Assignment_1_Matplotlib_Portilla_.ipynb

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      "name": "Assignment_1_Matplotlib-Portilla .ipynb",
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      "cell_type": "markdown",
      "metadata": {
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        "<a href=\"https://colab.research.google.com/github/AzizOzmen/Clarusway_Data_Science_Materials/blob/main/Assignment_1_Matplotlib_Portilla_.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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        "id": "9rQArTiMmKBZ"
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      "source": [
        "___\n",
        "\n",
        "<a href='http://www.pieriandata.com'> <img src='../Pierian_Data_Logo.png' /></a>\n",
        "___\n",
        "# Matplotlib Exercises \n",
        "Welcome to the exercises for reviewing matplotlib! Take your time with these, Matplotlib can be tricky to understand at first. These are relatively simple plots, but they can be hard if this is your first time with matplotlib, feel free to reference the solutions as you go along.\n",
        "\n",
        "Also don't worry if you find the matplotlib syntax frustrating, we actually won't be using it that often throughout the course, we will switch to using seaborn and pandas built-in visualization capabilities. But, those are built-off of matplotlib, which is why it is still important to get exposure to it!\n",
        "\n",
        "**NOTE: ALL THE COMMANDS FOR PLOTTING A FIGURE SHOULD ALL GO IN THE SAME CELL. SEPARATING THEM OUT INTO MULTIPLE CELLS MAY CAUSE NOTHING TO SHOW UP.**\n",
        "\n",
        "# Exercises\n",
        "\n",
        "**We will focus on two commons tasks, plotting a known relationship from an equation and plotting raw data points.**\n",
        "\n",
        "Follow the instructions to complete the tasks to recreate the plots using this data:\n",
        "\n",
        "----\n",
        "----\n",
        "\n",
        "### Task One: Creating data from an equation\n",
        "\n",
        "It is important to be able to directly translate a real equation into a plot. Your first task actually is pure numpy, then we will explore how to plot it out with Matplotlib. The [world famous equation](https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence) from Einstein:\n",
        "\n",
        "$$E=mc^2$$\n",
        "\n",
        "\n",
        "Use your knowledge of Numpy to create two arrays: E and m , where **m** is simply 11 evenly spaced values representing 0 grams to 10 grams. E should be the equivalent energy for the mass. You will need to figure out what to provide for **c** for the units m/s, a quick google search will easily give you the answer (we'll use the close approximation in our solutions).\n",
        "\n",
        "**NOTE: If this confuses you, then hop over to the solutions video for a guided walkthrough.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dCp45XRBmKBd",
        "outputId": "9d0b1300-3c86-4789-9d62-81f5e28ef7ff"
      },
      "source": [
        "# CODE HERE\n",
        "import numpy as np\n",
        "\n",
        "m = np.linspace(0, 10, 11)\n",
        "print(\"The array m should look like this: \\n\\n{}\".format(m))"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The array m should look like this: \n",
            "\n",
            "[ 0.  1.  2.  3.  4.  5.  6.  7.  8.  9. 10.]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EsKpmH0MvlYu",
        "outputId": "b122025d-9c7f-41d5-c6a8-d776f6759d85"
      },
      "source": [
        "m.dtype"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "dtype('float64')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ouNpv7vfmKBe",
        "outputId": "d8dfe8de-2277-4830-b94d-1f6313286bf0"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The array m should look like this: \n",
            "\n",
            "[ 0.  1.  2.  3.  4.  5.  6.  7.  8.  9. 10.]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CJZ8zHpLuIDm",
        "outputId": "793f8ba8-7cc2-4be0-de55-5cf0c31f05dd"
      },
      "source": [
        "c = 3 * 10**8  # speed of light is approximately 3×10**8 meters per second\n",
        "c"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "300000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TArPJy3nmKBg",
        "outputId": "84b8d4c6-739d-45b3-d640-a295a32bf894"
      },
      "source": [
        "# CODE HERE\n",
        "\n",
        "c = 3 * 10**8\n",
        "E = m*c**2\n",
        "print(\"The array E should look like this: \\n\\n{}\".format(E))"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The array E should look like this: \n",
            "\n",
            "[0.0e+00 9.0e+16 1.8e+17 2.7e+17 3.6e+17 4.5e+17 5.4e+17 6.3e+17 7.2e+17\n",
            " 8.1e+17 9.0e+17]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IRBhrYTCmKBh",
        "outputId": "58aec762-10b4-4229-952f-94b17685039a"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The array E should look like this: \n",
            "\n",
            " [0.0e+00 9.0e+16 1.8e+17 2.7e+17 3.6e+17 4.5e+17 5.4e+17 6.3e+17 7.2e+17\n",
            " 8.1e+17 9.0e+17]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nGOJ9BQlmKBh"
      },
      "source": [
        "### Part Two: Plotting E=mc^2\n",
        "\n",
        "Now that we have the arrays E and m, we can plot this to see the relationship between Energy and Mass. \n",
        "\n",
        "**TASK: Import what you need from Matplotlib to plot out graphs:**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "644pvtJOmKBi"
      },
      "source": [
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 28,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bgzaNaoRmKBj"
      },
      "source": [
        "**TASK: Recreate the plot shown below which maps out E=mc^2 using the arrays we created in the previous task. Note the labels, titles, color, and axis limits. You don't need to match perfectly, but you should attempt to re-create each major component.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "L3q_RBsnmKBj",
        "outputId": "87aab896-c84b-4836-95d6-6f5916784e94"
      },
      "source": [
        "# CODE HERE\n",
        "\n",
        "plt.plot(m, E, color=\"red\", lw=5)\n",
        "plt.xlabel(\"Mass in Grams\")\n",
        "plt.ylabel(\"Energy in Joules\")\n",
        "plt.title(\"E=mc^2\")\n",
        "plt.xlim(0,10);"
      ],
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 366
        },
        "id": "AOWJV9zZ02f3",
        "outputId": "bdf82b04-3fdc-45e6-8146-14cc09a203c3"
      },
      "source": [
        "fig = plt.figure()\n",
        "\n",
        "ax1 = fig.add_axes([0,0,1,1])\n",
        "ax1.plot(m, E, color=\"red\", lw=5)\n",
        "plt.xlabel(\"Mass in Grams\")\n",
        "plt.ylabel(\"Energy in Joules\")\n",
        "plt.title(\"E=mc^2\")\n",
        "plt.xlim(0,10);"
      ],
      "execution_count": 62,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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w4bCZxsCB8eF74YXwzDNhhKzwldOkEbCIiDusXh3O6W1ujq7r1QumTIFx46B79/T6k6KU6AjYzP7GzB4zs1+Z2Utm9ukkP09E5JTt3QuXXw5f+lJ8+A4bBi+9BJMmKXylSyQ9Av4e8GN3/5KZdQd6Jfx5IiLZOXIE7rkHZs6Eo0ej66qq4P77YciQ9HqTkpBYAJvZOcBlwA0A7n4UiPmvXEQkJevWhVuL9u2LrunRI+x2NXEi9OyZXm9SMpKcgj4feB1YZma/MLMHzaz3iUVm9nUze87Mnnv99dcTbEdESt7+/XD11XDllfHhO3QovPhiuN6r8JWEJBnAZwEfBx5w948BbwG3nVjk7ovcvdbdayt087qIJKG1FaZPD6uX166NrqushDVrwgi5qiq9/qQkJRnAzUCzu2/LPH6MEMgiIunZsCHsUjV5crju25lu3eD228P9v1dfHU4wEklYYteA3f1VM/utmfV3993A54CmpD5PROQdDhyA8eNh1ar4uvr6cJ5vdXU6fYlkJL0KehSwIrMC+mVgRMKfJyKlrq0tbB15111hY40o/frB7Nlw7bUa8UpOnDSAzayKMJXcamafAWqA5e7+5sle6+6NgM7iEpF0bNkSTizatSu6pqwsrICeOhX69k2tNZETZXMN+HHgmJn9HbAI+CDwSKJdiYicioMH4frr4bLL4sO3rg527gwjX4Wv5Fg2Adzu7m8D1wD3ufu/Atr8VERy79gxWLAgnFi0fHl0XUUFLFsGmzeHBVkieSCba8BtZvYV4Hrgysxz3ZJrSUQkC9u3h+nmHTuia8xg5EiYNg3Ky9PrTSQL2YyARwCfBqa5+z4zOx/438m2JSIS4dAh+MY34FOfig/fwYNDSC9YoPCVvHTSEbC7N5nZJKAy83gfMDPpxkRE3qG9PUwjT5oUQjhKeXnY4/nGG8OCK5E8ddIRsJldCTQCP848/qiZPZF0YyIif9HYCJdeGkI1LnxHjIDdu8MIWeEreS6bKeipwCeAN+EvtxZ9KMGeRESClhYYMwYGDYKGhui6mhrYuhWWLg0LrkQKQDYB3ObuLSc8155EMyIiALjDihVhd6p588L0c2f69IG5c8O14Lq6dHsUOUPZrIJ+0cyGA2VmdgEwGvhZsm2JSMlqaoKbb4ZNm+Lrhg+HWbPCjlYiBSibEfAoYADQCqwE/giMTbIpESlBhw+HBVYDB8aHb3U1bNwYRsgKXylg2ayC/jMwOfMlItK13GH1ahg7Fpqbo+t69Qrn844bB927p9efSEIiA9jMfgR41M/d/YuJdCQipWPvXhg1Ctavj68bNgzmzAnn9YoUibgR8KzUuhCR0nLkCMyYEb6OHo2uq6oKJxtdfnl6vYmkJDKA3f0/0mxERErEk0+GUe++fdE1PXrA7beHa8I9e6bXm0iKsjmOcB+dTEW7u+4FFpHs7d8f7ulduza+bujQcOtRVVU6fYnkSDa3IXU8z7cn8E/Ae5JpR0SKTmsr3HsvfOc7Yeo5SmUlfO97cNVV4RAFkSKXzSroE/d9m2tmO4ApybQkIkVjw4ZwT++ePdE13brBrbfCnXdC797p9SaSY9lMQX+8w8N3EUbE2YycRaRUHTgA48fDqlXxdfX1MH9+uLdXpMRkE6T3dvj+beAV4MuJdCMiha2tLaxavuuusLFGlH79YPZsuPZaTTdLycpmCvqzaTQiIgVuyxa46SbYtSu6pqwMRo+GqVOhb9/UWhPJR9kcR3iOmc02s+cyX/ea2TlpNCciBeDgQbj+erjssvjwrauDnTvDyFfhK5LVXtBLgT8Rpp2/TNgLelmSTYlIATh2LFy/7d8fli+PrquogGXLYPPmcGygiADZXQOucvd/7PD4W2bWmFRDIlIAtm0L0807d0bXmMHIkTBtGpSXp9ebSIHIZgR8xMwuPf7AzOqAmJv5RKRoHToE3/gGfPrT8eE7eDBs3w4LFih8RSJkMwL+JvBw5rqvAW8ANyTZlIjkmfb2MI08aVII4Sjl5XDPPXDjjWHBlYhEymYVdCMw0Mz6Zh7/MfGuRCR/NDaG6eaGhvi6ESNg5sxwzVdETiruOMLxEc8DtAL/F3ja3duTaU1EcqqlBf7t38JCq/aY/81rasJUc11der2JFIG4EXCfmJ+VA58DvoY25RApLu7wyCNhe8iDB6Pr+vSBb387bDV5ljbHEzlVcccRfutkLzaz57u2HRHJqaamEKibNsXXDR8Os2aFHa1E5LRkswo6krvrpj6RYnD4MEycCAMHxodvdTVs3AgrVih8Rc6Q5o1ESpk7PP44jBsHzc3Rdb16wZQpoa579/T6EyliCmCRUrV3L9xyCzz9dHzdsGEwZ044r1dEukw2xxH2AP4ROK9jvbvfnVxbIpKYI0fCvbozZ8LRo9F1VVXhZKPLL0+vN5ESks0IeC3QAuwg3H4kIoVq3bpwGtG+fdE1PXrA7beHTTd69kyvN5ESk00An+vuQxLvRESS88orMGYMPPFEfN3QoTBvXhj9ikiislkF/TMz+0jinYhI12ttDYchXHRRfPhWVsKaNWGErPAVSUU2I+BLgRvMbB9hCtoA1y1IInluw4ZwT++ePdE13brBhAkweTL07p1ebyKSVQBrBYZIITlwAMaPh1Wr4uvq68M2k9XV6fQlIu8Qtxd038zBC39KsR8ROV1tbeH67dSpYWONKP36wezZcO214cxeEcmJuBHwI8AVhNXPTph6Ps6BDyXYl4icii1bwolFu3ZF15SVhRXQU6dC376ptSYinYvbC/qKzD/PT68dETklBw+GLSSXL4+vq6sLJxbVaOmGSL44o72gRSRHjh0L12/7948P34oKWLYMNm9W+IrkGW1FKVJotm0L0807d0bXmMHIkeEWpPLy9HoTkawpgEUKxaFDYYeqBx8MhyhEGTw4TDfX1qbXm4icspNOQZvZvWY2II1mRKQT7e2wZEmYbl68ODp8y8th4UJoaFD4ihSAbEbALwGLzOwsYBmw0t1bkm1LRABobAzTzQ0N8XUjRoTDFSoq0ulLRM7YSUfA7v6gu9cB/0I4Eel5M3vEzD6bdHMiJaulJdwyNGhQfPjW1MDWrbB0qcJXpMBktQrazMqA6szXH4BfAuPN7AcJ9iZSetxhxYow3XzffWH6uTN9+sDcubBjR7jFSEQKTjbnAc8BrgQ2AtPdfXvmRzPNbHeSzYmUlKamsHfzpk3xdcOHw6xZYUcrESlY2VwDfh64093f6uRnnzjZizOj5+eAA8c39xCRDg4fhrvvhjlz4O23o+uqq8O9v/X16fUmIonJJoB/CfS3d+4Z2wLsz3Ix1hjCQi7tfSfSkTusXg1jx0Jzc3Rdr14wZQqMGwfdu6fXn4gkKpsAXgB8nDASNuBi4EXgHDP7prs/HfVCMzsX+AIwDRh/5u2KFIm9e2HUKFi/Pr5u2LAwMq6sTKcvEUlNNouwfgd8zN1r3X0Q8DHgZeDzwHdP8tq5wEQgYiUJmNnXzew5M3vu9ddfz7JtkQJ15EgYzV58cXz4VlXBU0/B448rfEWKVDYB/GF3f/H4A3dvAqrd/eW4F5nZFcBr7r4jrs7dF2XCvbZCt1FIMVu3DgYMgG9/G44e7bymR49wWtGuXXC5juIWKWbZTEE3mdkDwPFbjq7NPNcDaIt5XR3wRTMbCvQE+prZ9939n8+oY5FC88orMGYMPPFEfN3QoeE836qqVNoSkdzKZgR8PfBrYGzm62XgBkL4Rm7G4e63u/u57n4ecB3wjMJXSkprK0yfDhddFB++lZWwZk0YISt8RUpG7Ag4cwvRU+7+WeDeTkoOJ9KVSKHbsCHc07tnT3RNt25w661w553Qu3d6vYlIXogNYHc/ZmbtZnbOmez/7O6bgE2n+3qRgnHgAIwfD6tWxdfV14d7equr0+lLRPJONteADwMvmNlPgL9sxuHuoxPrSqTQtLWFrSPvuitsrBGlXz+YPRuuvTac2SsiJSubAF6d+RKRzmzZEk4s2rUruqasLByuMHUq9NWeNCKSRQC7+8NmdjZQ6e7a+1nkuIMHYeJEWL48vq6uDhYsCCcXiYhknHQVtJldCTQCP848/qiZneR+CpEiduxYCNT+/ePDt6ICli2DzZsVviLyV7K5DWkq4dCFNwHcvRH4UII9ieSv7dvhk58MK5xbItYlmsE3vwm7d8MNN8C7sjr1U0RKTDbXgNvcveWEwxgit5YUKUqHDsEdd8DixeEQhSi1tWF0PHhwer2JSEHK5q/mL5rZcKDMzC4ws/uAnyXcl0h+aG+HJUvCdPOiRdHhW14ODzwA//mfCl8RyUo2ATwKGAC0AiuBPxJ2xBIpbo2NcOmlcOONYQQcZcSIMN08cmRY7SwikoVsVkH/GZic+RIpfi0t4cSi++8PI+AoNTVhurmuLr3eRKRonDSAzezDwATgvI717l6fXFsiOeAOjzwCEybAq69G1/XpE040uvlmOCubZRQiIn8tmz89/h1YCDwIHEu2HZEcaWoKgbppU3zdV74Cs2bB+9+fSlsiUryyCeC33f2BxDsRyYXDh8NodvZsePvt6Lrq6rB3c70mfkSka2QTwD8ys5uANYSFWAC4+xuJdSWSNHdYvRrGjoXm5ui6Xr3C9eBx46B79/T6E5Gil00AX5/55792eM7RZhxSqPbuhVGjYP36+LprroG5c8N5vSIiXSybVdDnp9GISOKOHIEZM8LX0aPRdVVV4WSjyy9PrzcRKTmR9wGb2cQO3//TCT+bnmRTIl3uySdhwAC4++7o8O3RI5xWtGuXwldEEhe3Ecd1Hb6//YSfDUmgF5Gut38/XH01XHEF7NsXXTd0KLz4YjjPt2fP9PoTkZIVF8AW8X1nj0XyS2srTJ8OF14Ia9dG11VWwpo1sG5dmHoWEUlJ3DVgj/i+s8ci+WPDhnBP75490TXdusGtt8Kdd0Lv3un1JiKSERfAA83sj4TR7tmZ78k81hyd5J8DB0KoPvpofF19fbint7o6nb5ERDoRGcDurl3lpTC0tYVVy3fdFTbWiNKvX9hw49prw5m9IiI5pI1spbBt2QI33RRWLkcpK4PRo8MK5759U2tNRCSOAlgK02uvwcSJ8PDD8XV1deHEopqadPoSEclSNucBi+SPY8dCoPbvHx++FRWwbBls3qzwFZG8pBGwFI7t28N0844d0TVmMHIkTJsG5eXp9SYicooUwJL/3ngDbr8dFi8OhyhEGTw4jI5ra9PrTUTkNGkKWvJXezssXRqmmxctig7f8nJ44AFoaFD4ikjB0AhY8lNjY5hubmiIrxsxAmbODNd8RUQKiEbAkl9aWmDMGBg0KD58a2pg69YwQlb4ikgBUgBLfnCHFSvC7lTz5oXp58706RPO6N2xI9xiJCJSoDQFLbnX1AS33AI//Wl83fDhMGtW2NFKRKTAaQQsuXP4MEyaBAMHxodvdTVs3BhGyApfESkSGgFL+txh9WoYOxaam6PrevWCKVNg3Djo3j29/kREUqAAlnTt3QujRsH69fF1w4bBnDnhvF4RkSKkAJZ0HDkCM2aEr6NHo+uqqsLJRpdfnl5vIiI5oACW5D35ZBj17tsXXdOjR9jtatIk6KnjpkWk+CmAJTn794d7eteuja8bOjTcelRVlU5fIiJ5QKugpeu1tsL06XDhhfHhW1kJa9bAunUKXxEpORoBS9fasCHc07t7d3RNt25w661w553Qu3d6vYmI5BEFsHSNAwdCqD76aHxdfT3Mnx/u7RURKWGagpYz09YGs2eHQI0L3379YOXKMEJW+IqIaAQsZ2DLlnBi0a5d0TVlZTB6NEydCn37ptaaiEi+UwDLqXvtNZg4ER5+OL6urg4WLAgnF4mIyDtoClqyd+xYCNT+/ePDt6ICli2DzZsVviIiETQCluxs3x6mm3fsiK4xg5EjYdo0KC9PrzcRkQKkAJZ4hw7BHXfA4sXhEIUogweH0XFtbXq9iYgUME1BS+fa22HJkjDdvGhRdPiWl8PChdDQoPAVETkFGgHLX2tsDNPNDQ3xdSNGwMyZ4ZqviIicEo2A5b+0tIS9mwcNig/fmhrYuhWWLlX4ioicpsQC2Mw+aGY/NbMmM3vRzMYk9VlyhtxhxYqwQca8eWH6uTN9+sq8mi4AAA6ZSURBVMDcuWEhVl1duj2KiBSZJKeg3wZudfedZtYH2GFmP3H3pgQ/U05VUxPcfDNs2hRfN3w4zJoVdrQSEZEzltgI2N1/7+47M9//CXgJ+EBSnyen6PDhcPbuwIHx4VtdDRs3hhGywldEpMuksgjLzM4DPgZsS+PzJIY7rF4NY8dCc3N0Xa9eMGUKjBsH3bun15+ISIlIPIDN7N3A48BYd/9jJz//OvB1gMrKyqTbKW1798KoUbB+fXzdsGEwZ044r1dERBKR6CpoM+tGCN8V7r66sxp3X+Tute5eW6EVtck4ciSMZi++OD58q6rgqafg8ccVviIiCUtsBGxmBiwBXnL32Ul9jpzEunXhNKJ9+6JrevSA228P14R79kyvNxGREpbkFHQd8FXgBTNrzDx3h7s/leBnynH794d7eteuja8bOjTcelRVlU5fIiICJBjA7r4VsKTeXyK0tsK998J3vhOmnqNUVsL3vgdXXRUOURARkVRpK8pismFDuKd3z57omm7d4NZb4c47oXfv9HoTEZF3UAAXgwMHYPx4WLUqvq6+HubPD/f2iohITmkv6ELW1gazZ4dAjQvffv1g5cowQlb4iojkBY2AC9WWLeHEol27omvKysIK6KlToW/f1FoTEZGTUwAXmoMHYeJEWL48vq6uDhYsCCcXiYhI3tEUdKE4diwEav/+8eFbUQHLlsHmzQpfEZE8phFwIdi+PUw379gRXWMGI0fCtGlQXp5ebyIicloUwPns0CG44w5YvDgcohBl8OAwOq6tTa83ERE5I5qCzkft7bBkSZhuXrQoOnzLy2HhQmhoUPiKiBQYjYDzTWNjmG5uaIivGzECZs4M13xFRKTgaAScL1pawt7NgwbFh29NDWzdCkuXKnxFRAqYAjjX3GHFirBBxrx5Yfq5M336wNy5YSFWXV26PYqISJfTFHQuNTWFvZs3bYqvGz4cZs0KO1qJiEhR0Ag4Fw4fDmfvDhwYH74XXgjPPBNGyApfEZGiohFwmtxh9WoYOxaam6PrevWCKVNg3Djo3j29/kREJDUK4LTs3QujRsH69fF1w4bBnDnhvF4RESlaCuCkHTkCM2aEr6NHo+uqquD++2HIkPR6ExGRnFEAJ+nJJ8Ood9++6JoePcJuVxMnQs+e6fUmIiI5pQBOwv794Z7etWvj64YODbceVVWl05eIiOQNrYLuSq2tMH16WL0cF76VlbBmDaxbp/AVESlRGgF3lY0bwz29u3dH13TrBhMmwOTJ0Lt3er2JiEjeUQCfqQMH4NZb4dFH4+vq62H+/LDjlYiIlDxNQZ+utjaYPTsEalz49usHK1fChg0KXxER+QuNgE/Hli1huvmFF6Jryspg9GiYOhX69k2tNRERKQwK4FPx2mvhdqGHH46vu/TSMN1cU5NOXyIiUnA0BZ2NY8dgwQLo3z8+fCsq4KGHYPNmha+IiMTSCPhktm+Hm24KxwBGMYNvfhO+8x0oL0+vNxERKVgK4ChvvAG33w6LF4dDFKIMHhxGx7W16fUmIiIFT1PQJ2pvh6VLw3TzokXR4VteDgsXQkODwldERE6ZRsAdNTaG6eaGhvi6r30tHK5QUZFOXyIiUnQ0AgZoaQl7Nw8aFB++NTXw7LOwZInCV0REzkhpB7A7rFgRNsiYNy9MP3emTx+YOzcsxLrkknR7FBGRolS6U9BNTWEzjU2b4uuGD4dZs8KOViIiIl2k9EbAhw/DpEkwcGB8+F54ITzzTBghK3xFRKSLlc4I2B1Wr4axY6G5ObquVy+YMgXGjYPu3dPrT0RESkppBPDevTBqFKxfH183bBjMmRPO6xUREUlQcQfwkSPhdqEZM+Do0ei6qiq4/34YMiS93kREpKQVbwA/+WQY9e7bF13TowfccUc4YKFnz/R6ExGRkld8Abx/f7ind+3a+LqhQ8OtR1VV6fQlIiLSQfGsgm5thenTw+rluPCtrIQ1a2DdOoWviIjkTHGMgDdsCPf07tkTXdOtG0yYAJMnQ+/e6fUmIiLSicIO4AMHYPx4WLUqvq6+HubPDzteiYiI5IHCnIJua4PZs0OgxoVvv36wcmUYISt8RUQkjxTeCHjLlnBi0a5d0TVlZTB6NEydCn37ptaaiIhItgongA8eDLcLLV8eX1dXBwsWhJOLRERE8lT+T0EfOxYCtX//+PCtqIBly2DzZoWviIjkvfweAW/fHqabd+yIrjGDkSNh2jQoL0+vNxERkTOQnwF86FDYoWrx4nCIQpTBg8PouLY2vd5ERES6QP5NQS9ZEqabFy2KDt/ycli4EBoaFL4iIlKQEg1gMxtiZrvN7NdmdttJX/CrX8GNN4YRcJQRI2D3bvjGN8JqZxERkQKU2BS0mZUB84HPA83Az83sCXdvinzRW29Fv2FNTZhurqvr4k5FRETSl+QI+BPAr939ZXc/CvwAuOqU36VPH5g7NyzEUviKiEiRSDKAPwD8tsPj5sxz2Rs+PEw3jxkDZ+XnejEREZHTkfNFWGb2dTN7zsye+8uT1dWwcSOsWBG2kxQRESkySQbwAeCDHR6fm3nuHdx9kbvXunst73oXzJgBv/xlOEBBRESkSCUZwD8HLjCz882sO3Ad8ETsKwYMgEmToHv3BNsSERHJvcQurLr722Z2C7AeKAOWuvuLsS9S8IqISIlIdGWTuz8FPJXkZ4iIiBSinC/CEhERKUUKYBERkRxQAIuIiOSAAlhERCQHFMAiIiI5oAAWERHJAQWwiIhIDiiARUREcsDcPdc9/IWZ/QnYnes+itB7gT/kuokipN9rcvS7TYZ+r8np7+59TuUF+XbG3253r811E8XGzJ7T77Xr6feaHP1uk6Hfa3LecaJfljQFLSIikgMKYBERkRzItwBelOsGipR+r8nQ7zU5+t0mQ7/X5Jzy7zavFmGJiIiUinwbAYuIiJSEvAhgMxtiZrvN7Ndmdluu+ykWZvZBM/upmTWZ2YtmNibXPRUTMyszs1+Y2bpc91IszOxvzOwxM/uVmb1kZp/OdU/FwszGZf4c2GVmK82sZ657KkRmttTMXjOzXR2ee4+Z/cTM9mb+WZ7Ne+U8gM2sDJgPXA5cBHzFzC7KbVdF423gVne/CPgUcLN+t11qDPBSrpsoMt8Dfuzu1cBA9PvtEmb2AWA0UOvuFwNlwHW57apgPQQMOeG524CN7n4BsDHz+KRyHsDAJ4Bfu/vL7n4U+AFwVY57Kgru/nt335n5/k+EP8w+kNuuioOZnQt8AXgw170UCzM7B7gMWALg7kfd/c3cdlVUzgLONrOzgF7A73LcT0Fy983AGyc8fRXwcOb7h4Grs3mvfAjgDwC/7fC4GYVElzOz84CPAdty20nRmAtMBNpz3UgROR94HViWmdp/0Mx657qpYuDuB4BZwG+A3wMt7v50brsqKu9z999nvn8VeF82L8qHAJaEmdm7gceBse7+x1z3U+jM7ArgNXffketeisxZwMeBB9z9Y8BbZDmVJ/Ey1ySvIvwl5/1AbzP759x2VZw83FqU1e1F+RDAB4APdnh8buY56QJm1o0QvivcfXWu+ykSdcAXzewVwiWTejP7fm5bKgrNQLO7H5+leYwQyHLm/gHY5+6vu3sbsBq4JMc9FZODZtYPIPPP17J5UT4E8M+BC8zsfDPrTlgY8ESOeyoKZmaE62kvufvsXPdTLNz9dnc/193PI/z3+oy7azRxhtz9VeC3ZtY/89TngKYctlRMfgN8ysx6Zf5c+Bxa4NaVngCuz3x/PbA2mxfl/DAGd3/bzG4B1hNW5i119xdz3FaxqAO+CrxgZo2Z5+5w96dy2JNInFHAisxfxl8GRuS4n6Lg7tvM7DFgJ+HuiF+gXbFOi5mtBD4DvNfMmoG7gBnAKjP7n8B+4MtZvZd2whIREUlfPkxBi4iIlBwFsIiISA4ogEVERHJAASwiIpIDCmAREZEcUACLJMTMvOMGHWZ2lpm9ntTpSWZ2t5n9wym+5hNmtilzistOM3vSzD6SRH8i8k45vw9YpIi9BVxsZme7+xHg8yS4y5u7TzmVejN7H7AKGO7uP8s8dylQBbxwQu1Z7v52V/UqIhoBiyTtKcKpSQBfAVYe/0Fm9NmQOXjgZ8d3gDKzAWa23cwazex5M7vAzHpnRqe/zJzneu2JH2RmD5nZlzLfv2Jm38qMal8ws+pOersFePh4+AK4+1Z3/2GH91toZtuA78b0e4OZ/TBzDuorZnaLmY3P1P2nmb0nUzc6czb182b2g6745YoUMgWwSLJ+AFyXOfy8hneeRvUr4O8zBw9MAaZnnh8JfM/dPwrUEvZIHgL8zt0HZs5z/XEWn/0Hd/848AAwoZOfDyDsjBTnXOASdx8f0y/AxcAwYDAwDfhzpq4B+JdMzW3Ax9y9JvPvKFLSNAUtkiB3fz5zFORXCKPhjs4BHjazCwinp3TLPN8ATM6cObza3fea2QvAvWY2E1jn7luy+Pjjh2/sIIRjrMxIty/wtLuPyTz97+5+7CT9Avw0c+b0n8ysBfhR5vkXCH/xAHiesM3kD4EfZtG/SFHTCFgkeU8QzmJdecLz3yYE18XAlUBPAHd/BPgicAR4yszq3X0P4WSgF4DvmFk213tbM/88Rud/2X6RDqcNufsngX8jBO1xb52s3xM+C8IZya0dvj/+2V8A5mc+8+eZg+FFSpb+BxBJ3lLgTXd/wcw+0+H5c/ivRVk3HH/SzD4EvOzu88ysEqgxs18Bb7j7983sTeDGLuhrPrDNzNZ3uA7cK6a+036zYWbvAj7o7j81s62EU6TeDbx5ai2LFA8FsEjC3L0ZmNfJj75LmNK9E3iyw/NfBr5qZm3Aq4RrrYOB/2Vm7UAb8M0u6OvVzGKumWb2AcIZpn8A7o54SVS/2SgDvm9m5wAGzHN3ha+UNJ2GJCIikgO6BiwiIpIDCmAREZEcUACLiIjkgAJYREQkBxTAIiIiOaAAFhERyQEFsIiISA4ogEVERHLg/wPpxh70zbUWuQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H2gXJJw9mKBk"
      },
      "source": [
        "# DON'T RUN THE CELL BELOW< THAT WILL ERASE THE PLOT!"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_S5Kbyv5mKBl",
        "outputId": "53da4c9c-c176-4cbd-aadd-57679b160f27"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KRZzHkstmKBl"
      },
      "source": [
        "### Part Three (BONUS)\n",
        "\n",
        "**Can you figure out how to plot this on a logarthimic scale on the y axis? Place a grid along the y axis ticks as well. We didn't show this in the videos, but you should be able to figure this out by referencing Google, StackOverflow, Matplotlib Docs, or even our \"Additional Matplotlib Commands\" notebook. The plot we show here only required two more lines of code for the changes.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 366
        },
        "id": "UGI1J8GtmKBm",
        "outputId": "c122d728-9c58-48a9-b323-288ec41dbd5e"
      },
      "source": [
        "# CODE HERE\n",
        "\n",
        "fig = plt.figure()\n",
        "\n",
        "ax1 = fig.add_axes([0,0,1,1])\n",
