Eligibility_Traces_ITA.ipynb

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        "#Eligibility Traces  \n",
        "\n",
        "Mario Fiorino\n",
        "\n",
        "Nelle tecniche di RL basate sull \"eligibility traces\", l'agente conserva una \"traccia\" in memoria di tutte le azioni e gli stati incontrati nel corso dell'interazione con l'ambiente. Questa traccia viene progressivamente elaborata nel tempo, precisamente è soggetta a un processo di decadimento, che dipende sia dalla frequenza delle visite sia dalla loro \"recency\".\n",
        "\n",
        "L'aggiornamento complessivo della value-fuction dipenderà oltre che dal reward immediato e l'expected rewards, anche da tale \"traccia\".\n",
        "\n",
        "L'idea alla base del meccanismo \"eligibility traces\" è semplice: si usa un vettore (ovvero una porzione di memoria), denotato con $e_t(s)$ , che associa a ciascuno stato $s$ (e se si lavora con una Q-value anche a ciascuna azione $a$ ), ad un certo tempo $t$ un valore definito come :\n",
        "\n",
        "\n",
        "$e_0(s)← 0 \\; \\; \\; ∀s∈S$\n",
        "\n",
        "$ e_t(s) ← λ γ e_{t-1}(s) + \\mathbf{I} (s = S_t) \\; \\; \\;  ∀s∈S $\n",
        "\n",
        "dove:\n",
        "\n",
        "il primo rigo ci dice che all'inizio del training l \"eligibility traces\" per ogni stato ha valore zero.\n",
        "\n",
        "\n",
        "$S_t$ è stato visitato al tempo $t$. In altri termini \" the actual state at time t\" .\n",
        "\n",
        "\n",
        "$γ$ è il discount rate, $ 0 \\leq γ \\leq 1 $\n",
        "\n",
        "\n",
        "$λ$ è il  trace decay parameter, $ 0 \\leq λ \\leq 1 $\n",
        "\n",
        "$\\mathbf{I} (S_t = s)$ è l' indicator function, che vale $1$ quando la condizione al suo interno è vera, $0$ altrimenti.\n",
        "\n",
        "\n",
        "L'eligibility trace può essere utilizzato come fattore di scala per il TD error:\n",
        "\n",
        "$ δ_t=r_{t+1}+γ v_π (s_{t+1})- v(s_t)$\n",
        "\n",
        "L'aggiornamento della funzione di valore, che ora considera anche il parametro \"eligibility trace\", diventa:\n",
        "\n",
        "$v_π(s)←v_π(s)+ α [δ_t e_t(s)] \\; \\; \\; ∀s∈S$\n",
        "\n",
        "sia $α$, lo step-size, o lerning rate, che viene utilizzato per controllare l'entità  dell'aggiornamento.\n",
        "Si noti, che così facendo, ad ogni time-step $t$, dobbiamo aggiornare le stime della value function per ogni stato $s$.\n",
        "\n",
        "$\\;$\n",
        "\n",
        "Tale meccanismo tiene conto di due fattori:\n",
        "\n",
        "Frequency heuristic: assegna più credito agli stati più frequenti\n",
        "\n",
        "Recency heuristic: assegna più credito agli stati più recenti\n",
        "\n",
        "Di fatto si tiene traccia di quanto frequente e quanto recente un certo stato è stato visitato. Gli stati che non vengono visitati o che non vengono visitati da un po' avranno un valore di $e_t(s)$ pari o vicino a zero, il che significa che la nostra stima della value function per quegli stati non cambierà molto.\n",
        "\n",
        "$\\;$\n",
        "\n",
        "NOTA\n",
        "\n",
        "La formulazione esposta è detta \"Accumulating eligibility trace\". Sutton, nel paper : https://link.springer.com/article/10.1007/BF00114726\n",
        "ne cita un altra \" Replacing eligibility trace\",  che, invece di sommare $1$ quando si visita uno stato, resetta il valore $e_t(s)$ ad $1$: cioè :\n",
        "\n",
        "$e_0(s)← 0 \\; \\; \\; ∀s∈S$\n",
        "\n",
        "if $ s = S_t : e_t(s) ← 1 $\n",
        "\n",
        "if $ s \\neq S_t : e_t(s) ← λ γ e_{t-1}(s)  \\; \\; \\;  ∀s∈S $\n",
        "\n",
        "$\\;$\n",
        "\n",
        "Se si lavora con i metodi di **Value Function Approximation**, l'eligibility trace è un vettore $\\mathbf{z}_t$,  che ha lo stesso numero di componenti del weight vector $\\mathbf{w}_t$. Sutton sintetizza molto bene il meccanismo nel suo testo:\n",
        "\n",
        "*The mechanism is a short-term memory vector, the eligibility trace $\\mathbf{z}_t \\in R^d$, that parallels the long-term weight vector $\\mathbf{w}_t\\in R^d$. The rough idea is that when a component of $\\mathbf{w}_t$ participates in\n",
        "producing an estimated value, then the corresponding component of $\\mathbf{z}_t$ is bumped up and then begins to fade away.*\n",
        "\n",
        "*Learning will then occur in that component of $\\mathbf{w}_t$ if a nonzero TD error occurs before the trace falls back to zero. The trace-decay parameter  $λ \\in [0, 1]$ determines the rate at which the trace falls.*\n",
        "\n",
        "Nella pratica:\n",
        "\n",
        "\n",
        "$\\mathbf{z}_t$ viene inizializzato a zero all'inizio di un episodio; poi viene incrementato a ogni time-step $t$ con il valore del gradiente della value-fuction, e ridotto proporzionale ai fattori $γλ$ sopra definiti. In simboli:\n",
        "\n",
        "$\\mathbf{z}_{-1} = \\mathbf{0}$\n",
        "\n",
        "$\\mathbf{z}_{t} = γλ \\mathbf{z}_{t-1} + \\nabla v(S_t,\\mathbf{w}_t) \\; \\;  \\; 0 \\leq  t  \\leq Terminal$\n",
        "\n",
        "Sia il TD error:\n",
        "\n",
        "$ δ_t = r_{t+1} +γ v(s_{t+1},\\mathbf{w}_t)- v(s_t,\\mathbf{w}_t )$\n",
        "\n",
        "Il weight vector sarà così aggiornato\n",
        "\n",
        "$\\mathbf{w}_{t+1} = \\mathbf{w}_{t} + α δ_t \\mathbf{z}_{t} $\n",
        "\n",
        "**Convergenza per i metodi Value Function Approximation**\n",
        "\n",
        "Il testo di Sutton (PDF 317) afferma che nei casi di approssimazioni lineari:\n",
        "*has been proved to converge in the on-policy case if the step-size parameter is reduced over time according to the usual conditions (2.7). Just as discussed\n",
        "in Section 9.4, convergence is not to the minimum-error weight vector, but to a nearby weight vector that depends on λ.*\n",
        "\n",
        "*...In practice, however,  λ = 1 is often the poorest choice ...*\n",
        "\n",
        "$\\;$\n",
        "\n",
        "**Vantaggi**\n",
        "\n",
        "Il testo di Sutton (Cap 12.13) dichiara che:\n",
        "\n",
        "*Methods using eligibility traces require more computation than one-step methods, but in return they offer significantly faster learning, particularly when rewards are delayed by many steps. Thus it often makes sense to use eligibility traces when data are scarce and cannot be repeatedly processed, as is often the case in online applications.*\n",
        "\n",
        "*On the other hand, in offline applications in which data can be generated cheaply, perhaps from an\n",
        "inexpensive simulation, then it often does not pay to use eligibility traces. In these cases the objective is not to get more out of a limited amount of data, but simply to process as much data as possible as quickly as possible. In these cases the speedup per datum due to\n",
        "traces is typically not worth their computational cost, and one-step methods are favored.*\n",
        "\n",
        "\n",
        "$\\;$\n",
        "\n",
        "Ref :\n",
        "\n",
        "Reinforcement Learning: An Introduction, Richard S. Sutton and Andrew G. Barto, Second Edition - MIT Press, Cambridge, 2018. PDF 309\n",
        "\n",
        "https://amreis.github.io/ml/reinf-learn/2017/11/02/reinforcement-learning-eligibility-traces.html\n",
        "\n",
        "\n",
        "http://incompleteideas.net/book/first/ebook/node75.html\n",
        "\n",
        "Potrebbe interessare:\n",
        "\n",
        "Investigating Recurrence and Eligibility Traces in\n",
        "Deep Q-Networks\n",
        "\n",
        "https://arxiv.org/pdf/1704.05495\n",
        "\n",
        "\n"
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I0NbDRo0yEaff/rpp7Zt26rCAwcOvHjxopTyypUrGt61jqWmpuoa3n777f/+97+6Dyo/N2jQYPXq1XqlhxZ0fh40aBD52UPIvlftgAEDyM++N21F3mPyc5GT06CLAvn5+VOnTlX/kJOfXURkN38XOHbs2GKzl74ut3nz5mYbFy9dulRKee7cuaFDhwoh3HulqK97r1y5Uv3N+fDDD4tsLDo/33vvvevWrXOw3VWrVpUvX37x4sVfffWVg7uYFJs5c6YabN26dT/77DOTrcX+46FDh9q1a6d6+Nxzz5ncvOrMmTPq2H7iiSeEEO3bt+/bt++5c+d0t1evXq32bd269c6dO/V61xbWrVtXsWJFdTGUazU4steFCxcWL178/fffO1LY8TI3btyYPHmy0mjUqJGNaw3mzZunigkhXIvKjvdKlVT5WQjRqFEjT0donZ+FELm5uc52tXjLc/7ZU/7kZ0/J+le95Gf/mk8/H01WVpZ6h+dCfs7IyNCfozt7/jk7O/vhhx9WbyM4/+znB5k/Di89PV290f/3v/9tY3xnz55dv359kZ1ltdET79mk83Pjxo1/+OGHoumYzs9CiPHjxzve6KZNmxwvbF5SXU6o/tC99NJL5gWKd82mTZt0lvvoo4+sdea1117TxY4dO6aL6fx863dhxYoVer1rC4MHD1bfIvbc+WdHOrZ79+6ud16OX+qvHsr4zjvvKKj69etb+z6Uy/lZd8zZb4Lo/CyEGDt2rCMILpchP7tM57c7fvDBB1WqVCnK88/lypV79dVX/RbUfwdGfvbfufXPke3atUsIER4ePmvWLKdGmJeX9+WXX6q3C9WqVVu4cKHju+fn5ycnJ6t9q1Sp8sEHHzi+ryqpr9+OiIhYvHixs7tTHoHCCKj8HBYW9sorrxSmHrv7fvzxx7F3Xo5cAX716tU7xWMnTZpkt34p5ciRI9UuGRkZjpS3ViY9PV03HRsba3ITI72Xzs9CiLp16+7Zs0dv8tyCzs+JiYm///67hxpavHjxJ598Yqxc5+euXbueOnVKSvnGG28YlXr06GEs7/hy27ZtjfXExsa6cH5b5+cXX3zxwoUL1lo/ffq0/iaCys8nT56MjY2tW7euztV169ZV/bl69aqqZ8uWLSY9VD926tTJpKHXXnstNja2TJkyqrbQ0NDY2FiLz1Ns3bq1sc558+aZVGX3x0OHDqkazP+9O3/+fGxsbP369fWg7r777m3bttmtUxVITU1t0KCB2nfgwIHnz5+3uKO1/Kw69sYbb5jsVVBQoDqsOxYZGRkbG2v+2dM333yjcdSZ7cceeyw2NlbflEcIUaNGDVVG/96lpaXpvUwWWrRoYdIZ9eMLL7xgUjI2Nnbq1KkzZswIDw/Xepx/tqgXcCuvXLnyl7/8pSjzsxCiTJkynv6sKOAm0vMD1vm5Ro0aeXl5nm+QFhBwXSAtLa1atWrqHzyL71dsV62//yyEmDhxou3CJlv195+FEGPGjDHZavdHnZ9v/amcMmWK3fIUQMCNAio/CyFCQ0NtfNK9YcOGyNuvRYsWWWt91qxZqoz6b61atXTJFStWVKhQQb8frVat2pkzZ/RW84WWLVvqL5EKIcLCwqZNm2ZeTK1ZunSpalHdYlq9t27evLm18jbWd+7cOTIyskaNGrqrQojy5ctHRkYaz+AdO3YsMjLS+A5bCFG1atXIyEgdukxaSUhI0DhdunQxbh0yZIje1LRpU+OmCRMm6E2RkZG5ubk6P4eFhRk36eUnn3zSWINafvDBB1WBxx9/3Hzrww8/rHdXCxVuv4zflNb5uUyZMqpM2bJljUohISGRkZF//etfzeu3tqZ79+6RkZElSpQw1iOEqFixYmRkpFNXJuv8bPejlsuXL6fdfql3Nb/++qtJ6/rH9PR0KeWePXtMJloXCAoKioyM7NWrlxrgW2+9pZOzLqPeABvD5KOPPhoZGWksoI8xxx8bYePfu5iYGJMDWLVVpUoVBx8tkZubu2rVKrVX+fLlP/74Y4szqPPznDlzcnJydJndu3cLIcqWLWvyL2lMTIzJqHXHTO6Lru+/LYRITk6WUt59990W9xVCqPidlZVVvXp1a2VCQkJ09/TCkCFD9M3GjTuGhYWVK1fOuIb8rNECfUFdvx0cHHz8+HGPWug/uImJiT73/XuPyvhE5To/30oF5GefmLKA7WROTk7VqlX1P3iFyc9Dhgxx9mEVbszPb7zxhi8+bTJgDzw/GLjOz6VKlbJ2CnrXrl3q+5xCiKCgIH2Ba/369UMMr6CgoLJly4aHh4eEhKhfRr0xKCgoNDT01rUh4eHhJUuWvHXtcXBwcLVq1VREMTI++eSTevegoKDw8HD1XjYoKCgkJOSTTz4xeS+7bt26oKAg1Vy5cuVUEyqSxcbGXrlyxVi57eXHHntM1VOiRAlVT3h4uE6JQUFBGzduVO9kjNeR6j87asFai3l5ea1bt1Yda9q0qbFYfn5+hw4d1O4RERHGTl69evWpp55SkfLEiRMFBQU6P5u0a/wxJCTkueeeu379uq4qLy+vfPnyqowxYPfq1Utr6yGHhYWpkkFBQStXrlT/+uu3c7qhsLAwvUvlypXV+tKlS9v4FEb3R0p59erV1q1bq710PeHh4TqCBgUFbdu2zcG/xt99950+TmbNmnXxzqugoMDYqPny8ePH9TGmOqOOoiNHjhQUFJw4cSI4OFit1wew7q1a/8gjj1y7dk1KmZ+fP3DgwPDwcLWLPoqee+45/Qb4ypUrzZo1E0Lorao2NWp1kBvvOG3eYbWmoKDgxx9/VB0w/nuXnp6urjANDg7u0aNHbm7uzJkz9edKwcHBBw8etGty6+KCgoKCL774QtUfFBRk/i1o4+/d8uXLjf1U+VkI8Y9//EOvv//++/WoVcdmzZqlxl6yZMng4OADBw5cunRJlTfPz3l5eZGRkZUqVVJdKl26tNp37dq1ajh6U8mSJYcOHZp75xUfH6/+PkRFRRn/2mRmZv75z39WtVWuXPlO8dxly5aFh4drMVXA5G+OHpTXLvD9Z09NjcrPQogiy8/68zlPDYl6PSBAfvYAKlV6SuDEiRPqn7qKFSu+9957zjajzz8/88wzNi7/s1itG/NzRESE+TsVi42yEgG3COj8bPtxr2vWrFG/X0II/a3FnJwcvbJixYrR0dHqgT39+vUzObFTsWJFfW3FgAED9NbGjRsbR3H69Gl9N4F77723a9euUspvvvnGeD7t008/vXHjhtrr+vXr77//vjr3Gx0dvWHDBrVePWRECNGuXbvTp08bm7C2nJaWpm+C0KZNG13sk08+UYFEjfS3336TUqampkZHR0dFRenhR0VFRd9+qSildzdZ0Gcy1dDU1rS0tDZt2qiqwsPDjfFp5MiRav2XX36p3sSb5OeaNWuqdtV/77nnHt0lk4v+9Pl//fyqM2fOdO3aVZWPjo7WXV2zZk1ERISuZ+/eveoecnqNECIiImLVqlV6l/T0dPW83C5duti+skDvkpCQoCosXbq0XimlnDt3rk7jQgjH/xob77+tu7pnz55Dt1/qmnNjQ8Zla99/tvHPSn5+vr7I+Yknnjh79qyusHv37iEhIZUqVTJOpZTy9OnT+tnUJlcUz5o1SyfAb775xpFPDdT3lYQQzz//vLr3tZSySZMm6sOp7t276/688847+vMvx0+HrFixQjOa3KxL/94JIapXr65/71SLOj8nJSXpjt13332qsO6VXtAHYXh4uFppnp/Vev25lfmNwdXHQ6GhoYMHD9Y1q4XHH39cRegHHnhAb3r55Zf16Ixzpwro3ztVhvys3QJ9gfwc6EeAY+MnPzvmRCmvENBvdLp27WryrsWR/un8zPXbjnBRxm8EdH5+6KGHbNweTOfnBg0abN68WQ3fmJ9N7tvXr18/dZ5ZCFG5cmWTKzmff/559Tglk/z83HPPqTesbdq00SFZSrlmzRrjBZz6kTb6FJzJ9yZyc3Pj4uJUVV26dHHkD4L+9y4uLk6fLVTDXLBggb6YXOVntd74/WdjmLRxbFjMz71799Zv5YUQMTExugbj+3iVAI35uW7duib309YBw/wGSyo/ly9fXp8fVvdUVw8QNvnG+Oeff64/HViwYEFOTo7x/HNUVJT5V5R1x7p3725U0mMxWdD5uX379iabZs2apb+M43h+/vbbbx955JHatWsbMfXyQw89lHL7ZfHzFNv5+dZZcf3pj7Grp0+fVvVXr159zpw5xk3qgDG5f5i1w1vt+Ne//lX31vanMKq8zs9CCP2RscrPNWrUMHZGSjlp0qRH7rxMDm+TkvrH7777Tn9A8NZbbxmPEP17d/fdd5sf+To/165dW3/WZiM/jxw5UnXtiSeeUK27nJ9btWql+29cUL93FvNzixYt9HlvvcvcuXONV4OTn7VMoC+QnwP9CHBs/Pr9hOMfWDpWMaUQcL+Azs9CCOP1bA62RH52EIpifiag87MQwvzUjR6szs/vv/++XmkjP0spdQQyv82SlFIFDIv5uWPHjua3LPryyy/1yVW7+VlKeeHChcQ7L/Owp4egF9S/d507dzZ/My2lTEpKUtlm1qxZ+ttMRZmfO3XqpE7l6Zhq8f7bv//++x//+EfVVYvnn3XAOHjwYJcuXVTJQ4cOaQe9MHz4cLW1S5cu6enpxvxs8f7btjumq9UL06ZNU/NjvM5cbf3555/1xx/Wbt6m6zFZ+PzzzxMTE/XnHWoIxv8+//zzy5YtM4nl1vKzOorefvttk1aklDdv3vzwww9VzX369DEW2LBhgzqZbC0/nzhxwlheLc+fP79WrVqqwkLm54oVKy5btkx/zmXeloNr9MPt9NeM1Y46P5t8bqW26vxsvH5b5WcHO+b2/Ny/f/9bX6W2mJ/37dtnUYP7b1tkCfSVRZ+fH3jggS1btgS6u6+Nn/zsazMW0P3V+Tk6OlrdccQpDvKzU1wU9hsBZ/NzQkLC0aNH1fALn5+rV6+ub1K1bdu21q1bx8fHp6amWuQdOHCgShfm+blTp04zZsywcf7cYoXGlUuXLh02bJjJc4PV7aNmzJihr68WQmRlZakdXcjP+nyyvn57y5YtzZs37969+7Bhw9SXYGvWrKkvl9Xld+/erRq1G1N/+OEHpWQ7P0+YMEEVE0JYzM+rV68edvuVlpZmcv22W/Kzxs/Ly5vx/3/pi5yFEAMHDtQlHV+YO3eu6rzxpK4erxDipZdeMp5QtZafjS3u3LnT2M3p06frClu0aGG825n6rq/585/1+WeL+XnTpk36DluFzM+qY40aNdIdtjjFxtFZXLaYnzMyMvTFz87mZwc75mx+XrJkifpKSO3atfWQjQvvvfeeECIqKmrt2rVqpHoI5GeLU89KywJFn5+bNm1qvHel5W6x1ssEyM9eNiF0x5aAzs9Nmzb95ptvbBW1tI38bEmFdf4v4Gx+tvj954YNG5pcSKzPP9eoUcPi6V99hlBfvvvqq6/eynI9e/YcbeUVGxur3n+/8MIL6n6/+jyYWt+9e3e162uvvebyzE2ePNnYfqdOnVTl6r+vvPKKvpjThfycm5ur6tH5Wb2P79Wr15kzZ3Qk69ixo5Ty+++/V7n92Wef1Y+qKrL8bALo9vPPt65BmDdv3ujRo/VnBEZnvWxyotikV3Z/zMrKmnDnFR8fr6sVQjj4/OdTp06p4+GRRx4x7m6ybLz3nt38/OKLLxqPMbWs7iumqnU5P8+bN2/8+PEmfRNCxMfHu/Dp0u7du9u3b69q00+Zsnu/D4vnn+fNm6dvxWfsXnx8vBq+8eMMZ/OzfiCWsWaLyya/d0IIu/l55MiRDl7xbvdoLLIC3D/MU9RFn5+5f5in5tKT9ZKfPalL3W4W0PmZ67fdLEt1fi3glvz82GOPmSOp67fvv/9+8036+m0hhEl+tviu13ylekzUuXPnXnzxRfOtJUqUSEpKevPNNy02bW3l9OnTk5KSLL7L100Yv9lbmPwcFRX10UcfSSlNzoOphlR+njZtmvrR+Fgjv8nPs2dbANzZAAAgAElEQVTPNn7FVAubLBQyPxvn+uDBg48//riu38H8vHPnTr2LjQWn8rONetQmp/Lzo48+anz+U0FBwYIFC9544w2TVrp06ZKUlGS8B7URx9qyric+Pv7cuXNSSp2f27Vrt2vXLvMdLeZnKeXSpUsX3H699NJLJn0TQjz99NM6pnpVfrZ95znz4XvDGvKzp2aB/OwpWf+ql/zsX/Pp56NxV36Oj4/Xl6c6SKbfT/D8ZwfFKOY9Ap7OzxUqVLB4Ntja+WfzN9YW1+jHLJ85cyb59ssYjdQuFStWNLmG2Qb7e++9p7+wrVts27atqlyfhS5kfr558+aiRYtU/X379rWRn1NSUho3bqxK+l9+/vDDD433VK9atapy1v/V90J3JD+npqbG337Nnz/fxhRLKY8cOdK5c2el2qFDB/2wQGvXb58/f173RO31yiuv6E4uWbJErRRCuDE/z5s3T3/H3sZw9P3DLN7vIyMjQ/VTffVX97Njx446ptqoXG/6z3/+o++P/d///jc7O1s/a23AgAG6mHHBWn7WZc6dO6f61qNHD90xIURiYqIq41p+joiI0FNjbeGnn35STZh8bqX7phf09587duzoyHToHb1hgfzsqVkgP3tK1r/qJT/713z6+WjclZ+HDRvmrBT52VkxynuPgKfzsxDCxv3DLJ5/XrRo0Q57L/MMkJqaqnYy3qm7YsWKLVu2NN7zzKL8rFmzjA+p2r59u6pKf9Fa3z+skPn51q3ITp06pTJD3759P/74Y30OVl1HqjZVqFBBPQ5K/ViM+XnIkCHqul/3Xr89aNAgHZz+9a9/7dmzx2ReEhMTVQFH8vOBAwdU4erVqy9evNikKpMf9RvgW6E3MzNTbbWYn3NycvSV2Lce+Prss8/u2LFDP5BJPY9Kj8Kp/Lxu3TobB7hO9SY9N/nRdn7WhX///fcdO3boZ5u7cDtYfd+Bpk2bnj9/Xg/Z5fys+3bixAnl0LBhQyGE48+vioiImDdvnq5HXb9dp04dvcbuguP5WQihv7Jht1ovKUB+9tRE6D8fPP/ZU8R+US/52S+mMVAGQX4OlJlmnG4V8ML8vGPHjsIMMS0tLTU1dfv27fqNvvE+wBZrHjFihC78008/FRQUmBTzUH5+++23VbtLly5Vz+vS3dAL7777rr5jmZSyyK7fHj9+fO3atUNDQ2vWrHnu9kt3qfD3D9P5OSUlxfxZx2PHjtVX0TuVn4UQkyZNMpk7kx/1G2C7+Tk7O1sP+amnnrp8+bJJVfr5VSbnn0+fPq2uZXDq/tsmldv90Tw/P/300//5z38s7njhwgV9VzZnz6bq/KxuwaVMOnbsaPwowdio+fnnXr161a5d28ZUqlsbOJ6fn3nmGeOF6GlpaWFhYcHBwU8++aSxJ3q5adOmtWvXNn7NROfnmjVrmt/tf9KkSWFhYXr2yc9aMtAX9J8P8nOgHwo2x09+tsnDRu8SID9713zQGx8R8ML8/K9//cs8U2VnZw8YMCA0NHTjxo3q5PNvv/0WGhrarVs3Y7zU6idPntRvfx3Pz9u3bzcPz9nZ2X369FG1Ff78c0FBwbZt2249fSo4ODgkJERVq2+wmpqaqrutFkxOqLorP7/77rvqEdxCiJ9++skEfOrUqcHBwaoDO3bsKCgo8ND5Z4s3tRo2bJhGsBG69FzfvHlz/fr1apc33ngjIyPDYuDJyckZNWqUHtfhw4f1XFs8/6zzc8eOHY13t1Lt5ufnq3s+q3aN55/bt28fFBRkfv/tF198Uc34gQMHdNOqtuzs7Oeffz709qtq1ar6xLgeo/mCzs8vv/yyup1efHx8mTJlQkND77rrLv0FByllVlZWRkaGvu7a2fz8t7/9TR+oarAtW7Y0Pp7dpG/m+Vk9U6106dJRUVHGjkkpr1+/npGR0bRpU6fOPwcHB48fP97Ybvny5dUTqjIyMkz+IFy9elU9Tsz4/Krc3Nynn35aDefo0aNXrlxRtd24cePtt9/WB4kqYPFwMrbubcucf/bUjJCfPSXrX/WSn/1rPv18NO7Kz3369LH4AFgbfFy/bQOHTV4u4IX5WQhhcloyPT3deJ8wdVm1/r176qmnzFOWa/l59erVxnRx9erVX3755YUXXlBvo4UQhc/PUkodMFS1NWrU0Dc3Pnv2rG5LCFG1atVVq1YZDyHH8/OQIUOM5+gqVKgghNDPf5ZSDh06VLdlPJeYkZHxyiuv6E179+51+/Or9Pnnf/7zn7+YvfSnFSrbG4dvbXnbtm3GL1TPmzfPrNZfXn/9dT2ou+66y/isMov5OScnp27dumqXhIQEfYydPHnyl19+MU6EyflnfXs8k/PPUkr9Lf39+/frYyk9PX3w4MG6b7/++qu1YRrX6/xcuXLlRYsWqU1NmjRR9dx7771aQD83SwhRt25d4xFurNDGcvfu3XX3hBCtW7e2UVgf3vpzq2effVZ/WNOoUSPdsV9++cVYc4sWLVS1dr//LIRQ3yzQadx4pX3Pnj2NTaivQgQHB3fv3t3Y7b///e/6Mofw8HC1yzvvvGMcqVomPxvdAnqZ/BzQ0+/w4MnPDlNRsPgF3JWfhRATJ050ajz6fTz3D3PKjcLeIFC8+blMmTL6jgNz587VXwYWQmzatGnrnZe+2FII0bRpU3VHXOPvXZ8+fe6U/b//65tjR0REzJkzxzb17NmzIyIi1HvlVatW6arGjh1r8mb6yy+/3LZtm6pt8+bN99xzjyowYcKErVu3mpz4staoDhhq36VLl+qSJvn57bff1pvUgjG2mZyCUwX085+FELNnz9a7m+fn6dOnV61aVfXh66+/1qMePXq0WtmwYcO2bduqTys8dP5ZNWTjv0FBQVu3bv3555/1QKwtbNy4sW3btlFRUTZqU5uio6MPHDhgrGfLli36GUhvvfWWosjLyzP+s9K7d2+1Xj9HzdjQ008/vXXr1rNnz6pq1e3x6tSpo3bRkXjEiBHlypVTO0ZFRamtxvtRN23aVD1w29g9i8s6PxvvH9anTx+Tc8XGTjZr1kx/CmCxTmsrX331VXWCV9XmbH6WUvbp08fkTmzGjqlPdnSwdyQ/q931p0vZ2dktWrQwqdP4Y48ePcxH99JLL+kIbSxsXG7ZsqXumHkN3rmG88+emhfys6dk/ate8rN/zaefj8b4Rsf4fsLBYfP8ZwehKOZnAsWbnxs3bmz0nD17tvEsovFdrFpu06bNkSNH1C5nz561/UheIUT16tXt3jxM1TZr1ixjejc23aRJkzp16ug1ZcqU2bBhg9pr9uzZev2tC1BnzZrlyKmqX3/99cEHH9Q7GvNzenp6x44d1ab69euvXr3a6OPU95+jo6N1P6WU5vlZSjlt2jQdoXV/1EJMTMyWLVt06+7Nz/PmzatVq5ZJi+rHRo0aJSQkmMTgZs2a6Z7YXvj000+NN5AzaaJx48YJCQkWv2A/d+5ck8K3TgufP39ePwDZZGt8fHxCQoK6Mllv+vjjj1X39O3l1XeG1bPK1KaRI0eWKVNG76IXYmNjExIS9OFte5i3TmWr/Hz33Xd/+umnxsL9+/fXZ7lV5TExMQm3X8ZHdhl3cWR59OjRqpKEhATb/8L++uuvqqTxwJZSFhQUmIu1aNFCFTZeAfH999/ff//9TZo0SUhIMD4i6/fff09ISFAPRVdD0/lZSnn27NmEhIS4uDhNqhY6derUs2dPa2N8+eWXExISVMmIiAg9xoSEhOrVq3fo0MHYMWuVeNt68rOnZoT87ClZ/6qX/Oxf8+nnoyE/+/kEMzzPCOj8XK9evWXLlllrZM2aNeotZrt27fTJwJycnFsnOatVq2Y8z6lrGDly5ODbr1mzZumVemHUqFGDBw9+66239Bq18OGHH6q91DdI9Vvhli1bDh482ORGzcePH1eFW7VqpUuqhbCwsMGDB3/wwQcm9dv48YMPPjAJk/Xr1x88ePCGDRuWLl06ePBgdY66ZMmSY8eOVfWY5GchhP4ipY2GpJT6+7p/+MMfTOJcWlraE0880aBBg5UrV5pXos8/x8TEGO/LrUuq889NmjT5+uuv9UqVn8uVKzdlyhTjSinl9OnTK1euXKJECSWp//vtt98aS169elVvWrFihXGTWj5z5owuYLFjJrvMnz9flS9ZsqQQIiIiQv24du1aKeXChQt1bYMHD7Z7VzBj5Z988olxX+Py//zP/xhLGpe3bt2qStarV6979+6DBw++fv26lDI1NVWtb926tbqZvPpRXTl88uRJY/368UijRo1SD46qVauWMTyrFkePHq326t69e7169dTy1q1bjf2xu6w69sknn5iXzMjIMPZKf7vevGTRrzl16pSxbz/++KPFPqSkpBg//TGW+fe//61rMPmDIKXct2+f3qoWzpw5Y9zd4rIqOXPmTOPWDz744MSJE8Y1vrJMfvbUTJGfPSXrX/WSn/1rPv18NORnP59ghucZgVs3SRp3+7V8+XIbLRw5ckQVM4a9vLy8cePG2X3oro1qbWyaMGGCalH997vvvrNReMuWLcbC48aNe++992yUt7Zp3rx5xnpMguKCBQvGjRs3efJkvfvOnTuN5ceNG6fu5KQLWFs4evSo2nH79u3mZX799VfjiTVjgVsPEFI7Wsuot/4Sjhs3ziQ8SyknT548Y8YMY1V6efbs2eYfZOitnl6YPHnyuHHjFixY4OmGHKx/+fLlqamp5oW///77cePG7d+/33yTxTWZmZnjxo3TZ6QtlklNTbX9e2dxL1YiYFuA/Gzbx/Wt5GfX7QJpT/JzIM22z4/VXfm5ffv2+vSagyjG72GOGTPGwb10sb179+pTZ+Znh3QxFhBAAAEEEEAAAdsC5GfbPq5vJT+7bhdIe5KfA2m2fXusubm5Xbp00SlUfTtr2rRp3e+8+vXrp0a4efPm7t27q28Vvvnmm3e2d9fP9qhXr5466TRhwoSjR4+qvU6fPq1LGhd+//337Ozszp0766YbNmzYvXt3fTddKeWFCxeGDx++e/fuWbNmrVy5snv37iZn0oz5uUmTJikpKb49GW7q/c8//2yk9tdla89rdZMi1SCAAAIIBJYA+fn/5tv4yG8p5dKlSz///HPjsXDp0qU4w0t9HWL48OGGdf+7qE6MzJ07V99n0uLzn9955524uDj1pQKTpo2NOrLcsmVL9bayV69ejpT3yzIzZswwmQhf+bFatWo6FbRp06aQ3U5KStq6dauxEnWWLy8vLy4uTsWbr7/+Oi4u7vPPPx83blxcXJy67af5UTF+/HhVz7lz58y3urZm3bp1cXFxxiupVMeMHWbZawWMNxQRQtSqVSsuLs74VcaSJUuqzqubrN59991xcXHqmZD6INcLtWvXjouLq1y5ckxMjNrL4g1XhRCxsbHqS3F6X7XQsGFDbdW8efOwsLB77723WrVqtWvXFkI0aNBAb42LizM+eEMIUb9+fePWgF2Ojo42UfXLH++77z4Hb7fr2l829kIAAQQQCCgBN+TnGTNm1PP9V3BwsHEQ4eHhVapUMa4xudlgeHh4vXr1zO/vFxYWVq9ePeNbxtq1axvrUcvqJo2RkZH16tUzadq8sO01+u1OuXLlbJf0460VK1bUDoG8ULp0aZMbq6pjTD2ar1SpUvXq1VOJvUqVKuoBD1FRURYPDP34h7vvvttiARdW6qaN+wbyfDF2BBAoGoHC3BQ3oN4UMlgEEEAAAbsChc3P8+fP1w/sLpp/BWkFAQR8WqBUqVJlzV6lS5c2Dqp06dImRUz+zoSGhpoUMP6obypr/ISrZMmS+pmNan2JEiVCQ0ON7bJsVyAoKMhIzbJtgTJlygQFBZUuXTo4OLhs2bIhISHq+C9RooQ+CFUNJW+/bNSm7qBr/NWwO1kWC9j+3bHRAZ/eZPFCMLvvkCiAAAIIIICAuUBh87P5cwUs/oPthSsrVapUN+BfQUFBRoNKlSpVqVJFPeg8KiqqTp06wcHBxgJq2Rg5SpUqZV5ArTGf9KpVq+rCxqarVKliMh36OZBly5ZVu6gz9rpOix3TlbPgzQKLFy82/0u0efNmY5/NHzKxZs0aYwHb9+fs0aNH3bp1mzRp8ttvv+m93nvvvddee039eOzYsZiYmAcffHDv3r26AAuOCDzxxBPm08caawK///57fHz85s2bX3nlFSnl+PHj16xZI6Xs2rXrhQsX6tat27VrV7XvggUL5syZY60eKeXUqVPr1q2rH3hz9epVR+bLvIz+wrmNttiEAAIIIIAAAtYECpufV65c2cY3X7bfqVjz8rP1jz76qHFECxcuXLFixauvvtqmTZvU1NScnJwnn3zSWEAtv/jii3rOn3nmGfMCak1cXJwuphbWrVunCxubXrFixcKFC/UmKWVWVpbaZcSIEWr9u+++a6zNYseMNbCMAAIIIIAAAggggAACCLhXoLD52b29oTYEEEAAAQQQQAABBBBAAAEEvFOA/Oyd80KvEEAAAQQQQAABBBBAAAEEvEuA/Oxd80FvEEAAAQQQQAABBBBAAAEEvFOA/Oyd80KvEEAAAQQQQAABBBBAAAEEvEuA/Oxd80FvEEAAAQQQQAABBBBAAAEEvFOA/Oyd80KvEEAAAQQQQAABBBBAAAEEvEuA/Oxd80FvEEAAAQQQQAABBBBAAAEEvFOA/Oyd80KvEEAAAQQQQAABBBBAAAEEvEuA/Oxd80FvEEAAAQQQQAABBBBAAAEEvFOA/Oyd80KvEEAAAQQQQAABBBBAAAEEvEuA/Oxd80FvEEAAAQQQQAABBBBAAAEEvFOA/Oyd80KvEEAAAQQQQAABBBBAAAEEvEuA/Oxd80FvEEAAAQQQQAABBBBAAAEEvFOA/Oyd80KvEEAAAQQQQAABBBBAAAEEvEuA/Oxd80FvEEAAAQQQQAABBBBAAAEEvFOA/Oyd80KvEEAAAQQQQAABBBBAAAEEvEuA/Oxd80FvEEAAAQQQQAABBBBAAAEEvFOA/Oyd80KvEEAAAQQQQAABBBBAAAEEvEuA/Oxd80FvEEAAAQQQQAABBBBAAAEEvFOA/Oyd80KvEEAAAQQQQAABBBBAAAEEvEuA/Oxd80FvEEAAAQQQQAABBBBAAAEEvFOA/Oyd80KvEEAAAQQQQAABBBBAAAEEvEuA/Oxd80FvEEAAAQQQQAABBBBAAAEEvFOA/Oyd80KvEEAAAQQQQAABBBBAAAEEvEuA/Oxd80FvEEAAAQQQQAABBBBAAAEEvFOA/Oyd80KvEEAAAQQQQAABBBBAAAEEvEuA/Oxd80FvEEAAAQQQQAABBBBAAAEEvFOA/Oyd80KvEEAAAQQQQAABBBBAAAEEvEuA/Oxd80FvEEAAAQQQQAABBBBAAAEEvFOA/Oyd80KvEEAAAQQQQAABBBBAAAEEvEuA/Oxd80FvEEAAAQQQQAABBBBAAAEEvFOA/Oyd80KvEEAAAQQQQAABBBBAAAEEvEuA/Oxd80FvEEAAAQQQQAABBBBAAAEEvFOA/Oyd80KvEEAAAQQQQAABBBBAAAEEvEuA/Oxd80FvEEAAAQQQQAABBBBAAAEEvFOA/Oyd80KvEEAAAQQQQAABBBBAAAEEvEuA/Oxd80FvEEAAAQQQQAABBBBAAAEEvFOA/Oyd80KvEEAAAQQQQAABBBBAAAEEvEuA/Oxd80FvEEAAAQQQQAABBBBAAAEEvFOA/Oyd80KvEEAAAQQQQAABBBBAAAEEvEuA/Oxd80FvEEAAAQQQQAABBBBAAAEEvFOA/Oyd80KvEEAAAQTcI5CVlbXc8Dpy5Ih76qUWBBBAAAEEEAg8AfJz4M05I0YAAQQCSeDMmTPC8JoyZUogjZ6xIoAAAggggIA7BcjP7tSkLgQQQAABbxMgP3vbjNAfBBBAAAEEfFeA/Oy7c0fPEUAAAQTsC5jk51atWm3bts3+bpRAAAEEEEAAAQTMBMjPZiSsQAABBBDwIwGT/CyEWLJkiR+Nj6EggAACCCCAQNEJkJ+LzpqWEEAAAQSKXoD8XPTmtIgAAggggIC/CpCf/XVmGRcCCCCAwP8KmOfnqlWrbt68GR0EEEAAAQQQQMBZAfKzs2KURwABBBDwJQHz/CyEKFWq1L///W9fGgZ9RQABBBBAAAEvECA/e8Ek0AUEEEAAAY8JWMzPQog1a9bk5eV5rFkqRgABBBBAAAE/FCA/++GkMiQEEEAAAS1gzM+RkZG1atXST4NOS0vTxVhAAAEEEEAAAQTsCpCf7RJRAAEEEEDAhwWM+Xn48OEjRowgP/vwdNJ1BBBAAAEEilWA/Fys/DSOAAIIIOBhAZP8vGrVqoYNG6oIPWnSpJs3b3q4fapHAAEEEEAAAf8RID/7z1wyEgQQQAABcwGT/CylfPbZZ/Up6EmTJpnvwhoEEEAAAQQQQMCiAPnZIgsrEUAAAQT8RMA8P2/atKlx48YqQoeHh/vJOBkGAggggAACCHhegPzseWNaQAABBBAoPgHz/Cyl/OGHH+rWrSuEKFmy5NChQ4uvd7SMAAIIIIAAAr4kQH72pdmirwgggAACzgpYzM9SytjYWHUKOjo62tk6KY8AAggggAACgSlAfg7MeWfUCCCAQKAIkJ8DZaYZJwIIIIAAAp4XID973pgWEEAAAQSKT8Bafs7MzKxRo4YQIigoqEuXLjk5OcXXR1pGAAEEEEAAAd8QID/7xjzRSwQQQAAB1wSs5WcpZatWrfSNuBMTE12rn70QQAABBBBAIHAEyM+BM9eMFAEEEAhEARv5WUrZsmVLFaE7duz422+/BSIQY0YAAQQQQAABhwXIzw5TURABBBBAwAcFbOfnixcv6lPQ3IjbB6eXLiOAAAIIIFCkAuTnIuWmMQQQQACBIhYgPxcxOM0hgAACCCDgxwLkZz+eXIaGAAIIICDJzxwECCCAAAIIIOAuAfKzuySpBwEEEEDAGwVs5+esrKzRo0erS7ibNm36zTffeOMY6BMCCCCAAAIIeIcA+dk75oFeIIAAAghYFzh37lxPw2v9+vXWy5pusZ2fpZQZGRlvvPGGitD33Xffpk2bTKvgZwQQQAABBBBA4LYA+ZkDAQEEEEDA2wWOHz+u7/IlhKhfv35KSoqDnbabn6WUKSkpuv6GDRtu27bNwcophgACCCCAAAIBJUB+DqjpZrAIIICATwqY5GchxPLlyx0ciSP5OTMzc+rUqTpCJycnO1g5xRBAAAEEEEAgoATIzwE13QwWAQQQ8EkB8/wcFhb23XffFRQU2B2PI/lZSrls2TLys11MCiCAAAIIIBDgAuTnAD8AGD4CCCDgAwLm+Vll3ZSUlJs3b9oegIP5ee3atZUqVVLVLlq0KCcnx3a1bEUAAQQQQACBABQgPwfgpDNkBBBAwMcErOVnIcSlS5dsD8bB/CylnDlzpj4FvWTJEiK0bVi2IoAAAgggEIAC5OcAnHSGjAACCPiYgDE/33PPPY8++miNGjVU1rX7RWjH8/PatWvvueceHaEXLVqUn5/vY1J0FwEEEEAAAQQ8KUB+9qQudSOAAAIIuEPAmJ/HjBkjpezZs6cKusHBwV988YWNRhzPz1LKlStXNmjQQEforKwsGzWzCQEEEEAAAQQCTYD8HGgzzngRQAAB3xMwz8+ffvrpXXfdpYJuhQoVFi1aZG1UTuVnKWVSUhL52Rom6xFAAAEEEAhwAfJzgB8ADB8BBBDwAQHz/CylXL58eUREhMq6ERER8+bNszgSZ/Pzxo0bGzdurKp95ZVXLNbJSgQQQAABBBAITAHyc2DOO6NGAAEEfEnAYn6WUn711VdhYWEq6z766KMWh+RsfpZSxsfHqzpDQkJefvlli9WyEgEEEEAAAQQCUID8HICTzpARQAABHxOwlp9v3TS7cuXKKutWqVJlypQp5gNzIT/v2bOnUaNGqtr69eub18kaBBBAAAEEEAhMAfJzYM47o0YAAQR8ScBGft67d68KukKISpUqvffeeyYDcyE/SylbtWqlqi1VqlSfPn1M6uRHBBBAAAEEEAhMAfJzYM47o0YAAQR8ScBGfi4oKNizZ0+JEiVU3C1btuycOXOMYzPm55dffrmgoMC41dry5cuXo6KiVJ0PPvigtWKsRwABBBBAAIGAEiA/B9R0M1gEEEDAJwVs5Gc1nt27d+uz0OPGjTM+d8qYn4UQFq/xtojSokULVWfLli0vX75ssQwrEUAAAQQQQCCgBMjPATXdDBYBBBDwSQG7+fnQoUN169bVEXrixIlXr15VQzXm56pVq9p40pU5zQMPPKDq7NChw6lTp8wLsAYBBBBAAAEEAkqA/BxQ081gEUAAAZ8UsJufpZQ7duxo0qSJjtCTJ09WEdqYn4cPH+7U+DMyMnSFgwYNcmpfCiOAAAIIIICA/wmQn/1vThkRAggg4G8CjuRnKeWWLVtiY2N14t2/f7+UsjD5+fr16926ddOnoPfu3etvsowHAQQQQAABBJwRID87o0VZBBBAAIHiEHAwP0spJ0+erPPz8OHDr1+/Xpj8LKU8evSornDs2LHFMXraRAABBBBAAAFvESA/e8tM0A8EEEAAAWsCjufnn376qW3btjrxDh48WOfn2NjYlJQUa01YW3/58uVBgwapCv/whz9s377dWknWI4AAAggggIDfC5Cf/X6KGSACCCDg8wKO52cp5c6dO9u0aaMjdM+ePdVy7969XYP4/vvvdW2tW7fetWuXa/WwFwIIIIAAAgj4ugD52ddnkP4jgAAC/i/gVH6WUu7du7dZs2Y69BYyP1++fPm1117Tta1atcr/xRkhAggggAACCFgSID9bUmEdAggggIA3CTibn6WUf/zjH3XiLWR+llKuXLlS11anTp09e/Z4Ew99QQABBBBAAIEiEiA/FxE0zSCAAAIIuCzgQn6+ePFio0aNdOgVQrh8/baUMisra9KkSbq2H374weWxsCMCCCCAAAII+K4A+dl3546eI4AAAoEi4CG6UM8AACAASURBVEJ+llLm5+cbI3RCQsK1a9dcJvvoo4/Kli2rIvTXX3+dn5/vclXsiAACCCCAAAI+KkB+9tGJo9sIIIBAAAm4lp+llAUFBfqksRBi+PDhhVEbO3asru3o0aOFqYp9EUAAAQQQQMAXBcjPvjhr9BkBBBAILIHC5OcHH3xQh94///nPqampLtstWbIkMjJS1fbxxx/n5eW5XBU7IoAAAggggIAvCpCffXHW6DMCCCAQWAIu52cpZXp6eteuXXWEnjJlSmHsXnjhBV3VlStXClMV+yKAAAIIIICAzwmQn31uyugwAggg4JMCFy9eXLFihWtdL0x+llKmpaX97c5r06ZNrvVB7bV8+fJ77rlHReh33323MFWxLwIIIIAAAgj4nAD52eemjA4jgAACPilw8ODB2rVrjxo1Kjk52dkBFDI/O9uc7fI9evRQ+blMmTK2S7IVAQQQQAABBPxMgPzsZxPKcBBAAAFvFLh69aqOncOGDXO2i16Vnzdt2qROQZOfnZ1HyiOAAAIIIODrAuRnX59B+o8AAgj4gMCFCxf014br1KnzxRdfONVpr8rPUso//OEPQoigoKD+/fs7NRAKI4AAAggggIBPC5CffXr66DwCCCDgGwLG/CyEqFWr1tq1ax3vurfl58OHD0dFRQkhSpUq1bdvX8cHQkkEEEAAAQQQ8GkB8rNPTx+dRwABBHxDwCQ/CyHCw8PvuuuuPXv2ODIAb8vPUsr69eurM+qtWrVyZAiUQQABBBBAAAE/ECA/+8EkMgQEEEDA2wXM87MKnyVLlty/f39BQYHtAXhhfr5x40a5cuWEECVKlOjRo4ft/rMVAQQQQAABBPxDgPzsH/PIKBBAAAGvFjDm50qVKoWHh+uvQwshDhw4YLv3XpifpZTly5dXo2jfvv2ZM2dsD4GtCCCAAAIIIOAHAuRnP5hEhoAAAgh4u4DOz9WqVZs5c+a8efPatWunU3TZsmV37txpYwzemZ87deqkPwV4/vnnbfSfTQgggAACCCDgHwLkZ/+YR0aBAAIIeLWAzs+JiYm6o/Hx8Tp/1qhRIyUlRW8yWfDO/JyTk/Poo4+qIXTo0MHuWXSTQfEjAggggAACCPicAPnZ56aMDiOAAAK+J2AxP8+ZM+fFF19U3yIWQtSrV+/999/fvHmz+fC8Mz9LKY0d69Kly969e807zxoEEEAAAQQQ8BsB8rPfTCUDQQABBLxXwGJ+Vt2dMWNGcHCwPhE9aNAg82EYY+qYMWPMCxTXmsuXL//1r3/VnZ85c2Zx9YR2EUAAAQQQQKAIBMjPRYDs2SauXLkyYMCAadOmebYZakcAAQQKIWAjP0spZ82apSNodHT0gAEDvvvuO2NrXpufpZQ//fST7jz52ThrLCOAAAIIIOB/AuRnn59T9e27qlWrTp061ecHwwAQQMBPBWzn59zc3NmzZ+sUKoRo2rTpjz/+qDG8OT9funRp9OjRqvMxMTHdunXbv3+/7jkLCCCAAAIIIOBPAuRnn5/NEiVKqPdtVapUmT59us+PhwEggIA/Cuj8XKVKlffee898iFlZWXPmzDFG6IYNG+7bt0+V9Ob8LKVct26dsecWv8JtPmTWIIAAAggggIDPCZCffW7KTDus87MQokKFCrNnzzYtwc8IIIBAcQvo/CyEGDZsmMXuZGVlHTt27M0339RZtGbNmr/99pvJbbq86vvPaiCZmZkTJ07U3SY/W5xfViKAAAIIIOAHAuRnn59EY34WQowdOzY3N9fnR8UAEEDAvwQcyc9qxLm5uW+88UZISIiKo2XKlDlz5syBAwd0OvXC/CylzM3Nff3111UnQ0NDy5Yte+LECf+aQ0aDAAIIIIAAApL87PMHgUl+FkJ89NFHPj8qBoAAAv4l4Hh+VuMeOHCgDswmC96Zn6WU48ePN3Y1JCTEv+aQ0SCAAAIIIIAA+dn3jwHz/Pzqq69evnzZ90fGCBBAwH8EnM3PU6ZMCQ8PN8ZRvey1+Xnx4sU1atTQ/QwODt61a5f/TCEjQQABBBBAAAFJfvb9g8A8PwshxowZQ4T2/bllBAj4j4DOz7Vq1VqwYIEjA5s8ebLFCO21+VlKOXToUJ2fhRC1atVyZKSUQQABBBBAAAFfEeD6bV+ZKav91Pm5fv36cXFx+q3bqFGjrl69anU3NiCAAAJFKKDzc/PmzX/44QcHW54yZUqFChX0nzW14M35+Ysvvhg4cGDNmjVVVytVqrRixQoHB0sxBBBAAAEEEPB+AfKz98+RnR7q/NyrV69t27Y9+OCD+r0md6+xY8dmBBAoKgGdn23cf9tiX6ZPn16yZEn9Z01dX2OxpPes/Oijj6pUqaL6XLNmzU8//dR7+kZPEEAAAQQQQKAwAuTnwuh5xb7G/CylHDVqlH6j2adPH+7F7RWTRCcQCHgBnZ8feOCBrVu3OuUxb94840OtvPn8sx7XZ599VrZsWfXX+K677vr444/1JhYQQAABBBBAwHcFyM++O3f/13OT/Lx///727dvrCN27d2+fHyEDQAAB3xfQ+TkxMdGF0WRmZq648zpw4IALNRT9LqtXr9Z/imvXrp2QkJCcnFz03aBFBBBAAAEEEHCjAPnZjZjFU5VJfpZS9u/fX79pq1SpUvF0i1YRQAABg0Ah87OhJp9ZvHnz5qpVq/RfYyHEtGnTfKb3dBQBBBBAAAEELAmQny2p+NQ68/x85syZhx9+WL1pCwoK6ty5s08NiM4igIAfCuj8XK5cufHjx/vhCC0NKTc31xihq1atunbtWksFWYcAAggggAACviFAfvaNebLRS/P8LKXMzMxs1aqVitANGjTIycmxUQObEEAAAU8LXLhwoVSpUuqPUpkyZaZPn+7pFr2k/vz8/FWrVulboJUpU+abb765efOml3SPbiCAAAIIIICAUwLkZ6e4vLGwxfysOnrXXXepd6stW7Y8f/68N/aePiGAQGAI5Ofnb9y4UQhRtmzZsWPHBsag/98ov/zyy0qVKqk/yEKIDRs25Ofn/7/NLCGAAAIIIICAjwiQn31koqx300Z+jo+P11s7dOjw22+/Wa+GLQgggIAHBVR4FkK4dv8wD/asqKr++OOPq1evbozQRdUy7SCAAAIIIICA2wTIz26jLK6KdELu1auXeR8ef/xx/XbtxRdfNC/AGgQQQKAIBLp27ar+FrVt29ZXbqDtdpYFCxbUqlVL/01OTk7evHmz21uhQgQQQAABBBDwnAD52XO2RVRz79691bsxi/k5MzMzISFBFWjfvv2CBQuOHDlSRD2jGQQQQOCOwNWrV//0pz8JIerWrfv555/fWR1w/58/f35kZKSO0DExMQFHwIARQAABBBDwZQHysy/P3u2+nzt3zkZ+llKeP3/+mWee0W/XunXr9p///Mfnh80AEEDA1wQOHjwYyNdv6+n66KOPRo8eXbZsWSFE9erVP/vsM72JBQQQQAABBBDwcgHys5dPkP3u2c3PUsq0tLR+/frpCP34448fP37cftWUKBKBDz/88OTJk0XSFI0gUGwC165dUxfLNGjQYOXKlcXWD69peP78+epv8l133TVs2LDVq1d7TdfoCAIIIIAAAghYFSA/W6XxlQ2O5Gcp5ZdffqnzsxBi+/btvjJAP+7np59+mpiYWKNGjc6dOycmJnI/Xj+ea4aWk5Pz7rvvqr9Cw4YNA0RKOXfuXP1nuWHDhjwamqMCAQQQQAAB7xcgP3v/HNnpoYP5+dy5c0OHDtXv1R544IHTp0/bqZrNnhRYvny5fsCYmpe8vDxPNkjdCBSzgLp+WwhBflYzcePGjYULF+o/y/Xq1duwYUMxTxLNI4AAAggggIBNAfKzTR5f2Kjzc4UKFSZPnmyjy5cuXRo4cKB+r1a/fv3r16/bKM8mjwpcvHjx0KFDTz75pJ6Re++9Nzo6um/fvh5tl8oRKC4B8rO5fHZ29oIFC/QfgZo1a27ZssW8GGsQQAABBBBAwEsEyM9eMhGud0PnZyHESy+9ZLuiN954Qz/vSggRFRVluzxbPS3w7LPP6rfOaiEkJOS5557jWm5Py1O/CwKnTp2qVq1a+O3XuHHjbt686XglZ8+erVixojrIOf9sdLtx48bcuXODgoIUTvny5Xfv3l1QUGAswzICCCCAAAIIeIkA+dlLJsL1bjiVn6WUI0aMCA0NVW/UwsLCXG+YPd0hYJ6f1dT079//6tWr7miBOhBwp8CuXbvUISqEGDt2bFpaWnZ2tiMNGJ97TH42F5s3b165cuW07a5du4jQ5kqsQQABBBBAoNgFyM/FPgWF7YDOz5UrV3733Xcdqe7ll19Wj04JDQ09cOCAI7tQxkMCOj/fd999MTEx+t2zEGLw4MEXLlzwULtUi4BrAsb8rA7XOXPm/Pzzz7m5ubYrvHz5cnR0tNqF/GzRasaMGeHh4fqPwO7duy0WYyUCCCCAAAIIFKMA+dmD+Lt3705PT/dgA7er1vm5V69ejrfVpk0b9S6tRo0a69ev//nnnx3fl5JuFND5eenSpRkZGV27dm3ZsqV+Az1s2LD169cXwVHkxhFRlX8LmOdndbguW7bM7sD5/rNdoqlTp1atWlWRlitXju9C2xWjAAIIIIAAAkUsQH72FPi2bduaNWv22muvefoqXJ2fW7duvWPHDgfH89ZbbxmvFXzggQe2bdvm4L4Uc6OAzs9CCHX/7cOHDz/00EM6QgshXn/99WvXrrmxUapCwGUBnZ/vu+8+fT5ZHa5ffPGF7WrJz7Z91NapU6fqs9A1a9bkjtyOoFEGAQQQQACBIhMgP3uKesCAAeo95T/+8Y/33nvPU81IqfOzI/cPM3Zj8uTJISEhOqe1atVq69atxgIsF4GAeX6WUu7Zs+ePf/yjnhohxD/+8Q+718cWQW9pAgGdn0eNGpWcnDxy5MjatWurY7VcuXJvv/22jRRNfnbw+JkxY4b+fLNu3bo8F9pBN4ohgAACCCBQBALkZ08h6/wshChZsuTEiRM91JLL+VlK+c477xhDWuvWrYcPH753714PdZVqzQUs5mcp5c8//2wSoYcNG+a5o8i8Y6xBwKKAMT+rAl9++WX16tX1X5LatWsPHz583bp15ruTn81NrK0x3pG7YcOGq1evtlaS9QgggAACCCBQlALkZ09pG/OzEKJcuXK9e/f2xInowuTn3NzcadOm6Te+aqFdu3ZHjhzxlAv1GgQ+//zzunXran91/bbevmfPnocfflhvVUfRm2++qQuwgEDRC5jnZynlV1999cknnxiP1ejo6K+++sqke+RnExDbP86dO1eTNmrUaM2aNbbLsxUBBBBAAAEEikCA/OwpZJP8rN4GVatWrWPHjkuWLHFjq4XJz7ceZ3X9+vWNGzeOHTtWv1ETQjRv3rxjx45859aN02Sxql9++aVjx45a3iQ/SykPHTq0cePGRo0a6TIVK1bs2LHjzJkzLVbISgQ8LWAxP0spCwoKvvjiC32gCiEaNGjQsWPHnTt36i6RnzWFIws3btxYuHChJr3nnnv+53/+x5EdKYMAAggggAACnhMgP3vK1mJ+Vu+EIiIiHLlXrYM9K2R+Vq1kZGTs27dv0KBB+r2aEKJZs2YO9oFiLgtYu37bWOF///vfmjVrGqcmPDx89uzZxjIsI1A0Atbys5QyNzd3+fLlxgNVCFGnTp3Dhw9LKS9fvtygQQO1ledXOThZ2dnZxghdq1atlJQUB/elGAIIIIAAAgh4QoD87AnV/63TmJ+PHz/+448/Gt9Wli9fPjk52S1t6/zco0ePQt7r+9q1a/369TP2MyIionPnzm7pJ5VYFHAkP0spz58/f/ToUePUhIWFRUREfP311xarZSUCHhKwkZ9VhD579uz7779vPFbDw8MjIiKqVaumV5KfHZ+dGzduGC/krlixIs+FdlyPkggggAACCLhdgPzsdtL/q9CYnzMzM6WUO3bsqFixon4HqRa2bdt28+bNwnRC52ennv9su8Unn3wyODhYd7Vjx44ZGRm2d2GrawIO5mdV+bFjxyIiIkyOouTk5LNnzxbyKHKt8+wVgAK287MRZNy4caGhofrPiHGB/GyEcmR5/vz5YWFh2nDnzp0FBQWO7EgZBBBAAAEEEHCvAPnZvZ7/rzbz/Cyl3LRpU0xMTEREhH4bJITYtm3bvn37jh49+v92dmZJ5+dHH3309OnTzuxqq2x8fPx9992n+9m9e/d9+/adP3/e1j5sc17Aqfysqt+4cWNkZKSeGrXw448/Ot84eyDgtIDj+fnW6ejRo0fHxMSYp2jys9PuUs6aNaty5cr6F3/Xrl0uVMIuCCCAAAIIIFBIAfJzIQGt7m4xP6vSn3zySVRUlH4bpBYaNmz473//22p11jfo/Ozs85+tV/l/W27cuNG2bVtjP1944YWNGzdeunTJ7r4UcFDAhfwspVy3bl3Hjh1r1aqlZ6dUqVIbN27csWOHg+1SDAHXBJzKz6qJgQMHGu+TJ4To3r37xo0b09LSXOtDwO41bdq0qlWrqt/6MmXK/PDDDwFLwcARQAABBBAoLgHys6fkjfnZ/IbbixYt6t27t/ELgep+Xdu3b3e2Q57Lz1LKCxcu9O7d+5FHHtE5TQjx6quvpqenO9tPylsUcC0/q6oWLVpk8kFMvXr1Nm/ebLEhViLgFgEX8rNq96mnnjL+Gbn//vs5Vl2YkalTp1apUkVJVq9e/ZtvvnGhEnZBAAEEEEAAAZcFyM8u09nZ0Zif//73v1ss/f7771eqVMn4nrJVq1ZTp079+eefLZa3uNKj+Vm1eOjQoU6dOhn7+corr1y/ft1if1jplEBh8rOUctGiRcOHDzceRY0bN546der333/vVDcojICDAi7n52vXrg0fPvzPf/6zECI2Nvbbb791sEWKmQhMnz69QoUK6g9ynTp1pk6dCqYJET8igAACCCDgOQHys6dsjflZ3T/MYkvz58+fMGGCMZoKITp06LBnzx6L5c1XFkF+llLu27fv7bfffvDBB3VXhwwZMn78ePP+sMYpgULmZ9XWvHnzSpUqpadGCNGmTRsitFMTQWEHBVzOz6r+1NTUW39JyHsOalsrNmfOnJCQEP0r36xZs5EjR7pw+ZK1+lmPAAIIIIAAAtYEyM/WZAq73sH8LKXMz89fvHjx66+/rt8MCSEeeuihvn37OvL9wKLJz4pjx44drVu31v0sU6bMa6+9VlipwN7fLflZSvnpp5++++67emqEEK1atfrpp58CW5fRu1+gkPnZ/R0K1Brnz59v/H0XQrRu3bpv376//PJLoJIwbgQQQAABBIpCgPzsKWXH87PqQXp6+vr16//2t78Z3xK1bdvW7oOjijI/Syn37Nmzfv362rVrq36WL1++a9eu7777rqcc/b1ed+VnKeX169enT59uPH7uv//+rl27njhxwt8VGV/RCZCfi87aZkt5eXnrb7/GjBlj/K1v3bp1165dbVz0ZLNWNiKAAAIIIICAHQHysx0glzc7m59VQxcuXPj59qtz587qLVFMTExsbOzTTz9trSc6P3fp0uXUqVPWirl3/aFDh3bu3KnftIWHh8fefn311Vfubcjva3NjfpZSZmZmquNn0KBBenaio6NjY2O7dOni95gMsAgEyM9FgOxUE+np6eq3Xn23XP3iN23aVP1N5lFhTmFSGAEEEEAAAbsC5Ge7RC4WcC0/68YuXbr0hz/8QUegkiVLRkZGWnwnpPNzmTJlxo4dq2vw9EJBQUFaWto///lP3UkhRKVKlSIjIw8ePOjp1v2mfvfmZ81y5cqVtLS0+Ph4PTtBQUGRkZG9e/fWZVhAwAUB8rMLaEWzS3p6elpaWosWLfRvvRAiNDQ08vZr4cKFRdMNWkEAAQQQQMC/BcjPnprfQuZnKWVeXl5cXFx4eLh+M1SiRImhQ4devHgxJydH9/vIkSOqQGJiYn5+vl5fNAsFBQW5ubmfffZZ2bJldT+Dg4MPHjzIY6IdmQIP5WfVdH5+fnx8fHh4eIkSJdTslChR4i9/+cvFixezsrIc6R5lEDAK5Ofnb9q0SR1Lo0aNMm5i2UsE8vLycnNz77777vDwcH2bbiFEUFBQSEjIunXrLl68ePPmTS/pLd1AAAEHBW7evHnxzosvaDiIZix2/fp15Zebm2tc797l5s2bh4SEnDt3zr3VFqa2a9euderUKcSZ15///OfCtBgI+5KfPTXLhc/Pqmd5eXnR0dF169bV6VQIMXny5GvXrqkCOho99thjZ86c8dR47NX70UcfRUdHV6xYUfezUqVKv/76q739An27R/Ozxm3Tpk2DBg301AghRowYwUO8tQ8LDgqcOHFCH0XkZwfRirHY3r17o6Oja9asqWdNLWzbto3bjBXlvOTn5x+y8rpx40ZR9sQ/2jpy5Iji9KG7e/z666+qz8eOHXNtFi5duqR/kf/yl7+cP3/etXoCdi99m95t27a5BSE7Ozs1NdWkqmbNmgkhqlSpYrK+GH80vs/Uh5DthT/96U/F2GGfaJr87Klpcld+Vv07evRo06ZNjYf7O++8k5KSkpOTo/OzEOKll17y1Hgcq3fixImVK1fW/axTp05KSgqXc9vAM/5dy8vLs1GykJvOnz/fvHlzPTVCiFdffTUlJUV/EFPI+tk9EATOnj2rjyLys6/M+Ndff/3II4/UqlXL+OtfpUqVlNuvw4cP+8pAfLSf27ZtS05ONuIblz/99NMtW7b46NA82u3r16+rQzQlJeX48ePGtsqXL68Mn3jiCeN6b16Ojo5WfY6NjXWtn8b8LITo37//6dOnXasqMPfS+fn9998v/CV4OTk58+fPb968+aFDh4yeXpifJ02aFB4e3rx5c5MHnRr/EKnlhx566JHbr9dff904KJbNBcjP5ibuWePe/KxufJ2YmHj//fcbj/g5c+YYfyz2/CylnDhxYmJiYmhoqO5YXFzczz//7B5Wv6ulyPKzlPLYsWOJiYmtWrXSUyOEmDJlSnZ2tt+5MiBPCfD9Z0/JerjeRYsW3XXXXcbffbXcrl27ZcuWHTlyxMPtB2j1//znP6tUqWLOblxTqlSpZcuWbdy4MUCNrAz76NGjWsnk3i6BmZ8/+ugjDaIW5s2bZwWP1RYEdH7+4x//WPirNX///Xc1C88884yxsZEjRyYmJiYlJRlXFvvypEmTjh8//sILLyTeecXFxan+t2zZ8s66RC6HcXymyM+OWzlX0pifp0+f7tzO1ktv2rQpNjbW5G+o/tEb8rPq+2uvvaZ7JYR4+OGHZ8yYwYlo84ktyvysWv/pp5+Mt6YTQowfP37+/PnmfWMNAuYC5GdzE19Zs3jx4mG3X0OGDDH+fRZCdOvWbcaMGebXIvrK0Lyzn+vWrTN+ZqFuAqqmQP23Ro0aeiLuvvtuHmBhnEcb+XnEiBF9+/atXr26DwXIwp9/LlmypD5a1IIPDd84s8W1rPOzW67ftpafi2t0zra7bNkydRQtWLDA2X0pL6UkP3vqMDDm53LlyrmxmW+//dbkLLT6HWjatKlXfYA9ceLEoUOHGv/cP/bYY6PvvDx6/wY3anu6qqLPz1LK7du3T5gwwXgUlS1bVs3M8uXLPT1k6vdpAfKzT0+f6vzNmzcnTJgwePBg499nIcTTTz89evToq1ev+sEYvWEIjz/+uBIuXbr0hAkTPvnkE5NeLVmyxPiNp27dupkUCOQfbeRnKWV6evqiRYt8yMcT+fnRRx81uXjYh0CKvqvek59ff/310aNHO/7xR3Jy8v79+90r5qH8nJaWtnjxYvd21TtrIz97al6M+dnxXxIHe7N58+YFCxZERUUZ3/306tXLwd2LrNilS5f+/ve/Gzupl/v16zd69Ogi64nXNlQs+VlpbN68Wf+LruflnnvuSbr9+uGHH7wWjY4VowD5uRjx3dv0hQsXFixY0L9/f/3rrxZ69erlPZcyuXfIRVybzs82Hh72xRdffPDBB0q+du3aS5YsKeJOem1ztvOz13bbWsf0v7auff/5lVdeUTe7adCgwcCBA/Xv7Nq1a621qNe/+uqr6p919V+78WbDhg3G8klJSZ67Y/+QIUOSkpLGjx+ve6sXXn/99aSkpOHDh+s1hVxwJD9/+OGHeuwjRoyw1uLNmzd79eqlZuGee+4xnngYN25cUlKS8Wk43377bVJS0tatW1VtI0aMCAoKEkJUr15dtbVu3TprDX333XdJSUmNGzdu3769KvzXv/5VSvnbb7+pH1esWGFtX9vrHc/PH3zwgWorKyvr/PnzajkpKWn16tXGJoYNG5aUlNStW7eoqChdJikpyfaVp9OnTzcWTkpKmjNnjrFavXz27FmTkurHs2fP6jJFuUB+9pS2MT976EkD3333XaVKlSpUqJB8++Wd3zG+cOFCcnLy888/r//c64WwsLD4268PP/zQU9Pg3fUuWrTI+CGIR+8fZlFi+/btycnJxrum69m5//771excuHDB4r6sDEwB8rOfzfvJkyeTk5O7deumf/eFEKVKlYqPjx8zZoyfDbbIhrNkyZL4+PiIiAilavseE5mZmRp/wIABFjt59OhR9QfZdsBetWpVfHz8pk2bVCXPPvus2kv91/yj/MzMTLVp0qRJFts9c+aMrsHk/Hlubq7epBc2b95ssZ7Vq1fb6NjcuXNN9vrTn/7Uvn17zdKwYcP4+Hh92W1OTo5q8a233jLZUT37U/dHL6SkpJiXlFKuWbMmPj7+22+/VVv79u2rd/n/2DvvgCqO9f0PgnQBCygaC6hgVBJFUVRQrLEQS+wtFowoaiwhxBY1tliIPT+viVGTWKPRa42xRwV71IgtlqBBbMhFRRAQ5udlru93snvO8XA4B4Hz7B8wOzPvlM+7u2ef3dmZ4OBgdcPkQnbu3ClnFuGBAwfKeSicS/0sbhXKlSsXFRV1586dwYMHCzh169bVMXnBzJkzg4ODHRwciCRj879gXAAAIABJREFUrHz58sHBwRo12+nTp4ODg6mpZNWuXbuwsDDqC+d8wYIFor8apwFfvHgxkaGDPzo6miIpYGVlxRhzdnYWMeLwnjNnTnBwsKOj48vlZmxsbIKDg9XTWY0YMUKYKBpGjezfv39wcHBoaCjF6NDPv/zyiyhNXq3A1tZWRC5YsIAK4ZyHhYXRozGByNPT8+eff+acT5o0Sawa2KNHDzJZsGABY+ydd94RpdnZ2RFYERCHd3R0NJmIwLFjx3x8fBSZLSwsgoODAwMDRfxnn32msNJzV3/93KlTJ1FX69atmzVrRu2RfyCGDBmi/r5A5Kxfv75i/j/RwpUrVwYHB7u6ulKBIuDu7h4cHLx+/Xq5I8+ePZMvCLJJ06ZNTSSy5Aaow9DPaibGickD/cw5//333/OnbFZAvHv37onsrVGjRvJxL8Jubm5+2Zu2n15FaYVm99atW23btiUgea+fBckzZ84I7yxatIgaQ4F3333Xz8+va9euhQY7OpIbAtDPuaGXb21v3bp14sQJxeSCTk5Ofn5+8+bNy7fNzrcNGzt2LF1CGWMkITQ2mPRz48aN1TeazZo18/Pzq169uijQ3d1d/FyePHlSXdrcuXMZYx4eHiKP4o62dOnSijHPSUlJotjixYvPmjVLXeDNmzepI/LtMudc4+2sp6enn5/ftWvX5KJ27dolvgPX1jBxDyC/SpWnIKUGVKlS5dy5c5xzEg8a59+Wb/HJVjTszz//1NawqKiovn37KoiJhm3ZskW24pyfO3fOz8+vYsWKVD4FrK2t/fz8Ro8erTAhUWrA+2dqWLVq1USx8o/1sWPHFHWJ3VmzZslfB1ALRaBChQq//vqrbHjlyhUvLy9FNtq1s7MbOnQo5adxKxqXENN4A7x582YqTVtAHN4lSpRQZHByclLMIUcfoNWoUYNaJQfEIefl5UWR2vTzwYMHK1WqpKhR3i1VqtSSJUuonBo1asipIjxnzhzO+XvvvSd25fWrhH6WTY4cOXLixIlly5bJkYrXuX/88Ye87OiMGTPEfRpNnids81I/y61t377933//LZiEhoaKE9bV1VU08sSJE8OGDaP8NWrUSEhIIICc89WrV8uzP2zfvv3EiRPr168nE8WQhMePH4ukJk2aUBVBQUEi0t/fXy48b8LQz6birPHyYarKCk659+/fj83eNE6j7+rqWiF7eyMPk94IxTc4flvd35SUlNjY2AkTJtAljAJWVlYVKlTQ9qBXXRRiCisB6OfC6lnO+b1792JjY0uVKkUnPmOsWLFiFV5tRv8Gr7DClPVzVFRUVlaWjp5mZmaKn8X79+8rsjVt2lReolL2i5ubW4UKFRTjg4R+lrO5uLjs2bOHYlxcXNatW0e1kH5mjMnqiDKQfu7Ro8d//vMfEd+1a9cKFSqIMaiMsaCgoDlz5lAVjDF3d3e5YT/++KOcqi0sz2OkUT8zxsSHRSQhFPq5W7ducsPUFbm7u8vvS58+fUq/d25ubhpvSxhjJUqUkCeXuXnzZunSpdWFyzF2dnaK0b+50c++vr6MMScnp7i4OOGCx48f0yyAZcqUUYvY+fPni/e3olV//PGHOMZiY2Nnz54tIkuVKkUfat27d0/WM+PHj6f89IawWbNmdGAYRT/v379f1LJ161aZngj/+uuvsbGxJ06cELsODg7Tp0+nBhhRP2/ZskVU8cUXX1CvY2Njo6KiqFXyeo137tyh8yIgIECYJCUliUuoeNSlQz8fPXpUXBDE8tFTp04Vtbi6up46dYo6eOzYMap9ypQpdFd8/fp1in/5bC6P9fNbb70l+kt6OCwszMbG5uVMtJaWlqSoOedJSUmxsbE0skkxyvqrr74SvVi5cuXL207x9ig9PZ3eijs7O69du5ZoiEcJvr6+8kVSXpa1YcOGlDlvAtDPpuIM/aybbGpqakpKyoEDB5yyN3H60UXBxsbG1ta2UaNGSdmb7of3uivK56n5Sj8LVhkZGSnZW8eOHYV3yC9FihSxzd6WLFmS7Zkk030Wlc8dZ7bNg34u9K5PTU29ffu2k5OTvb09nfsiYG1tbWtrW7p0aXH6i7+F+PpssK9JPx85ckS3eNZRRfPmzYV4fvvtt8U1WfwNDw+n16S2trZyCbJ+dnBw+Ouvv1JTUzMzM1NSUtauXStEqZWV1Y4dO4RVVlbWH3/8IZw7cOBAhSuTk5Ppp1keWN64cWNhUq1atZSUlLS0NPGrER4e7uTkZGlpyRiTX0Er9LODg8PNmzepR99//70oTW5YamrqhQsXRDxjbPz48SK/+MXRpp+bNGkiTLy9val8ERgwYIBomI2NzePHjwka3cczxhwcHG7cuCEbRkZGigLXrl1LA8Tow2xra+upU6fK+RMTE0m19u3bV+ZpsH5u3769OAyKFy9OzX45TJ2UP2NMMWzh+fPndAQ6ODjExMTIB+Hy5csJ7P79+1+OOs7Kyrp8+bKI7N27d0pKCnWWc56amiqSGjdu/OzZMxHTu3dvEamW7pxzjTfA8vtnOzu7AwcO0P3DyZMnqUm2trZr1qxJSUkRqVlZWcePHxep4eHhRMBY+vnYsWPibLKxsVF84JCVlXX06FFRtaWl5cKFC6n2rKwsIaFbtmxJkSKgXv9Zfv98+PBh2Rec86+//pr6To8z/vrrL/E0p2jRopMmTZLdkZWVRUdgHutnNzc3+ZAW/e3Xr5+4UdS4GjkdJzY2NgRqzZo1Ytz+smXL5A/FOecvXrz44YcfBBBaF+bJkye2traenp7Pnz+nQkTg+fPnnp6eIn9AQIAi1aS70M+mwqvx8mGqygp+uQsWLKiavWl86jx06NCr2Zu4dhf87v5fD/Khfv6/xr0KVatWTXhHfj4tLlj79+8XrtH4I/qqAPwvPASgnwuPL1/Xk6ioKHHiV61aVXzUR/d5cmDkyJHiIiD+0j3x64ovzOmkXjSOstan53fu3Klbt674Fl2df/To0eIrSgsLCzlV1s+///67nCS+WRWOW7p0Kd0HX716lbw5ZcoU2eT8+fMiycHBgQZvU8OKFi0qZ6Zw8+bNhRXFyPq5bNmyivmE6I0TY2zbtm1kJYuEyZMnUzznXKN+jo+P9/PzY4xZWVnJmSncr18/oUnc3NwokvRz2bJlL1y4QPEisHDhQoJz/PhxESka5uDgMGnSJEX+zMzMAwcOkIk8SarB+rlNmzaiwDp16sjV6dDPS5cuFSbu7u7qI/Cnn36iNcmFfs7IyBD57e3tFa/NRY2VK1dmjNnZ2Ylx6XR4M8Y0/vRrvAGW9bNi1itZP6sXfD179qxo3sCBAx89eiSalBv9vG7dOlro+PfffxdXOXW96enpP//8s6j65ft/xZcsYv2qnOrnEydOyE7Upp/p/bb83IoM4+PjK1SoIBqWl++f5QdP1BhtgUePHl29evX9998ngJRTXBBKlSolPhqneBHYsWOH8Ah9Ai1G11epUkWRU+y2aNFCjIWpV6+exgwmioR+NhFYzY/fTFVZISo3NDQ0ICCABobRiScCixcvPnz4MD2iKwT9LhD6mTjv27cvICBAXtGUHFSzZs3D2RuWkCVchTIA/Vwo3fraTs2YMSMge9M2xpUuBXv27BGXgsOHDys+N31tLYUjQ1xcHL11UasXPfvYpUsXgVTbS5WPP/5YDBAgXcc511M/M8boPv727ds0R5FCP4tXqcWKFZPv0bt27Soa1qhRI4190a2fd+3apbDau3cvvUHKjX7u1q2baJg2/cw5Fz3VqJ/VDeOca9TPt2/fDggIkLUx9ejgwYN0IiiWp869fibJJ6qT9fOGDRvk93iknxUyldr5/fffB2Rvp0+fFjOuiWa/9957lEcOJCYmBgQEfPzxxyLyTelnxpj4zPjlxG+50c+MsevXr8sdlMPnz58/fPhwWlraxo0byZum08+bN2+meyq6udWtnznnp0+fFm2Tz025F68N03Mr+bsJjVY0f5j8FYM6Z3R0NF35Dx8+LM8SL5oqTBITEydOnMgY0zjhgrpYzrnQz+XKlZPLl8PiSvj2228rns1pLM1YkdDPxiKpLEfj4zdlJuxrIdCrV6/O2VuDBg3k65cIW1lZbczejhw5oqWAAhNdsPSzwLp27Vrhnc6dO6tHeHbt2lV4R/7+rcD4Aw19HQHo59cRKuTpgwcPptO/c+fOdBervlAzxlq2bCmuBhs3bjSfC8L27du9vb0FkNzr58TERG2HlJjHyMXFhaaPJv3cqFGjGzduKAzlcaSknznnhw8fFq3t1q2bbCX0c/369eVySD+vXLmSnCsHSI1v375dGMrvn3XLVKPoZx3LaIu2OTk5kRKg98+6G8YYk59TEJCLFy/KfZenVg4JCaFsnHPD9POpU6dq164tvLNu3Tq5rg8++EA+6ej7WM75a/Wz3DAxCbkoSpt+VuRfvXo1zZ2Wl++fjaWfg4KC7t69K3fqxo0bxFZ4Sh7lLuDk/v1zw4YNNT5SnDRpkqgin+tnOzs7GZoc3r17N325IB+Wcljkp+kYcqqf5aI0hosXL65tHQG5qcYKQz8bi6SyHOhnJRGD9s+dOxeWvdWsWVN9wtSoUWPJPzea0sCg2vLaKCoqSp7wVv7EJa+bYmh9EydODAsL69Wrl9o7o0ePXrJkie71PwytFnZvjAD08xtDny8rPnjwoLhEh4WF0XJN6qsBY0xcEJYsWfL999/ny64Ys1H0gi4P9DNj7N133xWtJ/38yy+/qPtz4MABMROV/P6Zc37t2jWaN5gWX/3xxx/Fx8/a9LNGL8uRpUuXFm3IA/18+PBh6pqO2wDS9j4+PqJthunn+Ph4ceshr6Ah950x1qBBA3lmbAP0c3R0tL+/v6JYbbuLFy8mj+dUP9Nwbj31M+c8l/OHKV6M6zl+u1atWvTgg57c5XL+7bt37y5ZsoQWc9aG1yjvn+XHQ+SsP/74g4boF0T9vHv37iVLltCMeqVKlaJfhLCwMHkKcdFlE+lnR0fH2bNnE9U8CEA/mwoy9LNxye7cuXNK9kYXeo2XuSFDhkzK3r7++mvjNsAUpe3Zs4d+AxhjBVE/CywJCQlTpkzp3r272imWlpbCI6tXrzYFQ5SZxwSgn/MYeAGq7uUbG3GV/vjjj9WXAopxcnIS14RJkybRi9MC1E19mkr6OSQkhKat1maYlpZGQGhVXhq//dr3z/rr5+joaFpCUn7/zDmnoaqkn8Unr4yxAqGfd+3aRasKmVo/JyQk9O/fn45nOTBu3LhRo0aJGF9fX/F1sfC7Afr5s88+kwvXHXZ0dKQDLKf6edasWaJwPfWzfOuSl++fGzRoQKMO6d7JAP08YMAA+o46OjpaBvtyeIW4iNFfej2Q+/fPGvXzyZMnad47PfVzUlLSoEGDRLPzcvy2xvfP9N3Ey8N1ypQpijnY6EsWxv6nNw3Wzy9XNSOnqAOKNbrpXDBdAPrZVGyhn01Edt26dUtfbfL6cvIVkDFWsmTJUGlTL0xvoubltNiCOH5bWx9v3LghPEOzs8pOqVChguSQ0CtXrohyEhMTQ0NDFy1apK1YxOcrAtDP+cod+bMxSUlJry7SS4ODg+XrgCJcu3Zt+bLw9OnT/NmjnLaK9LO2CZbkAmn9Z8YYTRdkCv2sbfy2rJ8DAwPFxGNCP5csWVIxxw+N346MjCQvawysWrVKdDMP3j9zzuk+3qT6OSUlpUePHuIwDgwMVHT8+fPnf/31l0jN/fht0s/jxo1TVCTviq9DraysJk6cKIDro5/Xr18fGhp6+fJlfb5/5pzHxcWFhoYuX76cc378+HH6ti4v9bOxxm/L3z+Tfm7Tps3SpUsV30XHxsa2bt1aODT3+rl169aKmdKFv9Tjtx8/fhwREcEYq1atmrwuush/+/ZtupDmpX5W36etX7+eJi/QeN6p9fPff/8tHj/Vr18/KipK9Ej+e+rUKfGjcPjwYRGve/4w2TYvw9DPpqIN/WwqslK5d+/e3Zy96b5Fezmrp6+vb8d/bp9//rlU0hsLFib9TBDPnj0r/KKer5su+gEBAcIh4sfJzc1N9s/Zs2epNATyFQHo53zljvzfmEuXLomrgfgrfyBKVwMKtG3bVr4OiPDBgwfzfzcVLYyJiaFptDQKDDl/LvWzi4sLvefUPX772rVr9NGs4v1zXFwc3bRs3rx57NixDg4OjLFKlSrJTeWck35u3769Iknbbh7rZ8Wi0HKrxPhtZ2fnffv2ificjt9+/PixOFzr16+v8XfKWPp569atNPZVzPIld0