Intro_sul campo_RL_ita.ipynb

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        "# Reinforcement Learning - Tutorial in italiano\n",
        "Mario Fiorino \n",
        "\n",
        "Il **Reinforcement Learning (RL)** è un campo del Machine Learning, in cui l'agente apprende, non attraverso un set di dati fisso, ma, interagendo con l'ambiente. In pratica si usa l'esperienza per guidare le decisioni future e conseguire determinati obiettivi\n",
        "\n",
        "*Concetti principali:*\n",
        "\n",
        "- ambiente\n",
        "- segnale di ricompensa (Reward signal)\n",
        "- agente\n",
        "- insieme di azioni possibili (nota: le azioni possono avere conseguenze a lungo termine)\n",
        "- stato agente\n",
        "- politica (policy e apprendimento di \"una optimal policy\")\n",
        "- uno stimatore (value function)\n",
        "- modello del ambiente (che puo essere presente o meno)\n",
        "\n",
        "*Key point* :\n",
        "\n",
        "Apprendere una mappatura tra stati e azioni (o volendo determinare una optimal policy; cioè una sequenza di azioni) in modo da massimizzare il segnale di reward nel tempo.\n",
        "\n",
        "Questo tipo di apprendimento è solitamente modellizzato tramite i [processi decisionali di Markov](https://it.wikipedia.org/wiki/Processo_decisionale_di_Markov#:~:text=I%20processi%20decisionali%20di%20Markov,il%20controllo%20di%20un%20decisore.)\n",
        "\n",
        "*Dove è usata la tecnologia RL?*\n",
        "\n",
        "Dalla finanza: pricing, trainign portafolio; al controllo robotico; alla gestion delle risorse: \"adaptive decision control\"; fino alla gestione dinamica dei Big Data  : \"recommendation system\".\n",
        "Per maggiori info : [cliccare qui](https://www.v7labs.com/blog/reinforcement-learning-applications)\n",
        "\n",
        "\n",
        "*Perché il RL è difficile?*\n",
        "\n",
        "Una delle parti più difficili del RL è dover mappare l'ambiente e includere tutte le mosse possibili. Oltre a definire un segnale di reward adeguato ai propri scopi. Questo ci impone a pensare in termini di :\n",
        "\n",
        "- conseguenze a lungo termine delle azioni\n",
        "- raccogliere attivamente esperienza in modo utile\n",
        "- affrontare l'incertezza del mondo esterno (informazioni parziali)"
      ],
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      "source": [
        "# Esempio intorduttivo e formalizzazione del problema\n",
        "\n",
        "Per dare un'idea di cosa sia il RL, in questo notebook si utilizzerà Python per creare un ambiente molto semplice unidimensionale. L'agente \"U\", partendo dallo stato \"I\", deve imparare a raggiungere lo stato stato \"G\" (Goal), muovendosi a destra o sinistra.\n",
        "\n",
        "[. I . . . . . G]\n",
        "\n",
        "Ambiente può così essere rappresentato nel framework Markoviano:\n",
        "- Insieme finito di 8 stati,  S: [0,1,2,3,4,5,6,7]. Dove l'ultimo stato, il 7, è il Goal da raggiungere. Stato iniziale S = 1\n",
        "- Insieme di finito di 2 azioni discrete,  A : [\"desta\", \"sinistra\"]\n",
        "- Funzione di transizione da uno stato all'altro, deterministica :  \n",
        "   - input: (azione \"destra\", stato S)     -> output :    S+1\n",
        "   - input: (azione \"sinistra\", stato S)   -> output :    S-1\n",
        "   - input: (azione \"sinistra\", stato S=0) -> output :    S=0\n",
        "   - Stato S = 7, fine.\n",
        "- Segnale di Reward R(S,A). Cioè la ricompensa ottenuta partendo dallo stato S agendo secondo l’azione A. Anche questa funzione è determinisitca : \n",
        "    - per ogni spostamento; reward immediato = 0. \n",
        "    - in caso di raggiugimento dello stato S = 7 , reward immediato = +1\n",
        "\n",
        "- Fattore GAMMA,  γ = \"discount factort\", è un iperparametro costante che tiene conto di possibilità di premi non immediati. Il suo valore è compreso tra 0 ed 1. In pratica la prima ricompensa che si ottiene è quella che pesa di più, poi mano a mano che si considerano reward più lontani nel tempo essi contribuiranno\n",
        "sempre meno. Nel caso GAMMA ≈ 0 l'agente sarà “avido” considerando prevalentemente i premi immediati, opposto al caso GAMMA ≈ 1 in cui l'agente presterà attenzione alla ricompensa a lungo termine\n",
        "\n",
        "Una \"policy\", spesso indicata con il simbolo π;  è una mappatura tra stati e azioni. In questo semplice esempio la \"policy\" è deterministica, ed è una semplice funzione : Stato -> Azione\n",
        "\n",
        "Una \"optimal policy\" è definita come politica che sceglie le azioni nel tempo in modo da massimizzare il valore atteso del ritorno della funzione $G$ , chiamato anche \"total discounted reward\" :  \n",
        "\n",
        "$G(S_{0},A_{0},S_{1},A_{1},S_{2},A_{2},... )$ =  $R_{0} + γ  R_{1} + γ^{2} R_{2} + . . . $\n",
        "\n",
        "Cioè la somma pesata da GAMMA  dei reward ottenuti durante una sequenza finita di stati-azioni. Nota, per valori γ < 1  i reward più lontani nel tempo contribuiranno sempre meno \n",
        "\n",
        "Per trovare una \"optimal policy\" è necessario definire uno stimatore che ci dice quanto è buono lo stato $S_{t}$ in cui ci troviamo se seguiamo una certa policy $\\pi$ . Gli stimatori più comuni sono:\n",
        "\n",
        "-  State-value function : ci dice quanto è desiderabile essere in un certo stato in relazione alla sequenza di stati futuri che verranno raggiunti a partire da esso seguendo una certa policy :\n",
        "\n",
        "$V_\\pi (S_{t})$ =  $R_{t+1} + γ  R_{t+1} + γ^{2} R_{t+2} + + γ^{3} R_{t3}. . . $\n",
        "\n",
        "\n",
        "- Action value function : questa valuta la bontà (o le conseguenze) di una certa azione in un determinato stato, a patto di seguire poi una certa policy :\n",
        "\n",
        "$Q_\\pi (S,A)$ =  $R(S,A) + V_\\pi (S_{next(S,A)}) $\n",
        "\n",
        "Dove $(S_{next(S,A)}) $ è lo stato in cui finisce l’agente eseguendo l’azione A stato S. Mentre $R(S,A)$ è immediato reward che ottiene eseguendo A in S.\n",
        "\n",
        "\n",
        "Formalmente imparare una policy (\"optimal policy\") che massimizzi il valore del ritorno atteso da qualsiasi stato viene scritto: \n",
        "\n",
        "$\\pi^{*}$ =  $ \\underset{\\pi}{\\arg\\max} \\hspace{0.2cm}  V_\\pi (S),  \\hspace {0.7cm} \\forall S $"
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      "source": [
        "# Q-learning \n",
        "\n",
        "Al fine di ottenere una \"optimal policy\" che risolva il problema proposto nel nostro sistema, in modo semplice; sarà usato l'algoritmo iterativo [Q-Learning](https://it.wikipedia.org/wiki/Q-learning). [Qui versione in inglese](https://towardsdatascience.com/reinforcement-learning-explained-visually-part-4-q-learning-step-by-step-b65efb731d3e). Questo di fatto ci consentirà di rappresentare sotto forma di tabella, per ogni stato del sistema, il valore della \"Action value function\", o anche detta \"Q-fucntion\".\n",
        "\n",
        "*\n",
        "\n",
        "*Un pò di teoria*: \n",
        "\n",
        "\n",
        "Q-learning fa parte di quella categoria di algoritmi classificati metodi \"Temporal-Difference\" (TD). I metodi TD nascono dalla combinazione di\n",
        "due idee: Metodo Monte Carlo e di Programmazione Dinamica (DP). Come i metodi Monte Carlo,i metodi TD possono imparare direttamente dall'esperienza grezza senza un modello dell'ambiente. Come DP, i metodi TD aggiornano le stime basandosi in parte sulle stime apprese in precedenza (questa procedura è detta \"Bootstrapping\"); senza però, e questa è una distinzione importante, attendere la fine del processo epslorativo, o meglio la fine dell'episodio (in pratica gli \"update\" di questa metodologia sono basati su un \"singolo campione\" successore, e differiscono dagli aggiornamenti dei metodi DP, basati su una distribuzione completa di tutti i possibili successori). La relazione tra i metodi TD, DP e Monte Carlo sono un tema ricorrente nella teoria del RL.\n",
        "\n",
        "La \"update rule\" generale di questa metodologia:\n",
        "\n",
        "$ NewEstimate ↤ OldEstimate + StepSize [Target - OldEstimate]$\n",
        "\n",
        "Più nello specifico, in un caso semplice TD(0):\n",
        "\n",
        "$V(S_{t})  ↤ V(S_{t}) + α [R_{t+1} + γ V (S_{t+1}) - V(S_{t}) ]$\n",
        "\n",
        "\n",
        "Il TD error misura la differenza tra i valori : $[R_{t+1} + γ V (S_{t+1})) - V(S_{t}) ]$ , e dipende dallo stato successivo e dalla prossima ricompensa, quindi non è disponibile fino allo step temporale successivo.\n",
        "\n",
        "L'algoritmo Q-learning è di tipo : off-policy, ovvero che valuta o migliora una policy (detta \"target policy\")diversa da quella utilizzata per campionare i dati. (detta : \"behaviour policy\")\n",
        "\n"
      ],
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    },
    {
      "cell_type": "markdown",
      "source": [
        "# Moduli importati"
      ],
      "metadata": {
        "id": "z4fGncNwmz5U"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import time\n",
        "import random \n"
      ],
      "metadata": {
        "id": "fy-BqqQymtt7"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Formalismo Markoviano ed Iper-pametri"
      ],
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    },
    {
      "cell_type": "code",
      "source": [
        "N_STATES = 8  # numero di stati\n",
        "ACTIONS = ['sinistra', 'destra']     # azioni disponibili\n",
        "\n",
        "#IPER-PARAMETRI\n",
        "EPSILON = 0.5   # gestisci ϵ-greedy policy\n",
        "ALPHA = 0.1      # learning rate :  Il tasso di apprendimento determina con quale estensione le nuove informazioni acquisite sovrascriveranno le vecchie informazioni. Un fattore 0 impedirebbe all'agente di apprendere, al contrario un fattore pari ad 1 farebbe sì che l'agente si interessi solo delle informazioni recenti.\n",
        "GAMMA = 0.9      # discount factor\n",
        "\n",
        "MAX_EPISODES = 80   # episodi massimi\n",
        "FRESH_TIME = 0.3    # fresh time display"
      ],
      "metadata": {
        "id": "nUHS9YARnIwh"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Q-table\n",
        "\n",
        "Qui la costruzione della tabella-Q della Action value function. Ha una riga per ogni stato e una colonna per ogni azione. Ogni cella contiene il valore Q(S,A) stimato, in un determinato momento, per la corrispondente coppia di parametri : stato-azione. \n",
        "\n",
        "Si inizia inizializzando tutti i valori della tabella-Q a zero. Man mano che l'agente interagisce con l'ambiente e ottiene feedback, l'algoritmo migliora iterativamente questi valori Q finché non convergono ai valori Q ottimali.\n",
        "\n",
        "\n",
        "*Note Tecniche*\n",
        "\n",
        "In questo nootebook si fa usa della libreria Pandas. \n",
        "Un DataFrame è una struttura dati bidimensionale, cioè i dati sono allineati in modo tabulare in righe e colonne. Pandas DataFrame consiste di tre componenti principali, i dati, le righe e le colonne https://datascience.eu/it/programmazione/python-pandas-dataframe/\n"
      ],
      "metadata": {
        "id": "ktq2uqootdoB"
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    },
    {
      "cell_type": "code",
      "source": [
        "def build_q_table(n_states, actions):\n",
        "    \n",
        "    my_data  =   np.zeros((n_states, len(actions))) # inizializziamo tutti i valori della tabella-q a 0\n",
        "    \n",
        "    \n",
        "    #Come riempire una tabella con valori random :\n",
        "    #my_data  =   np.ones((n_states, len(actions))) * np.random.rand(8,2)\n",
        "    \n",
        "    table = pd.DataFrame(\n",
        "        data=my_data,     \n",
        "        columns=actions,    # nomi delle colonne sono le sue azioni possibili\n",
        "    )\n",
        "    #print(table)    # otteniamo una tabella dove per ogni riga è indicato uno stato, ed ogni colonna un azione\n",
        "    return table"
      ],
      "metadata": {