        "ax1.plot(m, E, color=\"red\", lw=5)\n",
        "plt.grid(axis = 'y', )\n",
        "plt.xlabel(\"Mass in Grams\")\n",
        "plt.ylabel(\"Energy in Joules\")\n",
        "plt.title(\"E=mc^2\")\n",
        "plt.xlim(0,10)\n",
        "ax1.set_yscale('log')\n",
        "plt.grid(True, which=\"minor\");\n"
      ],
      "execution_count": 76,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "9Dy6jIOM53yE",
        "outputId": "5ef132fe-eb10-486c-e4d9-52ba3740920a"
      },
      "source": [
        "plt.plot(m, E, color=\"red\", lw=5)\n",
        "plt.xlabel(\"Mass in Grams\")\n",
        "plt.ylabel(\"Energy in Joules\")\n",
        "plt.title(\"E=mc^2\")\n",
        "plt.xlim(0,10)\n",
        "plt.yscale('log')\n",
        "plt.grid(True, which=\"minor\");"
      ],
      "execution_count": 75,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ijB7XQMNmKBn"
      },
      "source": [
        "# DONT RUN THE CELL BELOW! THAT WILL ERASE THE PLOT!"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_5kLwSccmKBn",
        "outputId": "c43120b3-c677-427c-8182-09d5d7b458fe"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": true,
        "id": "r6XrjyBsmKBn"
      },
      "source": [
        "---\n",
        "---\n",
        "\n",
        "## Task Two: Creating plots from data points\n",
        "\n",
        "In finance, the yield curve is a curve showing several yields to maturity or interest rates across different contract lengths (2 month, 2 year, 20 year, etc. ...) for a similar debt contract. The curve shows the relation between the (level of the) interest rate (or cost of borrowing) and the time to maturity, known as the \"term\", of the debt for a given borrower in a given currency.\n",
        "\n",
        "The U.S. dollar interest rates paid on U.S. Treasury securities for various maturities are closely watched by many traders, and are commonly plotted on a graph such as the one on the right, which is informally called \"the yield curve\".\n",
        "\n",
        "**For this exercise, we will give you the data for the yield curves at two separate points in time. Then we will ask you to create some plots from this data.**\n",
        "\n",
        "## Part One: Yield Curve Data\n",
        "\n",
        "**We've obtained some yeild curve data for you from the [US Treasury Dept.](https://www.treasury.gov/resource-center/data-chart-center/interest-rates/pages/textview.aspx?data=yield). The data shows the interest paid for a US Treasury bond for a certain contract length. The labels list shows the corresponding contract length per index position.**\n",
        "\n",
        "**TASK: Run the cell below to create the lists for plotting.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o-b54NprmKBo"
      },
      "source": [
        "labels = ['1 Mo','3 Mo','6 Mo','1 Yr','2 Yr','3 Yr','5 Yr','7 Yr','10 Yr','20 Yr','30 Yr']\n",
        "\n",
        "july16_2007 =[4.75,4.98,5.08,5.01,4.89,4.89,4.95,4.99,5.05,5.21,5.14]\n",
        "july16_2020 = [0.12,0.11,0.13,0.14,0.16,0.17,0.28,0.46,0.62,1.09,1.31]"
      ],
      "execution_count": 77,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zFDwItsDmKBo"
      },
      "source": [
        "**TASK: Figure out how to plot both curves on the same Figure. Add a legend to show which curve corresponds to a certain year.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "pu-KqdX6mKBp",
        "outputId": "410837b0-2dba-40f3-f86b-5dbaae5460cc"
      },
      "source": [
        "# CODE HERE\n",
        "\n",
        "plt.plot(labels, july16_2007, label = \"july16_2007\")\n",
        "plt.plot(labels, july16_2020, label = \"july16_2020\")\n",
        "plt.legend();"
      ],
      "execution_count": 80,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7effbbad2b10>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 80
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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3kYz62AvM62s9Ebn0RNLyjbWMjAyWL1/O5s2bufLKK2lpaWH27Nm9Pqe1tZWqqipef/11duzYwerVqzl69GivIy7279/PAw88wEsvvdSv+pnZBdvdtGkTS5cuHZRuD9BPyEUkhhISEmhvb+983NP44rvvvpsnn3ySJ554gs997nN9breoqIg/+ZM/wcxYuHAhcXFxVFRU9Lh+SUkJt99+O0899RRTpkwBoLCwkJKSki7rFBYWAjBq1ChOnToFwKlTpy7oWtm4ceOgdXuAglpEYmjChAkcOHCApqYmampqePnll8Out2jRIk6cOMFPf/rTiALwtttuY9u2bYDXDdLc3ExeXl7YdWtqavjYxz7G+vXrWbp0aef8MWPGMGLECF5//XWcczz11FN84hOfAODWW29lw4YNAGzYsKFzPsCZM2fYvn17l3kXS0EtIjFhZowbN47Vq1cza9YsVq9e3eWLve5Wr17N0qVLycnJ6Zy3du1alixZwsGDBykqKuKxxx4DvGF7R48eZdasWaxZs4YNGzb02O3xgx/8gCNHjvCtb32rc2hdWVkZAD/84Q+5++67mTp1KlOmTGHVqlUArFu3ji1btjBt2jR+/etfs27dus7tPfPMM9x0002kp6df9GvUwTrGBQ6m4uJi19f4RxGJjXfeeYcrr7wypnWorKxk/vz5vP/++xE/5+Mf/zhf/epXWbFiRRRrNjTCvQdmtss5VxxufbWoRWRInTx5kiVLlvQ6tjlUTU0NV1xxBampqZdFSA+ETnMqIkNq7NixHDp0KOL1s7Oz+7V+T1588UUeeOCBLvMmTZrEM888c9HbjjYFtYgMCzfffDM333xzrKsxIOr6EBEJOAW1iEjAKahFRAJOQS0iEnAKahGJiUv5fNT33XcfM2bMYM6cOdx+++3U1NR0PufBBx9k6tSpTJ8+nRdffLHX+kfMOTfotwULFjgRCaYDBw7EugoRWbZsmduxY0ev62zfvt3t2rXLzZw5s8v8rVu3uhUrVrjGxkbnnHOnT5/ucRu7d+92paWlzjnn9u3b58aOHdu57JprrnGvvfaaa29vd7fccot7/vnnnXPOvfjii66lpcU559z999/v7r//fuecc/v373dz5sxxjY2N7ujRo27y5MmutbX1gjLDvQfATtdDpmp4nshw9v/WwYf7Bnebo2fDqvV9rnYpn4/6pptu6nzO4sWL+fnPfw7As88+y5o1a0hOTmbSpElMnTqVN998kyVLlvT5evRGXR8iEmhBPB91qMcff7zzHCClpaWMGzeuz+f0l1rUIsNZBC3fWAvy+ai//e1vk5CQwKc+9amInzMQCmoRiZn+nI/6O9/5DjNmzLio81H3dOHt/p6PGuDJJ59k8+bNvPzyy53/AAoLCzlx4kSPzxkodX2ISMxcquejfuGFF/je977Hc889R1paWudzbr31VjZu3EhTUxPHjh3j8OHDLFy4MOLXoycKahGJiUv5fNT33nsvZ8+eZeXKlcydO5cvfOELgPdl5OrVq7nqqqu45ZZbePjhh4mPj7/418rpfNQiw4rORx17Oh+1iASazkfdf/oyUUSGlM5H3X8KapFhyDnX61C1y1FQzkc9kO5mdX2IDDMpKSlUVlYOKDDk4jjnqKysJCUlpV/PU4taZJgpKiqipKSE8vLyWFdlWEpJSenyi8dIKKhFhpnExEQmTZoU62pIP6jrQ0Qk4BTUIiIBp6AWEQk4BbWISMD1GdRmNs7MtpnZATPbb2ZfHoqKiYiIJ5JRH63A15xzu80sE9hlZluccweiXDcRESGCFrVz7pRzbrc/fRZ4B7j4E6yKiEhE+tVHbWYTgXnAG2GW3WNmO81spwbSi4gMnoiD2swygF8AX3HO1XZf7px7xDlX7Jwr7ukqCiIi0n8RBbWZJeKF9E+cc7+MbpVERCRUJKM+DHgMeMc590/Rr5KIiISKpEW9FPgMsNzM9vi3j0a5XiIi4utzeJ5z7rfA8DpxrYhIgOiXiSIiAaegFhEJOAW1iEjAKahFRAJOQS0iEnAKahGRgFNQi4gEnIJaRCTgFNQiIgGnoBYRCTgFtYhIwCmoRUQCTkEtIhJwCmoRkYBTUIuIBJyCWkQk4BTUIiIBp6AWEQk4BbWISMApqEVELlZ7O5x6C/b/Kiqb7/PitiIiEkZ9Bby3DY78Gt57GerLIXkEzPg4xA9utCqoRUQi0dYKpTu9YD7yazi5B3CQmgtTlsPUP/LuBzmkQUEtItKzMyVw5GUvmI9uh6YzYHFQdA3c+FcwdQWMmQtx8VGthoJaRKRDSyN88Pvz4Vz+rjc/cyxcdavXap68DFJzhrRaCmoRGb6cg8r3zndnHP8ttJ6D+CSYcC3M+7QXzvkzwCxm1VRQi8jw0nQWjr3qh/PLUPO+Nz93Csz/rBfME5dCUnps6xlCQS0ilzfn4MN954P5xOvQ3gqJ6V43xtIvwZQVkDsp1jXtkYJaRC4/9ZVwtGPo3FaoO+3NHzUbltzrtZrHLYKEpNjWM0IKahG5fJx4E7Z8Az54DW/oXE7XoXOZo2NdwwHpM6jN7HHg40CZc25W9KskItJPdeXw62/Cnh9D5hi4YR1MXQljoz90bihE0qJ+EvgB8FR0qyIi0k/tbbDzcdj699BcD9d+CZbdD8mZsa7ZoOozqJ1zr5rZxOhXRUSkHz54A57/mvdF4aRl8NHvQ/70WNcqKgatj9rM7gHuARg/fvxgbVZEpKu6Mq8f+q2fwohC+B9PwlW3xXScc7QNWlA75x4BHgEoLi52g7VdERHAO9fGzsdg67ehpQGu+yp85OuQnBHrmkWdRn2ISPC9/xo8/3U4/TZMvtHr5sibFutaDRkFtYgE19nTsOX/wN6NMKIIVj8FV956WXdzhBPJ8LyngRuAPDMrAb7hnHss2hUTkWGsrRV2PArbvgOtjfCRr3m3AP2seyhFMupj7VBUREQEgOO/g+fvg7L93k+7V30P8qbGulYxpa4PEQmGsx/CS38L+/4TssbB//yxd7WUYdbNEY6CWkRiq60F3nwEtj0IbU3eSI6PfA2S0mJds8BQUItI7Bz/rd/NccD7yfeq78LIKbGuVeAoqEVk6NWegi1/C/v+C7LGw5qfwvSPqpujBwpqERk6bS3wxr/CK+u96evv9364om6OXimoRWRoHHvV6+Yofxem3Qyr1kPu5FjX6pKgoBaR6Ko9CS/9Dbz9C8ieAGs3wvRVsa7VJUVBLSLR0doMb/wItn/Pu/TVDX8JS78MiamxrtklR0EtIoOn8QycegtO/gH+8BOoOAhXrIJbHgz0NQmDTkEtIgPTXA+n9nqhfHK3d1955Pzy/Cth7c9g+i2xq+NlQkEtIn1rOQcfvu2Hsn+rOAiu3Vs+ohDGzoOr13r3Y+dBWm5s63wZUVCLSFetzd55NkJDuewdr58ZIL0ACufDzNu8QB4zFzJHxbbOlzkFtchw1tbqDZfrDOXdcHo/tDV7y1NzYOx8WHrz+ZbyiLH6YcoQU1CLDBftbVBxuGtL+cN90HrOW548wrtq9+Ivng/l7AkK5QBQUItcrs6UwIk3oNT/ou/UW9Bc5y1LTIcxV0PxXV43xth5kDMJ4uJiW2cJS0Etcjloa4XT++DEm/DB615A15Z6yxJSYPRsmPu/vG6MsfO8y1jFxce2zhIxBbXIpajxDJzY4QXyidehZBe01HvLRhTCuEUwfjGMWwijZkF8YmzrKxdFQS0SdM5B9XEvlD943Ws1lx0AHFic11qe96nz4ZxVFOsayyBTUIsETWuz15/c0Vo+8SbUnfaWJY+Aomvgqk/A+EVQWAzJGbGtr0Sdglok1hqquraWT+72LugK3qiLyTd4reVxi6DgSvUtD0MKapGh5Jz3M+sPXj/fWq445C2LS/BHYnzeay2PWwSZo2NbXwkEBbVItLQ0en3LVUe9H5WceNNrOZ+r8pan5nhhfPUaGLfYGyanM8tJGApqkYvRVAfVx7ww7rwd8261pYA7v+7Iqd7lpjpayyOnadyyRERBLdKXc9V++B4Nufdv9WVd103P965aMvE6777jNnKy14IWGQAFtYhzUF8RpmXs385Vd10/c6wXvlfc7J1juSOMcyZByojY7INc1hTUculyzjt/RXsruDZvuuO+c7rVn2737uvLw4TxMWg+e367FueNRc6dDDNvPx/CuZMhZ6IuxCpDTkE9nLW3Q1uTd6a01mbvvq3Juzp0q38fbnnntH/rcd1wy1u8eR0B2iVcOwK3vVvIdg9ff1lo/29/xSV4Q99yJ8P4JSHdFJMgezwkJA/ayyxysYIV1CU7vXuL88aKxiWAxfvT8eenzV8WFx9+XYsbvDN+OeeFQmtTBMHUW8j1EmKhAdQZUO0RBlh7Hy3Kjue3X9jKvJigC8fivYCLT/JuCcneT5fj/fuOZYmpIe9XgveFWuf73DE/rtv7HOY46HXduG7HhH+fmuMFctY4iA/W4S/Sk2AdqRv+GFoaBmdbF4R6H2EA3QI0ZHqwAy0+yQuvhCSIS/RCrKd/ON2DKj7RO8lOf/att6DrDNSkkID169c5ndQtbBPDLE/SDzFEoiRYQb3mJ95ZwHpsXfbyUbjXdSNodeIubPl1Ca7uYdWfYAtZNz5R5/cVkX6JKKjN7Bbg/wLxwL8759ZHpTZTlkdlsyIil7I+R9ubWTzwMLAKuApYa2ZXRbtiIiLiieRnUQuBI865o865ZmAj8InoVktERDpEEtSFwImQxyX+vC7M7B4z22lmO8vLywerfiIiw96gnWjAOfeIc67YOVecn58/WJsVERn2IgnqUmBcyOMif56IiAyBSIJ6BzDNzCaZWRKwBnguutUSEZEOfQ7Pc861mtm9wIt4w/Med87tj3rNREQEiHActXPueeD5KNdFRETCMOcG+efRgJmVA+8P8Ol5QMUgVifo5caybO3z5V9uLMvWPvfPBOdc2JEYUQnqi2FmO51zxcOl3FiWrX2+/MuNZdna58Gj6wCJiAScglpEJOCCGNSPDLNyY1m29vnyLzeWZWufB0ng+qhFRKSrILaoRUQkhIJaRCTghiSozexxMyszs7d7WeebZubMbGrIvK/48/o93MXMUszsTTN7y8z2m9nf9bDek2bWYGaZIfMe8svN62+5IdvINrOfm9m7ZvaOmS0Js86g7nO3bff6mpvZSjN7zcy73IyZxZvZH8zs2ossd5yZbTOzA/7r/uWhKDuS99vM/reZ/Szk8Qgze8/MJg+03JBtHTezfWa2x8x2hlkejX2e7pfXcas1s69Eq9yejikzyzWzLWZ22L/P6ba8wH99RofMe9jM/jLCcns8pqJZdm/HlHmn1HjDzI6Y2c/MO71G6HNnmtkhM0sNmfffZrY2kn2+gHMu6jfgemA+8HYv63wT2Av8Tci83wFvA8UDKNOADH86EXgDWBxmvSf9cj/tP47zH5cAeRexzxuAu/3pJCA72vs8gNd8Y0gdvwI8GmadhH6WOwaY709nAoeAq6JddiTvt7/O74E/8h8/BPz1xe6z/5zjfR0v0Xi9Q54XD3yI96OJqJTb0zEFfA9Y50+vA74b5rlfAH7sT8/3j/vESOrQ2zEVzbJ7O6aA/wTW+NP/CnwxzPPXA//gT98GvDTQ97vfB8RAb8DE7m9wt+XfBL4F7PAfT8H72for+KEFrAX24QXZBW9IL9tOA3YDi8IsexL4K2CT/3g58KPQPzzgL/wy3wa