QO169fXzSpcuXKIp70c7169S5evChn5pzv3bu3Y8eOQvYo5t/W9v65U6dOzZo1Y4z17NlTlPZGxm/rr5/Dw8PFpcbLy4u6//nnn9OlhnQy6Wd6+kD5Oef0e2eU8duK7yaoIrV+5pzT+s809T3lf1P6+YMPPqA2iMCIESMIqZ76mXNOF4SVK1cqCuScr1+/XpRJ61fp1s9Dhw4VvxQap45Xl2+sGOhnY5FUlkM/RYwxeV4HZT7sG4PAzZs3o15tR44cofNZR8DJyamBpk29vpwxGqi1jEKpn6m3Z86ciYqK2rRpkw5HaEx6++23ZeeMGDGCykTgzRKg+4mxY8e+2Zag9oJI4Pjx4+JSPXv2bI3nvjqySpUq8tVAHaZBj/kKyMCBA0VffH19df+sGKafhw8fLhSC/Im1bv28YcOGcuXKiVYp9LO8jo63t7dYIMrGxkat3Eg/a1u/asSIEcJH5A66XWaM6Z6mSx7gmtP1q65cuSKW3jXp/Nuknzt16kQdlAPG0s/z5s2jc0HtBblGtX6+e/duSEiIMKeXeGQiz4yl0M8uLi5Tp06lnBQQC1AbSz+PGTNGMZugnt8/66+fxdpvjLHc6Oe7d+/SB/NG0c+zZ89+8uQJUaWAbv1crly5n376iTKnp6fXqVOHjo28fP+sHr+tWz8vXLiwVKlS1FTqAl0QKleurBgceubMGS8vL2FC+vn06dPW1ta2traDBw+mQihQpUoVkR/rVxGTgh2Afn5T/svKyrqu2mj+fTqTtQU8PDw8X2158I66cOtncQykp6erHPK/iCtXrmhzhBxvZ2f3yif/+K9Yz+NNHXJmVS/0s1m523SdTU5OpstCu3bt5PM9p+EyZcr847og7axdu9Z0XdBd8v3794OCgkRf3nnnHR2Zq1evLrK1aNHi/v37Iufdu3eFBqhataraduTIkUI8a1v/WeP8YTrGb8v6mfjb29urq757965YZlmjfh41ahQNMSBbul02qX7mnNN3pA0bNqTaKdC3b1+x+tpff/1FkfT+uUyZMn/88QfFi4B6/Srd+vmdd96hhXmLFSsWGRlJBeb0+2fSz8uXL9f9/IX0s5WVVZcuXUSNLz8QFX4sW7asPGZ43759rq6uImnBggXPnj3jnGdlZUVFRYlIR0fHL7/8kprNOafy/f397927J5K0vX/+/vvvPT09aYFu+QUSrf9cqlQpxWMU4+rnkJAQMfVdjvSzi4uLPLVhrVq1yJWCTO7Hb8uPh4jwjz/+WLx4cVGF/CiQ3j+LDxLFVe3atWviIZHIzxjLS/18/vx5arYIPHz4kKbQo/fPBw8eFK11dnamdtL3z5zzJ0+ejBs3TiTReZeYmOjp6Vm2bFkRP3r0aHm5aXFVsbGx8fT0lEcKdO3a1crKSphAPyu8U1B3oZ/zledSU1OfvNpiY2PtVZulpaV8nouwlZWV4z83V1fXZJ1bTnttDvpZB5OsrKxXbvnf/zFjxiicY2trq3aNiHFwcJD9M23aNLVzUlJSMjIydN9/6GghkhQEoJ8VQLCbewLy9ZkuCMuXL1dcCsSura1tkSJFXrsMtbhE2NjYODo6alx5KPfNfm0JH3zwQZEiRURL3nnnHfXVqUmTJmLRFwsLC3t7+27duslltmzZUrz38/LySk5OTk1N5ZynpaWNGTOGbhkVElf3+2fd+jktLU3+bJsxpljjh9rWqlUr0TBHR8cGDRpQv+SGya+qDNPP165do4v/uHHjRC1ilWOSZ4qh2u+9955omLu7O7UqOTl5zJgxjo6O4ldeblhGRsaXX34pHPTzzz/LSyiLzurQz5aWlmFhYXIt6lVCwsPD09PTRVH66+cXL158//33dITv3LmTyGsMPHv2jJRe/fr1xXHy/PnzsLAw0WV7e3v6oSSk1tbW8lvNzMzMo0ePChRFixal/I6OjgJp7dq1U1JSqAGhoaHqwh0dHanZoiiN+nnmzJmikVSaAfr52bNnYs7nIkWKyK0lR4sGvPb98/Hjx0lsW1tbr127tnnz5vJZKaf+8MMPdJDEx8czxiwtLR0dHWVHC31bsmRJ6h2dd87OzmfOnKF4EVi2bFnRokVFa2X9/OLFi59++sne3p5SX75+t7e3F9cK8qNh+vnIkSNOTk6iUv3Xf5YFLfWib9++olV0PybaZmVlJa7YdA10dHQkiZuWlhYREUGnpKOjo/hgRCAdMWKE4u1IfHw8PZiT78xF4cWLF3/y5Il4GEQNM3UA47dNRRj62VRkTVNuSEiIh7S5u7vT1V//gJWV1Q3tG1125R6YuX6WUWgLX758WfLMf4N0GdXHNb6+vkuXLu3Zs6d2z9x48OCBttoRryAA/awAgt08JnDlypVevXr9+9//VlwWaFdx9S5durT6njXP2ty+fXtxj6jjYmVhYdG4cWONTWrevDndfQYFBd24cSM8PFwUVaZMGQ8PD8U42Nzo55fvIWkcqahC41hT0c4WLVpQwxRdUzfMMP3MOVd/jSUEhjb9zDnX0TDGWLly5WRi+jeM1n9+8uSJh4eH4hhTEJB3P//8czErnv76ee/evVRCqVKlDhw4oPHYkCMDAwOFyrWxsQkNDaWkoUOHkvyjMh0dHT08PFasWEHZRCAmJsbDw4PeTlP+ChUq1KlTR5FZLGHl4eGhOLydnJzEmWhvb88YK1++PKkaev9csmRJxfvnc+fO0QJI8+fPV9R18eJFMZeKs7OzPL1z/fr16cEBtZYxVrp0aWqYRv3s7u4eGxtLtfz666/yMGNRVMWKFcUohh07dlDhrq6uJHHv37/v4eGhbli7du08PDx8fX2p/BUrVggm9NU9JYnAvHnzRIZTp04pkjjnixcv9vDwcHBwcHd39/DwqFq1akZGxtatW0WrDNPPnPNt27aJStevX6+uVI4JDQ0VOXVfEEQe+kvLO/fp04ciW7duLZccHh4ukiwtLYsUKSLCw4cPl/NQ+ObNmx4eHopVEgUTjcKeDE0UgH42EVgO/WwqsnlS7tmzZ/2ljUbX0GXUgMDOnTujVRut+1eg16/KE5/8XyWjR4+WnONPox8NcIowCQ4OVnnmHxHyb+3/tcMsQ9DPZun2gtTp33//Xb4+HDp06M22vn379vQ1pvoaVatWraCgIB0tpHnIhG3ZsmVF7+TPnsl89erVIlXxVaHIsH79eiITExNDVhT45ptvKIO/v7/uqVtatmzp7+8vfyBasWJFf39/dcN++eUXKlZjwzZs2CAy0OpEoknnzp2jjyHFWFwxglQMjHdwcAgPD6fGU6BVq1a0FjQBr1Klir+//7Vr1yjby5HJv/zyS8WKFRlj6u8wRTb6Ytzb21smdv78eblhopZatWpRN729vRljwlliyWKhn4sWLfrhhx/KbVCHT548SeVs375dnUFjTFBQkL+/P83fTnlCQ0OpNBGYPn06paoDO3fuVOSXnzio87dv317OP3fuXJHn008/9ff3j4uLI5ODBw+KnIrFn0WGI0eOiNR169aRCQWOHTvm7++vnv85MTFRrl2ExVEkGta1a1cqZNmyZSKDehzyli1bFOWQJDt69Cgl7d69m0oTgePHj/v7+y9cuFARb/Td8ePH03NAmj/M1dW1QKzV+loa77//fqtWrV6b7eU3GnQUCaecO3dOHytT5IF+NgXV/5YJ/Wwqsm+i3JkzZ3b451avXj36YTZWoOCu//wmfPJ/dV64cOGfzvnfXi4/qpTd2qFDhy16bNqGO/5fWwt+CPq54PsQPchrAk+fPtV4jerQoUN8fLzu1qSnp8u28ieaug3zJvXatWvUPFq82ohVR0VFUfmkvZ8/f96hQweN4llU/fDhQ7ISAW2zuP/73//u0KGDtheDYq7gDh06qKdbi46OVlRx584d6viJEyc6dOjw448/UsywYcM6dOgwYMAAikEABLQRSE5OpjuOS5cuKbKRfu7fv78iCbt5RgD62VSooZ9NRTZ/lHv27NmPtGz6z1UmK7TevXtrHOCdP7pbIFuRmpqqxUX/jba1te3Zs6fsgtyHhw8fviwX22vvpPODG6Cf84MX0AYQAAEQAIHCSkA8ABL3JIr1q168eEEf7UM/v8EDAPrZVPChn01FNt+XGxcXN1H7Jh8YJNgGDRpEg4Xyff8KSQNnzZr1n//8R5ujcvSJNfkxl4GBAwdONfE2e/bs3PgvKSkpNDRUdBPrV+WGJGxBAARAAARAQBsBmn+7cePGU6dOFZ8PvBytPXnyZLrTgH7WRi8P4qGfTQVZlkm6PyIyVQtQbr4k8PDhw8WqjdYsyZdNNsdGffvttyov/SOCfsAKVsDa2npYLjZ5ujvoZ3M8MdBnEAABEAAB0xO4e/eurCPee++9YcOGubi40C1H9erVdXx3YPoGmnsN0M+mOgLk4x762VSUUS4IvCECPxm6KWaPpN/CAhfw9vbWf26bN+QlVJsDAgsXLuzyahs4cKDCcsmSJa8Su/Tr10+RyjmfNWsWZRg2bJgiQ2RkJKUOGTJEkfpyd/LkySKDegKkRYsWiaTExMSQkBC1LWJAAARAoPARiIuLGzx4sPreoESJEj/99NPhw4cLX5cLUI+gn//nrIyMjECjbmJSe3HcQz/nwSnxxRdfCAdqXAhk+vTpgYGBV69e5Zy3b99e0Z5Zs2bRmgTq1Llz5/72229Dhw4NDAxs2bKlwlbeVdvKqe/KppjKAAAgAElEQVS//36HDh3kGIQ1Epg6dSqdi4rlPTnnM2fOpNTAwMA+ffrIhcyZM4dS1dM5fvXVV5QaGBjYpUsX2fZlePLkyZShY8eOitRp06ZRqrphX375JaW2adNGYUu7J06csLGxcXd3/03aOnbsqP6N9Pf3F1m6dOmiSK1cubJIGjJkiCIpL3c9PT337NkzcuTIwMBAHecdYenbty9xEIqLkl6enj179pRT586dK6cGBgbK67LMnz9fTv3ggw9kW845XRBENsU4N3FBoBIUR9GsWbMoSd0wzvmECRMogzy/q2jDpEmTKDUwMFAh+eTDOzAwUK1Fw8PDyVzRsNmzZ1PSe++9p+iy4vBWN0w+vAMDAxUiuXfv3nTwuLq6Kgrv378/pVpZWSkaNmfOnBIlSlAGW1vboUOHUglfffWVvDxMhQoVKIlzvnDhwsDAQGdnZ2Hu7u4upy5ZsoQeOdWvX189fbF83gUGBvbu3Vs2FxeECxcuyJEIgwAIgECBIBAfHy9+64OCghYuXCjCb2pB+wJBLM8aaRz9PHnyZK+Cv9Fvv9EDVatW9fLy6tGjh+zXESNGyMw6d+4sp44aNUpOVeiu8PBwObVdu3ay7bhx4+RUxW3WxIkT5dTmzZvLtlOmTJFTvby8FDemo0ePpgwBAQGyLef8008/pVQvL68cNezzzz+XbZs1ayYX/sUXX8ip6obJc0F5eXnJUnb27NlipfiKFSt6eXlZWlq2bduWCv/qq6+cnJzKlSsnyre0tJR118KFC52dncuWLStWhLewsFA0bOrUqdQwS0tLLy+vTp06UeEzZsyQUy0tLWXdNWfOHEr18vKileWF+bx58+RULy8vhXpXnHeKhk2bNk02DwwMpFYJFSqnNmjQQE7V3TChH2Rz3Q1r2rSpXLiiYeqjSL6Pt7S0DA4Ols3l+3jGWLVq1eRUedyHhYVFixYt5NShQ4fKZ7eVlZV83k2fPp2WFWWMWVpaKs67Pn36kLmlpaV8eEdGRopjTGQoUqSIjvPOwsLC09NTblhYWBiVzBgrU6bMlStX/v77b5Fn5MiRcipj7N133xVJjx49GjhwoCK1SpUqV6Stc+fOcoZKlSpJiVe6desmp4rClyxZooiUdxs3bnzlypXRo0czxtzd3cU6n4yxRo0ayZ3inMvjvV1cXG7evClnULS8atWqcip9aC2qLleunLyK2L1791q3bk2teuutt2RbznmvXr0otWTJkn/99ZecQW4YY+ztt9+WU0NCQsiWMValShU5lXMuzxFYqVIlRaoCqbwQKOdcPrwZYz4+PgpzuV+Kw3vQoEHUMAsLC8V5pzi8K1asqCi5e/fuwvzo0aOMsdq1a8sZ7ty5QweGYpkfznl8fDylXrlyReHKu3fvUmqJEiWuXLmicBalnj9/XqGf7927R6lXrlxRVH3//n05VV11fHx848aNRb+KFSumsWEpKSlyTxEGARAAgYJF4M6dO7SSdsFqeWFtrXH085t9B0L3E/kwULRoUetXW5MmTeTDqHv37q9S/vtfLNROGXr37i2n+vn5URLnvH///nJqrVq15NSPPvpITq1Zs6acOnToUDnV29tbTh0xYoScam1trVBWffr0oQy2trYKaTRgwABKtba2VjRs8ODBcmqNGjXkqsPCwuRUedV7zvnHH38sp1pbW/v7+8vmycnJidImT8eVkpIipfw3qEjt16+ftbX1/v37RTZF6qBBg+SqFXf5I0eOlFMrVaokLzH/7NmzHj16UIZy5crJhY8dO5aSrK2ty5QpI/coJSVFdnTJkiVlW875sGHDZHNFw0aNGiWnenh4yIWHh4fLqQr5kZKS0rdvX8qgaBjnfMiQIZRqbW2tkB/Dhw+XUxXyY9SoUStWrCCPJCUlyQ3jnOtw5WtTnz17RiUrHP3y+Y4iNTExUeEs2VZtrqNhuo8xddUKVz579uyDDz7YtWuXaICCibrZsrmoulWrVkeOHClfvnxCQoKcqk/Vil4/efIkLS1NESnvPn36lHOempoqRyYmJiqarXCWOlXRL93NVpvL7shNqtrRuhv22n7JDVMcYwpbddWc86dPnxJY3Ux0p+pgkpmZqbFqxZlo2K66XrmcrKws3RnkzHqGidh//vMfPU2QDQRAAARAAAQMJmAc/Txu3Dg7Ozs3NzcrK6uyZcsaS8cWy96MVZq6HBcXl/Im3mi5c4M9BEMQAAEQAAEQAAEQAAEQAAEQAIH8QMA4+vnlM/Xw8PBz58517NgxISGhrpG2efPmLVq0yEiFaShm3bp1+cEHaAMIgAAIgAAIgAAIgAAIgAAIgED+J2A0/Zz/u4oWggAIgAAIgAAIgAAIgAAIgAAIgIDBBKCfDUYHQxAAARAAARAAARAAARAAARAAATMiAP1sRs5GV0EABEAABEAABEAABEAABEAABAwmAP1sMDoYggAIgAAIgAAIgAAIgAAIgAAImBEB6Gczcja6CgIgAAIgAAIgAAIgAAIgAAIgYDAB6GeD0cEQBEAABEAABEAABEAABEAABEDAjAhAP5uRs9FVEAABEAABEAABEAABEAABEAABgwlAPxuMDoYgAAIgAAIgAAIgAAIgAAIgAAJmRAD62Yycja6CAAiAAAiAAAiAAAiAAAiAAAgYTAD62WB0MAQBEAABEAABEAABEAABEAABEDAjAtDPZuRsdBUEQAAEQAAEQAAEQAAEQAAEQMBgAtDPBqODIQiAAAiAAAiAAAiAAAiAAAiAgBkRgH42I2ejqyAAAiAAAiAAAiAAAiAAAiAAAgYTgH42GB0MQQAEQAAEQAAEQAAEQAAEQAAEzIgA9LMZORtdBQEQAAEQAAEQAAEQAAEQAAEQMJgA9LPB6GAIAiAAAiAAAiAAAiAAAiAAAiBgRgSgn83I2egqCIAACIAACIAACIAACIAACICAwQSgnw1GB0MQAAEQAAEQAAEQAAEQAAEQAAEzIgD9bEbORldBAARAAARAAARAAARAAARAAAQMJgD9bDA6GIIACIAACIAACIAACIAACIAACJgRAehnM3I2ugoCIAACIAACIAACIAACIAACIGAwAehng9HBEARAAARAAARAAARAAARAAARAwIwIQD+bkbPRVRAAARAAARAAARAAARAAARAAAYMJQD8bjA6GIAACIAACIAACIAACIAACIAACZkQA+tmMnI2uggAIgAAIgAAIgAAIgAAIgAAIGEwA+tlgdDAEARAAARAAARAAARAAARAAARAwIwLQz2bkbHQVBEAABEAABEAABEAABEAABEDAYALQzwajgyEIgAAIgAAIgAAIgAAIgAAIgIAZEYB+NiNno6sgAAIgAAIgAAIgAAIgAAIgAAIGE4B+NhgdDEEABEAABEAABEAABEAABEAABMyIAPSzGTkbXQUBEAABEAABEAABEAABEAABEDCYAPSzwehgCAIgAAIgAAIgAAIgAAIgAAIgYEYEoJ/NyNnoKgiAAAiAAAiAAAiAAAiAAAiAgMEEoJ8NRgdDEAABEAABEAABEAABEAABEAABMyIA/WxGzkZXQQAEQAAEQAAEQAAEQAAEQAAEDCYA/WwwOhiCAAiAAAiAAAiAAAiAAAiAAAiYEQHoZzNyNroKAiAAAiAAAiAAAiAAAiAAAiBgMAHoZ4PRwRAEQAAEQAAEQAAEQAAEQAAEQMCMCEA/m5Gz0VUQAAEQAAEQAAEQAAEQAAEQAAGDCUA/G4wOhiAAAiAAAiAAAiAAAiAAAiAAAmZEAPrZjJyNroIACIAACIAACIAACIAACIAACBhMAPrZYHQwBAEQAAEQAAEQAAEQAAEQAAEQMCMC0M9m5Gx0FQRAAARAAARAAARAAARAAARAwGAC0M8Go4MhCIAACIAACIAACIAACIAACICAGRGAfjYjZ6OrIAACIAACIAACIAACIAACIAACBhOAfjYYHQxBAARAAARAAARAAARAAARAAATMiAD0sxk5G10FARAAARAAARAAARAAARAAARAwmAD0s8HoYAgCIAACIAACIAACIAACIAACIGBGBKCfzcjZ6CoIgAAIgAAIgAAIgAAIgAAIgIDBBKCfDUYHQxAAARAAARAAARAAARAAARAAATMiAP1sRs5GV0EABEAABEAABEAABEAABEAABAwmAP1sMDoYggAIgAAIgAAIgAAIgAAIgAAImBEB6Gczcja6CgIgAAIgAAIgAAIgAAIgAAIgYDAB6GeD0cEQBEAABEAABEAABEAABEAABEDAjAhAP5uRs9FVEAABEAABEAABEAABEAABEAABgwlAPxuMDoYgAAIgAAIgAAIgAAIgAAIgAAJmRAD62Yycja6CAAiAAAiAAAiAAAiAAAiAAAgYTAD62WB0MAQBEAABEAABEAABEAABEAABEDAjAtDPZuRsdBUEQAAEQAAEQAAEQAAEQAAEQMBgAtDPBqODIQiAAAiAAAiAAAiAAAiAAAiAgBkRgH42I2ejqyAAAiAAAiAAAiAAAiAAAiAAAgYTgH42GB0MQQAEQAAEQAAEQAAEQAAEQAAEzIgA9LMZORtdBQEQAAEQAAEQAAEQAAEQAAEQMJgA9LPB6GAIAiAAAiAAAiAAAiAAAiAAAiBgRgSgn83I2egqCIAACIAACIAACIAACIAACICAwQSgnw1GB0MQAAEQAAEQAAEQAAEQAAEQAAEzIgD9bEbORldBAARAAARAAARAAARAAARAAAQMJgD9bDA6GIIACIAACIAACIAACIAACIAACJgRAehnM3I2ugoCIAACIAACIAACIAACIAACIGAwAehng9HBEARAAARAAARAAARAAARAAARAwIwIQD+bkbPRVRAAARAAARAAARAAARAAARAAAYMJQD8bjA6GIAACIAACIAACIAACIAACIAACZkQA+tmMnI2uggAIgAAIgAAIgAAIgAAIgAAIGEwA+tlgdDAEARAAARAAARAAARAAARAAARAwIwLQz2bkbHQVBEAABEAABEAABEAABEAABEDAYALQzwajgyEIgAAIgAAIgAAIgAAIgAAIgIAZEYB+NiNno6sgAAIgAAIgAAIgAAIgAAIgAAIGE4B+NhgdDEEABEAABEAABEAABEAABEAABMyIAPSzGTkbXQUBEAABEAABEAABEAABEAABEDCYAPSzwejykWFGRkZSUlI+ahCaAgIgUEgJnDp1qkj2NnLkyJSUlBz1MiMjY/PmzcJ8woQJDx48eP78uf4lpKen//DDD0WKFBkzZkxObTnnaWlpDx48ePr0qf41IicIgAAIgAAIgAAIKAhAPyuAGHP31q1bMTExaWlpxixUVVZMTMyWLVvq1asXExMTHx+vSkdEficQGxsbk71lZWXl97aifWZP4NSpU+zVFhERERMTo78ijYmJeWX6v/9Llix59uyZPlDT0tLWrFkjm0dGRiYnJ+tjm56eHhMTs2zZMsbYhx9++PDhQ32skAcEQAAEQAAEQAAE1ASgn9VMjBNz+fLlBg0aMMZWr1596NAh4xSqqRQLCwu6pxw1apSmLIjLvwQuXrzo5+cnPLhnz55jx47l37aiZSDAuayfxXE7d+7c/fv36/OgUK2fGWNff/31/v37X7x4oZvuzZs36UJHgXnz5u3fvz89PV237d27d8mEMfbRRx/t378/ISFBtxVSQQAEQAAEQAAEQEBNAPpZzcQ4MR999BHdsdnY2Kxdu3bPnj3GKfqfpXTq1IkqatOmzdq1a69fv/7PLNjLvwQ+/PBDch9jrGzZsvv27cu/zUXLzJ6AWj+LA/hf//rX5s2bdePRqJ+F+dq1a3XbatTPwvabb77597//rcNcoZ+FVURExNq1a/V8+62jcCSBAAiAAAiAAAiYFQHoZ1O5W9bP4natUqVK27ZtM3p99+/fF+XT3x49esyfP//evXtGrwsFGp2AQj+/HLBQpUqV+fPnHzx40Oh1oUAQyD0BbfqZMVasWLHVq1frqELWzw0bNqxevTpdtWxsbObPn79hwwZt5rJ+9vPze/fdd8mWMebs7Dx//vwtW7ZoNNeon4X5lClTMjMzNVohEgRAAARAAARAAATUBKCf1UyME6PWz4yxqlWrjh07du/evcapI7sUtX4W94X9+/cfO3ZsRkaGEetCUUYnoNbPwn116tQ5cOCA0atDgSCQSwKkn5s0aTIze/P09CQp6+bmNnbsWG0ymPRzgwYNoqKiduzYMXPmzHLlypH5W2+9NXbsWI0vk2X9PGHChF9//XXmzJmVKlUiW8aYp6fnxo0b1R3UoZ8ZYxEREfPmzVNbIQYEQAAEQAAEQAAE1ASgn9VMjBOjUT+LW71atWrt37/fONVwTvq5Xr163333XZs2beQbyqFDhxqrIpRjCgKyfv7mm2+mTZtG7vP19R0wYMDZs2dNUS/KBAHDCJB+Hjt2rChh165d3333naOjIx26lStXXr9+vbp80s/Vq1ffvn27yLB169YSJUqQLWOsWrVqagmt0M/CdseOHWXKlJFtq1SpopbQCv3cpUsXMTkFGTo7O8+ePVvdYMSAAAiAAAiAAAiAgIIA9LMCiNF2Zf1sa2v7zTff0L0aY6xGjRrt2rW7cOFC7usj/dyzZ0/O+eXLl1u0aEF1WVlZtWvXLiIiIvcVoQRTEJD1c0ZGxpMnT2bMmEHuY4zVrVu3Xbt2GI1vCvgo0wACav0sCtm9e7d83Hp4eGzatElRPulnxtiMGTModd++fRs2bJDNq1atunPnTsrAOdeonznnBw8e3LJli2xbuXLldu3aycM3ZP3csWPH69evnz17dvv27fKb8xIlSsyaNUuuEWEQAAEQAAEQAAEQUBOAflYzMU6MrJ+PHj2ampp68uTJOXPmyPd53t7esbGxuayP9HOJEiW++uorcaPZsGFDuSJHR8fPPvsslxXB3BQEFPqZc/748ePp06fL7mOM+fj4pKammqIBKBMEckRAm37Oyso6efLk6tWr6dB966236tatGxUVReWTfu7evfudO3connOekZGxadMmsmWMVahQoW7duufOnRPZnj9/vmLFCpFhwoQJsm1mZub27dtlW8aYh4fH8ePHRTZZP48ZM4ZsY2JiSpUqRYbFixevW7fud999RxkQAAEQAAEQAAEQAAEFAehnBRCj7cr6mRYpffbsmeLtoru7e+XKlXNTK+lnxhitX/XgwYNbt265u7vTraGdnV358uUXLFiQm7pga3QCav3MOU9OTr5169awYcPIfWJQq9FrR4EgkFMC2vSzKCctLe3HH3+Uj1tXV9fy5cuLARSknz/++GN1venp6bdu3Vq6dKls7ubm9tdff4nMx44dE0kK/Szk961bt1atWiXbiqofPnyoTT9zzuPi4s6dOydbOTs7v3YycHXjEQMCIAACIAACIGAmBKCfTeVojfqZc/7ixYvp06e7uLgULVqUbto8PT2fPHliWFMePHhQrFgxUdSQIUPkt5RpaWmurq4uLi70aaKlpeWiRYsSs7fXLrhqWHtglSMC6enprVq1Eu5TTPaWkZHx/Pnzrl27uri4iFW+rbO3Tp06JSYmpqSk5KgiZAYBoxDIzMwU46Xt7e3/9a9/qcvMzMx8/vz5vHnzbGxs6BJnbW398OHDR48eiZfMdnZ28+fPV9uKK+TSpUtdXFysra2FedGiRZ2dnRMTE/fs2SNi1PpZFCWqnjt3rqLqxMTE/fv3C1v5/bOwysrK+uOPP1xcXOzt7UUeKysra2vrffv2JSYmZmVlaWwnIkEABEAABEAABMyTAPSzqfw+ceJEBwcHcTdG75/lykaMGOHl5UUqumbNmleuXLl7966cR8/whQsXREXFixfXeEd78uRJ+V20yLx3714s3KInYZNma926tfCIQj/LlTZt2lRIaJGTMTZs2LDExEQ5D8IgkDcEduzYwRij+cO0VTp79mwnJyc6YuWAxvfPinImTZpED/5kW8aYNv1MJcyYMYOeKips1fqZrHbs2OHm5qbIf+7cuRs3blAeBEAABEAABEAABMycAPSzCQ+A9u3bi1sxjfpZVNyzZ09LS0u6Y2vbtu1vv/0WFxeXo2YJ/ezq6rpo0SJthgcOHAgMDKxQoQLVxRjbvXv3iRMntJkgPm8I6KOfOefNmzevW7eu7L7Ro0f/9ttvSUlJedNO1AICnPMnT57MmjVLH/3MOZ8+fXpgYCA9SaSjt3Pnzrdu3Xotz/Hjx2tU4H379n3tRfKLL74IDAykV8pUdbdu3W7fvq2t6o0bNwZmb/KU4OXKlcM0+NqIIR4EQAAEQAAEzI0A9LMJPa6Pfuac9+7dm+7tRKB///763FxS04V+btSo0Wtv8tatW+fh4SFX5+bmZsTFtKhJCOhPQE/9zDmPj48PCgqS3ccYmzZtmsGD//VvJHKCgCBw/fr1Ro0aMcY6dux49epVfbCEh4d36dJFcdz26NHj5s2brzWfMGFCly5d5IeMopwBAwbokMFU7OjRo2kcODWgd+/e9E015VQEvvzyy+LFi5OJt7f3Tz/9dObMGUU27IIACIAACIAACJgbAehnU3n8wIEDPj4+4vZLx/tnznl6evqwYcMU95f9+/f/+++/9Wwcjd+m+cN0GK5Zs2bYsGGlS5emW0MPD4/FixfLy73oMEeS0QmQftY49l5R3fXr14cNG9a4cWNyH2Ns0qRJaWlpipzYBQETERDjtxlj8+bN07+KQYMGyQctY2z58uV6mo8YMUJhyxjbsGGDPuafffbZgAEDFOarVq16re2cOXOGDRsmS/eAgAAM2HktN2QAARAAARAAgcJNAPrZVP7dvn27t7e3uGn7/PPPX1tNXFxcr1695Ju8Pn36TJw4Ubf2FsWSfq5Xr95vv/322ro45999952Li4tcXe3atfft26ePLfIYlwDp5xIlSuhZ8qlTpxQvoj/99FOxepmeJSAbCBhMwDD9/OzZs6lTp/bv319cdpo3b/7777/r2Ya0tLTRo0fL16u2bdvGxMToaf706dOwsDAyb9myJS2L9doSJk2aRIaMscaNG0+cOPHixYuvNUQGEAABEAABEACBQkkA+tmEbqXx246OjvpUExsbu2zZsg4dOsi3a/369XutLelnxtjMmTNfm19kWLt27cKFC+W6ateujbfQetIzYjYD9DPn/NSpU8uWLatVqxZ50NHRUX/vG7H9KMrcCBimnwWluLi4Zdmb/uJZGD5+/FgYir8XLlzIEfaEhAQyf+13LnLJaWlpy5Yt+/TTT+lEY4y1bNny2rVrcjaEQQAEQAAEQAAEzIQA9LMJHZ1T/SyacvXq1Xbt2sn3ah06dNA9MNsw/SwWTVWsturj49OhQwf9X+yYEJ/ZFG2YfhZ4jh8/TsMcGGMuLi4dOnRYsmSJ2cBDR98Agdzo5zfQXGNUmZCQEBERIV+WAwICOnTo8OzZM2MUjzJAAARAAARAAAQKDAHoZxO6yjD9zDm/efNmdHS0r68v3a7Z29uPHDlSW1sN1s+c89TU1Ojo6C+//JLqYoxVr17d398fs1JpA27c+NzoZ875hQsXoqOj5XmG3dzc9PmU2ri9QGnmQ8AM9TPnPCEhITo6euDAgfKl0s/Pr1OnTubjevQUBEAABEAABEAA+tmEx4DB+lm0KT4+vkqVKnSvZmdn5+HhoXGAbm70s6grOTl5+vTpVJcIVK1a1YR0UPQrArnUz6KYS5cuye5zcXHx8PDYvn37q0rwHwSMRsA89bPAl5iYeOPGjVatWtHpZmVl1bFjR6PBRUEgAAIgAAIgAAL5mwD0swn9k0v9zDlPSUlJSkqSXy1aWVnZ29uvWLHiyZMnL168EK0n/Vy0aNG5c+ca1qX09PTk5OThw4fL881WrVr1yZMnKSkphpUJK30IGEU/Z2VlJScnHz582NbWlu7sbWxsdu/e/eTJk6ysLH1agjwgoA8Bc9bPgk9qampQUJCjo6M414oUKdKxY8cnT548f/5cH4DIAwIgAAIgAAIgUHAJQD+b0He518+icffu3fP09HR3dyddJALbtm3LyMgQI3hFTP/+/RMTE3PZpbCwME9Pz6JFi1J1QUFB169fT0hIyGXJMNdIwCj6mUreu3evp6envHQtY+z06dOUAQEQyCUB6GcCWLNmTbpOMsbCwsKuX7/+9OlTyoAACIAACIAACIBAISMA/WxChxpLP4smHjt2TB7OLW7atm7dmpWVRe+fczT/tu6ed+/evX79+vKtYZ8+fe7cuaPbCqkGEDCufhYNWLlyZZkyZch9lpaWUVFR+q/ZY0AvYGI+BKCfydepqakNGjTw8fGhc40x9sUXX0RFRWFqMaKEAAiAAAiAAAgUJgLQzyb0pnH1M+f8wIEDHbO38uXL0+3azz//vGDBAtrV+IG0YZ1MS0t77733qGTG2IABAzZv3vzgwQPDCoSVRgKm0M+c82+//bZjx44lS5YkD3p6ekZFRWlsAyJBQH8C0M8KVlevXlU8bWSMLVq0CMO5FaCwCwIgAAIgAAKFgAD0swmdaHT9TG1dsWJFuXLlSBfJASPqZ875o0ePQkNDSeCJikaNGrV06VJ8FE3uyGWA8JYoUSKXRanNIyMjXVxc6AipXr360uwN76LVrBCjJwHoZzWoc+fOhYaG+vn50bnGGIuMjFy6dOnGjRvV+REDAvmHQHx8/NKlSw8fPpzHTXr06NHSpUv37NmTx/Xqrm7ZsmXr1q3TnYdzfuPGDfFjivU+X8sKGUCg8BGAfjahT02nnznn33///aRJkxwcHOTbNSOO35a5XLly5f3331dU9HI11ClTpmCdJBmUYWGT6mfO+aJFiyZMmKBw38uRBVOyt3v37hnWbFiZLQHoZ22uP3To0KRJk6pXry6fbi+nrhDn2t69e7UZIr5QElizZo1wvY6/jx49erN9T0hIEKuy+fn5HTp0KM8a8+zZs2HDhjHGatSosWvXrjyrV3dF8+bNK1KkSKlSpXS4TCR1795dnObt2rW7eNOYZBEAACAASURBVPGi7mKRCgIgUMgIQD+b0KEm1c+i3StWrJBv1Jo2bWqimaIuXry4ZMmSoKAguTrGWMmSJcOyt59//tmEKAt10abWz5zzFy9eqNcnE67s1q1bWFhYREREoWaMzhmTAPSzbpq7d+9Wz1XBGKtdu7a4Wl66dEl3CUgtHATatWun+MVU7/bu3TssLOzzzz9/U12+evUqtWrKlCl51oyEhASqd8SIEXlWr+6KtI3so6ZqDGzatEl3sUgFARAoZASgn03o0DzQz5zzTZs2bXy1mXpQ7rlz515WVaNGDfVPSNWqVTtnb2fPnjUh08JYdB7oZ875s2fPxGEiHvkrPGhjYyPct2DBgsLIGH0yJgHo59fSPHTo0MaNG9evX6840cRuQECAON1eWw4yFGgC+uhncUjY29uPHTv2jXT2Tenn58+fz58/X3Q//+jnHTt2FClSRONpqy1y0KBBf//99xvxHSoFARB4UwSgn01IPm/0swk7oKXo8+fPHz58+NChQxp/TmrUqBGQvbVr105LAYj+B4G80c9U5b179w5nby1btlR70NXVNSB727lzJ5kgAAIyAehnmYaOcGZmpjjX5syZoz7XGGMB2duoUaN0FIKkgkuA9PO+ffvEkSD/DQwMlI+KYsWKvREJ/ab0s3iqK4Bcv349/3j5yJEjsptEuGHDhsJZe/bsUaRiXZL84zu0BATyjAD0swlRF1b9LJBlZWVdzd6WL18u3wRQuEiRIlWrVu3bt68JEReKovNYPxOz+Ph44cESJUqQ1yhQunTpqq+29PR0skIABKCfc3oMJCcni3Otf//+dIpRwN7evmrVqjNmzMhpscifzwmQfk5NTVU39c6dO+KosLOzEweDg4PDhAkT1DlNGvMG9bNJ+2XcwmkKGKxLZ1ywKA0ECigB6GcTOq5w62cCl56enpS9jR492jZ7s7CwoFtDS0tLp+xt1qxZKdlbZmYm2SLAOX9T+pngP378OCkpKTo6WrjPysqK3CcCTk5OderUSUlJSUtLIysEzJYA9LPBrk9JSUnK3mrXrm1ra2tjY0PnmrW1tbhU7tixQ1wqNYoug6uGYR4TSE9Pp2u7blfGx8fTYfDRRx9pbGdmZqY4KlJSUjIyMjTmEZHp6ekpKSkvXrzgnKempqakpJw9e7ZNmzbCXG2rWz9Tvd98842Tk9PixYtFOa/9HRdVU5s11k6Fy49onz9/npKSIohRBrkc3VULc8ovfrMEk5SUFN22OqjqqZ+p12lpaRkZGdQMRdUvXrwQSREREeKsd3JyunXrlu7jJDU19fz585Tfycnpm2++UZRMXRBd7tWrF+WvXr26qFSmTfkRAAEQyBEB6Occ4cpZZjPRz2oorVu3rlChwltvvUX3BHJg69atsbGxt27dUhuaZwzdY5li/SoDkH7zzTcVsjdbW1vZcYyxdu3axWZvT548MaBkmBQOAtDPxvLjgwcPKmRv8jrtdNI5OzuL0+3BgwfGqhHl5BkBMam18KZuXZScnExOV+vnrKys2NjYbdu2UZ6JEyeKA0PjA83w8HDG2KpVq2JjY11dXclKBMLDw58+fSpD0KGfb926deTIEUUJYnffvn2xsbFyORS+d+9ebGysxmFNkZGR8sqXFy9eFKXJ3z/Xq1fv5dpvjo6OsbGxGzduVNd+8OBBjTL4wYMHsbGxlStXlk06d+4cGxsbEhIiIs+fP0/t1D+QkJDQvHlzUYLu989OTk4iW7NmzWbNmiW3RMzRnZGRERsbu3LlSjmJwiVKlNA2Gvzvv/9WP9oWhps3b1Y8Fnny5MmoUaOoWEWgW7duiYmJ+ncfOUEABNQEoJ/VTIwWY7b6WRBMTEz08/Pz9vZWXLvFroODw4ns7c8//zQa8YJZUH7Tz0Tx448/9sve1B4cN26ccN+JEyfEiw6yQqDQE4B+NrqLd+3aJc41jUK6efPmJ06ciIuLM3q9KNB0BKZNm+bs7CwunrnRz8eOHVNfgUXM2rVrFe8S4+Pje/furS2/iJ8wYYIsn3ToZ0dHRyrK1dVVMTe1paWlerrQ69ev161bl6zUgfnz5ycnJwvsOvSz2lCOUa+zFRsbSxJXzqkIG6afBw0aROXo1s+NGzemnHLA29v7xo0bWVlZdPFkjJUpU0ac9X5+fjSG39PT8/Lly4rD8sKFC25ubowxW1tbMnm5MB5VsWXLFvmHeOnSpZRUrVo1MqGl9fr163f37l1FLdgFARDQnwD0s/6scpzTzPWz4HXu3Lng7E3jgi6MsYYNG27L3rQ9zM4x94JmkG/1M4Hs0KFDcHBwgwYN6CdZDmzcuHHbtm1Hjhyh/AgUbgJ0Czhv3rzC3dO87938+fPFBVM9+qN3797iUimLn7xvIWrUn4Du75+pnM2bN4sraunSpRcvXkzxIuDi4sIYc3Z2FgeG+Fu2bFlh8uOPP8r5586dK1+cW7RoQVa+vr6UtG3bNrJ6rX52cXEJDg5evHjx+vXrRWn0bvmtt96ickSgV69eVAtVHRwcTMqNMXbmzBmRWR/9XKZMGbmc4sWLM8asra337dsnVz1ixAiqt1WrVmTy7rvvUjxjzNT6OSUlRa5OrG4dHBws6s3IyBCprq6uwcHBK1asoC4MHz7c2tpapDZv3pziRUD4rmjRokOGDKGkH374oUKFClQdPZWIj48fOnSoiK9Tp05MTAyZnDhxgvJjrQ3CggAIGEAA+tkAaPqaQD/LpDZt2hSSvZUqVYqu4HKgT58+32Zvjx8/lg0LfTj/62fhgsuXLwsPKu5IhBMrV64s3Ef3RoXecWbbQejnPHD9J598EhIS0rlzZ/kiKcLjx4//9ttvV61alQfNQBUGE/jtt998fHyEy7S9f966deu3334rhJOrq6taPP/00092dnYODg5Tp06VW7Js2TJ6/bhmzRpK2r17N1XKGJMHA584ccLf31+0Z/jw4ffv3xdW2vTzhg0bxPf59evXp/JFYPbs2eLVevHixbds2UKpx44dE6OvGWO9evWieM653LDPP/9ciD3d+tnJySkkJOTrr7+Wy6F5sCtVqiTHk37u3LmzPEBdMVJ68uTJ8gByuQQd4VWrVpUvX16g0/3+WdbPXl5eISEhe/fupZJJP7du3ZoiKTB69GhRRbVq1Q4cOEDxu3fvFjq5ePHiFCkCH330kTBhjC1btkxE0uOYhg0bnjp1Sja5efMmrbsB/SyTQRgEckoA+jmnxHKQH/pZI6yvv/56/PjxY8aMoeu+IjBmzJjp06cvWbJEo3nhiywo+pnI79mzZ3z2RjdwsgebNWs2PXu7ffs2mSBQmAhAP+eZN+/fvy/ONbrrpXPN2tpanGj09/Tp03nWMFT0WgLy989TpkwhN8kBUmXOzs5Lly5VlPnDDz+UKlWqSJEis2fPViRxzps1ayYOhjJlysip4vtnxtjAgQMVD6OjoqJoGNGQIUOSkpI459r0s/iQ2NnZ+f/9v/8nly/C1apVY4wVK1ZM/qWmb24HDRoki1hh8ssvv5C2j4uLe/bs2ccffyy6oP7+mTFWpUoVdb0a9fORI0fo0cClS5dkq9OnTzdt2pTOGsbYvXv35Az6hHfs2CH6yxjTXz+HhIQoCs/IyHB0dBw/fvzKlSsVSWKX2ik/fWjTpo2InzJlisJq8+bNVatWFak0c7vQzwEBAceOHVPk55zTh/TQz2o4iAEB/QlAP+vPKsc5oZ91IHv+/PmC7G3AgAH0myEHnJycPpa23377TUdpBTqpwOlnor1+/foFCxYoZkkhJ3bp0kVy4Mf0dJzMESigBKCf895xZ8+eXbBgAYkEOsvkQFBQkHzGTZ48Oe/biRqJwN69e+VBy7Kn1GEPDw8ypIBYINra2ppi5MDPP/9cpkwZ8RmtHE/6+ffff5fjRXjcuHFUu/hmSpt+XrVq1YIFC+QxxlTawoULxThqR0fHOXPmUDzp5z/++IMi5cCvv/4qfvefPn36ckEHakwu9fO0adNEp4YPH/7o0SO5Rs65/AsVERGhWwArbMWu/t8/0/vnGjVqyG+eRTmZmZnLly+Xq9i8ebN8zpJrSD+vXr26YsWKIl7jdHHbtm0TSMWX8Ddu3BBfDUyaNEmuiMKknxs3bownboQFARDIKQHo55wSy0F+6Gd9YN2+fXtd9qZ78g9fX9/u/9zGjh2rT/n5P0/B1c+CbXp6+rp166ZMmUK//RoD7u7usgPlj7Ju3rw5c+bM/O8ptFAQgH5+U0fCiRMnxNVSPa+y+qSzt7eXz7hdu3a9qWabbb30/bPaO4oYBweHiRMnKkDp1s9Tp04Vsz1re/+sUT+fP38+KChI1B4cHJyWlqZNP4vG3L9/Xz6KRFg+/Hx9fanZr9XPlFMEdIzftrOz27FjhyI/51zj+2fSzwcPHlSbXLp0qW3btqLLefb9c3BwsLolcsyhQ4e6d+/u5eWlOBLELulnWjF+yZIl8gxhclFy+OjRo6KEGjVqqB3XvXv3gIAAqnHdunWyLcIgAAL6E4B+1p9VjnNCP+cI2ZUrVw5kbxpHBdMVnwKOjo5BWrYPPvggR1W/2cznzp0Tk6vlk/WrDKORlJQk3HfgwAE68slZ6sC7775L3qtTp06JEiVoVwSuXbtmWEtgZWoC0M+mJvza8qOjo+l0++KLL9TnlzqmSpUq8inWuXNnUcsvv/wSFBS0YcOG11aKDDkiMHv2bJpna/fu3eQvOSC/oPb391eUL/SzhYWF7DgKi3nFcvr+mXNOA8vXrVv34sULHfq5TZs2uoc8MMZIP69Zs4YWrdT2/lnRQR362cnJSZFZ7Bqgnznn9GnxG9fPDx48EB6kAeHqU1X+epz0s57fQ5F+1lisIhL6WeMxhkgQ0IcA9LM+lAzMQyrC0dHRwCLM0uzPP/+8KG2vfbGp+ElgjFlaWr79z02e4yQfQq1duzZjrEDrZ5lqfHw8OfDMmTNqB+kT4+HhIfswPDxcrgLhN0gA+vkNwldX/fjxYzrdLl68KC4mrz3FrKysxPklZnJ2c3OTT7dGjRqpK0JMjgiQTGWMaZs/7ObNmxcvXhRrF9nZ2Q0bNkyuQujn17oyR++fZf2se/x2q1atLCwsFLWPHz9eHGweHh4iifTzl19+SZmhnzW+f/b396fPlRljAwYMkM9ceppgLP08ceJERfmKXfEBvHzIIQwCIKAnAehnPUEZkg362RBqKpvU1NQEafP29rbSsql/7Onn3MHBocSrLTU1NV3TlpWVpao8LyJ69OhhZWVVmPSzTC0rK0vy3n+DoaGhVlZWW7duTUhIuHfvnsKZ2pxobW39yoH/+x8bG6vJjf+LE97MysrKyMiQ24Nw7glAP+eeoelKSEpKojNuz549ivNLsVukSBG6SMoBCwsLxekmdk+fPp2env7gwYP69etrO/ve1IXUdEgNK5n0s6WlpTb9LEq+ffu2gG9jYzNmzBiqjvSzwmszZswgFyckJMhf/C5evJhWPtM4fvvFixf0SlOHfm7dujUdG/Xq1aPqaPJqen1K+jklJSU0NFR0RJt+fvHihThssrKyHj16RKudq79/Nuz98969e9WHX2Zm5siRI0XD3uz7ZxqP0KxZs4SEBFpxijxO56B6/LaLi4vG759fvHjRokWLEiVKiE/o6f1zeHi4xqMuMzNTuCAzM5PqRQAEQCCnBKCfc0osB/mhn3MAyxhZu3btWvafm5jjhH6TdAe2b98ep317/vw55/zOnTt37941RmP/r4yHDx/WqFGjsOrn/+unfqEpU6b804dl3dzcdDtOY2p0dHRcXNyRI0fq1Kmj3atxtIiLfq1Drv8SgH4uNMfB/v37Fadb2bJlSThpPLNeG/nnn3/qOOPi4uLu3r2blpaWkJBQaDBq7Ajp51u3bmnMQJHJycmCaocOHSiSc677+2fO+b179+Li4mQTef1njfqZpuxijOnQz2KYtIWFhXrxKlGdWj9zzun7571796o/1k1KSurSpYvoqWg2vXFV62dHR0eNP7Uax28vWLDAwcFBlKyYf1sxf5hh+jk8PJyeSuiefozmD9P4/pn0s8b1qzjndHKRfh41apRYRYwxptbPiYmJNDO/UOMnT54UtYwaNSouLo6ed9BBQvOHYf5tYoIACBhAAPrZAGj6mkA/60vKZPl27NhRW9rEMDn6icpR4Lvvvjtz5oydnZ27u/sZndvly5dz1KGCPn9YjjprQOY///xT8mFtugXJkfu0Za5evbo2Z2p7hWJAFwqZCfRzIXOoojstWrSQz7hy5cppO30Miy9Tpsz3338fGBio7dQ7c+ZMIZj+gPTzzp07db/rI/3cpEkTWWwPHDjQxsZG2/zbf/75p6enJ2NMvlLp1s/379+nBS+8vb3j4+O1rV8lZKq9vb3i2BC7V69erVSpkvA+vX+W9TNjTPFo8t69ex9++KEw8fb2Fqk69HORIkXat2+vrl2jfuac0/rPmzZtksccvXw/T0mMMcP0c2xsbOPGjUXjTaSfL126JH/rRPqZc07rVykWc375QF9e/5neZtP6z4yx2bNnywuJJScnz58/X3QE+ll9dCEGBPQnAP2sP6sc54R+zjEyExuEhYW11rQZ9waxcuXKu7Rs+/fvf/z4sSKxTp064ves0Hz/bFI3fvXVV5p8+N84cTfJGPP398/NsxLhjuLFiys89dpdxS2jSTm8wcKhn98g/LyvevPmzdrOOBFP5504cYzy19fX97Wnm44MGl+95jG6efPm0TzVGkfSUntIPzPGPvroI4rnnIvvlXbt2hUVFSXHnz179t133xWoe/bsSUmyfl68ePGuXbtIur8cPEXjq319fa9cuSKsNM4fJmSqjY3Nrl27oqOjqfyLFy/u2rWrZs2a5GVZP//rX/+i6T/Xrl1LVi/HI8hLQJ05c0Yk6dDPORq/LetnxthPP/1EVa9cuZKaarB+lhtvXP186dIlcRjT8wjRWlk/T5w4UUy07ujoqDjm6eF7kyZN6BiLioqS56WbM2cOWZF4ZoxBP9NBggAIGEAA+tkAaPqakH4eOHCgvjbI9yYILF++vJ/2TdsKE/Kvsp5hJyenqVOnassM/ZxL52/atEm48dq1a5988olGl9Jamtq8kJv4UaNGrczdViAmdIF+zuWBWsjM6bzTeMaJSJOed+pztm7duuoTUSyQm5fwaf0q0jYaa9ehnz/77LOiRYsyxipWrCjWEz5//vzKlSvr168vem1hYSGXuWvXLvE1EDH57rvvBIohQ4ZQ5LZt28hKo36eNm1asWLFRH5PT0+CqV5msmLFiitXrjxy5IgosFevXlQLWQ0ePJgiW7Ro8ddff4nMRtTPP/74I0nQIkWKUNUhISFU9RvXz0OHDhWN8fHxES1877335OZR2N/f/8SJE+QjX19fSlIH2rZt++DBA8r8cuT//v376fGKOj9jzMfH59dff5VNEAYBEMgRAejnHOHKWWbSzzSuJmf2yJ0/CPz8888ROjdvb2+NP1E5jYR+zgOH//DDDzqcSR/15dR3xsr/ySefzMrz7erVq/qTj4+Pp/mH5s2bp78hcpozgfxw3uXxD/GuXbvoeqJbP6elpZHCVLx/5pzTOlXe3t6zZs2SFdeAAQMiIiIUx1V4eLjuy1Hr1q0vXrxIVhr1s/hsWEh3dWk9evSIiIig73Jffkrdv39/UeDatWsjIiJKlSqltmKMtW3bVv6+yYj6mXO+evXq8uXLa6yXIg0bv22s988ZGRnUEkWgf//+ERERcmRAQMCxY8cE1QULFkRERGicmKBTp07iO3ZyqAjs2bOnVq1acoEiXLly5YiIiF9++UWRH7sgAAI5IgD9nCNcOcsM/ZwzXgU297Zt2yK1bDSBqvpnTB2zaNGiAsugkDR8+/btWjz5j2h6M6N2YkGMef/998fovcnvl6CfC8lx/6a7oc95RwODGWNVqlShE9LPz0/Pky6P9fPu3bvffvtt0Tbd+plzfuPGDZHTx8dn165dskMWLFig7mDv3r0jIyMfPnwo5+ScHzhwgD4IGj16dGRkJC0PXqtWLQFN/l765cjnR48eEUx5qDbnfNGiRePHj6famzdvLnKKtYiXLFkyceJExli1atUUemzVqlWRkZFk6OvrKwxjYmLkBl+8eLFy5cqRkZH79++n+DVr1kRGRmp7mrx27dqSJUtaWVl9++23ZEKBDRs2KOabrFu3bmRkJH29bJh+/vXXX2lEtD7jt8uXL79582ZqFQUyMzMJtSIgvv1RRMqvoDnn8+fPV2SIjIzUMVPA3r171fk1NoxaiAAIgICeBKCf9QRlSDboZ0OoFS4bmo+U7iR0BORZTwoXhsLWmzJlyujwo/kkQT8XtiM7H/dHHo/arFkzailNiPXa8y6P9TPnXM/x27J+ZoxNnDiResc5f/78ubpra9askfNQWP7+WXwE/vDhQ2HevXt3yqZ/4ObNm1T7hAkTFIZi5a02bdoo4jnnWVlZZNi7d291Bs75xYsXg4KCNCa5ublpjH/5nrlKlSp2dnbaUumdv6i9X79+nPPRo0eLXcP0M+f8/fffFyXoo5/r1aunrXmIBwEQKBwEoJ//50exhl6LFi3GjRuncO3gwYNbtGjRuXPnl9fQM2fOtNC0paen37p1S5FCQ5jy/mdb0QXsvikCV65c2aP3RhO9vKnWol49CRw6dEi3V2kG1MDAQEXOwqS9ST+HhISIq9/gwYPVDENDQx8+fJiUlBQSEqJO5Zz36tVLvTSLnLNLly7yriLcsWNHUbv66i3u41u0aKGxYYpysMs5F793guenn36qYDJ06FD5Z27q1KlyhuHDh8upkyZNklNHjRolp7Zo0SIyMpIyfPLJJ4rU2bNnU2pERISjoyPpMVk/x8TE1KtXj5JEQHHeCU2V9z/Ev//+uzj91Ys5UddE4NmzZ3ShULxRzMzMpKQxY8YwxkJDQ8XU2YpCOOdq/ZyWlibMDZOOKSkpVLuiYZzz1NTUPXv2aJytLSsriwwVb7yp2U+fPlXPKS1SDx06RNkUgaNHj+7bt08RSbtRUVFU7549e2JiYtatW1ehQgVxYBgGgXN+9uxZUaxuV7548WLPnj2K98bUNgRAAAQKDQGj6edRo0b55GKLjo7+4IMPclGAZtN169ZRw+rWrRsXF6c5n48PzSfp6OioyCPW/bO0tPTx8fHw8FD8TovdmjVr6phlqkaNGj4+Pn379uVatjt37shTaMq5mjRpIu/mq/D9+/d139fmcWtDQkJ8pE1xxxwaGiol+qgndevZs6ecYfTo0Vza+vbtK6fK61Vyzvv37y+nDh06VDLlgwYNklN9fHzGjh0rZ+jatStl0N2wDz/8UDZ8+eJCbpi2o0isFNqtWzeFbR7spqam+vj46GiYxjYMHjzY59XWqVMnRZ6hQ4e+Svzf/08++UTO06tXLznDyJEj5dQPP/xQTh0+fLicOnDgQDnVx8dn/PjxlEFumMim+P6we/fuPj4+NNhPcYL07t1b/qSwadOm56VNMUlMYGCglHhePU41ODh4dPZ2/vz5Bg0aaLw0mTRS6OeQkBD6EtLW1tbHx0fWsaGhoba2ttWqVatevbqNjY3i8B4+fLiPj0/RokVr1qwpeGo878Tl18fHR3Hecc7bt29vaWkpulmsWDH53R2dd4wx0TAd552Pj49CLiouCD4+PtOmTaMjQbxdFG0WfydPniyntm/fnlKHDBkiJ3HOFb93ioZ169aNbH18fMLDw2VzRcNGjRolp+bm8Oacv/POO3TMODg4fPbZZ3LhikO0a9eucipNaiVK6Nixo5waEBBAJYuAfDA0bdpUkSpf62iRW5FH1s+c87Zt2ypsFeedv78/Yyzv9bPcfaOEHz16dP78ecVkUXLJav0spxbi8Jdffunj43Py5El1H2fNmkWHh8H6WV0sYkAABMyZgNH0c6dOnegKZUDAxcXFysrKAEPdJsWKFaMbO8ZYyZIldec3aWrRokXd3NzkO6H333/fLXsrVaqUlZWVm5ub4k4oMDDQwsJC5HFzc5Nv9Lt27UrxFJDvHVu2bEnxbm5uijc/bdq0kVPd3NxkBdK+fXs5VT34KjAw0M3NTTRbrcqaNm0qmyt0bKtWreRU+RZK3AnJqW5ubmPGjKFTVNEwNzc3WRo1a9ZM9qC1tXVYWBjZytOuMMaKFi2qaJhCn4gRB8K8X79+suxhjMlLUw4aNEiRqhjPpp6zVEbao0cP+eBXNKxPnz6K1AEDBlCn+vfvL1dtZWXVp08fSuX/v707Vq1iCeMAPiA2Iogg24mFQkAJGBEVDhijx0TMKRK1CER8AUnnG1jY+RSC4CPoS1hZWdhlC00ipHbu5S4zjHOcgBijN/md5jvx292Z/Z2cuP/syW6MKysrg+fwYq2trZXdR48eldrVQefa2lrZ7bquvLbN48ePq26+hMwwxGQyGRYIIUxPbHV1tVy9mlh5uHzs2LHytSjvh5lf7l85jp9MJqXJTx3HhxCqXw3kPz4c5laSPnnypHyxQghVwKj+Wn55eXmPic3Pz+/s7Oz+94gxLi4uZo0Qwmg06r9/lB9/vX79etnMN0Ept7C+vj4sM5lMyn/Pzzc2NoZAUr3vbt68WV5FvHrfLSwslDtVbfzatWvb29vlAvl2ryGEK1euVN0YY/lxzdu3b5dDV++7amIxxrm5ubw7IYTqA67VWc379+9//fq1nNuFCxfy6ouLi1W3nNi9e/fKFWOMs7Ozed0QQvkDIcZYxdTqZ2w5satXr1Ymo9Eob3lubm5ra6sc+tatWyGEDx8+5G+AUizn583NzWGBqvv58+e8Yt/31dBfvnzp+/7jx48hhOmJDd1Pnz6FEC5fvtz3fbnxoXvmzJn3799funSp6m5tbfV9P9wOamZmptqpodv3/fHjx8+fP9+a2Ldv30qKQ/n8aObnly9fDjcsPH369PTVEOXnQ/mtbqcI/FmBvyU/5//vD/LJyZMnuwN/LYkMhQAABbBJREFU/DA/D7Ooks+/NyEYYmqeY5mfY4xlTH3w4EH1nXQA+TlP7OnTp+Xo5cS6rqti6k/l5/IUxHCuKQ969+7dctBff760tDRs/MaNG9NbW15ezkNPHw3HGEej0bDAeDyuVn/48GFet+u6KuzFGO/cuZMXmD7dmifWdV0V9oaTYHndpaWlauicn4dlqpgaY5yfn8+rl2Evxljl5yrsxRjLiVVhL8aY83PXddMTq+bpy4MRuHjx4h4D7d3dY0UtAgT+BoHd3d18k6Qffqz6b5jk75jDxsZGPnosfz1UXn3t7du3v2No2yRA4AgK7Ft+zh+Tnv3/PF69enUEX3K7TIAAAQIECBw+gaN5/jnG+OLFi1OnTuUIPf3k7Nmz1dXFD9+rb48IEDgwgX3Lzwc2YwMRIECAAAECBAhUAm/evMmXYZu+3Fe18CH78vnz5+Px+MSJE1V4Pnfu3Hg8fvfu3SHbX7tDgMAfFJCf/yC+oQkQIECAAAECBPZH4NmzZ+vfP16/fr0/m7YVAgQIJAH5OUmoBAgQIECAAAECBAgQIECgLSA/t210CBAgQIAAAQIECBAgQIBAEpCfk4RKgAABAgQIECBAgAABAgTaAvJz20aHAAECBAgQIECAAAECBAgkAfk5SagECBAgQIAAAQIECBAgQKAtID+3bXQIECBAgAABAgQIECBAgEASkJ+ThEqAAAECBAgQIECAAAECBNoC8nPbRocAAQIECBAgQIAAAQIECCQB+TlJqAQIECBAgAABAgQIECBAoC0gP7dtdAgQIECAAAECBAgQIECAQBKQn5OESoAAAQIECBAgQIAAAQIE2gLyc9tGhwABAgQIECBAgAABAgQIJAH5OUmoBAgQIECAAAECBAgQIECgLSA/t210CBAgQIAAAQIECBAgQIBAEpCfk4RKgAABAgQIECBAgAABAgTaAvJz20aHAAECBAgQIECAAAECBAgkAfk5SagECBAgQIAAAQIECBAgQKAtID+3bXQIECBAgAABAgQIECBAgEASkJ+ThEqAAAECBAgQIECAAAECBNoC8nPbRocAAQIECBAgQIAAAQIECCQB+TlJqAQIECBAgAABAgQIECBAoC0gP7dtdAgQIECAAAECBAgQIECAQBKQn5OESoAAAQIECBAgQIAAAQIE2gLyc9tGhwABAgQIECBAgAABAgQIJAH5OUmoBAgQIECAAAECBAgQIECgLSA/t210CBAgQIAAAQIECBAgQIBAEpCfk4RKgAABAgQIECBAgAABAgTaAvJz20aHAAECBAgQIECAAAECBAgkAfk5SagECBAgQIAAAQIECBAgQKAtID+3bXQIECBAgAABAgQIECBAgEASkJ+ThEqAAAECBAgQIECAAAECBNoC8nPbRocAAQIECBAgQIAAAQIECCQB+TlJqAQIECBAgAABAgQIECBAoC0gP7dtdAgQIECAAAECBAgQIECAQBKQn5OESoAAAQIECBAgQIAAAQIE2gLyc9tGhwABAgQIECBAgAABAgQIJAH5OUmoBAgQIECAAAECBAgQIECgLSA/t210CBAgQIAAAQIECBAgQIBAEpCfk4RKgAABAgQIECBAgAABAgTaAvJz20aHAAECBAgQIECAAAECBAgkAfk5SagECBAgQIAAAQIECBAgQKAtID+3bXQIECBAgAABAgQIECBAgEASkJ+ThEqAAAECBAgQIECAAAECBNoC8nPbRocAAQIECBAgQIAAAQIECCQB+TlJqAQIECBAgAABAgQIECBAoC0gP7dtdAgQIECAAAECBAgQIECAQBKQn5OESoAAAQIECBAgQIAAAQIE2gLyc9tGhwABAgQIECBAgAABAgQIJAH5OUmoBAgQIECAAAECBAgQIECgLSA/t210CBAgQIAAAQIECBAgQIBAEpCfk4RKgAABAgQIECBAgAABAgTaAv8A5VJZhTt7UJ0AAAAASUVORK5CYII=\", width=\"500\">\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TZhCNqg2qfBd"
      },
      "source": [
        "**Implementation Issues**\n",
        "\n",
        "Cap 12.12  - PDF 338; il testo di Sutton afferma:\n",
        "\n",
        "*It might at first appear that tabular methods using eligibility traces are much more complex than one-step methods. A naive implementation would require every state (or state-action pair) to update both its value estimate and its eligibility trace on every time\n",
        "step. This would not be a problem for implementations on single-instruction, multipledata, parallel computer or in plausible artificial neural network implementations, but it is a problem for implementations on conventional serial computers. Fortunately, for typical values of λ and $\\gamma$ the eligibility traces of almost all states are almost always nearly zero; only those states that have recently been visited will have traces significantly\n",
        "greater than zero and only these few states need to be updated to closely approximate these algorithms.*\n",
        "\n",
        "*In practice, then, implementations on conventional computers may keep track of and update only the few traces that are significantly greater than zero. Using this trick, the computational expense of using traces in tabular methods is typically just a few times\n",
        "that of a one-step method.*\n",
        "\n",
        "*Note that the tabular case is in some sense the worst\n",
        "case for the computational complexity of eligibility traces. When function approximation\n",
        "is used, the computational advantages of not using traces generally decrease.*\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-GZaSLjzuJEj"
      },
      "source": [
        "## Coding with look-up table"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "g6qD5Sgfw4l0"
      },
      "source": [
        "### Moduli"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "g3faToEhJKDh"
      },
      "outputs": [],
      "source": [
        "# codice di riferimento : https://github.com/moripiri/Reinforcement-Learning-on-FrozenLake/blob/master/Chapter6.ipynb\n",
        "# Teoria : http://incompleteideas.net/book/first/ebook/node77.html\n",
        "\n",
        "import gym\n",
        "\n",
        "import random\n",
        "import numpy as np\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "import copy\n",
        "\n",
        "import warnings\n",
        "warnings.filterwarnings('ignore')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mLn2HFLQxnmR"
      },
      "source": [
        "### SARSA with Eligibility Traces\n",
        "\n",
        "or SARSA($\\lambda$) algorithm"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "DxMUGZt0rml0"
      },
      "outputs": [],
      "source": [
        "class SARSA_lamda:\n",
        "    def __init__(self, env, gamma=0.9, lamda=0.5, alpha=0.1,  eps=0.3, max_episode=100):\n",
        "\n",
        "        self.env = env\n",
        "        self.nrow = env.nrow\n",
        "        self.ncol = env.ncol\n",
        "\n",
        "        self.state_dim = env.observation_space.n # self.nrow * self.ncol\n",
        "        self.action_dim = env.action_space.n\n",
        "\n",
        "        self.gamma = gamma\n",
        "        self.lamda = lamda\n",
        "        self.alpha = alpha\n",
        "        self.eps = eps\n",
        "        self.max_episode = max_episode\n",
        "\n",
        "        self.q = np.zeros([self.state_dim, self.action_dim])\n",
        "        # For educational purposes, self.q_c is used solely as a baseline comparison,\n",
        "        # operating independently of the factor \"eligibility trace\"\n",
        "        self.q_c = np.zeros([self.state_dim, self.action_dim])\n",
        "\n",
        "    def action(self, s):\n",
        "        if np.random.random() < self.eps:\n",
        "            supp = {0,1,2,3}.difference({np.argmax(self.q[s, :])})\n",
        "            su = list(supp)\n",
        "            action = np.random.choice(su)\n",
        "        else:\n",
        "            action = np.argmax(self.q[s,:]) # act greedy on Q\n",
        "        return action\n",
        "\n",
        "    def out_q(self):\n",
        "      #print(self.q)\n",
        "      return self.q, self.q_c\n",
        "\n",
        "    def run(self):\n",
        "\n",
        "        for episode in range(1,self.max_episode+1):\n",
        "\n",
        "            #  Sutton's book initialize eligibility trace here:\n",
        "            eligibility = np.zeros([self.state_dim, self.action_dim])\n",
        "            # Putting this line of code before the episode loop, in this case, seems to slow down convergence\n",
        "\n",
        "            # Epsilon greedy policy\n",
        "            if episode % (self.max_episode/5) == 0:\n",
        "                self.eps = self.eps - 0.05\n",
        "            #   print(\"eps=\",self.eps)\n",
        "\n",
        "            observation = self.env.reset()\n",
        "            action = self.action(observation)\n",
        "            done = False\n",
        "\n",
        "            episode_reward = 0\n",
        "            local_step = 1\n",
        "\n",
        "            while not done:\n",
        "\n",
        "                next_observation, reward, done, _ = self.env.step(action)\n",
        "\n",
        "                ###Reward setting\n",
        "                # give penalty for staying in ground\n",
        "                if reward == 0:\n",
        "                    reward = -0.001\n",
        "\n",
        "                # give penalty for falling into the hole\n",
        "                if done and next_observation != 15:\n",
        "                    reward = -1\n",
        "\n",
        "                if observation == next_observation: # prevent meaningless actions\n",
        "                    reward = -1\n",
        "\n",
        "                ######\n",
        "\n",
        "                next_action = self.action(next_observation)\n",
        "\n",
        "                delta = reward + self.gamma * self.q[next_observation, next_action] - self.q[observation, action]\n",
        "\n",
        "                self.q_c[observation, action] += self.alpha * delta\n",
        "\n",
        "                # Eligibility and Q update\n",
        "                for i in range(self.state_dim):\n",
        "                    for j in range(self.action_dim):\n",
        "\n",
        "                        if i == observation and j == action:\n",
        "                           eligibility[i, j] = self.gamma * self.lamda * eligibility[i, j] + 1\n",
        "                        else:\n",
        "                           eligibility[i, j] = self.gamma * self.lamda * eligibility[i, j]\n",
        "\n",
        "                        self.q[i, j] += self.alpha * delta * eligibility[i, j]\n",
        "\n",
        "                #To clarify the mechanism eligibility trace\n",
        "                if (episode == 1)  or  (episode == 20) or (episode == 40) or (episode == 50):\n",
        "                   rounded   =  [list(np.round(x,4)) for x in eligibility]\n",
        "                   rounded_q =  [list(np.round(x,4)) for x in self.q]\n",
        "                   rounded_qc = [list(np.round(x,4)) for x in self.q_c]\n",
        "                   print(\"\")\n",
        "                   print(\"Episode: {} - Step: {}\".format(episode, local_step))\n",
        "                   print(\"Elig: {}\".format(rounded)    )\n",
        "                   print(\"Q   : {}\".format(rounded_q)  )\n",
        "                   print(\"Q_c : {}\".format(rounded_qc) )\n",
        "\n",
        "                observation = next_observation\n",
        "                action = next_action\n",
        "\n",
        "                episode_reward += reward\n",
        "                local_step += 1\n",
        "\n",
        "\n",
        "            #print(\"Episode: {} -> Step: {}, Episode_reward: {}\".format(episode, local_step, episode_reward))\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zcTkpL0PyDc-",
        "outputId": "0f3c452d-4cf0-4ff4-f2d5-eb41fe0928b3"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "\n",
            "Episode: 1 - Step: 1\n",
            "Elig: [[1.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.1, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.1, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 1 - Step: 2\n",
            "Elig: [[1.45, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.2305, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.19, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 1 - Step: 3\n",
            "Elig: [[0.6525, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.2306, 0.0, -0.0001, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.19, 0.0, -0.0001, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 1 - Step: 4\n",
            "Elig: [[0.2936, 0.0, 0.45, 0.0], [0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.2306, 0.0, -0.0001, 0.0], [0.0, 0.0, -0.0001, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.19, 0.0, -0.0001, 0.0], [0.0, 0.0, -0.0001, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 1 - Step: 5\n",
            "Elig: [[0.1321, 0.0, 0.2025, 0.0], [0.0, 0.0, 0.45, 0.0], [0.0, 0.0, 0.0, 1.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.2438, 0.0, -0.0204, 0.0], [0.0, 0.0, -0.0451, 0.0], [0.0, 0.0, 0.0, -0.1], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.19, 0.0, -0.0001, 0.0], [0.0, 0.0, -0.0001, 0.0], [0.0, 0.0, 0.0, -0.1], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 1 - Step: 6\n",
            "Elig: [[0.0595, 0.0, 0.0911, 0.0], [0.0, 0.0, 0.2025, 0.0], [0.0, 0.0, 1.0, 0.45], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.2438, 0.0, -0.0204, 0.0], [0.0, 0.0, -0.0451, 0.0], [0.0, 0.0, -0.0001, -0.1], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.19, 0.0, -0.0001, 0.0], [0.0, 0.0, -0.0001, 0.0], [0.0, 0.0, -0.0001, -0.1], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 1 - Step: 7\n",
            "Elig: [[0.0268, 0.0, 0.041, 0.0], [0.0, 0.0, 0.0911, 0.0], [0.0, 0.0, 0.45, 0.2025], [1.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.2438, 0.0, -0.0204, 0.0], [0.0, 0.0, -0.0451, 0.0], [0.0, 0.0, -0.0001, -0.1001], [-0.0001, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.19, 0.0, -0.0001, 0.0], [0.0, 0.0, -0.0001, 0.0], [0.0, 0.0, -0.0001, -0.1], [-0.0001, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 1 - Step: 8\n",
            "Elig: [[0.012, 0.0, 0.0185, 0.0], [0.0, 0.0, 0.041, 0.0], [1.0, 0.0, 0.2025, 0.0911], [0.45, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.2438, 0.0, -0.0204, 0.0], [0.0, 0.0, -0.0451, 0.0], [-0.0001, 0.0, -0.0002, -0.1001], [-0.0001, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.19, 0.0, -0.0001, 0.0], [0.0, 0.0, -0.0001, 0.0], [-0.0001, 0.0, -0.0001, -0.1], [-0.0001, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 1 - Step: 9\n",
            "Elig: [[0.0054, 0.0, 0.0083, 0.0], [0.0, 0.0, 0.0185, 1.0], [0.45, 0.0, 0.0911, 0.041], [0.2025, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.2444, 0.0, -0.0212, 0.0], [0.0, 0.0, -0.047, -0.1], [-0.0451, 0.0, -0.0093, -0.1042], [-0.0204, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.19, 0.0, -0.0001, 0.0], [0.0, 0.0, -0.0001, -0.1], [-0.0001, 0.0, -0.0001, -0.1], [-0.0001, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 1 - Step: 10\n",
            "Elig: [[0.0024, 0.0, 0.0037, 0.0], [0.0, 0.0, 0.0083, 1.45], [0.2025, 0.0, 0.041, 0.0185], [0.0911, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.2446, 0.0, -0.0216, 0.0], [0.0, 0.0, -0.0477, -0.2305], [-0.0633, 0.0, -0.013, -0.1058], [-0.0286, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.19, 0.0, -0.0001, 0.0], [0.0, 0.0, -0.0001, -0.19], [-0.0001, 0.0, -0.0001, -0.1], [-0.0001, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 1 - Step: 11\n",
            "Elig: [[0.0011, 0.0, 0.0017, 0.0], [0.0, 1.0, 0.0037, 0.6525], [0.0911, 0.0, 0.0185, 0.0083], [0.041, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.2447, 0.0, -0.0217, 0.0], [0.0, -0.1, -0.0481, -0.2958], [-0.0724, 0.0, -0.0148, -0.1067], [-0.0327, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.19, 0.0, -0.0001, 0.0], [0.0, -0.1, -0.0001, -0.19], [-0.0001, 0.0, -0.0001, -0.1], [-0.0001, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 20 - Step: 1\n",
            "Elig: [[0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.6466, -0.2318, -0.3078, -0.569], [-0.2639, -0.4095, -0.1864, -0.5197], [-0.2101, -0.1863, -0.2256, -0.3401], [-0.1241, -0.1, -0.5094, -0.2474], [-0.5414, -0.1464, -0.271, -0.1704], [0.0, 0.0, 0.0, 0.0], [-0.271, -0.0251, -0.19, -0.0454], [0.0, 0.0, 0.0, 0.0], [-0.3574, -0.19, -0.0559, -0.1053], [-0.0767, -0.0476, -0.039, -0.1], [-0.0248, -0.0312, -0.1, -0.0141], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.1, -0.2724, -0.0642, -0.0266], [-0.0652, -0.2367, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.5274, 0.0551, 0.0536, -0.447], [-0.0932, -0.4095, 0.0739, -0.4139], [-0.0565, 0.0472, 0.0047, -0.2891], [-0.0211, -0.1, -0.3517, -0.194], [-0.3996, 0.0287, -0.271, -0.0612], [0.0, 0.0, 0.0, 0.0], [-0.271, 0.0046, -0.19, -0.0268], [0.0, 0.0, 0.0, 0.0], [-0.266, -0.19, 0.0161, -0.0259], [-0.0242, 0.0065, 0.008, -0.1], [0.0002, -0.0001, -0.1, -0.0085], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.1, -0.19, -0.0001, -0.0052], [0.0067, -0.1961, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 20 - Step: 2\n",