        "id": "qYPG5ZrZthi8"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Funzione per generare \"True Random Number\""
      ],
      "metadata": {
        "id": "Q7Iho7cXdUxx"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def gen_random():\n",
        "  k = time.time()\n",
        "  time.sleep(random.random()* 0.01)\n",
        "  z = ( (k/time.time()) * random.random() )\n",
        "  #print(z)\n",
        "  return z"
      ],
      "metadata": {
        "id": "nGXDaqDKcWWd"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Scegli un'azione, o la questione di \" exploration vs exploitation\" \n",
        "\n",
        "All’inizio l’agente eseguirà azioni casuali, in quanto non ha informazioni sul Q(s,a), il suo obiettivo sarà quindi di esplorare lo spazio stati-azioni al fine di riempire la Tabella-Q. Quando l’agente incomincerà a disporre di una quantità considerevole di informazioni su Q(s, a) potrebbe scegliere deterministicamente (evitando la scelta casuale), in modo \"greedy\" l’azione che lo porta ad un reward più alto.\n",
        "Si noti che scegleindo sempre a caso l’azione da intraprendere, sfocerebbe in un costo computazionale enorme, ritardando la convergenza enormemente. Proprio per questo bisogna trovare un equilibrio fra lo sfruttamento delle informazioni di cui già si dispone ed il provare nuove soluzioni (\" exploration vs exploitation\" )\n",
        "\n",
        "Approccio ϵ − greedy.\n",
        "\n",
        "Dove ϵ è la probabilità di scegliere un'azione random invece di quella migliore, indicata dai valori che in quel momento popolano la tabella Q. \n",
        "In questo notebook tale scelta è vincolata in parte ai valori inziali della tabella Q. Se uguali a 0, o meno.\n",
        "\n",
        "\n",
        "\n",
        "Aiuti Tecnici Pandas:\n",
        "\n",
        "https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.iloc.html#pandas.DataFrame.iloc\n",
        "\n",
        "\n",
        "https://www.w3schools.com/python/pandas/ref_df_idxmax.asp"
      ],
      "metadata": {
        "id": "15o7IQ3XyMVm"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def choose_action(state, q_table):\n",
        " \n",
        "    state_actions = q_table.iloc[state] # prende tutti e due i valori della riga di un certo stato dato in ingresso: \"state\".\n",
        "    # In pratica da qui esce la coppia di numeri float sotto le colonne ['sinistra', 'destra'], di un certo stato\n",
        "     \n",
        "    k = gen_random()\n",
        "    #print(\"\\t \\t \\t \",k, ((k > EPSILON) or (state_actions[0] == 0) or (state_actions[1] == 0)))\n",
        "\n",
        "    #  Selezionare un’azione fra quelle possibili seguendo il criterio ϵ − greedy\n",
        "    if (k > EPSILON) or (state_actions[0] == 0) or (state_actions[1] == 0) : \n",
        "                                 # ... or  (nel caso i valori della tabella-q sono ancoa a zero)    \n",
        "        action_name = np.random.choice(ACTIONS)\n",
        "    else:   \n",
        "        action_name = state_actions.idxmax()    # Pandas sostituisce argmax con idxmax\n",
        "        # agisce greedy, cioè da in uscita l'azione della riga \"state_actions\" con valore più alto\n",
        "        print(\"\\t  +++!exploitation!+++\")\n",
        "    return action_name"
      ],
      "metadata": {
        "id": "LUhumFhKyM02"
      },
      "execution_count": null,
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    },
    {
      "cell_type": "markdown",
      "source": [
        "# Interazione con l'ambiente\n",
        "\n",
        "\n",
        "Qui è implementata la funzione deterministica di transizione da uno stato all'altro:\n",
        "\n",
        "- input: (azione \"destra\", stato S) -> output : S+1\n",
        "- input: (azione \"sinistra\", stato S) -> output : S-1\n",
        "- input: (azione \"sinistra\", stato S=0) -> output : S=0\n",
        "- Stato S = 7, fine.\n",
        "\n"
      ],
      "metadata": {
        "id": "EgBnosCbE7Q4"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def env_feedback(S, A):\n",
        "\n",
        "    if A == 'destra':    \n",
        "        if S == N_STATES - 2:   # controllo se si è prossimi alla fine\n",
        "            S_next = S + 1      #Goal\n",
        "            R = 1\n",
        "        else:\n",
        "            S_next = S + 1      # agente si muove verso destra\n",
        "            R = 0\n",
        "    else:   \n",
        "        R = 0\n",
        "        if S == 0:              # se agente è nello stato 0 rimane sul posto\n",
        "            S_next= S  \n",
        "        else:\n",
        "            S_next = S - 1    # agente si muove verso sinsitra\n",
        "    return S_next, R"
      ],
      "metadata": {
        "id": "I7t8gDgOE71h"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Semplice Interfaccia Grafica\n",
        "\n",
        "Qui è sviluppata l'interfaccia grafica unidiemnsinale, ed i sui relativi update nel tempo.\n",
        "\n",
        "[. . . U . . . G]\n"
      ],
      "metadata": {
        "id": "2o47oBsuRUM3"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def update_env(S):\n",
        "\n",
        "    env_list = ['.']*(N_STATES-1) + ['G']       \n",
        "    \n",
        "    env_list[S] = 'U'\n",
        "    interaction = ''.join(env_list)\n",
        "    print('\\r{}'.format(interaction), end='')\n",
        "    time.sleep(FRESH_TIME)\n"
      ],
      "metadata": {
        "id": "Gl8R2TZSO1Mf"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Cuore dell'algoritmo Q-learning\n",
        "\n",
        "Il cuore dell'algoritmo fa uso di un processo iterativo di aggiornamento e correzione basato sulla formula :\n",
        "\n",
        "![Screenshot 2023-01-03 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GxtbYD9clqRljDH24rKkUoz7FGOMMcYYY4wVO0o/aEBOf2GSJOXb+b8syzh9+rT6/4LSMsYYYwquFGOMMcYYY4wVO8HBwShVqhQAIC4uDqVKlUJMTEy+ad966y0AOYMOlCpVCjqdrsjyyhhj7PnElWKMMcYYY4yxYmf69OmQJEn9E0Ux31eqLUnLGGOMKfJ/sZIxxhhjjDHGbMSwE31rpmWMMcYUfPVgjDHGGGOM2YTSsosxxhizBa4UY4wxxhhjjBU5URTRtGlTvPbaa9Dr9bbODmOMsRKIK8UYY4wxxhhjRYqIEBQUhNTUVNy/fx9BQUGQZdnW2WKMMVbCcJ9ijDHGGGOMsSJDRJg+fTpmzpyJli1bQpZlzJo1C3Z2dggKCuL+wRhjjBUZrhRjjDHGGGOMFYnbt28jODgYCxcuRJUqVRAWFgZRFOHt7Y3Q0FAAwKeffgoHBwcb55QxxlhJwI9hGGOMMcYYY8+UJEnYuHEjPD09sXDhQgDAkiVL0KJFC7z99ttYtGgRACA0NBTt2rXDd999B1EUQUS2zDZjjLEXHLcUY4wxxtgLTRRFaDQaEBHS09MhCIKts8TYC6t06dKoUKECAODy5cu4ePEifv/9d/z+++9IS0tT082cORM+Pj7qq5IDBgxAWloapk2bhgsXLmDixImYPXs2XFxc0Lp1a2i1Wri4uKBSpUp8HjNWBKpWrQqNRgNBEPh8Yy80rhRjjDHGWLFh2CrkaVqISJIESZJw/PhxHD58GIcPH8alS5eQkpKCsmXLWiOrjLFciAivvvoqBEFAWloaRFE0SePu7o4vvvgCXbt2Neo7TBAETJ06FS4uLpgzZw7i4uJw8+ZN3Lx5Ezt37lRfraxRowYePnyIMmXKFNl2MVbS1KtXDy+99BLeeOMNvP766+jYsSM6dOiA0qVLc59/7LlgSQzJlWKMMcYYKzYuXryofk5JSUGnTp0sml+WZVy5cgVz5szB1q1bce3aNaPpFSpUwPXr162SV8aYqfr16+PcuXMm31etWhVffPEFPv/8c9jb530LIggCunfvjvfeew/z5s3D3LlzcevWLaM0yjl9794962eeMQYAcHZ2RnR0tPr///znP3BwcEC/fv3wxRdfoFatWlw5xoq13bt3q58fPXqktmDOCx/JjDHGGCuWLH1dQxRFhIWFoWPHjli8eLFJhRhjrOg5Ozvj008/RWxsLCZNmpRvhZghe3t7TJ48GbGxsRg3bhyaNGlSBDlljBUkMzMTixcvRseOHfHDDz/k2RKUseJClmWz0wrEvVcyxhhjrJg4ceIEWrRoAQDYt28f2rdvX+g8RIQ9e/Zgzpw5iIyMNJr2yiuvoF69eqhbty6qVauGCxcuwNHR8ZnknbGSLjs7Gw8ePICXlxfeeOMNNGrUCE2bNlX7JXoSRARZlpGWloY///wTV65cQXh4OJo3b27l3DPGFJmZmWjWrBkyMzPx119/4ezZs0hNTTVK0717d3zxxRfQarXc5xgrdlatWgVfX18AKPSVe359kjHGGGPFhmFgbU6QTUQ4ePAgPDw81O9cXFzg5uaGHj16wMPDgzsJZuw5JggC7OzsUK9ePdSrVw8AMH78eBvnirGSg4hARDh69Ci2bNmC6OhoHDt2DJGRkYiMjMQff/yBLl268HWWPbf49UnGGGOMPbcePHiAYcOGAQAaNmyIn3/+GYmJiViwYAE8PT2fqoUKY4wxVtIJggCNRoO3334bX3/9NY4cOYJff/1V7fPTz88P9+7de6rBcRizJa4UY4wxxthzKSsrC/3798f58+cxduxYxMbGYtiwYdz5L2OMMfaMaDQa+Pr6YseOHQgICMDNmzfh6emJ7OxsW2eNsSfCUSNjjDHGnjuSJGHixInYuXMnPv30UyxYsABvvPGGrbPFGGOMlQh2dnYICgpCYGAgjh8/juHDh0OSJFtnizGLcaUYY4wxxp47sbGxWLJkCRo2bIj58+dz6zDGGGOsiGk0GgQEBMDX1xerVq3C7t27bZ0lxizGHe0zxhhj7LlTtWpVTJs2DcHBwVwhxhhjjNmIvb09goODUadOHVSrVs3W2WHMYlwpxhhjjLHnTrNmzdCsWTNbZ4Mxxhgr8ZycnBASEmLrbDD2RPjRKmOMMcYYY4wxxhgrcWxWKabX6xEYGIitW7faKgs2p9PpEBgYyB0SFpGkpCQEBgbi5s2bts6KzUyfPh1Xr161dTZYMSPLMpYvX46IiAhbZ8VmUlJSuDxmjDHGrEi512HPv7Vr1yIwMBCiKNo6K881jrmB9PR0TJgwoVgdSxZVismyDFEUceXKFcTExECn00EURRCRRSsVRRG9evVCfHw8vL29LZr3RdKxY0fExcUhODiYh7DNAxFBkiSIoohDhw4hOjoaKSkpT3TTGhMTg+bNm6NDhw54/fXXn0Funw/Vq1dHrVq1+HhjKlmWERQUhJUrV6JPnz62zo7NODs7486dO/D09ERWVpats8OKESIy+ZNlOc/vGWPseWYYex88eBDR0dG4desWZFm2eFlr166Fj49Pib7Xe5E0atQIYWFhCAkJKVaVGUVBlmVIkoS7d+9Cp9MhJiYGoihafF5IksQxN4Bq1aohOTkZXl5exSbmNqtPMUmSsGLFCkRHRyMhIQEXL15Upzk6OsLPzw8TJ05EhQoVIAhCgcsSRRHz589HWloaYmNjYWdn93Rb8BwTBAFfffUVunbtCkEQMH36dO4sGDkX5HPnzmHJkiVITExEQkIC/vnnH3W6t7c3Pv74Y3zwwQdmHT9Xr17F1KlTMXPmTHh6ehZ6jL7IRowYgdjYWDg7O+PPP/9E6dKlbZ0lZkOyLOOnn35CaGgooqOjUapUKVtnyWYEQYC/vz88PDwwYMAAbNiwAfb23O1mSSfLMqZPn272daNbt25o2bIl7O3tS/S1hjH2fCks9u7bty8GDx4Mb29vs2Lvo0ePYvTo0fD390fr1q2fZdZZEWnevDlCQ0MxevRoCIKAoKCgF/46J8sydDod1q1bh4SEBCQlJanTKlWqhMGDB+PDDz+Eq6troftClmWsWLGCY27kxNyzZs1C586di0/MTQWQZZlOnjxJAwYMIAAUFBREGzZsoDNnztC9e/coLi6O/Pz8CAC1b9+eDhw4QLIsF7RI+u233wgALV68uMB0JcnEiRMJAP3888+2zorNiaJIixYtoho1apCLiwstXLiQ4uPj6e7du5SamkqLFy8mV1dXAkDBwcGk1+sLXV6vXr3I1dW10LQlxZ9//kkODg7UpUsXEkXR1tlhNnT+/HmqU6cOTZo0iSRJsnV2ioVff/2VANCkSZMKvZ6xZ+PEiRMEgADQ/v37bZoXURTJzc2NtFot1a5dW80XANJqteTm5kZubm7k6upKlSpVIgDUqFEjCgsL4/KVMfZc0Ov1ecbed+7cMYm9Q0JCCi3bRFGkDz74gLy8vDj2fgEp9/6//PKLrbPyzMiyTPfv36f/+7//IwA0YMAAWrFiBSUmJpIkSZSQkECTJk0iAFStWjVauXJloecFx9ymvv/++2cac69cuVKN2R4+fFhg2nwrxSRJorlz55KDgwMBoHnz5uX5A8qyTLNnz1ZXuG/fvnxXJooide/enVxdXTlYNHD37l1ycXGh9u3bl+iLx4kTJ6hXr14EgNzd3fM9eLOysqh69eoEgD766KMCj6XNmzcTAFqyZMmzyvZzad68eeoFzVY3/lzhYFuSJNHw4cOpQYMGlJ6ebuvsFBuyLNPQoUOpdOnSlJKSYuvslEjFqVKMKOeYkCSJVq9ereYrLCxM/d7wLzw8XE3j7+/P5ZwZ+OaAMdt5FrH3okWLCAD98ccfzyrbzIbS09OpWbNm1L59+xfyfl6WZdq4cSO1bNmSANAnn3ySbx3IkiVL1Gv+okWL8l2mYcx98+bNZ5n954osyzRkyJBnFnM/daWYJEkUEBCgLuTatWsFLkSSJPUJQv/+/fM9QZQKigULFpi5KSXHV199RQBo8+bNts6KTZw4cYKcnZ0JAAUEBBQaJC9evFg9Pnfu3JlnGr1eT927d6emTZty0J3LrVu3qHz58tStWzebVMSKoki+vr4UHR1d5OtmOZTy+D//+Y+ts1LsbN261eyyiFlfcasUU4wYMULNV3Jycp5pRFFUbxxfffVVOnLkSBHn8vkSHR1NnTp1KtEPBBmzlWcRe1+7do1q1apF/fr14+vnC0y5b92yZYuts2JVsizTmjVr1ON8y5YtBT7ckmWZfH19CQA1aNCAMjMz80zHMXf+DGNuaz9ItKRSzKQDKyJCUFAQQkNDAeSMGlK9evUCX8HUaDRo1qwZAGDdunXYtWuXSRq9Xo81a9agZs2aGDx4cIHLK4m6d+8OIGf/WXP0M3oOOv89efIkBg0ahFOnTqFNmzZm9a3m4eGhfl60aJFJR4dEhNjYWERGRmLAgAHcV1suDg4O8PLywh9//IG9e/cW+foFQcCVK1eKfL0shyiKWL16NYCcAT+YMW9vb9SoUQPr1q3D48ePbZ0dVgzIsow///wTANCqVSs0btw4z3SCIKBq1aoAgMePH+P+/ftFlsfnVXR09AvfLw1jxU3u2DsoKKjQWNnd3V39vGjRIpP7C1mWsWrVKly5cgVubm4ce7/AunXrBiBnMIUnGYShuFq7di0GDRoEAAgICMAHH3xQ4PVJEAS8++67AICzZ89iwYIFJmk45i6YEnOvXbsWjx49slk+TEqrnTt3qhVi48aNM6p8KIhhgHjmzBmT6QkJCdiwYQM8PDxQuXLlJ83vC6tdu3ZwdnbG2rVrcenSJassU5Zl9O3bFzqdzirLexYkScLMmTNx6tQpAMAPP/xgVgeeDRs2RJUqVQAAiYmJJgWyJEnqULdKhSMzpowGtHXr1hfqgsYKl5CQgI0bN6J+/fpo0aKFrbNT7Gg0GnTq1Alnz57Ftm3bbJ2dInfhwgWLHs4oI5W9yGRZRnJyMoCcG8P8gmRJknDt2jUAwMsvv4y2bdsWWR4ZY8wcoigaxd5Lly41qwLLMPa+dOlSnrG3cvPfvn17K+eaFSfvvPOO1e9bbS09PR1BQUEAoFYUm/PApnnz5urnzMxMk8pijrkLptFo4OXlhXPnztk05jYqAUVRxLx58wAAlStXxsSJE81+emf4I6ekpBgdEESEgwcPAsip/LEE/Xfoc0mSisWNu5IXa7e+EgQBPXr0AADs27fPKss8ePAgNm3ahNdee80qy3sW1qxZg/Xr1wPIqZE3LFgKIssynJ2dAQA3btzA1atXTdLExMSgdu3aaitGc8my/Mx+Z0speXkWx/7gwYNhZ2eHPXv2FItzi/2PLMsQRfGZlXuGLV4sfZIryzKys7Mhy3KxOD+e1Xnav39/AMD+/ftL1PlBRAgODsacOXPMqhhLTU2Fj48PFi9eXAS5s52jR4/i4cOHAACtVpvveRMZGYnMzEwAQI8ePfDSSy8VWR4Zy+1ZxhAvKkmS1D+Fcq3J75psuJ8Lux4pyxJFUb3OF/W1NCIi4olibyJSY++bN2+a5PvChQtITk5+4thb2b+2ji2KQnG6t30ShvettnjjxNpkWcacOXNw9uxZAMCUKVPMjo9dXFzUzxkZGSbHL8fchSsOMbfR2JerVq1CTEwMAOC9995DnTp1zF7QxYsX1c/Xr183mkZEOHToEACYXfACOTt/x44d0Ol0SExMBADMnz8fzZo1K9ImuUSEkydP4sCBA0hKSsLNmzfh4uKCgIAAAMC1a9fg5OT01Ovp2rUrvv76a8TGxmLIkCFmtZgqSFRUFNq3b4+mTZs+dd6eBUmSsHDhQvX/Xbt2NbsSVqPRIC0tTf1/enq60W9w4sQJXL161aJlyrKM1NRU7N69GzExMbh37x7c3Nzg7+9f5Dc2sizjt99+w6lTp3D06FHUrFkTH330EVq0aIG4uDh4eHg89fFRqlQpeHh4ICYmBqmpqUV6nDyvQcCzJkkStm7ditTUVJw8eRKiKOLNN9+Ej48PWrVq9dS/OZBTnp0/fx6A8YW8MNnZ2Yif0SJ8AAAgAElEQVSPj1f/AGDAgAEYOXJkkb8ikZSUhMOHDyM1NRWJiYlo1aoVZs2aBY1Gg+vXr6N27dpPvQ4vLy+89NJL2LFjB2RZLjGvgQiCgKlTp8LZ2RmZmZn49ttv8z3url+/jn79+qFy5coYM2ZMEee0aBl2C2H4CpEhURSxfPlyAICzszOmTp3KlWKFsHWQ/yJSYtZdu3bh2LFjSE9PR6NGjTB69GiTMl+WZQQFBcHZ2RkDBgywUY6Lh+joaGzfvh0nTpwAADRt2hTff/89Ll26hNDQUFy6dAkajQY1a9bEhAkT0LJlS4iiiF9++QXbtm1TX5V2c3PD+PHj1RZVhs6ePYvvvvsOhw8fxrVr1/Do0SM0aNAA77//PoYPH45atWoZpQ8ICFBjWCJSP8uyjNDQUAQGBppMlyQJISEh+ZbboigaveLVtWtXs/eRYez9999/m0w/d+4cgJzyz9zYW5IkJCYmqrHF/fv30apVK8ycORMvv/yy2Xl7XsiyjC1btuDMmTM4ceIEXnrpJWi1WgwbNgw3btxA9erVYW9vX/iCioEuXbqo962+vr7PdZx06tQpzJ07F0BO5ZVS4WcOw/vRf//912gaEannBcfc+evUqZPtY26lc7Hs7Gzq37+/2hnZunXrLOrI7IsvvlDnnThxolHnitnZ2epQ5WlpaWYt79q1a/T++++TVqulOXPm0IoVK2jmzJkEgO7cuWNR3p6GLMu0a9cucnJyorp169LYsWMpPDyc3nvvPerduzeVK1eOAFilY7hz584RAKpSpcpTj+Zx5coVcnR0pGXLlj11vp6VvXv3qsdMmzZtLOqQ88GDB+q8AExGz5s7dy4BoA8//NCs5UmSRGFhYeqIYbNnz6bt27eTVquloUOHFunoKnq9nsaNG0cA6L333qOVK1fSmDFj1IEsAFBgYKBV1jV48GACQN99951VlmcuSZJIq9VyR/sGbt++TV5eXgSAfHx8aOHChfTtt99S1apVCQD9+OOP6jkiyzIFBATQ+fPnLV6PXq+nrl27EgBasWKF2fP4+PiQs7MzRUdHk06no2PHjtE777xDf/zxR5GNsCfLMkVHR1OdOnWoSpUq5OfnRytWrKAuXbpQ7dq11ZGCsrOzn3pdkiRRzZo1CQAdP37cCrl/vuj1enJyciJvb+889+e///5LVapUoSFDhli9fCxuHe1LkkTt27cnAKTVao22V5ZlEkWRTp06RT4+PgSAXF1d6cSJEzzypBmio6MJwAs5gpmt7Ny5k2rXrm0UIwEgZ2dnSkxMNEq7efNmKl26NF2+fNlGuS0+fvzxR2rWrJm6v9zc3OiHH36gWrVq0bJly2jXrl3k7+9PAKhixYp05swZGjJkCHXo0IHWr19PUVFR1KFDhzzLCaKcQTj69u1LAGjChAmUnZ1Nqamp9N133xEAatGihUlH0NOmTSOtVkvu7u5Gv6Wbm5saB+T+nZs3b57v+aTc0xjG3paUU3///bc6b/Xq1SkrK8to+jfffGNR7C2KoroNa9asoaioKIqOjiatVkuhoaEvXEf9oiiq8X379u1pxYoVNHr0aLWTceXf54U171ttSa/Xq3UMAGj27NkWzb9t2zajOhDDgWP0ej1169btqWLumJiYYh1zW2OgnGcVcz/R6JMZGRnqTJUrV7bo4JZlmQYMGKDOv3jxYqPpd+7cUac9fvy40OU9evSIXFxcCACdOnVKXUdoaKg6ZHBRkGWZ1q1bR2XKlKEqVaoY/ehnz55Vt8nV1dUqBffDhw/VZT5NxZ9er6chQ4bQkCFDiu2ITrIs02efffbEBdDx48fVeevUqWNyk6Is+8svvzRreUqgM2LECPW7O3fukKOjIwGgmJgYi/L3pERRpIEDB5qMwmE4ugmsOErppEmTCAB99tlnRXoDx5VixhITE9XfduHChUa/RWpqqnqcK+Xnzp07CSh8ZOC8iKKojhZsznDpkiRR7969CQCtX79e/X769OlqeVxUx45SHgOgvXv3qt/funVLvZlxdXW1SnAmyzK1adPGqufb80av15Obmxu1bNnSaJ/q9XoqX748+fv7P5NAuLhVip06dcroZjQgIED98/f3Vyuz27dvT4sXL36ubw6KGleKWVd8fLx6rDZq1IjGjh1LH3/8MTVp0oQAkJ+fnxqviqJIffr04VF2/0uWZZIkiZYtW6ZWfNWqVYsyMjLUNKIoqteaihUrkq+vr9FDg1u3bqn7P3d8oxzrSjli+JBLicX8/PyM4nal0l2WZRo6dCgBoMaNG6uVUZIkkbu7O9WtW5c2bNhAt2/fLvC3lCSJJkyY8MSxt2Gs4uLiYrXYe/Lkyep3O3bsUNfxIpULhvG9j4+P0e9kWCHz22+/2TCXljFsoFCUDVasTa/X0zvvvEMAqEyZMhbfOy9YsEDdD0uWLDGKiUVRpPr16z91zB0YGMgx9xN4otEnlT6/AFg8YggZNA0EgDfffNNo+p07dwAAlSpVMqsp7JUrV5CUlAStVotGjRqp61BeV+zbt2+RNLm/evUqvvrqKzx69AgTJ040as765ptvqq+Ctm7d2irN/F555RVUqFABwP/2maVEUcRXX32FpKQkfP3118W2Ca4kSWpzUMDy0TiOHDmifs7dTFuSJNy9excAUK1atUKXJYqi+sqv8k4zABw7dgw3btyAq6srtFqtRfl7ErIsY+bMmYiIiECDBg2MOngUBAHvv/++mvbtt9+2yjrfeOMNAMC9e/f4NRYbEUVRbab9/fffY9y4cUbHc4MGDdCuXTtcunQJ8+bNgyzLWLt2LXx8fNTfz9L13bt3DwDw+uuvF5r+8ePH2LFjB7RaLXr37g0gpzyOi4sDUHTl8YMHDzBjxgw8evQIU6ZMUUf7AYAqVaqgUqVKAIC2bdtabSQ7pfx40vL4eWdvbw+dToeyZcvC09NT7QfHxcUFEyZMQFBQkFVe6S3uDPtLcXNzM5p27do1tduJ0aNHY9SoUTbbJ0SEtWvXIiUlxSbrZ7YliiLmz5+PSpUqYe/evfjzzz+xaNEiLFu2DKtXr4azszPCw8PVgSAOHjyIPXv24OOPP36uX3uyFkEQoNFo1FeB7t27B39/f3U0WSDn9UHlFah79+5hzpw5KFWqlDpduQ4BwJ49e4yW7+HhgaFDhwIApk2bpu5zQRDQp08fAEB4eLjavYEyzc7ODoIgYP78+WjTpg1Onz6NL7/8ErIsIywsDLdu3cKmTZvQp08fVK5cucDfUpZl9doNAJ6enhbtI8PYu3r16kbrEkXRothbr9fj6NGjAIBZs2ap3x84cAAA4OfnZ1HerEEURUyfPt3qXXwQERYsWICIiAhUr14dc+fONdp3rVq1Uj/bYnAWIkJERITF1w7D+1blt38eXbp0ST3uOnToYHEdiNJnGADUqVPHKAYVRVF9vfJpYm6lPCmOMbe1rh82j7mJcmolf/jhB7UmbdKkSRbVwkVERKjzenp6mtQYJiQkqE+tzHkaZdi09+uvv6Zt27bRgwcPSKfT0f79++nBgwcm8yQnJ5O7u7vVnipIkkSjRo0iAFS7dm2T5Rq2fsuvOWRycjINGzbM7FZGkiRRgwYNCAAdPXrUovyKokg7duwgT09P0mq1tHv3btLr9Vb7s8brSIb+/fdftZkkgDx/0/zIskxarVadNyIiwmi6JEnUo0cPAkCrVq0qdHlKawj8t8l7eHg4JSQkUHZ2Nu3atYvOnj2b53xBQUFWbeZ84MABeuWVVwgAzZs3z2S68nSvQYMG+Z5HQUFBNGzYMLPXuWrVKgJAPXr0sOqTYkmSCjyesrKySKvV0s6dO4v0uCtuJElSnxA6OjrSrVu38kynPCFydXWl7OxsKl26NK1Zs8YknSzLFBQURIcOHcp3nXq9Xn2d/fr164Xm0bA8njlzJkVERND58+cpJiaG9u3bR3///Xee+bCk7CuMLMtG+yn3sWrY+m3lypX5LqOwfZPb8OHDCQDNnTv3qfL/vLt79y5ptVrq3r07de7cmT7//PNn+gS/OLUUk2WZPvzwQwJA9vb2Jl1AyLJMa9asUfO7ZcuWApe3fv16cnd3t1p5q7ze8OOPP6rHa1G1bDZHdnZ2gWW80ur133//LTDdi9Ri5FnZvn17gXHPTz/9pD6Fl2WZRo0aRX5+fvyaby6GLbrOnDljNE2WZbV1U+3atU1alIiiSLVq1SIgpyuO3ERRVFt+SZKk/v/x48fqOnft2pVv3gxbUS1btowcHR0pMjLS7N/w7t276vwwo+WEIaVVWn6xtyiK1LNnTwJAq1evLnR52dnZ6rL8/f0pPDycDhw4oMbeN27cyHM+a8feOp2OIiIiaNasWWocYe2WkxkZGVSvXj0CQN98843J9M2bN6vxfX5l3fr162n06NFWvXb8/vvvNH/+fOrTp88TXTsM71sTEhIsmu9p70utWW5FRkaqx+LAgQMtWva5c+fUrpSaN29uUiZcuHBBXTbH3AV7FjG3xa9PSpJEwcHB6kw//PCD2SuTZZm8vb2NKohyH0wxMTFqhYM5J/OlS5eMCm38tznj5MmT8y0slJvGCxcumJ33ghieIIMHDzaZrgRyeV00c+dJp9OZtU7llTIAFBUVZVF+lUqgZ/lnzVcxs7Ky6KWXXsr3hCuIEvgBOa+r5M6X4X405/U8SZJo7NixJtvbunVrio2NzbNwlCSJANCwYcOsUjBLkkTvv/++uu4jR46YTFf6tMnreCTKORebNGlCWq3W7DwpwZ+bm5tVf98pU6ZY5ZhzdnamkydPWi1fxc3169fVbZ0wYUK+6VasWEEAqFKlSvTo0SN69913TfryIMoJ7gBQeHh4vsvS6/XqOs250czOzlaDHsPyePz48fleYCwt+wpz7949ql69OgGg7t27mxzft2/fVvN28eLFPJdhzr7JTenjY9q0aU+V/xfBsWPHqEmTJuTj45PnsWdNxalSTJIkcnZ2VgPevM4ZvV6vphk3blyB55XSp1Bh1zzllfnCymVJksjNzY3GjBmj3rAWl0qxpKQkdb887V+vXr1svTnF3ubNm426XchNlmXq3LkzBQYG0q1bt6hChQqFVuKWRIaVYrnPP8NKMcNXIBWiKKoPWfOqFFPSHDp0iPz9/al3795Ut25do2O9oLhVlmWaPHmymnb8+PEWVRgfOHBAnfdpY++8+kyzJPYWRZGGDRtmcq737NmTkpOT8zyOlfiloHjJMO3QoUMLjYcDAgKoX79+NHHiRDUP1qwUy933W+7y2XD6hx9+mOe6lQrJJk2amHXtGDp0qFnXjvfee48mTJjwxNeOJ71vtcY9Qn7n15NQ+sIDQGPGjLFo3qCgIHXe4ODgfOtAOOYu3LOIuS1+fVIQBIiiCEXdunVhrr1792L79u0AgJYtW2LIkCEmr65UrFgRQM4wpeaoWbMmVq5cafQa5qNHjzB79mx8/vnnJs0GZVlGfHw8HBwcrDICAgCcPHlS/WzYZFChNCF2cnLKc38RkdoMtV69emavV9lHlStXtii/GzduxH/+8x9Ur14dvXv3xj///AO9Xm+1v+zsbKu+EiIIArKzswEA9evXN3s+IsKaNWvU/+c3Sqclx5xGo8G0adNMmmofPXoUHh4euHLlisk8u3fvBpBzzFvjVS0iUo+p2rVro2XLlkbTHz16hISEBAD5vzp58uRJpKSkoG7dumbn6datWwBymvxb8/WJmTNnFng8ZWVlQavVYufOnQWmO3HiBJo0aWK1fBUnRKQO/QwAvXr1yjdtjRo1AOQ0T/fz88OUKVPyHNVOeS3CsCl+XpRmz+acH6VKlcL8+fONztNHjx5hwYIF8PLyMnnN4EnLvoKkpKSorzi3aNHC5PhWXm+rWbMmatasmecyzN03htLT0wFYXh6/aO7du4eJEyeiYcOGePDgAaZMmQJJkmydrSKRkZGBU6dOAcgZjS6/clJJc/LkyXxfvXnw4AF0Op3JK5j5uXz5cqFluUajQVxcHBYtWlTsRrps1qwZTpw4UWAZv3PnTgA5I3YVlG7jxo023prir2fPnggJCcn3mBEEAZ07d8aGDRsQERGB+vXrG3XLwHLkvsewREHnqyzLiI2NRdu2bdG2bVscPXoU7777LjZt2oR//vnH7OXPnDlTfQ3r8ePHFuXv0aNH6uf69eubHSuaE3sLgqDGFkpsWRA7OzsEBASgW7duRt9v2bIFb731Vp6xt3Id79ChQ6HLFwQBly5dKjRdSEgIIiIiMHv27ELTPgn672iwitzxvSiKOHToEACgXbt2eV5jlNdemzVrZtY609LSzLp27NixA/Pnz3+qa4cSR7722mtmz1PYPYI5fyEhIU+c59wMzwtLtuPx48dG50WvXr1M9ruTk5P6mWPugtk65lYrxRo3bqx+efjwYaNERARZlvP8IcLDw9X/BwUF5dmHlSU3YLIsQxAEDBo0CAcPHsTPP/+MAQMGqDto9+7daj4M8xUXF4fGjRuDclq/mbXxBeXh9OnT6v9zD78uyzKOHTsGAGjTpo16YVDWq+TpxIkT8PDwgKOjo9l5UvaRUqljLnt7e0yePBmxsbGwt7fHoEGDQESwt7e3yl+pUqWs1k8PkFMYOzs7A8gZ6jW3vI43IKePBqUA6t+/P0aMGGGSL0suzMoxVK1aNYSFhWHv3r3w9/dHmzZt1DT79+83Sa9UYDVq1Mgq73anpaWpv71WqzW5KB47dgxZWVkA/tffgLJeJU/K++be3t5PdLxZsw8FjUZT6DEF5ARFhR13L3JfJ4aVYg0bNjRrnmrVqqFLly5G3ynHgNJPX2HHpbllsiRJkGUZXbp0wcGDB7F+/XqMHDkSDg4OAIBDhw4ZBa5KPp6k7CuIUuEAmF5giQi///47AOOAMvf5Ye6+MVyuUn5YWh6/SERRRM+ePVGlShWsX78ekZGRiIqKQnBwcImoGDMs/11cXPK8Dhr2J6L0AWRIOQZTU1Nx584dtY/Kwo7DBw8emJVHQRAgCEKxqxQDcgL8gsp4ZV8Vdr14ka8DRalWrVo4ffo0li1bBh8fH96vhSjsHC1oeu5p8fHx6NixIxISEuDj44Pff/8dn3/+uUm5Utg6N27cqN48Ll++HMuWLTM7fmvRooX6+ebNm3k2MshrWTt37jSKvUeOHJnn8s19IK2sx8nJCVu2bMGuXbvg7++v3hcAprG3JEnYsmULKleujA4dOph1HTf3vuVZngeyLKvXCFdXV7UPLsXly5cRHR0NAGjfvj0AqPeyyrVj1apVAP5X6VHYtj98+NCsvCn750mvHUSk/ta5t6sg5twjFPZnzXtSw8YGSp+LhpRYOLeFCxeqcfyMGTPQtGlTkzS1atVS73msEXNfvXpVTV8cYu7cdSDPc8ytlgKGFT+GAZ4kSYiKisLAgQPRr18/o9rutWvX4tdffwUALFq0yKS2X6HcgN29e1e9sc/L5cuX8cEHH6BGjRq4ePEiqlatimHDhiEiIgLr1q1Tl6Hs3OnTp6Njx47w8vICkFMIVK1aFYGBgfmuw9xKM6WTt9q1a6NBgwZG02RZVlvttG7dGgAwfvx4BAYGIjAwEB07doSnpyeuXbsGWZbh6emJvn37FrrO7OxstaNCS2qqDdWvXx9r1qxBpUqV4OfnZ9QCsDgx7Dj+3r17OH78OICc3+f27duYPXs2unfvjsDAQPXGS5ZlfPPNNwBytnPVqlX5tl4z58JMRAgKCkLNmjXx4YcfQqPR4N1330VoaCgOHDigPs1XOiWXZRkeHh7o2LEjlixZgrp162LUqFHQaDT5HlOyLEOSpEKPudu3b6uf83oCplTC1axZEy1btkRiYiI8PDwgiiI8PDzg4eGB3377DfXq1cP3338PDw8PtQPTgij7p1KlSiWiw+ziRrkAODo6mn3Of/vtt0a/lU6nU4/LPXv24N1334WTkxM8PDzyPO4EQVDPDyWwzoskSWqn4evXr8drr72Gvn37YunSpdi8ebOaTrnY63Q6vPrqq2jSpInZZZ8sy2aVxzdv3lQ/u7q6mixj69atAP5XKRYeHo4PP/wQMTExFu2b3JTfp6S2FBNFEZ6enqhSpQrWrVunVmInJSXh+++/R1BQ0AtdMUZERgPC5H5Apjhx4oT6uVy5cibT+/XrB09PT0yePBlATksIBwcHTJ8+vcB1Gz69NkdxrBRjxYtyU52WlqZ27s7yV9iNd0HTDafJsoy5c+cCyKk8mDdvnlEH/YbXdEEQEB0djWnTppnciOt0OgwaNAizZ8/GTz/9BCBngA+lxWVhKlWqhBEjRgAAMjMzjW5ks7KyMGnSJPTr1w8//PCDOu3GjRv48ssvAfwv9s6rEskwtigo9pZlGcHBwahZsyYmT54MOzs7dOrUCaGhoUhKSlKPUcPYW6PRoF69ekhJSUGTJk3Uzr0Luo5bu7P83JSbf3MqTm/cuAEg71Y3kZGRAHI6L2/UqBFkWYa7uzsOHjyIjh07onz58li8eDEAqJWCOp2uwPVZeu0wPBYtYY371uLgvffeUytkDc8LWZaRnp4Ob29v9OvXz2igiR07dmDKlCkAAB8fH0ydOjXP8kAQBLW1mDVibqWsKC4xtyAIasxt6f1IbraOudVmXdWqVUOPHj2wdetWxMfH486dO6hQoQIGDRoESZLw0UcfYffu3Rg5ciQOHDiA5ORkzJgxAwAQEBCA0aNH51vTXr58eVSuXBl37txBRkYG6tSpY5KGiJCYmKgWDnFxcUbNAJVRKw0LFK1WCzc3N8THx2PPnj349ttv1YIzL/v378fixYtRvXp1jB492mSUTIUgCGjbti22b98OJycnk+3atGmT2qywffv2+Oeff7BhwwZ8/fXXaNWqFbRaLeLi4rBnzx5MmzbN7MoG5WQpW7YsypYta9Y8ebGzs4Ovry88PDzQoUMH9QJYnGg0GnTo0AHffvstgJynUC1btsT58+fRsWNHfPLJJxg5ciSmTp2Kxo0bo3///ggKCkJUVBRq1KiBlJSUfEfWFAQBtWrVAlDwhVmSJOzZswc3btwwGl0MyNmHSs28UphpNBoEBgZClmV06tQJffv2xSeffKI+pc9r+d9//z327t2L7t2746OPPsr3WGjZsiVef/11pKenmxyXoiiqr2u6u7urTZ6VpwVKxWHnzp2NWs8pFbYFUfZPtWrVrPrUhRVOEAS1LHz99dfzLT9FUVQDKiCnwt5w1EmNRoOAgAC1taC3t7f62+d3gVbmL+j8iI2NxfLlywEAf//9t9G0Nm3aoEaNGnBxcVFHi6lVqxYiIyMRGxuLGTNmFFr2nT9/Xr1J+Pzzz00ePhhSmme3bdsW1atXN5qWmpqKv/76C8D/nvZt27YNrVq1Ul/PMHffGDJ8Appf8/AXmSiK8PLygoODAyIiIox+S3t7e9y6dQs1atTApUuX8PPPP7+QleqGlWINGjQwamWhkGXZaPRuwxHZ9Ho99uzZg4iICPW68dZbb+HYsWPQaDSF3lCb21JModzYWONJMXsxKfFF7969LeoqpaSSJCnfWFOpFDGnlZEkSWpXM+PHj1djVIXS8gLIucZXqlQJ+/btM1p+dnY2QkNDMXjwYLUrmeTkZHz33XeYMmUKmjdvDkdHxwLzodFo4O3tjWXLluHu3btYv349Bg4ciPv376Nly5aYPn062rVrh/79+6Nt27Z46623MH78eCQnJ6N27dqFxt7mxBbK9fjGjRu4deuWUXllb28PFxcXnD9/3ij2FkURsbGx6NSpEz766CPExsaq6yxoW5+0LCzsd5UkCUuXLsX69evRt2/fAkcd1mg0cHJywqlTp9CpUyeT5SgPxVu1agWNRoPdu3cjKSkJbdq0QXR0NDIyMjB48GA0bdpUvXYUlLeivHYYPlh/mvtWW7Ozs4OPjw9OnTqFAwcO4Ny5c6hXrx42bNiA1atXY+LEiTh9+jRGjBiBxMREpKSk4IsvvgAAfPDBB1i3bl2+v4kgCGjYsCHOnTv3wsfclt6PGCoWMbdhB2Nnz55VO1YLDQ2l1NRUql69OmVmZhLR/zoXj42NJQDUsGFDSkxMLLTTP0mSaMCAAQSADhw4kG86pXP7zp07G43CJooi+fn5EQA6ffq00TyyLFOXLl2oTp06BeZDFEXy8fFRO1sbOnRogekPHTqkplW2n4joyJEjVKVKFQJAzZo1o+zsbNqwYQO9/vrraqeGsizTwIEDC81TbgcPHiQA1K5dO6t08tinT588O6IvLiRJoi+//JIAULly5ejRo0c0dOhQCgkJUdPMnDmTAgMDaeDAgQTkjNpizoiEx48fJwDUtWvXfPelJEnUpk0bKl++vMlINllZWVSjRg3q0aOHyf7bv38/ATmjghREGXVV+Tt37ly+aSVJUkfdMMxLdnY2jRkzRl3G2rVriYioc+fORiP/pKamEgCaMWNGgXkyJMsyde3alQDQtm3bzJ7PGpTOOc3pjPVF9vDhQ2rcuDEBoMOHDxtNkySJTp48SQMGDKBmzZqpx8CuXbtIkiQKDAyk5ORkNb0ygnBhHW0qI8Io51N+4uLiCAC1adOGMjIyjPK1ePFiAkC//fabybIHDhxI9vb2lJ6enu+yJUmioUOHqts0cODAAsu8xMRENe39+/fV7/V6vdFItHfu3KHU1FSqWLHiE+0bQ6IoUtmyZalatWrFtgx9Vi5dukQ9e/YkHx+fAjuGvXbtGr311ltWH6jD1h3tK6PCxcfHq/kYOXIk6fV6k+NUkiTq3bt3np3/jh07lgYMGECSJJEkSeTg4JDnyFayLJv8SZJEZcuWVUfZyv2XF19fXwJAW7dutf5OeUaUTs15dMmioYz4xx3sm1LOLcOO9rOystTRIpW/Tz/9lICcjvazsrLUMkE5b5Xrtb+/v3ru6/V6dbQ2wLgDf8PO+QHQt99+S/PmzSOtVkvZ2dkkiiLt3buXPvjgAzVPiqysLGrUqBEBOYMwKdcibg4AACAASURBVCO1FtS5vCiKauxdt25d+vfff6l37960bt06Nc348eNp8uTJalz6ww8/mFXGK52KFxR7K9ftypUrm8Seyn1QXrH3woULCQAtWLDAZJl5lZH6/44sL0mSWWWoco8LFN7R/tmzZ43i+3379uWb1nBwhNDQUKP9sHTpUnUZEydOJKKczsZHjBih5lEURXJwcKABAwY8s2vHkCFDCLC8o33l9+rbt6/VR+wsanq9Xr0nGjhwIP37779UoUIFunnzJhHl7Ou2bdvS5s2bydXVlSpWrEhRUVGFXrs45jaPYcxtzXjAko72jar769Wrh4ULFyIgIAABAQGIjIxEqVKlcPfuXWRkZCAhIQFubm7w8PDAmDFjMHfuXLz88stmdean1Wqxdu1aJCUloV27dnmma9++PZo3b45y5cph7dq1aNSoES5evIjY2FhcuXIFqampJjWb586dw86dO9GnTx+zmzEDOa9qUgE14q1bt4afnx/Cw8MxZswYDB8+HD///DN0Oh3Cw8MxadIk/PXXX1i8eDEWLlyIsLAwtZZY6XOsVatWFrW+Ud6fN+zf7WkMGzYM77//PlJSUuDi4mKVZVqTRqPBrFmzcOvWLaxYsQINGzbEtWvXMGvWLNy+fRvHjx+HIAgICQlB3bp1sXnzZrz//vtmtUho2rQp6tWrZ/S6b26CIGDOnDkYPny42onoyy+/jDNnzmDZsmX44osvMHr0aJOnYkq/Ct7e3gXmQXkFV3Hp0qV8WzFqNBoMHz4cy5cvx4oVK1C5cmVkZ2dj06ZNcHZ2xrRp0zBz5kz8+eefePnllxEfH6+2qgT+1/G/JZ3mEpHaf6Algx0w63n11VexZs0atGjRAoGBgWjdujVat26N5ORkJCcnY/fu3ejduzciIyPx448/IjQ0FHv37kV8fDyOHTumvn6ltFapUaNGvq94KQRBUMuDvPrzU7Rv3x49evTA33//jfDwcDRp0gT379/H2bNnsWTJEixfvhw9evQwmkcp+5ycnFC1atUC82DYvD8hIaHAJ7MuLi5YtWoVhgwZghEjRuCTTz7B6tWrERsbCz8/P/z1119ISUnBhg0bsGnTJgQFBalN4S3ZN4aOHz+Ohw8folu3biWq3x0iQmBgIOzs7NRXJvNTvXp1rF+/HlOmTMHixYsxYcKEIszps3HhwgX4+fmpr/Ir9u/fr3bV8PXXX6txjEajga+vL3777TcAObGFXq/H8uXL8ccff+C7776DRqPB2bNnkZmZiQ4dOpjEBWPGjMHFixdx4cIFpKenQ5Zl6PV6iKKI/v37G/UZVqpUKbz00ksIDQ1VnxgrlNcnLX11hpUcp0+fRvny5dG9e3dbZ6XYCQ8Px8qVK43ixjZt2qBChQqYPXs2Vq5cieTkZLX/1vj4eHTq1AlEhOjoaHh5eeHBgwfq/IsWLUJ8fDzeeustLFy4EJMmTcLgwYMB5Nxj+Pr6oly5ctDpdKhWrRoWLFiA8ePHq93SjB07Fl5eXkhLSzPqR6hz587Q6XTqwAmpqakAgNWrV6v9IXXo0AGhoaF5bqednZ1R7F2vXj1cu3YNI0eOxJ07d5CQkICqVasiJCQEHTp0wKFDh9SW14V56623AKDA2Fuj0aBnz54oXbo0jhw5gocPH6JUqVI4d+4c5syZg9mzZ+PTTz81ir0NW+Tm7mLk5s2bCA4OBpDT8spwgLA7d+6gX79+6na/9NJL6l9YWFih25Of3IMAnDlzRu0PLDdBEDBr1izMnj0bP/74o9qiatu2bShVqhQCAwMREhKC1NRUzJ8/H6GhocjMzFSvExcuXEBmZibc3NxMXsn18/NDWloaLl68iPv376vb/qTXDkvt27cPQE6Louf9bRN7e3uEhYXhk08+QUREBJKSklCpUiWkp6cjKysLR44cgVarRa9evTBixAjs3LkTr732WqHxoaUx94MHD0p8zG2rY8nobl8QBPTq1Qvu7u5YvHgx1q1bh0uXLqkVUS1atECFChUQEBCAwMBAowJr0aJFGDVqVL7NapUAMiYmBqNGjcozTYUKFbBo0SJERUXh0KFD2LhxI5o2bQovLy/0798fZcuWNdlRSr9JHTt2LLQZbUREBDZs2IDTp0/jyJEjhaZfunQpXF1dcfz4cXUkiK3/z96Zx9WY/v//dU4xlkEhkX2PKCO7UZFMDEmRfWQ3aMaM5TufmTZiZpAxaGyT3ShLKkuDzgkZS7JUQ4osMWJCGGY7577v9++Pfvc959Q5pxPVKa7n43EedN/Xfd3va3tf7+t9X0tsrDQV8NChQ4iOjsaHH36IIUOGSJXr6tWruH79OubMmVOsk1327NkDIH8pXUkMwgYNGgQXFxejToExFXK5HOHh4Rg5ciTCwsLw999/48svv8SXX34JKysrqZFlZGTAzMxMyk+O4zB9+nStgx4KxtunTx9s2bIFqampOpe9iMtkN27ciKioKERERKBKlSro2LEj1q5diwEDBujcMPn06dOwsbEp8lTE/v374/Lly9i3bx9iYmJQpUoVg+G7d++O9PR0bN68GUqlEpaWlvjggw8QFBQEIoJKpcK1a9eQmJiIxMREqa0REZKTk2FjY6O1SWlRREdHIy8vD507dy6xE0sYxUMmk8He3h737t3DmjVrkJWVheTkZLRs2RLe3t5Ys2aN1OkGBgbC2toae/fuRfv27bF69WotPXHhwgWdJ+XqQtwMNDExUW/HaG5ujrVr12Lfvn24fPkyjhw5gnbt2qFDhw7ScueCz4m6b8aMGUV+pIiMjMTevXvx5MkT3L17t0h9PHr0aMjlcpw6dQrLly9H69atsWnTJjg7O2Pw4MEIDw/HTz/9hIYNG2LWrFmF8kafwaoPcWDSu3fvt8opJpPJEBAQgObNmxs1CLK1tX3jTgZ0cnKSPpoVPE2KiLQOYgHyl08EBQUhOTkZu3fvxo4dO9CsWTN888038PDwAPDfSUy6jMThw4dDrVZr7c9GRAgNDcXw4cO16p+5uTmqV68uLe/XhDnFGIYQBAH79u1Dr169TC1KuaRp06ZwcnLSav8ymQxEBAsLC9jb28PCwqKQU0bcu6pPnz4wMzMr9HFSXCo5evRo9OjRA2fOnMGZM2cQGxsLCwsLTJw4UXrm0aNHuHLlCgYOHIhJkybh/v370sEcIkQk6aT3339fSx5R3qKQy+XYuHGjlu0tHuBjZWUFW1tb9OrVC4cOHdKa/KBWqzFv3jysWrVKZ7x169aFvb090tLS9NreYn9uaWmJ8+fPY+vWrbC2tkb79u2xc+dOnbY3kH/iXceOHSXHm0j9+vXh6emJv/76C2q1WrouCAJ8fX3x1VdfaenwqlWrolq1akXmkSH69euHlJQU7Nu3D+bm5lp7MOnC3NwcKpUKixYtwvHjx1GrVi28//770odNIkJmZiaio6MRHx+vtT+Xvr5DLpdjzJgx4DhOa/80IsLy5cuL1XeIWxQVByLC3r17AeSPXyq6UwzI1wGxsbHYtWsXNm7ciPT0dKkOt2nTBtbW1tLEIc192Hbt2gULCwu9e6uL48XExESt9qsJs7nLgc2tbwqZuHwgNzeXFAoFPX/+nP79919ycnKiyZMna027O336NLm7uxucWqtWq+mDDz6gRo0aGTXVUJxyLE571UdgYKDW0iOlUqk11U8X27dvp4kTJxo9PU/Mi4Jy6LsuTocVZTpy5AhdvHjR4DsuXrxIAKhz585aU6NfFzEvKwLiFPO0tDTKyMggtVpNP//8MwGgs2fPaoWbOXMm/fDDDwbj27t3LwGgZcuWGQwn5hHHcZIM+njx4gUBoMGDB0tTkYuaHqpWq6lRo0Z09+5dg+FExDpfsNwEQZBkLBi+WbNmWjLFxcUV+R5xSeoPP/xgsI2VBmz5ZGEK6j1diPW0oO5KTU3VqutF1QGO42jo0KFFTvvXlEulUhWpj0XdJy7NEQRBa0q1Ls6cOUNt27Ytlj7WtQxAzJeC14ubN+I7WrZsSVZWVvTbb78ZJRej5DD18slXheM4+vvvv0mpVEpLV4jy65yPjw/VqFFDqufBwcGUkJCgNy5BEMjZ2blYywjmzJlDAOj7779/vYSUIWz5ZNnBcRy1b9+ePv/88zLv8xn/oWlzFqz3hvr/0kK0e1NTUyXb29/fnwDQrVu3pHBqtdoo21tcKmas7S0uSzdke1+5coUA0McffyzJfPDgQYPxcxxHderUMbquF2f5pOYzHh4etGPHDqPD67PvdZW9Zt8h3gsODqYTJ07ofYcgCOTk5PRKfUdxlk+KW8S4u7sbta1NRUJsn3l5eXTs2DF6/Pix5APp0aOHVjnl5OSQtbU1PX78WG98HMfRgAEDmM1t4B2lZXMXZ/mkXlecXC6XNht3dXVFzZo1pSNQN23ahO+++w7x8fEICAjApEmTMHr0aL2zxIB8D+i4cePw22+/aR2zqwuZTCZtJGhoM1pBEHDp0iUA+RsUCoKAadOmaW1YqeuZCxcuwNra2uiNgcW8KCiHrutEhKNHjwLIn/EFAD/++KO0tEIfMTExAIDJkye/8ikguhDzsiIgHtHbsWNHtG3bVuu49uDgYERGRuLHH3/EuHHjkJqaismTJxuMz9PTE87OzkhKSjJ4CqeYR2ZmZpIM+rh69SqA/NM4ZDIZdu/eDVdXV4Nf5niex2+//VZourI+xDpfsNxkMpkkoyapqam4c+eOJNOFCxfg4+Nj8OSdvLw8HD16FO+99x6mTZtW5l94iKjQRrNvOwX1ni7EelpQd4mbzoqnxPj5+SE0NFTvu8zMzDBz5kwAwJkzZ4ySq1KlSgb1saj73n33XenLtZeXl9Ym5Lo4deoUOnXqZLSeEmUoKIeYLwWv68qbotIcFxeHmzdvwsvLS+tQAwbDEGZmZqhSpQr69eundWS8IAiIj49H586dIZfLIQgCFi9ejLZt25bo+8Wv/X///XeJxluayGQyODs7s8MByoArV64gPT0d7dq1eyNmdVRUNG3Ogn15UZuolwai3Wtvby/Z3iJbtmxBbGwsVq9ejbFjxyI1NRVTpkwxGN/s2bPRpk0bo21vc3PzIm3vY8eOAcg/5Q8AVq9eja+//rpIvVG9enWD918XjuOQnJxc5MoREUP2va6y1+w7ZDIZbt++jeDgYNja2pZYGoBXmykmnkDo7e1douPW8oDYPi0tLeHm5oY6deqgUqVKkMlkOHfuHFasWIFjx45h8eLF8PX1hY+PDywtLfXGJx6AB7w9NrfoA/Hz80NkZKTBd5QXm1u/BtIBEaFp06YAIB0tDuRPIx01alSRz48aNQphYWH44Ycf0Lt379c+rYqI8OLFCzg6OoKI0K9fP7Ru3dqgLDk5OVi9ejUuXrz4Wu/Wh0wmw5MnT6TKsGDBAlSvXl1a766LZ8+e4cCBA3B2dpZOM2TkI55AcfToUcnZCOTv/VDUGngzMzNpPXR8fDwGDhz42vK8fPkSQP507c2bN2Py5MlQKBQGHbdffPEF3NzcSu10NvE45Pr16yM+Ph6fffYZoqOjDSq8bdu2IS8vDytWrDBoiJQWZmZm2LZtW5m/901F3L+uZs2a+PTTTxETE4Ps7GyDz7i6umLChAkIDw/HRx99ZLTTVh8ymQx5eXmwt7dHzZo1MX/+fOTm5mLSpEl6n8nJycGmTZuwYMGCUtN7BfPm0KFDuHnzpt7w9P+XstesWdPgqcoMhrHIZDI8ffoUbdq0wfXr1zF9+nTMmzevyJPijIGIkJCQALlcLi3R//vvv6V+qaitJUyNq6truZfxTYCIEBUVBSD/IzKDYQhxD6SC+5KFh4cXaXvXrl0bH3/8MT777DMoFAppWebrIOrKR48eITIyEgsXLkRqamqReqNGjRpFxp2QkFBoGwlRpwL5Y1x9hIaGomHDhoWWdJYUmn3H5cuX4ejoiPDw8Ne214D/+g6ZTCb1Hbm5uVAqlQAMb0uUm5uL2NhYODs7Y+LEia8tS0VA0weyYMEC6XrdunWxZMmSIm3F0aNHIyws7K2xuWvUqGG0zb179+7yYXMXZwoaz/PS6R/ir0aNGkUuDdRk06ZNBMDoqaZF8fPPP1Pbtm2pSZMm5OPjU+SJK56enjR27NhSnZ78888/U4cOHcjc3Jy8vLyKfNfnn39OAGjfvn2lJlNFRaVSUbNmzbTq3OzZs42e9slxHLm6upKrq2uJnI7GcRz5+PiQo6MjOTg40LFjxwyGj4uLIwB04cKF1363Pniel2Rq37497dq1y2D4K1eukJWVFXl4eLx1p+q9qTx48IB69uwpnYhlbPu4cOECWVlZ0eeff14iOjE1NZW6d+9OPj4+NGzYMINy8DxPU6dOJVdX11JdOlXcvNm+fbvWyWGMsqeiLp/UhyAI9M0331DTpk2pevXq9OWXXxZZt4xdPikuRRd/Tk5OWn+zOswg+u/0sfbt27Olqowiefr0KVlYWLyy7a1WqyXbuyTqm1qtJh8fH6pTpw699957lJKSUuQzHMdR9+7di1w+eezYMS2dqfkreDK9JidOnKB3332Xtm/fXuz0GItm31GnTh3atm2bUX2HMbZOUX2HoXybPHkyAaCoqKhXSldFRBCEQj4QALRp0yajl+ju3LlTOmmU2dz5rFq1qlRt7uIsnyyWU4yI6Pbt2/Tpp58SABo5ciRFR0cXa28CnufJz8+P7O3t6dGjR8V9vd44jVmHn56eTgDKZO2zsTKJe2b5+fkxB4UOeJ6nHTt2UI8ePahDhw4UEhJS7PLLzs4mS0tLCg0NLZEGp7n/WFHMnDmTli5dWuoDE/H4aWM6y1GjRpGFhYW05x3jzcBYnaOJIAiSE6ik9nczVo67d+8SAKOM25KSqai+6uHDh2Rra0u+vr4lurcjo3i8aU4xEWPqoEhx9hTT3PND8/9s3yiGiFqtpn79+tGsWbOYo5RRJDzP04YNG6hZs2bUu3dvWrp0abFt7zt37pClpSUtX768RHRRcWxvonynWFHOHRFNnWms/hw0aBBNnz69TNpTcWw7QRCoVq1aRvUdmmkt2I/oY926dQSAli9f/tY52O/cuUOffPIJAaChQ4dSeHh4sW3usLAwZnP/f86ePUs1atQgX1/fUvPNFMcpJiMq/kYOarUaRCStA3+V54cMGYJ//vkHCoWiTJdvGTqCtKwhIjg7O6NevXrYtWvXKx+J+6ZDRBAEAYIgQCaTvVJ9SUpKQo8ePXDs2DG4ubmVgpS6oXzHc7mpc+Hh4Zg6dSp27dqF0aNHm1ocRjmA53mEhobi0KFDUCqVZaqHSM8pPKaAiODn54fo6Gjcvn2b6WMTkpqaik6dOgEATp8+/daelpeVlYWWLVuWmzbCqLgQEWJiYjBkyBCTbJnAqHgQEXiel/rp4tYb+v8no3/wwQc4evRooVN7Sxsiwu3bt9GiRYtSi7882feaJCQkoG/fviXed6SkpMDNzQ3du3dHTEzMW6lLOI4DEenc49kYeJ7HN998g6NHj771NrerqysyMzNL1ebeuXOntJ/by5cvDe4z+EotuVKlSqhcufIrK4JKlSrh4MGDcHJywuHDh18pjlelPCmvEydOwMXFBZGRkWwAZgBxg/lKlSq9sgLu3r07UlJSkJiYWOTRySVJeTvo4O7du4iMjGQOMYaEmZkZ5s6di5kzZ0p7zpQV5aVzBoD09HRYWloiOzub6WNGuaBVq1blqo0wKi4ymQzDhg17KwexjFdDdIS9qu0tk8nQpUsXnDx50uABaKWFTCYrNYeYGH95su81Ka19GjMyMvDxxx8jNjb2rdUlYpt41bI3MzPDF198AV9fX8TFxZWwdIYpT/bEo0eP0KFDh3Jlc7/STDEGg8FgMBiM0oDNFGMwGOUVcYYQAJ2nsjEYDAajfFDqM8UYDAaDwWAwGAwG423h3r17GDNmDMzMzGBmZobIyEj07dsXv//+u6lFYzAYDMZrwJxiDAaDwWAwGAwGg6GH2NhYODk5wc3NDTzPg+M4+Pv748SJE3jx4kWpvpst6mEwGIzShTnFGAwGg8FgvPWIg9zIyEhTi1Li8DyPgIAAREREmFoUhg6ICPHx8UhISDC1KMVCEIQKKXdx4XkeixYtQosWLeDr6wu5XA65XI7GjRuja9euOveuCg4Ofq13CoKA69evY+XKlZDL5RAE4bXiYzAYDIZ+mFOMUeYkJCRAoVCwL1/lEKVSifj4eFY2ZQBrBxULIoJCoYBCoTC1KIxSZMmSJVi8eDFSUlJMLUqJIQgCFi5ciMWLF+PatWumFoehAyLCkiVLEBISguzsbFOLYxRivRowYMAb349t3LgRly5dwsiRI6UNtokI58+fR5cuXQrtK5aQkICFCxcazJfAwECDh42NHDkSAQEBWL58eckkgsFgFEK06950HVbR4HkeCoUCSqWyzN7JnGKMMkcQBLi5uWHChAlMCZUjnj17hk8//RRLlixh5VIG8DzP2kEFIjY2Fm5ubjh58qSpRWGUEmZmZli3bh2uXr2KsWPHIi0tzdQivTZEhODgYISEhKBv375YsGCBqUVi6EAul2PChAk4ceIEBg0ahF9//dXUIhlErFeLFi2Cu7s7nJ2dTS1SqcHzPA4cOAAg/yRzkYSEBPz999/o2rWrllOMiJCYmIjBgwcX2bcbur93717s3r37NaVnMBiGOHnyJNzc3MrU+cIwDBFh9+7dcHNzw4kTJ8rsvcwpxihzXFxc4O7ujh07diAwMJA5BMoBPM+jSZMmuHr1KiZOnFhuj5l+k+jbty9rBxUEhUKBYcOGoXHjxvD09DS1OIxSQiaTYdKkSZg3bx7S09MxevRoJCcnm1qsV4bneQQFBSEkJASNGzfGqlWr8O6775paLIYexo8fDz8/P6Snp2PUqFHl1ikrCIJUr9q0aYPVq1fD3Nzc1GKVGjKZDEeOHIG1tTU6duwoXc/MzAQAdOvWDSkpKTh+/Dj27NmDvXv3IiwsDJ07d8bx48f19u3GLodkyyYZjNLDw8MD9erVw8cff4wzZ86YWhwGgN27d2Ps2LFo3Lgxhg0bVmbvZSNfRpljbm6OlStXolWrVli8eDGCgoJYp29CHj58CFdXV7x48QILFy7E2LFjTS3SWwFrB+UfIkJycjK8vLwAAN9//z06d+5sYqkYpUnlypWxePFiDBs2DOnp6ejduzfmzJmDmzdvVhjHtSAIUCgUcHV1RUhICAAgLCwMHTp0MLFkDEOYm5vju+++Q58+fZCeno6BAwfim2++wZ9//mlq0QDk68MLFy5g2LBhUr1au3YtWrVqZWLJSp+OHTvC1tZW+lsQBBw5cgQWFhZo164dvvrqK9y9exdXr17FlStX8OzZM2nGmD6eP39ulE7heR4A22yfwSgNunTpgiVLliArKwtDhgxBdHQ0a2smgogQERGB0aNHA8i3ud97770yFYDBKHMEQaBDhw4RAAJAnp6epFAoSBAEU4v21sBxHG3YsIHatGlDAMjX15fUarWpxXqrYO2g/PLHH39QQEAAVatWjQDQd999RxzHmVqst4KUlBSpTZw+fdokMjx+/JgcHBwkOaytrWn69OkUExNDHMcRz/Plop0KgkCCIBDP85SRkUErV66kDz74QJIbAK1cuZJ4nje1qAwjSU1NpXfffVcqv44dO9KyZcsoMTGxzOudIAjEcRwdPHiQZs6cSRYWFpJcGzZseCvqlSAItH79erKysiKVSkWPHj0if39/srOzo06dOtE///xDTZo0oby8PCIi2rhxI1WqVInu3r2rFUfB3/jx4ykqKqrQ9YLUrl2bALwVec1gmAKO42jWrFmSbps5cyZlZGSUiz7+bUAQBHr06BH5+flJZbBixYoS0Xk7duyQ4nz58qXBsDIi5g5lmAZBELB+/XrMmjVLujZp0iT07dsX/fr1Q/369SGTyQptYMp4dQRBQE5ODmJjY3Ho0CEcOXIEANCrVy/Ex8ejWrVqJpbw7cOYdsCWs5Y+RAQiQlpaGg4cOIDo6Ghps/WZM2di9erVMDMzM7GUbwcbN27E9OnTAQCrVq3CJ598YhI5bt26heXLl2P9+vVa162srNClSxdYWVmhbt26SEtLQ4cOHXDu3Dl4enrCxsYGDRo0gIuLi3RK3asgCII0S+TMmTM4f/48MjMzUb16dQDAu+++i9u3b+PmzZvIyspCXl6e1vMdO3bEvHnzMG7cOKZDKhjR0dFYuXIlTp06pXW9du3a6NatG6pXrw4HBwd06tQJAwcOhJmZ2WvZSkQEQRCgVCqRk5ODpKQkPHjwAP/88w8SExPx999/S2EbNmyIuXPn4tNPP31r6hXP89i3bx/8/PxQqVIlbN68GfXr18fChQtx5coVrFixAkOGDIEgCBg5ciQyMzORmpoqlcnChQuxatUqmJubQ6VS4d9//4VKpdI5O/z48eNwcXGR/rawsMDz58/B8/xbk98MRlnDcRz69esn6dzatWtj1qxZ6NKlC9zc3FClShU2Hi1BRJv73LlzOHLkCA4cOIDU1FQAwMcff4w1a9aUiM39xRdfYOnSpQDyZ+fWrFlTb1jmFGOYFEEQsGrVKqxYsQL379/XutexY0e0aNEC9erVg6WlJapXrw5ra+tSlyc5ORldunSBjY0NnJycYGFh8VqGiGhs8jyPx48f4+rVq1AqlWjevHkJSl4YQRCkPS+ePn2KZ8+e4fnz54U2Ch8xYgSCgoJgZ2dXqvIw9FOcdlCtWrVSbweaZGZmomrVqmjdujWsra3xwQcfQCaTvVabEAf6Ypv49ddf8fPPP2stTylteJ7HgwcP8OzZM6l9ZGdn4+rVq1rhPv/8cyxbtow5xMqQDRs2YMaMGQCAlStXYs6cOSaThed5HD58GKGhoYUcFCKurq5QKpWwsrLCo0ePpOtWVlYYNGgQRo0aBTc3N6PrEBHhzz//xPLly3H27FkkJSXhjz/+0ArTsGHDQrpCxMzMDPPmzcOCzFjN2AAAIABJREFUBQtgaWnJDPkKCsdxWLNmDVatWmXwRMoePXrAzc0N3bt3h7u7e7F0lSAIyM3NRWxsLJKSkpCQkGDwXVOnTsX8+fPRqlWrt7JeiU4ssf8TBAFEJOU5EcHa2hoTJkzQOjVSHABqItpdPj4+WtcL9q01atTAy5cvmVOMwShl0tPTERwcjL1792pdNzc3R+/evVGvXj1YWVnh3XffRbNmzUq9PWZkZMDCwgJNmzZF48aNpQ9tr6N7RZ3FcRxu376NxMRE/P7776hXr14JSl4YjuNw//59PH/+HHl5ecjLy8OVK1eQk5OjFa6kbe7iOMXY8kmGyREEga5fv05Tp07VWvJR8NetWzeD90vrN3XqVIqNjS320ilBEOjhw4e0fv168vX1JTs7OylOKyurMpG9Q4cOeu+1b9+etmzZwpaElROMbQeOjo4maQeadfeLL76gpKSkYtcdnufpt99+o/Xr19PEiRO12oS1tXWZpkNcFqnv5+7uTgqFgi1ZMQHx8fFSORw9etTU4pAgCKRWq+mbb76hli1bFqor/fv3L1Kv+/n50d27d4tcjqFWq2nXrl1FtvOGDRsWula5cmUaMmSItMyOUfHheZ7u3LlDc+bMMUqvTZo0ia5du2ZU+avVagoPD6d27doVGW/v3r0pOjqa2QtFcP36dQJAe/bsIUEQCIDeNh8QEECRkZFFxunm5kYAWz7JYJQFPM/Tli1bqH379ia1tQGQpaWl1t+tW7emgIAAOn/+fLH1AcdxdO7cOVq2bBkNHz6cGjVqJMUrk8lKPS1169Yt0uZWKpUlrueOHj0qvaOoLYKYU4xRbuA4jqKjo6l37946G4ypnGKvY2za2trqjMvUTrF58+ZRbm4uWy9fDimqHZjaKSb+qlevTkFBQfTnn38W2SYEQSCVSkVhYWHUqlUrnfGVF6dYkyZNaNWqVWx/PROiUCik8oiPjze1OBKic+zkyZMUEBBAU6ZMocGDB1P//v2pU6dO1KJFC+rSpQs1bdqUqlevXqhutWzZktatW6fTsSAIAqWlpdH48eP11lkbGxt67733yMHBgTp16kROTk40ZswYmj9/Ph08eJCePHnCBs5vKOKecWvWrCEXFxeDuq1+/foUGhqq14HF8zydOXOGvL29DcbTpEkT+vbbbykxMZE5w4xE1F3nz5+nKVOm0NixY/WGLcopJu7nNmzYMAJA+/fvZ+XAYJQB4h5X8+bNM6mdXdAppsv+Lmocx/M8/fnnnxQUFKTTLgFM6xQrbZtb8yNrUe9gyycZ5ZK4uDgoFAqcPXsWDx48wIMHD+Dg4IDLly+X+rs5jtN7r379+pg/fz4++eQTnUeQC4KApKQkrFixAlFRUXrjadmypcElCiWFra0tHjx4gAYNGqBt27YYPHgw+vTpg+bNm7Np+BUAXe2gQ4cOSEtLKzMZiEha7qiLrl27Yv78+fDy8tI53VkQBBw6dAirV6+GUqnUG0+9evUK7YlUmlSuXBl//fUXbGxsUL9+fXTt2hXu7u7o06cPateu/VYuDSovKJVK9O/fHwAQHx8v/b88QQWWQ8lkMulv8V5mZiZiY2Nx+PBhraPefXx8sGvXLq0lV3FxcZgwYQKePHkCAKhTpw569uyJgQMHomfPnmjdujWqVasGQRCk5wRBkPbdZPX17UEQBPz999/4/fff8eTJE9y6dQsHDx7EoUOH8Pz5cymcq6srtm7dikaNGknXeJ7HwoULsXz5cvzzzz/S9S5dumDgwIFo2bIlmjdvjjZt2sDKyuq1l+q8bQiCgIULF2LRokVwdHTE+fPn9dpaI0aMwPDhwzFy5Eid94OCgnD58mU8fvwYeXl5ePz4MZ48eSK1ewaDUboQEW7duoXjx4/j1KlT+PXXX/Hbb7+hTp06yMrKKvX316pVS7IJdNG1a1fMmzcP3t7eOu1vnucRFRWF0NBQJCcn643ndfekNAYLCws8fvy4kM3t5ORUqts8KBQKuLm5AQDUarXOsbsIc4oxyi3iwEL8laUh8OTJE/z+++949OgRfvrpJyiVSty7d0+67+rqirVr16JNmzbSNUEQEBwcrGVsVqlSBR9++CGmT5+OunXrwtLSEpaWlqhatWqZpEVzsMSM24pJwXbA83yZlyPP83j06BFyc3Nx8+ZNnQMwX19f/Pjjj1odDs/zmDp1KrZs2SJda9iwIby8vODl5SW1h1q1aplkE1OxTTDHQvmiIjjFioMgCIiIiEBoaKh0eENAQAACAgJQqVIlpKenY8CAAbh//z5at26NJUuW4MMPPyyzfoJR8SEiPH36FPv27cOOHTvwyy+/AAA8PDwQFRUFc3Nz8DyP/fv3S3tY9e3bV9rvrmnTpuxDWQlCREW23aKcYgwGo/ygaYfLZDKDH4tL8p3ivo9F2d/h4eFajjGO4zB16lRs3bpVutayZUt4enpiyJAhqF27NiwtLWFhYYHKlSuX6Zi0LG3u4jjF2PJJBsMIeJ6nmJgYreUGvXr1IpVKRUT5S9727Nkj3WvRogV9//33dP/+fbachfHGIQgC5eXl0YYNG+j999+X6v2MGTOk6clqtZq+/PJL6V7fvn1p+/btpFarWZtgGKS8Lp98XV68eEEBAQFS2jZv3kwvXrwgZ2dnAkAjR46kFy9emFpMRgWH53nau3cvOTg4EAAKCQkhtVpNmZmZUt1btGgRW4rHYDAYFQxBEOjJkye0du1a6ty5s6TT586dK+n0gvb3xIkTX2lv7DeB4iyfZE4xBqMYCIJAiYmJknPM29ub/v33X8rIyJAa3fTp0+nu3bumFpXBKBPEAZi4KemSJUtIpVJRZGQkAaAaNWrQkiVL3srOmPFqvKlOMRHRMVatWjUaNGgQAaDJkyczZzGjRLl16xb17duXAFBkZKS0b+Phw4fZfqIMBoNRweF5nn744QeqWrUqAaB169aRSqWi3bt3S/Z3fHz8W21bsD3FGIxShud5jBw5ElFRUQgMDMSGDRvw+++/Y+fOnRgzZgxb8sJ460hLS8Po0aORnp6OiIgIfPHFF8jLy0NCQgIcHR1Zm2AYzZu2fFIXBw8ehIeHBwCgZ8+e+OWXX9jyNUaJ89dff2H06NE4duwY/vnnHyxevBhfffWVqcViMBgMRgkRFxeHqVOnIicnB+