+EkF5WcAx/C9rY7HPEb7mY4D3gJnAESA35DX5V//A/KeLfN+fBVYOZdl9vN9z/Ney2H9dk/z5r+AF907gawMos/N4icXrDdwE/C7a5YY7poCDwJiQsg6GeV4c8Bpwo39/vT//TryTvG0Ftvf3mBqqskOPKbwAr8APWWAJ8GIPzzkIzAXeBab5878J/Adeo+zpSPY5WBe3hVrghJnNwruKzM+AzwGY2Vjgu8ACoBp4ycxuc879qqeNmXcZsV3AVOBh59wbPax6CLjV/9i0Fvgx3qXHMLMFfh063qA3zGy7c+4PvezHJKAceMLMrvbr8GXnXH2097k/nHOnzOwhvIP3S865qpDFRcC1zrm2gW7fzCYC8/CCIOplR/J+O+f2mtmLwMvAJ5x31aIOSW7gvypzeDWr7KMAAAMuSURBVO+PA/7NOXfBMK0ov95rgKfDVizK7zMwyjl3yp/+EBgVpg7tZvZFvFB8zjn3asji+cCcbvUKK8wxFdWywx1T5nWJ1jjnWv3Vwl5MxTnXYGZfB17F+0d4OGTxVcB1zrlzfe0zBPPLxI14B91twDMh868BXnHOlfsv0E/wPor1yDnX5pybi3cwLvTDsCe/9MtdBPwmZP51wDPOuXrnXJ2/3kf62IcEvAPgR865eUA93seyngzaPg/Aw0C8c+7JbvP/6yJDOgP4Bd4nkNqhKLsf7/fDQKlz7pVu838WZt1IXeecm4/3D/7PzKyn92nQX2+/f/RW4L96WS0q73N3zmsyhh3z65zbg/dp5ofdFm2JMKR7PaaiUXY/MyTc8zcBNWHKfS7SkIZgBvVm4DPAB738gfeLc64G2Abc0stqPwP+Hu+Na7/IIkuAkpAW3c/xgrsng77PkfL3NdzBHa71HxEzS8T7g/qJc+6XQ1m2v92+3u92/zZo5TrnSv37Mrx/tgt7WC8a+7wK2O2cO91L/aLyWvtOm9kYAP++rJd1w732fdahl2Mq6mXDBcdUJZBtZh09En1dTGXA5XYIXFA75xqAB4Bvd1v0JrDMzPL8jyNrge09bcfM8s0s259OBVbi9RP1VO77wF9z4X++3wC3mVmamaUDt9O1xR1uWx/idWdM92etAA70sv6g7HMQ+KMLHgPecc790xCW26/3e5DLTjd/1JB/jNyE13obKmvpodtjiDwH3OFP34HXhzxo+jimolZ2T8eU33LfBvxpNMoNZ6iG5z2N1z823cxKzOzzva3vnNvonNvdbd4pvO6DbcBbwC7nXG8vzhhgm5ntxbtKzRbn3OY+yv0359x73ebtxvvS5U28frF/76N/usOfAz/xy58LfKePsgdjnzv19zUfREvxPh0sDxk29tEhKLff7/cgGgX81szewjtO/ts598JQFOz/Y1iJ1yUX7bJ6OqbWAyvN7DDwR/7jwdTbMRXNsns7ph4A/sLMjgAj8f6RRI1+Qi4iEnCB6/oQEZGuFNQiIgGnoBYRCTgFtYhIwCmoRUQCTkEtIhJwCmoRkYD7/y8npqq2H1C0AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "N-CM88tIAjKK",
        "outputId": "07eced63-cd30-48ec-9c9d-af7206fcce20"
      },
      "source": [
        "plt.plot(labels, july16_2007, labels, july16_2020)\n",
        "plt.legend(['july16_2007', 'july16_2020']);"
      ],
      "execution_count": 84,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MVziIlKPmKBp"
      },
      "source": [
        "# DONT RUN THE CELL BELOW! IT WILL ERASE THE PLOT!"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ifw3lUzMmKBq",
        "outputId": "cf086719-44f7-40a4-c34c-a67923460a7e"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2awJY_TTmKBq"
      },
      "source": [
        "**TASK: The legend in the plot above looks a little strange in the middle of the curves. While it is not blocking anything, it would be nicer if it were *outside* the plot. Figure out how to move the legend outside the main Figure plot.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "J9HEDvgDmKBq",
        "outputId": "ad2cd3cb-d82c-4b8b-c855-2378df9ec326"
      },
      "source": [
        "# CODE HERE\n",
        "\n",
        "plt.plot(labels, july16_2007, labels, july16_2020)\n",
        "plt.legend(['july16_2007', 'july16_2020'], loc = \"right\", bbox_to_anchor=(1.85, 0.8, -0.5, -0.5));"
      ],
      "execution_count": 101,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "zobI3LfmCUUd",
        "outputId": "246fd5bd-67d0-47cd-a997-c0a13da7d550"
      },
      "source": [
        "plt.plot(labels, july16_2007, label = \"july16_2007\")\n",
        "plt.plot(labels, july16_2020, label = \"july16_2020\")\n",
        "plt.legend(loc = \"right\", bbox_to_anchor=(1.85, 0.8, -0.5, -0.5));\n"
      ],
      "execution_count": 102,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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52btgwYK2V199Nfnss8/u6u7ulnnz5nUO9hqPxyMnT540f/HFF/u3bNkSd8stt0ytrq7ebTIN3DFbUVER88gjj+S8//77Xw2nfiaTCSLSZ9wrr7ySPHfu3PbhdhsD7DomIqIQioqKUr4DjADA6XRKoPnuuuuuxhdeeCF9zZo16bfeemvjUMvNyspyXX/99S0mkwmLFi3qMJlMqq6ubsDG4uHDh6Ouv/764ueee+5oWVmZEwAKCgq6fS1YAKiqqrL6Wrjp6enuqqqqKH18VFpaWp+u6ddeey3txhtvHHa3MRBE0IpIjIhsE5GdIrJXRFaeSUFERBT5pk6d6jx06FBsZ2enNDY2mj/55JOkQPMtXrzYceLECeuGDRvS77jjjiED7Oqrr2758MMPEwFg165d0d3d3aasrKyA+2kbGxvNV1111bSVK1fWXHHFFQ7f+IKCgu6EhATvhx9+GO/1erFu3br0ZcuWtQDAlVde2bJ69ep0AFi9enX6kiVLWnyva2pqMm/bti3xlltuaTm9tKEF06J1AlislJoN4BwAS0Rk/pkURkREkUtEUFxc3H311Vc3l5aWli1btqyorKxswP2oy5cvby4vL2+32Ww93bFXX331lIsuuqj06NGj0ZMmTZr1u9/9LgMA7r333sajR49GT5s2reymm24qWrNmzdGBuo0ff/zxzGPHjkX/6le/yvadmuM7SvmZZ56puvvuuwsLCgpmFhYWOm+44YZTALBy5coTmzZtSiooKJi5efPmpJUrV57wLW/dunUpF198cWtSUpI3YIFDvS9KBX/FLhGJA/AJgO8ppT4daL7y8nJVUVFxJvUhIpqQRGS7Uqr8TF+/c+fOytmzZw/ZBWuUuro687nnnjvj+PHju4N9zaJFi4rvv//++mXLlrUZWbfRsnPnzozZs2cX9h8f1D5aETGLyBcAGgBsDBSyInKXiFSISIXdbh9xhYmIaHyorKyMmj9//ln33HNPfTDzNzY2mgsLC2fGxMR4IyVkBxPUUcdKKQ+Ac0QkBcAGEZmplNrTb541ANYAWos25DUlIqIxqbCwsLuysnLP0HNqMjIyPMOZfyCvv/560kMPPdTnClF5eXnOjRs3Hh7pskNpWKf3KKVaRGQTgCUARvwmERERnanrrruu9brrrtsX7noMJZijjm16SxYiEgvgcgAjvswWERHRRBBMi3YygBdExAwtmF9TSr1jbLWIiIgiw5BBq5TaBWDOKNSFiIgo4vDKUEREFBLj+TZ5K1asyJ0yZUpZSUnJjMsvv3xqY2Njz63wHnzwwaz8/PyZhYWFM19//fWAF+AYDIOWiIhCIlS3yXvrrbdOuzax/23yDh06tPfhhx+uG2gZvtvkHTx4cN/atWuP3nnnnT233PPdJq+ysnLPkSNHYtavX58EAFdeeWXrwYMH9x48eHBfcXFx18MPP5wFANu3b49544030g4cOLD3/fffP3j//ffnu90D3jgoIN5UgIgo0rx5Tx4a9oX0frTInNGB5c8MeleguLi4Oa+99tqhJ554YtKmTZsOAdpt8srLyx333ntvk2++p556Kn3Xrl1xzz//fDWg3SZv3759sc8991z10qVL2w8cOGDtv+zh3ibPN+x/m7yGhgaL7zZ5AHpuk3fjjTe2Xnvtta2+11xwwQWO9evXpwLA+vXrU6699tqTsbGxqrS01FVQUODcvHlz/GWXXeY4veTA2KIlIqJRddtttzVv3Lgx2XfDgRdffDFjxYoVg17VynebvFmzZpWed95507ds2RLUD4lgb5Pnb+3atRlLliw5BQC1tbXWvLw8l29adna2q7q6+rQfAoNhi5aIKNIM0fIMt7F8m7yf/OQnWWazWd19991ndKeeQBi0REQUMsO5Td5jjz2WVVJS0jWS2+RlZ2cH7EIe7m3yAODpp59O/+CDD1I+/vjjg74Az8nJ6dOCPX78eJ8WbjDYdUxERCEzXm+Tt379+qTf//73We+9996hxMTEnl8K1113Xcsbb7yR1tnZKfv377dWVlbGLFy4MOj9swCDloiIQmQ83ybvBz/4Qb7D4TAvXry4pLS0dMYtt9ySDwDl5eVdy5cvP1lSUlK2ZMmSkieffLLKYhleZ/CwbpMXLN4mj4hoeHibvPFvRLfJIyIiGghvkzc4HgxFREQjwtvkDY5BS0RE41LE3CaPiIjGBa/X6w14Kg0ZT3/vvYGmMWiJiCLDHrvdnsywHX1er1fsdnsygIDd4ew6JiKKAG63+866urpn6+rqZoKNqNHmBbDH7XbfGWgig5aIKALMnTu3AcA14a4HnY6/eoiIiAzEoCUiIjIQg5aIiMhADFoiIiIDMWiJiIgMxKAlIiIyEIOWiIjIQAxaIiIiAzFoiYiIDMSgJSIiMhCDloiIyEAMWiIiIgMxaImIiAzEoCUiIjLQkEErInkisklE9onIXhG5bzQqRkREFAmCuR+tG8APlVI7RCQRwHYR2aiU2mdw3YiIiMa9IVu0SqkTSqkd+nAbgC8B5BhdMSIiokgwrH20IlIIYA6ATwNMu0tEKkSkwm63h6Z2RERE41zQQSsiCQBeB3C/Uqq1/3Sl1BqlVLlSqtxms4WyjkRERONWUEErIlHQQnadUuoNY6tEREQUOYI56lgAPAfgS6XUk8ZXiYiIKHIE06JdAOBbABaLyBf64yqD60VERBQRhjy9Ryn1CQAZhboQERFFHF4ZioiIyEAMWiIiIgMxaImIiAzEoCUiIjIQg5aIiMhADFoiIiIDMWiJiIgMxKAlIiIyEIOWiIjIQAxaIiIiAzFoiYiIDMSgJSIiMhCDloiIyEAMWiIiIgMxaImIiAzEoCUiIjIQg5aIiMhADFoiIiIDMWiJiIgMxKAlIhoprxc4sRPY+2a4a0JjkCXcFSAiGpccjcDhTcChvwCHPwQcdiA6CSj9BmDmVyv14tZARBQMjxuordCC9dBfgONfAFBAbBowdTFQfJn2zJClfrhFEBEN5FQNcOhDLViPbAGcpwAxAbnnAYt+BhRfCkw+BzCZw11TGsMYtEREPt1dwLH/6Q1X+35tfGI2MOMardVadAkQmxreetK4wqAloolLKaDpcG93cOUngLsTMFuBgguBObdq4WorBUTCXVsapxi0RDSxONuAo1v1cP0QaKnSxqdNBc79thashQsAa3x460kRg0FLRJFNKaBud2+wVv8d8LqBqHitG3jBvcDUS4G0KeGuKUUoBi0RRR5HE3DEd+rNR0B7vTZ+0tnABf+ktVrzzgcs1vDWkyYEBi0RRY7qbcDGnwPH/gbt1JvUvqfeJGaFu4Y0AQ0ZtCLyPIBvAGhQSs00vkpERMPUbgf+8gvgixeBxMnAwp8CxZcD2Tz1hsIvmBbtWgD/F8B/GlsVIqJh8nqAiueBjx4FXA7gwnuBSx4AohPDXTOiHkMGrVJqq4gUGl8VIqJhOPYp8N4PtQOdplwCXPVvgG16uGtFdJqQ7aMVkbsA3AUA+fn5oVosEVFf7Q3aftidLwFJOcANa4EZy3meK41ZIQtapdQaAGsAoLy8XIVquUREALRrDVc8B3z0GNDdAVz0v4GLfwREJ4S7ZkSD4lHHRDT2Vf0NeO9HQP0eoGiR1k2cMS3ctSIKCoOWiMautnpg4yPArleApFzgxv8EzrqG3cQ0rgRzes/LABYCyBCRGgA/V0o9Z3TFiGgC87iBz/4d2PRLwN0FXPxD7cHLItI4FMxRxzePRkWIiAAAlX8F3vsx0LBXuzTi0seBjOJw14rojLHrmIjGhrY64M8PA7tfA5LzgH98ESj9BruJadxj0BJReHm6gW1rgE2/AjxO7Ujii38IWOPCXTOikGDQElH4VH6idxPv0y6ZuPQ3QPrUcNeKKKQYtEQ0+lpPABsfBnb/EUjOB256CZh+FbuJKSIxaIlo9Hi6gU//AGz+tTb8tQe0C0+wm5giGIOWiEbH0a1aN7F9PzDtSmDpr4G0onDXishwDFoiMlbrceDP/wLseR1IKQBufgWYvjTctSIaNQxaIjKG2wV8ugrY8jjgdQMLHwQW3AdExYa7ZkSjikFLRKHTdQo4sRM4/jnw+Tqg8QBQshRY8isgbUq4a0cUFgxaIjozLgdwYpcWqsd3aM9Nh3qn284Cbn4VmL4kfHUkGgMYtEQ0tO5OoG6PHqr6o/EAoLza9KQcIHsOMPtm7Tl7DhCXFt46E40RDFoi6svt0q4z7B+qDV9q+1kBID4TyDkXKFuuBerkc4DESeGtM9EYxqAlmsg8bu10m55Q3QHU7wU8Lm16bCqQfS6w4MrelmpSNi8sQTQMDFqiicLrARq/6ttSrdsNuDu16dFJQPY5wPzv9YZqSgFDlWiEGLREkepUDVD9KVCrH6h0YifgatemRcUDk2cD5bdr3cDZc4DUKYDJFN46E0UgBi1RJPC4gfrdQPU24NjftYBtrdWmWWKArLOBc27RuoGz5wAZ0wCTObx1JpogGLRE41HXKaD6My1Qq/8O1GwHuh3atKQcIO98IH8+kDcPmDQTMEeFt75EExiDlmisUwportRC9djftVZrwz4AChCT1lqd883ecE3ODXeNicgPg5ZorHG7tP2pvtZq9TagvV6bFp0E5J4HzFgG5J8P5JQD0QnhrS8RDYpBSxRuHSf7tlaP7wDcXdq0lAKgaKHWWs07H8g8i/tWicYZBi3RaFJKu0zhsb/3tlYbD2rTTBb9SOA7tNZq3vlAYlZ460tEI8agJTJKd5e2b/XkEe2iENXbtJZr50ltemyqFqazbwLy5mun2fDONkQRh0FLNBLOdqD5qBamPY+j2qO1FoDqnTe9GJh+VW9rNX0az1slmgAYtERD6WzWw/OI37P+cDT0nTfeBqQVAYUXac++R3qR1oIlogmHQUukFOBoDNAy1R+dzX3nT8zWwrPkSu0eq74wTZ0CxCSFZx2IaMxi0NL4pZR2/V6vG1Aebdj33DPs1oe92rPDHiBMjwKutt7likk7FzWtCCj7h94QTSsCUgsBa1zYVpmIxh8G7UTm9QIep3anFrdLe/Y4AU834NafA03vGdYfA84baHq3Ns4XgH3C0ReY3n4h2T889Wn++z+Hy2TRTp1JKwLyL/Dr5p0CpOQDluiQvc1ENLGNraCtqdCexaSdK2iyAGLWh829w6JPM5kDzyum0N1xRCntS93tDCJYBgupQULIP0B6AsYbZAB5h2jR+V7vPb2VN5KgCkTMWkCZrdrDEq1d+s+sP/umRcX6fV4W7YCgns/ZN97U73MOsB0MOq+p3zahP8emaoGanAeYx9bmT0SRaWx907xwNdDdEZplnRbKQ3yZA/0C0G841IFktmrhY7ECpigthAb6wdA/aMxR2kXih7NugwVVTyBa/QJSr1/PsLVfWEYFmG7lhRSIiAIYW0F70zrtLiQDtu4G6UocdN4gWn1Qp7e8+gRP/7AZTjD5zWuO4v09iYgmkKCCVkSWAPg9ADOAZ5VSvzakNlMXG7JYIiKicBnybHkRMQN4BsBSADMA3CwiM4yuGBERUSQI5rI08wAcUkodUUq5ALwCYJmx1SIiIooMwQRtDoBqv79r9HF9iMhdIlIhIhV2uz1U9SMiIhrXQnahVaXUGqVUuVKq3GazhWqxRERE41owQVsLIM/v71x9HBEREQ0hmKD9DMA0EZkiIlYANwF4y9hqERERRYYhT+9RSrlF5J8AfADt9J7nlVJ7Da8ZERFRBAjqPFql1HsA3jO4LkRERBFHlArx5QUBiIgdQNUZvjwDQGMIqzPWyw1n2VznyC83nGVznYenQCnFI0kjkCFBOxIiUqGUKp8o5YazbK5z5JcbzrK5zkSakJ3eQ0RERKdj0BIRERloLAbtmglWbjjL5jpHfrnhLJvrTIQxuI+WiIgokozFFi0REVHEYNASEREZaFSCVkSeF5EGEdkzyDy/EBElIsV+4+7Xxw37cHkRiRGRbSKyU0T2isjKAeZbKyIdIpLoN+4pvdyM4Zbrt4wUEVkvIvtF5EsRuSDAPCFd537LHvQ9F5HLReRvIiL632YR+VxELhxhuXkisklE9unv+32jUXYwn7eI/C8RedXv7yQROSwiRWdart+yKkVkt4h8ISIVAaYbsc7T9fJ8j1YRud+ocgqSIHAAAAXiSURBVAfapkQkTUQ2ishX+nNqv+mZ+vuT5TfuGRF5MMhyB9ymjCx7sG1KtEvSfioih0TkVdEuT+v/2jIROSgisX7j3hWRm4NZZ4owSinDHwC+BuBcAHsGmecXAHYB+Be/cX8FsAdA+RmUKQAS9OEoAJ8CmB9gvrV6ubfqf5v0v2sAZIxgnV