            "Elig: [[0.0, 0.45, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.6466, -0.2296, -0.3078, -0.569], [-0.2639, -0.4095, -0.1864, -0.5197], [-0.2101, -0.1863, -0.2256, -0.3401], [-0.1241, -0.1, -0.5094, -0.2474], [-0.5414, -0.1413, -0.271, -0.1704], [0.0, 0.0, 0.0, 0.0], [-0.271, -0.0251, -0.19, -0.0454], [0.0, 0.0, 0.0, 0.0], [-0.3574, -0.19, -0.0559, -0.1053], [-0.0767, -0.0476, -0.039, -0.1], [-0.0248, -0.0312, -0.1, -0.0141], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.1, -0.2724, -0.0642, -0.0266], [-0.0652, -0.2367, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.5274, 0.0551, 0.0536, -0.447], [-0.0932, -0.4095, 0.0739, -0.4139], [-0.0565, 0.0472, 0.0047, -0.2891], [-0.0211, -0.1, -0.3517, -0.194], [-0.3996, 0.0337, -0.271, -0.0612], [0.0, 0.0, 0.0, 0.0], [-0.271, 0.0046, -0.19, -0.0268], [0.0, 0.0, 0.0, 0.0], [-0.266, -0.19, 0.0161, -0.0259], [-0.0242, 0.0065, 0.008, -0.1], [0.0002, -0.0001, -0.1, -0.0085], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.1, -0.19, -0.0001, -0.0052], [0.0067, -0.1961, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 20 - Step: 3\n",
            "Elig: [[0.0, 0.2025, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.45, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 1.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.6466, -0.23, -0.3078, -0.569], [-0.2639, -0.4095, -0.1864, -0.5197], [-0.2101, -0.1863, -0.2256, -0.3401], [-0.1241, -0.1, -0.5094, -0.2474], [-0.5414, -0.1424, -0.271, -0.1704], [0.0, 0.0, 0.0, 0.0], [-0.271, -0.0251, -0.19, -0.0454], [0.0, 0.0, 0.0, 0.0], [-0.3574, -0.19, -0.0559, -0.1076], [-0.0767, -0.0476, -0.039, -0.1], [-0.0248, -0.0312, -0.1, -0.0141], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.1, -0.2724, -0.0642, -0.0266], [-0.0652, -0.2367, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.5274, 0.0551, 0.0536, -0.447], [-0.0932, -0.4095, 0.0739, -0.4139], [-0.0565, 0.0472, 0.0047, -0.2891], [-0.0211, -0.1, -0.3517, -0.194], [-0.3996, 0.0337, -0.271, -0.0612], [0.0, 0.0, 0.0, 0.0], [-0.271, 0.0046, -0.19, -0.0268], [0.0, 0.0, 0.0, 0.0], [-0.266, -0.19, 0.0161, -0.0281], [-0.0242, 0.0065, 0.008, -0.1], [0.0002, -0.0001, -0.1, -0.0085], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.1, -0.19, -0.0001, -0.0052], [0.0067, -0.1961, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 20 - Step: 4\n",
            "Elig: [[0.0, 0.0911, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 1.2025, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.45], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.6466, -0.2292, -0.3078, -0.569], [-0.2639, -0.4095, -0.1864, -0.5197], [-0.2101, -0.1863, -0.2256, -0.3401], [-0.1241, -0.1, -0.5094, -0.2474], [-0.5414, -0.1314, -0.271, -0.1704], [0.0, 0.0, 0.0, 0.0], [-0.271, -0.0251, -0.19, -0.0454], [0.0, 0.0, 0.0, 0.0], [-0.3574, -0.19, -0.0559, -0.1035], [-0.0767, -0.0476, -0.039, -0.1], [-0.0248, -0.0312, -0.1, -0.0141], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.1, -0.2724, -0.0642, -0.0266], [-0.0652, -0.2367, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.5274, 0.0551, 0.0536, -0.447], [-0.0932, -0.4095, 0.0739, -0.4139], [-0.0565, 0.0472, 0.0047, -0.2891], [-0.0211, -0.1, -0.3517, -0.194], [-0.3996, 0.0428, -0.271, -0.0612], [0.0, 0.0, 0.0, 0.0], [-0.271, 0.0046, -0.19, -0.0268], [0.0, 0.0, 0.0, 0.0], [-0.266, -0.19, 0.0161, -0.0281], [-0.0242, 0.0065, 0.008, -0.1], [0.0002, -0.0001, -0.1, -0.0085], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.1, -0.19, -0.0001, -0.0052], [0.0067, -0.1961, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 20 - Step: 5\n",
            "Elig: [[0.0, 0.041, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.5411, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 1.0, 0.2025], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.6466, -0.2291, -0.3078, -0.569], [-0.2639, -0.4095, -0.1864, -0.5197], [-0.2101, -0.1863, -0.2256, -0.3401], [-0.1241, -0.1, -0.5094, -0.2474], [-0.5414, -0.1303, -0.271, -0.1704], [0.0, 0.0, 0.0, 0.0], [-0.271, -0.0251, -0.19, -0.0454], [0.0, 0.0, 0.0, 0.0], [-0.3574, -0.19, -0.0539, -0.1031], [-0.0767, -0.0476, -0.039, -0.1], [-0.0248, -0.0312, -0.1, -0.0141], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.1, -0.2724, -0.0642, -0.0266], [-0.0652, -0.2367, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.5274, 0.0551, 0.0536, -0.447], [-0.0932, -0.4095, 0.0739, -0.4139], [-0.0565, 0.0472, 0.0047, -0.2891], [-0.0211, -0.1, -0.3517, -0.194], [-0.3996, 0.0428, -0.271, -0.0612], [0.0, 0.0, 0.0, 0.0], [-0.271, 0.0046, -0.19, -0.0268], [0.0, 0.0, 0.0, 0.0], [-0.266, -0.19, 0.0181, -0.0281], [-0.0242, 0.0065, 0.008, -0.1], [0.0002, -0.0001, -0.1, -0.0085], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.1, -0.19, -0.0001, -0.0052], [0.0067, -0.1961, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 20 - Step: 6\n",
            "Elig: [[0.0, 0.0185, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.2435, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.45, 0.0911], [0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.6466, -0.2291, -0.3078, -0.569], [-0.2639, -0.4095, -0.1864, -0.5197], [-0.2101, -0.1863, -0.2256, -0.3401], [-0.1241, -0.1, -0.5094, -0.2474], [-0.5414, -0.1297, -0.271, -0.1704], [0.0, 0.0, 0.0, 0.0], [-0.271, -0.0251, -0.19, -0.0454], [0.0, 0.0, 0.0, 0.0], [-0.3574, -0.19, -0.0528, -0.1029], [-0.0767, -0.0476, -0.0364, -0.1], [-0.0248, -0.0312, -0.1, -0.0141], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.1, -0.2724, -0.0642, -0.0266], [-0.0652, -0.2367, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.5274, 0.0551, 0.0536, -0.447], [-0.0932, -0.4095, 0.0739, -0.4139], [-0.0565, 0.0472, 0.0047, -0.2891], [-0.0211, -0.1, -0.3517, -0.194], [-0.3996, 0.0428, -0.271, -0.0612], [0.0, 0.0, 0.0, 0.0], [-0.271, 0.0046, -0.19, -0.0268], [0.0, 0.0, 0.0, 0.0], [-0.266, -0.19, 0.0181, -0.0281], [-0.0242, 0.0065, 0.0105, -0.1], [0.0002, -0.0001, -0.1, -0.0085], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.1, -0.19, -0.0001, -0.0052], [0.0067, -0.1961, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 20 - Step: 7\n",
            "Elig: [[0.0, 0.0083, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.1096, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.2025, 0.041], [0.0, 0.0, 0.45, 0.0], [0.0, 0.0, 0.0, 1.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.6466, -0.2292, -0.3078, -0.569], [-0.2639, -0.4095, -0.1864, -0.5197], [-0.2101, -0.1863, -0.2256, -0.3401], [-0.1241, -0.1, -0.5094, -0.2474], [-0.5414, -0.1314, -0.271, -0.1704], [0.0, 0.0, 0.0, 0.0], [-0.271, -0.0251, -0.19, -0.0454], [0.0, 0.0, 0.0, 0.0], [-0.3574, -0.19, -0.056, -0.1035], [-0.0767, -0.0476, -0.0435, -0.1], [-0.0248, -0.0312, -0.1, -0.0299], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.1, -0.2724, -0.0642, -0.0266], [-0.0652, -0.2367, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.5274, 0.0551, 0.0536, -0.447], [-0.0932, -0.4095, 0.0739, -0.4139], [-0.0565, 0.0472, 0.0047, -0.2891], [-0.0211, -0.1, -0.3517, -0.194], [-0.3996, 0.0428, -0.271, -0.0612], [0.0, 0.0, 0.0, 0.0], [-0.271, 0.0046, -0.19, -0.0268], [0.0, 0.0, 0.0, 0.0], [-0.266, -0.19, 0.0181, -0.0281], [-0.0242, 0.0065, 0.0105, -0.1], [0.0002, -0.0001, -0.1, -0.0243], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.1, -0.19, -0.0001, -0.0052], [0.0067, -0.1961, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 20 - Step: 8\n",
            "Elig: [[0.0, 0.0037, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0493, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0911, 0.0185], [0.0, 0.0, 0.2025, 0.0], [0.0, 0.0, 0.0, 0.45], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.6466, -0.2295, -0.3078, -0.569], [-0.2639, -0.4095, -0.1864, -0.5197], [-0.2101, -0.1863, -0.2256, -0.3401], [-0.1241, -0.1, -0.5094, -0.2474], [-0.5414, -0.1354, -0.271, -0.1704], [0.0, 0.0, 0.0, 0.0], [-0.271, -0.0251, -0.271, -0.0454], [0.0, 0.0, 0.0, 0.0], [-0.3574, -0.19, -0.0634, -0.105], [-0.0767, -0.0476, -0.0599, -0.1], [-0.0248, -0.0312, -0.1, -0.0664], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.1, -0.2724, -0.0642, -0.0266], [-0.0652, -0.2367, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.5274, 0.0551, 0.0536, -0.447], [-0.0932, -0.4095, 0.0739, -0.4139], [-0.0565, 0.0472, 0.0047, -0.2891], [-0.0211, -0.1, -0.3517, -0.194], [-0.3996, 0.0428, -0.271, -0.0612], [0.0, 0.0, 0.0, 0.0], [-0.271, 0.0046, -0.271, -0.0268], [0.0, 0.0, 0.0, 0.0], [-0.266, -0.19, 0.0181, -0.0281], [-0.0242, 0.0065, 0.0105, -0.1], [0.0002, -0.0001, -0.1, -0.0243], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.1, -0.19, -0.0001, -0.0052], [0.0067, -0.1961, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 40 - Step: 1\n",
            "Elig: [[0.0, 0.0, 0.0, 1.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.6466, -0.3105, -0.24, -0.7598], [-0.2639, -0.4095, -0.1251, -0.5197], [-0.2101, -0.072, -0.2256, -0.3401], [-0.1241, -0.1, -0.5094, -0.2474], [-0.6494, -0.1444, -0.4095, -0.2517], [0.0, 0.0, 0.0, 0.0], [-0.271, 0.1169, -0.271, -0.0454], [0.0, 0.0, 0.0, 0.0], [-0.466, -0.3439, 0.0502, -0.105], [-0.0809, -0.1109, 0.1582, -0.271], [-0.0355, 0.4391, -0.1, -0.0664], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.19, -0.2724, -0.0479, -0.0883], [-0.0572, -0.2367, 0.7176, 0.0639], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.5274, 0.141, 0.0939, -0.6193], [-0.0932, -0.4095, 0.0837, -0.4139], [-0.0565, 0.0976, 0.0047, -0.2891], [-0.0211, -0.1, -0.3517, -0.194], [-0.523, 0.1126, -0.4095, -0.103], [0.0, 0.0, 0.0, 0.0], [-0.271, 0.0958, -0.271, -0.0268], [0.0, 0.0, 0.0, 0.0], [-0.3937, -0.3439, 0.082, -0.0281], [-0.0209, 0.0115, 0.0883, -0.271], [-0.0008, 0.125, -0.1, -0.0243], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.19, -0.19, 0.0062, -0.0178], [0.0074, -0.1961, 0.7176, 0.0482], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 40 - Step: 2\n",
            "Elig: [[0.0, 0.0, 1.0, 0.45], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.6466, -0.3105, -0.2274, -0.7542], [-0.2639, -0.4095, -0.1251, -0.5197], [-0.2101, -0.072, -0.2256, -0.3401], [-0.1241, -0.1, -0.5094, -0.2474], [-0.6494, -0.1444, -0.4095, -0.2517], [0.0, 0.0, 0.0, 0.0], [-0.271, 0.1169, -0.271, -0.0454], [0.0, 0.0, 0.0, 0.0], [-0.466, -0.3439, 0.0502, -0.105], [-0.0809, -0.1109, 0.1582, -0.271], [-0.0355, 0.4391, -0.1, -0.0664], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.19, -0.2724, -0.0479, -0.0883], [-0.0572, -0.2367, 0.7176, 0.0639], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.5274, 0.141, 0.1065, -0.6193], [-0.0932, -0.4095, 0.0837, -0.4139], [-0.0565, 0.0976, 0.0047, -0.2891], [-0.0211, -0.1, -0.3517, -0.194], [-0.523, 0.1126, -0.4095, -0.103], [0.0, 0.0, 0.0, 0.0], [-0.271, 0.0958, -0.271, -0.0268], [0.0, 0.0, 0.0, 0.0], [-0.3937, -0.3439, 0.082, -0.0281], [-0.0209, 0.0115, 0.0883, -0.271], [-0.0008, 0.125, -0.1, -0.0243], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.19, -0.19, 0.0062, -0.0178], [0.0074, -0.1961, 0.7176, 0.0482], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 40 - Step: 3\n",
            "Elig: [[0.0, 0.0, 0.45, 0.2025], [0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.6466, -0.3105, -0.2247, -0.753], [-0.2639, -0.4095, -0.1192, -0.5197], [-0.2101, -0.072, -0.2256, -0.3401], [-0.1241, -0.1, -0.5094, -0.2474], [-0.6494, -0.1444, -0.4095, -0.2517], [0.0, 0.0, 0.0, 0.0], [-0.271, 0.1169, -0.271, -0.0454], [0.0, 0.0, 0.0, 0.0], [-0.466, -0.3439, 0.0502, -0.105], [-0.0809, -0.1109, 0.1582, -0.271], [-0.0355, 0.4391, -0.1, -0.0664], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.19, -0.2724, -0.0479, -0.0883], [-0.0572, -0.2367, 0.7176, 0.0639], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.5274, 0.141, 0.1065, -0.6193], [-0.0932, -0.4095, 0.0896, -0.4139], [-0.0565, 0.0976, 0.0047, -0.2891], [-0.0211, -0.1, -0.3517, -0.194], [-0.523, 0.1126, -0.4095, -0.103], [0.0, 0.0, 0.0, 0.0], [-0.271, 0.0958, -0.271, -0.0268], [0.0, 0.0, 0.0, 0.0], [-0.3937, -0.3439, 0.082, -0.0281], [-0.0209, 0.0115, 0.0883, -0.271], [-0.0008, 0.125, -0.1, -0.0243], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.19, -0.19, 0.0062, -0.0178], [0.0074, -0.1961, 0.7176, 0.0482], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 40 - Step: 4\n",
            "Elig: [[0.0, 0.0, 0.2025, 0.0911], [0.0, 0.0, 0.45, 0.0], [0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.6466, -0.3105, -0.2282, -0.7545], [-0.2639, -0.4095, -0.127, -0.5197], [-0.2101, -0.0893, -0.2256, -0.3401], [-0.1241, -0.1, -0.5094, -0.2474], [-0.6494, -0.1444, -0.4095, -0.2517], [0.0, 0.0, 0.0, 0.0], [-0.271, 0.1169, -0.271, -0.0454], [0.0, 0.0, 0.0, 0.0], [-0.466, -0.3439, 0.0502, -0.105], [-0.0809, -0.1109, 0.1582, -0.271], [-0.0355, 0.4391, -0.1, -0.0664], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.19, -0.2724, -0.0479, -0.0883], [-0.0572, -0.2367, 0.7176, 0.0639], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.5274, 0.141, 0.1065, -0.6193], [-0.0932, -0.4095, 0.0896, -0.4139], [-0.0565, 0.0804, 0.0047, -0.2891], [-0.0211, -0.1, -0.3517, -0.194], [-0.523, 0.1126, -0.4095, -0.103], [0.0, 0.0, 0.0, 0.0], [-0.271, 0.0958, -0.271, -0.0268], [0.0, 0.0, 0.0, 0.0], [-0.3937, -0.3439, 0.082, -0.0281], [-0.0209, 0.0115, 0.0883, -0.271], [-0.0008, 0.125, -0.1, -0.0243], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.19, -0.19, 0.0062, -0.0178], [0.0074, -0.1961, 0.7176, 0.0482], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 40 - Step: 5\n",
            "Elig: [[0.0, 0.0, 0.0911, 0.041], [0.0, 0.0, 0.2025, 0.0], [0.0, 0.45, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.6466, -0.3105, -0.2348, -0.7575], [-0.2639, -0.4095, -0.1417, -0.5197], [-0.2101, -0.1221, -0.2256, -0.3401], [-0.1241, -0.1, -0.5094, -0.2474], [-0.6494, -0.1444, -0.4095, -0.2517], [0.0, 0.0, 0.0, 0.0], [-0.3439, 0.1169, -0.271, -0.0454], [0.0, 0.0, 0.0, 0.0], [-0.466, -0.3439, 0.0502, -0.105], [-0.0809, -0.1109, 0.1582, -0.271], [-0.0355, 0.4391, -0.1, -0.0664], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.19, -0.2724, -0.0479, -0.0883], [-0.0572, -0.2367, 0.7176, 0.0639], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.5274, 0.141, 0.1065, -0.6193], [-0.0932, -0.4095, 0.0896, -0.4139], [-0.0565, 0.0804, 0.0047, -0.2891], [-0.0211, -0.1, -0.3517, -0.194], [-0.523, 0.1126, -0.4095, -0.103], [0.0, 0.0, 0.0, 0.0], [-0.3439, 0.0958, -0.271, -0.0268], [0.0, 0.0, 0.0, 0.0], [-0.3937, -0.3439, 0.082, -0.0281], [-0.0209, 0.0115, 0.0883, -0.271], [-0.0008, 0.125, -0.1, -0.0243], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.19, -0.19, 0.0062, -0.0178], [0.0074, -0.1961, 0.7176, 0.0482], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 50 - Step: 1\n",
            "Elig: [[0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.6466, -0.3105, -0.1081, -0.7575], [-0.2639, -0.4686, 0.0103, -0.5197], [-0.1886, 0.1114, -0.2256, -0.3401], [-0.1241, -0.1, -0.5094, -0.2474], [-0.6494, -0.1444, -0.4095, -0.2517], [0.0, 0.0, 0.0, 0.0], [-0.3439, 0.3067, -0.271, -0.0454], [0.0, 0.0, 0.0, 0.0], [-0.466, -0.3439, 0.0502, -0.105], [-0.0809, -0.1109, 0.1582, -0.271], [-0.0355, 0.5761, -0.19, -0.0664], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.19, -0.2724, 0.0385, -0.0883], [-0.0171, -0.2367, 0.8649, 0.0639], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.5274, 0.141, 0.2015, -0.6193], [-0.0932, -0.4686, 0.127, -0.4139], [-0.0452, 0.2284, 0.0047, -0.2891], [-0.0211, -0.1, -0.3517, -0.194], [-0.523, 0.1126, -0.4095, -0.103], [0.0, 0.0, 0.0, 0.0], [-0.3439, 0.2645, -0.271, -0.0268], [0.0, 0.0, 0.0, 0.0], [-0.3937, -0.3439, 0.082, -0.0281], [-0.0209, 0.0115, 0.0883, -0.271], [-0.0008, 0.1859, -0.19, -0.0243], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.19, -0.19, 0.0842, -0.0178], [0.0087, -0.1961, 0.8649, 0.0482], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 50 - Step: 2\n",
            "Elig: [[0.0, 0.0, 0.45, 0.0], [0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.6466, -0.3105, -0.1041, -0.7575], [-0.2639, -0.4686, 0.0192, -0.5197], [-0.1886, 0.1114, -0.2256, -0.3401], [-0.1241, -0.1, -0.5094, -0.2474], [-0.6494, -0.1444, -0.4095, -0.2517], [0.0, 0.0, 0.0, 0.0], [-0.3439, 0.3067, -0.271, -0.0454], [0.0, 0.0, 0.0, 0.0], [-0.466, -0.3439, 0.0502, -0.105], [-0.0809, -0.1109, 0.1582, -0.271], [-0.0355, 0.5761, -0.19, -0.0664], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.19, -0.2724, 0.0385, -0.0883], [-0.0171, -0.2367, 0.8649, 0.0639], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.5274, 0.141, 0.2015, -0.6193], [-0.0932, -0.4686, 0.1359, -0.4139], [-0.0452, 0.2284, 0.0047, -0.2891], [-0.0211, -0.1, -0.3517, -0.194], [-0.523, 0.1126, -0.4095, -0.103], [0.0, 0.0, 0.0, 0.0], [-0.3439, 0.2645, -0.271, -0.0268], [0.0, 0.0, 0.0, 0.0], [-0.3937, -0.3439, 0.082, -0.0281], [-0.0209, 0.0115, 0.0883, -0.271], [-0.0008, 0.1859, -0.19, -0.0243], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.19, -0.19, 0.0842, -0.0178], [0.0087, -0.1961, 0.8649, 0.0482], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 50 - Step: 3\n",
            "Elig: [[0.0, 0.0, 0.2025, 0.0], [0.0, 0.0, 0.45, 0.0], [0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.6466, -0.3105, -0.1008, -0.7575], [-0.2639, -0.4686, 0.0266, -0.5197], [-0.1886, 0.1277, -0.2256, -0.3401], [-0.1241, -0.1, -0.5094, -0.2474], [-0.6494, -0.1444, -0.4095, -0.2517], [0.0, 0.0, 0.0, 0.0], [-0.3439, 0.3067, -0.271, -0.0454], [0.0, 0.0, 0.0, 0.0], [-0.466, -0.3439, 0.0502, -0.105], [-0.0809, -0.1109, 0.1582, -0.271], [-0.0355, 0.5761, -0.19, -0.0664], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.19, -0.2724, 0.0385, -0.0883], [-0.0171, -0.2367, 0.8649, 0.0639], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.5274, 0.141, 0.2015, -0.6193], [-0.0932, -0.4686, 0.1359, -0.4139], [-0.0452, 0.2447, 0.0047, -0.2891], [-0.0211, -0.1, -0.3517, -0.194], [-0.523, 0.1126, -0.4095, -0.103], [0.0, 0.0, 0.0, 0.0], [-0.3439, 0.2645, -0.271, -0.0268], [0.0, 0.0, 0.0, 0.0], [-0.3937, -0.3439, 0.082, -0.0281], [-0.0209, 0.0115, 0.0883, -0.271], [-0.0008, 0.1859, -0.19, -0.0243], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.19, -0.19, 0.0842, -0.0178], [0.0087, -0.1961, 0.8649, 0.0482], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 50 - Step: 4\n",
            "Elig: [[0.0, 0.0, 0.0911, 0.0], [0.0, 0.0, 0.2025, 0.0], [0.0, 0.45, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.6466, -0.3105, -0.0989, -0.7575], [-0.2639, -0.4686, 0.0309, -0.5197], [-0.1886, 0.1372, -0.2256, -0.3401], [-0.1241, -0.1, -0.5094, -0.2474], [-0.6494, -0.1444, -0.4095, -0.2517], [0.0, 0.0, 0.0, 0.0], [-0.3439, 0.3278, -0.271, -0.0454], [0.0, 0.0, 0.0, 0.0], [-0.466, -0.3439, 0.0502, -0.105], [-0.0809, -0.1109, 0.1582, -0.271], [-0.0355, 0.5761, -0.19, -0.0664], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.19, -0.2724, 0.0385, -0.0883], [-0.0171, -0.2367, 0.8649, 0.0639], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.5274, 0.141, 0.2015, -0.6193], [-0.0932, -0.4686, 0.1359, -0.4139], [-0.0452, 0.2447, 0.0047, -0.2891], [-0.0211, -0.1, -0.3517, -0.194], [-0.523, 0.1126, -0.4095, -0.103], [0.0, 0.0, 0.0, 0.0], [-0.3439, 0.2855, -0.271, -0.0268], [0.0, 0.0, 0.0, 0.0], [-0.3937, -0.3439, 0.082, -0.0281], [-0.0209, 0.0115, 0.0883, -0.271], [-0.0008, 0.1859, -0.19, -0.0243], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.19, -0.19, 0.0842, -0.0178], [0.0087, -0.1961, 0.8649, 0.0482], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 50 - Step: 5\n",
            "Elig: [[0.0, 0.0, 0.041, 0.0], [0.0, 0.0, 0.0911, 0.0], [0.0, 0.2025, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.45, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.6466, -0.3105, -0.0981, -0.7575], [-0.2639, -0.4686, 0.0327, -0.5197], [-0.1886, 0.1413, -0.2256, -0.3401], [-0.1241, -0.1, -0.5094, -0.2474], [-0.6494, -0.1444, -0.4095, -0.2517], [0.0, 0.0, 0.0, 0.0], [-0.3439, 0.3368, -0.271, -0.0454], [0.0, 0.0, 0.0, 0.0], [-0.466, -0.3439, 0.0502, -0.105], [-0.0809, -0.1109, 0.1582, -0.271], [-0.0355, 0.5962, -0.19, -0.0664], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.19, -0.2724, 0.0385, -0.0883], [-0.0171, -0.2367, 0.8649, 0.0639], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.5274, 0.141, 0.2015, -0.6193], [-0.0932, -0.4686, 0.1359, -0.4139], [-0.0452, 0.2447, 0.0047, -0.2891], [-0.0211, -0.1, -0.3517, -0.194], [-0.523, 0.1126, -0.4095, -0.103], [0.0, 0.0, 0.0, 0.0], [-0.3439, 0.2855, -0.271, -0.0268], [0.0, 0.0, 0.0, 0.0], [-0.3937, -0.3439, 0.082, -0.0281], [-0.0209, 0.0115, 0.0883, -0.271], [-0.0008, 0.2061, -0.19, -0.0243], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.19, -0.19, 0.0842, -0.0178], [0.0087, -0.1961, 0.8649, 0.0482], [0.0, 0.0, 0.0, 0.0]]\n",
            "\n",