vXr8eMGTNgY2OD7Oxsw8sF3wLYnmIMRhkgCAKGDRuGAwcOAABWrVoFPz8/NvhnvLX8+uuv8PDwwJ07dwAACQkJ6Nu3r4mlYlQ03ganGAA4OTkhLS0Np06dQseOHU0tDuMNJTExEc7Ozhg7dix27NjBbBQGg8F4w7h48SKGDh2K+/fvAwAuXLgAR0dHE0tleorjFGOfJRmMV0Qul8Pf3x8A0KpVK8yaNYsZm4y3mo4dO+KTTz4BAMyYMQMuLi4mlojBKL8cP34cjx8/Zg4xRqni5OSEf/75B1u3bmU2CoPBYLyBODo6wtvbGwCwePFi5hB7BdhMMQbjNeE4DgDe+imqDIaISqWCmZmZziOiGYyieFtmijEYDAaDwWCUBEQEtVqNypUrm1qUckNxZoqxUTyD8ZowZxiDoQ3rkBkMBoPBYDAYjLJBJpMx+/s1YMsnGQwGg8FgMBgMxluLQqHAr7/+amoxGIwKiyAIUCgUYIvQGBUR5hRjMBgMBoPxRvLXX38hLCwM69evN7UojDKE53mkpaXh4cOHbICG/GU1PM+D53mWHzrgeR5ubm743//+B57nTS0Og1EhCQ4OhpubG5RKpalFYTCKDXOKMd54BEGAUqmEUqk0+gtGRTAaeZ6HUqlEQkICEhISTC0OoxQoqu5WhHpaXhDbi/jThIhYXr6hZGZmws/PD0uXLoUgCKYWh1HKEBFiYmLg4uKCRYsWoUGDBtiyZYupxTIpgiBALpfD3Nwc5ubmCA4Olu6JTuO1a9eaUELTI5PJ8Omnn+Lw4cMICgpiuoLBKCabNm1CSEgI7Ozs4OzsbGpxyi2vMnarCPZpVlYWlEol4uPjK4S8umBOMcYbT3BwMPr374/+/ftj8eLFRYaPi4vD4MGDtQzH8oYgCDA3N0f//v3h6uqKkydPmlokk/MmOjb27NmjVXc10xcUFITBgwfj8OHDJpSw4jBy5EgpLxMTE6XrRIRZs2Zh6NChePLkiQklNI43rY6XNs2bN2dG+lvEb7/9hs8++wzjx49HYGAggPyj6YtLYGAgIiMjdd4jIgQGBlYYx4lcLgfHcQgJCSl0T3QaL1++vMKkRx+vUy5yuRzLly9Hnz59sGTJEgQFBbEZYwyGERARQkJCMGXKFADApUuXUKlSJRNLVT55lbFbUFAQvLy8yrV+FgQBrVu3Rv/+/TFgwIByLashmFOM8cazcOFCqNVquLi4GBX+3LlziIuLw8mTJ8ttw5bL5eB5HkePHjW1KOWG4OBgBAUFmVqMEmXkyJHgeR7NmjXTui4IAhYtWoS4uDicP3/eRNJVLPbs2aPlDBMRBAHr1q3DwYMHkZqaagLJjIeIIJfLy61eKo9YWFggNTUVW7ZsgVzOTJ43nfDwcNy5cwf9+vWDvb09kpKS8NVXXxUrDiLChQsXIJPJdN6/evWqTgdTecbMzAw9e/YsdN3GxgYjRoww2j4qz1y7dg3x8fGv/HylSpWgVCpRtWpVLF68GFOnTsWJEyfYhwgGQw8XL16Ep6en9AEiMzOTHT5mgOKO3URbPyYmBgsXLixl6V4dMV1iPaiosJrLeOORyWR6jVtd9O3bF9WqVUPjxo3L9SBKLpfDzMzM1GKUG5KTk9G1a1dTi1GiyGQyCIKAZs2aaRnmcrkcsbGxSE9PR/fu3U0oYcVBLpejV69eOq+vW7cOHMehW7duJpDMeJKSkuDk5GRqMcoVgiCAiCCTybQchqLeN+RAJCIIggCZTCbFUbC/EAShUJya/ULB92te09TP4l5Ocrlc63lRBgDSdfFawbAF3ynKrhnOkDwFZRfvif8aSp+IrjjKI+KHhFdp048ePYJCocCECRN03q+oHyJ02UHW1taIiIiAXC4vlp1UHklKSsI777zzWnGYm5vj1q1b0rLbLVu2wMPDA56envDy8kLNmjUrfD4xGK+DIAjIzMzE9u3bsX79ejx79gwAsGPHDrRs2bJC9A+mpDhjN9HWv3HjBj7//PNSluz1eBPKnTnFGG8F4qDHGPr27Yu+ffuWskSMkoTneVy7du2Nc4oBugcyAODh4QEPD48ylqZio0sHyGQyzJgxwwTSFJ/k5GQ2INNAEAS4uroCAE6cOIHJkydj06ZN6Ny5M5YvXw4XFxet+zzPS4abuK/HF198gcuXLwMAOnTogJSUFMlg5XkeixYtglKpxOnTp1GnTh3MnDkTQUFBMDMzgyAI6NevH7Kzs3Hnzh08fPgQ8+fPx927d5GSkoKJEydi5cqVWLZsGeLi4kBEaN68Ofz8/ODo6FhI/oCAANjY2GDv3r24efMmGjRogPXr18Pe3l4qd47jsGnTJvz444+4ePEi2rVrh+HDh2PhwoUgIq34oqOjcfjwYYSHh8POzg4ODg7Yvn27lD5BEODi4oJTp05h2rRp+OWXX/DXX38hPDwcrq6u4Hkevr6+2LlzJwCgfv36GDx4MBYsWIDWrVuXRREXC00HnqbTUMw78f7Zs2dRu3ZttG3btpAziIgQFhYGtVqNOnXqFHJY8jyPn3/+WYpPpOCAgOd5pKeno3LlymjZsqXW7ImCsolyFXSCCoKAixcv4vnz5+jbt2+xHZKiQ1d8jy79J6ZBdJoag7hVwd69e+Hl5QW5XI7MzEy0b99eKwzP8zhy5Ajs7OzQtGlTnXn0119/ITMzE507dy7kkNZcvii2NzENBcuN53nExcVppUkMpymTIAhISkpCs2bNYG1tXWhwKpPJYG1tjfPnz8PV1RUvXrzAgQMHcODAAcyaNQsDBgxA9+7dYWVlhXr16uH69evo0KED08uvAMdx4DgOtra2aNSoEapWrVrsj9i6EAQBHMfhyZMnSEtLw6VLl9C5c+cSkvrtguM48DyPFy9e4OnTp3j27BmSkpJw6NAhrXDff/89Ro8ezT7UlwIVyc6v8LNqicEoYTiOI7VaLf1b8LparSZBELSuR0RE0IwZM0ihUGg9oxkmPj6eZsyYQUuXLqXr169r3ed5njiOo127dtHIkSNp69atWmF4nicnJydydnYmnufp5s2bFBMTQy9evCCe57XCKRQKUigUFB8fryWnpqze3t4UERFBHMcVClMS+cJxHCUlJVF4eDh9//33lJWVpSWnSHx8PAGgwMDAQvmRk5NDq1evptmzZ1NycrLedCoUCsrLyyOlUlkoPRzH0d69e2nSpEkUHR2ts2xMTVZWFgUGBhIACggIII7jiOM4rTCPHz+mAwcO0LfffkuHDx/WWW6CIFB6ejoFBgaSv78/3b17lwICAqR8E/Nszpw5tHz5clKpVBQYGKgVD8/zlJqaSoGBgRQSEkJ3797VWW6G4HmesrOzSalUUnZ2NnEcR87OzlLdFdMjlp1SqSxWXkVERFBgYCCdO3euUD4VrP8cx9HLly/p2LFjdOfOHa20cBxXKKxKpaL4+HjKzs4uVI8061tOTg4lJCQUer/YvqZNm0YxMTFa9S0rK4sUCgUdO3aMEhISKC8vjxQKBV26dKlQPJrpycrKIqVSSQ8ePCCVSlWovYiyxcfHU0JCglY+KJVKunHjBgmCQDdv3iSlUknJycnSs48ePSKlUklZWVk6ZeB5ntRqNS1fvpwCAwMpNTVVyhdBEEipVGrpmoyMDIqIiKCbN29q5bUgCHT69Gmys7MjZ2dnUqlUxHFcobrF8zylpKTQ//73P/r222/p3r17xa5/5QGFQkEACADFx8frDScIAi1btozatGlDAKhnz5507NgxAkAuLi5Sv9GsWTMCIOWFIAi0dOlSAkBnzpwhQRAoLS2NANCECROIKL9e9O/fn4YPHy49p1arKTAwkNzc3CR9HR8fTx4eHgSAxo8fT1lZWUREtG/fPkmOFStWSHrJwcGBPDw8iOd5EgSBdu7cSS4uLgSAGjVqRHv37pX6s169ehEAunz5MhHll6+npydZWFjQxYsXiYho06ZNBIBWrVolpTcgIIAA0IgRI2jmzJkkCAIlJSURAFq9ejUJgkA8z9O8efPoo48+kurk1atXyc7OjhQKBRERXbt2jQDQwIEDpTzp1asXOTs7059//lnSxf5a8DxPffr0IScnJwJAHh4e5OLiItUfnudp3bp11KBBA5ozZw55eXmRg4MDBQYGaun4Ll26SHXPycmJnJycqE+fPsTzPB07doxatGhR6L6/v7+WHLGxsdSjRw8aMmQI1alThzp37izpT57npfIGQEePHqW2bduSlZUVTZ8+XauueXt7U6tWrahnz55kY2NDkZGRRrdnjuNowYIF1LJlS3JxcaEPP/yQjhw5oqX/eJ6X5ACgV48WzOd58+ZRmzZtaPjw4dS4cWNycXHR0qnZ2dn0f//3f2RpaUn29vbUpEkTsrOzo/T0dCmMWq2mOXPmkI+PD/n7+1OHDh0oJCREkiEiIkKSa8aMGRQXF0c9evSgtm3bUqtWrWjWrFlSXnh7e5O1tbXU3nSVC8dxdPz4cXJ0dCRXV1cpblG/60KlUtGSJUu08qjgr0mTJgbvs5/xvx49elBAQAAdPny42P2WIAiUm5tL69evp4kTJ1L79u2leOvUqWPytFXUX+/evQ3e79q1K2VnZ5dbO0MQBMk21RwbFLwuUtBmS0tLK6QfxPHVmjVraMqUKaRQKOjp06daYTiOo5SUFAoICKD58+dTUlKS1ns0x248z1NGRgadP3++0NjEkK1f1DivKMRxp7580bS/c3NzadOmTTRx4kRav349vXz5UqfeFMdiusYWGRkZ9P3339OuXbvo999/1zmeiI+Pl+xsMT8049BnTxtCzGsARY5hmVOMUaLEx8eTnZ2dVAE7deokOVuaNm1KQL7hP3z4cCLKNzp8fX1pwoQJFBoaSo0aNaKZM2dqNYTo6GhycXGhhg0b0jfffCM1OrFyC4JAP/zwA7Vq1Yq6detGO3bsoKCgIHJ0dJTC8DwvORa+/PJLqlOnDnl6elKNGjXI19dXapyRkZGS7M7OzloNTqVSkZeXF/n7+9OuXbto5syZ5O3tTSqVqsh8USgUWvlStWpVioiIIJ7nqX79+lr5IggCzZ8/nwBQdHQ0hYaGkq2tLfn4+BRSNOLgUdMg5Xmejh49Sq1bt6YNGzbQxo0bCQBNmTJFktXb21uSxd/fnxo2bEgAyM7OThrUqVQqmjZtGnl7e1NUVBQ5ODiQt7e3UYZzWSEIguTsBLQHMaKcHMfR+++/T/7+/hQREUHz58+nVq1a0YEDB7TKd+XKldSkSRPavHkzhYWF0aRJkwiANJCZO3cuWVtb0+eff06rV68mHx8frTqiVqtpzZo15O3tTdu2baO5c+cSANq0aZPRHZVarZYGtEOGDKGpU6eSu7u7VHfFNDk4OFDVqlULlb0hcnNzCQB99913FBERQVOmTKFu3brRnTt3pDCa9cLZ2ZlatGhBPj4+NHv2bAJAn376qdSmNMN6e3uTi4sLeXp60rhx46SworwF6xsAat26NTk6OkphNHXB/v37tepbwcHbpk2baNSoUTRs2DDq168ftWrVih48eFAoL729valKlSo0efJkGjNmjFQmAQEBRFR4UCg6A8LDw6lWrVpS2FmzZpGfnx/5+flRrVq1yNfXl5KTk8nDw4P8/f3JwcGBmjVrRo8fP9aqm7/++it169aNtm3bRp9++ikBoJUrVxLP8xQREUEtW7aUyrBp06bUtWtXmj59OgGgbt26aQ36mjZtSi4uLnoHfZr1b8uWLfTxxx8Xu/6VF4x1iomIbWb//v3E8zzt2LFDMlIFQZD0g5gPooNI06n98OFDGjJkCAUFBRER0dq1awnId5ppIj67du1a6ZpYp/fu3Std4ziOAJCDg4OWwTl+/PhCRqMuPU6UXw8BUOfOnSW9DvznuBPjtLe3p8aNG0vp0/WxRJRH1Flivjg6OtK5c+ekZxcsWCC1g4cPH9LgwYO14gkLC9NqK+UJjuOkuvDvv/9qDTA027qYVrFvPHLkiM44jh07pjVgEI1ysT4VHGjxPE9r166lKlWqUGJiohSnQqGgmjVrSo5MjuOkd7dv357u3btHXbt2pa5du0ofyWxsbLR0/qlTpwgAnTx50qh8AEDu7u50/vx56ZqXl1ehepGdnU39+/fXOZDRRUREBDVr1kwrrKZTTBAE6tq1KwGgCxcuENF/7XPjxo1ElK+rCrY/juPI3d2dli5dKpVbWloaNWvWjD7++GOaMGECPXnyhIiIPvvsMwJAqampUr6rVCqpnxQHeprOzqVLl1KVKlXo1KlTWmkBIJWLvrw8evQodevWTadTQLRr2a9kf5MmTSKVSmXUoFetVtOePXvIwcFBZ1zMKfbqvz59+ui8Xr16dQoKCiqXH8o1CQgIoEaNGklyi/2fOI4E8nWwqHMM2WxE+bokOjqa6tevT7NmzaLw8HAaMmSI1kdrjuNo2bJlZGNjQ19//TV9++23ZGNjo6XvxD7f39+fhg0bRiNGjKBhw4ZRgwYNaPv27ZL8mnW64Djvp59+oubNm+sd5xU3X8SPwZr5EhkZSRzHUe/evcnf35/i4+PJ39+fLCwsKDQ0tFD7FHW9Zv+gUqlo9erV5O3tTdHR0bR161aytbWVHIIF7fCwsDDpQ+a4ceOkD4hFlY0+mFOMYTJEL/Mnn3xCAOjcuXPSvQMHDtCAAQO0lEvnzp21Bn+ZmZkEgL755htpRlfdunW1jMMNGzYQ8N/AVvwi/8knn0jv8vX1JQBaX4mdnZ3JxcWF5s2bJzVkceD48uVL6VmVSkWWlpaFHB6iUtMkNDSUbGxsimxo4pf5lStXEgA6e/asdE80BjUHTqJCEI0+UVHNnTtXK15dgylx0PLzzz9L19RqNbm4uNDQoUMlWcRZM3Z2dhQXF0dz586lZs2aSbPS3nvvPerUqZNkiBYsm/ICz/OS0hNndmnKl5KSQgC0nJ+hoaHUsGFDSklJIaL8MmjTpg3t27dPeu769etUq1Yt4nme/vjjD6pevTrduHFDur9z506pjnAcR56enmRvb085OTlSGHEgExYWVmQ6OI6joUOHEgBKSkqSrqempkozhDRnuuibJagPsdPcsGGD9L6PPvqI3N3dtQaO//77r9QhivlD9N8AQrMj0wwr1lV9YcX61qVLF8rNzZXqmzgrqihdwPO8ZMi0a9eOMjMziSh/dgsAWrBggdYsLBsbG+revTvdvXtXurZr165CeaZpIIkDfU15LSwstBwzom4bP3681GazsrIIAIWHh0sy3L9/nwBQaGio9Oy6deskvSS2Q9HRpVk/RYfM4cOHJXnEwbg46NOs50XVvx9++MGoOlJeKK5TTCw/zZkoIrqcYtu3bzfYdkSHKgDKzc3Vuic6HKZPny6Vv2gIajqKxHDjx4/XMhx1GY1KpVKnPA8fPpTy4datW7R582YCQF999RX5+/tLPzHOgk6xnTt3SnGJH2A0+7Vt27ZJ8bu5uVFAQABduXKlUHpfvHhBP/74I23YsEFnWssT+r5UE+X3jaNHj5bSL7ZxFxcXnXHoSqOu+iSiVqvJ0dGRvLy8Cs0gdnFx0foIINZxZ2dnIsqflXft2jUiKuxEEuOoU6cODR482GD/KwgCTZkypZD9pfnOgvVMDG+MU0zMG3EmryAI9PPPP5O3t7fWfc13XL9+nTw9PenGjRvE8zxNnTqVrK2tC71PnL0pys1xnDSrTrPv1fcxsOCMapFz584RAPLy8tK6LraJzp07F5n2p0+f0po1a2jYsGFkaWkptRtxlir7lfyvfv36tG/fPr1lI84OE/tkfT/mFHv1X8GZYs7OzvT1119TcnKy0atkTIkVUNIwAAAgAElEQVRoO7Vq1apQOw8MDKSgoCBJX9y7d48A/TYb0X995sqVK6X4RR2lUCiI53lJn/7yyy9E9N8HaQCF9P+wYcMkJ5ZaraZmzZpJH8GI9Nv6MTExBBge5xlCHLcYky+pqakE5PeT4rXly5dTtWrVpI8uIgXtm6Js0+joaCkfxVn+7dq1k9IivlO0p5cvX663bPRRHKcY21OMUaLIZDKYmZlh+vTpWL16NaKjo6WNwA8fPowePXpIezzs27cPly5dwurVqwHk7wPQsmVLuLu749ChQ1iwYAE2btyIx48fY8CAAdJa9SlTpiAnJweBgYEgIqxcuRIA4O3tLcmxZMkSNGnSRNpfRZQtNTUV8fHx0p4FVlZWAPJPnBTDymQyNG/eXCtdISEhyMnJgZeXl9Z1Hx8fzJs3D4sWLcLChQv17oUg7pMwZMgQ+Pv7IyYmBt27d4dMJsOGDRtga2srpU8mk+HGjRsICQlBx44dwfM8nJ2dYW9vj4sXL2rt/VHwfX/++Se+/vprNGnSBAMGDJCum5ubo0+fPggJCcGxY8fwwQcfSGu/b968CXd3d7i7u2PZsmWQy+U4ePAgLl++jNWrV8PCwgKCIKBVq1ZS2cyfP19fFShzNPcW0bXnir29PTZv3ox69epBJpOB53kMHDgQ8+bNQ1RUFBwcHCCTyaBSqfB///d/ICJ4eXmhRYsWGDFiBADg/v37+PPPPzFv3jwsWLAA3bt3x5gxYxATEwMAUCgUiImJwahRo9CgQQPp3b169YKtrS2+/vprTJw4EdWqVdObDoVCgdjYWAQGBmptDt2hQwfUrVtXK+yr7LsxZcoU3Lt3D97e3lIdatKkCbZv346EhAS4urpqbQBqZWUFe3t76flhw4ahZs2aCA8Px5w5c2BpaakVtmPHjlJYT0/PQmHF+mZlZYW6deti2bJlWLp0KczMzLBnz54idYFcLkf9+vUBABMmTECbNm0AALa2tgDyN1kWCQ4ORk5ODn744Qc0btxYyjMfHx+MGTOmUF5SgX0QNOtQ06ZNtfYYrFWrFoD8fR7E9Iubem/fvh2TJk0CESE0NBRAvl4S97gR4zl27Jikb4gIJ0+ehEqlkt4rpi0pKQmDBg0qVKcL7j1UVP1bsmQJfH19Dda/ioxYfo0aNdJ7T5OsrKwi44yKigIAVK1aVef9a9euGdw/Q7xX8ORYQ2ELUq9ePTg7O+PkyZO4desW7ty5AwBwcnIqtHeLs7NzoXpibW2t9Y6mTZtq3R8/fjwAYP/+/Th58iTi4+MREhKC+/fvw8bGRjr5asWKFZg8eTJ69uyJPn36FJme8sqsWbMwbdo0xMXF4caNG0hLSwMAaY8sUacaU666OHv2LC5evAgXFxct/SyWy8WLF5GdnY0WLVpI98QyEfWYIAi4f/8+AODu3btap3l17NgRL168MKj7iQhnzpwBADg6OuoNp4mNjY1R4QBgzJgxWLRoETw9PdGpUydYWFhgyZIl2LdvH4gIv/32m1a6AKB169aIjo4GkL9H0ZkzZyS9rIko76lTp9CtWzct3VzQJiuIoXLJzMzUG4etrS1OnDhRqFwKYmFhgdmzZ2PWrFkQBAFPnjzBgwcPcPXqVbRs2ZLtKfYK8DyP+/fv4+XLl3j8+DHu3buHs2fPIjk5GQDw8OFDDB8+HOPHj8fmzZu19uUTBAFRUVFYsmSJ1qnRLVu2xJgxY1CnTh3Url0bNWrUQJUqVVC7du0yT9+bAMdxUKlUaNSoERo2bIh33nmnQm2oLo4Phg4dihUrViAmJkayyeLi4rB//37pgJ7vvvsOgH6brV+/fti4cSNq1aqFTz75RIp/1apViIqKQr9+/fD8+XOEh4dj0KBB0sFOVlZWSElJQUZGRqF+W61Wo1KlSgDy901s2rQpTp48Kd3XZevzPI8ff/zRqHGePsSxupgv0dHRGD58uNTn3717Vyrnjh07YsuWLdJ4med5DBo0CPPnz8fBgwe19nIuKGtRtml4eDg8PDy0bNoxY8bA3NwcSqVSilO0p0UZC5aNq6triehg5hRjlAq2trZ4//33ERsbi8WLF0MulyM5ORlbt24FkG/AiB3f3Llz8b///Q+VK1dG5cqVYWtri9OnT4OIcO/ePQD5HZ2IXC5HcHAwgPyOURwotG3bVgpjY2Oj8/ja5s2bazWcJk2aFAojl8tRo0YN6W/Nd9jZ2WmFbdiwIQAgMTHRqI1qmzdvjuHDhyM2NhYhISEwMzPDV199hYSEhEIyjBkzBqtWrcKlS5dw584drU1/RQoagtnZ2cjJyYGzs3MhWcS/s7OztZ5t2rRpISebaJQXLJu2bdvi9OnT5c4AFNOiyzCWyWSYMGEC9u/fjxEjRkChUOD58+fSPfHfjz76CIsWLcKIESPQqFEjDBw4EEOHDoVcLkfbtm0xZswY7Nq1C7GxsbCzs8PQoUMRGBgImUyGu3fvAvjPmaH57vr16yMjIwPZ2dlo166d3jSIcZQWMpkMs2bNwt69e7Ft2zY8ePBAp3NVX9m+88476NGjB44dO4azZ89i0KBBesNWqVKlUFixbGxsbLQ6emN0gYiYv5obOheEiKQ6rtmOi8obXfEA+U4wXfctLCwMyiDKbWtri8qVK+Odd96RnFKiA0+zvhZlaGqeICieTCiir/4BMLr+VWTE8tHlwNJVdq1atQIAqd7pesbb2xtRUVHIyspCp06dpHuPHj0CALRr165Q3JrlWXDz9lfRmX/88QdOnjwJKysruLi4ICcnBwBw+vRpg8ez63qXTCZDlSpVtGQKDg5GcHAwxo0bh1u3biEkJATbt2/Hnj17MGfOHIwbNw4RERHYvn07xo4dC7lcDoVCIcVRcCP78oC+vkAQBOzevRtffvklbG1tMWLECKxfv14y9g19bNJMp660iu1RzBtdzmdRnlu3bul0immGu3nzJgDA399fyxEg3i8qv9PT0w3e1yebMbRp0wanT5/Ghg0bkJiYiJSUFPTu3Rtr167FjBkzJNkLfsjR5OrVq+jSpYvedBw8eBCff/653vv6+vmCiOUiylScctGHOJisV68e6tWrBwcHhyKfYRiP6BSOiYnB2rVrkZGRgR07dqB27doIDQ2Fubk5BEGAUqnEuHHjoFKpULt2bYwaNQqDBw/W+oDOYAD5bXb48OGSU2zYsGG4du0aHB0dtT6kFWWziWPBxo0ba+kbe3t76QOyOHZq0qSJVhgHBwctXSHee5UDa54/f47Dhw8bNc4rCjFfYmNj4eXlhczMTHzwwQda+SKOj/bv3w8fHx+dYyh9FGWbHj58GM+fP4elpaV0XRyXa56ebYw9XRJUHHcvo0Ihl8vRr18/ZGRkICYmBvHx8XB3d0eHDh0AQOuL4k8//YQ//vgDjx8/Rk5ODhISEqRTwp4+fQog/2uFPsTjgNVqtd4wouFTo0YNrUYsGqSaRlZBxxPw30Do8ePHOuNPT083yrCUy+Xw9vZGRkYGoqKicOXKFXTt2lVr0CUIAvbs2QNbW1ucP38es2fPxvHjxyW5eI0TmQryxx9/SP/Xpyzz8vK0/q5fv34h2V+8eAGgcNkcP35c6wS38kLBwUxCQgKOHz8OIL/u+Pj4YMSIEXBxccG1a9cQHx8PANIgUSaTISgoSJqVVKdOHfz444+YPn06cnNzIZPJsH37duzcuRPTpk3D/fv38fXXX2P06NF48eIFnjx5olc2MW/FeqoPMY7iDFCKQ2pqKlxdXREWFoY5c+bgxo0b+Oijjwq909D7xUGDOMgoTlixbBo2bFjofcboAs33aQ5uNNureD83N1d/RuigqDzX52TQJwMR4dq1awCAe/fu4dmzZ/j9999x+/Zt8DyP48ePF5rVWNCJUlAuzRmRcrkcRISEhAQQkd76pznToqj6V5Ep7swe0UC7du2alj4VBEE66VGcySfOuhERZ5106tRJGnyJ79DnXDXkdDXEkSNHAOTPvJTJZNJsorS0tEJ9lr29faG+y5BTQZyhePjwYcjlcrRq1Qrbtm3D9OnTkZycDI7jJCfPhx9+KNXVU6dOAQAGDRqERo0aGeybTYE+x9aaNWswZswYtG/fHocPH8akSZO0Bs/Hjx/Xcvhp4uPjI321LoggCDAzMwMRoX///jrfrdlGRb1oaFa5OHj65ZdfYGZmVuhXFIY+Guh7p7H4+PhApVJh69atuHnzpjSTbc+ePeB5XqqjFy9e1BuHnZ0drl27Vui9op01ZMgQSS5ds/eMkZfneTg5OYGIJCe4LpuoYLkwTItcLkfjxo3h5+eHs2fPYuHChTA3N8eqVauwb98+cByHq1evYtq0aVCpVPDx8UFCQgLCwsIwcOBA5hBj6KRbt24YOHAgYmNjkZubi59++gkjRozQ0i/G2GzPnj0zaEuJYydx7KoPzTGp5jXxuq5xqIhoLwNFj/OKonv37lK+PHr0CNu2bcPAgQO14jVmDKUPY2xT0XGmb8a/5hjBUNmUBOVrZMt4o/D09AQAxMbGYs+ePejYsaPWoG7w4MEA8pcuilMnxd+JEycA/Dd4SUlJKRS/OJgRZz9cunRJ6z79/yPBC6JpXInedF1LHURkMpkkR8EvsLdv3wYAKS3GMGjQINjb2yMqKgrr16/H6NGjtd5/9OhRjB49GhMmTMBPP/0kLSMQZT1x4gQCAgIKyQ1of3XWNYsM0J51pw8xvbrK5saNG0an1VScOHFCcop5eHggKioKa9aswezZs9GgQQMp35o3b47AwEDEx8fD1dUVgwYNwrfffovLly9j06ZNyMnJwYEDB5CQkIDRo0dj7NixWL9+PfLy8hAYGIirV68iIyNDMrp1Ic7u0DUrURNjyuVVEQQB/fr1w9WrV7Fp0yaMHDkSlSpVkupIlSpVEBAQoHXkfUGISOoInZ2dpWvGhtW8p4mxugDQ7ZTW5VjS9VXKEEV1qEU5MArKIJfLpS+Hp06d0kqPTCbD9evXpbCGBn2G5OJ5HrNnzwaAEql/FRHNegbkOxFERyGg7RwX/05ISEDXrl2xdOlS3LlzBwsXLgTP8+B5HosWLYK3tzfkcvn/a+/co6Iq1z/+3QOe08pyqXmyQ2ammEfIY+JdY5gBFMtERPCSeb+bl0zDUzADoqadLicvSaJZrVTAUEDRpTGDDKeLIooiqJko4OV4lqm5rLNMZu/n9we//bb3zHAzS6znsxaLmb3f/bzP++x373n3s9/3eTB9+nQEBARg8+bNqKqqgqIoOHjwIGbNmoXQ0FBMmTJF1K8O6o4ePYpDhw6hrKxMLK0uKSlBbm4uTp8+DbvdLpbsORwO4TBWWbVqlVgiL8sy0tPTAQCTJ0+GwWBAjx49sGLFCmRmZmL69OlwOp1wOp0ICQlB3759AVQvVygoKABQ7Ry22+2w2+3IyckRy4xUOzRt2hTvv/8+vvnmGzFDSf39MRgM4i12SUkJiAj79+8Xy0pTU1PRtGnTRveCpCbUwfn8+fOFzupbfeDnWXla1H703Xff4datW24y1QeXd955B0SEfv36wd/fH3v27HFzlJ87dw79+vXz+CJOi/pCEQAKCwt1+9QXBLXdjyRJEst2XB1TDZl5VRN+fn7IyMgQ97nFixdj8+bN+N///geDwSCWQJ48eVIn98SJEzCbzTAYDAgKCsKPP/7oNmZTr4f+/ft7HIfVprdrGyRJQmFhIYgInTt3xv333++mk6fzwjQemjdvDqvVim3btuHhhx/G6NGjkZmZiWnTpqG8vBzJyclISUkRITAYpiYMBgPCw8Nx48YNbN++HRkZGTCZTLr9dY3ZJElC586dcf78ebd7s+rQUsdZ6monLbU5ugD9eLC239WnnnpKrFr6Jc95ap2qXbZu3Yo1a9a4Pc/W9QwVHx9f40ujusam/v7+oi2qTFc7GQwGREVFAfB8bkpLS+vV1vpwb4xmmHuSp59+Wnigjx07hhEjRuj2jxw5EgEBATh27JjwrgPVXvDExEQQEZ577jkAEIN2FTW+gDrzCqgeuGuJiYkRS0xqusG4eqjVz64PqOpNwnWapuqsa8iUbYPBgIiICKSnpyM3Nxfjx4/X7VcHhgEBAeImceDAAZSXl+PGjRt44oknalwi8sgjj2DEiBEoLS31OCjv1KkThg0bpjvG05KQwYMHi3Pzww8/iO2yLGP69Ol13tzvFlp7tG/fHoqioGnTpgCAZ599VuzTOvbUG2peXh5KSkqEPSZMmACj0QhfX18QEXbv3o1Lly6J/XFxcWjevDm6deuGyMhIdOrUCUVFRTrbnD17FufOncPIkSN16+k9MXDgQPj4+ODgwYM6Geo0Zdf2NeRBhojg5eUFX19fXbyyS5cuAaj+AX3vvffEMiEVrR5ff/01ysrK0Lt3b7dlxK76fPXVVygrK8Pzzz/vsaxrf6vrXqDqUdeyIHVWjhprID8/X7e/puVydwptbKIpU6YAqHaUaG0zdepUjBkzpt7ytJ/VvqduV+Naafuf9piG9L97ESLC0qVLkZ+fj6CgICQkJGDx4sU6GyxduhRAtXN26dKlwrGwcOFC7Nu3D9u3b4e3tze8vb3xpz/9SbxwMBgMyM/PR8+ePeHj4wMvLy8MGjQIw4cPx549e8QynqVLl6K8vBxGoxFZWVn4+OOPkZeXh5UrVyIwMBBXr17FkiVLkJeXh8WLF+Pq1aswGo1ITEzUOewAYM6cOdi3bx9atGgBb29vOJ1OlJSUiLickiQhJiYGKSkpKCgowP33348mTZrA398fa9euBVAd/3Lv3r0ICgrCunXrsGbNGpw+fRpvvPGGGPQvW7ZM3NMWLFiAqVOnwmAwoE+fPhg3bpyIY5eUlIRJkybhpZdegtlsxvz587FlyxaMHz8er7zyCt59991GMzODiGCz2cS9xeFwwG63i76gOoo++ugjXLt2DU6nEzExMejYsSMkScL69evx448/AoCIxZKfnw9FUeBwOMTxkiSJF37p6ek4evQoDhw4IJxESUlJKCgoQEJCAiorK1FRUYGYmBi0aNECDodDLLNUf3e8vLyEk1JlyJAhsFqt+Mc//oG33noLsixj27ZteOihh1BUVFSrA0CSquOUAtWxFUtLS4VDc968eaJdNpsNdrsdV69eFbP/9u3b5xbKwRWHw4Hdu3cjOzsbiqLg+++/x9ChQzF06FBIkoTJkydj1KhR2Lp1K1asWAFZllFZWYno6GhMnz4dBoMBq1atQnh4OJYvX47i4mJcv34deXl5eO+992CxWNC7d2/k5uZiw4YNot68vDzYbDbk5uaKmcCSJMFms4nft7///e9wOBzYunUrkpOThbMkICBAvJxNS0vDtWvX8M033yAmJgZt2rSBw+FoNP2YcSc8PBxZWVno3LkzJk6ciP379+ONN97AlClT7hmnPHP3GTZsGFq1aoWMjAy8+OKLumu+tjHbsGHDMGbMGEiSJJ5JXV+gBAYGYt++fWjdujWef/55nD9/XjfLXJ1RXNtKHy2eVkBodR00aFCDnvNqIzIyEq1atUJmZqaIp6zVQ32G0sYT1Y7Ftc/errrWNDY9c+YMzp07h7CwsDpfgEiSJMbMrucmNTUVSUlJd26FDTHMr8gHH3zgljVDi5pGu0+fPrR7925asWIFARAZLdSMcz4+PvTCCy9QQUGByCCnZpHQZvuwWCxUWVlJVquVoqKiyOl0ktVqpQULFogMIVarlWw2G8XFxYkMY/Hx8WSxWMhisYjsSf7+/hQXF0c2m40URaGCggK6//776c0336ScnBx69913ycfHhzZv3tzgLCyHDh0SurgeW1xcTP7+/hQeHk779++nr776ioKDg2nAgAEEVKdZ37BhA1ksFho3bhwBoKioKJF50el0UmxsLPXu3ZvWrVtHWVlZtGjRIgoPDxdZTqxWK82YMUNkFElISHA7R+q56du3L+3evZuWL19OQHVK+MaUfZKoOsNJ7969yd/fn44ePUrBwcFUWlpKRETvv/++6BtVVVU0b9486tWrF7Vs2ZKGDBlCAETWE5PJRF9++SWVl5fTvHnz6MqVK+R0OkWmGJPJRA6Hg7744gsaPnw4FRUVCVvcunWLIiIiaPTo0bRlyxZKTU2lsLAwio2NrVdWL6LqjCzNmzenWbNm0dmzZykzM5N69OghMqdMnTqVcnJyyGKxUHx8PAGg6OhoslgstfZB7TWyfv16OnnyJIWHh4u+vmDBAgKgS49sMplo+PDhVFBQQHv37iU/Pz9q166dLtuMp7J79uwhPz8/XSZJi8VS7/7m6V4gyzLFxcVRnz59ar1e1WtbURSRBWf58uV069Yt+uCDD8TxAGjOnDl069YtslgsFBUVJa5Hq9UqbAyA2rVrRxaLhU6dOkWxsbEiRfb48eNpw4YNlJOTI7JfqWVPnz6ty3Y5duxY2rVrF73wwgsEQPSpSZMm6e5LanvUNmmvayKid955hwBQeHg49erVi8LCwnT2U9NmZ2ZmUnJycoP7X2OhIdknFUURmTzVz1qcTmeN+4h+zk5VU1YiVbZarrb6tfW4bq+pLNHP2Se193DXLLquOJ1OXds86aPu97Rdm6lVleEqS93vdDrd2t4YfwPU7IPqn9Fo1GW7zsrKEr/5ACghIYFu3bpFQ4YMoZdffllcJ+q4o23bthQQEOCWPViWZRo+fDg1b96c5s6d62b/q1ev0syZM8nX15d8fX1p1qxZ4rdXzV7p+rd371639qSkpFBISAgBoG7dutF7771X77GG0+mkRYsWUatWrahp06Y0f/58SktLowcffJCMRiMZjUbKyckhk8lERqNR6KFm9a4JALRlyxYx9gCqMztr7zGyLFNGRgZFREQQAGrVqhWlpqbqdK+qqqLY2Fjq3r07PfDAA9S3b1/KyMgQZWw2m5uNkpKSKCIiQujvmm3S6XTqzq+2zyqKQsXFxTRixAhq0aIFdejQgYYOHVpnNjKm8ZCWlkYAdFnsGaa+KIpCkydPpmbNmtH58+fd9suyrBuz7dy5k5599lkxZlPLqOO4ZcuW0U8//USzZ8/WZWZ0Op3iGWPDhg10/PhxCgsLozlz5oixqXr/VMfv6pjTz89PNx6saazv+pyXmZlJVquVgoKCxG9NQ+0CgHbs2OG2X7WJxWKhiooKSk9PJz8/P2rWrJnuGSouLo6io6NFWfW3pKqqym1sOmjQIDE2Vcf3qk3U5wNt9mdFUWjNmjX0wAMP6MbTTZo0qXN825DskxLRrxTAhmFQvXxj5MiRyMnJcQsYq+J0OrFmzRrk5+ejS5cuGD58uC7rHRHhwoUL+Oijj5CVlYUHHngAdrtd5+VXFAWFhYX49NNPUVxcjICAALz99tvw8vJCQkKC24wLo9EoZpGoMy+0MzDUJQqKosBsNiM4OBiKouDYsWNIT08XMxP69++PAQMGNPhtlaIomDBhAkaNGiXePGi5ePEitmzZgi1btuCxxx6DxWLBQw89hPT0dPj4+GDEiBFiBoRW94SEBKH7rl278Pnnn+P8+fMwmUyYPXu20NPVJiquwZtlWcbq1avFuYmMjGy0gWWLi4uxcuVKOJ1OWK1WMX1YDdK4a9cu/Oc//0HXrl0xf/58ZGdno7CwEH379sXAgQMxcuRIpKSkYObMmdi+fTsGDhyIf/3rX3jkkUdgt9uRl5eH0NBQLF68GJWVlQgLC8Pq1at1515RFGzatAk2m01kghk3bly930ITEX744QesWLECKSkpCAwMRGxsLKZOnSoyfQUGBoo3+9rjast+quq2Y8cOZGdnw8fHB7169cLgwYOxadMmXLp0CQMHDkTXrl0hyzK8vb0RFBSEpKQkzJ8/X2StjI+P17WlvmXr299quhcoiqIrq8ry9fUVmQTVthuNRoSEhICIcPjwYSQlJeHDDz9EXFwc4uLiMHDgQLGk02q1IjEx0c1uzzzzjM7GRIRx48bhk08+0c2sbNeuHdq0aSPKqtfhhAkT0KFDByiKgqNHj4oluNHR0YiOjkbr1q1ht9vhcDh0dXfo0AFlZWW6OFTa61q1g8PhwI0bN9yWRymKgpUrV8LhcOCxxx5D9+7dMXbs2HtuFoTdbhfxmXJycsTn3ytqey0WCxITE++2Ovcs6n1Be/14CppP/z+zyPU4T7HAiMjj77v2Db2n/eqxqtyaYgbWtVTa6XSKfQ29jrU6qHqqetekU32XodXWPhVtcpC6bOR6TrQ6afXytK0mmTXVWVfiBKbx8tNPP8HLy6vG5wmGqY2dO3ciPT0dH3/8scdrX5ZlFBcXIysrC3l5eRg7diwmTpyou5fIsoytW7di27Zt2LZtG2JiYrB8+XJdGafTiZSUFOTk5ODmzZsYPHiwiOGrJopTUZ9J1fGg9l7n6TdJHetrn/MqKythMpkwZ86c2xrv7dy5E+vXr0dmZqbbfVNRFJSUlGDbtm04ceIEmjZtio0bN7o9QyUkJOiep4Gfx/i1jU1dx/dqeZPJJGK7qtuKioqQnZ2N3NxcREVFYcSIEbos256w2WwYMGAAgOrY47XdO9gpxjQKahqoaalrsKOV82tPqf4t6mnoILU2Gb9ETn3OTWOhtmxoDcmUVpftPf1Y3W5dtelQ24/jnZDrCa2jS11KU1NbGlK2vvwa/e3XsmVD6q/p4fp25f3a/e9u8kdxihER9u7di6KiIrz++uuwWCwIDAxEaGjoPXvuGIZhGOZepj5jtvo8B/4WY7E78ZxXH+5EW+6UDKD+z98NcYqxq51pFNSnc9fnQvqt4gv8FvXciZvbnZBxL8VsqE3XhrSjLrv9Fv1QW8ed/KFryEwAoH5tUZ00jbW//Vq2bEj9v+U5vJeu2T86atykqKgoHD9+HBcvXkRISAg7xRiGYRjmLnCnnjfvlWfF+nAn2tJYZNQEO8UYhmEYANXLCdVlxfn5+Zg0aRLGjh2rm8KsYrFYxLLB/Px8TJw4scayDMO4I0mSyDDJMAzDMAzD3B3YKcvksQ0AABCmSURBVMYwDMMAAPz8/ODv74+ZM2cCqJ6mfOXKFY9l/f398dRTT2HGjBkijkBNZRmGYRiG0VNX3LXGgqIosNls6NGjB1q2bHm31WEYhrnjsFOMYRiGAQCMGjXqVynLMAzDMMzPKIoiZlafPXsWZWVljS4pChEhKysLy5YtQ9u2bREWFoaMjAxERETcbdX+8DidTmRmZiIyMrJRO1QZ5l6BryKGYRiGYRiGYZjfCEmS8Prrr+Pxxx9HRUXF3VbHI2VlZZg9ezamT58Of39/AEBRUdFtybLZbCIhD/PLUBQFHTt2RHR0NDZt2nS31WGY3wU8U4xhGIZhGIZhGOY3QpIkDBgwAF988cXdVsUjRIRXX30VFy5cwIQJE0S8UZPJdFuypk2bJhKLML8co9GIW7duoX///ndbFYb5XcBOMYZhGIZhGIZhGEZw7do1PPnkkzAYDAgODkZwcPBtyTl79izOnj17h7X742IwGPDJJ59AluVGt+SWYe5V2CnGMAzDMAzDMAxTB0QkPqtJZtTtkiRBkiTxXVEUXVlPsZ+08lxRA/HXdLwq32AwiPoMBoPQoT4y6mrnX//6VxCRaJ+KLMuiva52UHVSv2dmZorPWl20+mn1JiLIsiy2acsqiiIcQa51udrldpIYuOqjfnd1Pql1aPVzlaHiek5UZFnW2cJVltpebRu0ttC2UStPrU/tE642cD13npBlWWdfjlvG/N7hHs4wDMMwDMMwDFMD8fHxMJvNuj9FUZCbm6vblpaWBkVREB8fD29vb3h7e+ORRx7BmDFjsGPHjnrVRUTIy8tDv3790KtXL/Tp0wdeXl5wOBwAqh0iZrMZISEh6NKlCz7//HMYDAa0bdsW8fHxwmEiyzJee+01dO7cGT169EBgYCDy8vJqdcSpxwUHBwunSUhICEwmk3DSmEwmhISEICQkRMQJU+3TuXNnmM1m4ZCZMWMGFixYAABYsmQJzGYzTCYTiAh2ux3BwcEIDQ1F69athTPJZDIhNDQUDz30EOLj4wEAdrsdISEhGDBgAMxmM8aPHw8vLy8MHTpUOIMURUFWVha6deuGp556Cr1790avXr1QWVlZL7vPnTsXISEh6NGjB+Lj4/HZZ58hMjISHTp0gNlsxpEjR3D48GEMGzYMwcHBGDZsGDZu3KhzfsqyjAkTJqBDhw7w9vaGr68vpk2bhosXL+rqOnDggOgfXl5eGDFihM5uaWlp+Nvf/oYmTZrA29sbfn5+SEhIAABMmDABISEhCA0NFdsOHTqE0NBQhIaGwmQy4eDBg4iMjET37t3RoUMHbNy4EQBgsVgQEhICs9mMl19+2S1ruKIoSE5ORvv27dGnTx/4+/tjxowZwsYM83uFnWIMwzAMwzAMwzA1EBQUBIvFgqKiIjRr1gyLFi0SM3AefvhhfPfdd4iOjkarVq1w/vx5LFmyBO3atYPT6cSlS5fQsmVLxMTE4OrVqzq5rjN/FEXBP//5T5jNZsyfPx+HDh3C/v37sXbtWphMJhQUFECSJMTGxmLMmDE4fvw43n77bezfvx8XL17EkiVLQESoqqpC27ZtcfPmTZw8eRKHDx9GaGgozGYzjh07VmtbDQYDYmNjhXMuLi4OFotFOMnmzp0Lo9GIvLw8cYzJZEJ4eDhOnTqlm/kUHR0Ni8UCAIiNjYXFYhHfJUkSmawvX74sZFksFgQGBuL777/XyXr99ddRXl4OAHjwwQdhsViQnZ2NxYsXC2dOREQEXnvtNZSWlqKgoABTpkzB448/Xq8EAePHj8czzzyDI0eO4NNPP8W5c+eQnp6OQ4cO4ezZs5g4cSLmz5+PDz/8EPv27YPRaMSUKVN0S0M/++wzfPrppwgKCoKiKPj2229x/PhxvPLKKzpn5cyZM7FlyxbhBOvZs6eQ8e2332LUqFH47LPPxP6uXbuK/S+++CJefPFFnf2feOIJxMbG4uzZs6isrMTChQuxYcMGFBUVYezYsZg8eTLMZjOCgoJgs9mwfft2rFq1CitXrhROUlmWMWjQIKxatQrZ2dkoLCzE8ePHoSgKvL292THG/L4hhmEYhmGYRoLNZiMABIBycnLutjoMwzBERKQoCj333HMEgEpKSsS2iIgIyszMFOX++9//0pAhQ8hisYhtOTk5BIDWrVunk2m1WgkAOZ1OIiI6cOAAAaCIiAhdOafTSW3atKEpU6aQLMtE9PO90mq1EhFRQUEBJSUlkSzLQu6JEyeEDLvdritfV1uDgoIIgKhPi9oem80mtlVVVREACgoKIkVRxHaLxUIAyG6317seVb5WV6fTSSaTiXx8fKi8vJxkWSaLxUK5ublUVVVF3bt3p4iICF3dsiyTyWSigIAAqqqqqrPdhYWFBIC6du0qzomiKGQ0GgkAHTx4UJRV7f/OO++IbdnZ2WQymSgrK8ut/UePHtUdl5qaKuqQZZkAkKIoFB8fTwDoyy+/FDbZsWMHvfTSS251u9pHteWpU6fcys6ZM0dX1mg0ktFoFHWsXbuWANBbb72ls0l+fj4BoClTpuhsyzCNHfU+AqDO659jijEMwzAMwzAMw9SCJEkYM2YMdu/ejYyMDPj7++Py5cuoqKjAkCFDRLmHH34YWVlZuHHjBrZt24YrV67g/PnzAIALFy7UWsc333wDAHj00Ufd6vb19UVWVhbWrl0r4ogBQOvWrQEAPXv2RM+ePSHLMg4cOAAA+OSTT9xic50+fdotRtjt2MIVbRwxrfz61qPGRKvpGDXGl7e3N9q2bQtJkpCYmAgA+OKLL3Do0CH06dNHd6wq7/Dhw6isrET79u1r1UGdkRUeHu4xiP3TTz/ttu37778XnwcPHoxBgwbh4sWLSE1N1c2AUz+bzWb07t0bo0aNgslkQosWLRAZGYmqqipIkoTRo0dj8eLFCAsLQ48ePdC+fXtERERg9erVtequ2geAx3Y2b95cV1aLoig4evQoAKBdu3a6fX379gUAfP3117qYbgzze4KXTzIMwzAMwzAMw9TBqFGj0L17d2RlZUFRFHz44YcIDg7WBSJXFAUxMTHw8fHBpk2bUFxcjOXLl9dL/unTpwEALVu2dNtHRLh8+bKILabStm1bt3J79+4FAISGhiIkJATBwcEwm82w2WyYNGlSnY4q0sQd08bMqs8xrgHcySWGGWkC7pNLQPq65EuSJIL/a8nJyQFQs90A4MyZM/Vqh6ternXVtl2WZYwcORJt27ZFRkaG23JZoLqd69atQ//+/XHq1ClkZGRg7NixYulrp06dkJeXh65du6KkpAQbN25EeHg40tLSaq27JkenJ1t7Ov7EiRMAgBYtWui2qzJLS0vrjEfHMPcq7BRjGIZhGIZhGIapA4PBgIiICBQWFiI7OxsbN26EyWTSlXnrrbfw9ttvY+HChUhPT8eaNWuwZ88esd81O6EWX19fAO4zeSRJwpUrV/CXv/xF1KeWue+++9zkREVFiX3BwcHiTw2QXxeeZlv9UtQ2m0wmEaC/obPVJEnCfffd53ZcaGioR3lEJILJ1zVLTHu8Vk5NDj5Ps61mzZqFbdu2ISUlBSkpKYiPj3dzMJaWluLkyZNwOByorKxEZmYmnn/+eSQmJqKiogK5ublo3rw5HA4HLl26hKSkJAQEBODNN990y1jpqrs2g2d926TSuXNnjzb57rvvAAD+/v6/aHYhwzRm2CnGMAzDMAzDMAxTD4YNGwagOqh6s2bNMHjwYLFPlmXhABs3bpzbUjMiQnx8POx2u/iupVOnTgCAsrIyt+POnTuHoUOH1umY8Pb2RnBwMAC4BZhXs2X+GtQ0o0zrqCEi3Lx5E02aNKlVlienoda542qDvn37onv37igrK3ObEXXu3Dl0794djz/+eJ1tUIPX1+S0rGsmVnJyMnx9fTFixAjhTFT/K4qC4OBgXLhwAR988AEAiAya69evBwDcvHkTDocD27dvh5eXF7y8vDBjxgy8+uqruqWYbdq0cdND67ysTU9P2w0Gg1g6evLkSd1+9Xvfvn3vmIOUYRob3LMZhmEYhmEYhmHqgZ+fHyIiIrB9+3ZERka6zcDp1q0bAGDfvn0Aqp0Kb775pijz5ZdfQpIkOJ1Ose3IkSNQFAU9evTAihUrkJGRgcLCQiiKghs3bmDRokW4fv06pk6dCi8vL8iyLJxQ165dc5t9Nm3aNHTr1g2LFy/GunXrIMsyDh48iBdeeAFjx46ttX1EhDNnzqBZs2YAqh1Frg4vdbba5cuXoSgKZFnG6tWrYTKZUFFRgZKSEqGP0WgUZYkIFRUVIjaXJEmIjIwEANEmp9OJAQMGAAAqKirgdDpBRDpHYWlpqU4ng8GAyZMnY/PmzUhLS4OiKFAURdgtOTm5zlhYiqKI7Jbnzp0T9Z4+fRrXr18X+qi2VmNwqWUlSUK/fv1w+vRpHDx4EACwc+dOpKSkiLaqS1/z8vKQmJgIWZaFrEGDBuHJJ58EESExMRFpaWnCkXjo0CFMnjwZBoMBsizrYtOpMsrKyoSe5eXlUBQF165dQ3FxMQCgsrJStOnw4cO4fv06KisrUV5eDiLCtGnTEBoaiqSkJNEfz5w5g6VLlwIAkpKSeKYY8/ulQSH8GYZhGIZhfkU4+yTDMI2djRs3Uq9evej69etu+5xOJ82ePZuefPJJAkBt2rShDRs2iKyCr732msjUqP2Li4sjoupsh6mpqdSxY0dq0qQJAaDBgwdTcXExEVVnKlSzIap/HTt21GWCJCL68ccfad68edSpUyfq2rUrBQYG0sKFC+vMIJiamuqmm2tGSUVRyGq1UlhYmCizbt06oZevry+lpKQIfV955RV67LHHqGfPnpSRkaGrT5Zlmjt3LnXq1EnIev/993X1f/7557rvDz74oJtOsixTVlYWdenSRZTr1asXHTlyxGMGTS2KotDs2bNFRsagoCAKCgqiAwcOUGBgIAUGBopt69ato9mzZ+u2q1kcjx49SqNHj6ZWrVoRAOrduzcVFBTQ+PHjqV27dpSSkkI2m42ioqJo+fLl1LJlSwJAXbp0oV27dhFRdUZSq9VKZrOZ/vznPxMAGjp0KJ08eZIURfF4bgoKCtx0T05Opjlz5rjp6alN69evF303OTmZHn30UQJAzZs3p+nTp9crcyfDNDYakn1SIuKIeQzDMAzDNA7sdruIDxMbG1vjcg0iwpIlS35L1RiGYQTabImuEBFkWYYkSSL7o3oMUD2zSf0sSZIIkq6diaPOdnKVocpX/9eW5VGVodZZ3+VvrvLp/5fYuZYhIqGjOoNNq4t26aB6jKcZW6osFdU+qo212Ta1x3hqj3bWnKvd6tNm7WdtvaqO2jpddXatX22r9hxoZanl1HPsySbqOdAeq9pce+7r0lMrx1NZ12Wu2v7LyyaZxggRwWq11niNE5GY6VhVVQVvb+8aZdW8h2EYhmEY5i6ybNmyGvdZLJbfUBOGYRg9tTkKJEny+ACmPaauGFC1OSNqc4TVV0ZtuMqvLbC7Vn5NSxTr0sFTnDBX3T0lH7idumrTobbPNdmgPvW7bvPUXk+ya6rTk50bomdDzyvDNFb+/e9/u2XkvR3YKcYwDMMwTKOBiGA0Gut8YKgpqDPDMAzDMAzz+4eIEBQUVGeZuuDlkwzDMAzDNBpcl9HUBr/JZhiGYRiG+WNS3xekdc5WZacYwzAMwzAMwzAMwzAM80fj/wDd3tlAttOvXQAAAABJRU5ErkJggg==)\n",
        "\n",
        "\n",
        "Chiaramente, per determinare una optimal policy è necessario scegliere ogni volta l’azione che produce il valore di Q maggiore.\n",
