryfYbQkGYnRpxfYAjh2sppVO8so3H6YZdsPMWXlbv69eAcA8dHhLofSOQnHkRoGlVeSYqlZjADjb3dW3ZnrNcBW4C5/lfKEO2Pw88A3gRJgqYhMUdV1LXVPwzibxEdHnI6pADidyubSclbsOMKKnUdYufMIzxVswqnw9PLZZLWPYUhWEoOzEhnSOYmBnRKJi7IU98bZw9+3rZ+qnqwrEJGW/NdoFLBJVbe47/UucA1gTsRolTgcQq8O8fTqEM8N57gW1aqorOHN3Lk4UruyuqSMVSVHmLpmD+DqBuuZFsegrERiTlQTv/0w/TMTiIkMC6QZRivGXyeyEBh+hmxRPbLmohOws85xCTC6he5lGEFJbFQ4/VLCyLmwx2nZwfLK0w5lTUkZ8zYc4EB5Ff9ev5Awh9ArPY7BWYkMykpiUKdEqmptiLHRPIhq018mEcnA9YM+Cfg+ru4sgATgJVXt22wa/vd9rwcuVdUfuo9vBUap6i/OqHcPcA9AWlraiMmTJ58uKy8vJy4uzqv9urKm4s25nurUJz9T1tBxffqHoi3N/UzOti2BfL9UlV2HKthfE83Wo062ljnZVlZLebWr3CFK5/gwshMcdEtw0C3RQZKcICkh+GxpqE5bbist+UwAxo8fX6iqIxutqKpN3oDbgQJca6oX1NmmAN/x5Zpe3ncskFfneCIwsaFzevfurXUpKCjwer+urKl4c66nOvXJz5Q1dFyf/qFoS3M/E2/Pby5bgu39cjqduvNQhU5bvVt/+lKe3vLqFzr44TzNnpCr2RNytcf9uXrV3+frxI9W6zuLt+u/Pp2tVTW1QWlLQ/K20lZa8pmoqgLL1IvfZV+z+L4BvCEi16nqh75cw0eWAr1EpBuwC7gR15eQYRiNICJktW9HVvt2xBwsJidnNKrKjkPHWbOrjGmLijjiCOezlbt52z0i7NElefTPTCBFKimN28ngrCRL4WL8F74uSnWLqk4CuorI/5xZrqpP+q1ZPahqjYj8HMjDNcT3NVVd2xL3Moy2gIiQnRJLdkqse0LkGJxOZfuh47w7cxG1CR1ZvauMBTtq+PyD1QBEhsHg4oUMykok4lgNWfvLcfrQLW60DnwNrMe6//re4eYj6lq7ZNrZvq9htBUcDqFbaixjO4aTk9MfgPyCAroMGMnqkjKmL17LYeCdJTs4We3kH6vnEh0GgzcsYlCnRAZ1SmRgpwS6pcYRZpMjWz2+dme97P77f82rjmEYwYhDhJ7p8fRMjyf56CZycs6lptbJu9PmEN2xN9MXr+VQrZNJX2ynssYJQExEGP07JjCoUyL9OybQPzOBXh3iiAq34catCX9nrKcBdwNd615LVe/0Ty3DMIKd8DAHWfEOckZkkXpsEzk546ipdbK5tIKiXWWs2VXG2t1lTF62k+NVta5zHELP9Dj6ZybQv6Mrnf7RSusKC2X8nSfyKTAfmA3U+q+OYRihTHiYgz4Z8fTJiOe6EVkA1DqV7QcrWLfnKOt2H2X9nqMs2HyAj1bsOn3eH5bOcp3XIYG+7vN7d4i3SZIhgL9OpJ2qTmgWTQzDaJWEOYTuaXF0T4vjysEdT8sPlFfy5Z5jTF2wgprYdIr3HePtJds5We3qDhOBrimx9OkQT3RlFSdT99A3I4Euye0sEWUQ4a8TyRWRb7mD3YZhGF6TGhfFeb2iqNnlymoMrq+WnYeO8+Xeo3y59xjFe4/x5d5jbDtQzSeblgOuRJRDspIY2jmJsLIaBhyrJC3eElEGCn+dyC+B34pIJVCNa+a6qmqC35oZhtHmCHMIXVNj6Zoay2UDM0/L8z4vIKP3ML7ce5RVJWWs2nmEF+duptapPLN8Np2SYhjZtT0X9k4jzGIsZxV/1xOJby5FDMMwPBEVJgzpnMSQzkl87xyX7ERVLZOmzkFSu7Fy5xEWbDrApyt3A/Dyl/O5oHcaF/ZOo8YmR7Yo/o7Oqi/RYhmwXVVthUPDMFqMmMgwerUPI+f87oArbf66PUf514zF7KgJ59X5W3hp7mZiwuGKg6u4ekhHzu2REmCtWx/+dme9gCtj7xr38SBgFZAiIj9W1Zl+Xt8wDMMrHA5hYKdEruwRSU7OWI6drGbR5oO88fkq8or28kFhCSmxkQxJdhLT5SDndE1u/KJGo/jrRLYBd51KPSIi/YHfAI8AHwHmRAzDCAjx0RFcMiCDyNIvGTPufOZuKOWzVbuZWbSH/H98QWZiNCNSauk2qCLQqoY0/jqRvnVzV6nqOhEZpqpbRGwInmEYwUF0RBiXDsjg0gEZzJhdQGVqbz5esYupxaXkPjGHvskODieWcHmdYL7hHf46kWIReRF41338PWCDe3XDaj+vbRiG0exEhwuXude1/2hGPrsjO/PG/I38+r1V/O7TtZyTBmm9yxjQMTHQqoYE/jqRO4CfAr/CNbz3P8B9uBzIeD+vbRiG0aIkRzv4Tk4v+ksJ0V0GMXnpTqau3k3+s/9haOckbh7dhSsHd7SZ8w3g7xDfE8Df3NuZlPtzbcMwjLOFQ4Rze6Rybo9UvplyhH0xXfn34u385oPVPJK7ju8Mz+Lm0V3o1cFmNZyJv0N8ewF/BvoD0afkqtrdT70MwzACQmyEcOd53fjBuK4s3nqIfy/ewb8Xb+dfC7cxqlsyt47J5tIBGUSGOwKtalDgb3fW68DvgadwdV/9gK/WWzcMwwhZRIQx3VMY0z2FA+X9eX9ZCW8v2c4v3llBalwUN43qzE2jutAxKSbQqgYUf11pjKp+DoiqblfVh4GL/FfLMAwjeEiNi+InOT2Yc994Xr/jHIZkJfJcwSbOezyfe95cxvyNpTjb6Mx4f79EToqIA9joXrZ2F5DuzwVF5GFca5SUukW/PZXgUUQmAnfhSjt/r6rm+XMvwzCMphDmEMb3TWd833R2HjrOO0t28N7Sncxct49uqbGMSa1m2PFqEttFBFrVs4a/XyK/AtoB9wIjgFuB2/1VCnhKVYe6t1MOpD9wIzAAuAx4QURsyIRhGAGhc3I7/veyviyceBHP3DiU5NhI3vmyitF/ns39H65m7e6yQKt4VvB3dNZS9245rnhIS3IN8K6qVgJbRWQTMApY1ML3NQzD8EhUeBjXuOedvDHlc76sSeOTFbt5d+lOhndJ4raxXbl8UEarXRbYJyciIlMaKlfVq31T5zQ/F5HbgGXA/1PVw0An4Is6dUrcMsMwjKAgOyGM23MGc//l/figsIR/f7GdX723kkdyI/neOZ25eUx2oFVsdkS16cEgESkFdgLvAIs5Y0SWqs5t5PzZQEY9RQ/gchQHAMWVgytTVe8UkeeBRao6yX2NfwLTVPXDeq5/D3APQFpa2ojJkyefLisvLycuLs6r/bqypuLNuZ7q1Cc/U9bQcX36h6Itzf1MzrYtwfp+tSZbgr2tOFVZd9DJ5zuqWbnftYL4oGTlku7R9E8Jw1EnPVQwPROA8ePHF6rqyEYrqmqTNyAMV1ziDWAF8EdggC/XauQ+XYEi9/5EYGKdsjxgbGPX6N27t9aloKDA6/26sqbizbme6tQnP1PW0HF9+oeiLc39TLw9v7lsCdb3y1NZKNoSSm1l56EKfXz6eh34UK5mT8jVnCcK9NX5W/TI8SqP5wbqmaiqAsvUi99pn7qzVLUWmAHMcOfJugmYIyJ/UNW/+3LNU4hIpqrucR9eCxS596cAb4vIk0BHoBewxJ97GYZhnC2y2rsC8cMi91DevhdvLtrOI7nr+GteMd8e1pF+4bWBVtEnfA6su53HFbgcSFfgWVzp3/3lLyIyFFd31jbgRwCqulZEJgPrgBrgZ25nZhiGETJEOIRrh2Vx7bAsinaV8eaibXy0fBeVNU6m7FrIrWOzuXxgZsjMiPc1sP4GMBCYDvyfqhY1corXqOqtDZQ9CjzaXPcyDMMIJAM7JfKX7w7ht9/qx2PvzWXRgUp++e5KHolbz02jOtPN6Qy0io3i65fIrUAF0Bu4t87aIQKoqiY0g26GYRhtgqR2kVzWLYI/3X4h8zaW8tai7TxXsAkBZpYWctvYbMYG6dK+vsZEQuM7yzAMI4RwOIScPunk9HHNiP/T+/9h0daDzFi7l57pcYxJqWbEyWrio4NnRrw5A8MwjCCkc3I7vtcnki8mfoMnvjuYdpFhTFpfxZg/fc6Dn6xh17Hg6OryN3eWYRiG0YJER4Rx/cjOXD+yM6998jlFVSlMXlZCVY2TKbsXcdvYrkQFMPmjfYkYhmGECN2TwnjyhqF8MfEbXN87gpLDJ/jZ28u5b+4Jnpm9kf1HT551nexLxDAMI8RIjo3kiu6RPHbHhRR8uZ+np63gqdkb+Hv+RoanO2iXfejUpOwWx5yIYRhGiBLmEC7u34Hw/dFkDzyHSV9s550vtnLDy4vIihM+GnmS9Pjoxi/kB+ZEDMMwWgHdUmN56Mr+jIrex+GEHnywYB1pcVEtfl9zIoZhGK2IqHDhxlFdyDi+hTpz+FoMC6wbhmEYPmNOxDAMw/AZn9YTCSVEpAzYWEeUCJR5uZ+Ka20TX6h7vabWqU9+pqyh41P7dWWhaEtzP5OG9PSmTlNtCdb3y1NZKNrSlttKSz4TgF6qmthoLW/yxYfyBvzD03Fj+3iZT9+b+zalTn3yhuxoQP+6spCzpbmfydm2JVjfr9ZkS1tuKy35TLy1RVXbRHfWZw0ce7PfXPdtSp365A3ZcebxZx7q+EqgbGnuZ+LtdZrLlmB9vzyVhaItbbmttOQz8fo6rb47yx9EZJl6szxkCNBabGktdoDZEqy0FlvOlh1t4UvEH/4RaAWakdZiS2uxA8yWYKW12HJW7LAvEcMwDMNn7EvEMAzD8BlzIoZhGIbPmBMxDMMwfMaciB+ISKyIFIrIlYHWxVdEpJ+IvCQiH4jITwKtjz+IyLdF5BUR+VRELgm0Pv4gIt1F5J8i8kGgdWkq7nbxhvtZ3BxoffwhlJ/DmbRU+2iTTkREXhOR/SJSdIb8MhEpFpFNInK/F5eaAExuGS0bpznsUNX1qvpj4AYgYMMam8mWT1T1buAO4HstqG6DNJMtW1T1rpbV1HuaaNN3gA/cz+Lqs65sIzTFlmB7DmfSRFtapn34M6MxVDfgAmA4UFRHFgZsBroDkcAqoD8wCMg9Y0sHLgZudD+QK0PVDvc5VwMLge+H8jOpc97fgOGtxJYPAmWHHzZNBIa667wdaN39sSXYnkMz2dKs7aNNpoJX1Xki0vUM8Shgk6puARCRd4FrVPXPwNe6q0RkPBCLq9GcEJFpqupsUcXPoDnscF9nCjBFRKYCb7ecxp5ppmciwGPAdFVd3rIae6a5nksw0RSbgBIgC1hJEPZ2NNGWdWdXu6bRFFtEZD0t0D6C7gEHkE7AzjrHJW5ZvajqA6r6K1w/uq+cbQfSAE2yQ0RyRORZEXkZmNbZz0WuAAAgAElEQVTSyjWRJtkC/ALXF+J3ReTHLamYDzT1uaSIyEvAMBGZ2NLK+Ygnmz4CrhORF2m+FBwtTb22hMhzOBNPz6VF2keb/BLxQH2rtzQ6E1NV/9X8qvhFk+xQ1TnAnJZSxk+aasuzwLMtp45fNNWWg0CwOcIzqdcmVa0AfnC2lfETT7aEwnM4E0+2tEj7sC+RrygBOtc5zgJ2B0gXf2gtdoDZEuy0JpvMFh8xJ/IVS4FeItJNRCJxBc2nBFgnX2gtdoDZEuy0JpvMFl8J9OiCAI1oeAfYA1Tj8tp3ueXfAjbgGtnwQKD1bCt2mC3Bv7Umm8yW5t0sAaNhGIbhM9adZRiGYfhM0I3OEpEhwEtAHLANuFlVj7rLJgJ3AbXAvaqa19j1kpKStGfPnqePKyoqiI2N9Wq/rqypeHOupzr1yc+UNXRcn/6haEtzP5OzbUuwvl+tyZa23FZa8pkAFBYWHlDVtEYrBrpPr54+vqXAhe79O4FH3Pv9cc28jAK64errC2vser1799a6FBQUeL1fV9ZUvDnXU5365GfKGjquT/9QtKW5n4m35zeXLcH6fnkqC0Vb2nJbaclnoqqKl2u0B2N3Vh9gnnt/FnCde/8a4F1VrVTVrcAmXDMzDcMwjAARjE6kiK+Stl3PV+Odmzp72S9Kj1VSUa1U1wbLRHTDMIzgIyCjs0RkNpBRT9EDQDGuWZUpuMY236uqKSLyPLBIVSe5r/FPYJqqfljP9e8BfgMkpaWlpb722muny2prawkLC2t0/7FVYew57pr4GS5KVBhEh+H6Gw4xYdAu3LXFhH+1Hx8B8ZHQzlFLYnQYEQ246br3bEx+pqyh41P7nuxrKt6c2xK2NGZTsNvS2H6gnklrsqUtt5WWfCYAV111VaGqNp7Z25s+r0BtQG9giXt/IjCxTlkeMLaxa/gaE/ls1S6d+PpMfXb2Bv3ztPX64Mdr9NfvrtB73lyqN/1jkX7rmXl63uOf66Dfz9Cu9+dq9oT6t4G/m6E5TxTo915eqL9+d4X+ZcZ6fWvRNv18/V59c8rnWlFZ/bW+yLbcz1v32GIinrGYiGd5W2krwRITCcbRWemqul9EHMCDuEZqgeur5G0ReRLoCPQClrSUHlcO7kjcoQ3k5PRqtG6tUyk/WcORE1UcrKjiwLFKFi5fQ2qnrhwor6K0vJK9ZSf5YstB9h2rpNb51dffQwvyyEiIpltqLN3SYumeGkv5/hp6HDpOVvsYXIlpDcMwgpOgcyLATSLyM/f+R8DrAKq6VkQm40rNXAP8TFVrA6TjfxHmEBLbRZDYLoLsFNeQusjSL+t1QDW1TkrLK9l95CSzFxYSl9GVLaUVbD1QzvQ1ezh8vBqAp5cXkBAdTv+OCQzomIijrJrMvcfokRZLeFgwhrIMw2iLBJ0TUdVngGc8lD0KPHp2NWpewsMcZCbGkJkYw7Gt4eTk9Pyv8sMVVXw4cz7tOvZi7e4y1u4+yqQvtlNZ4+SVNfNoFxnGiOz2pFFFu+xDDOmcSFS47/2ehmEY/tBq056IyFXAVZmZmXe//fZX6yyVl5cTFxfn1X5dWVPx5lxPdc6U1zqVLaUVlNZGs/lILcWHaikpdz23cAf0SHTQPa6WczrF0DXRwfGKiq/pHyy21CfzdNzcz+Rs2xKs71drssWf98uT/qFiS0s+E4Dx48eHfmC9ObbWOtnws7x8zSvao498tlavfHa+dnUH8kf+cZbe+vcZmle0R2fMym+SPk3V05s6Flj3vN+QLrW1Tt1SWq4z1+7VSV9s06dnbdAHP16jP35rmX73xQU6+g9TNeeJAh3/1wK9+G9z9NKn5urlT8/TK5+dr7f+c7He/+Fq/Z9X8/STFSW6dOtB3X3kuNbWOgNiS2NYYN2z3ALrRosRFynkDMjgkgGukdK5MwuoTuvF7PX7yV+3h3lvFRLhgPNLlnLFoEza1bTOL87WwMnqWop2lbF+z1HW7TnG+j1HKd57jBPV/x3yS2oXQWpcFKlxkXSJd5DRIZFaVZxOpdapOFWpcSoHy6so2lXGoYpqPty48vT58VHhjOzantHdUwg/Usu4WicRFl8z/MScSCshLlLIGZbFtcOymJ1fQEyXQfxrViHr9h4j/8v9RDpgWukKrh3WkfN7pdmPRwBxqrK65Ai5W6p4ZdMXLN12mKoa16TWxJgI+mXG871zOtM/M4HeGfFkJESTHBtJZPhXz2zOnDnk5Axr8D55swvoPmgkJUdOsOvwCdbuPsqSrQcpKC4F4G+FMxmencS5PVK5ZmjHljPYaNWYE2mFhDuEcT1TqS6J4sILL6Rw+2FemLqU+RtL+WzVbpJjI7lycCbfHZHFoE6JNoz4LFBepby3dAdzikuZV3ycirwFAPTNqOK2MdmM7p7CgI4JZCZGN9vziAoXenWIp1eH+P+Slx6r5F9T51PRLpPFWw/xRF4xT+QV0zfZwYH4Ei4fmEFslP00GN5hgfU2FCyMbhfLmgO1LNpdw4r9tVQ7oUu8g5zO4YzJDKddRP0/XhZY982WvYfLKa6IYuneWtYdrMGpQnK00DvBydCMaLpEn6RjcuAD66XHnSzcXcP8kioOnBSiwmBkh3BGJFczrFMsItLm2koo2NKmA+u4cmKtBZzAyDryUcBK97YKuLZO2RxcKVFOlad7c6/WGlj3N1hYdqJK31y0TS9/ep5mT8jVvg9O1/smr9TC7YfU6XT+V10LrHuWnymbNitf31uyQ2/952Lt7s5kcP7j+fqTl/J0TckRdTqdAX+/PJXl5+fr0q0H9f4PV+nA383Q7Am5evVz/9E5xfs1P7/+QRqBtsUC6573W3tgvQj4DvByPfKRqlojIpnAKhH5TFVr3OU3q+qys6loayUhOoJbx2Rzy+gurNlVxjtLdvDpyt28X1hC34x4bh6TzbXDOhFn3RqNUutUFm0+yAeFO5m2+jhVztV0SW7HpV0j+OmVoxnQMYG5c+cysFNioFVtEBFhZNdkRnZN5vdXDeDxd/OZuauS219bQs8kB5GdD3Buj5RAq2kEGQH5hVDV9cDX+n5V9Xidw2igdfa1BREiwuCsJAZnJfHAFf35dOUu3l68g4c+KeKxaev59rBO9A23TMb1saW0nA82VPHbRfnsLjtJQnQ44zqFc+9VoxjaOSkkHIcnoiPCuLBzBBNvuoDJy3by5Iy13PzqYkZ1S+aitFpyAq2gETQE3b+ZIjIaeA3IBm6t8xUC8LqI1AIfAn90f3IZzURcVDg3j87m+6O6sHLnESZ9sYMPCkuorHHy8c4F3DImm8sHZhIT2XZnyB89Wc3U1Xv4oLCEwu2HESCnTxK/vaIfF/frwBcL5jOsS/tAq9lsRIY7uGVMNukVW9gT043nCzbx2NZKVlYU8odrBgRaPSMIaLHAekPp3lX1U3edOcB99XVRiUg/4A3gAlU9KSKdVHWXiMTjciKTVPVND/f2OxW8pbd2UVENi/Y6Wbjfwf4TQnSYMiINzu0AXeLg1Mdka04F71TYUAaL9iqrDwnVTiEjRhndAUak1JIcE1rp0z2VefNOVdVC/i4nM3Y6iHDAtV2djM1w4HRaWznbtlgq+K+C5SMbKC+orxy4A3jOm3tYYN17fTxRUFCgTqdTF20+oL9+d4X2eXCaZk/I1Uufmquvzt+iB8srW11g3el06pqSI/qnaet07J9ma/aEXO33QK4+8PFqXbnj8OnBB4EKfLZEYL0ptmzaf0yvf3GhZk/I1Vte/UInT/28UX180bOxOsHYVnytY4H1ZkBEugE71RVYz8a1VO42EQkHklT1gIhEAFcCswOpa1tDRBjTPYUx3VN4+JoBfLZqN5OXlfBI7jr+PG09/ZId7IvdwTf7Z5AcGxlodX1CVSned4wPN1Tx8NI5bDt4nHCHcH6vVH57RT8iS4u55BuDAq1mUNAjLY537xnD7yfN5qNNh1mypZaKxK3cNrYrDofNO2pLNOhERCQLuBE4H9caHidwjaCaCkxXVZ8iriJyLfB3IA2YKiIrVfVS4DzgfhGpxjX896duxxEL5LkdSBguB/KKL/c2/CchOoKbR2dz8+hsivce46PlJXy0dCsTPlzDbz8uYkz3ZC4bmMmlAzoEWtVGqapxsnzHYeZtKGXmun1s2l+OAON6JvLjC3tw6YAM2rud4pw5GwKrbJDhcAjf6BLBj68+jx+/OpeHP1vHzHX7+PtNw0iJiwq0esZZwqMTEZHXca1hngs8DuzHNWKqN3AZ8ICI3K+q85p6U1X9GPi4HvlbwFv1yCuAEU29j9Hy9MmIZ+K3+jEmZi9pvYczvWgP09fs5aFPivjdp0V0iXdwcfk6RndLZnS3FBLbRQRUX1VlS2k58zaUMn/jARZtOcjxqlrCHcLIru25/dyBJJZt4epLRwdUz1CiU1IM/zMiitK4njz0aRFX/f0/vHTrCAZnJQVaNeMs4DGwLiIDVbXI44kikUAXVd3UUsr5g81YD9wsXFVlV7lSuK+GotIqth4TapwgQOd4Bz3ia+mdGk3HOCEj1kH1iYoWmbGuqhw8qWw/6jy9bS2r4WiVq7slvZ0wMCWMgalh9EsJIyZcGrQ3mGYUB2sq+G1ltfx9RSVlVcrt/SM5P6vxfxraclvxx5Y2PWP9bG4WWPdeH0/4a8uJqhr9YvMBfXrWBr3x5UXac+JXa9B3vT9XRz48Ve94bbH+MXetvrlwqz729iydt2G/vv7JbN1xsEKPnqjS/Px8ra6p1bzZ+XrsZLUeqajSA8dO6q7Dx3XFjsM6fc0eff0/W/TP09brr95doTe8tFAHP5x3+j7d7s/Vbz45R298Zrq+uXCrbjtQ7pMtjclC4f3yVNZcthwsr9Tvv7JIsyfk6oMfr9HK6lqf9WysTmtrK43JQjKwLiJr+PqkvzJgGa65Ggd98XJG2yE6IozR3VMY3T2FX9KL2fkFdO4/kk37y9m0v5wFRZvZU3aSBZsPns5m++KqJQA8vKjgqwvlTXf9nZXn8V4RYUJ6fDQZidFcPjCDAZ0SGdAxgX4ZCcREhrmy347t2lKmGkBybCRv/GAUf8kr5h/ztrB+z1FeuHk46QnRgVbNaAG8GZ01HagFTvUJ3ej+exT4F3BV86tltGbCHUKfjHj6ZLiyyw4J30VOzgXUOpWDFZXMmruQXgOG8p8ly8nq0Ycjx6tYW7yZHt27sWP7Vnr37EG4w0F4mBAR5iA9PooOCS7Hkdwu0kYHBQHhYQ5++61+DOqUyP9+sJqrn1vApB+Opme6790rRnDijRMZp6rj6hyvEZEFqjpORG5pKcWMtkeYw/UV0SnOwahuyRzfHk7OyM4AzHHuJCenF3Pm7CLngh4B1tTwlquGdKRHWhy3vbaEG15exJt3jgrZVDBG/TQ6Y11EVgH3qOpi9/Eo4BVVHSIiK1S14ZVxAoQF1kMzWNiY/qGUCj5Y369A2LK3wskTS09yvEb51fBo+iR/NZPa2opvtoRMYB04B1gDbHVvq3GlbI8FbvAm8BLIzQLr3uvjiUDZ0hLBwtYS+AzmwLondh85rhf9tUB7PzBN87/c55WejdVpy20lWALrja6RqqpLVXUQMBQYpqqDVXWJqlao6mRfPJyIXC8ia0XEKSIj68gjROQNEVkjIutFZGKdshFu+SYReVZsOT7DCCkyE2OY/KOx9OoQx91vLCN39e5Aq2Q0A406ERHpICL/BN5V1SMi0l9E7vLzvqfWEzlzouL1QJTbaY0AfiQiXd1lLwL3AL3c22V+6mAYxlkmJS6Kt+8ew/Au7fnFOyt4d8mOQKtk+EmjTgTXCKw8XGlPADYAv/Lnpqq6XlWL6ysCYt25smKAKuCoe4GqBFVd5P7MehP4tj86GIYRGBKiI3jjzlFc2DuN+z9aw4Jd1YFWyfADb5xIqrvbygmgrvU9altInw+ACmAPsAP4q6oewpV+paROvRK3zDCMECQmMoyXbx3BeT1T+WdRFZ+v3xdolQwf8WZ01hzgOmCWqg4XkTHA46p6YSPnNXk9EREZB/wUV6r39sB84HIgBfizql7srnc+8L+qWu8cFVtPJHTXSGhM/0CsJ+KrLcH6fgWTLSdr4Nk1sOcE/HwA9PAw+tfaimfdvbHJF5ptPRFgOLAA1yz1Bbi6swZ7E7X34tpzqLNeCPA8rtUMTx2/BtwAZAJf1pHfBLzszT1sdJb3+njCRmd5ltvorAKv9fHEp3n5Ov6vBTrw9zN03e6yeutYW/n6cSiNzloOXAicC/wIGKCqq733Z01iB3CRuIgFxridxx7gmIiMcY/Kug34tIV0MAzjLJIQKbx112hiI8O57bUl7Dx0PNAqGU3AoxMRke+c2oCrcS0Q1Ru4yi3zGRG5VkRKgLG41hM5lQzpeSAO1+itpcDrdRzWT4BXgU3AZlzpWAzDaAV0SorhrbtGUV3r5JZ/Lqb0WGWgVTK8pKG0J6fiDem4vkLy3cfjcXVDfeTrTdXzeiLluIb51nfOMmCgr/c0DCO46dUhntfuOIebX1nM7a8t4b0fjSE+OrDrzxiN401gPRe4292lhHu47fOq6tfXSEtjaU9CM5VDY/pb2hP/7Qh2W1aX1vD08kqGpoXx82FROESsrTSguzc2+UJzpj0pOuPYcaYsmDcLrHuvjycssO5ZboH1Aq/1aYou/5y/RbMn5Oqzszc0eP223FaCJbDuTRbfOe6YxTu4JgPeCBQ0fIphGIbv/GBcV9bsKuPJ2RsY0CnBqwltRmDwZnTWz4GXgCG48mf9Q1V/0dKKGYbRdhER/nTtIPpnJvDLd1eyt8IZaJUMDzQ0Out0gkNV/VhVf+3ePq6vjmEYRnMSExnGS7eMINwhPLviJOWVNYFWyagHj4F192zyD4FPVXVHHXkkcB5wO1Cgqv9qeTWbjgXWQzNY2Jj+Flj3345Qs2XdwVqeWHqCER3C+dnQKOr+79qW20rQB9aBaFwpSBYAu4F1uNYT2Q68Agz1Juji4dpPAF/iWpvkYyDJLf8mUIhr/ZJC4KI658wBioGV7i3dm3tZYN17fTxhgXXP8mAKRjelTqjZ8r+vzdTsCbn6fMHGRs9tK20l6APrqnoSeAF4QUQigFTghKoeaYIz88QsYKKq1ojI48BEYAJwALhKVXeLyEBc2YPrJlq8Wd15tgzDaDtc1jWc49GpPJFXzKBOiZzfKy3QKhluvBr0oKrVqrqnmRwIqjpTXdmAAb4AstzyFap6aqWatUC0iEQ1xz0NwwhdRITHrxtEr/Q4fv3eKg6U24z2YCEYRs7dSf0pTK4DVqhq3bfldRFZKSIPWVDfMNoW7SLD+ftNwzl6spr73l91qpvbCDCNzlj3+cLepYJ/ABgJfEfrKCIiA4ApwCWqutkt66Squ0QkHlfAf5Kqvunh3pYKPkTTWzemv6WC99+OULdl7m54f4twXTflgoy221ZCJhW8+7c9G7jYvR8DxHtzXiPXvB1YBLQ7Q56FK938uAbOvQN4zpv7WGDde308YYF1z/JgDka3psB63TpOp1Pv+tcS7fXbafrGp7MbvV5rbSvBElj3Zo31u3GtOPiyW5QFfOK9P6v3mpfhCqRfrarH68iTgKm4gu4L6sjDRSTVvR8BXIkr069hGG0MEeEv3x1CUrsIXlxVyYmqllpo1fAGb2IiPwPGAUcBVHUjrsy+/vAcEA/Mcsc4XnLLfw70BB5yy1eKSDoQBeSJyGpcw3t34RpmbBhGGyQ5NpKnvjeUvRXKI1PXBVqdNo03ubMqVbXqVBxbRMJx5dDyGVXt6UH+R+CPHk4b4c89DcNoXYzrmcrl3SJ4e/EOLuiVymUDMwOtUpvEm1TwfwGO4FpN8Be4JiCuU9UHWl4937EZ66E5C7cx/W3Guv92tCZbjhwt55miMPafcPLIuBiSox1tpq0E/Yx1/SqI7QDuBt7HFRu5G7fzCYXNAuve6+MJC6x7lodKMNqbslC0paCgQLeUlmu/h6brDS8t1JpaZ5tpKyETWFdVp6q+oqrXA/cAi903MAzDCDjdUmP5v6sHsHjrIV6csynQ6rQ5vBmdNUdEEkQkGVdQ+3URebLlVTMMw/CO747I4qohHXlq9kY2HbbRWmcTb0ZnJarqUeA7wOuqOgK4uGXVMgzD8B4R4dFrB5KZGM1Lqys5erI60Cq1GbwJrK8BLgHewDXbfKmIrFbVwWdDQV+xwHpoBgsb098C6/7b0ZpsOVO+6XAtf1p8glGZ4fxosCttfGttK6EUWL8eV8r2F9zH3YEPvQm4BMNmgXXv9fGEBdY9y0MxGO2pLBRtqU/+61fzNHtCrn6wbGe9dVpLWwmlwPr7qjpYVX/qPt6iqtf57N4AEXlCRL4UkdUi8rF7pjoicnOdSYYrRcQpIkPdZSNEZI2IbBKRZy0Bo2EY9XFl9whGd0vmd58Wse1ARaDVafV4E1iPFpGficgLIvLaqc3P+84CBqqrS2wDrvVEUNV/q+pQVR0K3ApsU9WV7nNexDU6rJd7u8xPHQzDaIU4RHjqe0MJD3Nw77srqHHaYNKWxJvA+lu4svFeCszFlTvrmD83VQ/riZzBTcA7ACKSCSSo6iL3Z9abwLf90cEwjNZLx6QYHr9uEKtLyvhwowXZWxJvAusrVHXYqWC6OwFinqpe1CwKiHwGvKeqk86QbwauUdUiERkJPKaqF7vLzgcmqOqVHq5pqeBDNL11Y/pbKnj/7WhNtjRmx7ub4D97hTv7KMPTPNsVim0lZFLBA0vcf+cBA3Etk7vFi/Nm48q0e+Z2TZ06D+BaY13OOHc0sKbO8TnA7DrH5wOfeRP0scC69/p4wgLrnuWhGIz2VBaKtjRmx8nqGr34z9O0z4PTdPXOI18rD+W2EiyBdW8SMP5DRNoDD+FaKCoO+J0XzqnBuSQicjuulO7fcCtclxtxd2W5KeG/u7yygN0YhmE0QFR4GL8YFs3jK5S731zGlJ+PC7RKrQ5vRme9qqqHVXWuqnZX1XRVfamx8xrC03oi7jIHrmHF79bRYQ9wTETGuEdl3QZ86o8OhmG0DRKihFduG8nRk9Xc/VYhVbUWaG9OGv0SEZEoXOudd61bX1X/4Md9n8O1Rsgs90jdL1T1x+6yC4ASVd1yxjk/Af6Fa2XF6dS/LrthGMbX6N8xgae+N5QfvVXIazVhfPMixWYJNA/edGd9CpQBhUBlc9xUPawn4i6bA4ypR74MV0zGMAyjyVw6IIPfXNqHJ/KKeWHOZn423uPPkNEEvBmdVaSqIffjbWlPQjOVQ2P6W9oT/+1oTbY01Q5V5bnlFRSWCvcOi6J37MmQbSuhlPbkH8Agb6L0wbjZ6Czv9fGEjc7yLA/FEU2eykLRFl/er7zZ+Xr13+drv4em60sfzv5anVCxJVhGZ3kMrLtTjKwGzgOWi0ixO03JKblhGEbIERnmCrRnJkbzt2UnmbuhNNAqhTQNxUTqnchnGIYR6qQnRDP5R2O59pl8fvjGUn40KJKcQCsVojQ0xHcfcC2umd+XAbtUdfup7axoZxiG0UKkxEUxYVQ0Azsl8sKqSj5eURJolUISj4F1EXkPqAbmA5cD21X1l2dRN7+wwHpoBgsb098C6/7b0ZpsaY62Eh4dy5NLK9hYJtzaP5JRyZUhYUvQB9b577Qj4cByb4Is3mzAI7jWKFkJzAQ6uuUpQAFQDjx3xjlzgGL3OSuBdG/uZYF17/XxhAXWPctDMRjtqSwUbWmutpI3O19/8PoSzZ6Qq//72sxG9Wmqnt7UCaZnotoMgXVcXyGnHE1NA/V84Ql1rVEyFMjlqzQqJ3GlV7nPw3k3qztVvKrub2adDMNoo0SGCS/dMoIrBmfyXnEV93+4muNVzf2z1zppKLA+RESOuvcFiHEfC6CqmuDrTdW1ZvspYgF1yyuA/4iIzQIyDOOsEhnu4Nkbh6HHDvDesp0s2XqIZ24cxqCsxECrFtR4/BJR1TBVTXBv8aoaXmffZwdyChF5VER2AjfjRUJHN6+7Vzx8yFY2NAyjuQlzCDf0ieTfPxzN8apavvPiAl6auxmnLWzlkUZnrPt8YZHZuBazOpMHVPXTOvUmAtGq+vs6sjuAkar68zqyTqq6S0TigQ+BSar6pod723oiIbpGQmP623oi/tvRmmxpybZSXg3vbIJVB4U+icqtvSEpKnhsCZn1RFp6A7KBojNkd3BGYL0p5XU3C6x7r48nLLDuWR6KwWhPZaFoS0u3FafTqe8s3q59H5yuQ/4vT99ftlNrap1N1tObOsH0TFSbJ7DeYohIrzqHVwNfNlI/XERS3fsRuCZCFrWchoZhGCAi3DiqC7n3nkd2Siz3vb+Kbz0zn1nr9p36h7bN400W35bgMRHpAziB7cCpNPCIyDYgAYgUkW8Dl7jr5LkdSBiuVRNfOdtKG4bRNumRFsfHPzmX6UV7+evMYu5+cxkjstsz4bK+jOqWHGj1AkpAnIiqXtdAWVcPRSNaRhvDMIzGcTiEKwZncsmADnxQWMLTszdww8uLGN8njV9d3JshnZMCrWJAaLHAeqCxGes2Yz3QtgTr+9WabAlkW6msVT7fXk3ulmqO10B2goMxabXkdIslJtzz4NFQeL+gGVPBh/pmgXXv9fGEBdY9y0MxGO2pLBRtCYa2UnaiSt9cuFUve3qeZk/I1b4PTtffvL9SC7cfUqfz60H4UHi/VL0PrAcqJmIYhtEqSIiO4NaxXbllTDavT8lnQ00aU1btZvKyEnqmx/HN/h34Rt90hnVpT5ij9U1vMydiGIbRDIgI3RPDuDNnMA9e2Z8pK3czZdUuXpm3hRfnbCapXQQ5vdPI0BqGHa8msV1EoFVuFsyJGIZhNDNxUeF8f3QXvj+6C2Unqpm/sZT8L/czp7iUQxVV/GP1THp3iGd4dnuGd2nP8C5JITtk2ALrFiwMWlsssN4ydrQmW0KtrThVKdpTweaKSDYfcbK5rJYT7jyPseFKz/bhdI530DHOQVxmoEQAAAneSURBVKc4IYETtE+wwHp9M87rTQXvLhsMLALWAmtwpUQB1xDfNcAm4FncDrCxzQLr3uvjCQuse5aHYjDaU1ko2hLqbaW21qnFe4/qO4u36y3PztBvPjlHe0ycqtkTcjV7Qq52nZCrOU8U6A/fWKp/mrpOH3xjpuav36cb9h7VGbPyvbbJFwjywPoTqvoQgIjciysB449FJByYBNyqqqtEJIWvUtK/CNwDfAFMw7Xa4vSzrrlhGEYz4XAIvTvE07tDPBnHt5CTcyFVNU62Haxgw75jzFpcRHW7eDbsK2fuhlKqapy8tW7p6fNTv5hFZmIMjqqTTD+wmvSEKA7vqebEmj2UHK7lvFon4WEtm5gkUJMN600Fj2t2+mpVXeWudxBARDKBBFVd5D5+E/g25kQMw2hlRIY7TjuWuEMbyMlxzbN2OpUpMwvo3G8YJYePM69wLRFJHdh79CRb9yj5xfs5WF6JU2HS+uUA3HqlEu57DkavCFhgXUQeBf5/e+cfc1Vdx/HXG1MhJXKaTbBBLljaJBBptcoeF2PNKWkR9MMYyVy6YsNNKSO32tpoZf/QD0Sx8I8UkDLBbEC5J520IAicCSapLZJNywkILBM+/XG+8Bxuz73Pvefe+9xf79d2tnM+55zv9/N+vvd7P/d7vuf5fuYBB4Ark3kSEJI2Au8AVkfE94BxQD4B8r5kM8aYnmDECPH2kSOYNv4cpo0/hzGvPUdf32QA+vv76evr49jx4JHN/Uy8dBqPbdnKyNObHEFos6XgJd0KfAWYDhwBfgd8EzgILI2IGemejwKLI+KaMnV7KXgvBd9yLe36+eomLb3cV7wU/MBE+sml4IHPAqty5+4gCwYXAHty9s8BK6op3xPr1ftTDk+sl7d34mR0uXOdqKWX+0oz2ySi+on1dlsKfiMwWdJb0yT7x4BnImI/cEjSB1NGw3nAwxhjjGkpLfk/EUm/AE5ZCj4i/pnOXQ/cTjbZ/mhELE72y4FVwCiyCfWFUYXzkg4Az+VMY8jmYarZPw/4VyGRp5ZX6zWD2UttlY5P7Odtnail0W1Syc9qrqlVS7t+vsqd60QtvdxXmtkmABMjYugE89UMVzp5A+4udzzUPlUO56qpt5ZrBrNX0lHB/7yt47Q0uk2GW0u7fr66SUsv95Vmtkm1WiJa9DhrmNlQ4bia/UbVW8s1g9kr6Sg93lDmmqK0Skuj26TachqlpV0/X+XOdaKWXu4rzWyTqsvp2mVPGoGkP0U1byd0AN2ipVt0gLW0K92iZbh09MJIpB7ubrUDDaRbtHSLDrCWdqVbtAyLDo9EjDHGFMYjEWOMMYVxEDHGGFMYBxFjjDGFcRCpA0lnSdou6epW+1IUSRdLukvSOkk3t9qfepB0raR7JD0saWar/akHSRdJulfSulb7UiupX9yX2uILrfanHjq5HUppVv/oySAi6aeSXpb0dIn9E5KelbRX0terKOprwNrmeDk0jdAREbsj4iZgDtCy1xobpOVXEXEjMB+Y20R3K9IgLc9HxILmelo9NWr6FLAutcWsYXd2CGrR0m7tUEqNWprTP+r5j8ZO3YArgMtICz8m22nA34CLgDOAXcAlwKXAIyXb+cAMsgUj5wNXd6qOdM8sYAvw+U5uk9x9PwAu6xIt61qlow5NtwNT0jX3t9r3erS0Wzs0SEtD+0fL8om0koh4XNKEEvMHgL0R8TyApNXAJyNiKfB/j6skXUmWUOsS4KikRyPieFMdL6EROlI564H1kn4N3D/YNc2mQW0i4LvAbyJiR3M9Lk+j2qWdqEUTWb6fC8nSX7fd044atTwzvN7VRi1aJO2mCf2j7Rq4hYwD/pE7rpj4KiKWRMQisi/de4Y7gFSgJh2S+iQtk7SCLO1wO1GTFmAh2QhxtqSbmulYAWptl3Ml3QVMTTl32pFymn4JfFrSchq3BEezGVRLh7RDKeXapSn9oydHImXQILYh/xMzIlY13pW6qElHRPQD/c1ypk5q1bIMWNY8d+qiVi3/BtotEJYyqKaIOAx8abidqZNyWjqhHUopp6Up/cMjkQH2Ae/KHV8IvNQiX+qhW3SAtbQ73aTJWgriIDLANmCipHdLOoNs0nx9i30qQrfoAGtpd7pJk7UUpdVvF7TojYYHgP3Af8mi9oJkvwr4K9mbDUta7Wev6LCW9t+6SZO1NHbzAozGGGMK48dZxhhjCuMgYowxpjAOIsYYYwrjIGKMMaYwDiLGGGMK4yBijDGmMA4ipieQdEzSztw2odU+NRJJUyWtTPvzJf2o5Hy/pLJL/UtaLWlis/003YfXzjK9wtGImFLupKS3RMSbw+lQg/kG8J067l8OLAZubIw7plfwSMT0LOkX+4OSNgCbku02SdskPSXp27lrl6QkP7+V9ICkW5P95C98SedJejHtnybp+7myvpzsfemedZL2SPp5WsIeSdMlbZG0S9JWSaMlPSFpSs6PJyVNLtExGpgcEbuq0DwrNxp7VtIL6dQTwAxJ/mFpasIfGNMrjJK0M+2/EBHXpf0PkX0Bv6osZehEsnwMIsuxcgVwmGz9oalkfWYHsH2I+hYAByJiuqQzgSclbUrnpgLvI1sU70ngw5K2AmuAuRGxTdLbgKPASrLEZ4skTQLOjIinSuq6HHi6xDZX0kdyx++BgdwxAJLWAr9P9uOS9gLvr0KbMSdxEDG9QrnHWZsj4tW0PzNtf07HZ5MFldHAQxFxBEBSNYvZzQQmS5qdjsekst4AtkbEvlTWTmACcADYHxHbACLiYDr/IHCHpNuAG4BVg9R1AfBKiW1NRHz1xIGk/vxJSYvJ/iY/zplfBsbiIGJqwEHE9DqHc/sClkbEivwFkhZRPvfHmww8Fh5ZUtbCiNhYUlYf8J+c6RhZP9RgdUTEEUmbybLszSEbdZRytKTuikj6OPAZstSqeUamsoypGs+JGDPARuAGSWcDSBon6XzgceA6SaPS/MM1uXteBKal/dklZd0s6fRU1iRJZ1Woew8wVtL0dP3o3PzESrJkQttyo6Y8u0mPq4ZC0njgJ8CciCgNGJOAv1RTjjEn8EjEmEREbJJ0MfCHNNf9OnB9ROyQtIYsZ/jfySahT3AnsFbSF4HHcvaVZI+pdqSJ81eAayvU/YakucAPJY0iGxHMAF6PiO2SDgI/K3PvHkljJI2OiENDyJwPnAs8lDS+FBFXSXon2eOt/UPcb8wpeCl4Y2pE0rfIvtzvHKb6xpKlMH5vRBwvc80twKGIWFmwjluAgxFxb2FHTU/ix1nGtDGS5gF/JEssNGgASSzn1LmWWnkNuK+O+02P4pGIMcaYwngkYowxpjAOIsYYYwrjIGKMMaYwDiLGGGMK4yBijDGmMA4ixhhjCvM/8Zkeuv4izukAAAAASUVORK5CYII=\n", 