ablim.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "ABLIM1 seq\n",
        "MPAFLGLKCLGKLCSSEKSKVTSSERTSARGSNRKRLIVEDRRVSGTSFTAHRRATITHLLYLCPKDYCPRGRVCNSVDPFVAHPQDPHHPSEKPVIHCHKCGEPCKGEVLRVQTKHFHIKCFTCKVCGCDLAQGGFFIKNGEYLCTLDYQRMYGTRCHGCGEFVEGEVVTALGKTYHPNCFACTICKRPFPPGDRVTFNGRDCLCQLCAQPMSSSPKETTFSSNCAGCGRDIKNGQALLALDKQWHLGCFKCKSCGKVLTGEYISKDGAPYCEKDYQGLFGVKCEACHQFITGKVLEAGDKHYHPSCARCSRCNQMFTEGEEMYLQGSTVWHPDCKQSTKTEEKLRPTRTSSESIYSRPGSSIPGSPGHTIYAKVDNEILDYKDLAAIPKVKAIYDIERPDLITYEPFYTSGYDDKQERQSLGESPRTLSPTPSAEGYQDVRDRMIHRSTSQGSINSPVYSRHSYTPTTSRSPQHFHRPGNEPSSGRNSPLPYRPDSRPLTPTYAQAPKHFHVPDQGINIYRKPPIYKQHAALAAQSKSSEDIIKFSKFPAAQAPDPSETPKIETDHWPGPPSFAVVGPDMKRRSSGREEDDEELLRRRQLQEEQLMKLNSGLGQLILKEEMEKESRERSSLLASRYDSPINSASHIPSSKTASLPGYGRNGLHRPVSTDFAQYNSYGDVSGGVRDYQTLPDGHMPAMRMDRGVSMPNMLEPKIFPYEMLMVTNRGRNKILREVDRTRLERHLAPEVFREIFGMSIQEFDRLPLWRRNDMKKKAKLF"
      ],
      "metadata": {
        "id": "J9NZVAOQ-Q07"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pylab as plt"
      ],
      "metadata": {
        "id": "Ijy7T_H7gud7"
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "ABLIM2 seq\n",
        "MSAVSQPQAAPSPLEKSPSTAILCNTCGNVCKGEVLRVQDKYFHIKCFVCKACGCDLAEGGFFVRQGEYICTLDYQRLYGTRCFSCDQFIEGEVVSALGKTYHPDCFVCAVCRLPFPPGDRVTFNGKECMCQKCSLPVSVGSSAHLSQGLRSCGGCGTEIKNGQALVALDKHWHLGCFKCKSCGKLLNAEYISKDGLPYCEADYHAKFGIRCDSCEKYITGRVLEAGEKHYHPSCALCVRCGQMFAEGEEMYLQGSSIWHPACRQAARTEDRNKETRTSSESIISVPASSTSGSPSRVIYAKLGGEILDYRDLAALPKSKAIYDIDRPDMISYSPYISHSAGDRQSYGEGDQDDRSYKQCRTSSPSSTGSVSLGRYTPTSRSPQHYSRPGSESGRSTPSLSVLSDSKPPPSTYQQAPRHFHVPDTGVKDNIYRKPPIYRQHAARRSDGEDGSLDQDNRKKSSWLMLKGDADTRTNSPDLDTQSLSHSSGTDRDPLQRMAGDSFHSRFPYSKSDPLPGHGKNGLDQRNANLAPCGADPDASWGMREYKIYPYDSLIVTNRIRVKLPKDVDRTRLERHLSPEEFQEVFGMSIEEFDRLALWKRNDLKKKALLF\n",
        "\n",
        "MYBPC seq (hairpin)\n",
        "RSAFRRTSLAGAGRRTSDSHED\n"
      ],
      "metadata": {
        "id": "wm4kJ2eV-aVt"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "* ABLIM1's LIM domains span 97-343\n",
        "* ABLIM2's LIM domains span 22-270\n",
        "Aligned sequences using blast\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "4U26G6MF-fPM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "fastaAblim1='MPAFLGLKCLGKLCSSEKSKVTSSERTSARGSNRKRLIVEDRRVSGTSFTAHRRATITHLLYLCPKDYCPRGRVCNSVDPFVAHPQDPHHPSEKPVIHCHKCGEPCKGEVLRVQTKHFHIKCFTCKVCGCDLAQGGFFIKNGEYLCTLDYQRMYGTRCHGCGEFVEGEVVTALGKTYHPNCFACTICKRPFPPGDRVTFNGRDCLCQLCAQPMSSSPKETTFSSNCAGCGRDIKNGQALLALDKQWHLGCFKCKSCGKVLTGEYISKDGAPYCEKDYQGLFGVKCEACHQFITGKVLEAGDKHYHPSCARCSRCNQMFTEGEEMYLQGSTVWHPDCKQSTKTEEKLRPTRTSSESIYSRPGSSIPGSPGHTIYAKVDNEILDYKDLAAIPKVKAIYDIERPDLITYEPFYTSGYDDKQERQSLGESPRTLSPTPSAEGYQDVRDRMIHRSTSQGSINSPVYSRHSYTPTTSRSPQHFHRPGNEPSSGRNSPLPYRPDSRPLTPTYAQAPKHFHVPDQGINIYRKPPIYKQHAALAAQSKSSEDIIKFSKFPAAQAPDPSETPKIETDHWPGPPSFAVVGPDMKRRSSGREEDDEELLRRRQLQEEQLMKLNSGLGQLILKEEMEKESRERSSLLASRYDSPINSASHIPSSKTASLPGYGRNGLHRPVSTDFAQYNSYGDVSGGVRDYQTLPDGHMPAMRMDRGVSMPNMLEPKIFPYEMLMVTNRGRNKILREVDRTRLERHLAPEVFREIFGMSIQEFDRLPLWRRNDMKKKAKLF'\n",
        "short = fastaAblim1[343:473]\n",
        "dshort = short.replace('STS','DTD')\n",
        "print(dshort)\n",
        "print(short)\n",
        "print(\"STS\" in short)\n"
      ],
      "metadata": {
        "id": "Pgm14IXGgvlB",
        "outputId": "ef27e72d-6d73-4c18-e3cc-6a005e2b1d27",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "EKLRPTRTSSESIYSRPGSSIPGSPGHTIYAKVDNEILDYKDLAAIPKVKAIYDIERPDLITYEPFYTSGYDDKQERQSLGESPRTLSPTPSAEGYQDVRDRMIHRDTDQGSINSPVYSRHSYTPTTSRS\n",
            "EKLRPTRTSSESIYSRPGSSIPGSPGHTIYAKVDNEILDYKDLAAIPKVKAIYDIERPDLITYEPFYTSGYDDKQERQSLGESPRTLSPTPSAEGYQDVRDRMIHRSTSQGSINSPVYSRHSYTPTTSRS\n",
            "True\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "ABLIM1's disordered N-term region spans 1-97 and C-term region starts after 373"
      ],
      "metadata": {
        "id": "yRcAAyL38aBz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "fastaAblim1Cterm = fastaAblim1[373:]\n",
        "len(fastaAblim1Cterm)\n",
        "fastaAblim1Nterm = fastaAblim1[0:97]\n",
        "index = fastaAblim1.find('MPAF')\n",
        "print(index) # confirming idx=0\n",
        "\n",
        "index = fastaAblim1.find('AQPMSSSPKETTF')\n",
        "print(index)\n",
        "msssp=fastaAblim1[index:(index+13)]\n",
        "print( msssp, len(msssp))\n",
        "msdsp=\"AQPMSDSPMKETTF\""
      ],
      "metadata": {
        "id": "wf-OCjlF8RQ-",
        "outputId": "f9ce2d2d-b448-4a82-de5e-ec262d7c41b9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0\n",
            "209\n",
            "AQPMSSSPKETTF 13\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## CIDER"
      ],
      "metadata": {
        "id": "oJK39lTlqy-X"
      }
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "9TuHPyXfFw9w"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!pip3 install localcider"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4AEvIX_rq6If",
        "outputId": "39208ac5-7150-4605-fada-0221dd73b735"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting localcider\n",
            "  Downloading localcider-0.1.21.tar.gz (110 kB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m110.1/110.1 kB\u001b[0m \u001b[31m2.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25h  Preparing metadata (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "Requirement already satisfied: numpy in /usr/local/lib/python3.10/dist-packages (from localcider) (1.26.4)\n",
            "Requirement already satisfied: matplotlib in /usr/local/lib/python3.10/dist-packages (from localcider) (3.8.0)\n",
            "Requirement already satisfied: scipy in /usr/local/lib/python3.10/dist-packages (from localcider) (1.13.1)\n",
            "Collecting BioPython (from localcider)\n",
            "  Downloading biopython-1.84-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (12 kB)\n",
            "Requirement already satisfied: contourpy>=1.0.1 in /usr/local/lib/python3.10/dist-packages (from matplotlib->localcider) (1.3.0)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.10/dist-packages (from matplotlib->localcider) (0.12.1)\n",
            "Requirement already satisfied: fonttools>=4.22.0 in /usr/local/lib/python3.10/dist-packages (from matplotlib->localcider) (4.54.1)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.10/dist-packages (from matplotlib->localcider) (1.4.7)\n",
            "Requirement already satisfied: packaging>=20.0 in /usr/local/lib/python3.10/dist-packages (from matplotlib->localcider) (24.1)\n",
            "Requirement already satisfied: pillow>=6.2.0 in /usr/local/lib/python3.10/dist-packages (from matplotlib->localcider) (10.4.0)\n",
            "Requirement already satisfied: pyparsing>=2.3.1 in /usr/local/lib/python3.10/dist-packages (from matplotlib->localcider) (3.2.0)\n",
            "Requirement already satisfied: python-dateutil>=2.7 in /usr/local/lib/python3.10/dist-packages (from matplotlib->localcider) (2.8.2)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.10/dist-packages (from python-dateutil>=2.7->matplotlib->localcider) (1.16.0)\n",
            "Downloading biopython-1.84-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (3.2 MB)\n",
            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m3.2/3.2 MB\u001b[0m \u001b[31m42.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hBuilding wheels for collected packages: localcider\n",
            "  Building wheel for localcider (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for localcider: filename=localcider-0.1.21-py3-none-any.whl size=116026 sha256=8ebe4a2f61843b945523933f3d380e60eaf5738a6bd4e9820c31da8a6178e189\n",
            "  Stored in directory: /root/.cache/pip/wheels/f3/81/3a/bc50ee0a0b35baa984d81c6c72e31316c88c11b33318d05a76\n",
            "Successfully built localcider\n",
            "Installing collected packages: BioPython, localcider\n",
            "Successfully installed BioPython-1.84 localcider-0.1.21\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pylab as plt\n",
        "import localcider\n",
        "from localcider.sequenceParameters import SequenceParameters\n",
        "from localcider import plots\n",
        "import re\n",
        "import os"
      ],
      "metadata": {
        "id": "6qWA6jDOq2wR"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "a='RMIHRSTSQGSIN' # contains S450 and S452 sites\n",
        "data = SequenceParameters(a)\n",
        "print(\"Cterm frag fp %4.2f\"%data.get_fraction_positive( ) )\n",
        "print(\"Cterm frag fn %4.2f\"%data.get_fraction_negative() )\n",
        "\n",
        "b='RMIHRDTDQGSIN'\n",
        "data = SequenceParameters(b)\n",
        "print(\"ppCterm frag fp %4.2f\"%data.get_fraction_positive( ) )\n",
        "print(\"ppCterm frag fn %4.2f\"%data.get_fraction_negative() )\n",
        "\n",
        "print(msssp)\n",
        "data = SequenceParameters(msssp)\n",
        "print(\"msssp fp %4.2f\"%data.get_fraction_positive( ) )\n",
        "print(\"msssp fn %4.2f\"%data.get_fraction_negative() )\n",
        "\n",
        "data = SequenceParameters(msdsp)\n",
        "print(\"msdsp fp %4.2f\"%data.get_fraction_positive( ) )\n",
        "print(\"msdsp fn %4.2f\"%data.get_fraction_negative() )\n"
      ],
      "metadata": {
        "id": "zdaKOPzyFyXm",
        "outputId": "1f1445c6-65b4-4f6e-d52a-5aa73a7583cb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Cterm frag fp 0.15\n",
            "Cterm frag fn 0.00\n",
            "ppCterm frag fp 0.15\n",
            "ppCterm frag fn 0.15\n",
            "AQPMSSSPKETTF\n",
            "msssp fp 0.08\n",
            "msssp fn 0.08\n",
            "msdsp fp 0.07\n",
            "msdsp fn 0.14\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# mybpc  comparison\n",
        "mybpcSeq = \"RSAFRRTSLAGAGRRTSDSHED\" # for frame of reference\n",
        "data = SequenceParameters(mybpcSeq)\n",
        "print(\"mybpc fp %4.2f\"%data.get_fraction_positive( ) )\n",
        "print(\"mybpc fn %4.2f\"%data.get_fraction_negative() )\n",
        "\n",
        "# C-term\n",
        "data = SequenceParameters(short)\n",
        "print(\"Short C-term fp %4.2f\"%data.get_fraction_positive( ) )\n",
        "print(\"Short C-term fn %4.2f\"%data.get_fraction_negative() )\n",
        "data = SequenceParameters(dshort)\n",
        "print(\"+p Short C-term fp %4.2f\"%data.get_fraction_positive( ) )\n",
        "print(\"+p Short C-term fn %4.2f\"%data.get_fraction_negative() )\n",
        "\n",
        "# GSK3B seq\n",
        "data = SequenceParameters(msssp)\n",
        "data = SequenceParameters(msdsp)\n",
        "\n",
        "print(msssp)\n",
        "fp = \"MSSSP %4.2f\"%data.get_fraction_positive()\n",
        "fn = \"MSSSP %4.2f\"%data.get_fraction_negative()\n",
        "# similar story, though mybpc is even more positively charged\n",
        "print(fp,fn) # 0.07692307692307693 0.076923076923076 msssp\n",
        "print(fp,fn) # 0.07142857142857142 0.14285714285714285 msdsp"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9jpQJu7fqQt5",
        "outputId": "b430f509-064a-4ec4-bd28-a66a92fe660f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "mybpc fp 0.23\n",
            "mybpc fn 0.14\n",
            "Short C-term fp 0.13\n",
            "Short C-term fn 0.13\n",
            "+p Short C-term fp 0.13\n",
            "+p Short C-term fn 0.15\n",
            "AQPMSSSPKETTF\n",
            "MSSSP 0.07 MSSSP 0.14\n",
            "MSSSP 0.07 MSSSP 0.14\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "entire protein\n"
      ],
      "metadata": {
        "id": "FMTOic_7tU2m"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "data = SequenceParameters(fastaAblim1)\n",
        "fp = data.get_fraction_positive()\n",
        "fn = data.get_fraction_negative()\n",
        "\n",
        "print(fp,fn)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bzY1LbqWq_vF",
        "outputId": "0f62b78e-89c6-4329-daf6-ff7787458ce9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.14267352185089974 0.11439588688946016\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "N-terminus/C-terminus"
      ],
      "metadata": {
        "id": "cxoT_asJtY2Q"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# n term\n",
        "data = SequenceParameters(fastaAblim1Nterm)\n",
        "fp = data.get_fraction_positive()\n",
        "fn = data.get_fraction_negative()\n",
        "\n",
        "print(fp,fn)\n",
        "\n",
        "\n",
        "# c term\n",
        "data = SequenceParameters(fastaAblim1Cterm)\n",
        "fp = data.get_fraction_positive()\n",
        "fn = data.get_fraction_negative()\n",
        "\n",
        "print(fp,fn)\n",
        "\n",
        "\n",
        "# c term + phospho\n",
        "# just a hack since we are adding two charges\n",
        "pfastaAblim1Cterm = re.sub(\"S\", \"D\", fastaAblim1Cterm, count=2)\n",
        "data = SequenceParameters(pfastaAblim1Cterm)\n",
        "fp = data.get_fraction_positive()\n",
        "fn = data.get_fraction_negative()\n",
        "\n",
        "print(fp,fn)\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "buTY8LAbta5T",
        "outputId": "51dda12f-47e4-42a8-c830-839ce7f945e1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.17525773195876287 0.08247422680412371\n",
            "0.14814814814814814 0.13333333333333333\n",
            "0.14814814814814814 0.1382716049382716\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Hofman applications of flory ideas\n",
        "Ideas from Hofman paper for determining attractive/repulsive corrections to scaling coefficient $\\nu$\n",
        "\n",
        "Populating values for Flory model\n",
        "\n",
        "$\n",
        "\\begin{align}\n",
        "R_g & = \\sqrt{ \\frac{2\\xi b}{\\left(2\\nu+1\\right)\\left(2\\nu+2\\right)}} N^\\nu \\\\ % S11 hofmann\n",
        "\\nu & = \\nu_0 + \\nu^*\\\\\n",
        "\\mbox{double check this eqn}\\\\\n",
        "\\nu^* &= \\frac{4\\pi\\lambda_B^2\\left( f-g \\right)^2}{\\kappa^2} - \\frac{\\pi\\lambda_B (f+g)^2}{\\kappa}\n",
        "\\end{align}\n",
        "$\n",
        "    Per Hofmann supp, $\\nu^*>0$ pertains to net repulsion (unfolding) while $\\nu<0$ corresponding to net attraction (folding).\n",
        "\n",
        "* $b=0.38 \\mbox{ [nm] bond length}$\n",
        "* $l_p=0.4 \\mbox{ [nm] pers. len, hofman}$\n",
        "* $\\lambda_B = 0.7 \\mbox{ [nm] Bjerrum length for er=80, check w my notes}$\n",
        "* $\\kappa = 1.0 \\mbox{ [nm] Inv. Debye}$\n",
        "* $f_- = 0.105 \\mbox{ frac -,w/o phospho}$\n",
        "* $f_+ = 0.134 \\mbox{ frac +,w/o phospho}$\n",
        "* $v_0 = 0.6 \\mbox{ excluded volume chain, ref. in Hofmann}$\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "62mLOy0E-EwR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# dbl check, but net repulsive if > 0, net attractive if < 0\n",
        "def vexcess(fp,fm):\n",
        "    lB=k=1.\n",
        "    t1 = (4*np.pi*lB*lB)*(fp-fm)**2\n",
        "    t1/=k**2\n",
        "    #print(t1)\n",
        "    t2 = np.pi * lB*(fp+fm)**2\n",
        "    t2/=k\n",
        "    #print(t2)\n",
        "    vs = t1-t2\n",
        "    #print(vs)\n",
        "    return vs"
      ],
      "metadata": {
        "id": "XaMZltW0te2B"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# values from the fp/fn calculations earlier\n",
        "print( vexcess(1,0) )\n",
        "print( vexcess(0.148,0.133 ) )\n",
        "print( vexcess(0.148,0.143 ) )\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HYFY_9jH-SP0",
        "outputId": "8e1140ef-20b1-4f05-a374-a9d7c0d8c50c"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "9.42477796076938\n",
            "-0.2452358641318729\n",
            "-0.26571904823327824\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Validated against Fig 2 in Hofmann et al\n",
        "b = 0.38 # nm [from Hofmann]\n",
        "lp = 0.4 # nm\n",
        "def rg(n,nu):\n",
        "    num = 2*lp * b\n",
        "    denom = (2*nu+1)*(2*nu+2)\n",
        "    scale = np.sqrt(num/denom)*(n**nu)\n",
        "    return scale\n",
        "\n",
        "\n",
        "#rg(1000,0.58)\n",
        "# Protein IN (left bottom panel) appears to have Nbond=60, and Rg of about 2. and a scaling\n",
        "# exponent of 0.58. The expression below reproduces this number\n",
        "rg(60,0.58)\n",
        "print( rg(133,0.58) )\n",
        "print( nFrag )\n",
        "133**0.58"
      ],
      "metadata": {
        "id": "Q3dUp3G7-tJ5",
        "outputId": "6b5796e8-c934-4265-b897-55300249f879",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 81,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "3.5991531473172373\n",
            "130\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "17.05430209806322"
            ]
          },
          "metadata": {},
          "execution_count": 81
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "nval =  10**np.linspace(1,3,20)\n",
        "nval = np.array(nval,dtype=int)\n",
        "\n",
        "nu = 0.58 # unfolded\n",
        "plt.plot(nval, rg(nval,nu),label='unfolded [Hofmann]')\n",
        "nu = 0.34 # folded\n",
        "plt.plot(nval, rg(nval,nu),label='folded [Hofmann]')\n",
        "\n",
        "\n",