            "Episode: 50 - Step: 6\n",
            "Elig: [[0.0, 0.0, 0.0185, 0.0], [0.0, 0.0, 0.041, 0.0], [0.0, 0.0911, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.2025, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.45, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q   : [[-0.6466, -0.3105, -0.0978, -0.7575], [-0.2639, -0.4686, 0.0332, -0.5197], [-0.1886, 0.1425, -0.2256, -0.3401], [-0.1241, -0.1, -0.5094, -0.2474], [-0.6494, -0.1444, -0.4095, -0.2517], [0.0, 0.0, 0.0, 0.0], [-0.3439, 0.3396, -0.271, -0.0454], [0.0, 0.0, 0.0, 0.0], [-0.466, -0.3439, 0.0502, -0.105], [-0.0809, -0.1109, 0.1582, -0.271], [-0.0355, 0.6023, -0.19, -0.0664], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.19, -0.2724, 0.0385, -0.0883], [-0.0171, -0.2367, 0.8784, 0.0639], [0.0, 0.0, 0.0, 0.0]]\n",
            "Q_c : [[-0.5274, 0.141, 0.2015, -0.6193], [-0.0932, -0.4686, 0.1359, -0.4139], [-0.0452, 0.2447, 0.0047, -0.2891], [-0.0211, -0.1, -0.3517, -0.194], [-0.523, 0.1126, -0.4095, -0.103], [0.0, 0.0, 0.0, 0.0], [-0.3439, 0.2855, -0.271, -0.0268], [0.0, 0.0, 0.0, 0.0], [-0.3937, -0.3439, 0.082, -0.0281], [-0.0209, 0.0115, 0.0883, -0.271], [-0.0008, 0.2061, -0.19, -0.0243], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [-0.19, -0.19, 0.0842, -0.0178], [0.0087, -0.1961, 0.8784, 0.0482], [0.0, 0.0, 0.0, 0.0]]\n"
          ]
        }
      ],
      "source": [
        "env = gym.make(\"FrozenLake-v1\", render_mode='rgb_array', is_slippery=False)#define the environment.\n",
        "\n",
        "sarsa_lamda_config = {\n",
        "    'env': env,\n",
        "    'gamma': 0.9,\n",
        "    'lamda': 0.5,\n",
        "    'alpha': 0.1,\n",
        "    'eps': 0.3,\n",
        "    'max_episode': 50\n",
        "}\n",
        "\n",
        "sarsa_lamda = SARSA_lamda(**sarsa_lamda_config)\n",
        "sarsa_lamda.run()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ub98h-f1DayN"
      },
      "outputs": [],
      "source": [
        "action_value_grid, q_comparison = sarsa_lamda.out_q()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vRmnkvRLw8wu"
      },
      "source": [
        "### Rendering Q value"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 521
        },
        "id": "46YF45_dG082",
        "outputId": "93502298-23d6-4f0b-b909-2bfe45befd40"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 600x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def visualize_q(q_func, ax, nrow=4, ncol=4, title='Q Value') -> None:\n",
        "    # visualize state-action value\n",
        "\n",
        "    q_func = q_func.reshape([nrow, ncol, 4])\n",
        "\n",
        "    h_ticks = np.arange(-0.5, nrow + 0.5, 1)\n",
        "    v_ticks = np.arange(-0.5, ncol + 0.5, 1)\n",
        "\n",
        "    # plot the state-action function\n",
        "\n",
        "    im = ax.imshow(np.zeros([nrow, ncol]), alpha=0.)\n",
        "\n",
        "    for tick in h_ticks:\n",
        "        ax.axhline(tick, color='black', linewidth=0.3)\n",
        "\n",
        "    for tick in v_ticks:\n",
        "        ax.axvline(tick, color='black', linewidth=0.3)\n",
        "\n",
        "    for h in range(len(h_ticks) - 1):\n",
        "        for v in range(len(v_ticks) - 1):\n",
        "            ax.plot([v_ticks[v], v_ticks[v + 1]], [h_ticks[h], h_ticks[h + 1]], color='black', linewidth=0.3)\n",
        "            ax.plot([v_ticks[v], v_ticks[v + 1]], [h_ticks[h + 1], h_ticks[h]], color='black', linewidth=0.3)\n",
        "\n",
        "    for (j, i, k), q in np.ndenumerate(q_func):\n",
        "        if k == 0:\n",
        "            ax.text(i - 0.3, j, np.round(q, 2), ha='center', va='center', fontsize=8)  # left\n",
        "        elif k == 1:\n",
        "            ax.text(i, j + 0.3, np.round(q, 2), ha='center', va='center', fontsize=8)  # bottom\n",
        "        elif k == 2:\n",
        "            ax.text(i + 0.3, j, np.round(q, 2), ha='center', va='center', fontsize=8)  # right\n",
        "        elif k == 3:\n",
        "            ax.text(i, j - 0.3, np.round(q, 2), ha='center', va='center', fontsize=8)  # top\n",
        "        else:\n",
        "            raise ValueError\n",
        "    ax.set_title(title)\n",
        "\n",
        "fig = plt.figure(figsize=(6, 6))\n",
        "\n",
        "#fig.colorbar(cm.ScalarMappable(norm=norm, cmap=cmap), ax=ax)\n",
        "ax = fig.add_subplot(111)\n",
        "ax.tick_params(left = False, right = False , labelleft = False ,\n",
        "                labelbottom = False, bottom = False)\n",
        "\n",
        "\n",
        "visualize_q(action_value_grid,ax)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 521
        },
        "id": "l0baYHbvoVoU",
        "outputId": "fb16955f-14f2-47e9-f7a6-dd50eef2e2b4"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 600x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "fig = plt.figure(figsize=(6, 6))\n",
        "\n",
        "#fig.colorbar(cm.ScalarMappable(norm=norm, cmap=cmap), ax=ax)\n",
        "ax = fig.add_subplot(111)\n",
        "ax.tick_params(left = False, right = False , labelleft = False ,\n",
        "                labelbottom = False, bottom = False)\n",
        "\n",
        "\n",
        "visualize_q(q_comparison,ax)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5bNNER3Zv8Zh"
      },
      "source": [
        "## Coding with function approximation  - Sarsa($\\lambda$) algorithm\n",
        "\n",
        "Il codice usato è ispirato al seguente codice:\n",
        "\n",
        "https://github.com/trunghng/reinforcement_learning_an_introduction/blob/main/chapter-12/moutain_car.py\n",
        "\n",
        "\n",
        "Lo pseudocodice può essere trovato nel testo di Sutton, PDF 327.\n",
        "\n",
        "$\\;$\n",
        "\n",
        "PREMESSE :\n",
        "\n",
        "Qui l'idea è di approssimare la funzione costo $v̂(s,\\mathbf{w})$ o $\\hat{q}(s,a,\\mathbf{w})$ con una funzione lineare rispetto i pesi $\\mathbf{w}$.\n",
        "\n",
        "Si prenda ad esempio la funzione $v̂(s,\\mathbf{w})$, si consideri il vettore:\n",
        "$\\mathbf{x}(s) = (x_1(s), x_2(s),...,x_d(s) )^\\intercal $\n",
        "detto **feature vector** dello stato $s$.\n",
        "Questo ha la stessa dimensione $d$ del vettore $\\mathbf{w}$.\n",
        "\n",
        "Usando la modellizzazione lineare, abbiamo:\n",
        "\n",
        "$v̂(s,\\mathbf{w}) \\doteq \\mathbf{w} ^\\intercal \\mathbf{x}(s) = \\sum_i ^d w_i x_i(s) $\n",
        "\n",
        "il cui gradiente rispetto $\\mathbf{w}$ si semplifica così:\n",
        "\n",
        "$ \\nabla v̂(s,\\mathbf{w}) = \\mathbf{x}(s) $\n",
        "\n",
        "\n",
        "Per approfondimenti, consultare il notebook:\n",
        "\n",
        "https://github.com/MarioFiorino/Tutorial-Reinforcement-Learning-ITA-Python/blob/main/Value_Function_Approximation_parte1_RL_ITA.ipynb\n",
        "\n",
        "\n",
        "*\n",
        "\n",
        "Nel codice seguente, sarà usato l'eligibility-traces per la stima di $\\hat{q}(s,a,\\mathbf{w})$, in un contesto di approssimazione di questa con un funzione lineare rispetto i pesi $\\mathbf{w}$.\n",
        "\n",
        "\n",
        "Per capire  le formule di update del codice, si consiglia fortemente la lettura del paragrago **12.5 True Online TD**, PDF 321 nel testo di Sutton.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Dh3DA-IOaY94"
      },
      "source": [
        "### Moduli"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "dZDQV9nBv_L4"
      },
      "outputs": [],
      "source": [
        "import sys\n",
        "import gym\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.image as mpimg\n",
        "from tqdm import trange\n",
        "from typing import List\n",
        "\n",
        "import warnings\n",
        "warnings.filterwarnings('ignore')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tsavzBHWacIi"
      },
      "source": [
        "### Tile Coding Software"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "id": "HQtL_wEMacf_"
      },
      "outputs": [],
      "source": [
        "#Tile Coding Software version 3.0beta by Rich Sutton\n",
        "#http://incompleteideas.net/tiles/tiles3.html\n",
        "\n",
        "\"\"\"\n",
        "Tile Coding Software version 3.0beta\n",
        "by Rich Sutton\n",
        "based on a program created by Steph Schaeffer and others\n",
        "External documentation and recommendations on the use of this code is available in the\n",
        "reinforcement learning textbook by Sutton and Barto, and on the web.\n",
        "These need to be understood before this code is.\n",
        "\n",
        "This software is for Python 3 or more.\n",
        "\n",
        "This is an implementation of grid-style tile codings, based originally on\n",
        "the UNH CMAC code (see http://www.ece.unh.edu/robots/cmac.htm), but by now highly changed.\n",
        "Here we provide a function, \"tiles\", that maps floating and integer\n",
        "variables to a list of tiles, and a second function \"tiles-wrap\" that does the same while\n",
        "wrapping some floats to provided widths (the lower wrap value is always 0).\n",
        "\n",
        "The float variables will be gridded at unit intervals, so generalization\n",
        "will be by approximately 1 in each direction, and any scaling will have\n",
        "to be done externally before calling tiles.\n",
        "\n",
        "Num-tilings should be a power of 2, e.g., 16. To make the offsetting work properly, it should\n",
        "also be greater than or equal to four times the number of floats.\n",
        "\n",
        "The first argument is either an index hash table of a given size (created by (make-iht size)),\n",
        "an integer \"size\" (range of the indices from 0), or nil (for testing, indicating that the tile\n",
        "coordinates are to be returned without being converted to indices).\n",
        "\"\"\"\n",
        "\n",
        "basehash = hash\n",
        "\n",
        "class IHT:\n",
        "    \"Structure to handle collisions\"\n",
        "    def __init__(self, sizeval):\n",
        "        self.size = sizeval\n",
        "        self.overfullCount = 0\n",
        "        self.dictionary = {}\n",
        "\n",
        "    def __str__(self):\n",
        "        \"Prepares a string for printing whenever this object is printed\"\n",
        "        return \"Collision table:\" + \\\n",
        "               \" size:\" + str(self.size) + \\\n",
        "               \" overfullCount:\" + str(self.overfullCount) + \\\n",
        "               \" dictionary:\" + str(len(self.dictionary)) + \" items\"\n",
        "\n",
        "    def count (self):\n",
        "        return len(self.dictionary)\n",
        "\n",
        "    def fullp (self):\n",
        "        return len(self.dictionary) >= self.size\n",
        "\n",
        "    def getindex (self, obj, readonly=False):\n",
        "        d = self.dictionary\n",
        "        if obj in d: return d[obj]\n",
        "        elif readonly: return None\n",
        "        size = self.size\n",
        "        count = self.count()\n",
        "        if count >= size:\n",
        "            if self.overfullCount==0: print('IHT full, starting to allow collisions')\n",
        "            self.overfullCount += 1\n",
        "            return basehash(obj) % self.size\n",
        "        else:\n",
        "            d[obj] = count\n",
        "            return count\n",
        "\n",
        "def hashcoords(coordinates, m, readonly=False):\n",
        "    if type(m)==IHT: return m.getindex(tuple(coordinates), readonly)\n",
        "    if type(m)==int: return basehash(tuple(coordinates)) % m\n",
        "    if m==None: return coordinates\n",
        "\n",
        "from math import floor, log\n",
        "from itertools import zip_longest\n",
        "\n",
        "def tiles (ihtORsize, numtilings, floats, ints=[], readonly=False):\n",
        "    \"\"\"returns num-tilings tile indices corresponding to the floats and ints\"\"\"\n",
        "    qfloats = [floor(f*numtilings) for f in floats]\n",
        "    Tiles = []\n",
        "    for tiling in range(numtilings):\n",
        "        tilingX2 = tiling*2\n",
        "        coords = [tiling]\n",
        "        b = tiling\n",
        "        for q in qfloats:\n",
        "            coords.append( (q + b) // numtilings )\n",
        "            b += tilingX2\n",
        "        coords.extend(ints)\n",
        "        Tiles.append(hashcoords(coords, ihtORsize, readonly))\n",
        "    return Tiles\n",
        "\n",
        "def tileswrap (ihtORsize, numtilings, floats, wrapwidths, ints=[], readonly=False):\n",
        "    \"\"\"returns num-tilings tile indices corresponding to the floats and ints, wrapping some floats\"\"\"\n",
        "    qfloats = [floor(f*numtilings) for f in floats]\n",
        "    Tiles = []\n",
        "    for tiling in range(numtilings):\n",
        "        tilingX2 = tiling*2\n",
        "        coords = [tiling]\n",
        "        b = tiling\n",
        "        for q, width in zip_longest(qfloats, wrapwidths):\n",
        "            c = (q + b%numtilings) // numtilings\n",
        "            coords.append(c%width if width else c)\n",
        "            b += tilingX2\n",
        "        coords.extend(ints)\n",
        "        Tiles.append(hashcoords(coords, ihtORsize, readonly))\n",
        "    return Tiles"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Premesse tecniche per comprendere il codice\n"
      ],
      "metadata": {
        "id": "FUZQ4QB4az-6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "w = np.zeros(9)\n",
        "x = np.random.rand(9)\n",
        "w = x + w\n",
        "\n",
        "w = np.around(w, decimals=3)\n",
        "print(\"w            : \", w)\n",
        "\n",
        "a = [0,1,5]\n",
        "print(\"w[a]         : \", w[a])\n",
        "w[a] += 10\n",
        "print(\"w[a]+10      : \", w[a])\n",
        "print(\"\")\n",
        "print(\"w            : \", w)\n",
        "print(\"\")\n",
        "print(\"np.sum(w[a]) : \", np.sum(w[a]))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eVl-gSbDa6xm",
        "outputId": "25d74746-36cc-484b-8179-f231b16a629a"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "w            :  [0.591 0.003 0.114 0.982 0.66  0.77  0.161 0.321 0.704]\n",
            "w[a]         :  [0.591 0.003 0.77 ]\n",
            "w[a]+10      :  [10.591 10.003 10.77 ]\n",
            "\n",
            "w            :  [10.591 10.003  0.114  0.982  0.66  10.77   0.161  0.321  0.704]\n",
            "\n",
            "np.sum(w[a]) :  31.364\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jns4cfoc7IXY"
      },
      "source": [
        "### True online Sarsa( λ ) agent\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "id": "_7Agrb_R7M2k"
      },
      "outputs": [],
      "source": [
        "class TrueOnlineSarsaLambda:\n",
        "\n",
        "    def __init__(self, env: object, lambda_: float,\n",
        "            alpha: float, gamma: float, epsilon: float,\n",
        "            n_tilings: int, n_eps: int, max_steps: int) -> None:\n",
        "        '''\n",
        "        Params\n",
        "        ------\n",
        "        env: OpenAI's MountainCar\n",
        "        lambda_: trace decay param\n",
        "        alpha: step size param\n",
        "        gamma: discount factor\n",
        "        epsilon: exploration param\n",
        "        n_tilings:  number of tilings used for tile coding\n",
        "        n_eps: number of episodes\n",
        "        max_steps: maximum number of steps\n",
        "        '''\n",
        "        self.env = env\n",
        "        self.position_scale = n_tilings / (env.high[0] - env.low[0])\n",
        "        self.velocity_scale = n_tilings / (env.high[1] - env.low[1])\n",
        "        self.lambda_ = lambda_\n",
        "        self.alpha = alpha / n_tilings  # alpha/n_tilings nella versione originale\n",
        "        self.gamma = gamma\n",
        "        self.epsilon = epsilon\n",
        "        self.n_tilings = n_tilings\n",
        "        self.n_eps = n_eps\n",
        "        self.max_steps = max_steps\n",
        "        self.iht = IHT(2048)\n",
        "\n",
        "        # NOTA : i vettori weights e trace sono inizializzati con le stesse dimensioni\n",
        "        self.weights = np.zeros(2048)\n",
        "        self.trace = np.zeros(2048)\n",
        "\n",
        "\n",
        "    def reset(self) -> None:\n",
        "        '''\n",
        "        Episode initialization\n",
        "        '''\n",
        "        self.start_state = self.env.reset()\n",
        "\n",
        "\n",
        "    def get_active_tiles(self, position: float, velocity: float,\n",
        "            action: int, terminated: bool=None) -> List[int]:\n",
        "        '''\n",
        "        Get (indices of) active tiles corresponding to\n",
        "        state-action pair [[@position, @velocity], @action]\n",
        "        (i.e., index of the tile in each tilings where the value = 1)\n",
        "\n",
        "        Params\n",
        "        ------\n",
        "        position: position of the car\n",
        "        velocity: velocity of the car\n",
        "        action: action taken at the state [@position, @velocity]\n",
        "        terminated: whether the car is in terminal state\n",
        "\n",
        "        Return\n",
        "        ------\n",
        "        active_tiles: list of (indices of) active tiles\n",
        "        '''\n",
        "        if terminated is not None and terminated:\n",
        "            return []\n",
        "        active_tiles = tiles(self.iht, self.n_tilings,\n",
        "            [position * self.position_scale, velocity\n",
        "            * self.velocity_scale], [action])\n",
        "        return active_tiles #active_tiles = [0, 1, 90, 3, 87, 78, 6, 81]\n",
        "\n",
        "\n",
        "    def get_value(self, position: float, velocity: float,\n",
        "            action: int, terminated: bool=None) -> float:\n",
        "        '''\n",
        "        Get state-action value of state-action pair [[@position, @velocity], @action]\n",
        "        Since the feature vector is one-hot and we are using linear function approx\n",
        "        => value at [[@position, @velocity], @action] is exactly the\n",
        "            total of weight corresponding to [[@position, @velocity], @action]\n",
        "\n",
        "        Params\n",
        "        ------\n",
        "        position: position of the car\n",
        "        velocity: velocity of the car\n",
        "        action: action taken at the state [@position, @velocity]\n",
        "        terminated: whether the car is in terminal state\n",
        "\n",
        "        Return\n",
        "        ------\n",
        "        value: state-action value\n",
        "        '''\n",
        "        if terminated is not None and terminated:\n",
        "            return 0\n",
        "\n",
        "        active_tiles = self.get_active_tiles(position, velocity, action)\n",
        "\n",
        "        value = np.sum(self.weights[active_tiles])\n",
        "\n",
        "        return value   # value = -0.7795991772541548\n",
        "\n",
        "\n",
        "    def get_value_with_active_tiles(self, active_tiles: List[int],\n",
        "            terminated: bool=None) -> float:\n",
        "        '''\n",
        "        Get state-action value with list of active tiles\n",
        "\n",
        "        Params\n",
        "        ------\n",
        "        active_tiles: list of (indices of) active tiles\n",
        "        terminated: whether the car is in terminal state\n",
        "\n",
        "        Return\n",
        "        ------\n",
        "        value: state-action value\n",
        "        '''\n",
        "        if terminated is not None and terminated:\n",
        "            return 0\n",
        "        value = np.sum(self.weights[active_tiles])\n",
        "        return value\n",
        "\n",
        "\n",
        "    def epsilon_greedy(self, position: float, velocity: float) -> int:\n",
        "\n",
        "        n_actions = self.env.action_space.n\n",
        "        available_actions = {0,1,2}\n",
        "\n",
        "        values = np.array([self.get_value(position, velocity, action_) for action_ in range(n_actions)])\n",
        "        #values = [-151.90793727 -144.34094926 -129.96974806]\n",
        "        action = np.argmax(values)   # act greedy\n",
        "        # action = 2\n",
        "\n",
        "        if np.random.uniform(0, 1.0) > self.epsilon :\n",
        "            non_greedy_actions = list(available_actions - {action})\n",