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\n", 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\n", 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\n", 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" ] @@ -524,7 +515,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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BTX2a8r+fN/DWzAyn4wRMeXrxvQE8BiTibqI4V1Vni0gb3M0WX/shnzmOnPwinv9yJac0qM7gnslOxzEnr5OIHMI9L1O8iBzGXZgEsKHnTalEhCcvbMfe7Hxe+GoVsVER3NyvmdOx/K48BcqaKBw0+qf1bDuQw6tXdSKykp1dXhGoaqTTGUx4i4wQXru6M/mFLp6avoLoqAiu61WxJiUtT4GyJgqHZB7IYeTMdZzfoQG9mtd2Oo4pAxF5oLT7VfVVP2zjZeBCIB/IAG5R1QMikoJ7io3VnofOtilrwlN0ZARvXNuVYR8sYMSUdKIjI7iqe5MTPzFMlKcXXycROeRpmugoIoe9bnfwUz5Tgpe+XoUqPHpeG6ejmLJL8Fy6A8OBRp7LMMBfR71tPrVKICYqgjev68rpqXV5ePJSpi7e5nQkvylPLz5ronDAgk37mbo4k3vObEnjmlWcjmPKSFWfBhCRGUBXVT3suf0U8LGftjHD6+Zs4Ap/rNeEnrjoSN66vhtDxszjgUlLiImM4NwODZyOVW5lLlDBaKIwf+RyKc9MX069hFiGndHC6TjGP5JxN8EdlQ+kBGA7Q/jjeYnNRGQRcAh4XFV/DsA2TRDFx0Ty9k3duendudwzYRFj4qI5tVUdp2OVS3mOQR0dDKo10AOY5rl9IfBTeUKZkk1ZtI0lWw/yypWdqBrr+Ewpxj/eB+aKyBTcx24vBcb6+mSbTy00OZl5SEvl+b1w+9g5jOgVT+ME34/khNprXZ4mvoA3UZjfZecV8tLXq+jUOJFLu9h4exWFqj4nIl/hHiIM3B0ZFp3E820+tRDkdObOPXK45L+/8ma68tldvalX3bczF5zOXZw/ptsIVhNFpTZqZga7Dufx5IXtKt2kZRVRsUFhF6rqvz2XRSU9pozbsPnUKqmGNeJ59+YeHMgp4Nax88ktCM95MP1RoI42UTwlIv8HzOEkmijMiW3df4TRP63n4s4N6da0ptNxjH/8KCL3iMgfzrIWkRgROVNExgI3lXMbNp9aJda+USKvX9OFZdsO8vT0FU7HKZNyH8gobxOFObEXvlqFCDw8yLqVVyCDcHdcmCAizYADQDzuL40zgNdUdXF5NmDzqZmz2yYxvH8LRqZl0LNZTS7t0tjpSCelPL34xKtNeyGwsLTHmLKZt3EfXyzdzl/PakXDGvFOxzF+oqq5wJvAm56JCesAOap6wNlkpqJ5cGAqCzbu57FP02nfMDGsJjss13xQQWiiwNN0uM3TRLFYRM7zuu9REVknIqtF5C/l3VaoKXIpT01bToPEOO44o7nTcUyAqGqBqm634mQCISoygv9c24WqsZHc9eHCsDoeVZ4CNQgowt1EkSkiK0RkA7AWGIy7iWKMHzLiWdfRs96/BBCRtsA1QDtPljePHvitKD6ev4XlmYd45Nw2VImxbuXGmLJJqh7Hy1d2Ys3OLF6ZsfrETwgR5elm7nQTxcXARE+X2Q0isg7oCfwWpO0H1KHcAl7+ZjXdm9bkok4NnY5jjAlzA1rX4/reybz9ywYGtKlH3xahfxKvX76WeyYm3O6PdR3H3SJyI+7zNB5U1f24xy2b7fWYrZ5lfxCuJxpOXJXHvuxC7ukYwcyZMwMT7ARC7aQ9X4RjZmOC5bHzTuHXdXv526QlfH3/6VSPC+155EKi3ai0s+GBkcCzuM+yfxZ4BXfvp5LOEflTh4xwPNEwY3cW3834iau6N+HmizsGLtgJhNpJe74Il8zFj92W4kBJIzwYUxZVYqJ49apOXDHqN56etoJXrurkdKRShUSBOtHZ8EeJyP+Azz03twLe48o3BjL9HC3oVN0dI+KjI/nbX2wa9wrMl3MFFRgDjAtsFFOZdEmuyfAzWvDGj+u4oFMDBrSu53Sk4wqJAlUaEWmgqkebDy/FPa08uMf++1BEXgUa4j4bfq4DEf1qxoqd/Lx2D09e0Ja6CbFOxzEBoqoDnM5gKq97zmrJjBU7eHTyMmY8ELpNfWXuxSciyT5eqpcz4z9EZJmILAUGAPcDqOpyYBKwAvf08nepavj0nyxBbkERz36+gtSkatzQp2LNjGn+SES+F5F2XrcvEpHHRaSnk7lM5RAbFcnLV3Ri1+Fcnvt8pdNxjqs8v6CC0kShqjeUct9zwHNlXXeoGTUzg637c/jw9l5ER/pjFCoTwhp7vmQhIn2BD4CJwBgRGaGqUxxNZyq8Tk1qMPT0FoyamcH5HRtwempdpyP9SXm6mVsThR9t3nuEkWnuP5Rw6P5pys2748ONwEhVfVhE6uFuvrYCZQLuvrNbuZv6Pl3GjPtPdzrOn5Snic+aKPxEVXlyWjpREcIT5/trtm8T4taJyBWegnQJMBVAVXcBdvDRBEVcdCT/uLwjmQdzePmb0DuBtzztSCU1USTjbqK41B/hKouv03eQtno39w9MpX6ib/O2mLB3P3AHsA1YpKqzADwnvVdzMpipXLqn1OKmPimM/W0ja/eH1mH88hSokpoohgL9cc9BY3yQlVfI09NXcEqD6tzcN8XpOCZIVHWHqg4EYlX1XK+7BgA/OhTLVFJ//0trGibG8056XkiN1VeeAmVNFH7w2rdr2Hk4l+cubU+UdYyoNETkJhHZA+wRkbEikgCgqjM8X/T8sY1KO9CyOTlVY6N44bIO7MhW/vPDWqfjHFOeT0TvJoqFxZoowmc8dwct3nKA937dwOCeyXRNtokIK5kngIFAG2Az8HyAtlMpB1o2J+/01Lr0axjFWzPXsyIzNAYvKXOBKtZEcZ7XXQOAH8qdrILLKyzioU+WkFQ9jkfPtYkIK6FDqrpIVXep6hO4BzoOlmMDLavqBuDoQMumkhvcJobE+Gge+XQphUUup+OUa8LCZK/r3netAv6f1/02llgJ3vwxgzU7s3j35u4khOhZ3CagGngGMl6Je58J1B9BmQdahvAdbNlp4ZgZgPxsrmoZx8glB3l83PcMaubsZ1OgTtRV3IO52lhiJVi14xBvpq3jks4NObNNktNxjDP+D+gIXAd0AKqJyJfAEmCpqk7wZSWBHGgZwnOw5VAQjpnBnfuh889gbf58Plu3hzsv6kdy7SqO5bETdYMsr7CI+z9aQmJ8NE9e2O7ETzAVkueD/xgRaYy7YHUAzgN8KlA20LLxNxHh2UvaM/DVn3hsyjLev7Vn8VayoLFuY0H26ow1rNx+iJcu70itqjFOxzEOKT5mJe59MR13YRrhj7EsRaSB183iAy1fIyKxItKMCjLQsvGfBonxPDyoNb+s28PkhdscyxHyo5lXJLMy9jD65/Vc1yuZs06xpr1K7nhN5Eeb2vzRRP4PEensWc9G3L1uUdXlInJ0oOVCKsBAy8b/ruvVlM8WZ/Ls5ys4I7WuI7MrWIEKkoNHCvjbpCU0q12VEeef4nQc47BgNJFXpoGWjf9FRAgvXtaB81//haenL+eNa7sGP0PQt1gJuVR58OMl7Dqcx2tXd6ZKjH0vMMaEvlZJCdw1oCWfL93OD6t2Bn37VqCC4KsNBXy3cicjzj+FTk1qOB3HGGN8Nrx/C1KTqvH4lHSy8gqDum0rUAE2K2MPn6wp4PyODWysPWNM2ImJiuCFyzqy/VAu/wzyiOdWoAIo80AO905YTP2qwkuXd3Ssq6YxxpRHt6Y1ubF3U8b+tpGFm/cHbbshXaBE5COvgS43ishiz/IUEcnxum+U01mLy84r5Nax88krKOLuLnFUi7XjTsaY8PX3QW1oUD2ORyYvJb8wOMMghXSBUtWrjw50CUwGPvW6O8NrEMxhDkUsUZFLuXfCItbsPMwb13WlUbWQfpmNMeaEqsVG8ewl7VmzM4u3ZmYEZZth8ckp7raxq/Dx7HqnPffFSr5ftYunLmzLGal1nY5jjDF+cdYpSVzQsQH/+WEd63ZlBXx74dLudBqwU1W9JyppJiKLcE+c+Liq/lzSE4M92OWX6/OZtKaAgU2jaJK3kbS0jWE7cGQ45g7HzMaEk/+7sB0/r93DY58uY+LQ3kREBO7YuuMFqrTBLlV1quf6YP7462k7kKyqe0WkG/CZiLQradT0YA52OXHuZiatWcZFnRryr6s7H3vjwnngyHDLHY6ZjQkndRNiefz8U