        "plt.ylabel('Rg [nm]')\n",
        "plt.yscale('log')\n",
        "plt.xlabel('nRes')\n",
        "plt.xscale('log')\n",
        "plt.legend(loc=0)\n",
        "\n",
        "# reference plt.scatter([1000],[rg(1000,nu)],edgecolor='orange',facecolor='white')\n",
        "# according to 6A, proT53 has a net charge of 0.3, vs 0.4 for proTa, IN is about 0.15\n",
        "# i'm guess netcharge has a maximum of 1.0 from (f^+ - f^-)\n",
        "# from 2 it looks ilke IN has v=0.58 and proTA = 0.67\n",
        "# i can't really figure out what numbers were used for the net charge listed in the hofmann paper, though they did seem to include\n",
        "# the net charges of the fluorophores\n",
        "\n",
        "\n",
        "nResCterm = 300\n",
        "# ratio of pos/neg. aa in ablim are pretty even (+40/300 vs -31/300), but they're slightly positive overall (9/300). Let's assume this gives us\n",
        "# a nu=0.61. promotyhsin a had about 5 more positive aa over 50ish residues and had nu=0.67 Adding 3 phosphates (-2x3) will almost balance positive w negative, so we'll use nu=0.58\n",
        "\n",
        "# The region spanning LIM4 (343) and VHP (710) is 366 residues (to 709)\n",
        "# The short fragment we simulated was 130\n",
        "nFrag = 130\n",
        "nFull=709 - 343\n",
        "\n",
        "# hofmann\n",
        "nProTa = 54+9 # for the FRET linker\n",
        "nu=0.65 # 70 #\n",
        "val = rg(nProTa,nu)\n",
        "plt.scatter([nProTa],[val], label=\"ProTa [Hofmann] \", # Rg=%3.1f [nm]\"%val,\n",
        "            facecolor='blue',edgecolor='blue')\n",
        "\n",
        "\n",
        "# unphospho\n",
        "# based on figure 9\n",
        "simVal = 5.0 # update\n",
        "plt.scatter([nFrag],[simVal], label=\"Sim.  Frag Rg=%3.1f [nm]\"%simVal,facecolor='k',edgecolor='k')\n",
        "# Pred\n",
        "nu=0.665 # estimated by where ProtTa fell\n",
        "val = rg(nFrag,nu)\n",
        "print(val)\n",
        "plt.scatter([nFrag],[val], label=\"Pred. Frag Rg=%3.1f [nm]\"%val,marker='x',facecolor='gray')\n",
        "\n",
        "# phospho\n",
        "# based on figure 9\n",
        "simVal = 4.6 # update\n",
        "plt.scatter([nFrag],[simVal], label=\"Sim.  pFrag Rg=%3.1f [nm]\"%simVal,facecolor='r',edgecolor='r')\n",
        "# corr\n",
        "nup=0.645; diff = nu - nup\n",
        "val = rg(nFrag,nup)\n",
        "plt.scatter([nFrag],[val], label=\"Pred. pFrag Rg=%3.1f [nm]\"%val,marker='x',facecolor='gray')\n",
        "\n",
        "# full\n",
        "# unphospho\n",
        "nu=0.65 # using ProTa value\n",
        "val = rg(nFull,nu)\n",
        "plt.scatter([nFull],[val], label=\"Pred. Full Rg=%3.1f [nm]\"%val,facecolor='w',edgecolor='k')\n",
        "\n",
        "# phospho\n",
        "nup = nu - diff\n",
        "val = rg(nFull,nup)\n",
        "plt.scatter([nFull],[val], label=\"Pred. pFull Rg=%3.1f [nm]\"%val,facecolor='w',edgecolor='r')\n",
        "\n",
        "plt.legend(loc=4,ncol=2)\n",
        "plt.gcf().savefig('rg.png')\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "aYoYaYnz-1Qs",
        "outputId": "17d8ab02-c2bb-452e-deb9-53d956ee2277"
      },
      "execution_count": 83,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "5.038590271792488\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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sy5ReoXRp7G3u0EQ5k0RHCCFElfL3qQTGrTzAvwkZADzZ0p8JjzXG1d7azJEJc5BERwghRJWQnp3HtPXHWPz3vwD4utoxtXconUK8zByZMCdJdIQQQlR6205cYeyKA5y/mglAvza1efvRhjjbSS1OdSeJjhBCiEorNSuXKeuOsXTXGQBqudkzvW8YHYJrmDkyUVFIoiOEEKJS2hodz/iIg8QlZwEwqF0gY7s2xMlWPtrEdfJuEEIIUakkZ+TywS9HWLHnHACBng583CeMe+t6mjkyURFJoiOEEKLS+O3IJd5edZD41Gx0OniufR1GhzfAwUY+zsStyTtDCCFEhZeUnsP7Px9m9f4LANSt4cj0vmG0CvIwc2SiopNERwghRIW24dBFJqw+xJW0bCx0MPT+urzxcAPsrC3NHZqoBCTREUIIUSElpGXz3prD/HIgDoD6Xk5M7xvGPbXdzRyZqEyqbaIzd+5c5s6di16vN3coQgghbqCUYu2BOCauOUxieg6WFjpGdKzLaw/Vx9ZKanFE8eiUUsrcQZhTSkoKrq6uJCcn4+LiYu5whBCiWotPzeLd1YfYePgSAA19nJnRtxmh/q5mjkxUNEX9/K62NTpCCCEqDqUUq/ef5/2fj3A1IxcrCx0vdw7m5c7B2FhZmDs8UYlJoiOEEMKsLqVk8XbEQTYfiwegiZ8LM/o2o7Gf1LKLuyeJjhBCCLNQSrF8zzk+WHuE1Kw8bCwteO2hYIZ3rIe1pdTiiNIhiY4QQohyd+FqJuMjDvJHzGUAmvm7MuPJZjTwdjZzZKKqkURHCCFEuVFKsXTXWaasO0padh42Vha8+XADnr+vDlZSiyPKgCQ6QgghysXZxAzeijjAthMJALQMdGd63zDq1XQyc2SiKpNERwghRJkyGBTf7fyXaeuPkZGjx87agjHhDRnSPghLC525wxNVnCQ6QgghyszpK+mMW3mAnbGJALSp48H0PmEE1XA0c2SiupBERwghRKnTGxQLt59mxsZjZOUacLCxZFzXhgy8NxALqcUR5UgSHSGEEKXq5OU0xq44wJ5/kwBoX8+Tj/uEEeDhYObIRHUkiY4QQohSkac3MP+vWGZtiiEnz4CTrRVvP9qIfm0C0OmkFkeYhyQ6Qggh7lrMpVTGLI8i6lwyAA80qMnU3qHUcrM3c2SiupNERwghiikrK4ucnJxbLiSYkpKCjY0NdnZ2Zois/OXqDcz74yT/3XyCHL0BZzsr3n2sMU+29JdaHFEhSKIjhBDFkJWVxZIlS0hPT+fZZ5/lwIEDxMXF4evrS1hYGN999x2Ojo4MGDCgyic7R+NSGLMiikPnUwB4qKEXH/UKxce1av/conKRREcIIYohJyeH9PR0kpKS+Oijj5g/fz4pKSm4uLjwwgsvGGt5cnJyqmyik5NnYO6WE8zdcoI8g8LV3ppJTzSmZ/NaUosjKhxJdIQQohhcXFzw8vLi5MmTeHh4MGTIEFatWkWvXr1wcXEhMTGRkJCQWzZrVQWHziczenkUxy6mAhDexJsPejbFy7lqJnWi8tMppZS5gzCnlJQUXF1dSU5OrrI3JiFE6dHr9QQFBZGSksKQIUPw8PAwvpaYmMiiRYtwcXEhNjYWS0tLM0ZaurLz9Px383G+/OMUeoPCw9GG959owmNhvlKLI8yiqJ/fsoKaEEIUQ2RkJOfOnSMlJYVVq1aZvLZq1SqSk5M5e/YskZGRZoqw9O0/e5XH/vsXc7ecRG9QdA/zZdMbD/B4Mz9JckSFV20Tnblz59K4cWNat25t7lCEEJVIXFwcoDVh9erVy+S1/OarG7erzLJy9Uxdd5Te/9vG8fg0ajjZ8OWzLZjbvwWeTrbmDk+IIqm2ic7LL7/MkSNH2L17t7lDEUJUIr6+vri4uBibrRITE/m///s/EhMTjX12XFxc8PX1NXeod2XPv4k8OieSeX+ewqCgZ3M/Nr3Rka5NK/fPJaof6YwshBDF0KxZM+PoqsTERBYuXEhKSgoLFy40Jj8vvPACzZo1M3eoJZKRk8fMjTEs2B6LUuDtYstHPUPp0tjb3KEJUSLVtkZHCCFKwt7eHi8vL5KSkli0aBEpKdocMikpKSxatIikpCS8vLywt698MwL/fSqBbnMi+WabluT0benPr693lCRHVGpSoyOEEMXk4eGBXq/Hz9ub5snJ+AJxwGUfH7y8vExGYlUG6dl5fLzhGN/u+BcAX1c7pvQOpXOIl5kjE+LuSaIjhBDFkJOTQ2ZmJrm5uYx47DEGz5+Pa0oKyS4uLOrenaTcXDIzMyvNhIHbTlxh3MoDnEvKBKBfmwDGP9oIFztrM0cmROmQREcIIYrBxcWFwV5eLDp5kiQPDxYNGUKvVatY1asXSS4uuCcmMrgSTBiYmpXLlHXHWLrrDAC13Oz5uE8Y99WvYebIhChdMmGgTBgohCgOvR6CgkhOSWHRkCEk3dBM5Z6YyOBFi3B1cYHYWKigEwZujY5nfMRB4pKzABjULpCxXRviZCvffUXlIRMGCiFEWYiMhHPncE1JoddNEwb2WrUK1+RkOHtW266CSc7IZfTyKIYs2E1cchaBng78MOxeJvdoKkmOqLIk0RFCiOK4NhFgsosLq26aMHBVr14k53+zrGATBv525BIPf/oHK/acQ6eD/3Sow/qR93NvXU9zhyZEmZJERwghisPXV+t4fK3Zyj0xkf/83//hnpho7LOT7OICFWTCwKsZObzx435e+PYf4lOzqVvDkeXD2/He441xsJFaHFH1SaIjhBDFkNKsGYteeMGY5AxeuJCAs2cZvHDh9WTnhRdIqQATBm44dJEus/5k1b7zWOhg+AN1WTfyfloFVa7h70LcDUnnhRCiGGzs7XH09obz57WOx9cmDHRNSWHwokUsGjwYx1q1sDHjhIEJadm8t+YwvxzQms/qezkxvW8Y99R2N1tMQpiLJDpCCFEMdnZ2DHjtNXJ++gmXiAhITja+5uriwpD27bHp0cMsc+gopVh7II6Jaw6TmJ6DpYWOER3r8tpD9bG1qpgjwIQoazK8XIaXCyFKSq/XRlfFxWl9cu6/32xDyuNTs3h39SE2Hr4EQEMfZ2b0bUaov6tZ4hGirBX181tqdIQQoqQsLaFTJ7OGoJRi9f7zvP/zEa5m5GJloePlzsG83DkYGyvphimEJDpCCFFJXUzO4p1VB9l8LB6AJn4uzOjbjMZ+UjstRD5JdIQQopJRSrF8zzk+WHuE1Kw8bCwteO2hYIZ3rIe1pdTiCHEjSXSEEKISOX81k/ERB/kz5jIAzfxdmfFkMxp4O5s5MiEqJkl0hBCiElBKsXTXWaasO0padh42Vha8+XADnr+vDlZSiyNEoSTREUKICu5sYgZvRRxg24kEAFoGujO9bxj1ajqZOTIhKj5JdIQQooIyGBTf7fyXaeuPkZGjx87agjHhDRnSPghLC525wxOiUpBERwghKqDTV9IZt/IAO2MTAWhTx4PpfcIIquFo5siEqFwk0RFCiApEb1As3H6aGRuPkZVrwMHGkre6NeTZtoFYSC2OEMUmiY4QQlQQJy+nMXbFAfb8mwRA+3qefNwnjAAPBzNHJkTlVW0Tnblz5zJ37lz0er25QxFCVHN5egPz/4pl1qYYcvIMONla8fajjejXJgCdTmpxhLgbstaVrHUlhDCjmEupjFkeRdQ5bXHQBxrUZGrvUGq5mW/1cyEqA1nrSgghKrBcvYF5f5zkv5tPkKM34GxnxbuPNebJlv5SiyNEKZJERwghytmRCymMWRHF4QspADzU0IuPeoXi42pn5siEqHok0RFCiHKSk2dg7pYTzN1ygjyDwtXemklPNKZn81pSiyNEGZFERwghysHBc8mMWRHFsYupAIQ38eaDnk3xcpZaHCHKkiQ6QghRhrLz9Px383G+/OMUeoPCw9GGyT2a0D3UV2pxhCgHkugIIUQZ2XcmiTErDnAiPg2A7mG+TH6iCZ5OtmaOTIjqQxIdIYQoZVm5ej7dFMPXkacwKKjhZMOHPZvStamvuUMTotqRREcIIUrRnn8TGbP8AKeupAPQs7kfEx9vgrujjZkjE6J6kkRHCCFKQUZOHjM3xrBgeyxKgbeLLR/1DKVLY29zhyZEtSaJjhBC3KW/TyUwbuUB/k3IAODJlv5MeKwxrvbWZo5MCCGJjhBClFB6dh4fbzjGtzv+BcDX1Y6pvUPpFOJl5siEEPkk0RFCiBLYduIK41Ye4FxSJgD92tTm7Ucb4mwntThCVCSS6AghRDGkZuUyZd0xlu46A0AtN3s+7hPGffVrmDkyIcStSKIjhBBFtDU6nvERB4lLzgJgULtAxnZtiJOt3EqFqKjk6hRCiDtIzszlw7VHWL7nHACBng583CeMe+t6mjkyIcSdSKIjhBC3sfnoJd5edZBLKdnodPBc+zqMDm+Ag43cPoWoDORKFUKIW7iakcP7Px9h1b7zANSt4cj0vmG0CvIwc2RCiOKQREcIIW6y4dBFJqw+xJW0bCx0MPT+urzxcAPsrC3NHZoQopgk0RFCiGsS0rKZuOYwaw/EAVDfy4npfcO4p7a7mSMTQpSUJDpCiGpPKcUvB+OY+NNhEtJzsLTQMaJjXV57qD62VlKLI0RlJomOEKJau5yazburD7Hh8EUAGvo4M6NvM0L9Xc0cmRCiNEiiI4SolpRS/LT/ApN+PszVjFysLHS83DmYlzsHY2NlYe7whBClpEiJjodH8UYZ6HQ69u7dS2BgYImCEkKIsnQpJYt3Vh3kt6PxADTxc2FG32Y09nMxc2RCiNJWpETn6tWrzJ49G1fXO1flKqV46aWX0Ov1dx2cEEKUJqUUy/ec44O1R0jNysPG0oLXHgpmeMd6WFtKLY4QVVGRm66eeeYZvLyKtiLvq6++WuKAhBCiLFy4msn4iIP8EXMZgGb+rsx4shkNvJ3NHJkQoiwVKdExGAzFOmhqamqJghFCiNKmlGLprrNMWXeUtOw8bKwsePPhBjx/Xx2spBZHiCpPOiMLIaqss4kZvBVxgG0nEgBoGejO9L5h1KvpZObIhBDlpUSJzoULF/jrr7+Ij48vUNvz2muvlUpgQoiKQa+HyEiIiwNfX7j/frCs4FPLGAyK73b+y7T1x8jI0WNnbcGY8IYMaR+EpYXO3OEJIcpRsROdhQsXMnz4cGxsbPD09ESnu37T0Ol0kugIUYVERMDIkXDu3PUyf3+YMwd69zZfXLdz+ko641YeYGdsIgBt6ngwvU8YQTUczRyZEMIcdEopVZwdAgICGDFiBOPHj8fCovK3b6ekpODq6kpycjIuLjK0VIh8ERHQty/cfIfI/26zYkXFSnb0BsXC7aeZsfEYWbkGHGwsGde1IQPvDcRCanGEqHKK+vld7BqdjIwMnnnmmUqf5MydO5e5c+fKMHghbkGv12pybvU1SCkt2Xn9dejRo2I0Y528nMbYFQfY828SAO3refJxnzACPBzMHJkQwtyKXaMzduxYPDw8eOutt8oqpnIlNTpCFLR1K3TufOfttmyBTp3KOprC5ekNzP8rllmbYsjJM+Bka8XbjzaiX5sAk2Z1IUTVU2Y1OlOnTuWxxx5jw4YNhIaGYm1tbfL6rFmzih+tEKJCiYsr3e3KQsylVMYsjyLqXDIADzSoydTeodRyszdfUEKICqdEic7GjRsJCQkBKNAZWQhR+fn6lu52pSlXb2DeHyf57+YT5OgNONtZ8e5jjXmypb/cg4QQBRS76crd3Z1PP/2UIUOGlFFI5UuaroQoSK+HoCA4f/7W/XR0Om30VWxs+fbRORqXwujlURy+kALAQw29+KhXKD6uduUXhBCiQiizpitbW1s6dOhwV8EJISo2S0ttCHnfvlpSc2Oyk19pMnt2+SU5OXkG5m45wdwtJ8gzKFztrZn0RGN6Nq8ltThCiNsq9tCpkSNH8tlnn5VFLEKICqR3b20Iea1apuX+/uU7tPzQ+WSe+Pwv5mw+Tp5BEd7Em02jHqDXPdJUJYS4s2I3XfXq1Yvff/8dT09PmjRpUqAzckRERKkGWNak6UqI2zPXzMjZeXr+u/k4X/5xCr1B4eFow/tPNOGxMF9JcIQQZdd05ebmRu+KNEuYEKJMWVqW/xDy/WevMmZ5FMfj0wB4LMyX959ogqeTbfkGIoSo9Iqd6CxYsKAs4hBCCLJy9Xy6KYavI09hUFDDyYYPezala1MzDO8SQty99ASI2w/BD5ktBFm9XAhRIez5N5Exyw9w6ko6AD2b+zHx8Sa4O9qYOTIhRLEY9HByC+z7Fo6tA0sbGB0Nts5mCafYic6lS5cYPXo0mzdvJj4+npu7+MiSCkKI4sjIyWPmxhgWbI9FKfB2seWjnqF0aext7tCEEMWRdBr2LYH930PKDSsBezeGlAtQM8QsYRU70RkyZAhnzpzh3XffxddXOgUKIUru71MJjFt5gH8TMgB4sqU/Ex5rjKu99R32FEJUCLlZcGwt7P0WYv+4Xm7nBmFPwT0DwTfMbOFBCRKdv/76i8jISJo3b14G4QghqoP07Dw+3nCMb3f8C4Cvqx1Te4fSKcTLzJEJIYrk4kHYuxgO/AhZV6+X1+kILQZBw8fAumJM5FnsRCcgIKBAc5UQQhTVthNXGLfyAOeSMgHo16Y2bz/aEGc7qcURokLLvAqHVmgJTtz+6+UutaD5ALhnALgHmSm4whU70Zk9ezZvvfUW8+bNIygoqAxCEkJURalZuUxZd4ylu84AUMvNnul9w+gQXMPMkQkhCqUUnP4L9i2GIz9BXpZWbmENDR+FewZBvc5gUY5rwRRTsROdp59+moyMDOrVq4eDg0OBCQMTExNLLTghRNWwNTqe8REHiUvWbpKD2gUytmtDnGxl4KcQFVLKBa1T8b7vICn2ennNRtBiIIQ9DY6V40tKiWp0hBCiKJIzcvnglyOs2KONwAj0dODjPmHcW9fTzJEJIQrQ50LMBq1p6sQmUAat3MYJmvbR+t7Uanl9wbtKotiJzuDBg8siDiFEFfPbkUu8veog8anZ6HTwXPs6jA5vgION1OIIUaFcjtHmvIn6AdIvXy+v3U4bNdWkJ9g4mi28u1WkO05KSkqx1oFKTU3F2dk8EwMJIcwrKT2H938+zOr9FwCoW8OR6X3DaBXkYebIhBBG2WlweJXW9+bszuvljl7QvJ+W4NSob774SlGREh13d3fi4uLw8ira0M9atWqxf/9+6tate1fBCSEqlw2H4piw+jBX0rKx0MHQ++vyxsMNsLOuuB0Vhag2lIJzu7U5bw6vghxtLTl0FlA/XOt7U/8RsKxaIyCLlOgopZg/fz5OTk5FOmhubu5dBSWEqFwS0rJ5b81hfjkQB0B9Lyem9w3jntruZo5MCEHaZTjwg9ax+PKx6+UedeGeZ6FZf3CpuuvJFSnRqV27Nl9//XWRD+rj41NgNJYQoupRSrH2QBwT1xwmMT0HSwsdIzrW5bWH6mNrJbU4QpiNQQ8nf9dqb6LXgSFPK7eyh8Y9tNqbwA6VrmNxSRQp0Tl9+nQZhyGEqGziU7N4d/UhNh6+BEBDH2dm9G1GqL+rmSMTohpLOq3V3Oz/HlLOXy/3u0frdxPaF+yq1zUqwx+EEMWilGL1/vO8//MRrmbkYmWh4+XOwbzcORgbKwtzhydE9ZObBUd/1kZOxf55vdzeXZvv5p6B4NPUfPGZmSQ6Qogiu5icxTurDrL5WDwATfxcmNG3GY39ij4qUwhRSuKitDlvDi6DrORrhTqo20lrmmr4GFjZmjPCCkESHSHEHSmlWL7nHB+sPUJqVh42lha89lAwwzvWw9pSanGEKDeZSXBwhdb35uKB6+WuAdfXm3Krbb74KiBJdIQQt3XhaibjIw7yR4w2kVgzf1dmPNmMBt4yV5YQ5cJggH//0mpvjq65vt6UpQ007K41TdXtVKHXmzInSXSEELeklGLprrNMWXeUtOw8bKwsGPVwA164rw5WUosjRNlLuQD7l1xbb+r09XKvJtfXm3KQiTjvpNiJzoEDB25ZrtPpsLOzo3bt2tjaSpugEJXZ2cQM3oo4wLYTCQC0qO3G9L7NCPYq2lxaQogSysvR1pvatxhO/HZ9vSlbl2vrTQ0EvxbVYlh4aSl2otO8eXN0t/kFW1tb8/TTTzNv3jzs7OzuKjghRPkyGBTf7fyXaeuPkZGjx87agtGPhPBchzpYWsiNVYgyczla63cT9QNkXLleHthBa5pq3ANsHMwXXyVW7ERn1apVjBs3jjFjxtCmTRsAdu3axSeffMLEiRPJy8vjrbfeYsKECcycObPUAxZClI1/E9IZu+IAO2MTAWhTx4PpfcIIqlF5F/MTokLLToPDEVrfm3O7rpc7eUPz/lqC41nPfPFVEcVOdD766CPmzJlDeHi4sSw0NBR/f3/effdddu3ahaOjI2+++aYkOkJUAnqDYuH208zYeIysXAMONpaM69qQgfcGYiG1OEKULqXg7C5tzptDqyA3XSvXWUKDrlrTVPDDYCldaEtLsX+TBw8eJDAwsEB5YGAgBw8eBLTmrbi4uLuPTghRpk5eTmPsigPs+TcJgPb1PPm4TxgBHlJFLkSpSrsMUUu1jsVXoq+XewZrNTfN+oGzt/niq8KKneg0bNiQadOm8dVXX2FjYwNoi3hOmzaNhg0bAnD+/Hm8veUPJkRFpTco5keeYtamGLLzDDjZWjH+0Yb0b1P7tn3whBDFoM+Dk5u1vjcxG66vN2XtAE16aQlO7XulY3EZK3aiM3fuXJ544gn8/f0JCwsDtFoevV7P2rVrATh16hQvvfRS6UYqhCgVxy+lMnrFAaLOXgXg/vo1mNYnjFpu9uYNTIiqIvHU9fWmUm9o3ajVEloMgia9wU5mEy8vOqWUKu5OqampLFmyhJiYGABCQkLo378/zs6VbwKxlJQUXF1dSU5OxsVF3nii6srTG5j35ynm/HacHL0BZzsr3u3emCdb+UstjhB3KzcTjqzRhoWfjrxebu8BzZ7Ram+8G5svviqoqJ/fJert5OzszIgRIwqUZ2ZmYm8v3wqFqGiOxqUwZkUUh86nAPBgQy+m9ArFx1WmgBDirlzYryU3B5ZD9g3rTdV7UOtYHPKorDdlZqXSrTs7O5vPP/+cGTNmcPHixdI4pBCiFOTkGfjf1hPM3XKCXL3C1d6aSU80pmfzWlKLI0RJZSTCweVagnPx4PVy19pwz7Pa0HC3APPFJ0wUOdHJzs5m0qRJbNq0CRsbG8aOHUvPnj1ZsGAB77zzDpaWlrzxxhtlGasQohgOnU9m9PIojl1MBSC8iTcf9GyKl7PU4ghRbAYDnP7z2npTP4M+Wyu3tIFGj2tNU3U6goUsj1LRFDnRee+995g3bx5dunRh+/btPPnkkzz33HP8/fffzJo1iyeffBJLS1lQTAhzy87T89nmE3zxx0n0BoWHow3vP9GEx8J8pRZHiOJKPqd1Kt73HVz993q5d6jWNBX6pKw3VcEVOdFZvnw53377LU888QSHDh0iLCyMvLw8oqKi5OYpRAWx/+xVxq6IIuZSGgDdw3yZ/EQTPJ2kj4AQRZaXA9Hrrq03tRm4NmbH1hVC+2oJjm9zGRZeSRQ50Tl37hwtW7YEoGnTptja2vLGG29IkiNEBZCVq+fTTTF8HXkKg4IaTjZ80KMp3UJ9zR2aEJVH/FGtaerAD5CRcL086H6taarR47LeVCVU5ERHr9cbJwgEsLKywslJVjIWwtz2/JvImBUHOHVZm0q+Z3M/Jj7eBHdHmzvsKYQgOxUORWiT+p3/53q5k8+19aaelfWmKrkiJzpKKYYMGYKtrVYFnpWVxYgRI3B0NF3wLyIionQjFELcUmaOnhkbo1mwPRalwMvZlo96hfJwY5mVXIjbUgrO7tRqbw7fsN6UhZW23tQ9AyG4i6w3VUUU+a84ePBgk+fPPvtsqQdTnubOncvcuXPR6/XmDkWIYvv7VALjVh7g34QMAPq29Ofd7o1xdbA2c2RCVGBp8dp6U3sXQ8Lx6+We9bV+N836gZOX+eITZaJEMyNXJTIzsqhM0rPz+HjDMb7doY3+8HW1Y0rvUDqHyM1ZiFvS58GJ37SOxQXWm+qtJTgBbaVjcSVUpjMjCyHK37YTVxi38gDnkjIB6NcmgPGPNsLFTmpxhCgg4aQ2JDxqqel6U/6ttaappr3BtvItWySKTxIdISq41Kxcpqw7xtJdZwCo5WbPx33CuK9+DTNHJkQFk5MBR9doTVP//nW93METwp7Ram+8GpkvPmEWkugIUYFtjY5nfMRB4pKzABjULpCxXRviZCuXrhCA1rH4wj6taergCshOufaCDoIf0mpvQh4FKxmFWF3J3VKICig5I5cPfjnCij3nAAj0dODjPmHcW9fTzJEJUUFkJMKBZVqCc+nQ9XK32lpy07w/uPqbLz5RYUiiI0QF89uRS7y96iDxqdnodPBc+zqMDm+Ag41crqKaMxggdqvWNHVsLehztHJLW20yvxYDIegBWW9KmJA7pxAVRFJ6Du//fJjV+y8AULeGI9P7htEqSNbREdXc1bOwfwnsWwLJZ66X+4TCPYO0ZRlkvSlRCEl0hKgANhyKY8Lqw1xJy8ZCBy/cX5dRDzfAzloWyhXVVF42HPtFa5o6uQWT9abCntSap/yamzNCUUlIoiOEGSWkZfPemsP8ckAb/lrfy4npfcO4p7a7mSMTwkwuHdGSm6gfIDPxenn+elONnwBre/PFJyodSXSEMAOlFGsPxDFxzWES03OwtNAxomNdXnuoPrZWUosjqpmsFDi0Uktwzu+5Xu7se329KY+65otPVGqS6AhRzuJTs3h39SE2Hr4EQEMfZ2b0bUaov6uZIxOiHCkFZ3ZoHYuPrIZcbTkT43pTLQZBvYdkvSlx1+QdJEQ5UUqxev953v/5CFczcrGy0PFy52Be7hyMjZWMEhHVROoliPpem7U44cT18hoNtKapZs/IelOiVEmiI0Q5uJicxTurDrL5WDwATfxcmNG3GY39ZH01UQ3o8+D4r9fWm9oI6tpiytaO0LSXNnIqoI2sNyXKhCQ6QpQhpRTL95zjg7VHSM3Kw8bSgtceCmZ4x3pYW0otjqjiEk7C3m+19abSLl0v92+jzXnTpJesNyXKnCQ6QpSR81czGR9xkD9jLgPQzN+VGU82o4G33NhFFZaTDkd+0vrenNl+vdyhhtYsdc9A8GpovvhEtSOJjhClTCnF0l1nmbLuKGnZedhYWTDq4Qa8cF8drKQWR1RFSsGFvVpyc3AF5KRq5ToLCO6iJTcNusp6U8IsJNERohSdTczgrYgDbDuRAECL2m5M79uMYC8nM0cmRBnISIQDP2oJTvzh6+XuQdqQ8Gb9wbWW2cITAiTREaJUGAyK73b+y7T1x8jI0WNnbcHoR0J4rkMdLC2kg6WoQgwGOLVF61h87Jfr601Z2UGjJ7S+N4H3yXpTosKQREeIu3T6SjrjVh5gZ6w2i2ubOh5M7xNGUA1HM0cmRCm6ekZba2r/Ekg+e73ct5nWNBXaF+xlRm9R8UiiI0QJ6Q2KhdtPM2PjMbJyDTjYWDKua0MG3huIhdTiiKogL1tbJXzvYji1FeN6U3auEPa0luD4hpkzQiHuSBIdIUrg5OU0xq44wJ5/kwBoX8+Tj/uEEeDhYObIhCgFFw9pTVMHfoTMpOvldTpqMxY3fAys7cwXnxDFIImOEMWQpzcw/69YZm2KISfPgJOtFeMfbUj/NrXRyWRnojLLStZGTO1bDBf2XS93qaWtN9V8AHjUMV98QpSQJDpCFNHxS6mMXnGAqLNXAbi/fg2m9QmjlpuspCwqKaXg3+1acnN4NeRlauUW1hDS7dp6Uw+ChSw0KyovSXSEuINcvYGv/jzFnN+Ok6M34GxnxbvdG/NkK3+pxRGVU+pF2H9tvanEk9fLaza8vt6UYw3zxSdEKZJER4jbOBqXwpgVURw6nwLAgw29mNIrFB9X6Z8gKhl9rrbe1N7F2r/5603ZOEHT3tp6U/6tZL0pUeVIoiPELeTkGZi75QRzt5wgz6Bwtbdm0hON6dm8ltTiiMrlyvFr6039AOnx18sD7tXmvGncE2xlQktRdUmiI8RNDp1PZvTyKI5d1KaxD2/izQc9m+LlLLU4opLISYfDq7Tam7N/Xy93rHltvalBULOB+eITohxJoiPENdl5ev67+Thf/nEKvUHh4WjD+0804bEwX6nFERWfUnDuH9j3LRyKgJw0rVxnAcEPa7U3DbqCpbV54xSinEmiIwSw/+xVxiyP4ni89uHQPcyXyU80wdPJ1syRCXEH6Qlw4Aet9uby0evl7nW09aaa9wcXP/PFJ4SZSaIjqrWsXD2fborh68hTGBTUcLLhgx5N6Rbqa+7QhCicQQ8nt2i1N8fWgSFXK7eyg8Y9tJFTgR1kvSkhkERHVGN7/k1kzPIDnLqSDkDP5n5MfLwJ7o42Zo5MiEIknb623tT3kHLuerlvM23Om6Z9wd7NXNEJUSFJoiOqncwcPTM2RrNgeyxKgZezLR/1CuXhxt7mDk2IgnKzrq039S3E/nG93M4Nwp6S9aaEuANJdES18vepBMatPMC/CRkA9G3pz7vdG+PqIB00RQUTd+DaelPLIOvq9XJZb0qIYpFER1QL6dl5fLzhGN/u+BcAX1c7pvQOpXOIl5kjE+IGmVfh0Aqt9iYu6nq5Sy1tral7BoB7kLmiE6JSkkRHVHnbTlxh3MoDnEvS1vHp1yaA8Y82wsVOanFEBaAUnP5Lq7058hPkZWnlFtbQ8FFtzpt6nWW9KSFKSBIdUWWlZuUyZd0xlu46A0AtN3s+7hPGffVlDR9RAaRcuL7eVFLs9fKajbQ5b8KelvWmhCgFkuiIKmlrdDzjIw4Sl6x9Ox7ULpCxXRviZCtveWFG+lyI2aDNeXNiEyiDVm7jrK031WIQ1Gop600JUYrkri+qlOSMXD745Qgr9mhDbwM9Hfi4Txj31vU0c2SiWrsco815E/UDpF++Xl67nTZqqklPsHE0W3hCVGWS6IgqY/PRS7y96iCXUrLR6eC59nUYHd4ABxt5mwszyE7T1pvatxjO7rxe7ugFzftpCU6N+uaLT4hqQj4BKii9Xk9ubq65w6gUkjNymLvlBJuPxWMFtK3tzJjwBjSt5QaGPLKy8swdoqgulIKLB7VOxSc2Qa42jQFOQRDUARo/oc1YnL/eVFaW2UIVoqKztrbG0vLuO+HrlFKqFOKptFJSUnB1dSU5ORkXFxdzh4NSiosXL3L16lVzh1IpZObouZqZi96g0AFOdla42FnJIpyifBn0kJuurRquv+ELioW11iRl4yijpoQoATc3N3x8fG55Ty/q57fU6FQw+UmOl5cXDg4O8oFdiDy9gUspWeRk5+HpCjaWlvi42mIvzVSivCilJTaZSZCTBVgDboAF2DprSzFYO0jHYiFKQClFRkYG8fHxAPj6lnz9QflUqED0er0xyfH0lM6zt6KUIjkzlwvJOeQZLLCwsqWmsw1eLnZYyAeKKA952ZCRABmJNyymCVg7goOnluBYyK1ViLtlb28PQHx8PF5eXiVuxpKrsQLJ75Pj4OBg5kgqply9gQtXM0nO1H5PdtaW+LvbS2djUfYMBm0ZhowEyEm7Xq6zBAcPLcGxtjdbeEJUVfmfh7m5uZLoVCXSXGVKKcXVzFwuXM281hdHh5eLLTWdbaUWR5StnAwtuclMAqW/Xm7jDI6eYOcKOgvzxSdEFVcan4eS6IgKLVdv4HxSJilZWi2O/bVaHOmLI8qMIU9LbNITIC/zermlDdh7aDU4Vrbmi08IUSzyVURUGNu2bSM0NBRra2t69uxJYnoOMZdSScnKRafT4eNiRz0vJ5Mkp1OnTrz++uu3PW5QUBCzZ8++q9gmTZpE8+bNC31969at6HQ6dDodPXv2vKtzFSYjI4M+ffrg4uKCTqer8CPzTp8+bfyd3O53VyEoBdmpkHQaLh6C5HPXkhwd2LmBRz3wagwuvlUuydHpdKxevdrcYQgzmzRpkvF6vdv7ZVEMGTLEeL6yfv9JoiMqjFGjRtG8eXOij5/k/U/mci4pA71B4WBjSX0vp0rR4Tg6OpqFCxcanw8ZMuSWiU9+YlScZGXRokVERkayfft24uLicHV1vfuAy1BAQABxcXG8+eab5g6lcHk5kHoR4o9AwgmtJgcFVnbaiuHeTcGjDti5VMrRU5cvX+bFF1+kdu3a2Nra4uPjQ3h4ONu2bTNuExcXR7du3cwYZeFu/PC98fHbb7+VeyxBQUHG8zs4OBAaGsr8+fPLNYYRI0YUORE5f/48zz77LJ6entjb2xMaGso///xz232aNGlCXFwcw4YNK6WICzdnzhzi4uLK/DwgTVeiAjl58iTPDnmeTGtXdFYKnU6Ht4stNZ1sK02/JS8vL9zc3Mrk2CdPnqRRo0Y0bdq0TI5f2iwtLfHx8cHJycncoZhSBshK0freZKdcL9dZaiOmHDzLbli4Xg+RkRAXB76+cP/9UAoTohWmT58+5OTksGjRIurWrculS5fYvHkzCQkJxm18fHzK7PyloUmTJgUSGw8PjwLb5eTkYGNjU6axTJ48maFDh5KRkcHy5csZOnQotWrVKpdEcdWqVfz999/4+fndcdukpCQ6dOhA586dWb9+PTVr1uT48eO4u7vfdj8rK6tyez+4urqW25c1qdERd+1WTUPNmzdn0qRJxuc6nY758+fTq1cvHBwcqF+/PmvWrAGuN3EkJCTw2kvDaervxvqIH6jv5cTRvTtp27Yttra2+Pr68tZbb5GXV/hMx/Hx8Tz++OPY29tTp04dlixZUmCbq1ev8sILL1CzZk1cXFx48MEHiYqKMtlm2rRpeHt74+zszPPPP09WOcxgu3LlSpo0aYKtrS1BQUF88sknxtc6derEJ598wp9//olOp6NTp06A9rv/8MMPGTRoEE5OTgQGBrJmzRouX75Mjx49cHJyIiwszOSbXEJCAv369aNWrVrGb6ZLly41iaVTp0689tprjB07Fg8PD3x8fEz+nnD7v2mFlJsFyefh0mFttfD8JMfGCdxqg3cT7V8bx7JJciIiICgIOneG/v21f4OCtPIycPXqVSIjI/n444/p3LkzgYGBtGnThvHjx/PEE08Yt7ux6SD/Wly2bBn3338/9vb2tG7dmpiYGHbv3k2rVq1wcnKiW7duXL58uZAzF01+c/C8efMICAjAwcGBp556iuTkZJPt8j98b3zY2NgYa0s/+ugj/Pz8CAkJAWDx4sW0atUKZ2dnfHx86N+/v3Eulnxr1qyhfv362NnZ0blzZxYtWlSkGtb8Y9atW5dx48bh4eHBpk2bTLb5+uuvjT9Pr169mDVr1l1/+Tl//jyvvvoqS5Yswdra+o7bf/zxxwQEBLBgwQLatGlDnTp1eOSRR6hXr16xz32n6zy/dnrjxo3cc8892Nvb8+CDDxIfH8/69etp1KgRLi4u9O/fn4yMjGKfvzRIolPBKaXIyMkr90dZTJj9/vvv89RTT3HgwAEeffRRBgwYQEJCAvbuXmzZG42TszPjJk3l4PHTvPrCIBLiL/Loo4/SunVroqKi+OKLL/i///s/Pvzww0LPMWTIEM6ePcuWLVtYsWIF//vf/wrc5J588knjRbhnzx5atGjBQw89RGJiIgDLli1j0qRJTJkyhX/++QdfX1/+97//lfrv40Z79uzhqaee4plnnuHgwYNMmjSJd99919gMFhERwdChQ2nXrh1xcXFE3PDh+Omnn9KhQwf27dtH9+7dGThwIIMGDeLZZ59l79691KtXj0GDBhn/pllZWbRs2ZJffvmFQ4cOMWzYMAYOHMiuXbtMYlq0aBGOjo7s3LmT6dOnM3ny5AI39Vv9TfN/jxWCQQ/pV7RFNS8fhfR4rbOxhRU4eYNXI229KQfPsp25OCIC+vaFc+dMy8+f18rLINlxcnLCycmJ1atXk52dXax9J06cyIQJE9i7dy9WVlb079+fsWPHMmfOHCIjIzlx4gTvvffeXcd44sQJli1bxs8//8yGDRvYt28fL730UpH337x5M9HR0WzatIm1a9cC2jDkDz74gKioKFavXs3p06cZMmSIcZ/Y2Fj69u1Lz549iYqKYvjw4bzzzjvFittgMLBy5UqSkpJMapG2bdvGiBEjGDlyJPv37+fhhx/mo48+Mtk3MjLS+Lcp7HHjFzSDwcDAgQMZM2YMTZo0KVJ8a9asoVWrVjz55JN4eXlxzz338PXXXxfrZ7xRUa7zSZMm8fnnn7N9+3bOnj3LU089xezZs/n+++/55Zdf+PXXX/nss89KHMNdUdVccnKyAlRycrK5Q1GZmZnqyJEjKjMz01iWnp2rAsetLfdHenZukeMODAxUn376qUlZs2bN1MSJE43PATVhwgTj87S0NAWo//shQkWdTVJRZ5OUs4ur+mr+/xm3efvtt1VISIgyGAzGsrlz5yonJyel1+uVUkp17NhRjRw5UimlVHR0tALUrl27jNsfPXpUAcb4IiMjlYuLi8rKyjKJt169emrevHlKKaXatWunXnrpJZPX27Ztq5o1a1bo72DLli0KUElJSSblgwcPVpaWlsrR0dHkYWdnZ7J9//791cMPP2yy75gxY1Tjxo2Nz0eOHKk6duxosk1gYKB69tlnjc/j4uIUoN59911j2Y4dOxSg4uLiCo2/e/fu6s033zQ+79ixo7rvvvtMtmndurUaN26c8Xlhf9P169eb7Ddx4sTb/u5KncGgVFaqUkmnlbqwX6nze68/rpxUKvOqtk15yctTyt9fKa3Lc8GHTqdUQIC2XSlbsWKFcnd3V3Z2dqp9+/Zq/PjxKioqymQbQK1atUoppVRsbKwC1Pz5842vL126VAFq8+bNxrKpU6eqkJCQu4pt4sSJytLSUp07d85Ytn79emVhYWF8r06cOFFZWFiYXDutW7dWSmnXlre3t8rOzr7teXbv3q0AlZqaqpRSaty4capp06Ym27zzzju3vH5vFBgYqGxsbJSjo6OysrJSgPLw8FDHjx83bvP000+r7t27m+w3YMAA5erqanyekZGhjh8/fttHSkqKcfspU6aohx9+2HgfvNX99ma2trbK1tZWjR8/Xu3du1fNmzdP2dnZqYULFxa6T2HX6Z2u8/x732+//WbcZurUqQpQJ0+eNJYNHz5chYeH3/L4+e+/W7nV52K+on5+S42OKDdhYWHAtVoqgxVOzi7ExV3CQqfDz80eCx1YW15/Sx49epR27dqZ9M/p0KEDaWlpnLv5m/G17a2srGjZsqWxrGHDhibVxlFRUaSlpeHp6WnyDSo2NpaTJ08aj9O2bVuTY7dr167EP3fnzp3Zv3+/yePmToxHjx6lQ4cOJmUdOnTg+PHj6PV6bif/9wrg7e0NQGhoaIGy/JotvV7PBx98QGhoKB4eHjg5ObFx40bOnDlT6HFBm4L95tqxG7dxdHTExcWlwDblRp8LaZfg8jFIOK7NXKwMYGkLzn5ax2LPutfmvinHPl+RkQVrcm6kFJw9q21Xyvr06cOFCxdYs2YNXbt2ZevWrbRo0cKkw/ytFOU9VRp/59q1a1OrVi3j83bt2mEwGIiOjjaWhYSEmFw7K1euNL4WGhpaoF/Onj17ePzxx6lduzbOzs507NgRwPj+jo6OpnXr1ib7tGnTpkjxjhkzhv379/P777/Ttm1bPv30U4KDg42vR0dHFzjWzc/t7e0JDg6+7cPZ2dn4s8yZM4eFCxcWq5+iwWCgRYsWTJkyhXvuuYdhw4YxdOhQvvzyyyIf40ZFuc5vfs84ODhQt25dkzJz3RukM3IFZ29tyZHJ4WY5b1FZWFgUaOq61crr1tbWZOXqOZeUSUZOHjodWFtCA28nbKzKZ8HDtLQ0fH192bp1a4HXyqoTsaOjo8nNELhlolZSN7bZ598Mb1VmMBgAmDFjBnPmzGH27NmEhobi6OjI66+/Tk5OTqHHzT9O/jGKs02ZUkrra5ORoHUw5tr7UGehDQt38Cy7PjdFVdSRJWU0AsXOzo6HH36Yhx9+mHfffZcXXniBiRMnmjTn3Kwo76ny+jvb2NgUuH7yOTo6mjxPT08nPDyc8PBwlixZQs2aNTlz5gzh4eEF3t8lUaNGDWMysnz5ckJDQ2nVqhWNGzcu8jEiIyPv2Hl53rx5DBgwgMjISOLj46ldu7bxNb1ez5tvvsns2bM5ffr0Lff39fUtEFOjRo1MksTiKO69QKfTmf/ecANJdCo4nU5X4Zc4qFmzpskwwZSUFGJjYwtsl5yZw4n4NAxKYXFtmGZNJ9tCk5z8C1MpZbzZbtu2DWdnZ/z9/Qts37BhQ/Ly8tizZ4/xG1t0dLRJB8MWLVpw8eJFrKysCAoKKvS8O3fuZNCgQcayv//++46/h7vRqFEjkyG/oP2sDRo0KPG054XZtm0bPXr04NlnnwW0BCgmJqZYN2uzu9V6U6CNlnLwBHv3irNaeFEXI7yLRQuLo3HjxhVm3pwzZ85w4cIF40iiv//+GwsLC2PH4uI6duwYCQkJTJs2jYCAAIACQ6pDQkJYt26dSdnu3buLfa6AgACefvppxo8fz08//WQ89s3Huvl5q1at2L9//22PnV+LNnDgQLp06WLyWnh4OAMHDuS5554rdP8OHTqY1IoBxMTEEBgYeNvzVlXSdCXu2oMPPsjixYuJjIzk4MGDDB482OTDOStXa3pJSs/FoBROtlY08HZGx+2n937ppZc4e/Ysr776KseOHeOnn35i4sSJjBo1CguLgm/dkJAQunbtyvDhw9m5cyd79uzhhRdeMC4MB9ClSxfatWtHz549+fXXXzl9+jTbt2/nnXfeMd4QR44cyTfffMOCBQuIiYlh4sSJHD58uJR+W7f25ptvsnnzZj744ANiYmJYtGgRn3/+OaNHjy71c9WvX59Nmzaxfft2jh49yvDhw7l06VKpn6fUGQxaYnPluDbvTdolLcnRWYJjTajZEGqGgGONipPkgDaE3N+/8FolnQ4CArTtSlFCQgIPPvgg3333HQcOHCA2Npbly5czffp0evToUarnWrVqFQ0bNiz2fnZ2dgwePJioqCgiIyN57bXXeOqpp0o8xLl27drY2Njw2WefcerUKdasWcMHH3xgss3w4cM5duwY48aNIyYmhmXLlhmb8oo7jcXIkSP5+eefjfeOV199lXXr1jFr1iyOHz/OvHnzWL9+vclxi9N05enpSdOmTU0e1tbW+Pj4mCSDDz30EJ9//rnx+RtvvMHff//NlClTOHHiBN9//z1fffUVL7/8crF+vqpCEh1x18aPH0/Hjh157LHH6N69Oz179qRevXoopYhPyeJ4vLYIooUF+Ls7UKeGIzZWd37r1apVi3Xr1rFr1y6aNWvGiBEjeP7555kwYUKh+yxYsAA/Pz86duxI7969GTZsGF5eXsbXdTod69at44EHHuC5556jQYMGPPPMM/z777/Gb1FPP/007777LmPHjqVly5b8+++/vPjii3f5W7q9Fi1asGzZMn744QeaNm3Ke++9x+TJk2/bvFBSEyZMoEWLFoSHh9OpUyd8fHzKbDbnUpGTAVfPwqVDcPXf64tq2jqDexD4NAVX/4q7qKalJcyZo/3/5g/S/OezZ5f6fDpOTk7GfiQPPPAATZs25d1332Xo0KEmH4qlITk5uUANQlEEBwfTu3dvHn30UR555BHCwsLuaoRjzZo1WbhwIcuXL6dx48ZMmzaNmTNnmmxTp04dVqxYQUREBGFhYXzxxRfGUVe2tsWb9bpx48Y88sgjxhFoHTp04Msvv2TWrFk0a9aMDRs28MYbb2BnZ1fin6koTp48yZUrV4zPW7duzapVq1i6dClNmzblgw8+YPbs2QwYMKBM46iodOrmzhXVTEpKCq6uriQnJ+Pi4mLWWLKysoiNjaVOnTplfmGUtcwcPeeSMsi8VpvjYmeNn5t9kRKcymjr1q107tyZpKSkMuvrU1lNmjSJ1atX37G63oQhDzKStOapm9ebcvAAe0+wKtvJ4UpdRASMHGnaMTkgQEtyevc2W1jmUqL3RRn56KOP+PLLLzl79mypH3vo0KEcO3aMyDLobF6azPX30Ol0rFq1qtAvW7f7XCzq53fF7vwhKh2DUlxOzSY+NRulFJYWOvxc7XFzsK40sxvfDX9/fx5//PECE/BVR2fOnKFx48bk5OQUrf+PUlptTXoCZF3F2LE4f70pBw+tFqeyvo9694YePcp1ZmRxa//73/9o3bo1np6ebNu2jRkzZvDKK6+UyrFnzpzJww8/jKOjI+vXr2fRokVlPg9XaTl48CBOTk5Mnz69WPMZlcSIESP47rvvyvQc+STREaUmMyePs0mZxj45LnbW1HK3NxkyXlW1bduW48ePA1S8JQ/MxM/Pz/jt8LZNAnk5kJmo1d7obxgZY2V/vWOxZRW5VVlawrVZrYX5HD9+nA8//JDExERq167Nm2++yfjx40vl2Lt27WL69OmkpqZSt25d/vvf//LCCy+UyrHL0muvvWYcoFCzZs0yP9/kyZONfRB9y7gjvjRdSdPVXTMoRXxKNpdTs1EorCy0eXFc7atHLY4oAWWArORr602lXi/XWWqJjYOn1udG3j9CVGvSdCXMLiMnj3M31OK42mt9capDLY4ogdxMLbnJTNL64eSzcdKSGzvXijViSghR6UmiI0rEYFBcSs3iSmo2CrCysKCWmx2uDpWsg6goewa9lthkJEDuDYv6WVhr/W4cPMCq8tRgCiEqF0l0RLGlZ2u1ONl5Wi2Om4MNfq52WEktjsinFOSkX5ux+KrWVAVoHYtdtNobWxdpmhJClDlJdESRGQyKiylZXEnTVkK2trSglps9LvbWd9hTVBv6XK1jcXoC6G9YMdvSFhw9wd4DLOX9IoQoP5LoiCJJy87jXFIGOXnaN3N3Bxt8pRZHQOVYb0oIUW1JoiNuS3+tFifhxlocd3tc7ORbebWXl6UtyVAZ1psSQlRb8nVcFCotK5fjl1KNSY6How0NvJ0KJDlKKYYNG4aHhwc6na5IM2tu3boVnU5nsuDmzRYuXFgqswzrdLrbLmLYqVMndNcWGS2rWUFXr15NcHAwlpaWvP7662VyjtI0ZMgQ4+/E5Hdn0N+w3tTR6+tNWVhV7PWmRJkbMmRIxV5KRNxR/jVfHrO7nz592ni+5s2bl+m5JNERBegNBs4lZXDqSjo5egM2lhbUqeGIv7sDlrdYTHPDhg0sXLiQtWvXEhcXR9OmTc0Q9d0ZOnSoSez5F+GtEp9OnToVO1kZPnw4ffv25ezZswUWGayI5syZc31F+vyOxVfPwqXDt15vyrtJxV5vqpq6MWG1sbEhODiYyZMnk5eXd+edK4j8+G983HfffeUex8KFC43nt7CwwNfXl6effpozZ86UWwwnTpzA2dm5yInIwoULCQsLw87ODi8vryIt6pm/mHFZCwgIIC4ujjfffLPMzyVNV8JEalYu55IyydVrfXE8nWzxcbHD0qLw/hUnT57E19eX9u3bl1eYpc7BwaHEKybfSVpaGvHx8YSHh+Pn51cm5yhtrq6uuDo5ak+Sz8OVG258ljbXmqY8Kt96U2aSlZVFTk7OLSc1S0lJwcbGpswmCe3atSsLFiwgOzubdevW8fLLL2NtbX3LmYBzcnKwsal4f9MFCxbQtWtX4/PCYszNzcXauuya1V1cXIiOjkYpRWxsLC+99BJPPvkkO3fuLLNz5svNzaVfv37cf//9bN++/Y7bz5o1i08++YQZM2bQtm1b0tPTOX369B33c3NzM1kIuaxYWlri4+NTLjPJS42OACDPYOBsYgaxV9LJ1RuwsbKgbk0narnZ3zbJGTJkCK+++ipnzpxBp9MRFBQEQHZ2Nq+99hpeXl7Y2dlx3333sXv37tvGsHDhQmrXro2DgwO9evUiISGhwDY//fQTLVq0wM7Ojrp16/L++++bfDs9fvw4DzzwAHZ2djRu3JhNmzaV7BdSDElJSQwaNAh3d3ccHBzo1q2bcTmIrVu34uzsDMCDDz6ITqdj69atxma5tWvXEhISgoODA3379iUjI4NFixYRFBSEu7s7r732Gnq93niuxYsX06pVK5ydnfHx8aF///7Ex8cbX89vEty8eTOtWrXCwcGB9u3bm6wsPWnSJJo3b87ixYsJCgrC1dWVZ555htTUVK32JisFEmO11cIBDDlow8LdwTMYvBqDs48kOUWUlZXFkiVLWLhwIcnJySavJScns3DhQpYsWUJWVlaZnN/W1hYfHx8CAwN58cUX6dKlC2vWrAGuNzd99NFH+Pn5ERISAsDZs2d56qmncHNzw8PDgx49eph8SOr1ekaNGoWbmxuenp6MHTuWkkyyr9Pp+OKLL+jWrRv29vbUrVuXFStWFNjOzc0NHx8f48PDw8NY6/rjjz/SsWNH7OzsWLJkCQkJCfTr149atWrh4OBAaGhogbXnUlNTGTBgAI6Ojvj6+vLpp58WqaZWp9Ph4+Nj/GL3/PPPs2vXLlJSUozbxMXF0b17d+zt7alTpw7ff/89QUFBzJ49u9i/nxtNmDCBhg0b8tRTT91x26SkJCZMmMC3335L//79qVevHmFhYTzxxBPFPu9t7xfXdOrUiVdffZXXX38dd3d3vL29+frrr0lPT+e5557D2dmZ4OBg1q9fX+zzl4Yqkejkf1jUr1+f+fPnmzuc0pXfbFCGj5Tkq5w4F8/V5KvocjOoaZtH/ZpOONneucJvzpw5TJ48GX9/f+Li4ozJzNixY1m5ciWLFi1i7969BAcHEx4eTmJi4i2Ps3PnTp5//nleeeUV9u/fT+fOnfnwww9NtomMjGTQoEGMHDmSI0eOMG/ePBYuXMhHH30EgMFgoHfv3tjY2LBz506+/PJLxo0bd5d/gDsbMmQI//zzD2vWrGHHjh0opXj00UfJzc01STJWrlxJXFycseYrIyOD//73v/zwww9s2LCBrVu30qtXL9atW8e6detYvHgx8+bNM7nx5+bm8sEHHxAVFcXq1as5ffo0Q4YMKRDTO++8wyeffMI///yDlZUV//nPf0xeP3nyJKtXr2bt2rWsXbuWP/74g2mTJ0D8EUg8abqopr0neDcFj6DKvaimmeTk5JCenk5SUhKLFi0yJjvJycksWrSIpKQk0tPTycnJucORSoe9vb3JuTZv3kx0dDSbNm1i7dq15ObmEh4ejrOzM5GRkWzbtg0nJye6du1q3O+TTz5h4cKFfPPNN/z1118kJiayatWqEsXz7rvv0qdPH6KiohgwYADPPPMMR48eLfL+b731FiNHjuTo0aOEh4eTlZVFy5Yt+eWXXzh06BDDhg1j4MCB7Nq1y7jPqFGj2LZtG2vWrGHTpk1ERkayd+/eYsUdHx/PqlWrsLS0xPKGhVkHDRrEhQsX2Lp1KytXruSrr74y+TIC0K1bN5ycnAp9NGnSxGT733//neXLlzN37twixbZp0yYMBgPnz5+nUaNG+Pv789RTT5V4dfZb3i+mTTPZZtGiRdSoUYNdu3bx6quv8uKLL/Lkk0/Svn179u7dyyOPPMLAgQPJyMgo5CxlSFVyubm5qn79+urcuXMqNTVVNWjQQF25cqXI+ycnJytAJScnl2GURZOZmamOHDmiMjMzrxdmpyk10aX8H9lpRY77008/VYGBgcbnaWlpytraWi1ZssRYlpOTo/z8/NT06dOVUkpt2bJFASopKUkppVS/fv3Uo48+anLcp59+Wrm6uhqfP/TQQ2rKlCkm2yxevFj5+voqpZTauHGjsrKyUufPnze+vn79egWoVatWFRp/x44d1ciRI03KYmNjFaDs7e2Vo6OjycPCwsK4fUxMjALUtm3bjPteuXJF2dvbq2XLlimllEpKSlKA2rJli3GbBQsWKECdOHHCWDZ8+HDl4OCgUlNTjWXh4eFq+PDhhca+e/duBRj3yf+9/vbbb8ZtfvnlFwUY31cTJ05UDg4OKiX5qlIZiUpdOa7GvDhItb2nqVLn9yp1IUqppDNKZaff8Xcniubq1atqzpw5atKkSWrOnDnqzJkzJs+vXr1aJucdPHiw6tGjh1JKKYPBoDZt2qRsbW3V6NGjja97e3ur7Oxs4z6LFy9WISEhymAwGMuys7OVvb292rhxo1JKKV9fX+O1rJR2H/b39zeeq6gANWLECJOytm3bqhdffNFkGzs7O5NrcNWqVcZrdPbs2Xc8T/fu3dWbb76plFIqJSVFWVtbq+XLlxtfv3r1qnJwcChwH7hR/jXr6OioHBwcFNo3AfXaa68Ztzl69KgC1O7du41lx48fV4D69NNPjWXnzp1Tx48fL/Rx+vRp47ZXrlxRAQEB6o8//jDGceN98VamTp2qrK2tVUhIiNqwYYPasWOHeuihh1RISIjJ3/pmt7rejfeLlBRj2ZgxY1Tbtm2Nzzt27Kjuu+8+4/O8vDzl6OioBg4caCyLi4tTgNqxY0eB4zdr1qzQmG75uXhNUT+/K30fnV27dtGkSRNq1aoFaJnyr7/+Sr9+/cwcWfV18uRJcnNz6dChg7HM2tqaNm3aFPpN7ejRo/Tq1cukrF27dmzYsMH4PCoqim3bthlrcECrQs/KyiIjI4OjR48SEBBg0g+mXbt2d/Wz/PjjjzRq1MikbMCAASZxW1lZ0bZtW2OZp6cnISEhd/xW6uDgQL169YzPvb29CQoKMmmz9vb2Nvk2uGfPHiZNmkRUVBRJSUkYDFpfqjNnztC4cWPjdmFhYcb/568MHB8fT+3atUGfS1Btf5zT/wWlNYv5etUgPvEquAVqc9/cotO5KDlXV1cGDx5srMH55ptvAHB3d2fw4MG4urqW2bnXrl2Lk5MTubm5GAwG+vfvz6RJk4yvh4aGmvR5iYqKMnZ6vVFWVhYnT54kOTmZuLg4k/e8lZUVrVq1KlHz1c3XaLt27QoMAvj000/p0qWL8bmvry+XL18GoFWrVibb6vV6pkyZwrJlyzh//jw5OTlkZ2fj4OAAwKlTp8jNzaVNmzbGfVxdXY3Ndrfj7OzM3r17yc3NZf369SxZssTkfhQdHY2VlRUtWrQwlgUHB+Pu7m5ynPzPq6IYOnQo/fv354EHHijyPgaDgdzcXP773//yyCOPALB06VJ8fHzYsmUL4eHhRT4WQFBQkMn7wdfXt0At1Y33HEtLSzw9PQkNDTWWeXt7AxTYrzyYPdH5888/mTFjBnv27CEuLo5Vq1YVGKI4d+5cZsyYwcWLF2nWrBmfffaZ8U164cIFkzdNrVq1OH/+fHn+CGXL2gHevlBqh8vTG4hLzuJqpjbviZ2VJbXc7HC4uZnK2qHUzlla0tLSeP/99+ndu3eB18qqI2dAQADBwcEmZfb2pTOy6OZOkzqd7pZl+clMeno64eHhhIeHs2TJEmrWrMmZM2cIDw8v0Oxx43HyV5A3pF2By5mQcQVrC7Qk59p6UzpnXwxYautOiTLh6upKr169jEkOQK9evco0yQHo3LkzX3zxBTY2Nvj5+WFlZXqtOzo6mjxPS0ujZcuWLFmypMCxatasWaaxFsbHx6fAdZif6Nwc/4wZM5gzZw6zZ88mNDQUR0dHXn/99VJpGrSwsDDG0ahRI06ePMmLL77I4sWLi3Wcbt26ERkZWejrgYGBHD58GNCardasWcPMmTMBbToPg8GAlZUVX331VYFmabj+5ebGLz81a9akRo0aJRoldrv70u22ueV96Kb9yoPZE5309HSaNWvGf/7zn1t+gP3444+MGjWKL7/8krZt2zJ79mzCw8OJjo4uUc/w7OxssrOvT01/YyeyCkmn02aVvUtKKZIzc7lwNYs8gzU6axtqOtvg5WKHRSn3uahXrx42NjZs27aNwMBAQOtbsnv37kI7+zVq1KjAyIW///7b5HmLFi2Ijo4ucMO78Rhnz54lLi7OeKHffIzS1qhRI/Ly8ti5c6ex701CQgLR0dEmN5nScOzYMRISEpg2bRoBAQEA/PPPP4XvkN+/K+VaopwaB25+gE6b48aj7vX1pizNfiuo8pKTkwv0Y1m1alWZ1+g4OjoWes3cSosWLfjxxx/x8vK65Sgx0D5Id+7caaxlyMvLY8+ePSY1GUX1999/M2jQIJPn99xzT7GPk2/btm306NGDZ599FtA+WGNiYozXY926dbG2tmb37t1aDSfa3yYmJqZYtSag9Q+qV68eb7zxBi1atCAkJIS8vDz27dtHy5YtAW1IeFJSksl+8+fPJzMzs9Dj3pgg7Nixw2RAwk8//cTHH3/M9u3bC60Zyq9Nj46Oxt/fH4DExESuXLlivCdXJ2avn+7WrRsffvhhgWaLfLNmzWLo0KE899xzNG7cmC+//BIHBwfjtyI/Pz+TGpzz58/fdgjv1KlTtaGz1x75HxhVWa7ewJnEDM4kZpBnMGBnbUk9L0d8XO1LPckB7cb64osvMmbMGDZs2MCRI0cYOnQoGRkZPP/887fc57XXXmPDhg3MnDmT48eP8/nnn5s0WwG89957fPvtt7z//vscPnyYo0eP8sMPPzBhwgQAunTpQoMGDRg8eDBRUVFERkbyzjvvlPrPd6P69evTo0cPhg4dyl9//UVUVBTPPvsstWrVokePHqV6rtq1a2NjY8Nnn33GqVOnWLNmTeFz8qTGaxP6JRy/tiwD2rBwFz9tYj9LG7BzlY7F5eTGjsfu7u785z//wd3dvUAH5YpgwIAB1KhRgx49ehAZGUlsbCxbt27ltdde49y5cwCMHDmSadOmsXr1ao4dO8ZLL71UYPLPzz//nIceeuiO51u+fDnffPMNMTExTJw4kV27dvHKK6+UOP769euzadMmtm/fztGjRxk+fDiXLl0yvu7s7MzgwYMZM2YMW7Zs4fDhwzz//PNYWFgYax2KKiAggF69evHee+8B0LBhQ7p06cKwYcPYtWsX+/btY9iwYdjb25scu1atWgQHBxf6uDEZadSoEU2bNjU+atWqhYWFBU2bNjU2ia1atYqGDRsa92nQoAE9evRg5MiRbN++nUOHDjF48GAaNmxI586dS/R7rczMnujcTk5ODnv27DFpm7WwsKBLly7s2LEDgDZt2nDo0CHOnz9PWloa69evv2374/jx40lOTjY+StoLvTJQSpGUkUPMpVSSM3PRocPbxY5gLyccbMr2G/y0adPo06cPAwcOpEWLFpw4cYKNGzcWaKvOd++99/L1118zZ84cmjVrxq+//mpMYPKFh4ezdu1afv31V1q3bs29997Lp59+arwpWFhYsGrVKjIzM2nTpg0vvPCCSft5WVmwYAEtW7bkscceo127diilWLduXanP51GzZk0WLlzI8uXLady4MdOmTTNWZ6MUZCZD8rXam7SL2qKaOguwv/at3DMYnLxlxuJylpKSYpLkDB48mICAAAYPHmyS7FSU2mUHBwf+/PNPateuTe/evWnUqBHPP/88WVlZxhqeN998k4EDBzJ48GDatWuHs7NzgS+rV65c4eTJk3c83/vvv88PP/xAWFgY3377LUuXLr2r2tAJEybQokULwsPD6dSpEz4+PgW6Q8yaNYt27drx2GOP0aVLFzp06ECjRo1K1AT+xhtv8MsvvxhHdX377bd4e3vzwAMP0KtXL4YOHYqzs3OZNa+DlkjfOIVEfhxt27ale/fudOzYEWtrazZs2FCm8wxVWLftqlzOuKnH9/nz5xWgtm/fbrLdmDFjVJs2bYzPf/rpJ1W/fn1Vr149NW/evGKds8KPuiqhnDy9ir2cpqLOJqmos0kq5mKKysjOK4Uoq55bjbqqNHIzlUo+p1TcAW3EVP4jPlqptMtK6e/ub37zNSmKLzMzU82fP/+Wo6vyR2PNnz+/VK77yqaivL/S0tKUq6urmj9/fqkf++zZswVGQlZU5vh7yKirInriiSdKNBFSVaSUIikjl7jkTPQGhU6nw9vZlhrOtmXSTFVV/O9//2P+/Pns2LHDZKRAhWTQa/PcZCRofXDyWVhpsxU7eNz1UgwjRozgu+++u7s4BaB1lB8wYMAtZ0Z2dXVlyJAhZTozsiho3759HDt2jDZt2pCcnMzkyZMBSqW5+ffffyctLY3Q0FDi4uIYO3YsQUFBxe7/Yy79+vXD09PT2ExZVvJHiubk5JR6f8abVehEp0aNGlhaWpq0rwJcunSpzKbrr8xy8gycv5pJapY2osrBxhJ/dwfsrKWp4naWLFli7BiY3zmxwlEKcjO05CYzCdQNIxdsXbQlGexctKaqUjB58mRGjx4NXB/BIUrOzs6u0ESmsA6/omzNnDmT6OhobGxsaNmyJZGRkdSoUeOuj5ubm8vbb7/NqVOncHZ2pn379ixZsqRSNBnlz+h+4wSIZcXPz884jYCtrW2ZnqtCJzr5b8DNmzcb21gNBgObN2++q85qVY1SisSMHC5ezUKvrtXiuNhS08m22J3rqqPizGlR7vR5kJmoJTh5NywRUMbrTXl5eZXLejeielMlmHenNNxzzz3s2bOnTI6dPwVEZVSc0Xl3y8rKqtzOZ/ZEJy0tjRMnThifx8bGsn//fjw8PKhduzajRo1i8ODBtGrVijZt2jB79mzj+hkCcvL0nEvKJC1bW+/JwcYKf3d7qcWpzJSC7FQtuclKxrgUAzqwd9MSHBsnGTElhBBFYPZE559//jEZ7jZq1CgABg8ezMKFC3n66ae5fPky7733HhcvXqR58+Zs2LDBOMtidaWUIiE9h4vJWRiUwkKnjaiq4WQjtTiVVV42ZCRqNTj6GyY3s7IHR0+wd9f64QghhCgys981O3XqdMfqy1deeUWaqm6Qfa0WJ/1aLY7jtVocW6nFqXyUQau1SU+AnOurAaOz1BIbB0+wqXizVAshRGVh9kRHFJ1SioS0HC6mXK/F8XG1w9NRanEqndxMrWkqI9G43hSgNUk5eMp6U0IIUUok0akksnOv1eLkaLU4TrZaLY6NldTiVBqGPG3EVEaiNoIq37X1pnDwBKuyHX0ghBDVjSQ6FZxSiitp2VxKycagFJbXanE8pBanclAKctKu9b25CuQPC9dpw8EdaoCts3QsFkKIMlJt68bnzp1L48aNad26tblDKVRWrp6Tl9OJu9bh2MnWivreznjKsPFiW7hwITqdDp1OV+jConfr4sWLPPzwwzg6OuLm5gapF6+tN3VC62CMAazswKUWeDfRFtW0czFbkrN161bj7+TmKfKFKK4hQ4aU+/tIp9OxevVqAE6fPo1OpzPOzVIdlcd97kaTJk0ynm/27Nllfr6SqraJzssvv8yRI0fYvXu3uUMpQClFfEoWx+PTyMjJw9JCh7+7A3VqOGJjVfH+ZEOGDDG+2W1sbAgODmby5Mnk5eWV+JhBQUHGY97qMWTIkGIf08XFhbi4OJOFMDt16nTLG8LChQu1ZKUYPp01i7gL59i/ZQ0xf67UVgvPX2/KwRNqNICaDcHJCyzNP3lY+/btiYuL46mnnjJ3KKKMlMW1WZpudZ3nr7ZdFjp16mQ8j52dHQ0aNGDq1KllPp9Pamoqr7/+OoGBgdjb29O+ffs7fvb89ddfdOjQAU9PT+zt7WnYsCGffvrpHc91q/tcWRk9ejRxcXFl+jcrDdJ0VcHk6g38m5BBDlrfGxc7a2q52WNdjARHr4fISIiLA19fuP9+KOuJLrt27cqCBQvIzs5m3bp1vPzyy1hbWzN+/PgC2+bk5GBjc/tJ7nbv3o1er3XS3b59O3369CE6Oto4i6y9ffGXONDpdGUzo3ZuFmQmcPLIPlo2Dqa+v4dWbu2oDQu3c6uQC2na2Njg4+ODvb092dnZ5g6nWtDr9URGRhIXF4evry/3339/mc9CW9rXZmmbPHkyQ4cONT4v69/H0KFDmTx5MtnZ2fz+++8MGzYMNzc3XnzxxTI75wsvvMChQ4dYvHgxfn5+fPfdd3Tp0oUjR44UOmGpo6Mjr7zyCmFhYTg6OvLXX38xfPhwHB0dGTZsWKHnKrP73C04OTnh5ORULjMp342KVz1QTeXkGVi0PZb41Gyy8/RYWugIcHcg0NOhWElORAQEBUHnztC/v/ZvUJBWXpZsbW3x8fEhMDCQF198kS5durBmzRrgepX2Rx99hJ+fHyEhIQAcPHiQBx98EHt7ezw9PRk2bBhpaWmAtlK3j48PPj4+eHhoiYOXlxc+Pj5YW1szYsQIatWqhYODA6GhoSxdurRsf0Dgiy++oF69etjY2BASEsLi+V/AlRi4fJSgJq1Z+ctvfLtiLbpaLRjy1iyo2QCdYw3mfT2fxx57DAcHBxo1asSOHTs4ceIEnTp1wtHRkfbt25us8nzy5El69OiBt7c3Tk5OtG7dmt9++80klqCgIKZMmcJ//vMfnJ2dqV27Nl999ZXx9fxq/IiICDp37oyDgwPNmjVjx44dZf57ErcWERFBcHAwnTt3pn///nTu3Jng4GAiyvjiLMm1efbsWZ566inc3Nzw8PCgR48enD592nhMvV7PqFGjcHNzw9PTk7Fjx5a4VsTZ2dl4rfv4+FCzZk1Ae4/f3BzSvHlzJk2aVKLz5HNwcDD+Pp577jnCwsLYtGmTyTZr1qyhfv362NnZ0blzZxYtWoROp+Pq1avFPl9mZiYrV65k+vTpPPDAAwQHBzNp0iSCg4P54osvCt3vnnvuoV+/fjRp0oSgoCCeffZZwsPDiYyMLHYMRb1fLFu2jPvvvx97e3tat25NTEwMu3fvplWrVjg5OdGtWzcuX75c7PObmyQ6FcCh88k88flffLvjX5TSRlQ18HbGvZgdjiMioG9fuHkttvPntfKyTnZuZG9vT07O9UnvNm/eTHR0NJs2bWLt2rWkp6cTHh6Ou7s7u3fvZvny5fz2229Fmi8pKyuLli1b8ssvv3Do0CGGDRvGwIED2bVrV5n9PKtWrWLkyJG8OfIVDm3/leH9Hue5Ea+yZctWAHb/tpquDz/EU089SVxcHHM++9y47wcffMCgQYPYv38/DRs2pH///gwfPpzx48fzzz//oJQy+bnT0tJ49NFH2bx5M/v27aNr1648/vjjnDlzxiSmTz75hFatWrFv3z5eeuklXnzxRaKjo022eeeddxg9ejT