8AcKc+bAWQYvQ6n8F7/opfHe8H8O8B5rEMs9zJAM7VhxMBHAQww+iyg/m89Xn+B8Bl+t9PAXhopOusv6ZyqO3FiPfb73VmAHXQLnpgSLkDbVMAHgfwU334pwB+E+C1dwN4UR8+V9/uo4Kpw2DblJFlD7ZNAXgNwE368B8AfC/A638N4P/ow8sB/DlUnzcf4+sxegUBhf3/QftN/wWAfwXwmf73VGiXfdwMPXQA3AxgN7QgOu0fapBlxwHYAeD8ANPWAvgZgLf1vxcDWOX/xQngB3qZewDcH0R5yQCOQj/YLBzrHOR7PhnAYQBlAA4BSPN7T/6gf7E8OcLP/b8BXD6aZQ/xec/S38ty/X216uM3QwveCgA/PIMye7aXcLzfAK4A8Fejyw20TQE4AGCyX1kHArzOBOBvABbpz1/Tx38X2k1KPgKwZbjb1GiV7b9NQQvgRughCeACAB8M8JoDAM4BsB/ANH38LwD8F7Qf1S+P5P+Lj/HxCOpax6OoFUC1iMwEsAzAqwBuAwARyQbwGwBzATQD+LOILFdKvTnQwkTEDGA7gGIAzyilPh1g1oMArtG7nW4G8CKApfoy5up18P2DfSoiW5RSnw+yHlMA2AH8h4jM1utwn1LKYfQ6D4dS6oSIPAXty+depdRJv8m5AC5USnnOdPkiUghgDrQvcsPLDubzVkrtEpEPAHwIYJlSyuU32arO/Ko+CtrnowCsVkqddpqHwe/3TQBeDlgxgz9nAJOUUif04ToAkwLUwSsi34MWam8ppbb6TT4XwKx+9QoowDZlaNmBtinRdim1KKXc+mw1AHIClNshIj8CsBXaD5mv/CbPAHCRUqpzqHWm8W8sHgz1CrQvjeUANviNPw/AZqWUXd/A10HryhqQUsqjlDoH2pfJPD3MBvKGXu75AD72G38RgA1KKYdSql2f7+Ih1sEC7R94lVJqDgAHtG6tgYRsnc/AMwDMSqm1/cb/cYQhmwDgdWg9AK2jUfYwPu9nANQqpTb3G/9qgHmDdZFS6lxoP9DuEZGBPqeQv9/6/sFrAPxxkNkM+Zz7U0opaD86Ak37Alpvwv/rN2ljkCE76DZlRNnD/A4J9Pq3AbQEKPcthuzEMRaD9h0A3wJwbJAv6GFRSrUA2ARgySCzvQrgUWj/eN4RFlkDoMavRbUeWvAOJOTrHCx9XQN9OQVqfQdFRKKgfSGuU0q9MZpl68sd6vP26o+QlauUqtWfG6D9WJo3wHxGrPNSADuUUvWD1M+Q91pXLyKTAUB/bhhk3kDv/ZB1GGSbMrxs4LRtqglAioj4egRzAdQaUS5FhjEXtEqpDgA/AfBYv0nbAFwiIhl6d87NALYMtBwRsYlIij4cC+ByaPtJBiq3CsBDOP2X58cAlotInIjEA/gH9G3xBlpWHbTu4On6qEsB7Btk/pCs81igH936HIAvlVJPjmK5w/q8Q1x2vOhHrevbyBXQWk+j5WYM0G08St4C8B19+DvQ9qGGzBDblGFlD7RN6S3nTQCuN6JcijyjdXrPy9D2D00XkRoRuWOw+ZVSryildvQbdwJa9+smADsBbFdKDbZxTwawSUR2AfgMWkv1nSHKXa2UOtxv3A5oB41sg7Zf6Nkh9s/6/DOAdXr55wD45RBlh2Kdewz3PQ+hBdBa54v9Tju5ahTKHfbnHUKTAHwiIjuhbSfvKqXeH42C9WC/HNouDaPLGmib+jWAy0XkKwCX6X+H0mDblJFlD7ZN/QTAD0TkEIB0aD8EiALiJRiJiIgMNOa6jomIiCIJg5aIiMhADFoiIiIDMWiJiIgMxKAlIiIyEIOWiIjIQAxaIiIiA/1//Jj7nINQc18AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "p6v_Iu5tmKBr"
      },
      "source": [
        "# DONT RUN THE CELL BELOW! IT WILL ERASE THE PLOT!"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FGmWgjnDmKBr",
        "outputId": "fc111b66-64a9-4eda-e00a-52fb98f81301"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eywjO4lumKBr"
      },
      "source": [
        "**TASK: While the plot above clearly shows how rates fell from 2007 to 2020, putting these on the same plot makes it difficult to discern the rate differences within the same year. Use .subplots() to create the plot figure below, which shows each year's yield curve.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6kG2JnwzGKwb"
      },
      "source": [
        "labels, july16_2007, labels, july16_2020"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 580
        },
        "id": "kRzhZ5PSmKBr",
        "outputId": "8adbc057-c2d1-43ff-9b7f-8446aa7d3a79"
      },
      "source": [
        "# CODE HERE\n",
        "\n",
        "fig, ax = plt.subplots(2,1, figsize=(11.5,9.5))\n",
        "ax[0].plot(labels, july16_2007, lw=1.7)\n",
        "ax[0].set_title(\"July16, 2007\");\n",
        "\n",
        "ax[1].plot(labels, july16_2020,lw=1.7)\n",
        "ax[1].set_title(\"July16, 2020\");"
      ],
      "execution_count": 125,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ERLxORk4+Y2ckk1vgYsqtHYmtFuF0SVJOdORUREREvIrbbXnww9VsP3ySh/o3pWeTaKdLknKkcCoiIiJeZWJSSuEg8S1rM75PvNPlSDlTOBURERGvkbQ5jZfmbqFxdCQv3thWHaACkMKpiIiIeIXd6VncP+sXKoYGM3l4R6LCQ50uSRygDlEiIiLiuJx8F2OmJ3M8O58JQzvQpHaU0yWJQ3TkVERERBxlreWJz9axYX8Go3s1ZnCbuk6XJA5SOBURERFHzVi2i3+v3EPXxjV4dEBTp8sRhymcioiIiGOSdx7lqa/WU7dKOK8NbU9IsKJJoNM7QERERByRlpnD+JnJGAxvDO9IzUoVnC5JvECJwqkxZocxZq0x5hdjzIpi1jczxiwxxuQaYx4u/TJFRETEn+S73Nzz/ioOZuTy5DUtaVe/qtMliZc4n976fa21h8+wLh24D7ju4ksSERERf/fst5tYvj2dmxJjGdKpvtPliBcpldP61to0a+3PQH5pPJ6IiIj4ry9X7+OtxdtpE1uFp65tpYH25TdKGk4t8J0xJtkYM/pCn8wYM9oYs8IYs+LQoUMX+jAiIiLiozYdyOCxT9ZQLSKUicM6EB4a7HRJ4mVKGk57WGs7AFcCdxtjel3Ik1lrp1hrE621idHR0RfyECIiIuKjjmfnM3Z6MrkFLl4b0oHYahFOlyReqETh1Fq71/MzDfgM6FSWRYmIiIh/cbstD330CzuOZPHwgKb0aFLT6ZLES50znBpjIo0xUad+B/oD68q6MBEREfEfE+anMG9jGgNa1mZc73inyxEvVpLe+rWBzzwXK4cA71trZxtjxgJYaycZY+oAK4DKgNsY8wDQwlqbUUZ1i4iIiI9I2pzGP+dtoXF0JC/e2FYdoOSszhlOrbXbgLbFLJ9U5PcDQGzpliYiIiK+bteRLO6f9QsRocFMGdGRqPBQp0sSL3c+45yKiIiIlFh2nouxM5I5np3PxGEdSKgV5XRJ4gM0famIiIiUOmstT3y+lg37MxjTqzGDWtd1uiTxEQqn4rN+SjnMN2v343Zbp0sREZHTzFi6k09X7qVbfA0eGdDU6XLEh+i0vvgct9vy8rwtvPpDCgCtYirzxKAWdI2v4XBlIiICkLwznaf+s4F6VcJ5bUh7QoJ1LExKTu8W8SnHs/MZ+e7PvPpDCk1qVWJIpzg27s9kyJtLGfXuClLSTjhdoohIQEvLzGHcjJUYDG8M70iNShWcLkl8jI6cis/YfCCTMdNXsONIFoNa1+GFG9oSWSGEO7s35NlvNzFv40Hmb05jWOc47u/XRDtEEZFylu9yc8/MVaRl5vLM71rTtn5Vp0sSH6Qjp+ITvl6zn+sn/siu9CweG9iMCUM7EFmh8LtVk9pRvHX7pcwc1ZmmtaN4b8lO+ryQxBtJqeTkuxyuXEQkcDzzzSaW70jn5sT6DOkU53Q54qOMtc50JklMTLQrVqxw5LnFd7jclhfmbGbSglSqVAzltSHt6XVJ9Bm3d7stn67ay4tzNnMgI4eYqhV5dGBTrm5Tj6AgDfosIlJWvvhlL/fP+oU2sVX4aExXwkODnS5JvJgxJtlam1jsOoVT8VZHT+Zx36xVLNp6mOZ1KzN5eEfiakSU6L7ZeS6mLtrGGwtSycpz0Ta2Ck8MbkGnRtXLuGoRkcCz6UAG10/4iYphwXx1bw9iqlZ0uiTxcmcLpzqtL15p/b7jXP36YhZtPcy17erx6bhuJQ6mABXDgrm3XxOSHunDkE5xrN17nJsmL2HM9BVsO6ROUyIipeV4dj5jpieTW+DitSHtFUzloqlDlHidL37Zy2P/XkO+y/Lnwc0Z2aPRBc/DXCsqnGd+15o7ujfk6W82Mmf9Qb7fmMbwLg24r18TqkeGlXL1IiKBw+22PPjhL+w8UtgfoHtCTadLEj+gI6fiNQpcbv72nw2FczCHhTB9ZCdG9Wx8wcG0qEtqRzHtjk5MH9mJhFqVmPbTDnq/MJ8pC9VpSkTkQr0+P4XvN6UxsGUdxvZu7HQ54id0zal4hcMncrnn/ZUs3ZZO65gqTBrRscxODbncln+v3MOLczaTlplLbLWKPDqwGVe3qVsqQVhEJBDM35zGndN+pnHNSD6/uztR4aFOlyQ+RB2ixKut2XOMsdOT2Xc8hxs6xvL361qVSy/PrLwCpizcxuQF28jOd9GuflX+PLg5iQ3VaUpE5Gx2Hcni6tcXU+By88U9PUioVcnpksTHqEOUeK2PV+zmhklLSMvM5W/XtuSFG9qU2/AjEWEhPHD5JSx4pA83J9Zn9Z5j3DBpCeNmJLPzyMlyqUFExNdk57kYMyOZ49n5vHhjWwVTKXXqECWOyCsovL50+tKd1KxUgTeGd+BSh45Y1qocznM3tOF2T6epb9cdYN7Gg4zo0pD7+iVQNUKdpkREAKy1PPHZWjbuz2BM78Zc2bqu0yWJH9JpfSl3aZk5jJ+xkhU7j9I+ripvDOtInSrhTpf1qwVbDvH01xvZfDCTyuEh3NevCSO6NqBCiAaUFpHAlZPv4o2kVF75fivd4mvw3p2dCAnWCVi5MLrmVLxG8s6jjJuRTFpmLkM7x/HXq1t4ZehzuS0fr9jNS3O3cCgzl7jqETw2sBmDWtdRpykRCSgncwt4f9ku3ly0jbTMXGKqVuTLe7pTo1IFp0sTH6ZwKl7h/WW7+OuX6zAYnrq2Jbf4wLzLJ3MLmLxwm2fIKTcd4qryxOAWdGxQzenSRETK1LGsPKb9tINpP+3gWFY+1SJCGdmjESO6NqRKRfXMl4ujcCqOyi1w8eSX6/lg+W7qVA7njeEdaB/nW+HuwPEcXvpuM5+s3IO1MLhNXR4b0Oy8Zq0SEfEFaRk5TF28nZlLd3Iyz0WdyuHc1asxQzrVJyJMXVWkdCicimMOHM9h7Ixkftl9jE4NqzNhWAeio3z3VNCGfRk8/c1GFqccJiw4iNu6NeCevk2oEqGjCCLi23anZzF5YSofrdhDXoGbBjUiGNc7nus7xHjl5Vfi2xROxRHLt6czfuZKDp/I5fZuDXlicHNC/eDieWstSZ5OU1vTTlA1IpT7LmvC8C4NCAvx/faJSGDZejCTN5JS+WL1PlxuS7M6UYzvm8CgVnXU4UnKjMKplCtrLe8t2cnf/rOB4CDD09e35vcdY50uq9QVuNx8tGIP/5y7mcMn8mhYI4LHr2zGgJbqNCUi3m/NnmNMmJ/CnPUHAWhXvyr39E2gX/Na2odJmVM4lXKTk+/iT5+t5dOVe4mpWpFJwzvSOraK02WVqRO5BUxekMqbi7aRk+/m0obVeGJwC9rVr+p0aSIiv2GtZdn2dCbMT2HR1sMA9Eioyfi+8XRtXEOhVMqNwqmUiz1Hsxg7I5l1ezPoFl+D14a0D6ihRvYfz+aFOZv5bNVerIWr29bj0QFNqV9dnaZExFnWWuZvTmPC/FSSdx4FoH+L2ozvm6Av0uIIhVMpcz+lHOaeD1aRfjKPu3o24rGBzQL2WqV1e4/zj683smTbEcKCg7ije0PG903Q0CsiUu5cbss3a/czMSmVjfszCDJwTdt6jOuTQNM6UU6XJwFM4VTKjLWWtxZv5+lvNhIWEsTzN7Tlmrb1nC7LcdZaftiUxtPfbCT10EmqRYRyf78mDOvSwC86hYmId8srcPP5qr28sSCV7YdPEhYcxA2JsYztFa8h8MQrKJxKmcjKK+Cxf6/lq9X7qF+9IpOHJ9KiXmWny/IqBS43H/y8m5fnbuHIyTwa14zk8SubcUWL2rq2S0RKXXaei1k/72LKwm3sP55DRFgwwzrHMapnY2pX9p5pokUUTqXU7TqSxejpK9h0IJOeTWry2pD2VI0Ic7osr5WZk88bSam8tXg7uQVuOjeqzhODm9MmVtd6icjFO56dz4ylO3l78XaOnMyjSsVQbu/WkNu7NaRapPbN4n0UTqVULdhyiPs+WMXx7HzG94nnof5NCQ7SUcCS2Hssmxc9naYArmtXj0cGNiOmakWHKxMRX3T4RC7v/Lid937aSWZuATUrVeCuno0Y1qUBlSpoNifxXgqnUiqstUxMSuXF7zZTMTSYl25sy5Wt6zpdlk9au+c4f/96A8u2pxMWEsTIHo0Y3yeeqHB1mhKRc9t3LJspC7cx6+dd5OS7ia1WkTG947mxYyzhoZrNSbyfwqlctBO5BTzy8Wq+XXeARjUjmTyiI5fUVk/Pi2GtZd7GNJ75ZiPbDp+kRmQYD1zehFs6xanTlIgUa9uhE0xakMpnq/aS77Ik1KrE+D7xXN22nvYb4lMUTuWibD98ktHvrWBr2gn6NavFP29up2GRSlG+y80Hy3fx8rytpJ/MIz46kj9e2VyztIjIrzbsy2BiUgrfrN2P20LrmCrc3TeB/i1qE6TLqsQHKZzKBft+40Ee+PAXMnMKuL9fE+7v10Q7wjKSkZPPxPmpvP3jdvIK3HRtXIMnBjenVYx/z7AlImeWvDOdCfNT+WFTGgCdG1Xn7r4J9GxSU19exacpnMp5c7str/2Qwr/mbSGqQgj/vLkdV7So7XRZAWF3ehYvfreZL37ZhzFwffsYHu7flHrqNCUSEKy1LNp6mAnzU1i2PR2Ay5rVYnyfeBIbVne4OpHSoXAq5yUjJ58HP1zNvI0HSahVickjOhIfXcnpsgLO6t3H+MfXG1m+I53w0CAmDO1Av+b6giDir9xuy3cbDjBhfipr9x7HGBjcui7j+sTTsp7OoIh/UTiVEktJy2T0e8lsO3ySgS3r8OJNbTUciYOstcxZf4BHPllDdp6LV25pz+A2GiFBxJ/ku9x8tXofE5NSSUk7QUiQ4XcdYhjbO57GOjAgfups4bREqcMYswPIBFxAwekPZgovfHkFGARkAbdba1deTNFS/mav289DH60mK9/FIwOaMr5PvK5pcpgxhoGt6hJbLYJb317OvR+sJCuvDTcm1ne6NBG5SDn5Lj5O3sPkBansOZpNeGgQt3dryF29GmvsYwlo53NIrK+19vAZ1l0JNPH86wy84fkpPsDltvxz7mYmzE+lcngI79x+KX2a1nK6LCmiVUwVPhzdhWFTl/HIJ2vIyXcxomtDp8sSkQtwIreAmUt3MnXxdg5l5hJVIYS7+8ZzR/dG1KxUwenyRBxXWudrrwXes4XXCCw1xlQ1xtS11u4vpceXMnI8K5/7Zq1iwZZDNKsTxeQRHWlQI9LpsqQYTWpH8fHYrgx9cxn/74v1ZOW5GNM73umyRKSEjp7MY9pPO5j20w6OZ+dTIzKMRwY0ZUTXBlTWBBwivyppOLXAd8YYC0y21k45bX0MsLvI7T2eZb8Jp8aY0cBogLi4uAsqWErPxv0ZjJmezK70LK5uW4/nft+aiDBdX+rNGtSI5KOxXRk+dRnPfLuJk3ku/nB5E11+IeLFDmbkMHXRNmYu20VWnou6VcILJ9y4NI6KYZrNSeR0JU0iPay1e40xtYC5xphN1tqF5/tknlA7BQo7RJ3v/aX0fLV6H49+sobcAhdPDGrOqJ6NFHB8REzVinw4pgsjpi7n1e+3kpVbwBODm+v1E/Eyu45kMWlhKp+s2EOey02jmpGM6x3Pde1jCAvRbE4iZ1KicGqt3ev5mWaM+QzoBBQNp3uBoj00Yj3LxMsUuNw8P2czUxZuo1pEKFNvS6R7Qk2ny5LzVCsqnFmju3Dr28uZung7Wfku/n5tK02QIOIFthzM5I2kVL5cvQ+X29K8bmXu7hvPla3qEqzPqMg5nTOcGmMigSBrbabn9/7AU6dt9iVwjzFmFoUdoY7relPvk34yj3s/WMmPKUdoWa8yk0d0JLZahNNlyQWqFhnGzLs6c+c7P/P+sl3k5Ll4/oY2hGh+bRFHrN59jAnzU/huw0EAOsRV5Z7LEujbVFMRi5yPkhw5rQ185vlghQDvW2tnG2PGAlhrJwHfUDiMVAqFQ0ndUTblyoVat/c4Y6Yns/dYNr/rEMPT17cmPFTXOvm6yuGhvDeyE6PfS+bTVXvJzi8cC1WnDEXKx6HMXOZuOMhXq/exZNsRAHo2qcndfRPo3Ki6QqnIBdAg/AHg05V7+OOna3G5LX8e3JzbujXUDtPP5OS7uOf9lczbmEafptFMGt5RXz5Eysju9CzmrD/AnFczRqsAACAASURBVPUHWLHzKNZCkIErWtTm7r4JtImt6nSJIl7vogfhF9+U73Lzj683Mu2nHdSsFMaEoR3o3LiG02VJGQgPDeaN4R35w4e/8J81+7n9neVMve1Sze4lUgqstWw5eII56w8we90BNuzPACAsOIg+l0QzsFUdLm9emxoao1SkVOgvl586lJnL3e+vZPn2dNrWr8qk4R2oW0Uzjviz0OAgXrmlPeGhwXySvIcRby1j2h2dqFJR4yeKnC+327J6zzFmrz/Ad+sPsv3wSQAiw4IZ3KYuA1rWoW/TaKI0PqlIqVM49UO/7D7G2OnJHMjI4ebE+vzftS11ijdABAcZnv99GyLDgnl3yU6GTFnK9JGddERHpATyXW6Wb09n9roDfLfhAAczcgGoFhHKTYmxDGhZh+4JNbU/FSljCqd+JvXQCW6evAS3tfzj+lYM7RSn60sDTFCQ4clrWlIxLIRJC1K5ecpSZo7qTO3K4U6XJuJ1cvJdLNxyiDnrDzJv40GOZ+cDULdKOLd3a8iAlnW4tGE1jYIhUo4UTv3M87M3kVvg5u3bE7msWW2nyxGHGGN4bGBTIsOCeWnuFm6ctISZozpTv7qGDhM5np3P/E1pzFl/gKTNh8jOdwHQODqSYZ3jGNiqDq1jquiLvYhDFE79yIod6cxZf5A+TaMVTAVjDPf2a0LFsGD+/vVGbp68hBmjOtM4upLTpYmUu1NDPs1ef4AlqYfJdxWOVNM6pgoDW9VhQMvaJNSKcrhKEQGFU79hreXpbzZiDDx+ZTOnyxEvMqpnYyLCQnji87XcNHkpM0Z1olmdyk6XJVLmzjTk06UNqzOwVR36t6xDTFV1FBXxNgqnfmLO+gOs3HWMGzvGKnjI/xjaOY6KYUE8/PEabpmylPfu7KSxGMXvnBryafa6wkBadMinvk1rMaBlbQ35JOIDFE79QL7LzXOzN1MhJIgH+1/idDnipa5vH0vF0GDu/WAVQ99cxjt3XMqlDas7XZbIRXG7Lb/sOcYcTyDdcSQLKBzy6SrPkE99NOSTiE9ROPUDs5bvYvvhk4zvE6+xTOWsBraqy5Rbgxk7PZlb31rOm7cm0qNJTafLEjkv+S43y7alM2f9b4d8qh4Zxk2JsQxsVYdu8RryScRXafpSH3cit4Dez8/HbS0LHu1LZR0dkBJYknqEUe/+TL7LMnFYBy5voQ504t1ODfk0e/0Bvt+Y9uuQT/WqhNO/ZR0N+STiYzR9qR+bsiCVIyfz+OvVLRRMpcS6xtdg+qjO3P72csbOSOZfN7fj6rb1nC5L5DdODfk0e90BFmz575BP8dGRDO8Sx4CWGvJJxB8pnPqwgxk5vLloO3HVIxjWuYHT5YiP6RBXjQ9Gd2HEW8u5f9YqsvNd3JRY3+myJMClZeYwd8NB5qw/+Jshn9rEVmFASw35JBIIFE592MvztpCd7+KRAU0JC9GpLDl/LetV4aMxXRg2dRmPfrKG7DwXt3Vr6HRZEmBODfk0e90Bknf9d8inTo2qM6ClhnwSCTQKpz4qJS2TD3/eTdvYKgxuXdfpcsSHJdSK4uMx3Rg6dSl//XI9WXkuxvWJd7os8WPWWjYfzGTOusJB8TeeNuTTwJZ16Ne8loZ8EglQCqc+6tlvN+O28PiVzQkK0vVWcnHiakTw0ZiuDJ+6jOdmbyIrr4AHr7hE1/JJqdGQTyJSUgqnPmjZtiPM23iQfs1q0TW+htPliJ+oV7UiH3oC6ms/pJCV5+LPg5sroMoFc7ktS1KP/DpLU1rmf4d8ujmxPgNa1daQTyLyPxROfYy1lqe/3USQgcc0TamUsuioCswa3YXb3lnOW4u3k5Xn4u/XtSJYR+flPOQVuPn8l71MSkpl2+GTQOGQT3d0b8iAlnVIbKAhn0TkzBROfcw3aw+wevcxbrm0PpfUVo9VKX3VIsOYOaozd077mQ+W7yI7r4AXb2yrMCHnlJ3n4sOfdzFl4Tb2Hc+hYmgwd3ZvxPXtY2gVU1lH4UWkRBROfUhegZvn52wiPDSIP1yhaUql7ESFh/LunZ0YMz2Zz3/ZR3a+i1eHtKdCiE6/yv/KyMln+pKdvL14O0dO5lE5PIT7+jXhjm4NqRYZ5nR5IuJjFE59yPvLdrLzSBb3XpZA7crhTpcjfi4iLIQ3b03knvdXMWf9QUa/l8zkER11faD86siJXN75cQfvLtlBZk4BNStV4I9XNmNo5zh1bBKRC6Zw6iMycvJ59YcUakSGMbpXY6fLkQARHhrMG8M78OBHq/lq9T5ue3s5b91+KZUqaNcRyPYdy+bNRdv4YPkucvLdxFStyKMDmnJjYn19eRGRi6a/MD5i8oJU0k/m8dS1LXVEQspVaHAQL9/cjoqhQXy0Yg/Dpy7j3Ts6USVC78NAs/3wSSYlpfLpqj3kuyzx0ZGM75PANe3qEaprkkWklCic+oD9x7OZumg7jWpGMqRTnNPlSAAKDjI8+7s2RISFMO2nHdzy5lKmj+xETQ2SHhA27s9gYlIqX6/Zh9tCq5jK3NM3gf4t6micZREpdQqnPuBfc7eQW+Dm0QFNdXRCHBMUZPjr1S2oGBbMG0mp3Dx5CTNHdaFOFV3/7K+Sdx5l4vwUvt+UBhROJ3p33wR6NampnvciUmYUTr3cpgMZfJK8h/ZxVRnYqo7T5UiAM8bw2MBmVKoQwgtzNnPT5CXMHNWZ+tUjnC5NSom1lsUph5kwP4Wl29IB6Ns0mvF9E7i0YXWHqxORQKBw6uWe+3YTbgt/GqSZesR73N03gfDQYP72nw3cNHkJM0Z1Jj66ktNlyUVwuy1zNx5k4vwUVu85jjEwuE1dxvWOp1VMFafLE5EAonDqxX5KOcz8zYfo36K2jliI1xnZoxERYcH86bO13Dx5CdNHdqZ53cpOlyXnqcDl5qs1+5g4P5WtaScICTLclBjLmN7x+sIhIo5QOPVSbrflmW83ERxkeHSgpikV7zSkUxwRYcE8+NFqbpmylPfu7ETb+lWdLktKICffxSfJe5i8MJXd6dlUCAni9m4NuatXY2KqVnS6PBEJYAqnXuqrNftYu/c4wzrHkVBLRy/Ee13bLobw0GDufX8Vw6Yu4+3bL6VTIx3p91Yncwt4f9ku3ly0jbTMXKIqhDC+Tzx39mik0RdExCsYa60jT5yYmGhXrFjhyHN7u9wCF/1eWkD6yTySHulDrSj1hhbvt2DLIUa/twJj4M1bE+nZJNrpkqSIY1l5TPtpB+/8uIPj2flUjwxjZI9GDO/SgCoVNWatiJQvY0yytTaxuHU6cuqFpi/ZyZ6j2TxweRMFU/EZvS+J5t07OzFy2s+MnLaCCcM6cEWL2k6XFfDSMnKYung7M5buJCvPRZ3K4dzfrwm3dKpPRJj+BIiI99Geycscz8rntR9SqFmpAnf11DSl4lu6NK7BjFGdue3t5Yydkcy/bm7HNW3rOV1WQNqdnsWkBal8nLyHvAI3DWtEMK5PPNe3jyUsROMli4j3Ujj1MhMXpHA8O59/XN+KSM1fLj6ofVw1Zo3uyoi3lnH/rFXk5Lm46dL6TpcVMLYezGRiUipfrt6Hy21pVieKu/smMKh1XYI1m5OI+AClHy+y91g27/y4g8bRkdycqD/m4rta1KvMh2O6MmzqUh799xqy8gq4vXsjp8vya6t3H2NiUgpz1h8EoH1cVe7pm8BlzWppjGQR8SkKp17kpe82k1fg5rGBzQjRNKXi4xJqVeLjMd0YOnUpT361gax8F+P7JDhdll+x1rJ0WzoTk1JYtPUwAD2b1GR8nwS6NK6uUCoiPknh1Eus33ecz1btJbFBNfqrE4n4ibgaEXw8tivDpi7j+dmbycp18VD/SxSaLpK1lvmb05gwP5XknUcBGNCyNuP7JGicWRHxeQqnXuLZbzdhLfxR05SKn6lbpSIfeq5BfX1+CifzCvjLVS30Pr8ALrflm7X7mTA/hU0HMgkOMlzfPoZxfeK5pHaU0+WJiJSKEodTY0wwsALYa6296rR1DYC3gWggHRhurd1TmoX6s0VbD7Fo62GubFWHjg2qOV2OSKmLjqrArNFduO3t5bzz4w6y81z84/rW6qBTQnkFbj5btYdJC7ax/fBJwoKDGNY5jjG94omrEeF0eSIipep8jpzeD2wEips8+0XgPWvtu8aYy4BngBGlUJ/fc7stz3yziZAgwyMDmjpdjkiZqRoRxoxRnRn57gpm/byb7HwXL93YVtdXn0V2notZP+9iysJt7D+eQ0RYMKN7NWZkj0bUrqwxkEXEP5UonBpjYoHBwD+AB4vZpEWR5fOBz0ulugDwxeq9bNifwa1dG9A4WtOUin+LCg/l3Ts6MXr6Cr74ZR/ZeS5eG9qeCiHBTpfmVY5n5zNj6U7eWryd9JN5VKkYyv39mnB7t4ZUiwxzujwRkTJV0iOnLwOPAme6qGk18DvgFeB6IMoYU8Nae6ToRsaY0cBogLi4uAsq2J/k5Lt4cc4WIsOCua9fE6fLESkXFcOCmXpbIve8v4rvNhzkrveSmTy8IxXDFFAPn8jl7cXbmb5kJ5m5BURHVeBPg5oxtHMDKmncYxEJEOc8n2aMuQpIs9Ymn2Wzh4HexphVQG9gL+A6fSNr7RRrbaK1NjE6WvNuv7dkB3uPZTO2dzw1K1VwuhyRclMhJJiJwzpwTdt6LNxyiNveWc6J3AKny3LM3mPZPPnlero/+wMTk1KpEhHK369rxaJH+zK6V7yCqYgElJLs8boD1xhjBgHhQGVjzAxr7fBTG1hr91F45BRjTCXg99baY2VRsL84lpXH6z+kUCuqAiN7anByCTyhwUH86+Z2RIQFM+vn3Qybuox377iUqhGBc9p626ETTFqQyqcr91LgtjSpVYnxfeO5qk09QnUtrogEqHOGU2vtH4E/Ahhj+gAPFw2mnuU1gXRrrduz7dulX6p/mTA/hYycAv40qDkRYToqIoEpOMjwzO9aUzEsmHd+3MEtU5Yytnc8/j7KlNta5m1M45u1+7EWWsdU4e6+CfRvUZsgjWAgIgHuglORMeYpYIW19kugD/CMMcYCC4G7S6c8/7Q7PYt3f9pJk1qVuKFjrNPliDjKGMNfrmpBRFgwE+an8sCHvzhdUrnp0rg6d/dNoEdCTY37KiLicV7h1FqbBCR5fv9LkeWfAJ+UZmH+7KXvNpPncvP4lZqmVAQKA+ojA5rRs0k0BzNynC6nXDSsEanZnEREiqHzyeVs3d7jfP7LPjo3qs5lzWo5XY6IV+nSuIbTJYiIiMN02K4cWWt5+puNgKYpFRERESmOwmk5WrDlED+lHuGqNnVpp9N5IiIiIv9D4bScuNyWZ7/dRGiwpikVEREROROF03Ly6co9bDqQyfAuDWhQI9LpckRERES8ksJpOcjJd/HSd1uIqhDCvZdpmlIRERGRM1E4LQdv/7idAxk5jOsbT/XIwJn9RkREROR8KZyWsfSTebwxP5W6VcK5s7umKRURERE5G4XTMvbaD1vJzC3gwSsuITw02OlyRERERLyawmkZ2nnkJDOW7qRZnSh+10HTlIqIiIici8JpGXphzmbyXZbHr2xGcJAG3BcRERE5F4XTMvLL7mP8Z81+uifUoPcl0U6XIyIiIuITFE7LgLWWZzzTlD4+UNOUioiIiJSUwmkZ+GFTGsu2p3Ntu3q0jq3idDkiIiIiPkPhtJQVuNw8++0mwoKDeLi/pikVEREROR8Kp6Xsk+Q9bE07wa1dG1C/eoTT5YiIiIj4FIXTUpSVV8A/526hcngI91yW4HQ5IiIiIj5H4bQUvb14O2mZudzdN4GqEZqmVEREROR8KZyWksMncpm0YBsxVStyW7eGTpcjIiIi4pMUTkvJa99v5URuAQ/11zSlIiIiIhdK4bQUbD98kpnLdtG8bmWuaxfjdDkiIiIiPkvhtBS8MGcTBW7LnwY1I0jTlIqIiIhcMIXTi7Ry11G+WXuAnk1q0rOJpikVERERuRgKpxfh1DSlxsDjVzZzuhwRERERn6dwehHmbjjIzzuOcn37GFrW0zSlIiIiIhdL4fQCFbjcPDt7E2EhQTykaUpFRERESoXC6QX6cMVuth06yR3dGxJTtaLT5YiIiIj4BYXTC3Ayt4B/zd1K1YhQxvfRNKUiIiIipUXh9AK8uWgbh0/kck/fBKpUDHW6HBERERG/oXB6ntIyc5iycBux1SoyomsDp8sRERER8SsKp+fplXlbycpz8ciAplQI0TSlIiIiIqVJ4fQ8pKSdYNbPu2kdU4Wr29RzuhwRERERv6Nweh6en70Jl9vyR01TKiIiIlImFE5L6Ocd6Xy34SB9m0bTLb6m0+WIiIiI+CWF0xKw1vL0NxsJMvD4lc2dLkdERETEbymclsDsdQdYtesYv+8QS9M6UU6XIyIiIuK3FE7PId/l5rnZm6gQEsSD/S9xuhwRERERv1bicGqMCTbGrDLG/KeYdXHGmPme9WuMMYNKt0znfLB8FzuOZDGyRyPqVtE0pSIiIiJl6XyOnN4PbDzDuj8DH1lr2wO3ABMvtjBvkJmTzyvztlItIpSxfeKdLkdERETE75UonBpjYoHBwNQzbGKByp7fqwD7Lr40501ZuI0jJ/O4r18TKodrmlIRERGRshZSwu1eBh4FztQb6EngO2PMvUAkcHlxGxljRgOjAeLi4s6r0PJ2MCOHNxdtI656BMM6a5pSERERkfJwziOnxpirgDRrbfJZNhsCTLPWxgKDgOnGmP95bGvtFGttorU2MTo6+oKLLg8vz9tCTr6bRwc2JSxE/cZEREREykNJUld34BpjzA5gFnCZMWbGaduMBD4CsNYuAcIBnx2pfuvBTD78eTdtY6swuHVdp8sRERERCRjnDKfW2j9aa2OttQ0p7Oz0g7V2+Gmb7QL6ARhjmlMYTg+Vcq3l5rnZm3Bb+OOg5hijaUpFREREyssFn682xjxljLnGc/Mh4C5jzGrgA+B2a60tjQLL29JtR5i3MY3Lm9eiS+MaTpcjIiIiElBK2iEKAGttEpDk+f0vRZZvoPD0v0+z1vKMZ5rSxwY2c7ocERERkYCjnj5FfL12P6v3HOfmS+vTpLamKRUREREpbwqnHnkFbp6fvZmKocE8cLmmKRURERFxgsKpx8xlO9mVnsVdPRtRu3K40+WIiIiIBCSFUyAjJ59Xv99KjcgwRvfWNKUiIiIiTlE4BSYlpXI0K58HLm9CpQrn1UdMREREREpRwIfT/cezeWvxdhrVjOSWTt49paqIiIiIvwv4cPrP77aQW+DmsYFNCQ0O+P8OEREREUcFdBrbdCCDT1buoUNcVQa0rON0OSIiIiIBL6DD6bPfbsJa+JOmKRURERHxCgEbTn9MOUzS5kMMaFmbxIbVnS5HRERERAjQcOp2W575diPBQYZHNU2piIiIiNcIyHD61Zp9rNubwZBO9YmPruR0OSIiIiLiEXDhNLfAxfOzNxMRFsz9/TRNqYiIiIg3CbhwOn3JTvYey2Z0r8ZER1VwuhwRERERKSKgwunxrHxe+yGFmpUqcFfPxk6XIyIiIiKnCahwOjEphePZ+fzhiiZEappSEREREa8TMOF0z9Es3vlpB42jI7k5sb7T5YiIiIhIMQImnE5ZuI28AjePD2xGiKYpFREREfFKAXNu+/Erm9GyXmWuaFHb6VJERERE5AwCJpxGhIVw86VxTpchIiIiImeh89siIiIi4jUUTkVERETEayicioiIiIjXUDgVEREREa+hcCoiIiIiXkPhVERERES8hsKpiIiIiHgNhVMRERER8RrGWuvMExtzCNhZzk9bEzhczs/plEBpq9rpfwKlrWqn/wmUtqqd/seJtjaw1kYXt8KxcOoEY8wKa22i03WUh0Bpq9rpfwKlrWqn/wmUtqqd/sfb2qrT+iIiIiLiNRRORURERMRrBFo4neJ0AeUoUNqqdvqfQGmr2ul/AqWtaqf/8aq2BtQ1pyIiIiLi3QLtyKmIiIiIeDGFUxERERHxGj4fTo0xbxtj0owx686yzZPGGGuMSSiy7AHPMq8ZOuFsjDHhxpjlxpjVxpj1xpj/O8N204wxWcaYqCLLXva0tWb5VXzhjDFVjTGfGGM2GWM2GmO6FrONz7+mRZ3rfWyMucIYs8QYYzy3g40xq4wx3cq30gtnjKlvjJlvjNngeQ/fX8w2/tDOc35WjTF3GWM+LHK7sjEm1RjTuHyrvXjGmB3GmLXGmF+MMSuKWe8Pr2lTT/tO/cswxjxw2jY+284z7X+MMdWNMXONMVs9P6udtr6W5/WvU2TZBGPMH8ur9pI62/7Hn9oJZ98HGWMaGWOWGWNSjDEfGmPCTrtvS2PMFmNMxSLLvjbGDCnPNvh8OAWmAQNLsN1a4JYit28E1pdFQWUkF7jMWtsWaAcMNMZ0OcO2KcC1AMaYIOAyYG+5VFk6XgFmW2ubAW2BjWfYztdf06KmcZb3sbV2LoWTVoz0LLoXWGGt/anodsaYkLIqsBQUAA9Za1sAXYC7jTEtim7gJ+0syWd1KlDfGHO55/ZTwNvW2m1FN/LydhbV11rbrrhxEv3hNbXWbva0rx3QEcgCPjttG19u5zSK3/88DnxvrW0CfO+5/StrbRrwLPAigDGmA9Dz1O1TvKTNZ9v/+FM74ez7oOeAf1lrE4Cj/Pf9CoC1dj3wKfAEgDHmOiDUWvtB0e3KvK3WWp//BzQE1p1l/ZMU7vx/9tyOB74BkoBEz7IhFIaddcBzTrfpHO2NAFYCnYtZNw34E/CV5/ZlwBvADqCmZ9mDnnauAx5wuj2n1V8F2I6ns16gvKaees/1Pq4LpAItKfwCUr3Iaz4JWAb80+l2nEd7vwCu8Od2nuOz2sbz3kz0vE/DPMuTgJeBFRT+MXW8Hedo46/7lrNs40+vaX/gR39rZ3H7H2AzULdI2zYXc78gYAnQ1/Ozl2f57cCXwA/AAqfbV0zdv+5//Lydv+6DAEPhLFAhnnVdgTlnuM9mCoPtJqCJZ/mTwHTgR+CDsqzbW1J+ecgAdhtjWlF4VPFD4A4AY0w9Cr9NdKTwm8R3xpjrrLWfO1VscYwxwUAykABMsNYuO8OmW4BrPKcmhgAzgCs9j9GRwnafeqMuM8YssNauKuv6S6gRcAh4xxjTlsL23m+tPVnMtj7/mp4Pa+1+Y8zLFO4Y77PWphdZHQt0s9a6nKnu/BhjGgLtKfxj/Rv+0M6SfFattWuMMXMoPFJzrbU2r8jqMOtFs7Wcg6Xw82WBydba/xmSxh9e0yJuAT4oboWftROgtrV2v+f3A0Dt0zew1rqNMeMoDGdfWmsXFlndAWhz2v+D44rZ//hdO4vbB5nCS/uOWWsLPJvtAWJOv6+1NssY8zCwkMIvU1uLrG4B9LDWZpdl/f5wWv98zKJwx3Idvz0lcymQZK095HnRZgK9HKjvrKy1Llt4WikW6OQJZWfyKYVt7QwsKrK8B/CZtfaktfaEZ7ueZVXzBQih8IP+hrW2PXCS006xnManX9MLMAEIttZOO235x77yR88YUwn4N4VH7TPOsJlPt/M8PqsTgL3W2qTTln9YzLbeqoe1tgOFX4DvNsac6XPm068pgOf6vGuAj8+ymc+3szi28NBZsWNPWmt/ofAswMTTVs31psAG597/+Es7zzMvFHf/r4Bj/G9bvyzrYAqBF07/A4wAdp3lj6LXs9YeA+Zz9mttPwT+RuGHxl0uhZWOPcCeIkeaPqEwrJ6JX7ymJeV5LYvbcRZ3ZNnrGGNCKfzDMNNa++mZtvP1dp5Sgs+q2/PvdD7TTmvtXs/PNAq/IHY6w3b+8JpeCay01h480wZ+0s5TDhpj6gJ4fqadZdvi3ste1eaz7H/8qp1FnbYPOgJULXK9aCxn74/iWFsDKpxaa7OAx4B/nLZqOdDbGFPTcyh8CLCgvOs7G2NMtDGmquf3isAVFF4LUixr7U4KL2g+/VvPIuA6Y0yEMSYSuJ7fHll1lLX2AIWn6pt6FvUDNpxle599TQONpxfzW8BGa+0/na6nrJzvZ9WXGWMijWdkEM/+pD+FR5b81RDOcErfT30J3Ob5/TYKr9P0SefY//hNO+HM+yDPUeH5wA2eTb22rT4fTo0xH1B4fU9TY8weY8zIs21vrZ1lrV152rL9FJ46ng+sBpKttd72gtUF5htj1gA/U3hE9D9nu4O1drK1NvW0ZSspvDh/OYXX20z1outNT7kXmOlpazvg6bNt7MOv6a/O933so7pTeJT7MvPfIXkGOV1UGTjvz6oPqw0sNsaspnCf8rW1drbDNZUJT/i+gsJLofzKWfY/zwJXGGO2Apd7bvuqs+1//KmdcPZ90GPAg8aYFKAGhYHd62j6UhERERHxGj5/5FRERERE/IfCqYiIiIh4DYVTEREREfEaCqciIiIi4jUUTkVERETEayicioiIiIjXUDgVEREREa+hcCoiIiL/v737jpOqPPs//rm2L8suvcPSkSJV7L0L2BIriWmPxjz5xUQTNZYYNSbGFkuMGuOTGJ9EH3tDRbGBhdhQ6R2U3jvL9rl+f8yAw7JlgNk9U77v14sXO+fcZ+a6mZnDd+9z7nNEEobCqYiIiIgkDIVTEREREUkYCqciIiIikjAUTkVEREQkYSicioiIiEjCUDgVERERkYShcCoiIiIiCUPhVEQkipk9ZmZ/CLoOEZF0pXAqImnBzCaZ2SVxfs5HzGyemYXM7Ie1rO9lZq+a2TYzW29md8b4vIeZ2VtmttHM1pnZs2bWKWq9mdkdZrYh8ucOM7PIun5m9nJku41mNsHMDqjx/L80s9VmttXMHjWz3P38pxARiRuFUxGRfTcN+H/AFzVXmFkO8BbwLtAR6Ao8HuPztgIeAXoA3YFtwD+j1l8KnA0MBYYAZwA/iaxrCYwDDgA6AJ8CL0fVdSpwLXBi5Ll7Ab+LsS4RkUancCoiacXMfmhmH9ZY5mbWp5a2M83sjKjHk7T31QAAIABJREFU2ZER0OEA7v6gu78DlNXyUj8EVrr7Pe5e4u5l7j49lhrd/XV3f9bdt7r7DuAB4MioJj8A7nb35e6+Arg78nq4+6fu/g933+julcC9wAFm1iZq23+4+yx33wT8fue2IiKJQOFURKRu/wIuino8Gljl7l/GsO1hwNdm9nok0E4ys8H7WMcxwKyox4MIj9ruNC2yrK5tV7v7hnq27RAVXkVEAqVwKiJSt8eB0WZWFHn8PeDfMW7bFbgQuB/oDLwGvBw53B8zMxsC3AhcHbW4ObAl6vEWoPnO806jtu0KPAj8qoFtAQr3pi4RkcaicCoiUgd3XwlMBs4xs5bAKOCJGDcvBT6MHKKvAP4EtAEGxPr6kVMNXgcud/cPolZtB4qiHhcB293do7ZtB7wJPOTuTzawLYTPaxURCZzCqYikmxKg2c4HZtaxgfb/S/jQ/nnAR5FzPGMxHfAGW9XBzLoDbwO/d/eao7WzCE+G2mkoUYf9zawV4WA6zt1vjWHbNVGH/UVEAqVwKiLpZhowyMyGmVkecHMD7V8CRgCXEz4HdRczy4k8hwHZZpZnZjv3q48Dh5nZSWaWCVwBrAfmRLZ9zMweq+0FzawL4Vn+D7j7w7U0+RfwKzPrYmadgSuBxyLbFgETgMnufm0d215sZgMjo8E37NxWRCQRKJyKSDpxd58P3EJ4VHIB8GEDG5QCzwM9gRdqrH6T8OH7Iwhf+qmU8AQk3H0e4RHXh4FNwFnAmZFD/ADdCJ8yUJtLCF/i6WYz277zT9T6vwGvADOAmYTPZ/1bZN23gIOBH0Vva2bFkbreAO4EJgJLgSXATfX9G4iINCWLOkVJRCRlmdkXwC3u/tI+bHsj0M/dL2qwcWzPl0N4BHdI5HJPIiISkRV0ASIijc3MBhGeiBTLJaBqbtsauJjwTP24iIyexjwxSkQkneiwvoikNDO7g/Dh92vcfclebvtjYBnwuru/3xj1iYjI7nRYX0REREQShkZORURERCRhBHbOadu2bb1Hjx5BvbyIiIiIBOTzzz9f7+7talsXWDjt0aMHU6ZMCerlRURERCQgZlbnHAAd1hcRERGRhKFwKiIiIiIJQ+FURERERBKGwqmIiIiIJAyFUxERERFJGAqnIiIiIpIwFE5FREREJGEonIqIiIikqQVrtrGtrDLoMnajcCoiIiKSZqqqQ/x10iLG3P8hfxw/N+hydhPYHaJEREREpOktXLuNK5+dzrRlmylu3YyzhnUOuqTdKJyKiIiIpIHqkPP3DxZz91vzqagK8f3Du3PNaf0pyE2sOJhY1YiIiIhI3C1at52rn53GF0s306VlPnedO4Qj+rQNuqxaKZyKiIiIpKjqkPPPyV9x14R5lFeF+O6hxVw3egDNE2y0NFriViYiIiIi++yr9SVc/ew0pizZRJeW+dxxzhCO6puYo6XRFE5FREREUkgo5Dz2n6+5c8JcyipDjD2kG9ePHkBhXnbQpcVE4VREREQkRSzZUMLVz03n06820qlFHrefM4Rj+7ULuqy9onAqIiIikuRCIefxT5Zw2/i5lFZWc/7Irtxw+kCKkmS0NJrCqYiIiEgSW7ZxB1c/N42PF2+kQ1EuD313BMf3bx90WftM4VREREQkCYVCzhOfLuW28XPYUVHNt0d04abTB9GiWfKNlkZTOBURERFJMss37eCa56czeeEG2hXmcv+FwzlpYIegy4oLhVMRERGRJOHuPPXZMv7w6mxKKqr51vAu3HTGQFo2ywm6tLhROBURERFJAis3l3LN89P5YMF62jbP4Z4LhnHqoI5BlxV3CqciIiIiCczdeWbKMv7w6hy2lVdxxtDO/O7MQbQuSJ3R0mgKpyIiIiIJatWWUq59fgbvzV9Hm4Ic/nruCEYN7hR0WY1K4VREREQkwbg7z3+xgt+9MottZVWMGdyJW84aRJvmuUGX1ugaDKdm9ihwOrDW3Q+sZf13gWsAA7YBP3X3afEuVERERCQdrNlaxnUvzODduWtp1SybB74znNOHdA66rCYTy8jpY8ADwL/qWP8VcKy7bzKzUcAjwKHxKU9EREQkPbg7L365gpvHzWJrWRWnDerI788+kHaFqT9aGq3BcOru75tZj3rW/yfq4cdA1/0vS0RERCR9rN1WxvUvzOTtOWto2Syb+8cO54whnTCzoEtrcvE+5/Ri4PW6VprZpcClAMXFxXF+aREREZHk4u6Mm7aSm8bNYvOOSk4e2IFbv3Ug7Qvzgi4tMHELp2Z2POFwelRdbdz9EcKH/Rk5cqTH67VFREREks26beXc8NIMJsxaQ4v8bO69YChnD+uSlqOl0eISTs1sCPB3YJS7b4jHc4qIiIikqlenr+S3L81k045KTuzfnj9+ezAditJ3tDTafodTMysGXgC+5+7z978kERERkdS0YXs5v315JuNnrKYwL4u7zxvKt0dotDRaLJeSehI4DmhrZsuBm4BsAHd/GLgRaAM8FPmHrXL3kY1VsIiIiEgyen3GKm54aSYbSio47oB23P7tIXRsodHSmmKZrT+2gfWXAJfErSIRERGRFLKxpIIbX57Jq9NXUZibxZ3nDOG8kV01WloH3SFKREREpJG8MXM1N7w0g/XbKzi6b1vuOGcInVvmB11WQlM4FREREYmzTSUV3PzKLF6eupLmuVnc/u3BXHBwN42WxkDhVERERCSO3pq9hutfnMG6beUc2acNd5wzhK6tmgVdVtJQOBURERGJgy07KvndK7N44csVNMvJ5A9nH8h3Dy3WaOleUjgVERER2U/vzl3DdS/MYM3Wcg7v1YY7zx1Ct9YaLd0XCqciIiIi+2hLaSW/f3U2z32+nPzsTH5/1iC+e2h3MjI0WrqvFE5FRERE9sGkeWu59vkZrN5axiE9W3PXuUPo3qYg6LKSnsKpiIiIyF7YWlbJra/O4ekpy8jLzuCmMwbyg8N7aLQ0ThRORURERGL0wYJ1XPPcdFZuKWNk91b86byh9Gir0dJ4UjgVERERacD28ipufW0OT366lNysDG4YM4AfHdmTTI2Wxp3CqYiIiEg9Ji9cz6+fm86KzaWMKG7JXecNpXe75kGXlbIUTkVERERqUVJexe2vz+XfHy8hJyuD60f35+Kjemm0tJEpnIqIiIjU8NGiDfz6+Wks21jK0G4tufu8ofRpr9HSpqBwKiIiIhLl2SnLuPq56eRkZnDNaf358dE9ycrMCLqstKFwKiIiIhLx9foSbho3i3aFuTxxyaH061AYdElpR78GiIiIiABV1SF++cxUdlRUc+e5QxRMA6JwKiIiIgI8NGkRXy7dzEWHFXP8Ae2DLidtKZyKiIhI2pu2bDN/fmcBvdoW8JvRA4MuJ60pnIqIiEhaK62o5pdPTwXg3guGkZ+TGXBF6U3hVERERNLaH8fPYfH6En5xQl+GdmsZdDlpT+FURERE0tbEeWv598dLGF7ckp8d3zvocgSFUxEREUlTG0sq+PVz08nPzuTe84fpWqYJQu+CiIiIpB135/oXZrBuWzm/PX0gPdoWBF2SRCicioiISNp57vPlvDFrNSf2b8/YQ7oFXY5EUTgVERGRtLJs4w5+98ps2hTkcPs5QzCzoEuSKAqnIiIikjaqQ86vnpnK9vIqbj9nCO0Kc4MuSWpQOBUREZG08bf3F/HZ15u48OBunDywQ9DlSC0aDKdm9qiZrTWzmXWsNzO738wWmtl0MxsR/zJFRERE9s/MFVu49635FLduxm9P112gElUsI6ePAafVs34U0Dfy51Lgr/tfloiIiEj8lFWG7wJVHXLuvWAYBblZQZckdWgwnLr7+8DGepqcBfzLwz4GWppZp3gVKCIiIrK/7nhjLgvWbudnx/fhoO6tgi5H6hGPc067AMuiHi+PLNuDmV1qZlPMbMq6devi8NIiIiIi9ftgwTr+OflrBndpwS9O7Bt0OdKAJp0Q5e6PuPtIdx/Zrl27pnxpERERSUObd1Rw1bPTyMvO4N4LhpGtu0AlvHi8QyuA6KvXdo0sExEREQmMu3PDSzNZs7Wc60cPoE/75kGXJDGIRzgdB3w/Mmv/MGCLu6+Kw/OKiIiI7LOXp67k1emrOKZfO753WPegy5EYNThVzcyeBI4D2prZcuAmIBvA3R8GxgOjgYXADuBHjVWsiIiISCxWbC7lty/PpGWzbO46V3eBSiYNhlN3H9vAegd+FreKRERERPZDKORc9cw0tpVV8dfvjqBDUV7QJcle0FnBIiIiklL+8eFXfLR4A+eM6Mqowbq6ZbJROBUREZGUMXf1Vu6aMI8uLfO56UzdBSoZKZyKiIhISiivquaKp6ZSGQpx7wXDKMrLDrok2QcKpyIiIpIS7n5zPnNXb+Mnx/TmkJ6tgy5H9pHCqYiIiCS9jxZt4H8+WMyATkX86uR+QZcj+0HhVERERJLa1rJKrnp2GtmZGfz5wmHkZCneJDO9eyIiIpLUbnp5Fis2l3LNaf3p16Ew6HJkPymcioiISNJ6dfpKXvxyBUf2acOPjugRdDkSBwqnIiIikpRWbynjNy/OpCgviz+dN5SMDN0FKhU0eIcoERERkUQTCjlXPzeNLaWV3D92OJ1a5AddksSJRk5FREQk6fzro6/5YMF6zhrWmTOHdg66HIkjhVMRERFJKgvWbOO21+fSqUUet5x5YNDlSJwpnIqIiEjSqKgKccXTUymvCnH3eUNp0Ux3gUo1CqciIiKSNO57ez6zVm7lkqN6ckSftkGXI41A4VRERESSwmdfb+Th9xZxQIdCrjr1gKDLkUaicCoiIiIJb1tZJb96ZipZGRnce8Ew8rIzgy5JGonCqYiIiCS8W16ZzbKNpVx5Sj8Gdi4KuhxpRAqnIiIiktDemLmaZz9fziE9W3PJ0b2CLkcamcKpiIiIJKy128q4/sUZFOZmcc/5Q8nUXaBSnu4QJSIiIgnJ3fn1c9PZWFLBPecPpWurZkGXJE1AI6ciIiKSkJ74ZCmT5q1j9OCOfGt4l6DLkSaicCoiIiIJZ/G67dz62hzaF+Zy69mDMdPh/HShw/oiIiKSUCqrQ/zy6amUVlbz8PcOolVBTtAlSRPSyKmIiIgklAfeXci05Vv4weHdObZfu6DLkSamcCoiIiIJ48ulm3hg4kJ6tyvg2lEDgi5HAqBwKiIiIgmhpLyKXz49FQPuu2A4+Tm6C1Q6iimcmtlpZjbPzBaa2bW1rC82s4lm9qWZTTez0fEvVURERFLZrePn8PWGHVxxUl8Gd20RdDkSkAbDqZllAg8Co4CBwFgzG1ij2Q3AM+4+HLgQeCjehYqIiEjqemfOGv7vk6Uc1L0V/31s76DLkQDFMnJ6CLDQ3Re7ewXwFHBWjTYO7LzRbQtgZfxKFBERkVS2fns51zw/nYKcTO49fxhZmTrrMJ3F8u53AZZFPV4eWRbtZuAiM1sOjAd+XtsTmdmlZjbFzKasW7duH8oVERGRVOLuXPfCDNZvr+DGMwZS3EZ3gUp38frVZCzwmLt3BUYD/zazPZ7b3R9x95HuPrJdO10aQkREJN09M2UZb81ewykDO3D+yG5BlyMJIJZwugKI/rR0jSyLdjHwDIC7fwTkAW3jUaCIiIikpiUbSvjdK7Np2zyH276tu0BJWCzh9DOgr5n1NLMcwhOextVosxQ4EcDMBhAOpzpuLyIiIrWqitwFakdFNXeeO4Q2zXODLkkSRIPh1N2rgMuACcAcwrPyZ5nZLWZ2ZqTZlcCPzWwa8CTwQ3f3xipaREREktvD7y3ii6Wb+c6hxZzQv0PQ5UgCyYqlkbuPJzzRKXrZjVE/zwaOjG9pIiIikoqmL9/MfW8voEebZtwwRneBkt3pWg0iIiLSZEorqrni6ak4cO8Fw2iWE9M4maQRhVMRERFpMre/PofF60q47Pg+DC9uFXQ5koAUTkVERKRJvDd/Hf/70RKGdmvJZSf0CbocSVAKpyIiItLoNpVUcPWz08jPzuTe84eSrbtASR30yRAREZFG5e5c/+IM1m4r5zdjBtCrXfOgS5IEpnAqIiIijeqFL1bw+szVHH9AO757aHHQ5UiCUzgVERGRRrNs4w5uGjeL1gU53HHuEN0FShqk6zeIiIhIo6gOOVc+M43t5VX87fyDaF+YF3RJkgQ0cioiIiKN4n8+WMynX2/k/JFdOXVQx6DLkSShcCoiIiJxN2vlFu5+cx7dWudz4xmDgi5HkojCqYiIiMRVWWU1v3x6KtUh597zh9E8V2cRSuwUTkVERCSu7powj/lrtvPT43ozskfroMuRJKNwKiIiInEzeeF6/vHhVxzYpYjLT+wXdDmShBRORUREJC627KjkqmenkZuVwX0XDCMnSzFD9p4+NSIiIhIXv315Jqu2lHHdqP70aV8YdDmSpBRORUREZL+9PHUF46at5Oi+bfn+4T2CLkeSmMKpiIiI7JeVm0u54aWZtMjP5q5zh5KRobtAyb7TtR1ERERkn4VCzlXPTmNbWRUPfmcEHVvoLlCyfzRyKiIiIvvs0clf8Z9FG/jW8C6MGdIp6HIkBSicioiIyD6Zt3obd06YR5eW+fzuLN0FSuJD4VRERET2WnlVNVc8PZXK6hB3nz+UorzsoEuSFKFwKiIiInvtnrfmM2fVVn58dC8O69Um6HIkhSicioiIyF75ePEGHnl/Mf07FnLlKboLlMSXwqmIiIjEbGtZJVc+M43sjAzuu3AYuVmZQZckKUbhVERERGJ287hZrNhcytWnHkD/jkVBlyMpSOFUREREYvLCF8t54YsVHN6rDRcf1TPociRF6SL8IiIiUid3Z/LCDdz/7gI+/WojhXlZ/Ol83QVKGk9M4dTMTgP+DGQCf3f322tpcz5wM+DANHf/ThzrFBERkSbk7kyat477313Al0s3YwZnDO3M5Sf2pUvL/KDLkxTWYDg1s0zgQeBkYDnwmZmNc/fZUW36AtcBR7r7JjNr31gFi4iISOMJhZy35qzhgXcXMmPFFjIzjG+P6MLPju9D73bNgy5P0kAsI6eHAAvdfTGAmT0FnAXMjmrzY+BBd98E4O5r412oiIiINJ7qkDN+xioenLiQuau3kZ1pjD2kGz89tg/FbZoFXZ6kkVjCaRdgWdTj5cChNdr0AzCzyYQP/d/s7m/UfCIzuxS4FKC4uHhf6hUREZE4qqoOMW7aSh6cuJBF60rIycrg+4d35yfH9tbhewlEvCZEZQF9geOArsD7ZjbY3TdHN3L3R4BHAEaOHOlxem0RERHZSxVVIV78cjkPTVrEkg07yMvO4OKjenLpMb3oUJQXdHmSxmIJpyuAblGPu0aWRVsOfOLulcBXZjafcFj9LC5VioiISFyUVVbz7JRlPPzeYlZsLqUgJ5P/PrY3lxzdk7bNc4MuTySmcPoZ0NfMehIOpRcCNWfivwSMBf5pZm0JH+ZfHM9CRUREZN+VVlTzf58u5ZH3F7FmazmFeVn84oQ+/OjInrQqyAm6PJFdGgyn7l5lZpcBEwifT/qou88ys1uAKe4+LrLuFDObDVQDV7v7hsYsXERERBq2vbyKxz9ewt8/WMz67RW0bJbNVaf04/tH9KAoLzvo8kT2YO7BnPo5cuRInzJlSiCvLSIikuq2lFbyv//5mkcnf8XmHZW0bZ7Dj4/uxUWHdacgV/fgkWCZ2efuPrK2dfp0ioiIpJBNJRU8OvkrHpv8NdvKq+hQlMuNpw9k7CHF5OdkBl2eSIMUTkVERFLA+u3l/M8Hi3n8oyWUVFTTpWU+vx7Vn/MO6kpetkKpJA+FUxERkSS2ZmsZf3tvMf/36RLKKkN0b9OMm47rw9nDu5CTlRF0eSJ7TeFUREQkCS3ftIOH31vEM58tp6I6RO92BVx2Qh/OGNKZrEyFUkleCqciIiJJZMmGEh6auIjnv1hOVcjp37GQy07ow6gDO5GZYUGXJ7LfFE5FRESSwMK123lo4kJenraS6pAzuEsLfn5CH04a0IEMhVJJIQqnIiIiCWzu6q385d2FjJ+xCncYUdySn5/Yl+P6tcNMoVRSj8KpiIhIApqxfAt/eXcBb85eA8ChPVvzixP7ckTvNgqlktIUTkVERBLI50s28cC7C5g4bx0AR/dty89P6MshPVsHXJlI01A4FRERSQAfL97AX95dwOSF4bt/n9i/PZed0Ifhxa0CrkykaSmcioiIBMTd+XDhev7yzkI+/XojAKcN6shlJ/ThwC4tAq5OJBgKpyIiIk3M3Zk4by33v7OQqcs2YwZnDO3MZcf34YCOhUGXJxIohVMREZEmEgo5b85ewwMTFzBzxVYyM4xzRnTl/x3fm97tmgddnkhCUDgVERFpZNUh57UZq3jw3YXMW7ON7Exj7CHd+OmxfShu0yzo8kQSisKpiIhII6mqDvHy1JU8OGkhi9eVkJOVwfcP785Pju1Nl5b5QZcnkpAUTkVEROKsoirEC18s56FJi1i6cQf52ZlcclRPLj2mF+2L8oIuTyShKZyKiIjESVllNc9MWcbDkxaxcksZBTmZ/PS43lxyVE/aNM8NujyRpKBwKiIisp9KK6p54pMlPPL+YtZuK6cwL4tfnNiX/zqyBy2b5QRdnkhSUTgVERHZR5XVIZ76dCl/fmcB67dX0KpZNled0o/vH9GDorzsoMsTSUoKpyIiInvJ3Zkwaw13vjGXxetLaNUsm+tG9eeiw7pTkKv/WkX2h75BIiIie+HzJZu4bfwcpizZRG5WBj89rjf/fWxvWuRrpFQkHhRORUREYvDV+