docs/notebooks/base_steps_tutorial.ipynb

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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analysis of local base-steps parameters\n",
    "\n",
    "* This tutorial discuss the analyses that can be performed using the [dnaMD Python module](http://do-x3dna.readthedocs.io/en/latest/api_summary.html) included in the _do\\_x3dna_ package. The tutorial is prepared using [Jupyter Notebook](https://jupyter.org/) and this notebook tutorial file could be downloaded from this [link](http://rjdkmr.github.io/do_x3dna/tut_notebook/base_steps_tutorial.ipynb).\n",
    "\n",
    "\n",
    "* Download the input files that are used in the tutorial from this [link](http://rjdkmr.github.io/do_x3dna/tutorial_data.tar.gz).\n",
    "\n",
    "* Two following input files are required in this tutorial\n",
    "    * ``L-BPS_cdna.dat`` (``do_x3dna`` output from the trajectory, which contains the DNA bound with the protein)\n",
    "    * ``L-BPS_odna.dat`` (``do_x3dna`` output from the trajectory, which only contains the free DNA)\n",
    "    \n",
    "    These two file **should be** present inside tutorial_data of the current/present working directory.\n",
    "    \n",
    "    \n",
    "* The Python APIs **should be** only used when ``do_x3dna`` is executed with ``-ref`` option.\n",
    "\n",
    "\n",
    "* Detailed documentation is provided [here](http://do-x3dna.readthedocs.io/en/latest/dna_class_api.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Importing Python Modules\n",
    "\n",
    "* [numpy](http://www.numpy.org/): Required for the calculations involving large arrays\n",
    "\n",
    "\n",
    "* [matplotlib](http://matplotlib.org/): Required to plot the results\n",
    "\n",
    "\n",
    "* [dnaMD](http://do-x3dna.readthedocs.io/en/latest/api_summary.html): Python module to analyze DNA/RNA structures from the do_x3dna output files.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import dnaMD\n",
    "%matplotlib inline\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initializing DNA object and storing data to it\n",
    "\n",
    "* [DNA object](http://do-x3dna.readthedocs.io/en/latest/dna_class_api.html#dnaMD.dnaMD.DNA) is initialized by using the total number of base-pairs\n",
    "\n",
    "\n",
    "* One base-step is formed by two adjacent base-pairs. Therefore, total number of base-steps is less than one of total number of base-pairs.\n",
    "\n",
    "\n",
    "* Six base-pair parameters (**shift**, **slide**, **rise**, **tilt**, **roll** and **twist**) can be read and stored in DNA object from the input file using function [set_base_step_parameters(...)](http://do-x3dna.readthedocs.io/en/latest/dna_class_api.html#dnaMD.dnaMD.DNA.set_base_step_parameters).\n",
    "\n",
    "* To speed up processing and analysis, data can be stored in a HDF5 file by including HDF5 file name as a argument during initialization. Same file can be used to store and retrieve all other parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Reading file : tutorial_data/L-BPS_cdna.dat\n",
      "Reading frame 1000\n",
      "Finished reading.... Total number of frame read =  1001\n",
      "\n",
      "Reading file : tutorial_data/L-BPS_odna.dat\n",
      "Reading frame 1000\n",
      "Finished reading.... Total number of frame read =  1001\n"
     ]
    }
   ],
   "source": [
    "## Initialization\n",
    "pdna = dnaMD.DNA(60)     #Initialization for 60 base-pairs DNA bound with the protein\n",
    "fdna = dnaMD.DNA(60)     #Initialization for 60 base-pairs free DNA\n",
    "\n",
    "## If HDF5 file is used to store/save data use these:\n",