79++nQYMG9OvXr8I0W1QnERER9O3bl9DQUHbs2EFqaqpxAdm+ffuWebJzoztdm7m5uYSHh+Ps7ExkZCTbtm3DycmJrl27Gvf75JNPWLhwId988w1//fUXiYmJrFq1qtx+htKglCIyMpJjx46Z1GLFxsbSt29fevbsSVRUFMOHD+edd94x2ffMmTPG2ozCHlOmTAEgLy8PvV5fYK0ze3t7/vrrryLHu2/fPrZv307Hjh1L9PMW5X4xceJEJkyYwN69e7GysqJ///6MHTuWOXPmEBkZyYkTJ3jvvfdKdH6zKsmy6lVJUZd5LwtZuXlqxoZjqu74X1TguLWq68xN6p/9B1VGRkaxj5WXp5S/v1LaMJ+CD51OqYAAbbvSNnjwYNWjRw+llFIGg0Ft2rRJ2draqtGjRxtf9/b2VtnZ2cZ9vvrqK+Xu7q7S0tKMZb/88ouysLBQFy9eNDn+li1bFKCSkpIKjaF79+7qzTffLPT1BQsWKFdX1wLlHTt2VNbW1srR0dHkYWtre337vFzVvm1rNfTZJ5U6v9f4ePLxcPXoIw8plaf9XD169FCDBw82OT6gJkyYYHy+Y8cOBaj/+7//M5YtXbpU2dnZFRq7Uko1adJEffbZZ8bngYGB6tlnnzU+NxgMysvLS33xxRdKKaViY2MVoObPn2/c5vDhwwpQR48eNTn2jX8/Ufry8vJUUFCQevzxx5Verzd5Ta/Xq8cff1zVqVNH5ZXBxVmSa3Px4sUqJCREGQwGY1l2drayt7dXGzduVEop5evrq6ZPn258PTc3V/n7+xf7fRQYGKhsbGxMrr05c+YYX/v0009Ntm/WrJmaOHGi8TmgVq1apZS6/p7ft29foee78Xq3trZWgLKzs1Pbtm0zbjNu3DjVtGlTk/3eeecdk3tQbm6uOn78+G0fCQkJxv3btWunOnbsqM6fP6/y8vLU4sWLlYWFhWrQoMEdf0e1atVSNjY2ysLCQk2ePPm22xZ2nyvJ/WLp0qUKUJs3bzaWTZ06VYWEhNzy+Df/rUpLZmamOnLkiMrMzCzwWlE/v6WPjplEnb3KmBVRxFzSmmq6h/oyoWswV+PPl2hEVWRkwZqcGykFZ89q23XqVMKgb2Pt2rU4OTmRm5uLwWCgf//+JlXMoaGhJt+ajh49SrNmzXB0dDSWdejQAYPBQHR09G2X+NDr9UyZMoVly5Zx/vx5cnJyyM7OxsGhZDMIDxgwoMA3toiVK5kydSokxkJWMkejoxn2zGOAxbX1pjzo8GBX5vz3v9oCm7cRFhZm/H/+zxUaGmpSlpWVRUpKCi4uLqSlpTFp0iR++eUX4uLiyMvLIzMzs0CNzo3HzW+Xj4+PL3Sb/FXI4+Pjadiw4Z1/MaJUREZGcvr0aZYuXYrFTZNAWlhYMH78eNq3b09kZCSdyuDiLO61GRUVxYkTJ3B2djY5TlZWFidPniQ5OZm4uDjatm1rfM3KyopWrVqVqPlqzJgxJoMLSmMF8dvJv96TkpKYOHEi7du3p3379sbXo6OjC4zGbdOmjcnz4i5IuXjxYv7zn/9Qq1YtLC0tadGiBf369SvSwqKRkZGkpaXx999/89ZbbxEcHEy/fv2KfO58xb1fFHavunmfykASnXKWlavn099i+PrPUxgU1HCy4YMeTekW6ktWVhZXS3jcuLjS3a64OnfuzBdffIGNjQ1+fn5YWZm+tW5MaO7WjBkzmDNnDrNnzyY0NBRHR0def/11k+r44nB1db1+07q23pSXXa42Y3HW1Wtb6cDBHXyaXF9vqogJqbX19RFW+UnsrcoMBm2OndGjR7Np0yZmzpxJcHAw9vb29O3bt8DPd+Mx8o+Tf4zbnfvmbUTZirt20TVt2vSWr+eXx5XRxVncazMtLY2WLVuyZMmSAsfK7z9TmmrUqHHLpMHCwqJA4pSbm3vX57vxel+2bBnBwcHce++9dOnSpcjHOHPmDI0bN77tNm+//TZvv/02APXq1eOPP/4gPT2dlJQUfH19efrpp6lbt+4dz1WnTh1ASzguXbrEpEmTSpTolPR+cXNZZbx/SKJTjvb8m8iYFQc4dTkdgB7N/Zj0eBPcHe9+lMO1L+ultl1xOTo6FusbTqNGjVi4cCHp6enGG+22bduwsLAwdogszLZt2+jRowfPPvssoH1wx8TE3PHGUyiltAn9MhKvrzdl0AM6cKwJDh40atyEbf8cZPCw65fMtm3bSn7O29i2bRtDhgyhV69egPbBc2NHUFG55NekHTp0iHvvvbfA64cOHTLZrrQV99ps0aIFP/74I15eXsZRjjfz9fVl586dPPDAA4DWD2XPnj20aNGiVGIGLam6MflLSUkhNja21I4P2qihkSNHMnr0aPbt24dOpyMkJIR169aZbHfzUHA/P787zteTP4jiRo6Ojjg6OpKUlMTGjRuZPn16seI1GAwyQrIEpDNyOcjM0fPB2iP0/XIHpy6n4+Vsy9eDWjHnmXtKJckBbQi5v3/hlQw6HQQEaNtVBAMGDMDOzo7Bgwdz6NAhtmzZwquvvsrAgQPvuDJ9/fr12bRpE9u3b+fo0aMMHz6cS5cuFT+I3IxrNTgJcPXf60mOjbM2743OAlz9wdqBMWPGsHDhQr744guOHz/OrFmziIiIYPTo0SX46W+vfv36REREsH//fqKioujfv3+l/BYlNPfff79x1MvNf0eDwcDUqVOpU6cO91eQi3PAgAHUqFGDHj16EBkZSWxsLFu3buW1117j3LX28ZEjRzJt2jRWr17NsWPHeOmllwqMSPr888956KGHShzHgw8+yOLFi4mMjOTgwYMMHjy4TIYxDx8+nJiYGFauXGl8fuzYMcaNG0dMTAzLli1j4cKFwPVajvymq9s9bkx0Nm7cyIYNG4iNjWXTpk107tyZhg0b8txzzxm3GT9+PIMGDTI+nzt3Lj///DPHjx/n+PHj/N///R8zZ840fsETRSeJThnbeSqBbnP+5P/+ikUp6NPCn01vdOThxrf/MC8uS0uYM0f7/83JTv7z2bPLfj6donJwcGDjxo0kJibSunVr+vbty0MPPcTnn39+x30nTJhAixYtCA8Pp1OnTvj4+BR9RlZDHqRfhsvH4HI0GHK1FcQtrMHJB7waQ41gsHUy2a1nz57MmTOHmTNn0qRJE+bNm8eCBQvKpE/FrFmzcHd3p3379jz++OOEh4eX6jdlUb4sLS355JNPWLt2LT179jQZddWzZ0/Wrl3LzJkzK8xcJA4ODvz555/Url2b3r1706hRI55//nmysrKMNTxvvvkmAwcOZPDgwbRr1w5nZ2djDWS+K1eumEybUFzjx4+nY8eOPPbYY3Tv3p2ePXtSr169u/rZbsXDw4NBgwYxadIkDAYDderUYcWKFURERBAWFsYXX3xh7MNna1uyteiSk5N5+eWXadiwIYMGDeK+++5j48aNJs1CcXFxJv3wDAYD48ePp3nz5rRq1Yq5c+fy8ccfM3ny5Lv7gaujMukmXYmU1airtKxc9d7qgypw3FoVOG6tunfKb+r3Y5duu8/tepcX1cqVBUdfBQRo5dWWwaAWfPWFcnVxVur8vhtGTu1TKuGUUpnJSt0wwqS6kVFX5WPlypUqKChIAcZHnTp11MpqfXFWDh9++KHy9/c3dxh3VNioq7Imo66qoQtXM3lq3g7OJWUC0K9NAOMfbYSLXdlP+9+7N/ToUf4zI1dI+pxrfW8SIO0SySmpONVvz8v/6c/HU6eAvXuFWIrBXCIjI+nWrRvZ2dl0797d3OFUeb179zY2B5XnzMii+P73v//RunVrPD092bZtGzNmzCjSHF8VQXJyMk5OTrz88st8/PHHZXquKVOmMGXKFDIyMsr0PHdLp1QZL/JRQc2dO5e5c+ei1+uJiYkhOTm50I53xWUwKPrP/5uziZl83CeM++oXbbhkVlYWsbGx1KlTp8DkUqKIlAGyUrTkJjvFWJyansml1Dywc8Otpi81ymD0SGWTmZnJ+fPnAa1TZnlNGy9ERffGG2/w448/kpiYSO3atRk4cCDjx48vMGKtoklNTTX2V3RzcyvzofqJiYkkJiYCWudxV1fXUj/H7T4XU1JScHV1vePnd7VNdPIV9RdVXJdSsnC0tcLJtugXhiQ6dyE3S0tuMhO1fjj5bBy1jsUVdL0pIYQQhSuNRKdip6eVmLeLJCplzqCHzKtagpObfr3cwgocPMDeE6zl7yCEENWZJDqiclFKGxaekQCZSVpTVT5bl2u1Ny7a0HAhhBDVniQ6onLQ52qJTUYC5GVdL7e01WpvHDzuuBSDEEKI6kcSHVFxKQXZqZBxRetgTH53suvrTWHjVOSlGIQQQlQ/kuiIiid/tuKMRG1Cv3zWDtf63rhfX29KCCGEuA35tBAVg8GgLaCZkQA5adfLdZbXmqY8wdrebOEJIYSonKTHpigXOp2O1atXF3whJwOunoVLh66tN3UtybFxBvcg8Gl6bb0pSXIqukmTJqHT6dDpdMyePbvMzzdkyBDj+W753hLlasiQIUVfiqWcnD59Gp1OZ1yAc+vWreh0ugLrclUn1fE6lURH3LXLly/z4osvUrt2bWxtbfHx8SE8PJxt27YZt4mLi6Nbt27akxvXm7oSrfXBUXqtM/GN603Zu9/16KmFCxcaL7IbH/Pnz7+r45ZEp06djOe3s7OjQYMGTJ06lbKeyurGG1v+o2HDhnfcb/ny5TRs2BA7OztCQ0MLrOh8K02aNCEuLo5hw4aVRui3NWfOHJPVrUVBN37I2NjYEBwczOTJk8nLy7vzzhXEra7f++67r8zOFxQUZDyPg4MDoaGh5XK/SEtL45VXXsHf3x97e3saN27Ml19+WeT9f/jhB3Q6XZGSzep2nUrTVRWk1+vLdZr5Pn36kJOTw6JFi6hbty6XLl1i8+bNJCQkGLfx8fbWamuS4rS5b4wdi3Vg56o1Tdk6l0nHYhcXF6Kjo03KbjWDZ05ODjY2ZTtya+jQoUyePJns7Gx+//13hg0bhpubGy+++GKZnrdJkyb89ttvxud3muF1+/bt9OvXj6lTp/LYY4/x/fff07NnT/bu3UvTpk0L3c/KyqrcZlh2dXUtk5lYy5ReX+7rs3Tt2pUFCxaQnZ3NunXrePnll7G2tmb8+PEFti2Pa6AkFixYQNeuXY3PyzrGyZMnM3ToUDIyMli+fDlDhw6lVq1a17+slYFRo0bx+++/89133xEUFMSvv/7KSy+9hJ+fH0888cRt9z19+jSjR4/m/vvvL9K5qtt1KjU6VUxERARBQUF07tyZ/v3707lzZ4KCgoiIiCiT8129epXIyEg+/vhjOnfuTGBgIG3atGH8+PHaxanPgdSL6CwsWL3ka8hM4vTZ8+hqtWDZb/9w/1OvYF+rMa3vf4iY48fZvXs3rVq1wsnJiW7dunH58uW7jlGn0+Hj42PysLe3Z9KkSTRv3pz58+ebzLq5YcMG7rvvPtzc3PD09OSxxx4rsArz9u3bad68OXZ2drRq1YrVq1ebVJEXxsHBAR8fHwIDA3nuuecICwtj06ZNJtusWbOG+vXrY2dnR+fOnVm0aNFdV7fn39jyH3eaGn7OnDl07dqVMWPG0KhRIz744ANatGhRpNXlb5Zfg9arVy8cHByoX78+a9asMb6e35ywceNG7rnnHuzt7XnwwQeJj49n/fr1NGrUCBcXF/r371/h19S5rYgICA6Gzp2hf3/t3+BgrbwM5deyBgYG8uKLL9KlSxfj7z+/uemjjz7Cz8+PkJAQAM6ePctTTz2Fm5sbHh4e9OjRg9OnTxuPqdfrGTVqlPEaGTt2bIlqJnU6HV988QXdunXD3t6eunXrsmLFigLbubm5mbx/PTw8jPvf3Bzi5ubGwoULix3LjZydnfHx8aFu3bqMGzcODw+PAtfp119/TUBAAA4ODvTq1YtZs2bh5uZW4nNu376dwYMH06lTJ4KCghg2bBjNmjVj165dt91Pr9czYMAA3n//ferWrVvi81fl61QSnSokIiKCvn37cu7cOZPy8+fP07dv3zJJdpycnHBycmL16tVkZ2drhcqg1doknIRLhyE1v9rSQqu5ca8DwMSps5jw7rvs3bsXKysr+vfvz9ixY5kzZw6RkZGcOHGC9957r9RjvtGJEydYuXIlERERxiQlPT2dUaNG8c8//7B582YsLCzo1asXBoM2OWFKSgqPP/44oaGh7N27lw8++IBx48YV67xKKSIjIzl27JjJt9PY2Fj69u1Lz549iYqKYvjw4bzzzjsm+545c8b4ey/sMWXKFJN9jh8/jp+fH3Xr1mXAgAGcOXPmtvHt2LGDLl26mJSFh4ezY8eOYv2c+d5//32eeuopDhw4wKOPPsqAAQOMa+TkmzRpEp9//jnbt283ftDOnj2b77//nl9++YVff/2Vzz77rETnN7uICOjbF0JDYccOSE3V/g0N1crLONm5kb29PTk5OcbnmzdvJjo6mk2bNrF27Vpyc3MJDw/H2dmZyMhItm3bhpOTE127djXu98knn7Bw4UK++eYb/vrrLxITE1m1alWJ4nn33Xfp06cPUVFRDBgwgGeeeYajR4+Wys96twwGAytXriQpKcnkOt22bRsjRoxg5MiR7N+/n4cffpiPPvrIZN/IyMg7XqdLliwxbt++fXvWrFnD+fPnUUqxZcsWYmJieOSRR24b4+TJk/Hy8uL555+/65+3yl6npb2kemVT1GXey8PtlqO/k7y8POXv76/Q2oQKPHQ6nQoICFB5eXmlHveKFSuUu7u7srOzU+3btlLjX31eRW36Qanze7XH5RgFqFUrVyqllIqNjVWAmj9/vvEYS5cuVYDavHmzsWzq1KkqJCTkrmJbsGCBApSjo6Px4e3trZRSauLEicra2lrFx8ff9hiXL19WgDp48KBSSqkvvvhCeXp6mvydvv76awWoffv2FXqcjh07Kmtra+Xo6Kisra0VoOzs7NS2bduM24wbN041bdrUZL933nlHASopKUkppVRubq46fvz4bR8JCQnG/detW6eWLVumoqKi1IYNG1S7du1U7dq1VUpKSqGxWltbq++//96kbO7cucrLy6vQfSZOnKiaNWtWoBxQEyZMMD5PS0tTgFq/fr1SSqktW7YoQP3222/GbaZOnaoAdfLkSWPZ8OHDVXh4+C2Pv2rVqkLjMru8PKWCgpR6/HGl9HrT1/R6rbxOHW27UjZ48GDVo0cPpZRSBoNBbdq0Sdna2qrRo0cbX/f29lbZ2dnGfRYvXqxCQkKUwWAwlmVnZyt7e3u1ceNGpZRSvr6+avr06cbXc3Nzlb+/v/FcRQWoESNGmJS1bdtWvfjiiybb2NnZmVzD+X/vW/3tXV1d1YIFC5RS1+81+ddl/nst/1q6lcDAQGVjY6McHR2VlZWVApSHh4c6fvy4cZunn35ade/e3WS/AQMGKFdXV+PzjIyMO16nN16DWVlZatCgQQpQVlZWysbGRi1atOi2v7/IyEhVq1YtdfnyZaWU6d+7MJXtOr3d52JRP7+lj04VERkZWaAm50ZKKc6ePUtkZCSdOnUqvRMb9PTp2pHuUX8Que0v/t5zkPVbtjH9fwuZ/9kMhgx9EayurTdlYVqBGBYWZvy/t7c3AKGhoSZl8fHxdx2is7Mze/fuNT63uCGOwMBAat60kvnx48d577332LlzJ1euXDHW5Jw5c4amTZsSHR1NWFiYyQJzbdq0KVIsAwYM4J133iEpKYmJEyfSvn172rdvb3w9Ojqa1q1bm+xz87GtrKwIDg4u0vkAk34FYWFhtG3blsDAQJYtW1Yq3wKL4sa/taOjIy4uLgX+tje/HxwcHEyq4r29ve9YjV8hRUbC6dOwdGmBawALCxg/Htq317YrzWvzmrVr1+Lk5ERubi4Gg4H+/fszadIk4+uhoaEmtRVRUVGcOHECZ2dnk+NkZWVx8uRJkpOTiYuLo23btsbXrKysaNWqVYmar9q1a1fg+c1NwJ9++qlJDaOvr2+xz1McY8aMYciQIcTFxTFmzBheeuklk2suOjqaXr16mezTpk0b1q5da3xub29frOv0s88+4++//2bNmjUEBgby559/8vLLL+Pn51egdhW0lcoHDhzI119/XWqrlFfV67TaJjpz585l7ty56PV6c4dSKoraq71Uer8b15u6ojVRKQN2lvDwA/fy8MPhvPvBVF54eRQTp81myItvFHoYa2tr4/911zoh31yWn2TcDQsLi0JvOI6OjgXKHn/8cQIDA/n666/x8/PDYDDQtGlTk+r+knJ1dTXGsmzZMoKDg7n33ntveSMrzJkzZ2jcuPFtt3n77bd5++23b/mam5sbDRo04MSJE4Xu7+Pjw6VLl0zKLl26VOIOjDf+XeHWf9ub//ZF2adSyL/mCuvEnV9eRiNTOnfuzBdffIGNjQ1+fn4FOqLffA2kpaXRsmVLk2aVfDd/KSgvPj4+t7yGdTpdgeQqNze3wHbFVaNGDYKDgwkODmb58uWEhobSqlWrO153N4qMjLxj5+V58+YxYMAAMjMzefvtt1m1ahXdu3cHtIRi//79zJw585b3h5MnT3L69Gkef/xxY1n+9WFlZUV0dDT16tUrcrxQda/TapvovPzyy7z88svGZd4ru6J+w7mrb0L6XMhM1GYsLrDelOe19aa0N33jJk1Y/dNPJT+XmSQkJBAdHc3XX39tHMHw119/mWwTEhLCd999R3Z2Nra2tgDs3r272OdycnJi5MiRjB49mn379qHT6QgJCSkwjPvmY/v5+d2x03N+Z81bSUtL4+TJkwwcOLDQbdq1a8fmzZt5/fXXjWWbNm0q8O1bFEH+NXfoENx7b8HXDx0y3a6UOTo6FqtmoUWLFvz44494eXnh4uJyy218fX3ZuXMnDzzwAAB5eXns2bOHFi1aFDu+v//+m0GDBpk8v+eee4q0b82aNU2+vB0/frzUO8IGBATw9NNPM378eH66dk8LCQkpcF3e/LxVq1Z3vE7za7Jzc3PJzc01qW0GsLS0LDRpaNiwIQcPHjQpmzBhAqmpqcyZM4eAgIA7/mzVhXRGriLuv/9+/P39jTUjN9PpdAQEBBR5+KGRUpCVDImntI7FKRe0JEdnAfYeJODBg/1e4bufNnHg8FFiY2NZvnw506dPp0ePHqXwk123atWqIs3/cjfc3d3x9PTkq6++4sSJE/z++++MGjXKZJv+/ftjMBgYNmwYR48eZePGjcycOROg0N9/YYYPH05MTAwrV640Pj927Bjjxo0jJiaGZcuWGUeQ5B87v+nqdo8bE53Ro0fzxx9/cPr0abZv306vXr2wtLSkX79+xm0GDRpkMtx45MiRbNiwgU8++YRjx44xadIk/vnnH1555ZVi/XwCbQh5UBBMmaLNAH4jgwGmToU6dbTtKoABAwZQo0YNevToQWRkJLGxsWzdupXXXnvN2Dw+cuRIpk2bxurVqzl27BgvvfRSgVGBn3/+OQ899NAdz7d8+XK++eYbYmJimDhxIrt27Sry++zBBx/k888/Z9++ffzzzz+MGDGiQA1DaRg5ciQ///wz//zzDwCvvvoq69atY9asWRw/fpx58+axfv16k+s/v+nqdo/85kEXFxc6duzImDFj2Lp1K7GxsSxcuJBvv/3WpInsxuvUzs6Opk2bmjzc3NxwdnamadOmFXKaAHORRKeKsLS0ZM6cOUDBD9v857Nnzy76fDp52VpSc+mwluRkJQNKW2/KNQC8m4J7IE6ePrRt25ZPP/2UBx54gKZNm/Luu+8ydOjQEg1Fvp3k5OQC8+GUNgsLC3744Qf27NlD06ZNeeONN5gxY4bJNi4uLvz888/s37+f5s2b88477xhHh93Yb6coPDw8GDRoEJMmTcJgMFCnTh1WrFhBREQEYWFhfPHFF8ZRV/m1R8V17tw5+vXrR0hICE899RSenp78/fffJs0QZ86cMflm3L59e77//nu++uormjVrxooVK1i9evVt59ARhbC0hE8+gbVroWdP01FXPXtq5TNnlvl8OkXl4ODAn3/+Se3atenduzeNGjXi+eefJysry1jD8+abbzJw4EAGDx5Mu3btcHZ2LtBn5cqVKwWmZbiV999/nx9++IGwsDC+/fZbli5dWuQmok8++cT4Ba5///6MHj0aBweH4v/Qd9C4cWMeeeQR43XeoUMHvvzyS2bNmkWzZs3YsGEDb7zxRrGv/xv98MMPtG7dmgEDBtC4cWOmTZvGRx99xIgRI4zb3HydiiIqdhfoKqaqjLrKt3LlygKjrwICAtTKayOebkuvVyo9QanLMddHTJ3fq9SFKKWunlUqJ6PEcVV13333nbK2tlYZGaX/O/rwww+Vv79/qR+3tBU2mqOsUdFHXeVbuVIbfaXVk2qPOnW08mqq0vztiuCFF15Q9913n7nDuKPKdp3KqCtRQO/evY1VzkWeGTknQ1tMMzNJW4ohn62z1vfGzvWul2Koar799lvq1q1LrVq1iIqKYty4cTz11FPY29/9mlz/+9//aN26NZ6enmzbto0ZM2ZUmiajgwcP4uTkxPTp03nppZfK9FwjRozgu+++K9NzlKrevaFHj3KfGVmUjZkzZ/Lwww/j6OjI+vXrWbRoEf/73//MHVaRVLfrVHct06q28jsj/397dx8VVZ3/Afw9DA86MDDACAMLhB6CYEUQEA6tFion3dpysXxIFgcj2wxRI9Ft9xQsHZN0rfUY2ZZHZFs6GtuBLdNNMklkTXkIf5WJ6eLDFsJJnOH5ce7vj4lrE4KAMwzMvF/nzDncp+/93MGv98P3fu/3q9VqB+14N1Y6OztRV1dnMEqvyeh6gfYb+gSnt+Pmeqm9vlPxZHfAls94B7Nt2za88cYbuHbtGry8vMTRZY3RbP7ss8/iwIEDaGpqgp+fH5KSkvD888/fdtoGc2tqahIHF5syZYrJO/k3NjaiubkZgL5z7K3eoKPxTSKRoKioaNxNBjocS5cuRWlpKVpaWjBt2jSkpaUZPGYaryZaPR3qvjjc+zcTHWtKdARBP99U23WgUwPD+aYU+gTHRPNNERERjZQxEp3x/SciGUdv94+vhV/Xzz3Vz3byj603boCU/xSIiMjy8O5mqQSd/k2p9utAV8vN9RIpMNlVn+DYydh6Q0REFo2JjqXp6bjZsVjXe3O9vdPNjsU27PxIRETWgYmOJdD16ROb9uv6qRn62djpW25kbjfnmyIiIrIiTHQmKkEAutv0yU2nRv+oCoC+Y7GzvvXGwZmPpoiIyKox0Zlo+uebarsO9HXdXC91ABzdf+xYbPwh0ImIiCYijgI3Edxqvqm+LnG+KbjfDXgEA06eFp/kJCcnT8gxN6yFRCKBRCKBQqEw+bkuXbokni88PNzk5yOiiYmJznjW2zms+abg4GTWR1TJycniDcfe3h4BAQHIzs5Gb2/v7Q8eA/7+/mJ8/R8fH58xj6O0tNQghilTpuDBBx8cMAOxKfz8+iUSCfbv3z/kMU1NTUhMTISzszMUCgVSUlLQ2tp623Pl5eXh/Pnzxgp9UL6+vqivr8dzzz1n8nMR0cTFR1fjjaADOjRAa4t+cL9+NrY/vhbuDtjdepqBzs5OdHd333LgpObmZtjb25tsxOWFCxciLy8PXV1dOHToEFJTU2FnZ2cwI3a/7u7uMZ9ZNzs7G6tXrxaXB5sSo6enxySzH/9UbW0tnJ2d8f333yMjIwMPPfQQLly4YPLvJC8vDwsXLhSXb9fqkpiYiPr6epSUlKCnpwerVq3CU089hXfffXfI4xQKBTw8PIwR8pCkUilUKhWcnJxMfi4imristkUnNzcXISEhmDVrlrlD0T+a+q4aOLZV34LT8v3NJMdBDrj6A56/BFx8hkxyCgoKsG/fPmi1WoNtWq0W+/btQ0FBATo7O01yCQ4ODlCpVLjrrruwZs0axMfH44MPPgBw83HTli1b4O3tjaCgIADA1atXsXTpUigUCri5uWHRokW4dOmSWGZfXx/S09OhUCjg7u6OTZs2YbQDecvlcqhUKvHTP3O3RCLB7t278cgjj8DR0RFbtmxBX18fUlJSMHXqVEyePBlBQUHizPD9ent7sW7dOjG2zZs3Q61WD+uxmoeHB1QqFSIiIrBhwwZcvXoV586dE7e3tLQgMTERjo6O8PLywmuvvYa4uDhs2LBhVNfeT6FQGHwHQyW933zzDf79739jz549iImJwezZs7Fr1y7s378f33///YjOm5WVhfDwcLzzzjvw9/eHi4sLli9fjpaWm+M7xcXFIS0tDRs2bICrqys8PT3x9ttvo62tDatWrYJcLkdAQAAOHz486usnIutktYlOamoqzp49i4qKCvMF0d4EfP4m8OZs4O25wNfv61t0bOwAuRfg8UvAPUDfknObSTW7u7vR1taGGzduID8/X0x2tFot8vPzcePGDbS1taG7u3vIcoxl8uTJBuc6evQoamtrUVJSgoMHD6KnpwcLFiyAXC5HWVkZysvL4eTkhIULF4rH7dixA/v27cPevXtx4sQJNDU1oaioyOixZmVlISEhAV9++SWeeOIJ6HQ6+Pj4oLCwEGfPnsWLL76IP/7xj3jvvffEY1555RUUFBQgLy8P5eXlaG5uRnFx8YjOq9VqxcdHP23NSU9PR3l5OT744AOUlJSgrKwM1dXVBsc+/fTTcHJyGvLzc6mpqVAqlYiOjsbevXuHTBpPnjwJhUKBqKgocV18fDxsbGxw6tSpEV0nAFy8eBHFxcU4ePAgDh48iM8++ww5OTkG++Tn50OpVOL06dNIS0vDmjVrsGTJEtx7772orq7GAw88gKSkJLS3tw9yFiKiWxjxnOkWZrjTvBtNX58gXDgqCO8lC0K2UhAynfWf7ClCR3G6cPb/qoWO9vZRFa3RaISdO3cKWVlZws6dO4UrV64YLGs0GiNfjJ5arRYWLVokCIIg6HQ6oaSkRHBwcBA2btwobvf09BS6urrEY9555x0hKChI0Ol04rquri5h8uTJwscffywIgiB4eXkJ27ZtE7f39PQIPj4+4rmG66677hLs7e0FR0dH8bNz505BEAQBgLBhw4bblpGamio8+uij4rKnp6ewfft2cbm3t1fw8/MbMrZjx44JAMQYoJ9sTHjkkUfEfZqbmwU7OzuhsLBQXKfRaASZTCasX79eXNfQ0CB8++23Q35+Kjs7Wzhx4oRQXV0t5OTkCA4ODuJ3cCtbtmwRAgMDB6yfMmWK8MYbbwx6HAChqKjIYF1mZqYgk8mE5uZmcV1GRoYQExMjLt9///3C7NmzxeXe3l7B0dFRSEpKEtfV19cLAISTJ08OKD8sLGzQmIho4uro6BDOnj0rdHR0DNg23Ps3++iMFc1VoKYA+KIA0F65uV4VCsxcCYQ+BtjIgLq6UXcsdnFxgVqtFltw9u7dCwBwdXWFWq026Sy1Bw8ehJOTE3p6eqDT6bBixQpkZWWJ20NDQw1aLc6cOYMLFy5ALpcblNPZ2YmLFy9Cq9Wivr4eMTEx4jZbW1tERUWN6vFVRkYGkpOTxWWlUin+/NNWi365ubnYu3cvrly5go6ODnR3d4tv9mi1WjQ0NCA6OlrcXyqVIjIyEjqdbkBZP1dWVgaZTIbPP/8cL7/8Mt58801x23//+1/09PQYlO3i4iI+7uvn4eExon4wL7zwgvjzzJkz0dbWhu3bt2PdunXDLuNO+Pv7G/yuvby80NjYaLDPjBkzxJ+lUinc3d0RGhoqrvP09ASAAccREQ2FiY4p9XYB5z4CvngHuHgM4mzhDi7AjCXAzCTAO/zm/kboP+Pi4oKEhAQxyQGAhIQEkyY5ADB37lzs3r0b9vb28Pb2hq2t4T8tR0dHg+XW1lZERkaioKBgQFn9/WeMSalUIiAg4Jbbfh7b/v37sXHjRuzYsQOxsbGQy+XYvn37qB7Z3MrUqVOhUCgQFBSExsZGLFu2DMePHx9RGU8//TT+8Y9/DLnPUG9IxcTE4KWXXkJXVxccHBwGbFepVAMSit7eXjQ1NUGlUo0oVgADOnhLJJIBSeGt9vnpOsmPfwAMJ5kkIurHRMcUOjTAZ68AZ/brB/fr5z8HiFgJBD88aKfiO6XVagf0YykqKjJ5i46jo+OgicStRERE4MCBA/Dw8LjlW2KA/q/+U6dO4b777gOgv9FWVVUhIiLCKDEPpry8HPfeey+eeeYZcd3FixfFn11cXODp6YmKigoxtr6+PlRXV494PJfU1FRs3boVRUVFSEhIwLRp02BnZ4eKigr4+fkB0P9Oz58/L54L0L9FtnHjxlFfY01NDVxdXW+Z5ABAbGwsNBoNqqqqEBkZCQD49NNPodPpDFrZiIjGO6vtjGxSdjLg/97TJzlyb2DORmDdF0DyQWDGUpMmOf2PrVxdXfHEE0/A1dV1QAfl8SAxMRFKpRKLFi1CWVkZ6urqUFpainXr1uF///sfAGD9+vXIyclBcXExzp07h2eeeQYajcagnNdffx3z5883amx33303Kisr8fHHH+P8+fN44YUXBnRaT0tLw9atW/Gvf/0LtbW1WL9+PW7cuCG2OgyXTCbD6tWrkZmZCUEQIJfLoVarkZGRgWPHjuHrr79GSkoKbGxsDMr28PBAQEDAkJ9+H374Ifbs2YOvvvoKFy5cwO7du/Hyyy8jLS1N3Of06dO455578N133wEAgoODsXDhQqxevRqnT59GeXk51q5di+XLl8Pb23s0XysRkVkw0TEFW3tgwRZgRSHw7FfA/BcAt2kmPWVzc7NBkqNWq+Hr6wu1Wm2Q7DQ3N5s0juGSyWQ4fvw4/Pz8sHjxYgQHByMlJQWdnZ1iC89zzz2HpKQkqNVq8RFSQkKCQTk//PCDQWuLMfz+97/H4sWLsWzZMsTExOD69esGrTsAsHnzZjz++ONYuXIlYmNj4eTkhAULFoxqnKK1a9fim2++QWFhIQDg1VdfRWxsLH7zm98gPj4ev/rVrxAcHDzqMZDs7OyQm5uL2NhYhIeH429/+xteffVVZGZmivu0t7ejtrYWPT094rqCggLcc889mD9/Ph588EHMnj0bb7311qhiICIyF4kwmp6dFqS5uRkuLi7QarWDPkIZK52dnairq8PUqVNHfFPrH0enra1twGOq/pYeR0dHJCYmmmzQQGum0+kQHByMpUuX4qWXXjJq2W1tbfjFL36BHTt2ICUlxahlG5tEIkFRUdGYTtORlZWF4uJi1NTUjNk5iWhsDHVfHO79m310LMSkSZOQmJh4y5GRXVxckJycbNKRka3N5cuXceTIEdx///3o6urC66+/jrq6OqxYseKOy/7iiy9w7tw5REdHQ6vVIjs7GwCwaNGiOy57LDz++ONwd3cXH0GaypUrVxASEoLu7m6EhISY9FxENHEx0bEgkyZNGjSRMXdrlaWxsbHBvn37sHHjRgiCgOnTp+OTTz5BcHCwUcr/y1/+gtraWtjb2yMyMhJlZWUGr8SPV99++y2AwafYMCZvb2+xFWewTtVEREx0iEbB19cX5eXlJil75syZqKqqMknZpjaSN+/ulK2t7Ziej4gmJnZGJiIiIovFRGccsvL+4URERACMcz9kojOO9I8Cy0kLiYiIbt4Pfz5y+kiwj844IpVKoVAoxKH3ZTLZiAegIyIimugEQUB7ezsaGxuhUCju6AUHJjrjTP88Qpy4kIiIrJ1CoRjV/Ho/xURnnJFIJPDy8oKHh4fBKLVERETWxM7OzihDVTDRGaekUumYjEVCRERkydgZmYiIiCwWEx0iIiKyWFab6OTm5iIkJASzZs0ydyhERERkIlY/e7lWq4VCocDVq1c5HxQREdEE0dzcDF9fX2g0Gri4uAy6n9V3Rm5paQGgn7uIiIiIJpaWlpYhEx2rb9HR6XQIDAxEVVXVsAfnmzVrFioqKobcpz/TZEvRTcP53sxprOMz1fmMVe6dlDOaY0dyzHD3ZT00xDo4Nuezhjo43P1NWQcFQUBLSwu8vb1hYzN4Txyrb9GxsbGBvb39kNngz0ml0mH/wpydnfkf7I9G8r2Zw1jHZ6rzGavcOylnNMeO5JiRls96qMc6ODbns4Y6ONL9TVUHh3PvttrOyD+Vmppq0v1Jb7x/b2Mdn6nOZ6xy76Sc0Rw7kmPG+7+l8Wq8f2+sg8Yrx9R1cLTnMAerf3RlKs3NzXBxcYFWqx3Xf0ERWTLWQyLzGg91kC06JuLg4IDMzEw4ODiYOxQiq8V6SGRe46EOskWHiIiILBZbdIiIiMhiMdEhIiIii8VEh4iIiCwWEx0iIiKyWEx0iIiIyGIx0TGThIQEuLq64rHHHjN3KERW5+rVq4iLi0NISAhmzJiBwsJCc4dEZFU0Gg2ioqIQHh6O6dOn4+233zbZufh6uZmUlpaipaUF+fn5+Oc//2nucIisSn19PRoaGhAeHo5r164hMjIS58+fh6Ojo7lDI7IKfX196OrqgkwmQ1tbG6ZPn47Kykq4u7sb/Vxs0TGTuLg4yOVyc4dBZJW8vLwQHh4OAFCpVFAqlWhqajJvUERWRCqVQiaTAQC6urogCAJM1e7CRGcUjh8/jocffhje3t6QSCQoLi4esE9ubi78/f0xadIkxMTE4PTp02MfKJGFMmYdrKqqQl9fH3x9fU0cNZHlMEYd1Gg0CAsLg4+PDzIyMqBUKk0SKxOdUWhra0NYWBhyc3Nvuf3AgQNIT09HZmYmqqurERYWhgULFqCxsXGMIyWyTMaqg01NTVi5ciXeeuutsQibyGIYow4qFAqcOXMGdXV1ePfdd9HQ0GCaYAW6IwCEoqIig3XR0dFCamqquNzX1yd4e3sLW7duNdjv2LFjwqOPPjoWYRJZrNHWwc7OTmHOnDnC3//+97EKlcgi3cl9sN+aNWuEwsJCk8THFh0j6+7uRlVVFeLj48V1NjY2iI+Px8mTJ80YGZF1GE4dFAQBycnJmDdvHpKSkswVKpFFGk4dbGhoQEtLCwBAq9Xi+PHjCAoKMkk8THSM7IcffkBfXx88PT0N1nt6euLatWvicnx8PJYsWYJDhw7Bx8eHSRCRkQynDpaXl+PAgQMoLi5GeHg4wsPD8eWXX5ojXCKLM5w6ePnyZcyZMwdhYWGYM2cO0tLSEBoaapJ4bE1SKt3WJ598Yu4QiKzW7NmzodPpzB0GkdWKjo5GTU3NmJyLLTpGplQqIZVKB3SqamhogEqlMlNURNaDdZDIvMZbHWSiY2T29vaIjIzE0aNHxXU6nQ5Hjx5FbGysGSMjsg6sg0TmNd7qIB9djUJraysuXLggLtfV1aGmpgZubm7w8/NDeno61Go1oqKiEB0djb/+9a9oa2vDqlWrzBg1keVgHSQyrwlVB03yLpeFO3bsmABgwEetVov77Nq1S/Dz8xPs7e2F6Oho4fPPPzdfwEQWhnWQyLwmUh3kXFdERERksdhHh4iIiCwWEx0iIiKyWEx0iIiIyGIx0SEiIiKLxUSHiIiILBYTHSIiIrJYTHSIiIjIYjHRISIiIovFRIeIiIgsFhMdIprQ/P39IZFIIJFIIJPJEBoaij179pg7LCIaJ5joENGEl52djfr6enz11Vf43e9+h9WrV+Pw4cPmDouIxgEmOkQ0rsXFxWHdunXYtGkT3NzcoFKpkJWVZbCPXC6HSqXCtGnTsHnzZri5uaGkpETcrtFo8OSTT2LKlClwdnbGvHnzcObMGXH7mTNnMHfuXMjlcjg7OyMyMhKVlZVjdYlEZEJMdIho3MvPz4ejoyNOnTqFbdu2ITs72yCR6afT6fD+++/jxo0bsLe3F9cvWbIEjY2NOHz4MKqqqhAREYH58+ejqakJAJCYmAgfHx9UVFSgqqoKf/jDH2BnZzdm10dEpsPZy4loXIuLi0NfXx/KysrEddHR0Zg3bx5ycnLg7++P+vp62NnZoaurC729vXBzc8OpU6cQEBCAEydO4KGHHkJjYyMcHBzEMgICArBp0yY89dRTcHZ2xq5du6BWq81xiURkQmzRIaJxb8aMGQbLXl5eaGxsFJczMjJQU1ODTz/9FDExMXjttdcQEBAAQP9YqrW1Fe7u7nBychI/dXV1uHjxIgAgPT0dTz75JOLj45GTkyOuJ6KJz9bcARAR3c7PHyNJJBLodDpxWalUIiAgAAEBASgsLERoaCiioqIQEhKC1tZWeHl5obS0dEC5CoUCAJCVlYUVK1bgo48+wuHDh5GZmYn9+/cjISHBlJdFRGOALTpEZFF8fX2xbNkyPP/88wCAiIgIXLt2Dba2tmIy1P9RKpXicYGBgXj22Wdx5MgRLF68GHl5eea6BCIyIiY6RGRx1q9fjw8//BCVlZWIj49HbGwsfvvb3+LIkSO4dOkS/vOf/+BPf/oTKisr0dHRgbVr16K0tBSXL19GeXk5KioqEBwcbO7LICIjYKJDRBYnJCQEDzzwAF588UVIJBIcOnQI9913H1atWoXAwEAsX74cly9fhqenJ6RSKa5fv46VK1ciMDAQS5cuxa9//Wv8+c9/NvdlEJER8K0rIiIislhs0SEiIiKLxUSHiIiILBYTHSIiIrJYTHSIiIjIYjHRISIiIovFRIeIiIgsFhMdIiIislhMdIiIiMhiMdEhIiIii8VEh4iIiCwWEx0iIiKyWEx0iIiIyGL9P29yPJgQtSeaAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "ZpRNNkam1smj"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "e1yI8abiVmAO"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Alston paper using Flory scaling\n",