/j7J0uZMG8z1/VqGrBtOV6gTjTYpYhEAZcB3byekwfkea4vEJEMIBX3lAKO+Dp9O49NWcbpqXX555WdAvqtwhhjnHRFt8Z8tngbL365irNPSSKpelxAthMOx6DOBlap6tajC0Sk7tEZQEWkOe7BLtc7lI/vVuzkngmL6NykBqOu70pMVDi8rMYYUzYiwnOXdCC/yMWTU9NP/IQyCodP0mv4c+eI04GlIrIE+AQYpqr7gp4M+HHVLu4cv5C2DaozZkhPG8bIGFMppNSpyn1np/LN8p18nb49INsI+U9TVb25hGWTcXc7d9TMNbu544MFpNavxrghvahuM+MaYyqR205rxvQlmTw5dTl9WtQhMd6/n4Hh8AsqJH23Yie3j51Py7rV+ODWXiRWseJkQks4n+huwkN0ZAQvXd6RPVl5vPjVKr+vP+R/QYWir5Zt554Ji2jXsDrjhlhxMqFJVa8+el1EXgEOet2d4TkB3phy6dA4kSH9mvH2Lxu4pHNDejWv7bd12y+okzR18TbunrCITk1q8P5tVpxM6Au3E91N+HngnFQa14zn0SnLyC3w39yX9gvqJIyfs4nHP0unV7NavH1TDxtfz4SLsDnRvSThePJ1OGaG8uW+urmLVxbk8Pcx33N5qxi/5LFPWB+9NTODF75axZlt6vHmdV2Ji450OpIxFepE9+MJx5OvwzEzlC93f2C9azHTl2Ry94V9aF0/odx5rECdgKry8jereTMtgws6NuC1qzsTHWktoyY0VJQT3U3F8MQFbZm5ZjcPT17K5OF9iSzngAX2SVuKIpcy4rN03kzLYHDPZP59TRcrTibchPyJ7qbiqFU1hicuOIXFWw7w/m8by70++7Q9jrzCIu6duIgP52zmzv4teP7S9uX+NmCMA0L6RHdT8VzSuRGnp9bl5W9Ws+1ATrnWZQWqBNl5hdw6Zj5fLN3OY+e14aFBbWw2XBOWVPVmVR1VbNlkVW2nqp1UtauqTncqn6l43MMgtcel8MRn6ahqmddlBaqYfdn5XPv2HH5bv5eXr+jI0NNbOB3JGGPCSpNaVXjwnFR+WLWLz5eWfRgkK1Beth3I4cpRs1i1/RCjru/Gld2bOB3JGGPC0s19U+jYOJGnpy/nwJH8Mq3DCpTH2p2HuWLkLHYdzmPckJ4MbJvkdCRjjAlbUZERvHhZR/YfKeC5L1aWaR1WoIAFm/ZzxajfKHQpk+7o49ehOowxprJq27A6t5/WnI8XbGXWuj0n/XwrUMDGPdnUqhrDp8P7ckqD6k7HMcaYCuO+s1vRom5VVu88fNLPtRN1gcu7Neb8jg1sdAhjjPGzuOhIvvzracRGnfznq/2C8rDiZIwxgVGW4gRWoIwxxoQoK1DGGGNCkpTnLN9wIyK7gU0ObLoOcPJdWJwXjrmdytxUVes6sN2gsf3npIRjZgix/adSFSiniMh8Ve3udI6TFY65wzGzKV04vqfhmBlCL7c18RljjAlJVqCMMcaEJCtQwTHa6QBlFI65wzGzKV04vqfhmBlCLLcdgzLGGBOS7BeUMcaYkGQFyhhjTEiyAmWMMSYkWYEyxhgTkqxAGWOMCUlWoIwxxoQkK1DGGGNCkhUoY4wxIalSzahbp04dTUlJCfp2s7OzqVq1atC3W17hmNupzAsWLNhT0Uczt/3Hd+GYGUJv/6lUBSolJYX58+cHfbtpaWn0798/6Nstr3DM7VRmEXFiGoqgsv3Hd+GYGUJv/7EmPmOMMSHJCpQxlZSIDBKR1SKyTkQecTqPMcVVqiY+EzpUlQNHCti4N5sdB3PJKSgip6AIl0uJjYokJiqCuOgI4qIjiYuOJCpCEBEAXKoUFimFLhcFRS7yC5WCIheFLhfpWwvYMXczRaq41L2dItfv193bBuX36wC+DJkcFSHcdlrzQLwcQScikcB/gYHAVmCeiExT1RXOJgst+YUuDhzJZ9+RfPZnF3Awp4CsvEKy8wrJLSg69ncTFSFUj4+melw0SdVjycpXVPXY36wpG1Rf2d4AACAASURBVCtQJmi27DvCzDW7+XntbuZs2MeBIwWB2VD6soCsNjYqosIUKKAnsE5V1wOIyETgYuCkC9T0JZnkF7r8HO93q7YVsGfB1mO3vWdg+MMXC88XD/cXEPcXGZeCy6W4PF9UCl1KYZGLgiIlr9BFXmERuQUujuQXkp1XRFZeAYdyCjmY83sxKqvHZs2gfaNEujWtSbemNendvDZx0ZFlXl9lZAXKBJSq8su6Pbz360Z+WLULgEY14jmnbRKpSQmk1K5KwxrxVImJJD4mEhH3t9a8Qhd5BS5yC4vIzS/6wy+iqIgIoiKFqAghOjLCcxGiIiOYP3cO/fr2ITJCEIFIESI8FwQ8/yAiHP1ue/RL7u9LKoVGwBav21uBXsUfJCJDgaEASUlJpKWl/WlFj32fzeEAfdc4ZtkSv68ySiA6EqIjIC5KiI0U4qOgSpTQtIpQLRGqxURTLVqoFiNUixaqRkN8lBAXJcRE/P63U+iCIwXKkUJlX66yZX8u+wphw+79zF6/F5dCbCR0qhtJj/pRdKnnbhUINVlZWSW+x04J+wIlIoOAfwORwNuq+qLDkYzHos37eWJqOunbDlGnWgx/PasVF3duSLM6VQPW9LGpSgQNa8QHZN0VTElvwJ9aOlV1NJ5J7Lp3764l9fD6suMRAjmt3Ow5s+ndqzfH+5PxXn70i8fRLyd4f0mJEPcXmYgIoiLctwPFuzdcdl4h8zbuY8aKncxYvoO5i/NIqh7L9b2acm2vZGpXiw1YjpMVar0Pw7pAWTt6aDqYU8A/vl7Fh3M3Uy8hlpev6MhFnRsSG2XNGyFkK9DE63ZjILMsK2pSq4pfAh3P+ioRJNcO7DYCqWpsFP1b16N/63o8e3F7Zq7ZxZhZm3jl2zWMmpnBnQNacuupzaz5rwRhXaDwYzu68Y/0bQcZ9sECMg/kcEvfZjxwTirVYsP9z6xCmge0EpFmwDbgGuBaZyNVfJERwpltkjizTRLrdh3mH1+v5uVvVvPhnM08e0k7zmyT5HTEkBLunxwnbEf3pQ090EKtXddXJ5v7120FjFmeT0KMMKJXHC0SdjH/t12BC1iCcH2tg01VC0XkbuAb3M3j76rqcodjVSot6yUw+sbuzMrYwzPTVzBkzHyG9GvGI+e2ISbKzgCC8C9QJ2xH96UNPdBCrV3XV77mVlVe/mY1/1uWQe/mtXjj2q7UcahdPVxfayeo6pfAl07nqOz6tqjD1Lv78cKXq3j31w3M27iPkdd3pXHN8G3W9JdwL9N+a0c3ZeNyKY9/ls6baRkM7pnMB7f2cqw4GROuYqMieeqidoy6vhsb92Zz+chZrNl52OlYjgv3AnWsHV1EYnC3o09zOFOlUVDk4r6PFjN+zmaG92/B85e2Jyoy3P+kjHHOoPb1+XhYH1ThylG/sWDTfqcjOSqsP01UtRA42o6+Ephk7ejBUeRSHpy0hGlLMnloUGseHtTGzpo3xg/a1K/O5OF9qVklmuvfnsPs9XudjuSYsC5Q4G5HV9VUVW2hqs85nacycLmUxz5dxrQlmTw8qA139m/pdCRjKpQmtarw8bC+NKoZz21j57NkywGnIzki7AuUCS5V5ZnPV/DR/C3ce2ZLhvdv4XQkYyqkugmxfHBrL2pWjebGd+eyaschpyMFnRUoc1JGzsxgzKyN3HpqM+4fmOp0HGMqtPqJcXx4W2/ioiO44Z25bN57xOlIQWUFyvhsyqKt/OPr1VzcuSEjzjvFjjkZEwRNalVh/G29yC90cdN7c9mbled0pKCxAmV8MmvdHh76ZCm9m9fiH1d0DOg4ZsaYP2pZL4F3b+5O5oEchoyZR3Y5RlkPJ1agzAll7M7ijg8W0KxOVd66obuNqWeMA7o1dZ8Ev2zbQe76cCEFRYGb4iRUWIEypTp4pIDbxs4nJjKCd2/uQWJ8tNORjKm0BrZN4rlLO5C2ejePTF72h7mxKqJwH+rIBFCRS7nrw4Vs3X+ED2/vbUOvGBMCBvdMZtehPF77bg31qsfy8KA2TkcKGCtQ5rg+Wp3PL5uO8I/LO9IjpZbTcYwxHvee1ZJdh3MZmZZBvYRYbunXzOlIAWEFypRo6uJtzNhUyM19U7iqR5MTP8EYEzQiwjMXt2dPVh7PfL6CugmxXNCxodOx/M6OQZk/WbXjEI9MXkZqzQhGnH+K03GMMSWIjBD+fU0XuiXX5IGPlvBbRsUbEskKlPmDQ7kFDHt/AdXiorizUyzRNvirMSErLjqSt2/qTnLtKgwdN5/VOyrWCOj26WOOUVUe/mQpW/fn8OZ1XakRZ38exoS6GlViGDukJ/Exkdw2bh77s/OdjuQ39glkjhn32ya+St/BQ4NaW6eICkBEXhaRVSKyVESmiEgNr/seFZF1IrJaRP7iZE5Tfo1qxDPqhm7sPJjH3RMWUlhBzpGyAmUASN92kOe+WMmZbepx26nNnY5j/ONboL2qdgTWAI8CiEhb3HOntQMGAW+KiJ19Hea6Jtfk+cs68Ou6vTz35Uqn4/iFFSjD4dwC7vpwIbWrxfDKlZ1sGKMKQlVneOZMA5iNe8ZpgIuBiaqap6obgHVATycyGv+6oltjhvRrxnu/buSrZdudjlNu1s3c8MRn6Wzdn8NHQ3tTs2qM03FMYAwBPvJcb4S7YB211bPsT0RkKDAUICkpibS0tABGLFlWVpYj2y0PJzP3rar8UD2ChyYtJD+zComxvn/hDLXX2gpUJTdl0VY+W5zJAwNT6W7HncKOiHwH1C/hrhGqOtXzmBFAITD+6NNKeHyJY+ao6mhgNED37t21f//+5Y180tLS0nBiu+XhdOam7Q5z/