        "            action = np.random.choice(non_greedy_actions)\n",
        "\n",
        "        return action  # action extracted\n",
        "\n",
        "\n",
        "    def learn(self, error: float) -> None:\n",
        "        '''\n",
        "        Update weight vector @self.weights\n",
        "\n",
        "        Params\n",
        "        ------\n",
        "        error: error\n",
        "        '''\n",
        "        self.weights += self.alpha * error\n",
        "\n",
        "\n",
        "    def update_trace(self, active_tiles: List[int]) -> None:\n",
        "        '''\n",
        "        Update trace vector as a dutch trace\n",
        "\n",
        "        Params\n",
        "        ------\n",
        "        active_tiles: list of (indices of) active tiles\n",
        "        '''\n",
        "        delta = 1 - self.alpha * self.gamma * self.lambda_ * np.sum(self.trace[active_tiles])\n",
        "\n",
        "        self.trace *= self.gamma * self.lambda_  # tutti i componenti del vettore self.trace decrementano\n",
        "        # di un fattore: self.gamma * self.lambda_ =  0.36\n",
        "        self.trace[active_tiles] += delta # solo i componenti attivi del vettore: \"self.trace[active_tiles]\"\n",
        "        # sono incrementati del fattore \"delta\"\n",
        "\n",
        "\n",
        "    def run(self, current_ep: int) -> int:\n",
        "        '''\n",
        "        Perform an episode\n",
        "\n",
        "        Params\n",
        "        ------\n",
        "        current_ep: current episode\n",
        "\n",
        "        Return\n",
        "        ------\n",
        "        total_reward: total reward in the episode\n",
        "        '''\n",
        "        self.reset()\n",
        "\n",
        "        position, velocity = self.start_state\n",
        "        action = self.epsilon_greedy(position, velocity)\n",
        "        active_tiles = self.get_active_tiles(position, velocity, action)\n",
        "\n",
        "        old_action_value = 0\n",
        "        total_reward = 0\n",
        "        n_steps = 0\n",
        "\n",
        "        while True:\n",
        "            n_steps += 1\n",
        "\n",
        "            #if current_ep + 20 >= self.n_eps:\n",
        "            #    self.env.render()\n",
        "\n",
        "            next_state, reward, terminated, _ = self.env.step(action)\n",
        "            total_reward += reward\n",
        "\n",
        "            next_position, next_velocity = next_state\n",
        "            next_action = self.epsilon_greedy(next_position, next_velocity)\n",
        "            next_active_tiles = self.get_active_tiles(next_position, next_velocity, next_action, terminated)\n",
        "\n",
        "            action_value = self.get_value_with_active_tiles(active_tiles)\n",
        "            next_action_value = self.get_value_with_active_tiles(next_active_tiles, terminated)\n",
        "\n",
        "            td_error = reward + self.gamma * next_action_value - action_value\n",
        "\n",
        "            self.update_trace(active_tiles)  # qui ricaviamo il valore di self.trace aggiornato\n",
        "            # allo stato corrente \"active_tiles\"\n",
        "\n",
        "            error = (td_error + action_value - old_action_value) * self.trace\n",
        "            error[active_tiles] -= action_value - old_action_value\n",
        "\n",
        "            self.learn(error) # qui aggiorna il weight vector: self.weights += self.alpha * error\n",
        "\n",
        "            old_action_value = next_action_value\n",
        "            active_tiles = next_active_tiles\n",
        "            action = next_action\n",
        "\n",
        "            if terminated:\n",
        "                break\n",
        "            elif n_steps >= self.max_steps:\n",
        "                #print('Max #steps reached!')\n",
        "                break\n",
        "\n",
        "        return total_reward\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "id": "7B5P1Qib7UQB"
      },
      "outputs": [],
      "source": [
        "def true_online_sarsa_lambda_plot() -> None:\n",
        "    '''\n",
        "    True online Sarsa(lambda) algorithm plotting\n",
        "    '''\n",
        "    env = gym.make('MountainCar-v0').env\n",
        "    n_eps = 500\n",
        "    alpha = 0.03\n",
        "    lambda_ = 0.4  # possibile modulare il contenuto di lambda da 0.99 a  0\n",
        "    epsilon = 0.85\n",
        "    gamma = 0.9\n",
        "    n_tilings = 8\n",
        "    max_steps = 1_000 # max step per episodio\n",
        "\n",
        "    reward_list = []\n",
        "    ave_reward_list = []\n",
        "\n",
        "    true_online_sarsa_lambda = TrueOnlineSarsaLambda(env, lambda_, alpha,\n",
        "        gamma, epsilon, n_tilings, n_eps, max_steps)\n",
        "\n",
        "    for ep in trange(n_eps):\n",
        "        total_reward = true_online_sarsa_lambda.run(ep)\n",
        "\n",
        "        reward_list.append(total_reward)\n",
        "\n",
        "        if (ep + 1) % 100 == 0:\n",
        "            ave_reward = np.mean(reward_list)\n",
        "            ave_reward_list.append(ave_reward)\n",
        "            reward_list = []\n",
        "\n",
        "        if (ep + 1) % 100 == 0:\n",
        "            print('Episode {} Average Reward: {}'.format(ep + 1, ave_reward))\n",
        "\n",
        "    env.close()\n",
        "    plt.plot(100 * (np.arange(len(ave_reward_list)) + 1), ave_reward_list)\n",
        "    plt.xlabel('Episodes')\n",
        "    plt.ylabel('Average Reward')\n",
        "    plt.title('Average Reward vs Episodes')\n",
        "    plt.savefig('./mountain-car-true-online-sarsa-lambda.png')\n",
        "    plt.close()"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#MAIN\n",
        "\n",
        "true_online_sarsa_lambda_plot()\n",
        "\n",
        "#if __name__ == '__main__':\n",
        "#    true_online_sarsa_lambda_plot()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YyWcD3cMJTy7",
        "outputId": "07d96358-24da-4cc6-e01c-e1337a35195a"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            " 20%|██        | 102/500 [00:11<00:28, 13.73it/s]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Episode 100 Average Reward: -594.2\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            " 41%|████      | 204/500 [00:16<00:11, 25.47it/s]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Episode 200 Average Reward: -230.68\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            " 61%|██████    | 303/500 [00:20<00:07, 26.94it/s]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Episode 300 Average Reward: -202.88\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            " 80%|████████  | 400/500 [00:23<00:03, 28.63it/s]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Episode 400 Average Reward: -195.59\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 500/500 [00:28<00:00, 17.44it/s]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Episode 500 Average Reward: -194.93\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Resume del training\n",
        "\n",
        "img = mpimg.imread('/content/mountain-car-true-online-sarsa-lambda.png')\n",
        "plt.imshow(img)\n",
        "plt.axis('off')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 406
        },
        "id": "N1qoVSG1qwFK",
        "outputId": "872fce0b-33ed-40bf-ab5b-b7a8b5d43693"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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Wi4Xa2lref/998vPziYmJwe12s2/fPqZMmcLZZ5+N3+9n5cqVP3gNPjIykvT0dDZt2sTUqVMxGo3s2bMndD6+7xjOPfdcnn/+edxuN126dCE7Oxto7iExmUyMHDmSkSNHMnToUG655RYOHz78syvDjz/+mJEjRwKwfPlyoqOjQ/s7mtfrpVOnTlx++eWcd955TJ48mc2bNzNmzBjsdjvr168P3Xa5e/dudDodcXFxWCwW3G43hw4dokePHni9Xr7++uvQ/AQ9evQgOjqa0tJSTjnllNBlpCOBwufzYbFYGD16NKNGjSI/P58HH3yQ8vJyCQCixUkAEO2Cpml89tlnJCUlMXToUDIyMkLrIiIieO6559iwYQOTJ09mypQpPPjggyQkJDBq1KjQ6y699NLQALYpU6ag1+tDH/TTpk077n779+/Pk08+yaxZs+jUqROLFy8OtXgNBgOTJk1iyZIl3HvvvYwYMYJVq1ZRVFQUCh3nnXcey5Yt4/LLL+dXv/oVFouFzZs3k5GRwe233/6Tjn3ixIl06tSJF198kccff5xzzjmH2267jQsuuICcnBwOHjxIbW0tt956KxkZGWRmZuJ0OrFareTk5GA0GomPj+fTTz9l5syZ6HQ6jEYjubm5LF68GJvNRnl5OUuWLPnB+RT0ej3XXHMNDz/8MAaDgaSkJP71r3/96HXssWPHct9991FYWMisWbNC+1i9ejULFixg2LBhRERE8NZbb5GZmXnM7/ZogUCA9evXHxOcdDodU6ZMCf38wQcfYDAYsNlsvPzyy5x55pl07dr1O9u65ppr6NmzJ507d+bw4cPU1NTQvXt3bDYbM2fO5IUXXsDr9RIdHc3f//53Jk2aRHp6emjMwn333cf+/fs5dOgQq1evDv2+u3XrxuWXX87DDz9MYWEhPXv2pLi4mLKyMm644QZKSkp48cUXGT16NHa7nUWLFtGlS5fQ3QxCtCQJAKJd0DSNffv2cdppp5GamnrMuvj4eCZMmEBFRQWapjFp0iSWLVvGyJEjj7nGnpmZycKFC3nxxRdZvHgxZrOZvn37kp+fj16vJyEhgdzcXEwmU+g9o0aNYtasWSxatIgtW7Zw2WWXsXXrVlJSUtDpdAwcOJCnnnqKefPmsXTpUqZOnUpFRUVoYFlmZiavvfYas2fP5q233kKv19O7d2/GjRt33OO02+3k5eUdMzDNbrdzyy238Prrr1NeXs5DDz1Ez549effdd1mxYgVZWVmcc845oRkR09LSmDhxIjabDbPZjNFoZNKkSXi93lCvgclk4vbbb+fZZ59l0aJF9O7dmzvuuIMPP/wQk8mEXq8/bsU0bdo0NE1j8eLFxMTEcOONN7J8+fJjyvttcXFxXHjhhWzYsIFx48YdU1lmZmaybNkygsEgeXl53HDDDce9NGIymejWrRuff/45X3zxRWi5wWDgtNNOC/18//3389Zbb7F//34uuugibrvtNkwmU2j7R7Y9YcIEPvjgA1auXElCQgKPPfYYZ5xxBgBXX301sbGxvPXWW/h8Pq688kouvfTS0DHed999PP/88yxZsoT8/Hxuvvlm3nnnHaD5ktAtt9xCTk4Ob7zxBqtXryY9PZ0zzzyT1NRULBYLaWlpvP322wSDQQYNGsTMmTNDvUNCtCSdkgmshfjZjlwfPtKqPXJv/T333MNZZ50lA7tayJo1a7jiiit466236NWrV2sXR4h2QXoAhPgFKisreeONN4iNjcVsNoe60QcOHNjaRRNCiB8kAUCIX8BiseD1ennppZdwOBz06dOHZ599NnSbmGgZVquVrKysHx1YKYT4L7kEIIQQQnRAMg2VEEII0QHJJYDvcfRTu6QrVwghOoajP/NP9s9+CQDfQynFrl272LJlS2jaUyGEECe3YDBIjx496Nu37w/Oi3EykJrteyilWL58Oe+99x6DBw8+6ZOgEEJ0dEopduzYQW5uLn369JEA0FEdmS3t9NNP59prr5WndgkhxElOKcWSJUtC0z+f7CQA/Ai9Xo/RaJQAIIQQJ7kjD33qKDrOkQohhBAiRAKAEEII0QFJABBCCCE6IAkAQgghRAckAUAIIYTogCQACCGEEB2QBAAhhBCiA5IAIIQQQnRA7WoioCMP6NE0LfTAhiOTNuh0OpRSKKXQNC207shsTkeWH/2+jjDTkxDixPq+J6ir4/zw7Vf6gxouXxBNKVCgoVCKbz67ml+vlEL75nuU+mYZaKHXHP3a5uVHynXM+qO3933rv7O9/+7vyPda6PvjvA9Q2lHv4Tjv+06ZvrW/b87DN//99zi/933HHt+Rc6lQRFpMTOydQla8/Zf+mjuEdhUAgsEgH3zwAS+//DJlZWUkJSVx8cUXM3XqVCwWC4cOHeIvf/kL69atIzU1leuuu45x48ah0+lYu3YtzzzzDIcOHSIvL49bbrmF3NxcCQFCdFBHKp+gUgQ1haap0PdBTaEpRVDjqO+/WR9UeANBnN4ADk8g9NXh8dPkDeDwBnB+s9zpaf75yOs8/iDN9bUC/vvZ830fQ7rj/KD77pr/LtEdZ9m3X3e8F37Pvr5vG83b+ZFtHLO/4yw/+h3HfvlJ2/jOedBBarSVfpkxEgB+onYVAJRSxMbGctNNN9GjRw/WrVvH3/72N3Jzc+nevTsLFixAKcUrr7zCZ599xrx588jNzcVkMvHCCy8wfPhwZs2axd/+9jdefPFFHnjgASIjI1v7sIQQP9OR1rg/qPAFg3j9Gt6Ahi/Q/NUbCOI7zs/eb/55/EHc/iBu3zf//EFcvsA332tHff/f17l8QQKaQgeYjXosRj0WoyH0/X+XNX+fGm0lO775e7PRgNmoQ6/ToaO5Ej1SH+vQodPxzfLm49Ppjl6mC1V3Oh3om990zDqd7rvb+s52vud9/93vN6/99naOvJbjrfv2tnShch79Wo7z3u+s+/Z2dN+3z2+XXYfFqKdbsnym/1TtKgCYTCZGjhwZ+nnAgAFERkbicrlobGxk165dTJ8+na5du2K1WnnnnXcoKSnBZrPhdDqZPHkyXbt25cwzz+SJJ57A4XBIABCijdA0FaqAXb4gTd7mry5fgCZvkKZvlru8zeua/AFc3ub13oDWHAICGv5g8z9fUOEPHPlewx/45mtQhV6jKTDodUSYDdjNBuxmIxEWAxFmI3aLgTi7DbvF+M265uURlubX2UzNlb7JoP/vV4MOk0GPyajHbNBj+ubnI+tN3yyTnkfRFrS5AOB0OnE4HMddl5CQgNlsBsDv97Nq1SpMJhNZWVn4fD48Hg+xsbHodDqio6OJjIykoqKC5ORklFKhyj4uLg63243f7z9m+4FAgIqKCtxuN5qmUVlZSUJCQngPWIg26EjL+uhrzxoqdF33h74GNK25K/xb3ePHdof7v1l+VHe5N0CgeUPfuXZ+3DIe9b0OsBoNRFmNRFqNxNhMRFlMRNmMRFqMRFmNoXVRFhNRVhNR1ubK3GYyYNA3V8r6b1qg+mO+p7nF/s1X/TGtVKnIRfvV5gLAv//9b15++eXjDrR56qmn6N27N4FAgHfffZdFixZxzz33kJGRQXFxMTqdDk3TgOaBgpqmYTQav+n+OnbdkWVHa2hoYN68eWzevBmlFIcOHeLqq68O/0EL0cqUUrh8QWqbfFQ5vdQ6fbj9R1ri37S+vQGajmqZh776mlviTd+01D3+IAow6nWhFu+3W8RH/pkNOiwmPZFW6zc/67Ga9ERYjESYDURYjNi++Rphbm6JR1j+2wo/8hq72YDJ8PNuapJKXHRUbS4ATJ06ldNOO+24ASA6Ohq/38/bb7/Nq6++yt13383gwYMBsFgs2Gw2qqurUUpRV1eH0+kkNTUVi8UCNFfwmZmZVFVVEREREepNOCI+Pp577703dMfA/Pnzw3/AQrSCIxX+oZom9lc3sbfSyeFaF+UNHkrr3ZQ3evD4mwOzzaTHajJgMze3lu1mA1ZTcwWcGGkhy2zHdtR6m1mPzWTEYmq+Nm751jXxo6+XW4x6LCbDMdfO9ccJ50KIE6/NBQCr1YrVaj3uumAwyPvvv8+cOXO48cYbSU9Pp7i4mKSkJGJjYxkyZAivvvoqiYmJrFixgujoaDIzMzGZTKSkpPDKK69wzjnnsHDhQvLz84mJiTlm+zqdDpPJBBDqPQgGg2E/ZiHCIXQ71jej171+jV3lDraW1LO5uIFd5Q6avAHc/iAev4bJoKNbciQTe6fSLyOGlBgrdnNzZW3Q6dDrdRiO/NMd/T3HXSeVuBBtW5sLAD8kEAiwb98+NE1j9uzZoQ+YJ598koKCAi677DKUUjz88MN06dKFu+++m+TkZADuuOMO5s6dywMPPMCoUaOYOXNmqGdAiJOFL6DR6PbT6PHT4Pazv7qJbSUNbCtpYGeZg6CmEfnN9e84u5k+GdHkpccwICuWbsmR2M3GY0aPHyGVuRAnH536vlktOjhN05g3bx7BYJDrrrsuNOGQEG2JL6BR1uDmcK2L4rrmrweqmiiqdXG4zoXXr5EeayUzzk52gp3seDtZCXay4yPoFG8jwmKUyl2IbyilWLx4MYWFhdx9990Yje2qjfw/O7mPToh27tv5PBBUFNW52FLcwI7SBnZXOqlyeKl3+Wlw+/D6NTonRdA7LZpf5WfQMzWKhEgzsTYzcXYTNrNBKnwhBCABQIg25citdB5/MHQPfEm9my3F9Xx9qJ7tpQ00egKhEfRmo4HsBDtjeyXTLyOGvIwYYu2mY67HS4UvhDgeCQBCtCL1zRSzdS4f5Y0eyuqbR+Hvr25iV7mDvZVOGtx+4iPMpMVY6Z0eQ0asjR4pkXRLjqRrUiTxEWap5IUQ/zMJAEK0ME1TVDo87K5wsqvcwe6KRsoavFQ5vVQ2enB4AiRFWeiVGsUFgzLpkhRJWqyVlCgriVEWYqwm9Hqp8IUQv4wEACHCQCmFP6gIfDMNbbXTy5biBjYX17PpcD3ljZ5vHjLT/NqkKAt9M2MYODybvIwYkqOs2EwGLKbm++Nl1jkhxIkmAUCIE0ApRaMnQG2Tj9omL+UNHnZVOCgsd1BY5qCk3kWkxUR8hJmECDODc+LpkRxJ7/RoeqfHkBJt5duNeqnwhRDhJAFAiJ9BKdV8n31VEwdrmjhY3cShWhel9W5K6t1UNnqJthnJSYhgcE4cFyZlkRlnIz3WRmacjaRIC8afOXWtEEKcCBIAhPgeR8+kpylwePzsKG1kU3E920oaOFzrwuFpng/f7QsSaTHQJz2G8/Iz6ZcZQ6cEO5GW5gfQRFiMGGUuCSFEGyIBQIhvKKXwBjQcngCNHj91TT72VjnZdLieLSUNHKxuQq/TEWlpfgBNjM3MwOx4+mZE0zcjhi5JkRiPeqocSDe+EKLtkgAgOqwjD8Qpa3BTVOumqM5FUa2Lg9XND8gpqXNj0OvIiLORGWdnYKdYchIi6JwYQXZCBJlxtuYBelLJCyHaIQkA4qT27Zn0PP4g+6qa2FnWyNaSBg5UN30zcM9HXZMPvU5H1+RIhnaOJ3dENNkJESRGWYi3m4m1m7BIhS+EOElIABAnlSMT63gCGh5/8zPr91c52VzcwKbD9ewsa8QT0DDqdRj1OmxmA12SIjg9L5X8rFi6JUcRaTFi/Oa59XqddOMLIU5OEgBEu+cLaFQ5PFQ5vFQ6vByqaWJPpZM9FU72VDrxBTUSI82kRFkpyI4jM85G9+QoctOi6JwYIQ/EEUJ0SBIARLsUCGpsLqpnzYFa9lc5KW3wUNXoocLhxeMPkhVnp1tyJKO6J9I5MYLUmOaZ9FKiLVLhCyEEEgBEO6SUoqLRw11LtlLR6EGn05GTYGd41wT6ZcXSLyOGGJsZq0mPzWSQgXpCCHEcEgBEu/T5nmpK6t3cPL4b0wZmER9hPma9VPhCCPHDJACIdieoFEs3ldA9OZJxvVJIiLS0dpGEEKLdkanJRLuzq6x5jv28jBhyEuytXRwhhGiXJACIdkXTFO9sKcWo1zGuVzImmU9fCCF+Fvn0FO1KhcPDugO1pERbGZwTL9f6hRDiZ5IAINoNpRSbi5ofwjMhN4Vom6m1iySEEO2WBADRbrj9QdYdqKHJG2TqgPTWLo4QQrRrEgBEu6CUorzBw+p9NYzunkhajK21iySEEO1au7oNUNM0duzYwXvvvUdxcTFpaWmcffbZ5ObmEgwG+eijj1i6dGno9ePHj2fq1KlYLBbKysp488032bNnDwUFBZx99tnExcW13sGI/4kCdpQ2cqjGxcxRnTEbJbsKIcQv0a4+Rf1+P5s2bQLg9NNPJxAI8OCDD3Lw4EE0TWPjxo3odDouuugiLrvsMgYNGoTRaMThcPDMM8+wZcsWRo4cyX/+8x8WLlyIz+dr3QMSP1lQU/xnaxmd4m3kZcSgl7F/Qgjxi7SrHgCz2cyvf/3r0M99+vThjjvuoLy8nIyMjGNeGxcXR2pqKnq9nqKiInbt2sX9999Pv379iI6OZv78+VxwwQUkJye39GGIn6G03s2nu6v4VX4GneLtMvpfCCF+oXYVAI7+0FdKUVRUhFKKuLi45vngc3I4cOAAS5cupbKykkmTJnHRRRfhdDrR6XTExzffNpaeno7T6cTr9R6zfaUUfr8fTdNQShEIBKSiaSPe21aOxWRgcE48drOhtYsjhBDtXpsLAP/617+YP38+SqnvrHvmmWfo06cPAGVlZTz11FNMmjSJzp07YzQamTJlCpMmTcJoNPLJJ5+wYMECTjnlFILBIEopjMbmwzUajaFlR6uuruaxxx5j/fr1KKUoKyvjd7/7XdiPWfwwpyfAxzsqSIqyMKSz3PsvhBAnQpsLABMnTqRfv37HXde5c2eUUuzfv58777yTcePGccUVV2AyNd8PHhMTE3ptXl4egUCApqYmrFYrOp0Ol8sFgMPhwGq1hgLBEfHx8dx77734fD40TeOVV14J01GKn0opxbqDNRTVuTi7fzppMdbWLpIQQpwU2lwASExMJDEx8bjrNE1j586dPProowwcOJDp06fj8/nQ6/UEAgEOHjxITEwMRqORVatWodfriYqKwmAwYLPZWL16NREREXz66ad06tSJyMjIY7ZvMBhCdwZomkZ0dDTBYDDsxyy+ny+gsXpfDU5vgDP7pUvrXwghTpA2FwB+iM/nY9GiRbz33nuUl5ezdu1aAB588EFycnJ4/fXXQ3cC2O12ZsyYERoIeMEFF/DKK6/w+uuvExMTw/XXX/+dACDanrIGD5uL6umZEkWvtKjWLo4QQpw02lUAsFgs3HLLLVxzzTXHLE9MTMRkMvHb3/421M1vsViIjo4OdfNPnjyZkSNH4vV6sdlsREdHo9e3q7sgOxxNKQorGtlR2sidk3vJg3+EEOIEalcBQKfTERsbS2xs7HHXx8TEHDMO4Ggmk4mEhIQwlk6caN6Axic7K4mzmxneJQHp/BdCiBNHmlSizWpw+Vi5q4phXRNIjrbK9X8hhDiBJACINuvT3VW4fUGGdI4nytquOquEEKLNkwAg2iRfQGPJ1yXkJNoZ2CkWvbT+hRDihJIAINqkbSUN7Kty0jcjlk4JEa1dHCGEOOlIABBtjqYUywsrCQQVE3ony+h/IYQIA/lkFW1Oab2b9QdrSY62MLLr8SeFEkII8ctIABBtilKK7aWN7Kl0MnVAOmaj/IkKIUQ4yKeraFM8fo31B+sIBjUm5Ka0dnGEEOKkJQFAtBlKKWqbfKzcVcnwrgmkxdhau0hCCHHSkgAg2pSNRXUcqnUxLjeFCItRJv8RQogwkQAg2gylYOnGErokRtA7LRqDXip/IYQIFwkAos04XNvEhkN19EmPpkuS3PsvhBDhJAFAtAlKKd7dUoZep+OUnsnYTIbWLpIQQpzUJACINqHO5WPV3moSIs0M7xIv1/6FECLMJACIVqeUYktxA4dqXIzqlkhipKW1iySEECc9CQCi1fkCGmv311Db5OO8gkxp/QshRAuQACBaXXmjh7UHasnvFEuXpMjWLo4QQnQIEgBEq1JKsbfSSWGZg8l9UmXqXyGEaCHyaStaVUBTvL+tnKRoCwXZccit/0II0TIkAIhWVeP08dHOCgZnx9EpwS7X/4UQooVIABCt6pPCCpSCgTnxRFtNrV0cIYToMCQAiFbjDQR5d0sZKdEWhuTIvf9CCNGSjK1dgP+V0+mkqKgIr9eLyWQiNTWVuLg49Ho9gUCAsrIyampqsNvtZGRkEBHRPKWsx+OhuLgYp9NJbGws6enpmM3mVj6aju3rQ3UcqG7i1B5JdJapf4UQokW1uwCwe/du/va3v6FpGh6Ph8TERG699VbS09PZsGEDs2fPRqfT4fV6GT9+PJdddhkGg4G33nqLpUuXYrVa8fl8zJw5k7Fjx2IwyJSzrSEQ1Fi9r4ZGj5+zBqSjl9a/EEK0qHYXAHr06MH//d//ER0dzeHDh7nnnnvYvXs30dHRLFq0iLy8PGbOnMlXX33FCy+8wPjx4zEajSxbtowLLriAU089lVdffZVFixYxaNAgYmNjW/uQOhylFBWNHjYeriMj1saArNjWLpIQQnQ47W4MQGRkJHFxcTQ0NHDo0CH0ej1xcXE4HA5KSkoYOnQoCQkJDBw4EKPRSHFxMdXV1fh8PgoKCkhISGD48OGUlpbS1NR0zLaVUmiaFvqnlGqlozz57a5wsK2kkV8NyMAqD/4RQogW1+Z6AHbs2MGmTZuOu27ixIkkJSWxefNm5s6dy8GDBxk8eDAZGRm43W78fj92e/OtZFarFbvdTm1tLSaTCaUUVqsVALvdjtfrJRgMHrN9l8vF559/TklJCUopVq9ezbBhw8J9yB2ON6Dx+d5qDHodp/ZKRjr/hRCi5bW5AFBXV8fevXuP2/oePXo0SikGDhzIX//6V4qKivjzn//MypUrGTZsGAaDAb/fD0AgEMDn8xEREYHRaESn0xEIBADw+/0YjUb0+mM7QJRSuN1unE4nSim8Xm/4D7gDcnj8LN9RydDO8aRGW2X0vxBCtII2FwCGDRvGoEGDjrvOZDIRDAbR6XRERUWRk5NDTEwMpaWlWK1WoqKiKCoqIhAIUFpaisvlIj09HZOp+f7y8vJy0tPTOXToENHR0aEegSMiIiKYOnVq6FKAxWJB07SwH3NHs+5ALZUOL1d1TSDGJvf+CyFEa2hzAcBgMHzvyHyfz8f777/PgQMHSExMZN++fRw4cIDLL7+c+Ph4zjzzTBYsWEB1dTXbt2+nd+/eZGVlYTKZGDhwIHPmzGHIkCGsWLGCKVOmEBMTc8z2dTpdqDV69PfixAkENd7YUEx2gl2m/hVCiFbU5gLADzEYDOTk5HD48GEOHz5MamoqDz/8MLm5uRgMBiZNmoTdbmfTpk0MHTqU0047LVTJX3311Xz88cccOnSISy+9lLFjx4Z6BkTL2VflZHtJA6O6J9E1KVJClhBCtJJ2FwD69etHv379jrvebrczadIkJk2a9J11SUlJXHzxxeEuovgBSimWF1YS0BSn9kyS0f9CCNGK2t1tgKL9qnZ6Wb23hmiriXG9klu7OEII0aFJABAtQinF9tJG9lQ6OL1vKpGWdtX5JIQQJx0JAKJF+AIaGw/X0ej2M6VvamsXRwghOjwJACLslFLUNvn4dHcVg7LjyU6IbO0iCSFEhycBQLSIneWN7CxzMKF3MhFmg4z+F0KIViYBQISdAt7dXEp6rI2+mbEY5OZ/IYRodRIARNhVO72s2FVFn4xousm9/0II0SZIABBhpZTiva1lAIzqmkiUVUb/CyFEWyABQISV0xtgRWEVsXYzI7slSutfCCHaCAkAImyUUuwobWR/tZPB2XFkxNpau0hCCCG+IQFAhE1AU3y5v4ZKh5fzBmail8F/QgjRZkgAEGFT2ejlqwO1dEmMpG9mzI+/QQghRIuRACDCQinFwZomthQ3MKVfGmaj/KkJIURbckKHZG/duhWHw/G962NjY+ndu/eJ3KVoowKaYvnOCuwWAyO6JmCQwX9CCNGmnNAAMH/+fAoLC/F6vezevZvk5GQSEhJoampi3759XHzxxTzzzDMncpeijXJ4/Ly3rZzBOfF0irfL6H8hhGhjTmgAeOSRRwgGg6xatYqPP/6YX//613Tq1In6+nr+9a9/ERcXdyJ3J9qw1ftqaPT4GZgdR6zd3NrFEUII8S0n9MJsREQE0dHRHDx4kC5dutCvXz+SkpLo1q0bkyZN4tNPPz2RuxNtVFBTvLWxhNRoK4Nz4mXqXyGEaIPCMi1bZmYmL7/8Mnl5eaSkpOB2u5k3bx59+/YNx+5EG7OtpIGdZY0Myo6jV2pUaxdHCCHEcYQlAIwdO5bKykqef/559Ho9gUCAXr16cd1114Vjd6IN0TTFqr1VODwBpvRNx2iQ0f9CCNEWnfAAoJTiiy++ICsri8cffxyXy4XFYiEzMxOzWa4Fn+yqnV6+PlRPjM3E8K4JrV0cIYQQ3yMsPQBlZWV4PB7Gjh0rlX4HopRid4WDrSUNnFeQSaQ8+EcIIdqsE/4JrdPp6Ny5M08//TQRERGkp6djMBgAiIuLY8CAASd6l6KN8AU11h6oxe0LclpeCjL0Twgh2q6wNNFcLhder5eFCxcSFxcXCgB5eXkSAE5SSimavAGW76ykIDuOrFi5918IIdqysASAU089lUGDBgHNFcMRJ+JywNdff83jjz9OSUkJCQkJXHjhhZxzzjkYjUbmz5/PnDlzsFgsAFxyySVcf/31WK1WduzYwTPPPMP27dsZMWIEN954I1lZWVJJnUDbShrZV+Xk3IIMYu2m1i6OEEKIHxCWAGC32/F6vRw6dAiXyxUKAbGxsb94MqCUlBRuvvlmsrOz2bZtG08++SQ5OTkMGjSIuro6zj33XK6//npMJhNWqxWr1Up1dTVPPfUUOTk53HzzzTz33HPMnTuXe++9F7vdfiIOucNTwBvri8iMs1HQKU7u/RdCiDYuLAGgpKSE2bNnc/DgQXbs2EFiYiLFxcVMnz6dPn36/KJtZ2RkkJGRgVIKl8tFdHQ0wWAwtP6rr77ib3/7G7169WLcuHFERERQXl5OfX09559/Prm5uVxwwQU8/fTTNDY2SgA4QUrq3Hx1sJaC7Di6p0RKz4oQQrRxYQkAq1atwu12c/XVV/OXv/yFBx54gEWLFhEbG/uj7w0Gg8dU6EczGo3o9XpWrVrF008/TVlZGRMmTCAvLw+9Xs/AgQOJiIggKiqKN998k23btnH77bfT1NQEQHR0NAAJCQm4XC58Pt8x29c0DZfLRSAQCH1/5HKC+H5KKVYUVuINaIzqlkikRUb/CyFEWxeWT+qqqir69u1L165diYiIICMjg2nTpvH4449zww03/OB7X3nlFWbPnn3M2IEjXnrpJfr168eAAQN47LHH+Prrr1m4cCE7duxgxIgRTJw4kQkTJqDT6ejXrx8PPPAApaWl39mOTqc77varq6t56KGH+Oqrr1BKUVlZye233/7zT0QH0ejxs2JXJXazkYm9U6T1L4QQ7UBYAkBSUhKHDx/GaDRiMpn45z//SXl5OcnJyT/63mnTpjF58uTjrjsyfiAyMpJu3bqRlZXFunXrWL9+PUOHDsVo/O/hREREoJQiEAiEuvmPPKq4pqaGiIiI7wxKTEpK4s9//jOapqFpGi+++OLPOv6OZkdpI3srnYzpnkhSlLW1iyOEEOInCNtdAJWVlSQkJHDppZeydOlSTCYTN95444++NyIigoiIiOOuCwQCbNy4EaUU6enpbN26lc2bNzN69Gg8Hg/r168nNTUVi8XC66+/jtVqJS4uDpPJRExMDG+99RbnnHMOb775Jj179gxdEjhCp9OFQoGmaZhMpu+9HCGa+YMam4rqqXB4mJqf0drFEUII8ROFJQBERUVhMjXfBjZ+/HhGjRqFTqfDZrP94m0fOnSIF198kZqaGtLS0pgxYwbjx49H0zS++OILPvzwQzRNIz8/nz/+8Y+kpqYC8Lvf/Y6nn36aK664guHDh3PttdeekPJ0ZEopapt8fL6nmj5pMfLgHyGEaEfCEgA++eQTli5dSlZWFn369CEzM5OsrCwsFktoUqCfw2g0cs4553DOOeccd/0999zDPffcc9x1/fr146WXXvrZ+xbHt7+qiU1F9dw0rhsRMvhPCCHajbB8Yg8ePBibzcbevXtZs2YNNTU1NDQ0MGbMGH73u9+FY5eiFSjgg+3lxNpNFGTHYZR7/4UQot0ISwBISEhg2LBhJCYmUldXx4YNGzh06BB5eXnh2J1oJU6Pn/e2lTEgK5auSXLvvxBCtCdhCQBLly7l3nvvJSoqirPPPptHH32UAQMGyJMBTzIf7ajE7Q8ytEsCCRHyuxVCiPYkLAEgNTWV8ePHY7VaaWpqYs2aNTQ0NJCXl0dGhowUPxl4/EE+3FFOjM3EyK6J0voXQoh2JiwBYMSIEeTl5VFZWUlRURHvv/8+f/vb3xgzZgzPP/98OHYpWpBSil3lDnaVO+ibEUPXpOPftimEEKLtCksAKCsrY+XKlaxdu5YtW7bg8/kYPXo0U6dODcfuRAvTFKzeV02lw8v/5WdiNOhbu0hCCCH+R2EJAJs3b2bdunX079+fyy+/nF69en3v5D6i/al2ell/sI7kKAtDusS3dnGEEEL8DGEJAOPHj2f8+PHs3r0bTdOwWCw0NDRgs9lkIGA7p5TicG3zvf8XDMrEZvr58zoIIYRoPWHpu3U6ndx5551Mnz6dJ598ErfbzSuvvCJz658EApri893VBDXF2F4pGOTefyGEaJfCEgA++ugjlFL885//xO/3o5Ri0KBBrFq1Khy7Ey3I5Qvw761lDMqJIzvBLqP/hRCinQpLAKipqSEvLy/0FD4Ag8GAx+MJx+5EC9p4uJ7Seg+DsuPk3n8hhGjHwhIAMjMz2bRpEw0NDQSDQRobG/nnP//JwIEDw7E70UKUUry1sYTkaAuDcuJl9L8QQrRjYfkEnzBhApmZmfz+979n165dXHzxxdTW1nLDDTeEY3eiheyvamL9wTp6pkSRlxHT2sURQgjxC4TlLoCIiAjuvPNOzjjjDEpKSoiMjKRbt27s2bOHQYMGhWOXIsyUUny6uwqnN8DE3ilYZfS/EEK0ayc0ACil8Pl8bN68mYqKCkaNGkWvXr349NNPufHGG8nJyZEA0E7Vu/x8dbAWs1HHuF7JrV0cIYQQv9AJDQCapvHss88yf/58AoEASUlJTJkyhS1btjB9+nROO+20E7k70UKUUuyudLC1pIFJfVKJk8F/QgjR7p3QABAMBnn//feZP38+NpuNX/3qV0RFRfHiiy8SFRV1InclWlBAU2w8VEdtk48pfdOQG/+EEKL9O+FjAFwuF3379iUqKorU1FTOOeccqfzbOac3wCe7quiTHk3XpMjWLo4QQogT4IQHgLq6Ot555x2sVisOh4OPP/6YmJjmEePJycmMHj36RO9ShJFSin2VTjYdruO3E7oTazfL5D9CCHESOKEBQKfTkZeXx+LFiwHo1asXy5YtC60fMGCABIB2aMnXJaREWxmYHY/JIJW/EEKcDE5oADCZTLzxxhsncpOildU4fXy2p4oeKVH0SImS1r8QQpwkZCo38b2UUny2p4omb4DhXeKJs5tau0hCCCFOEAkA4nu5/UE+3F6O1WRgYu9Uaf0LIcRJJCwzAbYEr9fLggULyMrKYty4cZjNZtxuN6tXr2br1q0kJyczduxY0tLSgOYHFK1YsYLi4mJ69OjB6NGj5e6EH1FY7mBPpZOCTnF0SrD/+BuEEEK0G2HpAVBK4Xa7+fDDD1m+fDk+n4/Dhw/T0NBwwrb/5ptv8sILL7BkyRK8Xi+apvHRRx8xe/ZslFKsXLmS2bNn09jYiMvlYv78+aEBiS+99BJLly7F7/efkPKcjIKaYnNRPcV1bs4tyEAvrX8hhDiphKUHoKSkhD/84Q8UFRWRmprKkCFDeP/992loaOCOO+74RdtWSrFhwwb+/e9/c/XVV7NhwwYAGhoaWLZsGeeddx4XXnghO3bs4N5776WoqAiTycS6deu44447GDhwIJ06dWLRokVMnjyZxMTEE3HIJ53aJh9f7K2mU7ydgk5xrV0cIYQQJ1hYegBWrFhBVlYWL7zwAkoplFIUFBSwfv36X7RdpRQlJSX885//5De/+Q1xcf+tmFwuF42NjXTu3BmTyURWVhYRERGUlJRQX18PQEZGBiaTia5du9LQ0IDH4/nO9gOBAD6fD5/PRzAY/EXlba+UUhTVulh/qI7T81KJsLTbK0VCCCG+R1g+2R0OB506dcJk+u+ocZ/Ph6ZpP/ref//737z55psopb6z7vbbb2f58uV06dKFgQMH8u6774bWBYNBgsFgaJ9GoxGz2UxTUxORkZEopTAamw/XZDIRCAS+U566ujrmzZvHtm3bUEqxd+9epk+f/rPOQXumFKzcVYlBp2NIZ7n3XwghTkZhCQBdu3bl9ddfJy8vD7/fT1FREc8//zynnHLKj763T58+WK3W4waAyMhI3n//ffbv38+CBQuoq6ujsbERg8HA73//e0wmE263G6UUXq8Xt9tNXFwcZnPz7HVerxcAt9uNxWLBYDj2kbZRUVFccMEFTJ48GaVUaEKjjsbjD/L2plL6ZsbQLTlSRv8LIcRJKCwBYOzYsZSWlvLAAw9QU1PDNddcw/Dhw7nqqqt+9L3Z2dlkZ2cfd52macyfPx+v14tSivfee49Vq1Zx++23k5CQQFpaGuvXr6dv375s2rQJv99PZmYmRqMRk8nEpk2biImJYd26daSlpREREXHM9o1GI507dwaau8HXrFnTIS8DrNpXTXWTlwsGZ5ESbW3t4gghhAiDsAQAs9nMjBkzmDBhAhUVFdjtdrp3737MJYHv80OtTYPBQHp6OtAcBpKSkoiKiiI5OZmIiAimTZvGc889x44dO3C5XEyaNIn09HQMBgNnnnkmr732Gu+++y5NTU3MmDHjO7cBHr3v4/VAdASBoMZ/tpQRZzczomuCjP4XQoiTVFgCQGFhIZs2bUIpFapUt27dSlRUFHl5eWRmZqLT6X5R17JOp2PcuHEMHDgQu92OXq9n8ODBPPTQQ1RWVhIREUFOTg52e/P96+eeey4DBw6ksbGRhIQEsrKyvnMJQMD+qia2lTTQLSmC3mnRrV0cIYQQYRKWALB582b+7//+j6ioKBISEnA6nZSVlZGSkoLP5+P222/noosu+kUVsE6nIzEx8Zjb+EwmE507dw514x/NbreTm5v7s/fXEWhK8cW+aiocXm4c1x2zUSaKFEKIk1VYAkBSUhLTpk3jhhtuICMjA4fDwfz589Hr9XTu3Jl58+Zx3nnnSQu8jalr8rH+YB0RZgNjeiTK4D8hhDiJhaWJt3PnTtLT00lOTgaaR+8PHz6czz77jOHDh+NyuX7SLYGi5SilKKpzsamojvG5KURb5cE/QghxMgtLD0B2djazZ8+mS5cu9O3bl/Lycp566ikKCgqoq6sjNTUVvV66l9uSoKZYd6CWOpefM/qmYdBL618IIU5mYQkAEydOpLGxkXnz5tHY2IjFYmHkyJH89re/xeVy8Yc//AGz2RyOXYufye0P8u6WMgZkxdI5MUK6/4UQ4iQXlgBgsVi4+OKLmTx5Mg0NDdjtdhISEjAYDERGRoYuDYi2o7DMwZ4KB9eO6UpipKW1iyOEECLMwhIANE2jvLyc5cuXU1xcTDAYRClFt27duPjii8OxS/ELKKV4e1MJ8REWBuXEydS/QgjRAYQlAGzbto177rkHq9XKli1b6Nu3Lzt37uSSSy4Jx+7EL1TW4OHT3VV0S46kf1asdP8LIUQHEJaReOvWrWPIkCE8+uijDBgwgBdeeIFbb71VBv61UZ/vqcLpDXBKjySiZPS/EEJ0CGGpkf1+P2lpaZjNZvR6PS6Xi759+/7ixwGLE8/p9fPlvhoAJvVJaeXSCCGEaClhuQTQrVs3CgsLsVqtxMXF8X//939UVlYyZsyYcOxO/ExKKXZXONla0sCYHkmkxdpau0hCCCFayAkPAEop+vfvT3Z2NvHx8dx666385z//wW63c8EFF5zo3YlfIKgpthTVU1rv5p4puciVfyGE6DjC0gPw2WefYbVa6dq1K926dePmm28Ox27EL+T0Bvh8TzWdE+XBP0II0dGc8DEAOp2OQCDA7t27cblcBINBNE1D07QO+4jdtkgpRUm9m9X7ahjbK5lYu1lG/wshRAcSlh6AzMxM5syZQ3l5Ob169cJkMqGUIj09nQkTJoRjl+JneGdTKVFWI0Ny4rHIk/+EEKJDCUsA8Pv9FBQU4PV62bJlC9Dc4mxqapIA0EY0eQN8sKOCHilR9EyLlta/EEJ0MGEJACNHjmTgwIEEAgF0Oh0mk4lgMIjRGJbdif+RUorV+2qobfLxqwHpJMvUv0II0eGEpd83GAyyYsUKbrnlFh588EEAPvnkE9atWxeO3Yn/kT+o8d62MmwmAxN6p6CXJ/8JIUSHE5YAsGbNGt544w0GDx5MSUkJmqZhMpl44403wrE78T/aW+lkZ5mDXmlR9EyJau3iCCGEaAVhCQA7d+5kxIgRnHHGGaHpf7OzsykpKQnH7sT/QFOKTUX1HK51MbV/OkaDDP4TQoiOKCyf/lFRUdTU1OByudA0DZfLxerVq8nOzg7H7sT/oN7lZ/W+GmJtJk7pkdTaxRFCCNFKwhIARo4cSVVVFXPnzmX37t088sgjvPPOO8yYMSMcuxM/kVKKkjo36w7UclqfVCKsMihTCCE6qrDUAJ07d+a2227jiy++IDMzk6ioKKZPn05+fn44did+IqXgy/01ePxBRnVPxCzd/0II0WGFJQDs3LkTn8/HlClTMJlMmM1mDAaD3GveyvxBjbc3ldAnI4YeKVHy+xBCiA4sLAHg4MGDPPPMMyQlJTF06FAKCgro1q0bSUlJJ6zS8fv9fPbZZyQkJJCXl4der2fv3r3s3Lkz9JouXbqQm5uL0WjE4XCwfft2ampqSE9Pp1evXthsHevpdxuL6tlf1cTVozuTHmNt7eIIIYRoRWEJAJMnTyY/P58NGzawbt06nn/+eXQ6HaeffjqXXHLJCdnHRx99xD333MPgwYP585//jMViYfHixXzyySeMGDECvV6PxWKhZ8+eeDwe/vWvf7Fy5UrS0tIoLi7mkksuYcqUKR1mciJNKZZtLiXWbmJolwQZ/S+EEB1cWGo/nU5Hamoqp59+OsOGDeO9997j6aefxuFw/OIAoJRi7969LFiwgEsuuYQ9e/Ycs3706NHcfPPNWCyW0KWHAwcO8PHHHzNz5kxGjhzJG2+8wVtvvcWYMWOIi4s7ZtvH+/5kUFzrYsOhOjrF2xmQFdvaxRFCCNHKwhIA6urq2LNnDx9//DGrVq1CKcX06dM5//zzf9F2lVLU1NQwd+5cZsyYQUNDQygA6HQ6oqOjWbhwIZ9//jlZWVnMnDmTYcOGUVtbSzAYpFevXkRGRjJgwAAWL15MU1PTMQHA6/Wyc+dO6urq0DSNwsJCunfv/ovK3BYopfhiXw0VDR4uHdoJu9nQ2kUSQgjRysISAFavXs3ChQvJzc3lrrvuoqCgALvdjsPh+NH3rlmzhs8+++y4LfALLriAlStXkpSUxIgRI3j//fdD6wwGA2eddRbjx4/HarWyePFi5syZQ5cuXfD7/SilMJvNAFgsFnw+H5qmHbN9j8fDmjVr2LVrF0optm3bdlIEgEZPgK8O1KLX6xifmyKD/4QQQoQnAAwePJi+ffuSkZERqkhfe+01AoEATz755A++12q1EhMTc9x1Pp+PRYsWUV1dzRdffEFZWRlVVVUkJiZy//33HzPR0Nlnn83nn39OXV0dRqMRnU6H3+8PbcdkMoVmKTwiJiaGa665Bk3TUErxt7/97ReeidanlKKo1sXm4npGdksgOUoe/COEECIMAUApRVRUFMFgkLfeeotXXnmF0tJSzjjjDH7961//6Pv79etH3759j7tO0zSefPJJmpqaUEqFHjA0bdo0DAYDDocDk8mETqejvLycYDCIyWQiLi4OvV7PgQMHSE5OprCwkPj4+O/cBaDT6TAYDBgMBjRNw2AwEAwGT8h5aS2agk1F9RTVufnDGbkY5ME/QgghOMEBQNM0PvjgAzZv3syePXuIjo4mIyODwYMHc8cdd2Cx/Hjr89ut8qMZDAb69OkT2tehQ4c4cOAA3bp1o6mpiZdffpmmpiaMRiNbt27llFNOIT09HYPBwOjRo5k/fz6ffvop27Zt4/zzz//enoaTiccf5D9by+iTFi33/gshhAg5oQEgEAhw1113MWnSJH7729/Su3dvXn/9dQ4cOHAidwM0t9YHDx5MRkYGVqsVpRTDhw9n//79aJrGsGHDyM/PJzIyEoDp06eTm5tLRUUFY8eOpaCgoEPcAni4tolNRfVMH55NonT/CyGE+MYJrQGNRiN33nkny5Yt47777mPq1Kk0NDQQDAZRSqGUOmEtUJ1OR+fOnencuXNo2dChQxk6dOhxXx8bG8vEiRNPyL7bC6UUyzaVEWU1MignHqtR7v0XQgjR7IQGAJ1Ox8UXX8y0adPYvHkz//rXv1i1ahXp6eksXbqUgoICevTocSJ3KX5AncvPB9vL6ZYUyYDMWOn+F0IIEXLCAwCAyWRi0KBB5Ofnc/DgQVavXs2KFSvYsWMHDz744IncpfgBq/dVU+/286v8dBIiza1dHCGEEG1IWC+CGwwGunbtSpcuXTjzzDN/0jwA4sTw+oN8truKoKaY1CdNWv9CCCGO0SKj4HQ6HXFxccfMuifCa0+lky3FDRRkx9I9JbK1iyOEEKKNkVFhJ6Ggptha0sDhGhfn5mcgbX8hhBDfJgHgJNTkDfDlvhqSoi3kd5JeFyGEEN8lAeAko5SiotHDZ3uqGN8rmfgIs1z/F0II8R0SAE5CH+2oQAcM75qAzSRP/hNCCPFdEgBOMr6gxrtbSumREkXP1Ghp/QshhDguCQAnmQ2H6iipd5PfKZb0WGtrF0cIIUQbJQHgJBIIary7uQyL0cD43BQM0voXQgjxPSQAnEQO17rYXFxPTmIEfTNipPtfCCHE95IAcJJQSrHxcB3FdS6m9E3FKoP/hBBC/AAJACeJRk+ANftr0et0nJ6X1trFEUII0cZJADgJKKUorXez9kAt43NTiLWZWrtIQggh2jgJACcBpWDj4TqqnV7G9UzCZJRfqxBCiB8mNcVJwK9pLNtUSq/UKHqlRcvc/0IIIX6UBICTwJ4KJ5uK6xmcE09GnE1G/wshhPhREgBOAu9sLiXGamJwTjwWo4z+F0II8eMkALRzVQ4Pn++pJi3WyqAcefKfEEKIn0YCQDumlOKLvdVUNHo4rXcqMTL6XwghxE8kAaAdc/mCrD1Qiz+ocXpeqlz7F0II8ZMZW7sA/yulFEqpY5bpdDp0Ol1o+ZGvR5Yf731Hr2uPlFIU17nZUtzAwOw4suLtrV0kIYQQ7Ui76wH46KOPyM3NpaCggEGDBnH99ddTVlaGUorDhw9z2223MWLECM4//3w++eQTAoEAwWCQtWvXcumllzJixAiuv/56du3a9Z0g0Z5oCraW1LO30sm5BRkY9e03zAghhGh57S4ABAIBBg0axJIlS1ixYgV//vOfSU1Nxev18sorr+D1elmwYAGTJ0/m+eefp6ysjOrqaubOncugQYP45z//SVRUFPPnz6epqam1D+dn8/iDfLyjguwEO30zYlu7OEIIIdqZdhcAAAoLC3nooYd4/vnnKSoqQqfT0dDQwM6dOzn77LPp3r07p59+OsFgkNLSUsrLy3E4HEyZMoVu3boxdepU9uzZg8PhOGa7Sim8Xi8ulwu3243P52ulI/xxlY1evthXw4iuCSRFWdr15QwhhBAtr82NAXC5XN/bMo+NjaVr167cdNNNpKen8+mnn3L33XfzxBNPYLFY8Hg8xMbGotPpiI6OJjIykvLycpKTk1FKERUVBUBcXBxutxu/33/M9isrK/njH//ImjVrAKiuruauu+4K7wH/DEop3ttWhsmgZ0jnBOxmufdfCCHE/6bNBYC3336bF1988bjX5//617/Sp08fevToAUBBQQG//e1v2b59OwUFBeh0OjRNA5orSU3TMBgMxx0keLxBgElJSfzlL39B0zQ0TeOll14K89H+PC5fgHe2lNI1KYIBWTHS+hdCCPE/a3MB4Fe/+hWTJk067rro6GiAUIVnMBgwmUx4PB4sFgs2m42amhqUUtTV1eF0OklLS8NisQDQ0NBARkYGVVVVREREYDabj9m+Xq/HarUCoGkaZrOZYDAYrkP92b46WEdlo5fRA5NIjba1dnGEEEK0Q20uANhsNmy241dqfr+fVatWEQgEyMjI4KOPPqKoqIgePXoQGxvLoEGDePXVV0lOTuaTTz4hMjKSjIwMzGYzSUlJLFy4kHPOOYeFCxfSv3//UKBoTwJBjU8KKwkqxaQ+Kehl9L8QQoifoc0FgB+i0+moq6tjwYIFNDQ00KNHDx555BH69euHXq9n+vTpaJrGfffdR+fOnbn77rtJSUkB4I477uC5557jnnvuYdSoUVx99dWh1n57cqC6iU1F9XRPimRAlkz9K4QQ4udpVwHAaDRy9tlnc/bZZx93fVxcHLfccgu33HLLd9Z17dqVP//5z+EuYlhpSrGttJEDVU3cfUYvpPEvhBDi52qXtwF2VE3eAGv312AzGxjZLbG1iyOEEKIdkwDQTiilqHZ6+XR3FWN7JpEYKff+CyGE+PkkALQjX+ytptHjZ3SPJGxy778QQohfQAJAOxHUFEs3ltI9OYpeqVHopfUvhBDiF5AA0E5sL21kd4WD/pkxdIqPaO3iCCGEaOckALQDmqZ4Z0spFpOBsb2SMRmk9S+EEOKXkQDQDpQ3elh/sJb0GCsFneJk8J8QQohfTAJAG6eUYuPheopq3UzonUKUtV1N3SCEEKKNkgDQxrl8Qb7cX4MnEGTqgHRp/QshhDghJAC0YUopyhrcfHWghtHdEkmJan9TFwshhGibJAC0YYrm0f+Halyc1icVk0F+XUIIIU4MqVHaMH9Q453NpXRJiiQvIwbp/RdCCHGiSABow0rq3Hy5v4ZBOXFkxNrk+r8QQogTRgJAG/afrWVYjQYGZ8djl6l/hRBCnEASANooh8fPhzsqSIuxMriz3PsvhBDixJIA0EZ9ua+GsnoPo7snkRIto/+FEEKcWBIA2iCvv/nef7c/wJR+adL6F0IIccJJAGhjlFIU17vZXFRPr9RoeqREtXaRhBBCnIQkALQxCthR2khhuYPzBmbKg3+EEEKEhQSANsbjD7JydyUJEWaGdI5v7eIIIYQ4SUkAaGPqmvx8uquK4V0TSYq0yPV/IYQQYSEBoI35pLACb0BjWJd4efKfEEKIsJEA0IZ4/UHe2lhCl8QIBmTFSutfCCFE2LS7Jub27dv5+9//jsfjAaBHjx5ccsklxMbGsnz5ct55553Qa0899VTOPPNMLBYL5eXlLF26lH379jFgwACmTJlCbGxsKx3F8W0rbeBgjYspfdPIire3dnGEEEKcxNpdADh06BA7duzg6quvJiYmhri4OCIiIggGg6xfvx6Px8MFF1yA0WgkMzMTo9GI0+lk9uzZVFRUMHbsWJYuXUpjYyMzZ87EbDa39iEBoCnFRzsqUEoxoXeyPPlPCCFEWLXLWsZoNGK1WklMTKRz585YLJbQOrPZjM1mIz09nczMTPR6PUVFRezYsYMbbriBiy++mCuuuILly5fT0NBwzHaVUgSDQQKBAIFAAE3TWuyYiutcrD9YR3qMjeFdElpsv0IIITqmdtcDEBcXR1xcHP/5z3+or6+ne/fuXH/99URHR5Odnc2ePXt47bXXqK2tZfLkyUybNg2Hw4FOpyMhIQGdTkdGRgZNTU2hywhHOBwOlixZwr59+1BK8fXXXzNlypSwH5NSim0ljeyrcnLtKV2l9S+EECLs2lwAeP3113n55ZdRSn1n3VNPPUW/fv147LHHsNlsFBYWMmvWLLZt28bo0aOZMmUKp512GkajkeXLl/Pqq68yevRogsEgSimMxubDNRqNBAKB7+zDZDLRo0cPYmNjUUpRU1PTIsfs9gVZf7CWoKaYmJvSIvsUQgjRsbW5ADB27Fhyc3OPGwBycnKw2+1EREQA0Lt3b9LT0ykqKgI4ZlBf//79WbBgAU6nE4ul+X56t9sNgNPpxGq1hgLBEVarleHDhwOgaRrl5eVhvwyglKLK6eXT3VWM6Z5ESoxVRv8LIYQIuzYXAJKTk0lOTj7uumAwGKrso6Oj2bx5M4cPHyYjIwO/38/hw4eJjo7GaDTy5ZdfotPpiIyMxGAwYLVa+fLLL4mIiOCzzz4jKyuLyMjIY7Z/dMWr0+larCLeVFRPab2b35zaFZvJ0CL7FEII0bG1uQDwQ4LBIJ9//jlLly5FKYXBYGDixIkMGDAAj8fDa6+9xubNm9HpdFgsFqZPn05aWhp6vZ5p06axcOFCFi1aRGRkJNddd913AkBrUMDSjaV0ToykT1o0Br20/oUQQoRfuwoAJpOJqVOncuqppxIMBjGbzcTGxmKxWFBKccMNN9DU1ASAzWYjJiYGk8kEwJQpUxgxYgQejwe73U5sbCx6fesPtjtQ1cSGQ7Wc0TeNzomtH0iEEEJ0DO0qABzp0j9ey12n0xEfH098/PEfoGMymb730kJrUUrxzuZSzEY9Y3okYTW1fiARQgjRMUiN04pqm3ys3ldDYqSFwTnxMvhPCCFEi5EA0EqUUmwsqudQbRNjeiSRGNk2ZiQUQgjRMUgAaCXegMaX+2podAc4Nz9DWv9CCCFalASAVlLW4GHDoVoGZMWSkxjR2sURQgjRwUgAaAWaUuypcFBY7mBKvzSZ+lcIIUSLk5qnFQSCiv9sLSMtxkZBdhxy678QQoiWJgGgFVQ7vazcXcWQnDgyY21y/V8IIUSLkwDQCpbvrEApGJgTT5S1XU3FIIQQ4iQhAaCFef1Blm0qJSPWJvf+CyGEaDUSAFrYVwdrOVznYmB2HDkJ9tYujhBCiA5KAkAL8gc1vthbTZM3yJS+adL6F0II0WokALSg8gYPm4rqyYq3MaBTbGsXRwghRAcmAaCFKKXYUdbI9tJGzi3IxGKUUy+EEKL1SC3UQjx+jS/31jQ/+a97YmsXRwghRAcnAaAFKKVwePwsL6xgWJcEUqKtcv1fCCFEq5IA0EK+3FdDtdPHqO6JRFtNrV0cIYQQHZwEgBYQ1BSLvy6mc2IE/TNj0cvcv0IIIVqZBIAWsKfSyY6yRvqkR9NZnvwnhBCiDZAAEGZKKT7eUYGmKU7tmSSj/4UQQrQJUhuFWaXDyxf7qomPMDOmR5IM/hNCCNEmSAAII6UU20oa2F/VxKQ+qUTJ4D8hhBBthASAMPIGNDYcqqPR7efMfmmtXRwhhBAipF0+i9bj8VBeXk5TUxMWi4XMzEysVivBYJDq6mpqamowm82kpaVht9vR6XT4fD4qKipwOBxERkaSkpKCxWIJazkdHj/7Kp2c0jOJrHh58I8QQoi2o90FAKfTyRtvvMHnn3+OpmlERkby29/+lm7durFz507+8pe/4Ha78fv9jBw5kquuugqr1crHH3/MggULMBgMBAIBfv3rX3PGGWdgNIbvFMRFmLnttJ4ElcJubnenWgghxEmsXdVKSik2btzIypUrueGGG+jVqxcej4fo6Gi8Xi9LliwhOTmZm2++mV27dvHEE08wceJEEhISWLRoEZMmTeKss87i7bff5vXXX2fkyJEkJCSErbxGvZ4eqVFh274QQgjxc7WrMQB+v5/Vq1fjcrl49tlnufDCC3n11Vdxu904nU727dvHyJEjSU1NZdCgQSQlJbF9+3aqq6tpampi6NChJCYmMnLkSCoqKnA6nSilQtsPBAKUlJSwd+9e9u7dS2VlZSserRBCCBE+ba4HoLCwkG3bth1TMR8xfPhwysrK2LZtG48//jipqak89thjxMbGMnHiRHw+HxEREeh0OqxWK5GRkVRXV+P1elFKYbVaAYiIiEAphdvtPmb7DQ0NzJs3j82bN6OU4tChQ1x99dUtctxCCCFES2pzAaCyspJNmzYdd13//v2x2WyMHj2aU089laioKMaPH8/GjRsZP348BoMBv98PNLfmjwQCg8GATqcjEAgAhF5jMh17W158fDz33nsvSik0TWP+/PnhO1AhhBCiFbW5ADBixAiGDBly3HVGo5EePXqwcuVKfD4fwWAQl8uFzWbDbrcTHx/PwYMH8fv9lJeXU1lZSffu3YmJiQGgoqKCrl27cvjwYSIiIkJ3CByh0+lCoUDTNIxGI8FgMPwHLYQQQrSwNhcAjEbj947MV0oxcuRIPvroI+bOnUtCQgKrV6/mtttuIy4ujjPPPJPZs2cTDAbZu3cvaWlpdO/enejoaEaNGsXzzz/Prl27WLlyJaeeeipxcXEtfHRCCCFE29DmAsAP0el0dO/enXvuuYePPvoIh8PBbbfdxpAhQ9Dr9ZxyyikYDAbWrFlD165dmTx5MomJieh0Oi6//HJSU1PZvXs3U6ZM4bTTTguNCRBCCCE6mnYVAKA5BPTp04c+ffp8Z53FYmH8+PGMHz/+O+tiY2O58MILW6KIQgghRJvXrm4DFEIIIcSJIQFACCGE6IDa3SWAlubz+XC73fIYXyGEOMkppfD5fMedh+ZkJAHge2iaBsBzzz3HggULftG2HA4Hdrsdg8FwIooWVk1NTZjN5u/MkdAWeTwegHYzmNPlcmE0GjGbza1dlB/l9XrRNA2bzdbaRflRgUAAr9dLREREaxflJ/H5fAQCAez2tv+AsGAwiNvtJjIysrWL8qOUUjQ2NoZu+/65XC4Xl19+eagOOJnpVEeJOv8jpRQejwefz4fRaPzZPQA+n49LL72URx99lK5du57gUp5YgUCAe++9l9NOO42xY8e26V6PIxM16fV6rrzySvT6tn01KxAI8OijjzJgwADOPPPMNn9uX331Vaqrq7npppvadHBVSrF27VpeffVV/vznP7f54KqU4u2332b79u3ceeedYX0Y2YmwZcsWnn76aebOndvmg2t1dTUXX3wx77zzzi9qFAQCAYxGIzabrU3/f3oitO2/vlak0+mw2Wy/uAVkMBgwGAyhyYrasiN/+Far9TuTJLU1mqZhNpvR6/XY7fZ2EQDMZjMWi6VdnFuLxYLZbG7zPVdHpvg2Go3Y7fZ2EQCOPrdtOQB8+9y29QBgs9kwGAzY7fZ20yvY2tr2p+ZJQKfThaYibg/0en27Kmtbr/iP1p7OrU6na3fntr1oT+dWynpya7vx8yRhMBi45pprSExMbO2i/Ci9Xs+5555Lp06dWrsoP0qn0zF69Gh0Ol27qFT1ej1nnHFGu/g70Ol0DB06FI/H0y4+ULt06cJFF13UpnsqjjZgwAA6derULs5tRkYGl19+ebs4txEREdxyyy1tvheoLZExAEIIIUQH1PYjqBBCCCFOOAkAQgghRAckYwB+AaUUpaWlbN68mdraWoYMGUL37t3R6XRomsb69evZt28fkZGRjBw5kvj4eADcbjdffPEFlZWVpKamMnLkSCwWS9jLW11dzddff011dTW9evWif//+GAwG9uzZw1dffYXf7wcgOTmZ0047DYPBgN/vZ82aNRQVFZGQkMCIESOIjIwM+3X3oqIitm3bRl1dHTExMRQUFJCamopOpyMYDLJu3ToOHDhATEwMI0eOJCYmBp1OR1NTE6tWraKmpoaMjAyGDx/eIqOX9+/fz/bt23E6ncTGxjJkyBDi4+PR6XR88cUX7N27N/TavLw8Bg4cCEBDQwOrVq2isbGR7Oxshg4dGvbrreXl5WzcuJG6ujqsVit9+vShe/fuAOzdu5fNmzdjMBjIz88nOzsbvV6Pz+dj8+bN7Nmzh7i4OAYPHkxCQkLY/w5qa2vZtGkTFRUVGI1GevbsSW5uLg0NDaxcuZKmpiag+Vkfo0aNIiEhgUAgwM6dO9m+fTt2u52BAweSnp7eomNFXC4Xq1evRq/XM2bMGPR6Pfv372fTpk0A5Ofn07lzZ/R6PX6/n61bt7Jr1y6io6MZPHgwSUlJLVrexsZGvvjiC6KiohgxYgQHDx5k7dq1+Hw+AFJTUznllFOwWq14vV42btzI/v37SUhIYMiQIcTGxoa1vE6nk1WrVlFRUQGA2Wxm9OjRZGRkUFNTw7p166ivr6dHjx70798fk8mEpmkcPHiQjRs3omkaAwYMoFu3bu1izFBLkR6AX2jLli28//77PPHEE6xYsSK0/Msvv+T+++9nx44dLFq0iEcffZRAIADAP/7xD+bMmcPu3bt5+umnef3111ukrHv27OHdd99l3rx5vPnmmwSDQQA+++wz5syZQ21tLXV1dTgcjtB7li1bxhNPPMGePXt46aWXeOGFF1qkrP/+97/55JNPKCoqYtmyZdx3332hiX+WL1/Oww8/zK5du1i4cCFPPfUU0Hz72rx585g/fz67du3iySef5J133mmR8r7xxhusXr2aw4cP88Ybb/DQQw+Fft8vv/wyb7/9NnV1ddTV1eF2u0Plfeqpp1i4cCE7d+7koYce4pNPPgl7WYuKitiyZQulpaWsWbOGu+66i+LiYnbt2sWDDz7IV199xcqVK5k1axaVlZUopVixYgWPPvoou3bt4rXXXuP5558PHUc4VVZWsmnTJkpKStiyZQsPPPAA27Zt48CBAzz77LPs3buXuro6GhsbCQaDKKXYsmULs2bNYsuWLbz33ns89dRTVFVVhb2sRyilWLduHXfddRcvvPACXq+X/fv3M2vWLNasWcMXX3zBww8/THFxMUopVq1axSOPPMLOnTtZsmQJs2fPxul0tlh5g8Egn3zyCXfffTd///vfUUqxZs0aXnjhBSorK0OfCUoplFK8//77PP744+zevZtXXnmFefPmhYJCuFRVVfHcc8+xefNm6urqqK+vx+/34/F4ePbZZ1m0aBG7d+9m1qxZfPrppyilqKys5KGHHuLTTz9l3bp1PPDAA+zZsyes5Wx3lPjZNE1TTqdT1dXVqRkzZqi5c+cqTdNUMBhUl1xyiXr66aeVy+VSxcXFqqCgQK1du1aVlZWpwYMHq9WrVyu3260++OADNWzYMFVXVxf28rpcLlVbW6sefvhh9Yc//EF5vV6llFLz589XF154oaqqqlJ1dXXK6/UqTdNUTU2NmjJlinr77beV2+1Wq1evVvn5+aqysjLsZa2trVX19fXK4/GooqIiNXDgQLVp0ybldrvVOeeco15++WXlcrnUzp071YABA9SuXbvU7t271eDBg9X27duVy+VSr7/+ujr11FNDxxlO1dXVqrGxUXk8HnXgwAGVl5endu/erZRS6qqrrlKzZs1S1dXVqqGhQQUCAaWUUlu3blUDBgxQ+/fvVy6XS/3tb39TZ511lvL5fGEtq8fjUU6nU3m9XlVXV6cmTpyo3nzzTfXXv/5V3XTTTaq6ulqVlpaqiy66SL3xxhuqpqZGXX311eqll15STU1Nau3atWrcuHFq//79StO0sJbV5/OFytrY2KiuuuoqNWfOHLVu3Tp1/vnnq/Xr16va2lrlcrmUpmnK7Xar+++/Xz3wwAOqsbFR7dq1S5177rlq5cqVYS/rEZWVlerXv/61uvPOO9WMGTNUY2Ojmj9/vrr22mtVRUWFqqioUDNmzFB///vfVX19vbrpppvU7NmzldPpVF9//bWaNGmS2r59e4uVd//+/eqKK65QN910k7ruuutUIBBQCxcuVJdeeqkqKipSdXV1yuPxKE3TVFVVlfr1r3+tXn/9deVyudSqVavU6NGjVVlZWdjLOG3aNPXhhx+qmpoa5XQ6VTAYVHv37lVjxoxRGzduVE1NTWru3LnqmmuuUfX19eqf//ynuvjii1VlZaWqrq5W1157rZo9e7YKBoNhLWt7Ij0Av4BOpyMiIoLY2Nhjbj2prq5m7969TJgwAZvNRnp6Oj179mTLli3s3r0bnU7HkCFDsFqtjB07FpfLdUwXcbjYbDbi4uK+0yUeFRVFbW0tV1xxBTNnzmTRokVomkZxcTEOh4MRI0ZgtVoZOnQoZrOZrVu3hr2scXFxxMTEYDabqa+vx2g0EhcXR2lpKSUlJUycOBGbzUbPnj1JTU0NdU8nJCTQrVs3bDYb48aNo7KyksOHD4e9vAkJCURFRWE2m6mpqcFms4WmJE1ISGDlypXMmDGD6667jvXr1wOwbds2srKyyMnJwWazMWnSJIqKiigrKwtrWS0WC8FgkJUrV/L6669jMpno1q0bu3btYvDgwcTFxZGamkqvXr3YtGkTtbW1NDQ00KdPH2w2G3369CE6OpqdO3eGtZwAJpMJvV7PqlWrWLJkCbW1tQwaNAiLxYLX6+Xee+9l5syZoR4sj8fDoUOH6NOnD5GRkWRnZ9OpUyd27NjRIlO7NjY28uijjzJ16lT69++PTqfD4/Gwc+dO+vfvT2JiIklJSfTu3ZutW7dSX19PdXU1ffr0wW6307NnTxISEtixY0fYywpQV1fH448/zrRp0+jRo0eoezwyMpKamhquvfZarr76al577TW8Xi/V1dW43W769OmD1WqlX79+WK1WCgsLw1pOo9FIdHQ0Tz31FDNmzOCBBx7g8OHDbN68mbi4OHr37o3NZqOgoIDa2lpqamrYtGkTffr0ITExMXRZbvfu3bhcrrCWtT2RMQBh4Ha7CQQCREVFhZZFRkbidDppamo6ZkZAvV6PxWJp1T/KUaNGkZ+fT0REBGvXruXRRx9l2LBheDweTCZT6ENBr9djs9latHuyrKyM5557jrPOOouMjAwKCwvRNC10DnU6HZGRkTgcDnQ6HVar9ZgPMaVU6DpxSzh48CB//etfmT59OklJSQBcccUVXHfddSilWLx4MX/84x954403aGpqOmb++qioKILBYIv8LTidztAllri4OEwmE263G5vNFro/3W63U1paSiAQQCkV+ls48qyIxsbGsJcTmp/5sGrVKvbv34/BYCAyMpLMzEwef/xxYmNj2bt3L0899RSdO3fm1FNPxefzYbFY0Ol0oZktj3Rhh5Pf72fx4sVERUVx9tlns2TJEqD5Uo/L5Trm3NpsttDnxJFZLY+cW4vFcsxluHDxer384x//oHPnzpx22mnMnTs3tG7o0KH06tWLqKgo1qxZw7PPPsvAgQPRNA29Xh+a3MxqtbbI30JiYiJ33nkndrudurq60KXT+Pj40MyKQGhmRb/fj9PpDI390Ov1REZG4nK5Qpc+hQSAsDgyJWlDQ0NomcPhICoqisjISJqamkIfRsFgEI/H06oPMklPTw99f+aZZzJ37ly2bt1Kt27d8Pv9oZbTkcopOjo67GU6UnH/6U9/IjY2lmuvvfaYaX+bmpqIi4tDKYXD4SA6OpqIiAjcbnfo3DocjtD/+C1R3qqqKh577DFyc3OZPn16aF3Pnj1D38+YMYOXX36Z0tLSUHA5oqGhAaPR2CJ/C6mpqdx///04HA7uvvtu3nrrLex2Oy6XC03TQgMqIyMjQxW/3+9HKYXX68Xn8xEbGxv2ckLzAL/f//73NDU18Ze//IVXX32Vhx56iNzcXKC5chg4cCA7duxgzJgxmM1mPB4PSin8fj9ut5vs7OywD/5qaGjg448/ZuvWrXz66adUVlZSW1tLVVUVvXr1Oubculyu0FTAer0er9cbOrcej+cXP9Dmp6iuruaDDz6goqKC9957j5KSElwuF0opZs+eTUpKCgCTJk3i1VdfpbCwkLy8PDRNC4VCt9vdIn8LNpstNFA1PT2dcePG8cknnzBmzJjQM1tMJlNo3I3ZbCYqKir0WatpGg6Hg4iIiDY9/XJLk0sAv4BSikAggMvlIhAIhD5s4uLi6NWrF++99x4Oh4MDBw6we/duCgoK6NWrFwaDgVWrVuF0Ovnggw+IjY0N/XGH05EK3O/3h8rq9/upra2lsbERt9vN/v37qaurIyUlhaysLOLi4lixYgVNTU18/vnnBINB+vbtG/ay1tTUcOeddxIMBvnd735HTEwMSinS09PJycnh3Xffxel0snnzZiorK0Pntr6+nm3btuF0Onn//fdJS0trkZkNKyoquOOOO0hKSuLaa6/FZrOF/j6qqqpwuVw0NTWxYcOG0OWB/v37U1paSmFhIU6nk3fffZcuXbqQlpYW1rLW19eHekyMRiOapqGUonfv3qxZs4aqqiqKiorYsWMHAwcOJCEhgfj4eDZu3IjT6WTTpk04nc5QBRxOTqeT+vp6oHlWzSPB0Ol0hrr8y8vLOXjwIElJSdjtdrp27cqmTZuor69n3759HD58mD59+oR95r3Y2Fgef/xxXnvtNebMmcOVV17JiBEjeOihh8jLy+Prr7+mrKyM0tJStm3bxoABA0KXWzZt2oTD4WD79u3U1dXRu3fvsJYVmu/2ef7553nllVeYM2cOF154IWPGjOGWW26hsbGRhoYGPB4P+/fvp76+nuTkZJKTk4mMjGTjxo2hv2e/339MyA2HI5cfPB4P9fX17N+/n6ioKAYOHEhDQ0Pob/PLL78kOTmZhIQEBg0axNatWykrK6O6upo1a9aQm5vbLp5w2VIkCv1CO3fuZMGCBWzYsIHi4mJqa2s5//zzuf7663nooYeoqKigrKyMM844g379+mEwGLj22mv561//Svfu3SksLOSGG25okVZ1SUkJc+bMYe3atXg8HgwGA2eeeSbbtm1j3759WK1WDh06xKhRoygoKMBqtTJz5kxefPFF1q9fz4EDB5gxY0bodsZwmjNnDosXL+bSSy9l7ty5GAwGzj//fHr27Ml1113HU089xd69eykqKuK8886jc+fOAFx++eXMmjWLLl26sGvXLn7729+2yNSgjzzyCMuXL+fiiy9m9uzZWCwWLrjgAqKjo3nmmWdCI6h37drFNddcQ0pKCklJSVxwwQX88Y9/JCsri8LCQu64446wt1A++OADNm3ahMViob6+Hrfbzfnnn49Op2P9+vXMmjULj8dDYmIiI0aMICYmhmnTpjF37lz27t1LWVkZp512GsnJyWFvVX/11Ve8//772Gw2mpqaKCoq4qabbuKrr75i2bJlxMTEUFNTg06nY/z48djtds466yyefPJJHnzwQRwOR+jWwXCX1Wg0kpWVFfp5y5YtoXAfExPDl19+yaOPPkowGMRms3HKKacQFRXFueeey+zZsykpKaGqqopRo0aRmZkZ9vKaTCZycnJCP6elpVFXV0d6ejpvv/02GzduxG63U1xcTL9+/ejXrx8xMTFcdNFFvPjii2zdupXi4mJ+9atfERcXF9ayHjx4kOeee46YmBhcLhelpaXccMMNocsXs2fPJjU1lQMHDnDjjTcSFRXFqaeeyvLly3nggQewWCxomsaECRPaxRTMLUWmAv4FlFKUlZWxbt260DKr1Ur//v1JTU1l69atFBUVhQanHOkm83q9bNiwgdraWhITEykoKGiRe9Vra2v5/PPPQ13kBoOBvLw8AoEA+/btw+/3Ex8fT+/evUP39QYCATZv3kxZWRmxsbHk5+e3yNPs1q9fT3FxcejnIwMn09LS0DSNLVu2UFxcTFRUFPn5+URFRaHT6XC73WzYsIH6+npSUlIYMGBAiwSAVatWUV1dHfrZaDQydOhQYmJi2LJlCxUVFeh0OlJTU+nTp09o3geHw8GGDRtwOp1kZGTQv3//sH9AHT58mN27d+N2u7Hb7XTr1o1OnTqhlOLw4cMUFhai1+vp3bs36enpoXvVCwsLOXToENHR0fTt2zfs935D822AO3bswOFwYLVaycnJoXPnztTU1LB169bQs+p79OhBWloaer2eQCDA/v372bt3LxaLhby8vBYJK99WXFxMZWVlKPgXFRWFBk7m5uaSmZkZOre7d+/mwIEDREZG0rdv39AcEi1p//79OBwO8vLyOHToEHv27MHn8xEfH0+vXr1CZfL5fOzYsYPi4mJiYmLo168f0dHRYS1vY2MjGzdupLGxEavVSufOncnJycFgMFBfX8+WLVtwOBzk5OTQq1evUM9WSUkJO3fuRNM0cnNz6dSpk8wDcBQJAEIIIUQHJH0hQgghRAckAUAIIYTogCQACCGEEB2QBAAhhBCiA5IAIEQH4vP5WLx4MYWFhb94ZjyPxxPalhCi/ZF5AIRoxxYvXsy8efNCM6AZDAYuvPBCrrrqquO+Xq/Xk52dfUJmmvN6vSxZsgSz2UyvXr1+8faEEC1LAoAQ7VhxcTHJycnMmjULaJ4vITo6moqKCjRNw+124/V6iY+PJykpCb1eT0pKSmi64fr6eiorK0PPrkhJScFkMoWWa5pGYmIiCQkJoXkhjkwZe/SERUem3S0vL8fpdGK1WklLS8Nms+H3+ykuLsbtdmMwGEhLS2uRia+EED9MAoAQ7VxERATZ2dnHLLvnnnvYuHEj2dnZVFdXY7FYeOyxx4iNjeXuu+/mggsuYOTIkcyePZs9e/ZgsVjo1KkTV155JdHR0Tz44IMUFxdjMpmw2+38/ve/p3v37qxYsYJnn32WuLg4IiIiqKioAJoDwAcffMCbb76JTqdD0zSGDx/O9OnT+eyzz5g7dy7x8fEYDAbOO+88Tj/99NY4VUKIo0gAEKKd+/zzz0MPHzKZTFx55ZVA8yyDt912Gzabjbvuuos333yTmTNnht5XXl7Otm3buO222+jTpw9NTU3ExsbywQcfhJ6wFxERwaOPPsqbb77Jbbfdxpw5c5g8eTIXXnghmzZt4sYbbwSan4A5b948brrpptBjV59++mmGDRvGu+++y4ABA7j11lvxer0tf4KEEMclAUCIdi43N5cbbrgBaL7G37lzZ/7zn/8wevRocnJyMBqNjB49ms8///yYAJCSkkJaWhp//OMfGTduHKeffjqJiYl8/fXXDBgwgG7dugEwYcIEli5dSmVlJfv372fs2LEkJCRQUFAQes3hw4f5/PPPKSsrw2QyEQwGCQaD1NbWMnHiRB5++GGqqqqYMGECEyZMaPmTJIT4DgkAQrRziYmJDBky5DvLjzzaFZpb6N9+3kRiYiJPPPEEW7du5YMPPuDWW2/lwQcfDD0k6Mh7XS4XJpMJk8mEwWAIteKVUng8ntD3OTk5zJs3L/Q0Q71eT0xMDGazmYKCAj7//HPmz5/Pl19+yZ/+9KewnQ8hxE8jtwEK0c75/X4cDkfo35FK+ZNPPuHrr79m69atfPjhh4wdO/aY99XU1LB+/XrS09M5++yziYyMpLGxkdGjR7Nhwwa+/PJLdu3axbJly+jfvz8JCQn079+fJUuWcPDgQZYtW8bhw4cByM7OJjs7m48//jj0qOk9e/bgdDr57LPPcLvdjB8/nuHDh3PgwIEWP0dCiO+SHgAh2jGTycSKFSsYN24c0NzqPuusswAYNGgQTz31FIcPH2bkyJFMmTIFnU6H2WzGYDDgdDpZuHAh27dvx2QyceqppzJo0CAiIyOZOnUq99xzD4FAgLFjx3LhhRdiMBi4/fbbue+++/j1r39NQUEB/fv3x2AwYLfb+eMf/8icOXO4+OKLsdlsjBkzhm7durFlyxZmzZqF2+0mNTWVu+66qzVPmRDiG/I0QCHaMU3T0DTtmGU6nY777ruPqKgobr31VvR6PTqdLvSYYU3T0Ol0odH6Rz4CjrwOmrv0j2z36OVH3q+UCi07sq2j1x1Zrtfrj9nWkWXySFYhWp/0AAjRjun1+lDF/m06nQ6DwYDBYDhm+dE/f3vd0e/9vu1+33u+b90PbUsI0XqkB0CIk9DevXsxGAzk5ORIa1sIcVwSAIQQQogOSPrlhBBCiA5IAoAQQgjRAUkAEEIIITogCQBCCCFEByQBQAghhOiAJAAIIYQQHZAEACGEEKIDkgAghBBCdEASAIQQQogOSAKAEEII0QFJABBCCCE6IAkAQgghRAckAUAIIYTogCQACCGEEB2QBAAhhBCiA5IAIIQQQnRA/w8Si33IrUl/zgAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [
        "-GZaSLjzuJEj",
        "g6qD5Sgfw4l0",
        "Dh3DA-IOaY94",
        "tsavzBHWacIi",
        "FUZQ4QB4az-6"
      ],
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}