        "https://pubs.acs.org/doi/full/10.1021/acs.jpcb.3c01619\n",
        "\n",
        "$D = A_0 N^\\nu$\n",
        "\n",
        "Figure below was validated against their Fig 1d by fitting their data to get an estimate for $A_0$\n",
        "\n"
      ],
      "metadata": {
        "id": "jGDGAVkk_SYE"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Did a quick estimate of $a_0$ based on the expression\n",
        "$\\langle r_e \\rangle = a_0 N^\\nu$ for the end-to-end distance dsimulation data\n",
        "\n",
        "\n",
        "Data (re**2) seems to match that presented in Fig 10\n",
        "\n",
        "Need to fit $r_i = a N^{\\nu_i}$ with an intercept of 0, so we can do\n",
        "\\begin{align}\n",
        "y &= m x \\\\\n",
        "x\\cdot y &= x\\cdot(m x)\\\\\n",
        "&= m x\\cdot x\\\\\n",
        "⇒ \\sum{xy} &=  m\\sum{xx}\\\\\n",
        "⇒m &= \\frac{\\sum{xy}}{\\sum{xx}}\n",
        "\\end{align}"
      ],
      "metadata": {
        "id": "kISWgH9N1tl5"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "BzPoG9NU_iKj"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "Ns = (np.arange(99)+1)*10\n",
        "nua = 0.5 # from Alston paper\n",
        "\n",
        "# fig 1d\n",
        "Na = np.array([50,100])\n",
        "xa = N**nua\n",
        "ya = np.array([42.5,60])\n",
        "a0a = np.dot(xa,ya)/np.dot(xa,xa)\n",
        "print(a0a,xa,ya)\n",
        "\n",
        "\n",
        "# from Fig 1f Alston\n",
        "A0 = 60./(100.**nu)\n",
        "print(A0)\n",
        "\n",
        "#\n",
        "sqrt_re2 = a0a * (Ns**nua)\n",
        "\n",
        "\n",
        "plt.plot(Ns,sqrt_re2 )\n",
        "plt.xlabel('res')\n",
        "plt.ylabel('$\\sqrt{<r_e^2>}$')\n",
        "plt.xscale('log')\n",
        "plt.yscale('log')\n",
        "plt.ylim([20,100])\n",
        "\n",
        "plt.scatter(Na,ya,label='Alston')\n",
        "plt.legend(loc=0)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 516
        },
        "id": "RPSrPAYC_hIE",
        "outputId": "e28f70f1-532d-42ca-fb19-32dd7e3bc1dc"
      },
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "6.0034692133618845 [ 7.07106781 10.        ] [42.5 60. ]\n",
            "3.0071234017636335\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7835271ed660>"
            ]
          },
          "metadata": {},
          "execution_count": 67
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pylab as plt\n",
        "\n",
        "# re=170, v=0.66, N=130 ---> a=6.84 (how compares to halston?)\n",
        "# re=130, v=0.63, N=130 ---> a=5.76\n",
        "# avg ~ 6.2\n",
        "# re ]\n",
        "rewt = 170\n",
        "rep=130\n",
        "x = np.array([Nsim**nup,Nsim**nu])\n",
        "y = np.array([rep,rewt])\n",
        "a0 = np.dot(x,y)/np.dot(x,x)\n",
        "print(a0,x,y)\n",
        "\n",
        "# Perform linear fit\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "Ns = np.arange(nFull)+1\n",
        "#a0=6.7\n",
        "# WT\n",
        "#nu = 0.66 # WT\n",
        "re_wt = a0*Ns**nu\n",
        "\n",
        "# p\n",
        "#nu = 0.64 # WT\n",
        "re_p = a0*Ns**nup\n",
        "\n",
        "## plot\n",
        "plt.plot(Ns,re_wt,'k-',label='Pred WT')\n",
        "plt.plot(Ns,re_p,'r-',label='Pred +P')\n",
        "\n",
        "# sim\n",
        "Nsim=130 - 1\n",
        "\n",
        "#plt.scatter(Na,ya)\n",
        "\n",
        "plt.scatter(Ns[Nsim],rewt,facecolor='k',label='Sim WT frag, <re>=%3d'%rewt)\n",
        "plt.scatter(Ns[Nsim],rep,facecolor='r',label='Sim pfrag, <re>=%3d'%rep)\n",
        "\n",
        "nfull = nFull-1\n",
        "plt.scatter(Ns[nfull],re_wt[nfull],facecolor='w',edgecolor='k',label='Pred WT full, <re>=%3d'%re_wt[nfull])\n",
        "plt.scatter(Ns[nfull],re_p[nfull],facecolor='w',edgecolor='r',label='Pred pfull, <re>=%3d'%re_p[nfull])\n",
        "plt.yscale('log')\n",
        "plt.xscale('log')\n",
        "plt.ylabel(\"<re> [nm?]\")\n",
        "plt.xlabel(\"N\")\n",
        "plt.legend(loc=0)\n",
        "plt.gcf().savefig(\"re_sim.png\",dpi=300)"
      ],
      "metadata": {
        "id": "eRmixDHG1Pc7",
        "outputId": "d5d8f154-370f-492d-95b8-0c50888cea33",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        }
      },
      "execution_count": 69,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "6.707816081694713 [21.36345634 23.54416603] [130 170]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "assuming gaussian chain for p(r)\n",
        "looks qualitatively similar to Fig 1f\n",
        "\n",
        "$P(r) = 4 \\pi r^2\n",
        "\\left( \\frac{3}{2 \\pi \\langle r_e^2 \\rangle} \\right)^{3/2}\n",
        "\\exp\\left( -\\frac{3r^2}{2 \\langle r_e^2 \\rangle}\\right)\n",
        "$\n"
      ],
      "metadata": {
        "id": "w6IW0dZ4_sT9"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1bcLczVAfGEc",
        "outputId": "3f1de8a1-9d2b-412a-d52b-05b42cadb437"
      },
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "6.0034692133618845"
            ]
          },
          "metadata": {},
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "def pr(r,re_sqd):\n",
        "    t1 = 4*np.pi * r**2\n",
        "    t2 = (3/(2*np.pi*re_sqd))**(1.5)\n",
        "    expt = (3*r*r)/(2*re_sqd)\n",
        "    t3 = np.exp(-expt)\n",
        "    return t1*t2*t3\n",
        "\n",
        "\n",
        "\n",
        "rs = np.arange(0,300)\n",
        "\n",
        "Ns = 51\n",
        "sqrt_re2 = a0a * (Ns**nua)\n",
        "print(sqrt_re2)\n",
        "re2 = sqrt_re2**2\n",
        "plt.plot(rs,pr(rs,re2),label=Ns)\n",
        "#plt.scatter(sqrt_re2,pr(sqrt_re2,re2),label=Ns)\n",
        "\n",
        "Ns = 151\n",
        "sqrt_re2 = a0a * (Ns**nua)\n",
        "print(sqrt_re2)\n",
        "re2 = sqrt_re2**2\n",
        "plt.plot(rs,pr(rs,re2),label=Ns)\n",
        "\n",
        "\n",
        "Ns = 351\n",
        "sqrt_re2 = a0a * (Ns**nua)\n",
        "print(sqrt_re2)\n",
        "re2 = sqrt_re2**2\n",
        "plt.plot(rs,pr(rs,re2),label=Ns)\n",
        "plt.ylabel('P(r)')\n",
        "plt.xlabel('Re,end-to-end distance [A]')\n",
        "plt.scatter(sqrt_re2,pr(sqrt_re2,re2),label=f\"re,N={Ns}\")\n",
        "plt.legend(loc=0)\n",
        "plt.title(\"validation\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 543
        },
        "id": "gzvo_ZNI_tNE",
        "outputId": "b2d09d95-2279-4675-a589-5ce1a75023ab"
      },
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "42.873345710184346\n",
            "73.77186477217029\n",
            "112.47495966267412\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'validation')"
            ]
          },
          "metadata": {},
          "execution_count": 49
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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Op+ex6UgG/csKSAohhC5K8uGVaMdf9+mT4OFrs9MNGjSIm2++mSZNmnDo0CGefvppBg8ezLp16zAajTa7Tm0kCZKotn+OWxKkIJucLz42mMPpeWxIOiMJkhBC2MDIkSOt2+3ataN9+/Y0bdqUlStX0q9fPx0jc36SIIlq21lW+bpd/Zq3IIE2DunbjcfYVFY6QAghdOPuo7Xm6HFdO4qNjSU0NJTExERJkK5AEiRRLVn5JRw5o/XP26KLDaBzQ22g956T2RSVmvB0k+ZfIYROFMWmXV3O4vjx45w5c4aoqCi9Q3F6kiCJatl1UuteaxjsQ5CPh03OGRPsTYivB2fyitlzMptODWs2M04IIWq73NxcEhMTrV8nJSWxfft2goODCQ4OZtq0aQwfPpzIyEgOHTrEE088QbNmzRg4cKD1PcnJyWRkZJCcnIzJZGL79u0ANGvWDD8/P0d/JKchdZBEtewoG3/UzkatRwCKotCpYRAA25IzbXZeIYSorTZv3kynTp3o1KkTAJMnT6ZTp04899xzGI1GduzYwb/+9S9atGjBuHHj6NKlC6tXr8bT09N6jueee45OnToxdepUcnNzrefbvHmzXh/LKUgLkqgWS/2jNtEBNj1vp4b1+HNvGtuOZdr0vEIIURv17dsXVVUvuf/333+/4jlmz54tNZAqIC1Iolr2ncoBoHWkjROkmCAAth6VgdpCCCH0IwmSqLKiUhOHTucC0DLS36bnbh8ThKLAicwC0rILbXpuIYQQorIkQRJVdigtj1KzSoCXG1GBNaugfSE/TzdahGtJl2WckxBCCOFokiCJKtufqo0/ahUVgGLjkvgAbcvqKu04IQmSEEIIfUiCJKrMMv6olY271ywsdZV2SYIkhBBCJ5IgiSrbm2JJkGw7QNvC0oK0UxIkIYQQOpEESVTZvlNaF5utB2hbxEUFYFDgdE4RqTJQWwghhA4kQRJVkpVfQlpOEQAtIuxTYdXbw0iLCBmoLYQQQj+SIIkqSSyb3h8V6IW/l7vdriPdbEIIIfQkCZKokkNpWoLUNMy+6/O0qy8DtYUQQuhHEiRRJZYWpGbh9k2QLEuYWMY7CSGEuNhHH31E+/btCQgIICAggISEBBYvXmzd37dvXxRFKfe49957y53joYceokuXLnh6etKxY0cHfwLnJWuxiSqxtiDZOUFqUTYA/GRWIVn5JQT62K87TwghXFWDBg149dVXad68Oaqq8uWXX3LjjTeybds22rRpA8D48eN54YUXrO/x8fG56Dx33303GzZsYMeOHQ6L3dlJgiSqxNKC1DTM167XCfByp0E9b46fLWBfSjbxsSF2vZ4QQriiG264odzXL7/8Mh999BHr16+3Jkg+Pj5ERkZe8hzvvfceAKdPn5YE6TySIIlKKywxcSwjH7B/FxtodZa0BClHEiQhhEOpqkpBaYHDr+vt5l3tFQpMJhPz588nLy+PhIQE6+vffPMNX3/9NZGRkdxwww08++yzFbYiifIkQRKVduRMHmYV/L3cCPPztPv1Wkf58+feVPalyDgkIYRjFZQWED8n3uHX3XDbBnzcq5a87Ny5k4SEBAoLC/Hz8+PHH38kLi4OgNtuu41GjRoRHR3Njh07ePLJJ9m/fz8LFiywR/i1iiRIotIOpeUBWuuRPdZgu5ClUvfesqVNhBBCXKxly5Zs376drKwsvv/+e8aMGcOqVauIi4tjwoQJ1uPatWtHVFQU/fr149ChQzRt2lTHqJ2fJEii0g6ddswUf4tWUdpA7f0pOZjNKgaD/ZMyIYQAratrw20bdLluVXl4eNCsWTMAunTpwqZNm3j33Xf5+OOPLzo2Pl5rFUtMTJQE6QokQRKVlpSutSDF2nmAtkXjEF+83A0UlJg4mpFPk1DHXFcIIRRFqXJXl7Mwm80UFRVVuG/79u0AREVFOTAi1yQJkqg0S4LUOMQxiYrRoNAywp9/jmex71S2JEhCCHGBKVOmMHjwYBo2bEhOTg5z5sxh5cqV/P777xw6dIg5c+YwZMgQQkJC2LFjB4888gi9e/emffv21nMkJiaSm5tLSkoKBQUF1iQqLi4ODw8PnT6Z/pyiUOSMGTNo3LgxXl5exMfHs3HjxsseP3/+fFq1aoWXlxft2rVj0aJF1n0lJSU8+eSTtGvXDl9fX6Kjoxk9ejQnT54sd46MjAxuv/12AgICCAoKYty4ceTm5trl89UWR844NkGC88Yhpcg4JCGEuFBaWhqjR4+mZcuW9OvXj02bNvH7779z3XXX4eHhwZ9//smAAQNo1aoVjz76KMOHD+eXX34pd4577rmHTp068fHHH3PgwAE6depEp06dLvq7Wdfo3oI0b948Jk+ezMyZM4mPj+edd95h4MCB7N+/n/Dw8IuOX7t2LaNGjWL69Olcf/31zJkzh2HDhrF161batm1Lfn4+W7du5dlnn6VDhw6cPXuWSZMm8a9//YvNmzdbz3P77bdz6tQpli5dSklJCWPHjmXChAnMmTPHkR/fZWTmF5OZXwJA41DHNTtbxiFJRW0hhLjYZ599dsl9MTExrFq16ornWLlypQ0jqj0UVVVVPQOIj4+nW7dufPDBB4DWdxoTE8ODDz7IU089ddHxI0aMIC8vj19//dX6Wo8ePejYsSMzZ86s8BqbNm2ie/fuHD16lIYNG7J3717i4uLYtGkTXbt2BWDJkiUMGTKE48ePEx0dfcW4s7OzCQwMJCsri4CAgOp8dJey/Vgmw2asISLAkw1P93fYddcdOsOoT9bTMNiHv564xmHXFULUHYWFhSQlJdGkSRO8vLz0DkfYwOW+p5X9+61rF1txcTFbtmyhf/9zf3ANBgP9+/dn3bp1Fb5n3bp15Y4HGDhw4CWPB8jKykJRFIKCgqznCAoKsiZHAP3798dgMLBhg+NnLbiCIw4ef2TRqmzJkeSMfHKLSh16bSGEEHWXrglSeno6JpOJiIiIcq9HRESQkpJS4XtSUlKqdHxhYSFPPvkko0aNsmaKKSkpF3Xfubm5ERwcfMnzFBUVkZ2dXe5Rl1gGaDt6oHQ9Xw8iA7Tsf7+MQxJCCOEgTjFI215KSkq49dZbUVWVjz76qEbnmj59OoGBgdZHTEyMjaJ0DZYB2o0c3IIE541DkoraQgghHETXBCk0NBSj0Uhqamq511NTUy+5sF5kZGSljrckR0ePHmXp0qXl+hkjIyNJS0srd3xpaSkZGRmXvO6UKVPIysqyPo4dO1bpz1kbHLG2IDm+Lsi5itqSIAkhhHAMXRMkDw8PunTpwrJly6yvmc1mli1bVm6hvfMlJCSUOx5g6dKl5Y63JEcHDx7kzz//JCQk5KJzZGZmsmXLFutry5cvx2w2W6uMXsjT05OAgIByj7rkyBltkdrGOtQian1eRW0hhBDCEXSf5j958mTGjBlD165d6d69O++88w55eXmMHTsWgNGjR1O/fn2mT58OwKRJk+jTpw9vvfUWQ4cOZe7cuWzevJlZs2YBWnL073//m61bt/Lrr79iMpms44qCg4Px8PCgdevWDBo0iPHjxzNz5kxKSkqYOHEiI0eOrNQMtromM7+YrAJtin+jYMcnSM3CtaVNDqbloqqqQ9aBE0IIUbfpniCNGDGC06dP89xzz5GSkkLHjh1ZsmSJdSB2cnIyBsO5hq6ePXsyZ84cnnnmGZ5++mmaN2/OwoULadu2LQAnTpzg559/BqBjx47lrrVixQr69u0LwDfffMPEiRPp168fBoOB4cOH895779n/A7ugYxkFAIT5e+LtYXT49ZuG+aEokJlfwpm8YkL9PB0egxBCiLpF9wQJYOLEiUycOLHCfRUVsLrlllu45ZZbKjy+cePGVKa0U3BwsBSFrKTkDK17rWGwPusSebkbaRjsw9Ez+RxMzZUESQghhN3V6llswjb0TpAAmoVp3WyJp2U5GCGEEPYnCZK4IkuCFKNnghRRliClykBtIYSwpZUrV6IoCm3atMFkMpXbFxQUxOzZs6t13v3793PNNdcQERGBl5cXsbGxPPPMM5SUlFiPmT17NoqilHtcWPl6wYIFDBgwgJCQEBRFsS6ma29O0cUmnNvxs/q3IDUP12ayHUyTFiQhhPMymVU2JmWQllNIuL8X3ZsEYzQ4bmJJcXExHh4e1Xrv4cOH+eqrr6yTpGrK3d2d0aNH07lzZ4KCgvjnn38YP348ZrOZV155xXpcQEAA+/fvt3594UScvLw8evXqxa233sr48eNtEltlSIIkrsjaglTPW7cYLDPZEiVBEkI4qSW7TjHtlz2cyiq0vhYV6MXUG+IY1DbKLtfs27cvbdu2xc3Nja+//pp27drx/vvv8/jjj7N69Wp8fX0ZMGAA//3vfwkNDb3suR588EGmTp3Kbbfdhqdnzcd6xsbGEhsba/26UaNGrFy5ktWrV5c7TlGUS9YgBLjzzjsBOHLkSI1jqgrpYhOXVWoyc+KsNoutYYiOXWxlCVJaThFZ+SVXOFoIIRxrya5T3Pf11nLJEUBKViH3fb2VJbtO2e3aX375JR4eHqxZs4ZXX32Va6+9lk6dOrF582aWLFlCamoqt9566xXP8/DDD1NaWsr7779/yWMGDx6Mn5/fJR9t2rS55HsTExNZsmQJffr0Kfd6bm4ujRo1IiYmhhtvvJHdu3dX/sPbkbQgics6lVVIqVnFw2ggwl+/Va79PN2IDvTiZFYhiadz6NIoWLdYhBDifCazyrRf9lDR/GkVUIBpv+zhurhIu3S3NW/enNdffx2Al156iU6dOpXrwvr888+JiYnhwIEDtGjR4pLn8fHxYerUqTz99NOMHz+ewMDAi4759NNPKSgouOQ53N3dL3qtZ8+ebN26laKiIiZMmMALL7xg3deyZUs+//xz2rdvT1ZWFm+++SY9e/Zk9+7dNGjQoFKf316kBUlc1rGy7rUGwd4YHNiPXpGmloKRqdLNJoRwHhuTMi5qOTqfivafzY1JGXa5fpcuXazb//zzDytWrCjXqtOqVSsADh06dMVzjRs3jpCQEF577bUK99evX59mzZpd8tGoUaOL3jNv3jy2bt3KnDlz+O2333jzzTet+xISEhg9ejQdO3akT58+LFiwgLCwMD7++OOq3gabkxYkcVnHzlrGH+nXvWbRPNyf1QfTZRySEMKppOVcOjmqznFV5et7boWD3NxcbrjhhgoTnKioK4+DcnNz4+WXX+auu+6qsD7h4MGDLxpDdL5GjRpd1EVmWdw9Li4Ok8nEhAkTePTRRzEaLy487O7uTqdOnUhMTLxirPYmCZK4rHNT/PUboG3RPOLckiNCCOEswis5/KCyx9VE586d+eGHH2jcuDFubtX7E3/LLbfwxhtvMG3atIv2VaeL7Xxms5mSkhLMZnOFCZLJZGLnzp0MGTKk6oHbmCRI4rIsA7QbOEELksxkE0I4o+5NgokK9CIlq7DCcUgKEBmoTfm3twceeIBPPvmEUaNG8cQTTxAcHExiYiJz587l008/rTApqcirr77KwIEDL3q9fv36lY7lm2++wd3dnXbt2uHp6cnmzZuZMmUKI0aMsCZSL7zwAj169KBZs2ZkZmbyxhtvcPToUe655x7reTIyMkhOTubkyZMA1pIAkZGRl539VlMyBklc1slMrUm4fpD+LUiWatonMgvIKyrVORohhNAYDQpTb4gDtGTofJavp94Q55B6SNHR0axZswaTycSAAQNo164dDz/8MEFBQdZ1TS3FGS/n2muv5dprr6W0tPr/1rq5ufHaa6/RvXt32rdvz7Rp05g4cSKffvqp9ZizZ88yfvx4WrduzZAhQ8jOzmbt2rXExcVZj/n555/p1KkTQ4cOBWDkyJF06tSJmTNnVju2ylDUyixcJi6SnZ1NYGAgWVlZBAQE6B2O3Vz16nJOZBbww3096dKont7h0PWlP0nPLeLniVfRvkGQ3uEIIWqBwsJCkpKSaNKkyUVVnKtCjzpI1TF16lRWrVpV4VqntcXlvqeV/fstXWzikkpNZlKytV/0BjoWiTxfs3Bf0nOLOJiaKwmSEMKpDGobxXVxkbpW0q6MxYsX88EHH+gdhtOTBElcUmpOESazirtRIcyv5lVVbaF5uD/rD2fIQG0hhFMyGhQSmoboHcZlbdy4Ue8QXIKMQRKXZBmgHRWofw0kC8tMtsQ0WbRWCCGE/UiCJC7pZKaWIDnDAG2LpmUDtQ+fztM5EiGEELWZJEjikk6UJUjRTpQgxYZpBdGSM/IpMZl1jkYIUZvInKXawxbfS0mQxCVZEqT6TjJAGyDC3wtvdyOlZtVaxFIIIWrCUpMnP1/+TaktLN/LKxWuvBwZpC0uyTIGqX6QfovUXshgUGgS6sueU9kknc6zdrkJIUR1GY1GgoKCSEtLA7RFW69UJ0g4J1VVyc/PJy0tjaCgoEoXxqyIJEjiks6NQdK/ivb5YsO0BOlwei4QoXc4QohawFKR2ZIkCdcWFBRU4yrbkiCJCqmqet4YJOdpQQKIlYHaQggbUxSFqKgowsPDKSkp0TscUQPu7u41ajmykARJVCgzv4T8YhPgXIO0AWJDtYHakiAJIWzNaDTa5I+rcH0ySFtUyNJ6FOrniZe7c/1jYZnJdjhdEiQhhBD2IQmSqJB1BpuTda8BNClrQUrPLSK7UJrChRBC2J4kSKJCJ51wir+Fv5c74f7a0ifSzSaEEMIeJEESFbJM8Y8OdL4ECc61Ih0+LWuyCSGEsD1JkESFTmY5bwsSyEw2IYQQ9iUJkqiQtQXJyWawWTQtG6idJAO1hRBC2IEkSKJCJ5xwodrzWWayHZIuNiGEEHYgCZK4SGGJifTcYsB5E6QmoVoX25EzeZjNssCkEEII25IESVzEMoPNx8NIkE/1F/qzp5h63rgbFQpLzNbxUkIIIYStSIIkLnIysxDQWo+cdcFGN6OBhsHaGnEyDkkIIYStSYIkLnIiMx9w3gHaFjKTTQghhL1IgiQucsLSguSkU/wtYqUWkhBCCDuRBElc5FTZGKSoAOdbZuR8siabEEIIe5EESVwkJVtrQYqSLjYhhBB1lCRI4iIpWVqCFOnsLUhlXWwnMgsoLDHpHI0QQojaRBIkcRFrghTo3AlSsK8Hgd5aGQKZySaEEMKWJEES5eQWlZJTVAo4f4KkKMp5i9ZKgiSEEMJ2JEES5Vhaj/w93fDzdNM5miuzDtSWmWxCCCFsSBIkUY6rdK9ZNC0bqC1dbEIIIWxJEiRRjmUGm6skSJaB2ockQRJCCGFDkiCJclLK1jVz9hlsFk3O62JTVVm0VgghhG1IgiTKsdZAcpEWpMYhvigK5BSWkp5brHc4QgghaglJkEQ5ljFIES6SIHm5G6lfVtBSBmoLIYSwFUmQRDmnslyrBQmwTvU/ckbGIQkhhLANSZBEOamWQdoBzr3MyPmsi9bKQG0hhBA2IgmSsCoqNVnH8bjKLDY414KUJMUihRBC2IgkSMIqLbsIAA83A/V83HWOpvKaSC0kIYQQNiYJkrA6fwaboig6R1N5li62oxn5mMwy1V8IIUTNSYIkrCwDtCNcpAaSRXSQNx5GA8WlZk5mFugdjhBCiFpAEiRhZSkS6Uoz2ACMBoWGIT6AdLMJIYSwDUmQhFVKljYGyZUGaFtYB2pLgiSEEMIGJEESVinZrrXMyPliJUESQghhQ5IgCasUFywSadFEaiEJIYSwIUmQhJUlQYoMdJ0ikRbWatqSIAkhhLABSZAEACazSmpO2RgkF+xisyRIx8/mU1Rq0jkaIYQQrk4SJAHAmdwiTGYVo0EhzN9T73CqLMzfE18PI2YVjmXk6x2OEEIIFycJkgDO1UAK9/fEaHCdIpEWiqLQJKxsHJIsOSKEEKKGJEESgOsWiTxfk1BZckQIIYRt6J4gzZgxg8aNG+Pl5UV8fDwbN2687PHz58+nVatWeHl50a5dOxYtWlRu/4IFCxgwYAAhISEoisL27dsvOkffvn1RFKXc495777Xlx3I5qdmuO4PNwjpQ+4wkSEIIIWpG1wRp3rx5TJ48malTp7J161Y6dOjAwIEDSUtLq/D4tWvXMmrUKMaNG8e2bdsYNmwYw4YNY9euXdZj8vLy6NWrF6+99tplrz1+/HhOnTplfbz++us2/Wyupja0IFlqIUkXmxBCiJrSNUF6++23GT9+PGPHjiUuLo6ZM2fi4+PD559/XuHx7777LoMGDeLxxx+ndevWvPjii3Tu3JkPPvjAesydd97Jc889R//+/S97bR8fHyIjI62PgIAAm342V5OWbZni77oJUmMpFimEEMJGdEuQiouL2bJlS7lExmAw0L9/f9atW1fhe9atW3dR4jNw4MBLHn8533zzDaGhobRt25YpU6aQn3/5mU9FRUVkZ2eXe9QmqTmWFiTXm8Fm0SRES5DScorILSrVORohhBCuzE2vC6enp2MymYiIiCj3ekREBPv27avwPSkpKRUen5KSUqVr33bbbTRq1Ijo6Gh27NjBk08+yf79+1mwYMEl3zN9+nSmTZtWpeu4krRsrQZSuL/rtiAF+rgT4uvBmbxijqTn0bZ+oN4hCSGEcFG6JUh6mjBhgnW7Xbt2REVF0a9fPw4dOkTTpk0rfM+UKVOYPHmy9evs7GxiYmLsHqujWAZpu3ILEmgDtc/kFXNYEiQhhBA1oFsXW2hoKEajkdTU1HKvp6amEhkZWeF7IiMjq3R8ZcXHxwOQmJh4yWM8PT0JCAgo96gtCktMZBdqXVJhLtyCBLLkiBBCCNvQLUHy8PCgS5cuLFu2zPqa2Wxm2bJlJCQkVPiehISEcscDLF269JLHV5alFEBUVFSNzuOqLN1rXu4GArxcu1HRUixSBmoLIYSoCV3/Gk6ePJkxY8bQtWtXunfvzjvvvENeXh5jx44FYPTo0dSvX5/p06cDMGnSJPr06cNbb73F0KFDmTt3Lps3b2bWrFnWc2ZkZJCcnMzJkycB2L9/P4B1ttqhQ4eYM2cOQ4YMISQkhB07dvDII4/Qu3dv2rdv7+A74BzODdD2QlFcr4r2+SwDtQ9LgiSEEKIGdE2QRowYwenTp3nuuedISUmhY8eOLFmyxDoQOzk5GYPhXCNXz549mTNnDs888wxPP/00zZs3Z+HChbRt29Z6zM8//2xNsABGjhwJwNSpU3n++efx8PDgzz//tCZjMTExDB8+nGeeecZBn9r5nBug7drjj+C8FqTTuaiq6vIJnxBCCH0oqqqqegfhirKzswkMDCQrK8vlxyN9/ncSL/y6h6Hto5hxW2e9w6mRwhITrZ5dAsCWZ/oT4uf6SZ8QQgjbqezfb92XGhH6s3axufgAbQAvdyP1g7wBWXJECCFE9UmCJDht6WJz8Sn+Fk1kyREhhBA1JAmSqBVVtM/XRJYcEUIIUUOSIAlSa0EV7fPJmmxCCCFqShIkYV2otra0IMVKgiSEEKKGJEGq486voh0eUDtakM7vYjObZZKmEEKIqpMEqY47v4q2v6drV9G2aFDPGzeDQlGpmZSy1jEhhBCiKiRBquNqUxVtCzejgYYhPoB0swkhhKgeSZDquNTs2lMD6XyWcUiy5IgQQojqqB19KqLaLF1sYbVkgLZF4xDLkiMVJEj5GZC6C3JSQFXBKwDCWkK9JlBLWtGEEELUjCRIdVxtqqJ9PuuabOm52gtFOfDPXNj+DZzcDlQweNs/GlpfD13HQXgrh8UqhBDC+UiCVMel1bIq2haWmWzJ6Tmw8RNY+Srkp587oF4TCGwABjfIS4f0A5BzEjbO0h6t/wUDXoR6jfX5AEIIIXQlCVIdl1bLqmhbxIb6UZ/TTM/5CBbt014MbgrdJ0Cbm8A/ovwbSovg8ErY+hXs+w32/gwHfof+UyH+PjDIcD0hhKhLJEGq4yxVtGtbF1tE5lZ+8XyGYCUHs7svhuumQZe7wOhe8RvcPKHFQO2RugeWPAlJf8HvT8OhFfDvz8Ar0KGfQQghhH7kv8V1nKWKdq3qYtu/GOWrGwlWcthhbsK6AT9B9/GXTo4uFBEHo3+GoW+BmxckLoVPr4OzR+0btxBCCKchCVIdVlBc+6pos38xzLsTTMVs9+3FiOJn2VsYUvXzKAp0uwfu/l0bvJ2+H74YAumJto9ZCCGE05EEqQ6zjD+qNVW0j22E+XeBuQTa3MSydq9TgFfNaiFFd4TxyyC0BWQfh9lDISPJVhELIYRwUpIg1WFpOWXjj2pDFe2zR+DbkVBaCM0Hws2f0jhMGzN0pKbFIgOi4a5FENYaclPgf8MgJ7XGIQshhHBekiDVYbWminZJIXw3GvLPQFQH+PfnYHQ7rxaSDapp+4XB6IXatP+zR2DeHdrMNyGEELWSJEh1WGptqaK95Ck49Q94B8PIOeDpB5xbbuRUViH5xaU1v45/JNyxQJvNdnwj/PaoVolbCCFErSMJUh2WVhuqaO9fDFu+ABRtKn5gA+uuIB8Pgny0mWtH0vNtc72QploLlWKAbf+DTZ/a5rxCCCGciiRIdZilirbLFonMS4efH9S2Ex6AptdedIilorZNutksmvWH617Qthc/CUfX2u7cQgghnIIkSHVYqqvXQPpzKuSd1gZPX/tshYdYEqQjZ2yYIAEkTIR2t4JqggX/gcIs255fCCGEriRBqsOss9hcsYsteQNs+1rb/td74F7xZ7CMQzp82sYJkqLA9W9DUCPISobFT9n2/EIIIXQlCVId5rItSKZSWPSott3pDojpfslDm4RqA7aT0nNtH4enP9w8SxuP9M8c2POT7a8hhBBCF5Ig1VEFxSZyXLWK9ubPIWWnNpus/7TLHmqXMUjna9gDrnpY2/7lYchJsc91hBBCOJQkSHWUZQabt7vRtapo556G5S9p2/2eA9/Qyx7eONQHgLP5JZzNK7ZPTH2nQGR7KMiAxU/Y5xpCCCEcShKkOspSAyk8wNO1qmivfhOKsrSCkF3GXvFwHw83IstayJJsPVDbws0Dhn0IilHrZjvwh32uI4QQwmEkQaqjXLIGUtZxrXsNtGn2BmOl3madyWavbjaAyHbQ4z5te9GjUGyjuktCCCF0IQlSHXV+C5LL+OsNMBVD46uhSZ9Kv82mS45cTt8pENAAMpO1WIUQQrisag0+yczM5Mcff2T16tUcPXqU/Px8wsLC6NSpEwMHDqRnz562jlPYWJplBpurtCBlJJ2b1n/N/2nT7CvJOtXf3gmSpx8MeR3m3gZr34P2t0J4a/teUwghhF1UqQXp5MmT3HPPPURFRfHSSy9RUFBAx44d6devHw0aNGDFihVcd911xMXFMW/ePHvFLGzAWgPJVVqQVr0O5lKtinWjhCq91TqTzda1kCrSaii0HKrFumSKrNUmhBAuqkotSJ06dWLMmDFs2bKFuLi4Co8pKChg4cKFvPPOOxw7dozHHnvMJoEK23KpGkjpB2HHXG37mv+r8tsbn1dNW1VV+w9KH/gSJC6Fwysg8U9ofp19ryeEEMLmqpQg7dmzh5CQkMse4+3tzahRoxg1ahRnzpypUXDCfiwJkksM0l7zLqhmaDkE6neu8ttj6vlgNCjkF5tIyykiwt51n4JjIf4/sPZ9+P3/IPYaMLpQKQUhhBBV62KzJEclJSXcfffdJCUlVep44XwsXWxOXyQyJxV2lHXXWgoyVpGHm4GYet4AHDpth4raFbn6MfAOhvT9sHW2Y64phBDCZqo1i83d3Z0ffvjB1rEIBylfRdvJu9g2ztJmrjXoDg3jq32a2DBtyRGbr8l2Kd5BcM3T2vaKV6Ag0zHXFUIIYRPVnuY/bNgwFi5caMNQhKO4TBXt4jzY9Km23fPBGp2qadlUf4e1IIFWyDK0JeSfgTXvOO66Qgghaqzafx2bN2/OCy+8wJo1a+jSpQu+vr7l9j/00EM1Dk7Yh8tU0d72DRRmQr0m2uywGmha1oJ0yFEtSKCNO+r/PMwdBRs+hvj7wD/CcdcXQghRbdVOkD777DOCgoLYsmULW7ZsKbdPURRJkJyYSwzQNptg3QfadsIDla6afSnNwssSpDQHtiABtBwM9bvCic2w+i2tTpIQQginV+0E6UoDtIXzOjdA24nHH+37DTKPagOdO95e49NZWpBOZBaQX1yKj4eDuhYVRVtU96t/acuk9JwIQQ0dc20hhBDVJkuN1EEuUUV782fac5e7wMOnxqer5+tBsK8H4MCB2haxfbSlUcwlsPI1x15bCCFEtVQpQXr11VcpKCio1LEbNmzgt99+q1ZQwr6sXWzO2oJ05hAcXgkoWoJkI82s45Ac3M0GWisSwD9z4PQBx19fCCFElVQpQdqzZw8NGzbk/vvvZ/HixZw+fdq6r7S0lB07dvDhhx/Ss2dPRowYgb+/v80DFjV3bpkRJ21B2vy59tz8OqjXyGanbRpeNpPN0eOQABp01QpdqmZZyFYIIVxAlRKkr776ij///JOSkhJuu+02IiMj8fDwwN/fH09PTzp16sTnn3/O6NGj2bdvH71797ZX3KIGrMuM+DthC1JJIWz/RtvuerdNT20Zh5SoRwsSQN+ntOdd32utZEIIIZxWlUeqdujQgU8++YSPP/6YHTt2cPToUQoKCggNDaVjx46EhobaI05hQ05dRXvPT1BwFgIaQPMBNj11U+tMNgePQbKI6gDNB8LB3+Hvt+HGGfrEIYQQ4oqqnCCZzWbeeOMNfv75Z4qLi+nXrx9Tp07F29vbHvEJG8svLnXuKtqW7rUud9V4av+FLGOQktLzMJlVjAYdakD1flxLkP6ZC72fsGkXohBCCNup8iy2l19+maeffho/Pz/q16/Pu+++ywMPPGCP2IQdpJUViXTKKtqpu+HYelCM0PlOm58+OsgbTzcDxSYzxzLybX7+SonpBrF9wVwq1bWFEMKJVTlB+uqrr/jwww/5/fffWbhwIb/88gvffPMNZrPZHvEJGzs3QNsJq2hv+1p7bjUE/CNtfnqjQbGuyabLTDaL3k9oz9u+huyT+sUhhBDikqqcICUnJzNkyBDr1/3790dRFE6elH/oXUGqs9ZAMpXAju+07Y532O0yuqzJdqHGV0HDntoivGve0y8OIYQQl1TlBKm0tBQvr/J/XN3d3SkpKbFZUMJ+rAmSs40/OrgU8tPBNxya9bPbZawz2fSY6n++Po9rz1tmQ26arqEIIYS4WJUHoaiqyl133YWn57k/sIWFhdx7773lFqxdsGCBbSIUNnXaMoPN2VqQ/pmjPbe/FYzudruMdU02R1fTvlDsNVC/C5zYoq05d90L+sYjhBCinConSGPGjLnotTvusF+XiLAtp2xBys+A/Uu07Q6j7Hqp81uQVFXVbxyWomhjkb4dAZs+g16PgHc9fWIRQghxkSonSF988YU94hAOklo2iy3SmWog7fxeW6cssj1EtrXrpWLDfFEUyCoo4UxeMaF+OiaKLQZCRFtI3aWVN7j6Uf1iEUIIUY4sVlvHpOU4YQuSpXut4212v5SXu5EG9bSaXbosOXI+RYGeD2rbGz6G0iJ94xFCCGElCVIdY6mD5DRjkNL2wcltYHCDdrc45JK6LzlyvrbDIaA+5KbCjnl6RyOEEKKMJEh1SH5xKTlFWhXtCGdpQbIkBc0HgK9jlqmxJEi6LTlyPqM79Lhf217zHkg9MSGEcAqSINUhltYjHw8jfs5QRVtVYdcP2raDWo/g/JlsTtCCBNBlDHgGwpmDcGCJ3tEIIYRAEqQ65VyRSCepon1iC2QeBXdfaDHIYZd1mlpIFp7+0HWstr1WCkcKIYQzkASpDkm11EBylhlsO7/XnlsNAQ8fh13WUk37RGYBBcUmh133suLvBYM7JK+DY5v0jkYIIeo8SZDqkLSyFqQIZ0iQzCbYXVZMtO2/HXrpED9P6vloxSidppstIAo6jNC2176rbyxCCCH0T5BmzJhB48aN8fLyIj4+no0bN172+Pnz59OqVSu8vLxo164dixYtKrd/wYIFDBgwgJCQEBRFYfv27Redo7CwkAceeICQkBD8/PwYPnw4qamptvxYTinNWkXbCQZoH12jzdzyCoKm1zr88k2dYdHaC/V8SHve+yukJ+obixBC1HG6Jkjz5s1j8uTJTJ06la1bt9KhQwcGDhxIWlrFa1OtXbuWUaNGMW7cOLZt28awYcMYNmwYu3btsh6Tl5dHr169eO211y553UceeYRffvmF+fPns2rVKk6ePMnNN99s88/nbFKtLUhOkCBZutfi/gVuHg6//LkEyQlmslmEtSwbi6XC+hl6RyOEEHWargnS22+/zfjx4xk7dixxcXHMnDkTHx8fPv/88wqPf/fddxk0aBCPP/44rVu35sUXX6Rz58588MEH1mPuvPNOnnvuOfr371/hObKysvjss894++23ufbaa+nSpQtffPEFa9euZf369Xb5nM7CMotN9y620mLY85O23Xa4LiFYZ7I5y0Bti4SJ2vM/c7UlWIQQQuhCtwSpuLiYLVu2lEtkDAYD/fv3Z926dRW+Z926dRclPgMHDrzk8RXZsmULJSUl5c7TqlUrGjZseNnzFBUVkZ2dXe7halLLqmiH6d3FdngFFGaCbzg0vlqXEJqGawO1nWYmm0XjXhDZDkryYeuXekcjhBB1lm4JUnp6OiaTiYiIiHKvR0REkJKSUuF7UlJSqnT8pc7h4eFBUFBQlc4zffp0AgMDrY+YmJhKX9NZOE0L0u6F2nObYWAw6hJC83B/AJLS8ygxOVFxRkU5Vzhy4ydgKtE3HiGEqKN0H6TtKqZMmUJWVpb1cezYMb1DqpK8olJyrVW0dUyQSoth/2/adtyNuoVRP8gbHw8jxSYzR8840Tgk0LodfcMg+wTs/VnvaIQQok7SLUEKDQ3FaDReNHssNTWVyMjICt8TGRlZpeMvdY7i4mIyMzOrdB5PT08CAgLKPVyJZQab7lW0j/wFhVlaAtAwQbcwDAaF5mXjkA6kOlk3m5sndLtH2173ob6xCCFEHaVbguTh4UGXLl1YtmyZ9TWz2cyyZctISKj4D2dCQkK54wGWLl16yeMr0qVLF9zd3cudZ//+/SQnJ1fpPK4m1VlqIO0paxFpfYNu3WsWLSK0brb9KTm6xlGhruPA6AEnNkvhSCGE0IGuC3JNnjyZMWPG0LVrV7p3784777xDXl4eY8dqyy6MHj2a+vXrM336dAAmTZpEnz59eOuttxg6dChz585l8+bNzJo1y3rOjIwMkpOTOXnyJKAlP6C1HEVGRhIYGMi4ceOYPHkywcHBBAQE8OCDD5KQkECPHj0cfAccxylqIJlKYd+v2nbrf+kXRxlLgnQwzQkTJL8waHcrbP8a1n8IMV/oHZEQQtQpuiZII0aM4PTp0zz33HOkpKTQsWNHlixZYh2InZycjMFwrpGrZ8+ezJkzh2eeeYann36a5s2bs3DhQtq2bWs95ueff7YmWAAjR44EYOrUqTz//PMA/Pe//8VgMDB8+HCKiooYOHAgH35Yu7syLFW0dV1mJHkt5J8B72BttpbOWkRqCZLTdbFZ9LhXS5D2/ASZxyDI9SYGCCGEq1JUVVX1DsIVZWdnExgYSFZWlkuMR3r5tz18sjqJe3o14Znr4/QJ4rdHYdOn0OkOuFH/QoinsgpImL4co0FhzwsD8XTTt8uvQrOvhyOr4apJcN0LekcjhBAur7J/v2UWWx1h6WLTbQyS2Qx7f9G244bpE8MFIgO88Pd0w2RWSUp3splsFgkPaM9bZkOxk8YohBC1kCRIdUSqtYtNpzFIxzZoa695BkKTPvrEcAFFUazdbE45UBug+UCo10Sb+bd9jt7RCCFEnSEJUh1hKRIZ7q9TC5JlcHbLQbqsvXYpLSK0qf4HnXUcksEAPe7TtjfM1FrihBBC2J0kSHXEuS42HVqQVBX2lRWHbDXU8de/DMtMtgOpTtqCBNDxNvAMgDOJkPin3tEIIUSdIAlSHZB7XhVtXWaxnd4HZ5PA6AlN+zn++pfhEgmSpz90Hq1tr9d/cLsQQtQFuk7zF45hmeLvq1cVbUv3Wmxf8PRz/PUvw5IgHc3Ip7DEhJe7E85kA+g+AdZ/SFHSSjKP/k1OQCQqKgoKBoOBIM8gAj0CMepcfFMIIWoLSZDqgFS9F6ndt0h7bjVEn+tfRqifB/V83DmbX0JiWi5t6wfqHRIA+SX57EjfwT9p/3A46zBJWUkkN25IHmZYeV+F7zEoWqLUKKARsYGxNA1qSrvQdrQJaYO70d3Bn0AIIVybJEh1QFqO1oIUpkcV7exTcHIroECLwY6//hUoikKLCH82JGVwIDVH1wQpKSuJP4/+ycrjK9mTvodStbTC4wyqir9nIEaDG6qqUmouJackB7NqJqMwg4zCDLalbbMe72X0ol1YO66KvoprG15Lk8AmjvpIQgjhsiRBqgPS9GxB2l/WetSgK/hHOP76lWBJkPbrMA4pszCTnw79xMLEhSRmJpbbF+ETQeeIzrSo14LYwFga+zciZP5Y/E/+g+HaMdD7ceuxJeYSsoqySMtP40jWEQ5lHeLA2QNsT9tOZlEmm1I2sSllE+9sfYfGAY0Z0mQINza7kWi/aEd/ZCGEcAmSINUB5xaq1aEFyZIgtXS+7jULSy0kR071P3D2AF/u/pIlSUsoNhcD4Ka4ER8dT/+G/UmITiDaNxpFUcq/Mf4B+HECbPwUek6ylkxwN7gT6h1KqHcocSHnKqWrqkpSVhIbUjaw8thKNqZs5Ej2ET7850M++ucjukd1Z0TLEVwbc62MXxJCiPNIglQHnFuo1sEtSEU5kPSXtu1k0/vP1yJcGzjuiGKR+zP2M/OfmfyZfG66fqvgVtza8lYGNBpAoOcVuvja3ARLn4XcFNizENrfetnDFUUhNiiW2KBYRrUaRU5xDiuPreSnQz+x4dQG66O+X33uaH0HNze/GR93n5p/UCGEcHGSINUBulXRTvwTTMUQ3BRCWzj22lXQKlJbi+dEZgFZBSUEett+QHNKXgpvb3mbxUmLAVBQuK7RdYxpM4Z2oe0ubim6FDcP6DYeVrwE6z+EdrdAZd8L+Hv4c0PTG7ih6Q2cyD3BDwd+YP6B+ZzIPcFrm15j1o5Z3N32bka0GoG3m3d1PqoQQtQKUgepDtBtHbbzZ69V4Y+4owX6uFM/SEsG9p3Ktum5C0sL+eifj7jhxxtYnLQYBYXBjQez4F8LeKvvW7QPa1/55Mii61itptTJbXBsY7Vjq+9Xn4c6P8Qf//6DZ3s8S0P/hpwtOstbW95i8A+D+Xbft5SaKx4oLoQQtZ0kSHWApQ5SuCNnsZlK4ODv2nZL5+1es2gdpY1D2mvDBGlb2jZu+eUWPtz+IYWmQjqHd2be9fN4vc/rNKvXrPon9g2F9rdo2+s/rHGc3m7e3NryVn4a9hMvXvUi9f3qc6bwDK9seIXhPw9n9fHV5Y43mVXWHTrDT9tPsO7QGUxmtcYxCCGEs5Eutlout6iUvGIT4OAq2kfXaAus+oRCTHfHXbeaWkcF8OfeNPaeqvk4pILSAt7b+h7f7P0GFZUw7zCe6P4EAxsNrHpr0aXE3wfbvoa9P0NmMgQ1rPEp3QxuDGs2jKGxQ1lwYAEzts/gcNZh7l92P30b9OX/evwf25NUpv2yh1NZhdb3RQV6MfWGOAa1japxDEII4SykBamWs4w/8vN0c2wVbUv3WotB4AKzoyzjkPal1KwF6eDZg4z8dSRf7/0aFZVhzYaxcNhCBjUeZLvkCCCyLTTpDaoZNn5iu/OizYgb0WoEv978K2PixuBmcGPl8ZVcv+BfPPTb+5zKyi93fEpWIfd9vZUlu07ZNA4hhNCTJEi1nKUGkkO711QV9muDkZ159tr5LF1s+1NzqtVlpKoqPxz4gVG/jeJw1mFCvUP5sN+HvHjViwR4BNg6XE2P+7XnrV9CcZ7NTx/gEcBj3R5j/vXz6RDWkSJzAZ6Rv+DT+CMMninW4yx3a9ove6S7TQhRa0iCVMtZqmg7dAZb2h7ISgY3L239NRfQKMQXb3cjhSVmktKrlmwUmYp4Zs0zPL/ueYpMRfSM7sn3N3zP1Q2utlO0ZZoPhHpNtK7Mf76122Wa1WvGfS3epvDUMFSTJ0bvY/g0eQ+PkJWAGdCSpFNZhWxMyrBbHEII4UiSINVy54pEOnD80YGywdlNeoOHa9TUMRoUWkZWfaD26fzT3P373fx86GcMioFJnSfxUf+PCPEOsVeo5xgMEH+vtr1+JpjNdrtUem4xJZk9yDs8mZKcOBTFjGf4ErwbforilmU9zpKQCyGEq5MEqZbTZZmRg39oz80HOO6aNtA6SusKq2yCtOfMHkb+NpIdp3fg7+HPR/0/4p5292BQHPhr1el28AyAMwfh0DK7XcZSZFQtDaTw+J0UnByOavbAzfcwvrHv4Oa/s9xxQgjh6iRBquVScxw8Bik/A45t0LZbDHTMNW0krgpT/deeXMvYJWNJy0+jSWATvh36LT2je9o7xIt5+kOnO7Xt9R/Z7TLdmwQTFeiFNsxcoTSrG3mHH8JU0ADFWIB3g2+o13AhHRr62i0GIYRwJEmQarlzVbQd9D/7xGXazKrwOJtMPXekcy1Il5/q/+vhX3ngzwfIL80nPjKeb4Z8Q6OARo4IsWLxE0AxaC1IafvscgmjQWHqDdoab5a5eGpJKPlH7qM4/RpUVaHUdz13LRnN8ZzjdolBCCEcSRKkWu60pYq2o1qQLMUhXax7DbCOQUrJLuRsXnGFx3y952umrJ5CqVrK4MaD+bD/h/h7+DsyzIvVa3xuMeANM+12mUFto/jojs5EBp6fbBsJLr6RCS2mU8+zHnsz9jLi1xEXFZcUQghXI4UiazFVVR3bgmQ2aeuvgct1rwH4e7kTE+zNsYwC9qZk07NpaLn9n+78lHe3vgvAHa3v4PFujzt2vNHl9LgP9v0K/8yFfs+BT7BdLjOobRTXxUWyMSmDtJxCwv296N4kGKNB4dYOXZi8cjI703fywLIHuLfDvdzb4V7nuUdCCFEF8i9XLZZbVEq+pYq2I1qQjm+CgrPgFQQNnL96dkVaR17czaaqKh9t/8iaHN3f4X6e6PaEc/3hb3QVRLaD0gKtLpIdGQ0KCU1DuLFjfRKahmA0aJ1ukb6RzB40mxEtR6Ci8tE/H/HIikfIL8m/whmFEML5ONG/8MLWUstmsPl5uuHriCraB5Zoz836g9E1Gycrmsn24T8f8uE/2ppnkzpP4r6O99m2KrYtKMq5wpEbP9HWwtOBh9GDZ3o8w8u9XsbD4MHyY8sZvXg0p3KlyrYQwrVIglSLpZStl1V+zIgdHSib3u+C3WsWFyZIX+z6gpn/aON6Huv6GPe0u0e32K6o7XDwDYPsE9oabTr6V9N/8dnAzwj2Cmb/2f2M+m0U29O26xqTEEJUhSRItVhK2fijKEckSJnHIG23NpuqWX/7X89O2kRrCdKB1Bzm7J3H21veBrSWozFtxugZ2pW5eULXcdq2Haf8V1bH8I7MHTqXlvVacqbwDHf/fje/Hv5V77CEEKJSJEGqxVKyCgCIdMQAbUtxyAbd7TZA2BEa1PMm0Nsd1Xcbr258GYBxbcc5d8vR+breDUYPbTzY8c16R0OUXxRfDf6Ka2OupcRcwpTVU/h056eoqqzZJoRwbpIg1WKWFiSHdLFZlhdp4XrT+8+nKAoNGxzGK/o7VFRGtBzBpM6T9A6r8vwjoO2/tW0naEUC8HH34b/X/JcxcVoL3Ltb3+WVDa9gMpt0jkwIIS5NEqRazGFjkEoKIOkvbbu5644/AtiSuoVkt1koipn6br14Ov5p5xuQfSU9ytZn27MQsk7oGoqFQTHwWLfHeLLbkygozN0/l0dXPUphqazdJoRwTpIg1WKnLAmSvbvYklZr08sDGkBEG/tey46OZB1h0opJmCmhJCcOY8YI55rKX1lRHbRp/+ZS2PSJ3tGUc0fcHbzR5w08DB4sS17G+D/Gk1mYqXdYQghxERf8119UVqqjutgOnte95mqtLWUyCjO4f9n9ZBVl0SKoDYUnRnIgJZ+iUhftBrJM+d/8ORRdfukURxvYeCAfX/cx/h7+bD+9nTsX38mJXOdo6RJCCAtJkGqpolIT6bnachl2bUFS1XPjj1y0e62wtJCHlj/EsZxj1Perz8fXfUCgly8lJpUDKbl6h1c9LQdDcFMozIJtX+sdzUW6Rnblq0FfEekbyZHsI9y56E4SzybqHZYQQlhJglRLpZUVifQwGgj29bDjhfZC1jFw84Imve13HTsxq2b+7+//45/T/+Dv4c+H/T8k1CeUdvUDAdh5IkvnCKvJYISeE7XtdR+CqVTfeCrQrF4zvh78Nc2CmnG64DR3/X4Xu9J36R2WEEIAkiDVWufPYLPrIGNL91qT3uDhY7/r2Ml7W9/jj6N/4GZw491r3iU2MBaAtq6eIAF0GAU+oZCVrA3YdkIRvhHMHjSb9qHtySrKYtzv49iUsknvsIQQQhKk2irFUQO0LdWzm7ve9P4lSUv4bNdnALzQ8wW6RXaz7mvfQEuQdrlyguTuDfH/0bbXvKt1hzqhQM9APhnwCfGR8eSX5nPv0ntZeWyl3mEJIeo4SZBqKYdM8c/PgGPrtW0XW15kf8Z+nl3zLAB3t72bG5reUG6/pYttX0q26w7UBuh2D7j7QMoOSFqldzSX5OPuw4z+M7gm5hqKzcU8vOJhfjv8m95hCSHqMEmQaimHFIk8tBxUM4S1hqCG9ruOjZ0tPMtDyx+i0FTIVdFX8VCnhy46xlJR26UHaoNW1bzTHdr2mvf0jeUKPI2evN33bW6IvQGTamLK6il8t/87vcMSQtRRkiDVUg7pYrNWz3ad1qNScymPrXqMk3knifGP4bXer2E0GC86TlEU1x+obdHjfm2NvEPLIMW5B0G7Gdx4qddLjGo1ChWVF9e/yP/2/E/vsIQQdZAkSLXUKcs6bPZqQTKbIHGptu1CCdJbm99iY8pGvN28ee+a9wj0DLzksbVioDZAcBNo/S9te+37+sZSCQbFwJTuUxjXVlt49/VNr/P5rs91jkoIUddIglRLpZZN87dbgnR8ExScBa8gbYFaF7Do8CK+3qvVBHql1ys0q9fsssdbWpBceqC2xVVl3Yi7vnea5UcuR1EUJnWexP0dtIKX/93yX2b+M1PnqIQQdYkkSLWQ2axaq2hH2StBsnSvNesPRjf7XMOGDmcd5vl1zwMwvt14+jfqf8X3WGay7T2VTWGJCw/UBqjfBRr10pYf2eAci9heiaIo3NfxPusYsRnbZ/D+tvdRnXQ2nhCidpEEqRZKzyui1KxiUCDMz9M+FzlYNr3fBbrXCkoLeHTloxSUFtA9sjsPdHygUu9rUM+bUD9PSs1q7WpF2jxbq7DtIsa3H89jXR8DYNaOWfx3638lSRJC2J0kSLWQZYB2mL8nbkY7fIuzjkPqLm3gb7Mrt8ToSVVVXlr/EomZiYR6h15yUHZFFEWhc8MgALYmn7VjlA7S7DoIawXFObBltt7RVMmYNmN4qvtTAHyx6wte3/S6JElCCLuSBKkWsvsMNkv3WoNu2jRyJ7YwcSE/H/oZg2Lg9d6vE+odWqX3d2pYD4BtyZl2iM7BDAbo+aC2vW4GlBTqG08V3d76dp7todWu+nrv17y84WXMqlnnqIQQtZUkSLWQ3WsguUj32v6M/by84WUAJnacWK5SdmWd34JUK1os2t0KAQ0gNxW2O98itldya8tbeaHnCygozNs/jxfWvSBJkhDCLiRBqoXs2oJUUgCHyyoyN3feBCm/JJ/HVj1GkamIXvV7Ma7duGqdp12DQIwGhdTsIk5muVaLS4XcPOCqSdr23++CqUTfeKrhpuY38XKvlzEoBn44+APPrnkWk9nFB9ELIZyOJEi10LllRrxtf/Kk1VBaoLVCRLSx/flt5LVNr3Ek+wjhPuG80usVDEr1ftR9PNxoHeUPwLbaMA4JoPOd4BumLWK7c77e0VTLDU1v4LWrX8OoGPn50M88/ffTlJpL9Q5LCFGLSIJUC53KsuMU/wNLtOcWA0FRbH9+G/j9yO8sOLgABYXpvaZTz6tejc7XKUZ7/9ajmTaIzgm4e0NC2Uy+1W9rRT9d0KAmg3izz5u4KW4sSlrEU6ufosTsei1iQgjnJAlSLWSpgRRh6y42VT1veZFBtj23jZzKPcW0ddMAuKfdPXSPqnkRy86NggDYdqyWtCABdB0HXoFw5iDs/UXvaKqtf6P+vNX3LdwMbvx+5Hee/OtJSZKEEDYhCVIto6qq/VqQUndD9nFw84YmV9v23DZQai7lqdVPkVOcQ/vQ9tzX8T6bnLdz2Uy23SeyKSp1zdaWi3gFQPy92vbqt7Tk10Vd2/Ba3un7Du4Gd5YeXcpjKx+jxAXHVgkhnIskSLVMdmEpBWVVn20+i+1gWetRbF+tm8bJfLLjE7ambcXX3ZdXe7+Ku8HdJudtGOxDsK8HxSYzu05k2+ScTiH+XnD3hZQdcHCp3tHUSJ+YPrx7zbt4GDxYfmw5k1dOpthUrHdYQggXJglSLWNZpDbIxx0v98oVRKw0a/faANue1wa2pW1j5g5tra5nejxDjH+Mzc59fsHIWjNQG7QaVt3u1rZXv+nSrUgAVze4mvevfR9Poycrj6/k4RUPU2Qq0jssIYSLkgSpljlxVkuQ6gfZuIUn7wwc26htO9n0/uzibJ7860nMqpkbYm/g+tjrbX6NWlUw8nwJE8HoCcc2QNIqvaOpsZ71e/JBvw/wMnqx+sRqJi2fRGFpLSjPIIRwOEmQapmTmVqCFG3rBClxKaBCZDsIrG/bc9fQS+te4lTeKRr4NeD/evyfXa7RqawFacvRWlIw0sI/ErrcpW2vmO7yrUgAPaJ68GH/D/F282bNyTU8uPxBCkoL9A5LCOFiJEGqZY5n2qkFyTq937lmry1OWsziI4sxKkZe7/06vu6+drlOx5gg3AwKKdmFHMuoZX9sez0Cbl5wbD0cWq53NDbRLbIbH/X/CG83b9afWs/EZRPJL8nXOywhhAuRBKmWsXSxNahnwwTJVAKJy7RtJ0qQ0vLTeGn9SwBMaD+BdmHt7HYtHw832jcIBGB90hm7XUcXAVHatH+AFa/UilYkgC4RXfj4uo/xdfdlY8pG7l92vyRJQohKkwSplrFLF1vyOijKBp9QiO5su/PWgKqqTF07lezibOJC4hjffrzdrxkfGwLAhsMZdr+Ww/V6WCvfcGKzy89oO1+n8E58fN3H+Ln7sSV1C/f+eS+5xbl6hyWEcAGSINUyJ+zRxWadvTZQWxHeCfxw8Af+PvE3HgYPXun1is2m9F9OD0uCVNtakAD8wqF7WZK54uVa04oE0CGsA58M+AR/D3+2pW3jP3/+h5ziHL3DEkI4Oaf4azdjxgwaN26Ml5cX8fHxbNy48bLHz58/n1atWuHl5UW7du1YtGhRuf2qqvLcc88RFRWFt7c3/fv35+DBg+WOady4MYqilHu8+uqrNv9sjlRcaiYtR5vWXN+WXWznLy/iBI7lHOONTW8A8FDnh2ga1NQh1+3SqB5Gg8LxswUcP1sLu2qumqTVRTq1HfYvuuLhrqRtaFs+HfApAR4B7Di9gwl/TCC7uBbVtBJC2JzuCdK8efOYPHkyU6dOZevWrXTo0IGBAweSlpZW4fFr165l1KhRjBs3jm3btjFs2DCGDRvGrl27rMe8/vrrvPfee8ycOZMNGzbg6+vLwIEDKSwsP933hRde4NSpU9bHgw8+aNfPam8pWYWoKni6GQjx9bDNSdMT4UwiGNwh9hrbnLMGTGYTz/z9DPml+XSJ6MIdre9w2LX9PN1oW18bh1Qru9l8QyH+P9r2iulgNusbj43FhcTx2cDPCPIMYteZXYz/YzxZRVl6hyWEcFK6J0hvv/0248ePZ+zYscTFxTFz5kx8fHz4/PPPKzz+3XffZdCgQTz++OO0bt2aF198kc6dO/PBBx8AWuvRO++8wzPPPMONN95I+/bt+eqrrzh58iQLFy4sdy5/f38iIyOtD19f+8yAcpTjmVqrRv0gbxRbLSRrqZ7d+CpteQqdfb33a7ambcXHzYeXrnoJo8HGxTCvoEdsMFBLu9kAej4IHv6QuhP2ue4abZfSKrgVnw38jGCvYPac2cM9f9xDZmGm3mEJIZyQrglScXExW7ZsoX///tbXDAYD/fv3Z926dRW+Z926deWOBxg4cKD1+KSkJFJSUsodExgYSHx8/EXnfPXVVwkJCaFTp0688cYblJaWXjLWoqIisrOzyz2czclMrYXMpgO0nWh6f+LZRN7b+h4Aj3d7nAb+DRweQ48m2jik9bWxBQm06to9ytawW/4ymC79O+GqWtRrwWcDtCRpX8Y+xv0xjozCWvr9FEJUm64JUnp6OiaTiYiIiHKvR0REkJKSUuF7UlJSLnu85flK53zooYeYO3cuK1as4D//+Q+vvPIKTzzxxCVjnT59OoGBgdZHTIztlrKwFZtX0S7MgqNrtW2dxx+VmEt4+u+nKTYX06t+L4Y3H65LHF0b18OgQHJGvnVZl1on4QHwrgfp+2H7N3pHYxfN6jXji4FfEOodyoGzBxj3+zjSC9L1DksI4UR072LTy+TJk+nbty/t27fn3nvv5a233uL999+nqKjitZumTJlCVlaW9XHs2DEHR3xlJyxdbLYaoH1oBZhLIaQ5BMfa5pzV9MmOT9ibsZcAjwCm9Zxmuy7EKvL3cq/d45AAvIOg9+Pa9srpUFwLB6QDsUGxfD7wc8K9w0nMTJQkSQhRjq4JUmhoKEajkdTU1HKvp6amEhkZWeF7IiMjL3u85bkq5wSIj4+ntLSUI0eOVLjf09OTgICAcg9nY/MutvOn9+tod/puZu2YBWgL0Yb7hOsaT3yTWj4OCaDbPRDUEHJOwfoP9Y7GbpoENuGLQV8Q4RPB4azDjF0ylrT8iieICCHqFl0TJA8PD7p06cKyZcusr5nNZpYtW0ZCQkKF70lISCh3PMDSpUutxzdp0oTIyMhyx2RnZ7Nhw4ZLnhNg+/btGAwGwsP1/eNbEzatgWQ2wcE/tG0dxx8VlhYy5e8pmFQTgxoPYnCTwbrFYhFfNg5p3aFanCC5ecK1z2rba97VFiuupRoGNOSLQV8Q5RvFkewj3P373aTkVdzFL4SoO3TvYps8eTKffPIJX375JXv37uW+++4jLy+PsWPHAjB69GimTJliPX7SpEksWbKEt956i3379vH888+zefNmJk6cCICiKDz88MO89NJL/Pzzz+zcuZPRo0cTHR3NsGHDAG2g9zvvvMM///zD4cOH+eabb3jkkUe44447qFevnsPvgS2oqmpNkGyyzMjxTZCfDl6B0LBHzc9XTe9te4+krCRCvUP5v3j7LERbVd1jgzEaFI6cyedYRu3sfgKg7b8hsr1WRf2vN/SOxq5i/GP4YtAX1Perz9Hso4xdMpbjOcf1DksIoSPdE6QRI0bw5ptv8txzz9GxY0e2b9/OkiVLrIOsk5OTOXXqlPX4nj17MmfOHGbNmkWHDh34/vvvWbhwIW3btrUe88QTT/Dggw8yYcIEunXrRm5uLkuWLMHLywvQusvmzp1Lnz59aNOmDS+//DKPPPIIs2bNcuyHt6H03GKKS80oCkQEeNX8hPt+1Z5bDAKj/atUV2RTyia+3vM1ANN6TiPIK0iXOC4U4OVO54ZBAPx18LS+wdiTwQDXTdO2N30KGUn6xmNn9f3q88XAL2jg14DjuccZs3gMhzIP6R2WEEIniqrWojUFHCg7O5vAwECysrKcYjzS9mOZDJuxhsgAL9Y/3a9mJ1NVeK8TnE2CW7+CuBttE2QV5JXkMfzn4ZzIPcHw5sN5vufzDo/hcj5YfpA3/zjAgLgIZo3uqnc49vXVMDi8QmtR+vdnekdjd2n5afxn6X9IzEwkyDOImdfNpE1IG73DEkLYSGX/fuvegiRs49witTZoPTq9T0uOjJ7QtIbJVjW9sekNTuSeoL5ffR7v9rguMVxO7xZhAKw9dIYSU+2qOH0RSyvSru/hxBZ9Y3GAcJ9wvhj4BW1D2pJZlMm438exOWWz3mEJIRxMEqRawloDqZ5PzU9m6V5reg14+tX8fFX01/G/+OHgDygovHjVi/i6O1+F87bRgQT7epBbVMrWo2f1Dse+ojpA+5Ha9uIna90SJBUJ8gri04Gf0jWiK3kledz75738dfwvvcMSQjiQJEi1hE1nsO37TXtuNbTm56qizMJMpq6dCsCdcXfSLbKbw2OoDINBoXfzUABWHajF45As+j8PHn7a4P0d8/SOxiF83X35qP9H9GnQhyJTEZOWT2JJ0hK9wxJCOIgkSLXEuQSphl1sWcfh5DZA0WV6/0sbXiK9IJ3YwFge6vyQw69fFX1aat1sdSJBCog6Vzzyz6lQ6HxL7diDl5sX/73mvwxuPJhStZQn/nqC7w98r3dYQggHkASpljjXxVbDFqT9i7XnmHjwc2xNqMVJi/n9yO8YFSOv9HoFT6OnQ69fVVc31xKk3SezOZ1TcQX2WqXHfRDcFHJTa/20//O5G9yZfvV0bmlxCyoq09ZN47OdnyHzW4So3SRBqiVOZllakGo4Bsky/sjB3Wtp+Wm8tP4lACa0n0CbUOefNRTq50nb+toMiNW1ebq/hZsnDHpV217/EaQf1DceBzIajDzb41nGttXqs72z9R1e3fgqJrNJ58iEEPYiCVItkFdUSmZ+CVDDWWwFZ+HI39q2AxMkVVWZunYq2cXZxIXEMb79eIddu6b6tKhD3WwALQZA84FgLoElT2klIeoIRVGY3GUyj3V9DIA5++bw+F+PU2SqA62HQtRBkiDVApbxRwFebvh71aCo48Gl2uK0Ya0hpKmNoruy7w9+z98n/sbD4MErvV7B3aBPYcrq6F3WzfbXgdOU1vbp/haDpoPBHRL/PLdeXx0yps0YXu/9Om4GN5YeXcq9S+8lu7hujMkSoi6RBKkWOHpGW+6iYYjrda8dyznGG5u08SwPdX6IpkGOS8xsoUujegT5uHM2v4TNtX26v0VIU0h4QNte/DgU1+LlVi5hcJPBzOw/E193XzanbmbM4jGyfpsQtYwkSLVActl6YI2Ca1AvqKQQDv6pbTsoQTKZTTzz9zMUlBbQJaILd8bd6ZDr2pKb0UD/1tqyOEt21aE/kL0fh4AGkJkMq17VOxpdxEfF8+WgLwnzDiMxM5E7Ft1B4tlEvcMSQtiIJEi1gGXB1JjgGrQgJa2Ckjzwj4boTjaK7PJm757N1rSt+Lj58NJVL2FQXPPHcVCbSAB+351Sd2Y2efrB0De17bUfQMpOfePRScvglnw95GuaBDYhNT+V0UtGsyW19lcbF6IucM2/SKKco2fyAGhYkwRp78/ac6shoCg2iOry9mfs54PtHwDwVPenaODfwO7XtJdezUPx8TByKquQHcez9A7HcVoOhtb/AtUEv0yCOjqjK9ovmq8GfUXHsI7kFOcw4Y8J/Hb4N73DEkLUkCRItYC1i626Y5BMJbC3bPyRAxamLTYVM+XvKZSaS+kb05dhzYbZ/Zr25OVu5JpWWs2oJbvrUDcbwODXwTNAW6Nt06d6R6ObIK8gPhnwCdfGXEuxuZinVj/Fh9s/rDstikLUQpIguTizWeVYWZHIarcgHV4FhZngGwaNrrJdcJfwwbYPOHj2IMFewTyf8DyKA1qs7M3SzbZkVx3qZgOtwna/57TtP6fB2SO6hqMnS9VtS62kj/75iCf/epLC0kKdIxNCVIckSC4uNaeQ4lIzbgaFqMBq1kDa86P23PpfYDDaLrgKbE7ZzOzdswGYmjCVEO8Qu17PUfq2DMPDaCApPY+Dabl6h+NYXcdpiXVJHvw0sU4sZnspBsXA5C6TmdZzGm6KG4uPLGbcH+NIL0jXOzQhRBVJguTiksum+Nev542bsRrfTlPJucVp2wyzXWAVyC3O5Zk1z6CiMqzZMK5teK1dr+dI/l7u9CpbvLZOzWYDMBjgxg/A3QeOrIbNn+kdke5ubn4zswbMIsAjgB2nd3D7b7dz8GzdqTwuRG0gCZKLO1o2/qja3WtJq7QK2g7oXnt90+ucyD1Bfb/6PNntSbteSw+WbrbFdS1BAgiOhf7TtO2lz0FGkr7xOIFukd2YM3QOjQIacTLvJHcsuoNlycv0DksIUUmSILm4YzVNkHYv1J5b32DX7rXlycv5MfFHFBReuuol/Dz87HYtvfSPi8DNoLD3VDYHU3P0Dsfxut0Dja+GknxYeH+dndV2vkYBjfhmyDd0j+xOfmk+D694mPe3vY9ZrbvdkEK4CkmQXJy1inZ1EiRTybnq2W1usmFU5Z0pOMO0dVrrwpg2Y+ga2dVu19JTsK8HfVtqs9m+33pc52h0YOlq8/CD5LXw99t6R+QUAj0DmXndTO5ofQcAs3bMYuKyibI8iRBOThIkF3ekrAZS49BqVNF2QPeaqqpMWzeNjMIMmgU1Y2KniXa5jrMY3rk+AAu3ncBkrkOz2SzqNYYhZQUkV0yH45t1DcdZuBvcebL7k7zS6xU8jZ6sPrGaUb+OksrbQjgxSZBcmKqqJJ3WEqTY6iRIuyyz1+zXvTb/wHxWHFuBm8GN6VdPx9PoaZfrOItrW4cT6O1OanYRaxLr6MylDiOh7XCtgOQP46CoDnY3XsINTW/gq8FfEe0bTXJOMrcvup2lR5fqHZYQogKSILmw9NxicopKUZRqLFRbUniuenbbf9s+OODg2YO8vul1AB7u/DCtglvZ5TrOxNPNyL86RAPwQ13sZgOtEvvQtyEwRquL9NtjUJdqQ11BXEgcc6+fS3xkPPml+UxeOZnXNr5GialE79CEEOeRBMmFJaVrrUcN6nnj6VbFFqADS6AoW1twtGGCzWMrLC3kib+eoMhUxFX1r3LJhWira3gXbdmU33enkFNYR//oeQfBzbNAMcCOubDtf3pH5FTqedVj5nUzuavNXQB8vfdrRi8ezfGcOppUC+GEJEFyYUnpWkHCxiHV6F7b8Z323P4WbXCtjb21+S0SMxMJ8Qpx6YVoq6NDg0CahvlSWGJm8c46OOXfolFPuPZZbfu3x+DUDn3jcTJuBjce7foo71/7PgEeAew6s4tbf7mVZUelFIAQzqDu/NWqhQ6nV3P8UX4GHPxD2253q42j0qb0z90/F4CXe71MqHeoza/hzBRF4ebOWitSnZzNdr6rHoYWg8BUBN+NhoJMvSNyOn1j+vL9Dd/TIawDOSU5PLzyYaZvmE6xqVjv0ISo0yRBcmFHyhKkJlVNkPb8BOYSiGgLEXE2jSk1L5Xn1mprc42JG8NV9e2/tpszurlzfQwKbEzKqJs1kSwMBhj2EQQ2hLNJsPC+Or0UyaVE+UXxxaAvrOu4zdk3hzsX30lSlhTcFEIvkiC5MMsYpCZhVSy6aO1es23rkcls4um/nyarKIvWwa2Z1HmSTc/vSqICvbkuLgKA2WuP6BuM3nyC4dYvwegJ+xfBipf1jsgpuRvcmdxlMjP6zSDIM4g9Z/Zw6y+38u2+b+vWAshCOAlJkFyUyaxypKxIZJW62DKTtSJ+KDafvfbF7i/YmLIRbzdvXu/9Ou5Gd5ue39Xc1bMJAAu2niArv44O1rao3xn+9Z62vfpN2PWDvvE4sd4NevP9Dd+TEJVAoamQVza8wn1/3kdafpreoQlRp0iC5KJOZhZQXGrGw2ggOsi78m/cOV97btwLAuvbLJ7NKZv5YNsHADwd/zSNAxvb7NyuqkdsMK0i/SkoMTFvc7Le4eivw0jo+ZC2vfB+OLlN33icWIRvBDOvm8mU7lPwNHqy5uQabvrpJpYkLdE7NCHqDEmQXFRimjaDrUmoL0aDUrk3qSps+1rbbj/CZrGkF6Tz+F+PY1JNXB97PTc2vdFm53ZliqIw9qrGAHy59iilJhl7Q//nofkAKC2EOSO1Fk1RIYNi4LbWt/HdDd/RJqQN2cXZPP7X4zzx1xNkFmbqHZ4QtZ4kSC7qQNnA32YRVRh/dHQNZBzW1sqy0dprpeZSnvzrSdIL0mkW1IxnezyLolQyYasDbuxYn3o+7pzILODPval6h6M/gxGGfwrhcZCbAl//W5tVKS4pNjCW/w35H/d2uBejYmRx0mJu/OlGFh1eJGOThLAjSZBc1IFUrQWpRbh/5d+0taxYX9vh4FnFgd2X8OH2D63jjt7q+xY+7tVYNLcW83I3clt8QwA+X3NE32CchVcg3P49BNSH9P0w9zatsru4JHeDOw90fICvBn9Fs6BmZBRm8OTqJ5m4fCKnck/pHZ4QtZIkSC4qMU1rQWpR2RakgkzYs1Db7jzGJjH8dfwvPtn5CQDTek4jNjDWJuetbe7o0Qg3g8LGpAw2HZHWEkAb/3b79+AZCMnrtDXbTKV6R+X02oe157vrv+OBjg/gbnDnr+N/MeynYczZOweT2aR3eELUKpIguSCzWeVg2Rik5hGVbEHaOV8b9xEep80oqqETuSeYsnoKAKNajWJwk8E1PmdtFRXozS1dYwB4+48DOkfjRCLiYNQcMHrAvl9h4b0gf+SvyN3ozr0d7mX+DfPpGNaR/NJ8pm+czuglo9l7Zq/e4QlRa0iC5IJOZBaQX2zC3ajQqLKL1G79SnvuPFpbTLQG8kvyeWj5Q2QXZ9MutB2PdX2sRuerCyZe2wwPo4F1h8+w9lC63uE4j8a94NavwOCmJfG/PCSFJCupaVBTvhz8Jf8X/3/4uvuy4/QORvw6ghfXvSiDuIWwAUmQXNDBsu612FA/3I2V+Bae3A4pO7T/qddw9ppZNfPMmmc4cPYAwV7BvN33bTyMHjU6Z11QP8ibkd21VqT/Lj0gg2vP13IwDP9MW9h229ew6FFJkirJoBgY2WokC29cyKDGg1BR+e7Adwz9cShz982l1CzdlkJUlyRILuhgqqV7rZLjj7bM1p5b36BVNa6Bj3d8zNKjS3EzuPHONe8Q6RtZo/PVJff3bYaHm4FNR87yd6K0IpXTZhgMmwkosPlz+PlB6W6rgkjfSN7o8wafD/yc5vWak12czcsbXmbkryPZnLJZ7/CEcEmSILkg6wy2yow/ys+Af7SFY+l6d42uu+zoMj7c/iEAz/Z4lk7hnWp0vromMtCLO+IbAfDWH9KKdJEOI+Cmj0Exwvav4Yd7wFTHK5BXUbfIbnx3/Xc8Hf80AR4B7D+7n7G/j+Wh5Q9xKPOQ3uEJ4VIkQXJBe05lA9AyshIJ0tYvobQAIttBo+ovHHvg7AGm/K0Nyr699e3c3Pzmap+rLru3byze7ka2H8vk539O6h2O8+kwAm75AgzusHsBzL0divP0jsqluBncGNVqFL/e9Cu3tLgFg2JgxbEV3PzzzTy75llS8lL0DlEIlyAJkospKjVZV4dvWz/w8gebSmCjNg2f+PuqPTg7vSCdh5Y/REFpAfFR8TIouwbC/b24v29TAF5dvI/8YhkjcpG4G2HUt+DmBQd/h9lDIVfWIauqel71eC7hOX7814/0a9gPs2pmYeJChi4Yypub3pSB3EJcgSRILuZASi6lZpV6Pu5EB3pd/uC9v0D2CfAN04pDVkNeSR73/3k/J3JPEOMfw5u938TN4FatcwnN+N6xNKjnzamsQj5Ynqh3OM6p+XUw+mfwDtbWbPu0H5yWEgnVERsUyzvXvMPXQ76ma0RXis3FfLnnSwYvGMz7297nbOFZvUMUwilJguRidp3MAqBNdOCVl/TYMFN77no3uF8hmapAibmER1c+yt6MvQR7BTOz/0yCvIKqfB5Rnpe7kWevjwNg1l+H2ZeSrXNETqphPNzzJ9Rroq3Z9ml/OLhU76hcVoewDnw+8HM+7PchLeq1ILckl1k7ZjHwh4G8tfkt0gtk4oAQ55MEycXstiRI9QMuf+CJLXBsgzaWo+u4Kl9HVVWeX/s8a06uwdvNmxn9ZtAwoGF1QhYVGNgmkoFtIig1qzz1w05ZyPZSQppqSVJMDyjKgm9ugb/e1BZeFlWmKApXN7ia+TfM5+2+b9MquBUFpQXM3j2bQT8MYvqG6TJGSYgykiC5mF0ntNaGNtFXGH+09n3tue1w8I+o8nU+2P4BPx/6GaNi5M0+b9I2tG2VzyEu74Ub2+Lv6cb2Y5l8/NdhvcNxXr6hMOaXslmYKix/EebdIYvc1oBBMXBdo+v47vrvmNFvBu1D21NkKmLOvjkMXjCYKaunsPvMbr3DFEJXkiC5kFKTmb1lM9jaRl+mBSl1D+xeqG33fLDK1/l237fM2jEL0Kbz927Qu8rnEFcWEeDF8/9qA2jFI3ccz9Q3IGfm5gHX/xdueO/c0iQzr4aja/WOzKUpikLvBr35esjXfDLgE7pGdKXUXMqvh39l5K8jGb14NH8c+UMKToo6SRIkF5J4OpeiUjO+HkYah/he+sBVrwGqNhsosmotPwsOLuCVDa8AcF+H+xjeonqDu0Xl3Ny5PoPbRlJqVrnv661k5BXrHZJz6zIGxv0BwbGQfVyb4bZiutRLqiFFUegR1YMvBn3B3KFzuT72etwMbmxL28ajqx5lyIIhfL7rczIKpdVO1B2SILmQLUe12SYdYoIwGC4xQDt1D+xZqG33ebJK5//l0C88v/Z5AO6Mu5P7OtxXzUhFZSmKwqs3t6dRiA8nMguYOGerjEe6kuhO8J+/oMMoUM2w6lWYdQ2c+kfvyGqFNqFtmH71dH4f/jsT2k+gnmc9TuWd4r9b/ku/+f14dOWjrD2xFrMqP6eidpMEyYVsPqIlSF0bX2a5kFWvac9xN0JEm0qfe3HSYp5Z8wwqKiNajuDxro9feZacsIlAH3dm3dkVHw8jaw+dYfrifXqH5Pw8/eGmmdoabt7BkLoTPrkWlr0Axfl6R1crhPuE82CnB1l6y1Je6PkCbULaUGou5Y+jf/CfP//D4B8G89H2jziVe0rvUIWwC0WV9Q6qJTs7m8DAQLKysggIuMKMMhu5+vXlHMso4Ku7u9O7RdjFB6Tuho96atv3ra10gvTjwR+ZunYqKio3NbuJ53s+j0GR3NnRFu88xX3fbAXgteHtGNFNZg1WSu5pWPTYuZbTwIYw6BVodX21i6OKiu3L2MeCgwv49fCv5BRrBWsVFLpGdmVwk8Fc1/A6KQUinF5l/35LglRNjk6QUrMLiX9lGQYF/pk6AH8v94sP+nYU7F8EccPg1i8rdd5v9n7DqxtfBeCWFrfwTI9nJDnS0Zu/7+eDFYkoCrx9awdu6tRA75Bcx95fYMkUyDqmfR3bF/pNhfqddQ2rNiosLWRZ8jIWHFzAxpSN1tfdFDcSohMY3GQw1za8Fl/3y4yVFEInkiDZmaMTpN92nOKBOVuJiwpg0aSrLz7g8Er46kZtoc/710FYy8ueT1VVZu6YaV18dnTcaB7r+ph0q+lMVVWeWbiLbzYkY1DgvVGduL59tN5huY7ifFj9Fqx9D0xlA95b/wuufeaKvxOiek7mnmTJkSUsTlrMvoxz3cOeRk8SohO4JuYaejfoTah3qI5RCnGOJEh25ugE6fmfdzN77RHGJDRi2o0XzEwzlcKsPpC6C7r/B4a8ftlzlZhKmLZuGj8d+gmAezvcy/0d7pfkyEmYzSpPLdjBd5uPYzQovH1rB27sWF/vsFxLRhKsnA47vgNUUAzaoO5ej0Boc72jq7UOZx1mcdJiFict5mj2UevrCgrtw9rTN6Yv18RcQ2xgrPx7I3QjCZKdOTpB6v/2KhLTcvngtgpaFNbNgN+fBq8geGgb+Fx6EHd2cTaTV05mw6kNGBUjT8c/za0tb7Vv8KLKTGaVx+f/w4JtJwB46NpmPNy/xaVnL4qKpe6B5S/B/t/OvdZiMPScCI2ukjFKdqKqKgfOHmDFsRWsPLbyoqKTkb6RJEQlkBCdQHxUPMFel5l4IoSNSYJkZ45MkJLP5NP7jRUYDQpbn72OQO/zxh9lJsOMeCjJ14rodRlzyfMcOHuAR1Y8QnJOMt5u3rzV5y2ublBBd51wCiazyutL9lmrbA9pF8mbt3TAx0MWC66y45vhrzfgwJJzr0V1gPj7tBmfHj76xVYHpOSl8Nfxv1h+bDkbT22kxFy+blXr4Nb0iO5B14iudAzvSICHYya+iLpJEiQ7c2SCNHtNEs//sof4JsHM+0/CuR1mM3x9Mxxeof1veMyvYKh4gPUvh37hhXUvUGgqJMo3ineveZfWIa3tGrewje82H+P/ftxJiUmlcYgPb93agS6N5H/c1ZJ+UGtx/edbKC3UXvPwh7Y3QcfbISZeWpXsrKC0gC2pW1h/cj3rTq3jwNkD5fYrKDSv15xO4Z3oHN6ZzhGdifSN1ClaURtJgmRnjkyQ7vxsA6sPpvP0kFZM6N303A5L15qbN9y7usKxFbnFubyx+Q0WHFwAQM/onrx69avU86pn15iFbW1MyuChb7eRkl2IosD4q2OZfF0LvNyNeofmmvLOwJbPYev/IPPcWBlCmmmzQFtfD1EdJVlygPSCdNafWs+GUxvYlrat3NglizDvMOJC4mgT0kZ7Dm0jg75FtUmCZGeOSpDyikrp9MJSik1m/pzcm2bh/tqO45vhi8HaTJ2hb0O3cRe9d1PKJp75+xlO5p1EQWF8+/Hc3+F+jAb5o+qKsgpKePHXPXy/5TgAkQFePHJdc4Z3boCbUUozVIvZDMlrYfscbf3Ckrxz+wJjoNVQaDkYYnqAu5duYdYl6QXpbEvbxtbUrWxL28a+jH2YVNNFx4V7hxMXGkfr4NY0DWpKs6BmNAxoiLuhghIoQpxHEiQ7c1SC9N3mYzzx/Q4ah/iw4rG+2syPnBSY1RdyTmnF8EZ8Xe5/umcLz/L+tveZf2A+APX96vPiVS/SLbKb3eIUjrNsbyrP/bSbE5kFADQL9+P+vk0Z2j4KTzdJfqutKFerI7b3F0j8UxvXZ+HmBQ17QJM+ENsHIjuAUcaCOUJ+ST4Hzh5g95nd7Dmzh93pu0nKTqpwqRM3gxuNAxrTNKjpuaTJvyEx/jH4uMs4M6GRBMnOHJUg3ThjDf8cy+SJQS25v28zKDgLX94AKTshrDXcs1RbdgEoNZfy3f7v+GD7B9Yqt8ObD+fxbo9LwbZaprDExNfrj/LBikQy87UBr6F+Hozq3pB/d2lAo8stZiyurKQADi2Hvb9qz7kp5fe7+2hrwjXoCg26QXRnCIiWLjkHyS/JZ//Z/exO382Bswc4lHmIxMxE8ksvvcxMqHcoMf4x1kdD/4bU969PpE8kod6h0rJeh0iCZGeOSJB2ncji+vf/xt2osG5KP0INefDNLXBiM/iGw7jfITiWYlMxPx36ic92fsaJXG1aeMt6LXmq+1N0jexql9iEc8guLOF/647y9fqjnMoqtL7ern4g17eP4ppW4TQP95OaMzWhqnB6PySt0gqyHlkDRVkXH+cVBOFxEN5ae0S0gdCWWtkNuf92p6oqKXkpJGYmWhOmw1mHSc5JJqui79d5jIqRMJ8wIn0iifCNOPfsG0m4TzjBXsGEeIVIK1Qt4VIJ0owZM3jjjTdISUmhQ4cOvP/++3Tv3v2Sx8+fP59nn32WI0eO0Lx5c1577TWGDBli3a+qKlOnTuWTTz4hMzOTq666io8++ojmzc8NYs7IyODBBx/kl19+wWAwMHz4cN599138/PwqFbMjEqRJc7fx0/aT/KtDNO8NCIA5I+DMQfCuB3f9RopfCD8f+pnv9n9Han4qAMFewTzQ8QGGNx8u/yOqQ0pNZv7Yk8qcDcmsPZSO+bzf6jB/T3o2DaFLo3q0rR9IXFSADO6uCbNZ+z08vkl7HNsEp/dBBeNkAPAMgHqNoF5j7RHUSHv4R4BfBPiGgfyu2lVWURbHc45zLOcYyTnJHMs5xrGcY5zIPcHp/NMVjnGqiLebN8FeweUeId4hBHkGEeARQIBngPZseXgG4OPmI/9BcTIukyDNmzeP0aNHM3PmTOLj43nnnXeYP38++/fvJzw8/KLj165dS+/evZk+fTrXX389c+bM4bXXXmPr1q20batVmH7ttdeYPn06X375JU2aNOHZZ59l586d7NmzBy8vbaDl4MGDOXXqFB9//DElJSWMHTuWbt26MWfOnErFbe8EadneVMZ9uRkPpZQVfQ5Tf8vrUJLPsaAGrLtqAssy97Du5DpUtG9fuHc4Y9uOZXiL4Xi7eds8HuE60nOL+H13Ckt2pbDpSAaFJeXHahgNCg2DfWgc4kPjUF9iQ32JCfYh3N+L8ABPgn08pCBlVZUWQfoBSNsLaXu0ApVpe86tC3c5igF8QssSpkgtafKpp7VIeQede/Yue80rEDx8tXFR8oe3xkxmE+kF6aTmp5KSl2J9tmyn5aeRUZhBkamoWuc3Kkb8PfytSZOvhy8+bj54u3nj4+6Dj5vPuefzti37vdy88DB64GHwwNPoiYfx3LOsm1k9LpMgxcfH061bNz744AMAzGYzMTExPPjggzz11FMXHT9ixAjy8vL49ddfra/16NGDjh07MnPmTFRVJTo6mkcffZTHHnsMgKysLCIiIpg9ezYjR45k7969xMXFsWnTJrp21bqglixZwpAhQzh+/DjR0Vde+8peCVJm9gn+3LaFhWs30sC0j3ifXaQY8jjs7s4u30COK6Xlju8a0ZVhzYYxuMlgPIweNotD1A5FpSa2Hs1k/eEz7DieyY7jWZzJK77se9wMCqF+ngR6u+Pv5Vb2cLc+e7kb8HAz4GE04OluxNNY9nXZax5uBtwMCoqiYFDAYNCeta/LXlMUFEVL1iyvWfZX9k9+ZXODyp7R1rmGogClBbhlH8MtKxlj1lHcspNxyzqKMecExrw0DAXpKBUMNq4MFQXV3cf6MLv7attuPqju3qhGD1SDOxg9tG2jOxgs2x5gcD9v2w1VMWotWYqibStGLXlTDKgGy7YRtew1yo5XFaXs2LJ9lvutcN625eYq5bfLntULXzv/m3HJ92rb6mXPbRuqqlJoLiSzOJuzxZlklmSTWZJFZnEWmSVZZJVkk1OSR15pHjmleeSW5pFbmktpJVumqstNccPD4I572cPD4I6HwaPs2R03xQ2jYiz3cDMYL37tvGeDYsSoGHAzuGFUDBgV7VnB8vtp0H5XUVAUA8ayrxUMZfsVDBccf+Hr2vvLn8dQ9jpov7MKCijQvmE3QgNtWwersn+/dZ2GUVxczJYtW5gyZYr1NYPBQP/+/Vm3bl2F71m3bh2TJ08u99rAgQNZuHAhAElJSaSkpNC/f3/r/sDAQOLj41m3bh0jR45k3bp1BAUFWZMjgP79+2MwGNiwYQM33XTTRdctKiqiqOjc/yCys7Or9Zkvx2xW+c+3Q9njZYJo+Af4DXcgqOyIUtwUN9qHtadndE+GNBlCTECMzeMQtYenm5GEpiEkNA0BtH/oU7OLOHw6l6QzeRxJzyMpPY/jZws4nVPEmbxiSs0qKdmFpGQXXuHsovKMQGzZ4xwDZkLIJlzJJEw5S5iSRTiZBCm5BJJHoFL2II+Asmc/Rfu+KKgoJXnlSxMIp6EChYpCtsFw7mE0kK8o5BsU8hUD+QaFAuuzQr7Bsv/ccUWKQnHZo1A5P5mEUrWUUlMpmAr0+6B29tSJO7l90BO6XFvXBCk9PR2TyURERES51yMiIti3b1+F70lJSanw+JSUFOt+y2uXO+bC7js3NzeCg4Otx1xo+vTpTJs2rZKfrHoMBgUfoyfe5lx8VAV/oxcBPiE0iexM03otaBbUjE7hnfDzqNw4KSEupCgKkYFeRAZ60bPZxYX2Skxm0nOLOJ1TRHZBKTmFJeQUlpJd9pxbVEphiYniUjPFJjPFpWaKSrXn4lIzRWWvmc0qZlV7qCpl21i/Nln3a0mbdb/5yg3aVzriSo3ilWkyv1K7unqFs1S+Xd5ANsFkE0xixRe6KGADZrwpxIcivMsePhTirWjPPhThRRHulOKOCXdK8aAUd6VEe7Z8fcHDgBkjZgyo57YVMwbMFe5TUDFaXz+3D8qSt7LAz2snOq9dR73oNaWC1y51XEXn5oLXnIIK/mbwB7TlpqvXWnje6TABxYpCiaKWS56KFe31IkWhRIEig0IpCqUKmFAwKVi3SxUotb6mYKL8vguPNynatc1oLZflvlbAjFK2D8zWfcp5+8+9Zvm6/D4tBpRzP/KWh4fBs0b3rCakkEclTZkypVzLVXZ2NjExtm+9+e+ty1HcPcqvtyaEg7gbDUQFehMVKOPYhBB1m64JUmhoKEajkdTU1HKvp6amEhlZcZ9jZGTkZY+3PKemphIVFVXumI4dO1qPSUtLK3eO0tJSMjIyLnldT09PPD3tn8kGBUj9GiGEEEJvug6B9/DwoEuXLixbtsz6mtlsZtmyZSQkJFT4noSEhHLHAyxdutR6fJMmTYiMjCx3THZ2Nhs2bLAek5CQQGZmJlu2bLEes3z5csxmM/Hx8Tb7fEIIIYRwTbp3sU2ePJkxY8bQtWtXunfvzjvvvENeXh5jx44FYPTo0dSvX5/p06cDMGnSJPr06cNbb73F0KFDmTt3Lps3b2bWrFmANsbi4Ycf5qWXXqJ58+bWaf7R0dEMGzYMgNatWzNo0CDGjx/PzJkzKSkpYeLEiYwcObJSM9iEEEIIUbvpniCNGDGC06dP89xzz5GSkkLHjh1ZsmSJdZB1cnIyBsO5hq6ePXsyZ84cnnnmGZ5++mmaN2/OwoULrTWQAJ544gny8vKYMGECmZmZ9OrViyVLllhrIAF88803TJw4kX79+lkLRb733nuO++BCCCGEcFq610FyVY5ai00IIYQQtlPZv99ShlMIIYQQ4gKSIAkhhBBCXEASJCGEEEKIC0iCJIQQQghxAUmQhBBCCCEuIAmSEEIIIcQFJEESQgghhLiAJEhCCCGEEBeQBEkIIYQQ4gK6LzXiqiwFyLOzs3WORAghhBCVZfm7faWFRCRBqqacnBwAYmJidI5ECCGEEFWVk5NDYGDgJffLWmzVZDabOXnyJP7+/iiKYrPzZmdnExMTw7Fjx2SNt0qQ+1V5cq+qRu5X5cm9qjy5V1Vjj/ulqio5OTlER0djMFx6pJG0IFWTwWCgQYMGdjt/QECA/PJUgdyvypN7VTVyvypP7lXlyb2qGlvfr8u1HFnIIG0hhBBCiAtIgiSEEEIIcQFJkJyMp6cnU6dOxdPTU+9QXILcr8qTe1U1cr8qT+5V5cm9qho975cM0hZCCCGEuIC0IAkhhBBCXEASJCGEEEKIC0iCJIQQQghxAUmQhBBCCCEuIAmSk5kxYwaNGzfGy8uL+Ph4Nm7cqHdIunv++edRFKXco1WrVtb9hYWFPPDAA4SEhODn58fw4cNJTU3VMWLH+uuvv7jhhhuIjo5GURQWLlxYbr+qqjz33HNERUXh7e1N//79OXjwYLljMjIyuP322wkICCAoKIhx48aRm5vrwE/hGFe6V3fddddFP2uDBg0qd0xduVfTp0+nW7du+Pv7Ex4ezrBhw9i/f3+5Yyrzu5ecnMzQoUPx8fEhPDycxx9/nNLSUkd+FLurzL3q27fvRT9b9957b7lj6sK9Avjoo49o3769tfhjQkICixcvtu53lp8rSZCcyLx585g8eTJTp05l69atdOjQgYEDB5KWlqZ3aLpr06YNp06dsj7+/vtv675HHnmEX375hfnz57Nq1SpOnjzJzTffrGO0jpWXl0eHDh2YMWNGhftff/113nvvPWbOnMmGDRvw9fVl4MCBFBYWWo+5/fbb2b17N0uXLuXXX3/lr7/+YsKECY76CA5zpXsFMGjQoHI/a99++225/XXlXq1atYoHHniA9evXs3TpUkpKShgwYAB5eXnWY670u2cymRg6dCjFxcWsXbuWL7/8ktmzZ/Pcc8/p8ZHspjL3CmD8+PHlfrZef/116766cq8AGjRowKuvvsqWLVvYvHkz1157LTfeeCO7d+8GnOjnShVOo3v37uoDDzxg/dpkMqnR0dHq9OnTdYxKf1OnTlU7dOhQ4b7MzEzV3d1dnT9/vvW1vXv3qoC6bt06B0XoPAD1xx9/tH5tNpvVyMhI9Y033rC+lpmZqXp6eqrffvutqqqqumfPHhVQN23aZD1m8eLFqqIo6okTJxwWu6NdeK9UVVXHjBmj3njjjZd8T129V6qqqmlpaSqgrlq1SlXVyv3uLVq0SDUYDGpKSor1mI8++kgNCAhQi4qKHPsBHOjCe6WqqtqnTx910qRJl3xPXb1XFvXq1VM//fRTp/q5khYkJ1FcXMyWLVvo37+/9TWDwUD//v1Zt26djpE5h4MHDxIdHU1sbCy33347ycnJAGzZsoWSkpJy961Vq1Y0bNhQ7huQlJRESkpKufsTGBhIfHy89f6sW7eOoKAgunbtaj2mf//+GAwGNmzY4PCY9bZy5UrCw8Np2bIl9913H2fOnLHuq8v3KisrC4Dg4GCgcr9769ato127dkRERFiPGThwINnZ2dbWgtrowntl8c033xAaGkrbtm2ZMmUK+fn51n119V6ZTCbmzp1LXl4eCQkJTvVzJYvVOon09HRMJlO5bzhAREQE+/bt0ykq5xAfH8/s2bNp2bIlp06dYtq0aVx99dXs2rWLlJQUPDw8CAoKKveeiIgIUlJS9AnYiVjuQUU/V5Z9KSkphIeHl9vv5uZGcHBwnbuHgwYN4uabb6ZJkyYcOnSIp59+msGDB7Nu3TqMRmOdvVdms5mHH36Yq666irZt2wJU6ncvJSWlwp89y77aqKJ7BXDbbbfRqFEjoqOj2bFjB08++ST79+9nwYIFQN27Vzt37iQhIYHCwkL8/Pz48ccfiYuLY/v27U7zcyUJknB6gwcPtm63b9+e+Ph4GjVqxHfffYe3t7eOkYnaZuTIkdbtdu3a0b59e5o2bcrKlSvp16+fjpHp64EHHmDXrl3lxv6Jil3qXp0/Tq1du3ZERUXRr18/Dh06RNOmTR0dpu5atmzJ9u3bycrK4vvvv2fMmDGsWrVK77DKkS42JxEaGorRaLxopH5qaiqRkZE6ReWcgoKCaNGiBYmJiURGRlJcXExmZma5Y+S+aSz34HI/V5GRkRdNBCgtLSUjI6PO38PY2FhCQ0NJTEwE6ua9mjhxIr/++isrVqygQYMG1tcr87sXGRlZ4c+eZV9tc6l7VZH4+HiAcj9bdeleeXh40KxZM7p06cL06dPp0KED7777rlP9XEmC5CQ8PDzo0qULy5Yts75mNptZtmwZCQkJOkbmfHJzczl06BBRUVF06dIFd3f3cvdt//79JCcny30DmjRpQmRkZLn7k52dzYYNG6z3JyEhgczMTLZs2WI9Zvny5ZjNZus/4nXV8ePHOXPmDFFRUUDduleqqjJx4kR+/PFHli9fTpMmTcrtr8zvXkJCAjt37iyXVC5dupSAgADi4uIc80Ec4Er3qiLbt28HKPezVRfu1aWYzWaKioqc6+fKZsO9RY3NnTtX9fT0VGfPnq3u2bNHnTBhghoUFFRupH5d9Oijj6orV65Uk5KS1DVr1qj9+/dXQ0ND1bS0NFVVVfXee+9VGzZsqC5fvlzdvHmzmpCQoCYkJOgctePk5OSo27ZtU7dt26YC6ttvv61u27ZNPXr0qKqqqvrqq6+qQUFB6k8//aTu2LFDvfHGG9UmTZqoBQUF1nMMGjRI7dSpk7phwwb177//Vps3b66OGjVKr49kN5e7Vzk5Oepjjz2mrlu3Tk1KSlL//PNPtXPnzmrz5s3VwsJC6znqyr2677771MDAQHXlypXqqVOnrI/8/HzrMVf63SstLVXbtm2rDhgwQN2+fbu6ZMkSNSwsTJ0yZYoeH8lurnSvEhMT1RdeeEHdvHmzmpSUpP70009qbGys2rt3b+s56sq9UlVVfeqpp9RVq1apSUlJ6o4dO9SnnnpKVRRF/eOPP1RVdZ6fK0mQnMz777+vNmzYUPXw8FC7d++url+/Xu+QdDdixAg1KipK9fDwUOvXr6+OGDFCTUxMtO4vKChQ77//frVevXqqj4+PetNNN6mnTp3SMWLHWrFihQpc9BgzZoyqqtpU/2effVaNiIhQPT091X79+qn79+8vd44zZ86oo0aNUv38/NSAgAB17Nixak5Ojg6fxr4ud6/y8/PVAQMGqGFhYaq7u7vaqFEjdfz48Rf9B6Wu3KuK7hOgfvHFF9ZjKvO7d+TIEXXw4MGqt7e3Ghoaqj766KNqSUmJgz+NfV3pXiUnJ6u9e/dWg4ODVU9PT7VZs2bq448/rmZlZZU7T124V6qqqnfffbfaqFEj1cPDQw0LC1P79etnTY5U1Xl+rhRVVVXbtUcJIYQQQrg+GYMkhBBCCHEBSZCEEEIIIS4gCZIQQgghxAUkQRJCCCGEuIAkSEIIIYQQF5AESQghhBDiApIgCSGEEEJcQBIkIYRd3HXXXQwbNkzvMGrs+eefp2PHjlV6z8qVK/n/9u4/pqmrjQP4t9RyLXCRSRkwBYu6jh8LzK2mAcYmA8KWZVP2I0BtqAT+IMsSQwcYNRGjc7I5JsvmkiWrsB8s2wJhgYEzG1nVMEaAyOYEZMUJ0ZjMoCFhYsHyvH+86Y23FFp4dcje55OYeM+55/E8lxvvk9tDj0KhkPaTqqurm7U7+b+FQqGAQqFYVH5arVYa7773FmNLjQskxpaJHTt2SA8TlUqFmJgYVFRU4NatW0s9tUXTarWoqalZ6mncc7m5uRgaGvLp3OVYTNXW1nrMb3JyEqtXr4ZGo4HD4ZjV393djcbGxn9iiowtGBdIjC0jzz77LK5evYqLFy/i6NGj+Pjjj1FZWbnU02JeqNVqPPjgg0s9jXsmJCTEY36NjY1ISEhAbGwsvv3221n9YWFhWL169T8wQ8YWjgskxpYRQRAQERGBqKgobNu2DZmZmfjhhx+k/pmZGRw+fBgxMTFQq9VISkpCQ0PDvDEdDgfKysqwZs0aBAYGwmAwwGazSf2uNxonT55EXFwcgoKCpELNxel0wmKxICQkBKGhoaioqIC3XYy2bNmCkZERlJaWSm/GXFwPVkEQoNVqUV1d7fXaeMvd9bFXe3s79Ho9AgICkJKSggsXLsjiVFVVITw8HKIooqioyKc3dG1tbdDpdFCr1UhPT8elS5dk/e5vhX799Vekp6dDFEUEBwfjiSeeQE9PD2w2GwoLCzE+Pi5dk/379wMAPv/8c+j1eoiiiIiICBiNRtlu5r7m19LSgs2bN2PlypXQaDTIycmR+rzdCwtltVphMplgMplgtVoXHYexJXFXd3ZjjN0zZrOZtm7dKh2fO3eOIiIiyGAwSG1vvvkmxcbG0vfff0/Dw