        "\n",
        "\n",
        "**________________________________________**\n",
        "\n",
        "\n",
        "\n",
        "Inoltre si dimostra che l'algoritmo converge se:\n",
        "- il sistema può essere modellato come un framework Markoviano (le probabilità di transizione fra stati devono essere nota a priori)\n",
        "\n",
        "-  i valori della ricompensa devono essere limitati da un valore costante c: $\\hspace{0.2cm}$ $|r(s, a)| < c $\n",
        "\n",
        "- l’agente deve selezionare le azioni in modo tale che ogni coppia (s, a) sia potenzialmente visitata un numero infinito di volte"
      ],
      "metadata": {
        "id": "n7NprY6fOSkT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def rl():\n",
        "\n",
        "    q_table = build_q_table(N_STATES, ACTIONS)  # inizializzazione della tabella q con tutti 0\n",
        "    \n",
        "    for episode in range(1,MAX_EPISODES+1):  # gli episodi sono una sequenza di transizioni fino al raggiungimento del Goal\n",
        "        print(f'\\n Episodio : {episode} \\n' )\n",
        "        step_counter = 1\n",
        "        S = 1    # stato iniziale\n",
        "  \n",
        "        update_env(S)\n",
        "\n",
        "        while S != 7 :\n",
        "\n",
        "            A = choose_action(S, q_table)\n",
        "            #print(f'\\nStato attuale: {S}, Azione scelta: {A}')\n",
        "\n",
        "            S_, R = env_feedback(S, A)  # Esegue un azione in un certo stato ed ottiene il reward ed i prossimo stato\n",
        "            #print(f'Nuovo stato ottenuto: {S_}, Reward ottenuto dalla transizione : {R} ')\n",
        "            \n",
        "            q_old = q_table.loc[S, A]  # è il \"vecchio valore\" di Q nella formula sopra. Di fatto sono gli attuali valori della Q table per lo stato S\"\n",
        "            \n",
        "            if S_ != 7:   # se non siano arrivati allo stato finale\n",
        "                q_learn = R + GAMMA * q_table.iloc[S_, :].max()   #  trova il valore massimo del next state tra le due azioni disponibili\n",
        "                # questo è il \"valore appreso\" di Q nella formula sopra.\n",
        "            else:\n",
        "                q_learn = R     # altrimenti abbiamo finito, siamo nello stato finale \n",
        "                \n",
        "\n",
        "            q_table.loc[S, A] += ALPHA * (q_learn - q_old)  # aggiorna la stima della funzione Q attraverso approssimazioni iterative\n",
        "            \n",
        "\n",
        "            #print(f'Tabella Q \\n {round(q_table,3)} ')\n",
        "\n",
        "\n",
        "            S = S_  # muoviti al prossimo stato\n",
        "            update_env(S)\n",
        "\n",
        "            if S == 7 :\n",
        "                print(f'\\n \\t Numero Episodi {episode}  Step totali {step_counter}\\n ') \n",
        "\n",
        "            step_counter += 1\n",
        "\n",
        "    return q_table"
      ],
      "metadata": {
        "id": "u3rW-yDpS7vb"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "if __name__ == \"__main__\":\n",
        "    q_table = rl()\n",
        "    print(f'Tabella Q \\n {round(q_table,3)} ')\n",
        "    print(\"\\n ** Fine addestramento ** \\n\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EQueBKLQsl4i",
        "outputId": "449b1d8a-87db-4414-fa22-523c2c4a77e6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Episodio : 1 \n",
            "\n",
            ".......U\n",
            " \t Numero Episodi 1  Step totali 6\n",
            " \n",
            "\n",
            " Episodio : 2 \n",
            "\n",
            "....U..G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 2  Step totali 109\n",
            " \n",
            "\n",
            " Episodio : 3 \n",
            "\n",
            "U......G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 3  Step totali 60\n",
            " \n",
            "\n",
            " Episodio : 4 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 4  Step totali 8\n",
            " \n",
            "\n",
            " Episodio : 5 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 5  Step totali 20\n",
            " \n",
            "\n",
            " Episodio : 6 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 6  Step totali 8\n",
            " \n",
            "\n",
            " Episodio : 7 \n",
            "\n",
            "..U....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 7  Step totali 12\n",
            " \n",
            "\n",
            " Episodio : 8 \n",
            "\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 8  Step totali 14\n",
            " \n",
            "\n",
            " Episodio : 9 \n",
            "\n",
            "U......G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "U......G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 9  Step totali 31\n",
            " \n",
            "\n",
            " Episodio : 10 \n",
            "\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 10  Step totali 8\n",
            " \n",
            "\n",
            " Episodio : 11 \n",
            "\n",
            "...U...G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 11  Step totali 12\n",
            " \n",
            "\n",
            " Episodio : 12 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 12  Step totali 18\n",
            " \n",
            "\n",
            " Episodio : 13 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 13  Step totali 18\n",
            " \n",
            "\n",
            " Episodio : 14 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 14  Step totali 12\n",
            " \n",
            "\n",
            " Episodio : 15 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 15  Step totali 8\n",
            " \n",
            "\n",
            " Episodio : 16 \n",
            "\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 16  Step totali 16\n",
            " \n",
            "\n",
            " Episodio : 17 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 17  Step totali 18\n",
            " \n",
            "\n",
            " Episodio : 18 \n",
            "\n",
            "U......G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 18  Step totali 16\n",
            " \n",
            "\n",
            " Episodio : 19 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "U......G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 19  Step totali 14\n",
            " \n",
            "\n",
            " Episodio : 20 \n",
            "\n",
            "U......G\t  +++!exploitation!+++\n",
            "U......G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 20  Step totali 12\n",
            " \n",
            "\n",
            " Episodio : 21 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 21  Step totali 8\n",
            " \n",
            "\n",
            " Episodio : 22 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 22  Step totali 8\n",
            " \n",
            "\n",
            " Episodio : 23 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 23  Step totali 8\n",
            " \n",
            "\n",
            " Episodio : 24 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 24  Step totali 14\n",
            " \n",
            "\n",
            " Episodio : 25 \n",
            "\n",
            "..U....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 25  Step totali 24\n",
            " \n",
            "\n",
            " Episodio : 26 \n",
            "\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 26  Step totali 10\n",
            " \n",
            "\n",
            " Episodio : 27 \n",
            "\n",
            "..U....G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 27  Step totali 8\n",
            " \n",
            "\n",
            " Episodio : 28 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 28  Step totali 6\n",
            " \n",
            "\n",
            " Episodio : 29 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 29  Step totali 10\n",
            " \n",
            "\n",
            " Episodio : 30 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 30  Step totali 8\n",
            " \n",
            "\n",
            " Episodio : 31 \n",
            "\n",
            "....U..G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 31  Step totali 6\n",
            " \n",
            "\n",
            " Episodio : 32 \n",
            "\n",
            "..U....G\t  +++!exploitation!+++\n",
            "U......G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 32  Step totali 13\n",
            " \n",
            "\n",
            " Episodio : 33 \n",
            "\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 33  Step totali 16\n",
            " \n",
            "\n",
            " Episodio : 34 \n",
            "\n",
            "U......G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 34  Step totali 8\n",
            " \n",
            "\n",
            " Episodio : 35 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "U......G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 35  Step totali 26\n",
            " \n",
            "\n",
            " Episodio : 36 \n",
            "\n",
            "..U....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 36  Step totali 20\n",
            " \n",
            "\n",
            " Episodio : 37 \n",
            "\n",
            "U......G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 37  Step totali 28\n",
            " \n",
            "\n",
            " Episodio : 38 \n",
            "\n",
            "U......G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 38  Step totali 12\n",
            " \n",
            "\n",
            " Episodio : 39 \n",
            "\n",
            "..U....G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 39  Step totali 8\n",
            " \n",
            "\n",
            " Episodio : 40 \n",
            "\n",
            "U......G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 40  Step totali 11\n",
            " \n",
            "\n",
            " Episodio : 41 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 41  Step totali 10\n",
            " \n",
            "\n",
            " Episodio : 42 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 42  Step totali 18\n",
            " \n",
            "\n",
            " Episodio : 43 \n",
            "\n",
            "U......G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 43  Step totali 13\n",
            " \n",
            "\n",
            " Episodio : 44 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 44  Step totali 12\n",
            " \n",
            "\n",
            " Episodio : 45 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "U......G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 45  Step totali 16\n",
            " \n",
            "\n",
            " Episodio : 46 \n",
            "\n",
            "U......G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 46  Step totali 12\n",
            " \n",
            "\n",
            " Episodio : 47 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 47  Step totali 8\n",
            " \n",
            "\n",
            " Episodio : 48 \n",
            "\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 48  Step totali 6\n",
            " \n",
            "\n",
            " Episodio : 49 \n",
            "\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 49  Step totali 12\n",
            " \n",
            "\n",
            " Episodio : 50 \n",
            "\n",
            "U......G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "U......G\t  +++!exploitation!+++\n",
            "U......G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 50  Step totali 20\n",
            " \n",
            "\n",
            " Episodio : 51 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 51  Step totali 6\n",
            " \n",
            "\n",
            " Episodio : 52 \n",
            "\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 52  Step totali 10\n",