n9+4fOdCYy+oZvPMw84nbs4K1CV2Ka92Tw+JZ2eKbW4a4DNihuOVPXs0u4XkZuAC4Cz9PeB27YC3mdfNwYyA5PQOKFVUgJ/P6c1z325kk8XbuPybo1P/KQQdNLHoESkqh1QDX8FRS7unbiYyAjhtWs6E2nHnSocERkEPAxcpKreM91NA64RkVgRaQa0AuY6kdEEzpBTm9EzpRZPTV/OnjCdQ+qEBUpEIkTkWhH5QkR2AauA7SKy3NONtVXgYxp/+8/3a1my5QAvXNaRRjXinY5jAuMNIAH4VkQWi8goAFVdDkwCVgBfA3epapFzMU0gREYIz1/WgZz8Il6ZscbpOGXiSxPfj8B3uLuopquqC0BEagEDgBdFZIqqfhC4mMafFmzazxs/ruPyro05v2MDp+OYAFHV47bbqupzwHNBjGMc0LJeNW7sk8J7szZwfe9k2jVMdDrSSfGlie9sVX1WVZceLU4AqrpPVSer6uX83jvIhLisvELu/2gxDWvE89RFbZ2OY4wJsL+e1YqaVWJ4evqKsJs/6oQFSlULii8TkTri1S2kpMeY0PTM9OVs3X+E167uTEKcTT4YKuzYrgmUxCrRPDAwlbkb9vFV+g6n45wUX45B9RaRNBH5VES6iEg6kA7s9ByENWHim+U7mDR/K8P7t7ChjBxmx3ZNMA3umUyb+gm88NXKsJoq3pcmvjeA54EJwA/AbapaHzgdeCGA2Ywf7T6cx6OfLqN9o+r89axUp+MY97HdFriP7dZX1SaqWg84DfdJtC+KyPVOBjQVR2SE8NCg1mzZl8Ok+VucjuMzXzpJRKnqDAAReUZVZwOo6ipfT/4yzlJVHpm8lOy8Ql67qjMxUTbCVQg4u6SmcVXdB0wGJouItcEavxnQuh5dk2vwn+/dHaTiokO/RdmXTyrv34M5xe4LryNuldRH87bw/apdPDyoDa2SEpyOY7Bjuyb4RIS//aU1Ow7lMn7OZqfj+MSXAtVJRA6JyGGgo4gc9rrdIcD5TDlt2pvNM5+voF/L2tzcN8XpOMbDju0aJ/RtUYd+LWvz5o/ryM4rPPETHOZLL75IVa2uqgmqGuX59+hta4IIYUUu5cFJS4iMEF6+wkYpDzF2bNc44sFzWrM3O58xszY6HeWETngMSkQeKO1+VX3Vf3GMP731UwbzN+3nX1d3pqGNFhFq7NiucUTX5JoMaF2Xt39ez819U6gaG7pDsvrSxJfguXQHhuMelr8RMAywMz1D1PLMg7z27RrO79CAizs3dDqO+TM7tmscc89Zrdh/pIAPZm9yOkqpfGnie1pVnwbqAF1V9UFVfRDoxu8ToAWMiDwlIts8Y4ktFpHzvO6zaatLkFtQxP0fLaZmlRj+3yXtfR5q3wRV8WO7h+zYrgmWrsk1Oa1VHUb/tJ6c/NAdhvFk+hsnA/let/OBFL+mOb7XVLWz5/Il2LTVpXn5m9Ws2ZnFy1d2sgkIQ1QJx3ar27FdE0z3ntWKvdn5jJ8Tur+iTqZAvQ/M9fyi+T9gDjA2MLF8YtNWl+DXdXt455cN3NSnKWek1nU6jjEmRPVIqUWf5rV566f15BaE5q8on4+OqepzIvIV7jPdAW5R1UWBifUnd4vIjcB84EFV3Y+P01ZXpimrswuUJ37NoUFVoW+13eXeZqhN/+yLcMlsnY9MKLj3rFYM/t9sPpq3hZtC8DQUX3rxydGZOFV1IbCwtMeURWnTVgMjgWdxHzh+FngFGIKP01ZXlimrVZV7JiziUH4On97Zl46Na5R7naE2/bMvwijz0TOmWwM9cE8iCHAh8JMjiUyl07t5Lbo1rclbMzMY3DPZ6Th/4ksT348ico+I/CG9iMSIyJkiMha4qTwhVPVsVW1fwmWqqu5U1SLPVB//4/dmPJu22svUxZl8vnQ79w9M9UtxMoEVzM5HIvI3EVERqeO5LSLyuqeD0VIR6erP7ZnwISLcPaAlmQdz+WzxNqfj/IkvBWoQUARMEJFMEVkhIhuAtcBg3B0YxgQqoIh4z6h3Ke6z7cGmrT5m6/4jPPFZOt2b1mTYGS2cjmNOTkA7H4lIE2Ag4D22zbm495dWuJu/R/preyb89G9dl7YNqjMqLQNXiM0XdcImPlXNBd7E3UsuGvc3vhxVPRDocB7/EJHOuJvvNgJ3eHItF5Gj01YXUkmnrS5yKQ9MWoICr13dmUgbLSLcHO18NAX33/ilwDg/rv814CFgqteyi4Fxnmb52SJSQ0QaqOp2P27XhAkR4a4BLbnrw4XM3xHLmU4H8nJSpxB7Bq8M6h+xqt5Qyn2VftrqUTMzmLthH69c2Ykmtao4Hcf46OhxW0/no6+BUz13Het85IdjuxcB21R1SbFz4RoB3nMuHO1g9Kd9uzJ1MvKncMscr0r9qsLUdbn0+PHHkDl3MnTHuDAntGTLAV77dg0XdGzAZV3/1IHRhLYfRWQyMFVVFwAL4Pdju7iP6/4IjCltJSfoYPQYcE5JTythWYmFsLJ0MvK3cMz8YMIW/v7JUmjQjv5t6jkdBzi586BMCMnOK+S+jxZTLyGW5y7pEDLfeIzPSjq2u56TPLZ7vA5GwHqgGbBERDbi7nixUETqYx2MTAku7tyIWnHCm2nrnI5yjP2CClPPfr6CjXuzmXB7bxKr2MAD4SbQx3ZVdRlw7Guwp0h1V9U9IjIN97mFE4FewEE7/mRioiI4t1k041fuZ97GffRIqeV0JJ/Og/K1c/wBVT1UzjzGB18t287EeVu4s38Lejev7XQcU04OHNv9EjgP9+grR4BbgrhtE8JObxzF15vhzR/X8d4tzg/M48svKF+GM1LcbeX+7H1kSpB5IIdHPl1Gp8aJ3D8w1ek4JkyoaorXdQXuci6NCVWxkcIt/VL454w1rMg8RNuG1R3N40s38wHBCGJOrMil3P/RYgqLXPz7mi5ER9ohRGOMf93QJ4VRM9czcmYG/xncxdEsJ/yEE5HvRaSd1+2LRORxEXH+918lMzJtHXM27OOpi9qRUqeq03GMMRVQYnw01/VO5oulmWzck+1oFl++gjdW1eUAItIX+AD32e9jROTSQIYzv1uwaT+vfbeWCzo24IpuAZ+GywSYiCT7eHG2jcVUSrf2a0ZUZASjf17vaA5fjkF5d3y4ERipqg+LSD3cww1NCUgyc8zBnALunbCIBolxPH+ZdSmvIMbiPnZb2ptpx3aNI+pVj+OKbo35ZP5W7jurFfWqxzmSw5cCtU5ErsA9wvIlwGUAqrpLRGIDGc64Ryl/bMoydhzK5eNhfageZ13KK4iFnsFhjQlJQ09rzsS5m3nn1w08eu4pjmTwpYnvftzj323DvVPNAvCcu1EtgNkM8NG8LXyxdDsPnpNK1+SaTscx/mOdj0xIS6lTlfM6NGD87M0czClwJMMJC5Sq7lDVgUCsqp7nddcA3EOxmABZs/MwT01fzqkt6zDsdBul3BgTXMP7tyArr5APZjszLbwvvfieEJEHPfMxHaOqM1R1aOCiVW45+UXcNX4h1WKjePXqTkTYKOUVTScR2SAi00TkeREZLCIdPC0TxoSEdg0TOSO1Lu/+ssGRaeF9aeK7gRLmixGR20TkUf9HMgBPTVvOut1Z/OvqLtRLcOYApQmopUA/4A1gL+5BXd8D9ohIemlPNCaYhvdvwd7sfD6ev+XED/YzXzpJ5KjqkRKWv497+vcX/BvJTFm0lY/mb+GuAS04tVUdp+OYAFHVTNyDtM44ukzcXTRbOhbKmGJ6NatFl+QavPXTegb3TCYqiAME+LKlnGKz2gKgqnm4Jwo0frR252Ee+zSdns1qcf/ZNpRRBfbfkhZ65ohaG+wwxhyPiDD8jBZs3Z/DF8uCO6awL7+gXgGmisiVqnrsSJnnPCjX8Z9mTlZ2XiHDxy+kamwk/xncJajfVEzQzfBxIGYbhNk47uxTkmhZrxoj0zK4qFPDoJ2L6ctYfB+LSBVggYjMBhbj/uV1JfBUYONVHqrKiCnLyNidxQe39iLJoRPjTNDYibombERECMPOaMHfPl5C2urdDAjShIY+zQelqmNF5FPgUqAdkA0MVtX5gQxXmYydtZHPFmfywMBU+rW0404VnQ3CbMLNRZ0a8uqM1YycmRE6BapYM0Sa51LSfdYUUUZzN+zj/32xkrNPSeLuAXZ83BgTemKiIrjttOY88/kKFmzaR7emgZ/Q0Nf5oLybItTzr3fThDVFlNGOg7ncOX4hybWq2PlOxu9E5B7gbtwdmr5Q1Yc8yx8FbsU97fy9qvqNcylNuLimZxNe/2EtI9PW8/ZNIVCgrCkicHILihj2wQJy8guZcHsvG2fP+JWIDAAuBjqqap6nYxMi0ha4BndzfUPgOxFJVdXgn4lpwkqVmChu7pvCv75by5qdh0lNSgjo9qybmENUlYc+WcqSrQd49erOtArwG20qpeHAi55TQlDVXZ7lFwMTVTVPVTfgnvrd5nczPrmpTwrx0ZGMmpkR8G1ZgXLI69+vY9qSTB76Sxv+0q6+03FMxZQKnCYic0Rkpoj08CxvBHgPC7DVs8yYE6pZNYbBPZOZtjiTrftLGsPBf3zqxWf8a9qSTF77bg2Xd23MsDOaOx3HhDER+Q4o6RvOCNz7d02gN9ADmCQizSm5a7uWsAwRGQoMBUhKSiItLc0PqU9OVlaWI9stj3DMDL7nbhflQlV5euLPXHdK4GZdsgIVZL+s3cODkxbTs1ktnr+svU0+aMpFVc8+3n0iMhz4VFUVmCsiLqAO7l9MTbwe2hj3kEslrX80MBqge/fu2r9/fz8l911aWhpObLc8wjEznFzuWYeX8MWyTF66sS+1qsYEJI818QXRsq0HueP9+bSoW43/