8NUW1tLgiCQzWabM25xcTGlpKTQ6dOnyW6305EjR0gQBBoaGiIiotraWlKpVJSZmUnd3d3U29tLcXFxZDQapRhvv/02PfDAA9TY2Ej9/f1UVFREoijK5utubGyM1q5dSwcOHJB2Pyci6unpIT8/Pzpw4ABduHCBamtrSa1WyzZJ9cRb7q6Nag0GA9lsNjp//jylpaVRSkqKFOPrr78mQRDok08+ocHBQdq7dy+JokhJSUlz/rujo6MkCAJZLBYaHBykL774gsLDwwkA3bhxQ7qGq1atksYkJCSQyWSigYEBGhoaom+++Yb6+vrI4XBQTU0NBQcHS9fEtRGu1WqltrY2Gh4eps7OTkpOTqbnnntOiulLft999x0plUrat28f9ff3U19fH7311ltSv7d7wRMA1NTUNKvdbreTIAh0/fp1Ghsbo5UrV9KlS5dmneeat+taMXa/4AKJsWXCbDaTUqmkwMBAEgSBAJCfnx81NDQQEdGtW7coICCAfv75Z9m4oqIiys/P9xhzZGSElEolXblyRdaekZFBu3fvJqL/PtwBkN1ul/qPHTtG4eHh0nFkZCS988470vH09DStXbt23gKJiGjdunV09OhRWZvRaKSsrCxZW3l5OcXHx88Zx5fcXQ/iH3/8UepvbW0lADQ5OUlERMnJyfTaa6/JYhgMhnkLpN27d8+a265du+YtkERRpLq6Oo/x3M+dS3d3NwGQCihf89u+fbvHeL7cC57MVSDt2bOHtm3bJh1v3bqVKisrZ53HBRK7X/FHbIwtI+np6ejr60NXVxfMZjMKCwvx8ssvAwDsdjtu3ryJrKwsBAUFSX8+++wzDA8Pe4x37tw5OJ1O6HQ62ZhTp07JxgQEBGDDhg3ScWRkpPTxzvj4OK5evQqDwSD1r1ixAnq9Xjqur6+XxT9z5sycOQ4MDCA1NVXWlpqaij/++ANOpxNnzpyRxaqvr19Q7omJibI8AEi5DAwMyPIAgOTk5DnnutgxFosFxcXFyMzMRFVV1Zw/nzv19vbihRdeQHR0NERRxNNPPw0AGB0dlZ03X359fX3IyMjwGN/Xe8EXTqcTn376KUwmk9RmMplQV1eHmZmZBcVibKmsWOoJMMZ8FxgYiI0bNwIAjh8/jqSkJFitVhQVFWFiYgIA0NraijVr1sjGCYLgMd7ExASUSiV6e3uhVCplfUFBQdLfVSqVrE+hUHhdY3SnF198UVZEuM9vIfR6Pfr6+qTj8PBw9Pf3A/At9ztzca17+qcf2vv374fRaERraytOnDiByspKfPXVV7L1QHf6+++/kZ2djezsbNTX1yMsLAyjo6PIzs7G1NSU7Nz58lOr1XPOydd7wRcnT57ElStXkJubK2t3Op1ob29HVlbWguIxthS4QGJsmfLz88OePXtgsVhgNBoRHx8PQRAwOjoqvV3wZtOmTXA6nfjrr7+Qlpa2qHmsWrUKkZGR6OrqwlNPPQUAuH37Nnp7e/H4448DAERRhCiKs8b6+/vD6XTK2uLi4tDR0SFr6+jogE6ng1KphFqtlopEl8Xk7klcXBy6urpQUFAgtf3yyy9exzQ3N8vavI0BAJ1OB51Oh9LSUuTn56O2thY5OTker8ng4CDGxsZQVVWFqKgoAEBPT4+vaUkSExPR3t6OwsLCWX13415wsVqtyMvLw969e2Xthw4dgtVq5QKJLQtcIDG2jL366qsoLy/HsWPHUFZWhrKyMpSWlmJmZgZPPvkkxsfH0dHRgeDgYJjN5lnjdTodtm/fjoKCAlRXV2PTpk24du0a2tvbkZiYiOeff96neezcuRNVVVV4+OGHERsbi/fee8+nL/7TarU4ffo08vLyIAgCNBoN3njjDWzevBkHDx5Ebm4uOjs78eGHH+Kjjz6aM44oigvOfa48duzYAb1ej9TUVNTX1+P8+fNYv379nGNKSkpQXV2N8vJyFBcXo7e3F3V1dXOePzk5ifLycrzyyiuIiYnB5cuX0d3dLX1UqtVqMTExgfb2diQlJSEgIADR0dHw9/fHBx98gJKSEvz+++84ePCgTzndqbKyEhkZGdiwYQPy8vJw+/ZttLW1YdeuXXftXrh27RpaWlrQ3NyMRx99VNZXUFCAnJwcXL9+nX+9n93/lnoRFGPMN+6/xeZy+PBhCgsLo4mJCZqZmaGamhp65JFHSKVSUVhYGGVnZ9OpU6ek89etWydbLDs1NUX79u0jrVZLKpWKIiMjKScnh3777Tci8rxouKmpie7872N6epp27txJwcHBFBISQhaLhQoKCrwu0u7s7KTExERp0blLQ0MDxcfHk0qloujoaDpy5IjX6+Mtd0+Lgc+ePUsA6M8//5TaDh06RBqNhoKCgshsNlNFRcW8i7SJiFpaWmjjxo0kCAKlpaXR8ePH51yk7XA4KC8vj6Kiosjf358eeughev3116WF1EREJSUlFBoaSgCkn9WXX35JWq2WBEGg5ORkam5uJgB09uzZBeXX2NhIjz32GPn7+5NGo6GXXnpJ6vN2L3gCt0Xa7777LoWEhNDU1NSscx0OB4WEhND7778vtfEibXa/UhAtYCEBY2xZu3nzJkJDQ3HixAls2bJlqafD/gUUCgWampoWva2MzWZDeno6bty4sey+QZz9u/FHbIz9H/npp5/wzDPPcHHE7qr8/HyEhobi8uXLCxqXkJCAixcv3qNZMfa/4TdIjDHGFs1utwMAlEolYmJiFjR2ZGQE09PTAID169fDz4+/eYbdP7hAYowxxhhzw+U6Y4wxxpgbLpAYY4wxxtxwgcQYY4wx5oYLJMYYY4wxN1wgMcYYY4y54QKJMcYYY8wNF0iMMcYYY264QGKMMcYYc8MFEmOMMcaYm/8Ak8W262ZWwt4AAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Application to ABLIM1 numbers\n",
        "* Assuming A0 is unchanged from early  (maybe MD data can help us update this)\n",
        "* Sorenson paper indicates that net charge densities approaching 0.15 gives eff conc 3v=1.75 --> v=0.58 vs maybe 3v=1.6--> 0.53 for densities < 0.02\n",
        "\n",
        "\n",
        "try using shading i used way below"
      ],
      "metadata": {
        "id": "Gt7PKH12_0ln"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "750-373"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6Dt1AJvqncd-",
        "outputId": "eadefd34-92a7-481b-e3f0-edfd3661bcd3"
      },
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "377"
            ]
          },
          "metadata": {},
          "execution_count": 53
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#truncC = 473-343   # from position 343 to 473 that we are running martini w\n",
        "#full = 750-373     # full length\n",
        "\n",
        "print(\"this 'full' number discrees with my earlier use of 366\")\n",
        "rs = np.arange(0,350)\n",
        "#nuUnphospho = 0.58 # for fully unphosphorylated molecule\n",
        "#nuPhospho = 0.53  # changing two phosphos in a long change doesn't alter v significantly\n",
        "\n",
        "# change in phospho might move from say 0.25 to 0.3, or 0.05 change\n",
        "Ns = nFrag\n",
        "sqrt_re2 = A0 * (Ns**nup)\n",
        "#print(sqrt_re2)\n",
        "#re2 = sqrt_re2**2'\n",
        "reTrunc = 170 # before\n",
        "re2 = reTrunc**2\n",
        "plt.plot(rs,pr(rs,re2),'r--',label=f'Truncated fragment re={reTrunc}')\n",
        "\n",
        "\n",
        "\n",
        "#Ns = full\n",
        "#sqrt_re2 = A0 * (Ns**nuPhospho)\n",
        "#print(sqrt_re2)\n",
        "#re2 = sqrt_re2**2\n",
        "repfull = 276 # before\n",
        "re2 = repfull**2\n",
        "plt.plot(rs,pr(rs,re2),'r-',label=f'full fragment re={repfull} (in vivo), +2P')\n",
        "plt.ylabel('P(r)')\n",
        "plt.xlabel('Re,end-to-end distance [A]')\n",
        "\n",
        "#sqrt_re2 = A0 * (Ns**nuUnphospho)\n",
        "#print(sqrt_re2)\n",
        "#re2 = sqrt_re2**2\n",
        "rewtfull = 311 # before\n",
        "re2 = rewtfull**2\n",
        "plt.plot(rs,pr(rs,re2),'k-',label=f'full fragment (in vitro), re={rewtfull}, 0 P')\n",
        "plt.ylabel('P(r)')\n",
        "plt.xlabel('Re,end-to-end distance [A]')\n",
        "\n",
        "\n",
        "b=30.4*10. # 30 nm --> 300 AA for actin/actin separation, dz from Irving 2011\n",
        "plt.scatter(b,pr(b,re2),label='Z-disk actin lattice spacing',s=50,edgecolor='blue',facecolor='white')\n",
        "plt.legend(loc=3)\n",
        "#plt.title('our data for ablim1 [UNORMALIZZED]')\n",
        "plt.gcf().savefig(\"pr_sim.png\",dpi=300)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 467
        },
        "id": "kMWv5O-X_zSk",
        "outputId": "213c26cb-17df-44b0-afe3-beb06a474704"
      },
      "execution_count": 77,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "this 'full' number discrees with my earlier use of 366\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Van valen application of  Worm like chain model\n",
        "(WLC is probabli not the best fit for IDPs or our data)\n",
        "\n",
        "\n",
        "Assuming here that\n",
        "* villin headpiece remains bound to actin\n",
        "* LIMs 2 and 3 are available to bind titin\n",
        "* LIMs 2 and 3 availability are modulated by MSSSP phosphorylation (between LIMs 2 and 3)\n",
        "\n",
        "The WLC chain uses the persistence length, $\\zeta$, which is approximately $b/2$ (I believe b is the width of an aa, roubhly 3.4) to give the mean squared end-to-end distance (\\eqn{eqn:r3}):\n",
        "\n",
        "Usintg the Rend equation\n",
        "\n",
        "\\begin{equation}\n",
        "\\langle R^2 \\rangle = 2 \\zeta L_0 \\left[ 1 - \\frac{\\zeta}{L_0}\\left(1- \\exp(-L_0/\\zeta)\\right)\\right]\n",
        "\\end{equation}\n",
        "where $L_0 = N L_b$ with $L_b$ and $N$ representing the length of an amino acid and the number of amino acids, respectively. \\mnote{verify b and Lb relationshuip}\n",
        "\n"
      ],
      "metadata": {
        "id": "RWUOZdeQqtVd"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "Je0EtFOB-RcE"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "zeta = 0.35 #persistence length [nm]\n",
        "lenPerResi = 0.34 # [nm]\n",
        "#D = 53 *lenPerResi   # Residue between CaMBR C termimus (R414) and AID N-terminus (I467) is 52 a.a.\n",
        "                     # thus the distance should be 3.4 x 53\n",
        "#L = 8 * lenPerResi  # residue number between C-terminal of DH and N terminus of AID (DH is absorbed on CaM's surface)\n",
        "\n",
        "# for the effective concentration\n",
        "def G_DZL(zeta,D,L):\n",
        "    prefac = np.sqrt(3/(4*np.pi*zeta*L))\n",
        "    prefac =prefac*prefac*prefac\n",
        "    expon = -3*D*D/(4*zeta*L)\n",
        "    return prefac * np.exp(expon)\n",
        "\n",
        "# for R**2, see Eqn 5 in the mapid paper\n",
        "def RR_ZL(zeta,L):\n",
        "    L = float(L)\n",
        "    prefac = 2*zeta * L\n",
        "    expon = np.exp(-L/zeta)\n",
        "    expon = (zeta/L) * (1-expon)\n",
        "    expon = 1 - expon\n",
        "    return prefac * expon\n",
        "\n",
        "RR_ZL = np.vectorize( RR_ZL )"
      ],
      "metadata": {
        "id": "e818Zwsbkrv3"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "Tt0osC0Sy8ef"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# prompt: twiny plot example\n",
        "\n",
        "fig, ax1 = plt.subplots()\n",
        "\n",
        "ax1.plot([1, 2, 3], [1, 2, 3], label='plot 1')\n",
        "ax1.set_xlabel('x-axis')\n",
        "ax1.set_ylabel('y-axis 1')\n",
        "\n",
        "ax2 = ax1.twinx()  # Create a twin y-axis\n",
        "ax2.plot([1, 2, 3], [4, 5, 6], color='red', label='plot 2')\n",
        "ax2.set_ylabel('y-axis 2')\n",
        "\n",
        "# Combine legends from both axes\n",
        "lines, labels = ax1.get_legend_handles_labels()\n",
        "lines2, labels2 = ax2.get_legend_handles_labels()\n",
        "ax2.legend(lines + lines2, labels + labels2, loc='upper left')\n",
        "\n",
        "plt.show()\n"
      ],
      "metadata": {
        "id": "AjhYMGL1y99T"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fig,ax = plt.subplots()\n",
        "\n",
        "\n",
        "nRes = np.linspace(1,97)\n",
        "Ls = nRes * lenPerResi # [nm]\n",
        "zeta = 300 # [nm]\n",
        "rr = RR_ZL(zeta,Ls)\n",
        "ax.plot(Ls,rr, label=f\"zeta={zeta} [nm]\")\n",
        "\n",
        "zeta = 10 # [nm]\n",
        "rr = RR_ZL(zeta,Ls)\n",
        "ax.plot(Ls,rr, label=f\"zeta={zeta} [nm]\")\n",
        "ax.set_xlabel(\"L [nm]\")\n",
        "ax.legend()\n",
        "\n",
        "axt = ax.twiny()\n",
        "axt.plot(nRes,rr,lw=0)\n",
        "axt.set_xlabel(\"Num. aa\")"
      ],
      "metadata": {
        "id": "UBTqs4lcuXK6",
        "outputId": "824586db-cba5-4bd1-b23e-c26c482cade4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 507
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 0, 'Num. aa')"
            ]
          },
          "metadata": {},
          "execution_count": 25
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "These all need to be double checked relative to the original Shoemaker(?) and Philips paper."
      ],
      "metadata": {
        "id": "GixKtDlwuYBA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "Ang_to_nm = 0.1\n",
        "Ang_per_res = 3.4 # [A]\n",
        "\n",
        "D = 40*2 * Ang_to_nm # about 40 Ang across for 2 LIM domains\n",
        "print (D, \" [nm]\")\n",
        "\n",
        "\n",
        "aaNterm = 98\n",
        "L_freeN = aaNterm * Ang_per_res * Ang_to_nm # M1-M98\n",
        "print (L_freeN, \" [nm]\")\n",
        "\n",
        "aaCterm = 358. ; print(\"double check\")\n",
        "L_freeC = aaCterm * Ang_per_res * Ang_to_nm # Q338-M696\n",
        "print (L_freeC, \" [nm]\")\n",
        "\n",
        "# 2 LIM domains (not four?)\n",
        "print(\"Need actual radii of gyration\")\n",
        "twoLIM=4*2 # 40 A per lim, 2 of them.\n",
        "MSSSPseq = 5*Ang_to_nm * Ang_to_nm\n",
        "fourLIM = twoLIM + MSSSPseq + twoLIM"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wT0u-hNnkVBN",
        "outputId": "45c001d8-fb57-49b7-feec-cb1560de96df"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "8.0  [nm]\n",
            "33.32  [nm]\n",
            "double check\n",
            "121.72000000000001  [nm]\n",
            "Need actual radii of gyration\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## We will use the Kd2= 0.565 uM of AID from experimnts as the reference unit\n",
        "\n",
        "# PKH I think we want the distance from a bound villin headpiece to the first LIM domain\n",
        "#tether_length = np.array([L_freeN,L_freeC])\n",
        "unphospho=L_freeC+fourLIM   # extended\n",
        "phospho = L_freeC + twoLIM\n",
        "tether_length = np.array([unphospho,phospho])\n",
        "\n",
        "conc = G_DZL(zeta,D,tether_length)\n",
        "\n",
        "#reference point\n",
        "ref_conc = conc[0]\n",
        "ref_unit = 1. #fit_tAID.  TBD\n",
        "\n",
        "effective_conc = (conc/ref_conc)*ref_unit\n"
      ],
      "metadata": {
        "id": "fzm4n-MukOBR"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.rcParams['font.size']=12\n",
        "plt.rcParams['axes.labelsize'] = 12\n",
        "plt.rcParams['xtick.labelsize'] = 12\n",
        "plt.rcParams['ytick.labelsize'] = 12\n",
        "#['figure.figsize'] = 2,1\n",
        "\n",
        "\n",
        "# C-terminus\n",
        "res = 1\n",
        "Lmin = res*Ang_per_res * Ang_to_nm  # tether length [nm]\n",
        "#res = aaCterm\n",
        "#Lmax = res*Ang_per_res * Ang_to_nm  # tether length [nm]\n",
        "Lmax =tether_length[0] # extended\n",
        "Ls = np.linspace(Lmin,Lmax,1000)\n",
        "\n",
        "#L_per_res = 0.34 #nm\n",
        "#zeta=3\n",
        "\n",
        "\n",
        "ls = np.linspace(tether_length[1],tether_length[0],10)\n",
        "\n",
        "# Flexible (e.g. Cterminal end is highly phosphorylated)\n",
        "fig, ax1 = plt.subplots()\n",
        "ys = (G_DZL(zeta,D,Ls)/ref_conc)*ref_unit\n",
        "ax1.plot(Ls, ys,'k--',label='++p C-term/swollen coil')\n",
        "conc = G_DZL(zeta,D,tether_length)\n",
        "effective_conc = (conc/ref_conc)*ref_unit\n",
        "ax1.scatter(tether_length[0],effective_conc[0],facecolor='white',edgecolor='blue',s=25,zorder=3,label='-p MSSSP')\n",
        "ax1.scatter(tether_length[1],effective_conc[1],facecolor='white',edgecolor='red',s=25,zorder=3,label='+p MSSSP')\n",
        "\n",
        "ys = (G_DZL(zeta,D,ls)/ref_conc)*ref_unit\n",
        "ax1.fill_between(ls, ys, edgecolor='none',facecolor='green', alpha=0.2)\n",
        "\n",
        "# Stiffer (C terminal comprises series of moderately-folded domains)\n",
        "zetaS=zeta*5.\n",
        "ys = (G_DZL(zetaS,D,Ls)/ref_conc)*ref_unit\n",
        "ax1.plot(Ls, ys,'k-',label='-p C-term /(coil+hairpin)')\n",
        "conc = G_DZL(zetaS,D,tether_length)\n",
        "effective_conc = (conc/ref_conc)*ref_unit\n",
        "ax1.scatter(tether_length[0],effective_conc[0],facecolor='white',edgecolor='blue',s=25,zorder=3)#,label='N-term')\n",
        "ax1.scatter(tether_length[1],effective_conc[1],facecolor='white',edgecolor='red',s=25,zorder=3)#,label='C-term')\n",
        "\n",
        "ys = (G_DZL(zetaS,D,ls)/ref_conc)*ref_unit\n",
        "ax1.fill_between(ls, ys, edgecolor='none',facecolor='green', alpha=0.8)\n",
        "\n",
        "#####\n",
        "ax1.set_xlabel(\"L [nm]\")#fontsize=8)\n",
        "ax1.legend(\n",
        "    #fontsize=10.5,\n",
        "    loc=0)#(0.5,0.6), ncol=1)\n",
        "\n",
        "#ax2.tick_params(labelsize=8)\n",
        "#ax1.tick_params(labelsize=7)\n",
        "ax1.set_ylabel(\"[IDR]$^{eff}$  [$\\mu$M]\")#,fontsize=8)\n",
        "ax1.set_yticks([0,2])#,6,8,10])\n",
        "\n",
        "\n",
        "plt.gcf().savefig(\"effconc.png\",dpi=300)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 462
        },
        "id": "V97x7lBeia__",
        "outputId": "944cc817-cc3d-4e3f-e714-1d64924b9818"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Doing some back of the envelope calculations for the myofilament.\n",
        "The N-terminal fragment of ABLIM1 is ca 97 a.a. A 100 aa fragment would be about 34 nm if end to end. In the WLC model, $R^2$ is 23 nm$^2$ or $R=4.8$.\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "9qPnplubkE1t"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "aaNterm = 97\n",
        "L_freeN = aaNterm * Ang_per_res * Ang_to_nm # M1-M98\n",
        "print (L_freeN, \" [nm]\")\n",
        "rsqd = RR_DZL(zeta,L_freeN)\n",
        "print(\"R^2: %3.1f [nm]\"%rsqd)\n",
        "print(\"sqrt(R^2): %3.1f [nm]\"%np.sqrt(rsqd))"
      ],
      "metadata": {
        "id": "DDQAHGLM97oF",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "be4f94af-74af-4585-862e-b9c5e8a26618"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "32.980000000000004  [nm]\n",
            "R^2: 22.8\n",
            "sqrt(R^2): 4.8 [nm]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The entire sequence is about 780 a.a. Sqrt of the squared distance suggests an avg distance of 13.6 nm.  "
      ],
      "metadata": {
        "id": "Rog9jibKlSCn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "aaNterm = 780\n",
        "L_freeN = aaNterm * Ang_per_res * Ang_to_nm # M1-M98\n",
        "print (L_freeN, \" [nm]\")\n",
        "rsqd = RR_DZL(zeta,L_freeN)\n",
        "print(\"R^2: %3.1f [nm]\"%rsqd)\n",
        "print(\"sqrt(R^2): %3.1f [nm]\"%np.sqrt(rsqd))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cfXAf-JRjGSY",
        "outputId": "8b58a411-ad41-4fbf-d233-8f9eff63f7f7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "265.2  [nm]\n",
            "R^2: 185.4 [nm]\n",
            "sqrt(R^2): 13.6 [nm]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "mEX_Jb4Cldfu"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}