            " \n",
            "\n",
            " Episodio : 53 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 53  Step totali 10\n",
            " \n",
            "\n",
            " Episodio : 54 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 54  Step totali 6\n",
            " \n",
            "\n",
            " Episodio : 55 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 55  Step totali 10\n",
            " \n",
            "\n",
            " Episodio : 56 \n",
            "\n",
            "...U...G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 56  Step totali 8\n",
            " \n",
            "\n",
            " Episodio : 57 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 57  Step totali 12\n",
            " \n",
            "\n",
            " Episodio : 58 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 58  Step totali 8\n",
            " \n",
            "\n",
            " Episodio : 59 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 59  Step totali 14\n",
            " \n",
            "\n",
            " Episodio : 60 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 60  Step totali 18\n",
            " \n",
            "\n",
            " Episodio : 61 \n",
            "\n",
            "U......G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 61  Step totali 11\n",
            " \n",
            "\n",
            " Episodio : 62 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 62  Step totali 12\n",
            " \n",
            "\n",
            " Episodio : 63 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 63  Step totali 8\n",
            " \n",
            "\n",
            " Episodio : 64 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 64  Step totali 16\n",
            " \n",
            "\n",
            " Episodio : 65 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 65  Step totali 12\n",
            " \n",
            "\n",
            " Episodio : 66 \n",
            "\n",
            "U......G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 66  Step totali 12\n",
            " \n",
            "\n",
            " Episodio : 67 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 67  Step totali 18\n",
            " \n",
            "\n",
            " Episodio : 68 \n",
            "\n",
            "U......G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 68  Step totali 18\n",
            " \n",
            "\n",
            " Episodio : 69 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 69  Step totali 8\n",
            " \n",
            "\n",
            " Episodio : 70 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 70  Step totali 12\n",
            " \n",
            "\n",
            " Episodio : 71 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 71  Step totali 18\n",
            " \n",
            "\n",
            " Episodio : 72 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 72  Step totali 16\n",
            " \n",
            "\n",
            " Episodio : 73 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 73  Step totali 8\n",
            " \n",
            "\n",
            " Episodio : 74 \n",
            "\n",
            "U......G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 74  Step totali 14\n",
            " \n",
            "\n",
            " Episodio : 75 \n",
            "\n",
            "U......G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 75  Step totali 8\n",
            " \n",
            "\n",
            " Episodio : 76 \n",
            "\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 76  Step totali 10\n",
            " \n",
            "\n",
            " Episodio : 77 \n",
            "\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 77  Step totali 8\n",
            " \n",
            "\n",
            " Episodio : 78 \n",
            "\n",
            "U......G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 78  Step totali 8\n",
            " \n",
            "\n",
            " Episodio : 79 \n",
            "\n",
            "..U....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 79  Step totali 8\n",
            " \n",
            "\n",
            " Episodio : 80 \n",
            "\n",
            ".U.....G\t  +++!exploitation!+++\n",
            ".U.....G\t  +++!exploitation!+++\n",
            "..U....G\t  +++!exploitation!+++\n",
            "...U...G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            "....U..G\t  +++!exploitation!+++\n",
            ".....U.G\t  +++!exploitation!+++\n",
            "......UG\t  +++!exploitation!+++\n",
            ".......U\n",
            " \t Numero Episodi 80  Step totali 10\n",
            " \n",
            "Tabella Q \n",
            "    sinistra  destra\n",
            "0     0.070   0.407\n",
            "1     0.252   0.566\n",
            "2     0.386   0.645\n",
            "3     0.474   0.725\n",
            "4     0.591   0.808\n",
            "5     0.685   0.899\n",
            "6     0.768   1.000\n",
            "7     0.000   0.000 \n",
            "\n",
            " ** Fine addestramento ** \n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Optimal policy\n",
        "\n",
        "Qui sarà mostrata la policy ottenuta dall'addestramento precedente. Di fatto sfruttando la tabella Q"
      ],
      "metadata": {
        "id": "z01olN_vjOmK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def policy(q_table):\n",
        "\n",
        "  step_counter = 1\n",
        "  S = 1    # stato iniziale\n",
        "  update_env(S)\n",
        "\n",
        "  while S != 7 :\n",
        "\n",
        "    state_actions = q_table.iloc[S]\n",
        "    #print(\"\")\n",
        "    #print(\"\\n\",state_actions,\"\\n\")\n",
        "    A = state_actions.idxmax()\n",
        "    \n",
        "    S, R = env_feedback(S, A)\n",
        "\n",
        "    update_env(S)\n",
        "\n",
        "    if S == 7 :\n",
        "         print(f'\\n Step totali {step_counter}\\n ') \n",
        "\n",
        "    step_counter += 1\n"
      ],
      "metadata": {
        "id": "uP8tGijnjmst"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "policy(q_table)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IhAOmJKroBwN",
        "outputId": "6c050965-f03b-4273-b4d5-4ca1769e290c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            ".......U\n",
            " Step totali 6\n",
            " \n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Modulando diversamente gli iperparametri"
      ],
      "metadata": {
        "id": "TAx7OXSYtU-N"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "N_STATES = 8  # numero di stati\n",
        "ACTIONS = ['sinistra', 'destra']     # azioni disponibili\n",
        "\n",
        "#IPER-PARAMETRI\n",
        "EPSILON = 0.81   # gestisci ϵ-greedy policy\n",
        "ALPHA = 0.1      # learning rate\n",
        "GAMMA = 0.9      # discount factor\n",
        "\n",
        "MAX_EPISODES = 40   # episodi massimi\n",
        "FRESH_TIME = 0.3    # fresh time display"
      ],
      "metadata": {
        "id": "5BJWLLAJ0juP"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(q_table)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gKU0ZSRfpL4p",
        "outputId": "246cd187-f617-4c7e-be22-b6c868071dba"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "   sinistra    destra\n",
            "0  0.000000  0.005958\n",
            "1  0.000211  0.169526\n",
            "2  0.020184  0.325069\n",
            "3  0.104797  0.465046\n",
            "4  0.040691  0.659556\n",
            "5  0.117890  0.847656\n",
            "6  0.288724  0.985219\n",
            "7  0.000000  0.000000\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "EPSILON = 0.81   # gestisci ϵ-greedy policy\n",
        "ALPHA = 0.1      # learning rate\n",
        "GAMMA = 0.1      # discount factor"
      ],
      "metadata": {
        "id": "Ir4muJJopDhc"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(q_table) #GAMMA = 0.1  dove i valori predominati sono nello stato 5 e 6. Molto bassi tutti gli altri "
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0d628bfvt92q",
        "outputId": "74f04c73-412d-432a-cb22-32472891cb90"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "       sinistra        destra\n",
            "0  0.000000e+00  1.690645e-09\n",
            "1  6.735730e-13  2.614330e-06\n",
            "2  9.055290e-09  4.496585e-05\n",
            "3  1.174883e-06  6.246055e-04\n",
            "4  9.335158e-06  8.089074e-03\n",
            "5  1.783729e-04  9.232708e-02\n",
            "6  6.881895e-04  9.852191e-01\n",
            "7  0.000000e+00  0.000000e+00\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "EPSILON = 0.81   # gestisci ϵ-greedy policy\n",
        "ALPHA = 0.1      # learning rate\n",
        "GAMMA = 0.5 "
      ],
      "metadata": {
        "id": "5e8Ht_QLtv_7"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(q_table) # GAMMA = 0.5 "
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5eOb8z8Sv-d_",
        "outputId": "3b08aff6-5413-4840-e947-e51e03d10970"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "       sinistra    destra\n",
            "0  4.226563e-10  0.000625\n",
            "1  2.491766e-05  0.008455\n",
            "2  6.083577e-04  0.026977\n",
            "3  2.310078e-04  0.079557\n",
            "4  4.340388e-03  0.203910\n",
            "5  1.695573e-02  0.464940\n",
            "6  4.881299e-02  0.985219\n",
            "7  0.000000e+00  0.000000\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "EPSILON = 0.81   # gestisci ϵ-greedy policy\n",
        "ALPHA = 0.8      # learning rate\n",
        "GAMMA = 0.9 "
      ],
      "metadata": {
        "id": "iXLiSq2Xs4wM"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(q_table) # ALPHA = 0.8"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ruoA-PQhwT3l",
        "outputId": "b5ef2341-f0ff-4dc9-d8f5-0a9652133598"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "   sinistra    destra\n",
            "0  0.228537  0.488635\n",
            "1  0.244586  0.590490\n",
            "2  0.531429  0.656100\n",
            "3  0.585529  0.729000\n",
            "4  0.647399  0.810000\n",
            "5  0.718950  0.900000\n",
            "6  0.630374  1.000000\n",
            "7  0.000000  0.000000\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Problema RL più articolato\n",
        "\n",
        "Nuovo Ambiente, e nuovi obbiettivi:\n",
        "\n",
        "L'agente \"U\", partendo dallo stato \"I\", deve imparare a raggiungere lo stato \"B\" (Bottino )e poi uscire nello stato \"G\" (Goal), muovendosi a destra o sinistra.\n",
        "\n",
        "[. B . I . . . G]\n",
        "\n",
        "Ambiente :\n",
        "- Insieme finito di 8 stati,  S: [0,1,2,3,4,5,6,7]. Dove l'ultimo stato, il 7, è il Goal da raggiungere. Stato iniziale S = 3\n",
        "- Insieme di finito di 2 azioni discrete,  A : [\"desta\", \"sinistra\"]\n",
        "- Funzione di transizione da uno stato all'altro, deterministica :  \n",
        "   - input: (azione \"destra\", stato S)     -> output :      S+1\n",
        "   - input: (azione \"sinistra\", stato S)   -> output :    S-1\n",
        "   - input: (azione \"sinistra\", stato S=0) -> output :  S=0\n",
        "   - Stato S = 7, fine.\n",
        "- Segnale di Reward R(S,A). Cioè la ricompensa ottenuta partendo dallo stato S agendo secondo l’azione A. Anche questa funzione è determinisitca : \n",
        "    - per ogni spostamento; reward immediato = 0\n",
        "    - in caso di raggiugimento dello stato S = 1 , reward immediato = + 0.3, se Flag \"Prima_volta == True \"; altrimenti: reward immediato = 0\n",
        "    - in caso di raggiugimento dello stato S = 7 , reward immediato = +1\n",
        "\n",
        "*Soluzione*\n",
        "\n",
        "Per risolvere questo ambiente sono necessarie due q_table. La prima per raggiungere il Bottino, cioè lo stato S1. La seconda, una volta ottenuto il Bottino (e lo Stato S1 ha come valore di reward = 0, come tutti gli altri stati), per raggiungere lo stato Goal.  "
      ],
      "metadata": {
        "id": "Ba5QQPCXqIjk"
      }
    }
  ]
}