hLufGMur89cjRmcM6IrV57Sj866JJRIXCmcioiI1GPD9nLuf2cBT3yylKqQc3Tftlw7qj+DOrcIujSRlKRwKiIiUovSimoenfwVf520iO3lVfTvWMj1owdwTL92QZcmktIUTkVERKJUh5znv1jOPW/OZ/XWMjq1yOPmMwfxreFdyMywoMsTSXkKpyIiIoRn4L83fx23vz6Xuau3UZibxTWn9edHR/YgLzsz6PJE0kZM4dTMTgP+DGQCf3f32+todw7wHHCwu0+JW5UiIiKNaOaKLdz2+hwmL9xAdqbxoyN78PMT+tK6QBfQF2lqDYZTM8sEHgROBpYDn5nZOHefXaNdIXA58EljFCoiIhJvyzft4J435/Pi1BW4w5ghnfj1qQfQvU1B0KWJpK1YRk4PARa6+2IAM3sKOAuYXaPd74E7gKvjWqGIiEicbSmt5KGJC/nnf76moirEwT1acf3oAQwvbhV0aSJpL5Zw2gVYFvV4OXBodAMzGwF0c/fXzEzhVEREElJ5VTWPf7yUv7y7gM07KunVroBrT+vPyQM7YKbJTiKJYL8nRJlZBnAP8MMY2l4KXApQXFy8vy8tIiISk1DIeXXGKu6aMJdlG0tp2zyHP5x9IBce3I2szIygyxORKLGE0xVAt6jHXSPLdioEDgQmRX7r7AiMM7Mza06KcvdHgEcARo4c6ftRt4iISEw+XryB28bPYdryLeRnZ3L5iX358TG9aJ6rC9aIJKJYvpmfAX3NrCfhUHoh8J2dK919C9B252MzmwRcpdn6IiISpAVrtnHHG3N5e85aMgzGHtKNX57Uj/ZFeUGXJiL1aDCcunuVmV0GTCB8KalH3X2Wmd0CTHH3cY1dpIiISKzWbi3j3rfn8/Rnywg5nDSgPdec1p++HQqDLk1EYhDTMQ13Hw+Mr7HsxjraHrf/ZYmIiOydkvIqHnl/Mf/zwWJ2VFQzpGsLrhs1gMN7twm6NBHZCzrhRkREklpVdYinPlvGfW8vYP32crq1zuf2U/tz+uBOZOh2oyJJR+FURESSkrvz1uw13PHGXBatK6FFfjY3jBnA9w7vTm6WbjcqkqwUTkVEJOl8uXQTt42fy6dfbyQnK4OfHNOL/3dcH1o0yw66NBHZTwqnIiKSNJZsKOHOCfN4bfoqAL41vAtXntKPrq2aBVyZiMSLwqmIiCS8jSUV/OXdBTz+8RIqq50j+7ThulEDOLBLi6BLE5E4UzgVEZGEVVZZzT8nf81DkxayrayKAzoUct3o/hzbr51uNyqSohRORUQk4VSHnJe+XMHdb85j5ZYyOhTl8tvTB3LOiK5kaga+SEpTOBURkYTywYJ1/HH8XOas2krz3CyuPvUA/uvInuTnaAa+SDpQOBURkYQwe+VWbnt9Dh8sWE9WhvGDw7vzixP70qZ5btCliUgTUjgVEZFArdxcyt1vzueFL5fjDqMO7MivT+tPz7YFQZcmIgFQOBURkUBsLavkr5MW8eiHX1FeFeKg7q24fvQADureKujSRCRACqciItKkKqpCPPHJEu5/ZwGbdlTSs20B15zWn1MHddAMfBFROBURkabh7oyfsZo7J8xlyYYdtCnI4fdnDeLCQ4rJzswIujwRSRAKpyIi0ug++3ojt742h6nLNpOXncHPT+jDpcf0ojBPtxsVkd0pnIqISKNZuHY7d7wxl7dmryHD4IKR3fjlyf3o2CIv6NJEJEEpnIqISFxtKa3k7dlreG3GKt6bv47qkHP8Ae24ZlR/+ncsCro8EUlwCqciIrLftpZFAun0Vby/YB2V1Y4ZHNKjNZef2Jcj+rQNukQRSRIKpyIisk+2lVXyzpy1vDp9Fe/PX0dFdQgzOLh7a0YP7siowZ3oUKTD9yKydxRORUQkZtvLq3hnzhpenR4+ZF9RFQJgZPdWjBnSiVEHdtL5pCKyXxRORUSkXiXlVbwzdy2vTV/JxHnfBNIRxS0ZM6Qzowd3pFOL/ICrFJFUoXAqIiJ7KCmv4t25a3lt+iomzltLeSSQDi9uyZjBnRg9uBOdWyqQikj8KZyKiAgAOyqqmDh3Ha/NWMm7c9dSVhkOpEO7teT0wZ0YNbgjXVs1C7hKEUl1CqciImmstKKaifPW8tqMVbw7Zy2lldUADO3aYtc5pN1aK5CKSNNROBURSTNlldVMmheeZf9OVCAd3CUcSMcMViAVkeAonIqIpIFwIF2LmFn8AAAORElEQVTH+BmreHvOGnZUhAPpgV2KGDO4M2MGd6K4jQKpiARP4VREJEWVVVbz/vx1vDZjFW/PXkNJJJAO7FS0a4S0R9uCgKsUEdmdwqmISAopr6rm/fnrGT9jFW/NXsP28ioABnQq4vQh4Vn2PRVIRSSBxRROzew04M9AJvB3d7+9xvpfAZcAVcA64L/cfUmcaxURkVqUV1Xz4YL1vDY9HEi3RQJp/46F4cs+DelE73bNA65SRCQ2DYZTM8sEHgROBpYDn5nZOHefHdXsS2Cku+8ws58CdwIXNEbBIiICFVUhPly4jtemr+bN2avZVhYOpAd0KGRMZIS0T3sFUhFJPrGMnB4CLHT3xQBm9hRwFrArnLr7xKj2HwMXxbNIEREJB9LJi8IjpG/OWs3WSCDt0745Fx8VPoe0b4fCgKsUEdk/sYTTLsCyqMfLgUPraX8x8HptK8zsUuBSgOLi4hhLFBFJX5XVISYvDJ9DOmHWGraUVgLQu10BPzyyJ6cP6UQ/BVIRSSFxnRBlZhcBI4Fja1vv7o8AjwCMHDnS4/naIiKporI6xEeLNvDa9FVMmL2azTvCgbRX2wJ+cHh3xgzpTL8OzTGzgCsVEYm/WMLpCqBb1OOukWW7MbOTgN8Ax7p7eXzKExFJD1XVIT5avIHxM1bxxszVbIoE0p5tC7jo0O6MGdKJ/h0LFUhFJOXFEk4/A/qaWU/CofRC4DvRDcxsOPA34DR3Xxv3KkVEUlBVdYhPvtrIq9NXMWHWajaWVADQo00zvnNoMWMGd2ZAJwVSEUkvDYZTd68ys8uACYQvJfWou88ys1uAKe4+DrgLaA48G9mJLnX3MxuxbhGRhFEdcsqrqqmoClFeFaK8MkR5VXX456qon6OWT1u2mTdmrmZDJJAWt27GBQd3Y8zgTgzqXKRAKiJpK6ZzTt19PDC+xrIbo34+Kc51iYjEJBRyKqqjQmDl7oHwm8D4TVisqCMw1ra8ojrU4HNWhfbtFPpurfM5b2RvxgzuxIFdFEhFREB3iBKRJuDubC+vYltZFVvLKsN/l1bu9vPOdWWV34TMb4Jh1Chk5e6BsaI61Ki152ZlhP9kZ5KTmUFudgYtm+XsWp6TlUFuVia52ZF2WZnfbBPZbo+2WRl0bdVMgVREpBYKpyLSoMrq0B4hcltZJVtLwz9vrbFu93ZVbCurZF8GF3OyMsiNBMKdoa4oP/ubEBgVCHNqCYQ5NbbNzc4gJ/Obn3cuz6kjSOZkZig8iog0MYVTkRTn7pRWVu82WrlnmAwHyK2RIBluV7UrgJZWVu/VazbLyaQwL4uivGw6FOXt+rkwL4ui/Ozdft65rkV+FoV52eRFBcuMDAVDEZF0o3AqksDcnfKqEGU7w2XUaGXNkcyao5XRy/bmnMgMg8JIeGxTkEvPtgUU5oUDZVEkQBZFAmVR/s7Q+c26wrwssjMzGvFfRUREUpnCqUgd3MMTbXZNfomaAFNRtecEnIrqGpNxdp4zuVeTcaKeM/LaeysnK2NXcCxuU1BLkKx79LIoP5uCnEwdyhYRkcAonErSqA4523eOCO463FwV0+zs2i7nU1Fz3a4JON9s15iyM223yTM5WRk0z82iTfOcPc6jzMvOrPfQeFHeN6OWedmZjVq3iIhIY1I4lSZTXlW9xyHpmA5PR85/3F5eFbdasjJsj5nWBbmZtM7K2X1iTWTdHhNroifg1DaxZrfJOrtvt/P5dD6liIjIntImnH6yeAMfLd7Q4OzcnevzsmvOAA7/nJmmgcLdKamo3iNQ1h4uv5nBvS0SLLeWVe71IermuVnhQ9L52XRplV/rqGGz3Kw9gmR9gXDn31k6J1JERCQhpU04/XjxRu57e8F+P8/OQ7Gxja7tHnhzawm8tS+v/zn35XzAqp2XAtptZnaNILnbZJvdJ97s7aWAsjJsV5Ds1CKPfh2a15hQs+ch6Z3nRBblZdM8LyttfxEQERFJZ2kTTsce2o3j+7eL6Y4wdU142e28xaiLgW8vr2JDye7bNqaczPoPJ+dkZVBaufso546KvbsUUP7Ocxzzs2lfmBsJj7sHyV2ztvOjZ2+HQ2d+tibViIiIyN5Lm3DavjCP9oV5TfJaO2d51zn5prYZ37Xc+SY6NIefb/fZ4NHPubW0crfnzMsOX6y8dUEuPdoU1BiZrH+2ti4FJCIiIkFJm3DalMx2zsLOhKbJwyIiIiIpQcNjIiIiIpIwFE5FREREJGEonIqIiIhIwlA4FREREZGEoXAqIiIiIglD4VREREREEobCqYiIiIgkDIVTEREREUkYCqciIiIikjDM3YN5YbN1wJImftm2wPomfs2gpEtf1c/Uky59VT9TT7r0Vf1MPUH0tbu7t6ttRWDhNAhmNsXdRwZdR1NIl76qn6knXfqqfqaedOmr+pl6Eq2vOqwvIiIiIglD4VREREREEka6hdNHgi6gCaVLX9XP1JMufVU/U0+69FX9TD0J1de0OudURERERBJbuo2cioiIiEgCUzgVERERkYSR9OHUzB41s7VmNrOeNjebmZtZn6hlV0SWJcylE+pjZnlm9qmZTTOzWWb2uzraPWZmO8ysMGrZfZG+tm26ivedmbU0s+fMbK6ZzTGzw2tpk/TvabSGPsdmdrKZfWRmFnmcaWZfmtkRTVvpvjOzbmY20cxmRz7Dl9fSJhX62eB31cx+bGZPRz0uMrNFZtaraavdf2b2tZnNMLOpZjallvWp8J4eEOnfzj9bzeyKGm2Stp917X/MrLWZvWVmCyJ/t6qxvn3k/e8YtexBM7uuqWqPVX37n1TqJ9S/DzKznmb2iZktNLOnzSynxraDzGy+meVHLXvNzMY2ZR+SPpwCjwGnxdBuBnBh1OPzgFmNUVAjKQdOcPehwDDgNDM7rI62C4GzAMwsAzgBWNEkVcbHn4E33L0/MBSYU0e7ZH9Poz1GPZ9jd3+L8E0rLo4s+jkwxd3/E93OzLIaq8A4qAKudPeBwGHAz8xsYHSDFOlnLN/VvwPdzOykyONbgEfdfXF0owTvZ7Tj3X1YbddJTIX31N3nRfo3DDgI2AG8WKNNMvfzMWrf/1wLvOPufYF3Io93cfe1wO3AnwDMbARw9M7HOyVIn+vb/6RSP6H+fdAdwL3u3gfYxDefVwDcfRbwAvAbADM7G8h29yej2zV6X9096f8APYCZ9ay/mfDO/7PI497AeGASMDKybCzhsDMTuCPoPjXQ32bAF8Chtax7DLgeeCXy+ATgr8DXQNvIsl9F+jkTuCLo/tSovwXwFZHJeunynkbqbehz3AlYBAwi/AtI66j3/GHgE+CeoPuxF/19GTg5lfvZwHd1SOSzOTLyOc2JLJ8E3AdMIfyfaeD9aKCPu/Yt9bRJpff0FGByqvWztv0PMA/oFNW3ebVslwF8BBwf+fuYyPIfAuOAd4H3gu5fLXXv2v+keD937YMAI3wXqKzIusOBCXVsM49wsJ0L9I0svxn4NzAZeLIx606UlN8UtgLLzOxAwqOKTwM/AjCzzoR/mziI8G8Sb5rZ2e7+UlDF1sbMMoHPgT7Ag+7+SR1N5wNnRg5NjAUeB0ZFnuMgwv3e+UH9xMzec/cvG7v+GPUE1gH/NLOhhPt7ubuX1NI26d/TveHuq8zsPsI7xl+4+8ao1V2BI9y9Opjq9o6Z9QCGE/7Pejep0M9YvqvuPt3MJhAeqTnL3SuiVud4At2tpQFO+PvlwN/cfY9L0qTCexrlQuDJ2lakWD8BOrj7qsjPq4EONRu4e8jMfko4nI1z9/ejVo8AhtT4dwhcLfuflOtnbfsgC5/at9ndqyLNlgNdam7r7jvM7CrgfcK/TC2IWj0QOMrdSxuz/lQ4rL83niK8Yzmb3Q/JHAxMcvd1kTftCeCYAOqrl7tXe/iwUlfgkEgoq8sLhPt6KPBB1PKjgBfdvcTdt0faHd1YNe+DLMJf9L+6+3CghBqHWGpI6vd0HzwIZLr7YzWWP5ss/+mZWXPgecKj9lvraJbU/dyL7+qDwAp3n1Rj+dO1tE1UR7n7CMK/AP/MzOr6niX1ewoQOT/vTODZepolfT9r4+Ghs1qvPenuUwkfBXioxqq3EimwQcP7n1Tp517mhdq2fwXYzJ59HdfYwRTSL5y+CnwPWFrPf4oJz903AxOp/1zbp4HfE/7ShJqksPhYDiyPGml6jnBYrUtKvKexiryXte04axtZTjhmlk34P4Yn3P2Futolez93iuG7Gor8qSlp+unuKyJ/ryX8C+IhdbRLhfd0FPCFu6+pq0GK9HOnNWbWCSDy99p62tb2WU6oPtez/0mpfkarsQ/aALSMOl+0K/XPRwmsr2kVTt19B3ANcGuNVZ8Cx5pZ28hQ+Fjgvaaurz5m1s7MWkZ+zgdOJnwuSK3cfQnhE5pr/tbzAXC2mTUzswLgW+w+shood19N+FD9AZFFJwKz62mftO9puonMYv4HMMfd7wm6nsayt9/VZGZmBRa5Mkhkf3IK4ZGlVDWWOg7pp6hxwA8iP/+A8HmaSamB/U/K9BPq3gdFRoUnAudGmiZsX5M+nJrZk4TP7znAzJab2cX1tXf3p9z9ixrLVhE+dDwRmAZ87u6J9oZ1Aiaa2XTgM8Ijoq/Wt4G7/83dF9VY9gXhk/M/JXy+zd8T6HzTnX4OPBHp6zDgj/U1TuL3dJe9/RwnqSMJj3KfYN9ckmd00EU1gr3+riaxDsCHZjaN8D7lNXd/I+CaGkUkfJ9M+FSolFLP/ud24GQzWwCcFHmcrOrb/6RSP6H+fdA1wK/MbCHQhnBgTzi6famIiIiIJIykHzkVERERkdShcCoiIiIiCUPhVEREREQShsKpiIiIiCQMhVMRERERSRgKpyIiIiKSMBRORURERCRh/H9iQGIbbpRJzwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 828x684 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nlT--6simKBr"
      },
      "source": [
        "# DONT RUN THE CELL BELOW! IT WILL ERASE THE PLOT!"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1m_H6_5ImKBs",
        "outputId": "2716e59a-74c1-4c57-fae5-09a7deec8d23"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yD3BmoEImKBs"
      },
      "source": [
        "**BONUS CHALLENGE TASK: Try to recreate the plot below that uses twin axes. While this plot may actually be more confusing than helpful, its a good exercise in Matplotlib control.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 441
        },
        "id": "mJbtwAgWLDT5",
        "outputId": "74961279-8678-4ec3-9cce-666df0dbbd65"
      },
      "source": [
        "# CODE HERE\n",
        "\n",
        "fig, ax1 = plt.subplots(figsize=(10.5,6))\n",
        "\n",
        "color = 'blue'\n",
        "ax1.set_ylabel('2007', color=color, fontsize=18)\n",
        "ax1.set_title(\"July 16th Yield Curves\")\n",
        "ax1.plot(labels, july16_2007, color=color)\n",
        "ax1.tick_params(axis='y', labelcolor=color)\n",
        "\n",
        "ax1.spines['left'].set_color('blue')\n",
        "ax1.spines['left'].set_linewidth(4)\n",
        "\n",
        "ax2 = ax1.twinx()  # instantiate a second axes that shares the same x-axis\n",
        "\n",
        "color = 'red'\n",
        "ax2.set_ylabel('2020', color=color, fontsize=18)  # we already handled the x-label with ax1\n",
        "ax2.plot(labels, july16_2020, color=color)\n",
        "ax2.tick_params(axis='y', labelcolor=color)\n",
        "\n",
        "ax2.spines['right'].set_color('red')\n",
        "ax2.spines['right'].set_linewidth(4) \n",
        "\n",
        "fig.tight_layout()  # otherwise the right y-label is slightly clipped\n",
        "plt.show()\n"
      ],
      "execution_count": 161,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 756x432 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cP5KQYKBmKBs"
      },
      "source": [
        "# DONT RUN THE CELL BELOW! IT ERASES THE PLOT!"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "28c2YnrmmKBt",
        "outputId": "05d2d38f-fa74-4230-9266-bd3c0368c86a"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([0. , 0.2, 0.4, 0.6, 0.8, 1. , 1.2, 1.4]),\n",
              " <a list of 8 Text yticklabel objects>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 73
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
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}