3did2KhIpyOZiu0z4EwAEUkFYoA9uGfCvkZEYkWkGdAKmOtYShOWhp3RnNwCF2NmbQzYNqxABUnG7ixufm8uNavGMHZITxLjrceeCbh3geae0dEnAjd5xvpbDkwCVgBfA3dZDz5zslolJTCwbRLjfttIdl5ghmW1AhUE27NcDB49GxEYN6SnDWNkgkJV81X1elVtr6pdVfUHr/ueU9UWqtpaVb9yMqcJX8POaMGBIwVMnBeYqTisQAXY+t1ZvDQvF5cqE27vTfO61ZyOZIwxftGtaU16NqvF2z+vJ7/Q/2OHW4EKoDU7D3PN6NkUqfLh7b3tXCdjTIUzvH8Lth/MZdqSEvvZlEtIFCgRuVJElouIS0S6F7vvURFZJyKrReQvXssHeZatE5FHgp+6dAs27ePKUb8B8EiP+ICfcW2MMU7on1qXNvUTGDUzA5erxLMVyiwkChSQDlwG/OS9sNiQLIOAN0UkUkQicU/4di7QFhjseWxI+HHVLq57ew61qsYweXhfGiWEystsjDH+JSIM79+Cdbuy+G7lTr+uOyQ+OVV1paquLuGu4w3J0hNYp6rrVTUfdw+li4OX+PjGztrIbePm07JeNT4e1ocmtao4HckYYwLq/A4NaFwznpEzM3CfducfoX6ibiNgttdt7yFZig/V0qukFQTrTPgilzJ+VT4/bC6kc91I7jilkPT57ia+in5WeSgJx8zGhLuoyAiGnt6cJ6cuZ+6GffRqXts/6/XLWnxQ2pAsqjr1eE8rYZlS8i+/Est2MM6E35uVx70TF/Hr5iPccXpzHhrUhkivaTMqw1nloSIcMxtTEVzZrQn//m4tI2dmhF+BKm1IllKUNiSLT0O1BNqSLQcY/sEC9mTn8/IVHbmye5MTP8kYYyqY+JhIbumXwj9nrGHl9kOc0qB6udcZEsegSnG8IVnmAa1EpJmIxODuSDEtmMFUlfFzNnHlqN8QESYP62vFyRhTqd3QO4WqMf6biiMkCpSIXCoiW4E+wBci8g3A8YZkUdVC3LOEfgOsBCZ5HhsUWXmF/HXiYkZMSadX81pMv+dUOjRODNbmjTEmJCVWiebaXslMX5LJln3ln4ojJAqUqk5R1caqGquqSar6F6/7ShySRVW/VNVUz33PBSvrisxDXPTGL3y+NJO/nZPK2Ft6BmwkX2OMCTe3ntqcyAjhfz+vL/e6QqJAhQNVZcyvG7jkv7+SlVvI+Nt6c/eZrYiIsOkyjDHmqPqJcVzWpTEfzdvCnqy8cq3LCpQP9mXnc/u4BTw1fQWntarD1/edTp8W/umlYowxFc3QM5qTX+TivV83lGs9VqBO4Je1exj0r5/4ac1unrygLW/f1N2a9IwxphQt6lbjL23r8/5vm8gqx1QcVqCOI6+wiBe+XMn178yhenw0U+7qy5BTm9kMuMYY44Nh/VtwKLeQCXM2l3kdoT6ShCPW7TrMvRMWs2L7Ia7tlcwT57clPsZmvzXGGF91blKDPs1r8/Yv67mxb9MyzSBuv6C8qCrv/7aR81//hR2Hcvnfjd15/tIOVpxMWBKRziIyW0QWi8h8EenpWS4i8rpnJoClItLV6aymYhrevwU7D+UxdVHZxlGwAuWx+3AeQ8bM44mpy+nVvDZf33caA9smOR3LmPL4B/C0qnYGnvTcBvcsAK08l6HASGfimYrutFZ1aNewOqN+KttUHFaggB9X72LQv35iVsZenr6oHWNv6UG9BJuW3YQ9BY6ON5PI78OBXQyMU7fZQA0RaeBEQFOxiQjDzmjB+t3ZzFhx8lNx2DEoIK+giKTqcUy8prPNemsqkvuAb0Tkn7i/jPb1LG/En2cDaARsL76CYM0GUJpwHKE+HDNDYHJXcSnJCRHMWriMuD2rTuq5VqCAQe0bcPYpSURF2g9KE15KmyUAOAu4X1Uni8hVwDvA2Rx/loA/LwzCbAAnEo4j1IdjZghc7gH9tUyDGliB8rDiZMJRabMEiMg44K+emx8Db3uulzZLgDF+V9YRd+xT2ZiKKxM4w3P9TGCt5/o04EZPb77ewEFV/VPznjFOs19QxlRctwP/FpEoIBfPsSTgS+A8YB1wBLjFmXjGlE78OX98qBOR3cAmBzZdB9jjwHbLKxxzO5W5qarWdWC7QWP7z0kJx8wQYvtPpSpQThGR+ara3ekcJyscc4djZlO6cHxPwzEzhF5uOwZljDEmJFmBMsYYE5KsQAXHaKcDlFE45g7HzKZ04fiehmNmCLHcdgzKGGNMSLJfUMYYY0KSFShjjDEhyQqUMcaYkGQFyhhjTEiyAuUwEblERP4nIlNF5Byn8xyPiFQVkbGerNc5ncdX4fL6mpMXTu+t7T9lpKp2KeMFeBfYBaQXWz4IWI17rLNHfFxXTeCdUM0P3ABc6Ln+Ubi97k68vnbx73tYyroceW9t/wlCVidfqHC/AKcDXb3faCASyACaAzHAEqAt0AH4vNilntfzXgG6hnD+R4HOnsd8GC6vu5Ovr1388x6G4r5Thv+D7T9luNho5uWgqj+JSEqxxT2Bdaq6HkBEJgIXq+oLwAXF1yEiArwIfKWqCwOb+I9OJj/uOYQaA4txuGn4ZHKLyEocen3N8YX7vgO2/wSDHYPyv+NNp3089+Ce5fQKERkWyGA+Ol7+T4HLRWQkMN2JYCdwvNyh9vqa4wv3fQds//Er+wXlfz5Ppw2gqq8DrwcuzkkrMb+qZhPa8wYdL3eovb7m+MJ93wHbf/zKfkH5X7hPpx2u+cM1t/ldRXgPw/X/EJK5rUD53zyglYg0E5EY4BrcU2yHi3DNH665ze8qwnsYrv+HkMxtBaocRGQC8BvQWkS2isitqloI3A18A6wEJqnqcidzHk+45g/X3OZ3FeE9DNf/QzjlttHMjTHGhCT7BWWMMSYkWYEyxhgTkqxAGWOMCUlWoIwxxoQkK1DGGGNCkhUoY4wxIckKVICISJGILPa6pDidyZ9EpIuIvF3OdYwRkSu8bg8WkRHlTwcicreIhPLQMuY4bN/xaR2VYt+xsfgCJ0dVOx/vThGJ8pwcF64eA/5f8YXl/H8Nwn/jfr0L/Aq856f1meCxfefkVch9x35BBZGI3CwiH4vIdGCGZ9nfRWSeiCwVkae9HjtCRFaLyHciMkFE/uZZniYi3T3X64jIRs/1SBF52Wtdd3iW9/c85xMRWSUi4z3TFCAiPURklogsEZG5IpIgIj+LSGevHL+KSMdi/48EoKOqLvHcfkpERovIDGCciKR41rPQc+nreZyIyBsiG22D9gAABAFJREFUskJEvgDqea1TgM7AQhE5w+vb8yLP9kp7rW70LFsiIu8DqOoRYKOI9PTHe2ecZftO5dx37BdU4MSLyGLP9Q2qeqnneh/cf6D7xD2Fcivcc7EIME1ETgeycY+F1QX3e7QQWHCC7d0KHFTVHiISC/zq+aPHs552uAd//BXoJyJzgY+Aq1V1nohUB3KAt4GbgftEJBWIVdWlxbbVHUgvtqwbcKqq5ohIFWCgquaKSCtgguc5lwKtcU9AlwSswP1t7WjGJaqqng+Uu1T1VxGpBuSW8lrtBUYA/VR1j4jU8so0HzgNmHuC186EFtt3bN8BrEAF0vGaKb5V1X2e6+d4Los8t6vh/kNKAKZ4vskgIr4M2ngO0FF+b5dO9KwrH5irqls961oMpAAHge2qOg9AVQ957v8YeEJE/g4MAcaUsK0GwO5iy6apao7nejTwhufbZBGQ6ll+OjBBVYuATBH5wev5g4CvPNd/BV4VkfHAp6q61bOTlfRadQI+UdU9nv/HPq917gLalPxymRBm+47tO4AVKCdke10X4AVVfcv7ASJyH8efB6eQ35tm44qt6x5V/abYuvoDeV6LinC/71LSNlT1iIh8i3sW0Ktwf3srLqfYtuGP/6/7gZ24d4AIINd7EyX9p3DvQJd7MrzoacY4D5gtImdz/Nfq3lLWGefJaioG23dKVmH3HTsG5axvgCGen+KISCMRqQf8BFwqIvGeNuQLvZ6zEXeTAMAVxdY1XESiPetKFZGqpWx7FdBQRHp4Hp8gIke/sLyN+4DrvGLfqo5aCbQsZd2JuL9huoAbgEjP8p/g/7d3x6xRRGEUht8DNikkhTZJK0gsrVMlxN4mauGKRX5AtBUhKVIE0gna7B9IQCwFUXSxMCkSAkERu9RiY9JEkGMxFzLBHYtkSWbX83Q7zHwXhj3ce7+ZZblXev4TwEwZexy4ZPtH+XzN9p7tVapWwxTN9+odcEfSlXK83qa4zt/tlBgNyQ6jn53soC6Q7TeSbgCfquecHAL3be9IWgd2gX3gY+2yNWBDUgeob/O7VO2HnfLQ9Dtw+x9j/5J0F3gmaYxqtTQHHNrelvSThrd4bH+VNC7psu2DPqc8B15Kmgfec7xCfAXMAnvAN6BXjt8C3tauX5Q0Q7Vi/QK8tn3UcK8+S1oBepJ+U7UxHpY608AyMXKSnf8jO/m7jSEgaYnqy792TuNNAh+AqbKS63fOI+DA9pl+z1FqdYGu7c2z1qrVvAk8tt0ZVM0YPsnOqWq2Jjtp8cUJkh4AW8CTpoAVLzjZnz812wuDDFhxFXg64JoRjZKdwcsOKiIiWik7qIiIaKVMUBER0UqZoCIiopUyQUVERCtlgoqIiFb6A3B3FghOdO7qAAAAAElFTkSuQmCC\n", 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" ] @@ -556,7 +547,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.5.6" + "version": "3.7.7" } }, "nbformat": 4,