    "# pdna = dnaMD.DNA(60, filename='cdna.h5')     #Initialization for 60 base-pairs DNA bound with the protein\n",
    "# fdna = dnaMD.DNA(60, filename='odna.h5')     #Initialization for 60 base-pairs free DNA\n",
    "\n",
    "## Loading data from input files in respective DNA object\n",
    "# Number of base-steps = Number of base-pairs - one\n",
    "# Number of base-steps in a 60 base-pairs DNA = 59\n",
    "# \"bp=[1, 59]\" will load local base-pair parameters of 1 to 59 base-steps\n",
    "# \" parameters = 'All' \" will load all six parameters (shift, slide, rise, tilt, roll and twist)\n",
    "pdna.set_base_step_parameters('tutorial_data/L-BPS_cdna.dat', bp_step=[1, 59], parameters='all', step_range=True)\n",
    "fdna.set_base_step_parameters('tutorial_data/L-BPS_odna.dat', bp_step=[1, 59], parameters='all', step_range=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Local base-step parameter of a base-pair directly from dictionary\n",
    "\n",
    "* The ``DNA.data`` is a python dictionary which contains all the data as a Python Dictionary. For a base-step, parameter as a function of time can be directly extracted.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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9+97DglX6+R5R2YKr4lNIy48WsH3/617EiTeZ+a3W2osyzVgSveDP8X97DafcWppI2QqaXHZCgZlbmHkUgAEAxhDRzgAuBzACwF4AegL4acC5tzLzaGYe3adPn9TLNvJXz2LM78YF7i850EqqX1TDYN//OKiNSm2YTsdTmt1plcwZsczxlSmqDFnXzySj6UobURzTWZiQ9PdFrvnI9SnELlp0efzfY9xk5fomADCaV+DnuSmL8Pj7X+C3T+oFygG/H1/6ogTmEVVPa3KTQBrqm8UiuwO9Bas24IuVXgE3Z9k6jPzlM/jcnlgZR5DdnMKkwTwLh8yjj5h5JYDxAI5m5gW2aWkTgH8BGJN1eRycJRl1+NNc3Pf2XBzw+/F49/MVie71h2enhjZwdd8+17zofnacm6bJwSJXcMu4YiYTkJUVMiwqyD/qDLtTmabgOJqJcNurM/GDB5L7WybNWa49319H4jwKZ3Z2Egd0Qenoo9DVwWoIhbia2FVPTMGOv3wGm5uL2OeaF7HvtS969j80aR7WbW7BfyfPj7zWGzOWusIDAG59ZWassqiUBmr5lQpZRR/1IaLu9ucOAI4AMJWI+tvbCMBJAD4Kvkrt8IekvjPb8jfMClEfyff/d4oaf9P4Gfg4JCwxqP6XawqhxTZwWGdbMcMEYZDmFaeDGTdlEQZf9qRnm7OATtq48xQKhN8EjKhNuer/9Oarck0h+Br+fY4G40TQRXHNU5+4zvRCghG/d56C8WmBFH2NIK756MGJVii4f1DgL5vJ5U7/5wQc+IfxgftNAihmLV3nyU6cZ00hqzWa+wO4i4jqYAmi/zDzE0T0IhH1gfVuJgO4IKPyxMKf5sLp3GJkWi4bXYSNfII6a8eOzTEbSOB9stYUQu73/fvf058T4/o3vVS+ZGXYSDnMFDF76Trcorwz/7HOuygknJH3txem4eLDtgcQPDGr3KdgXmec6rXJUFNwfus39xkcKwSbyz6kU6/Uzvzap6di/2G9AbS+WfwOh1z/EtrVF9C1sQFAvqNssoo++oCZd2fmXZl5Z2a+yt5+KDPvYm/7hhKhlCtKqbOt/06DC0vbUMlLD5ph64xO/fbVoFJUQ40/OGTEFMYJf3sNN78UbIsNkpEcw/qxeHX5OhFNCcNx35vrNQ36X7U/JDUuf3z+M/dz8Ixq8+ijTxeu0ZYvifmIlDDbL1ZuwLwVIf4zpUh+31slqOtc/+PlGbHzfa2z/Ql+7dR/epZz4ax3kWdxYCEzmg0oZbmwR+qxTtZvDrtGUKNy7NhBmkRcG3SStjvbtq3e9urMyIl4t75SEgIfzl+FR94Ltt8Gtc04Ji7d4kFhQqHMp2Bwq+aWIr5/33v46Asre2dd0twdCkHvO848hTNvf9t3ri0UEgjFkg+Nse+1L2L/64IHArqyF5nxxoyleC0k8isuD7+rj6BTMXHEV1M7vu/tz/HG9PDfXJoTY31YuX4z9r/uRXxs16c8kJX5qFXj1xA45qhFV1nDHc367c1FRlNL0Q2ldG8fUI5StFTAfSoYtTh29NP3HhR4zO+eMs/iGdS3xvEv6kwlcXwKoY5m+//0JWs9M7uTmo889w18P/7jzH9LS8S7D6NkPoo+ln3/nfNO/6cVcT772uPiF0DDY5OtZx72tJP81jTTZlz+iDUfyOQ3O0V9ffoyzFuxATeNn46/n7FnamWpBNEUIigW2e1c/Z2saXXSdVZh9Teos25pYZxz10Q3H4r//mWdSES50hg1PZ/SIulBprhKTRGqpvD69KV4dZrZPJcyh2RA+WIswaDlscnz8emiNdEHIp6ATDpv4uw73zF2NG9uLgbUoSoOx8lK/OefYR50V/9jyCK44r6QVNquELU/OMuCN1cpICIJIhQ0qB1JC7P7Al1Hr/1qQ30KSmtZr5kYF9begtpzU7GIVz4zn7wXZY9Poxo++UFl+ZAcgh5lpYLr8+Xr3cl7Z9w2wWNmKROqys2M8yZVULaTbnq9LHWIZz0Ff4cW42bqsfdMCJ95u8MVT7ufX5y62CgB5MOT5mGHnz+N2faMcfXZqee9HmFOScKpt76FXz5Wnmpbq0nVoK91NIZwbJ+UHa0SJoB/99Qn+Potb6ZRNCNEKGhQJ7q0KJqCY58tZWyMvhaBsH5zvCUmgyrIy5/6BIKmABubWjD4sidx0/jpBiu4Vd5i0lojISgSqNIyvjptKX74wPvGqa3d+/q+V0NoTdakVfjv5C9w4f9Osstg7mj2o2oKVzwaHunt9zuQ4lMI4skPrZTO02wthwFXoqnlPOO2CUiTsNqmE2Km/pqsYJ+1wdUUlMJf/cQUPP1hKWX2ra/MLEusWU1EKGhYsqbksCwyu5XNieQoaQpm19NHgIT5FPT7rvKlY/DPhQCAFeutVBf/fnM2Rl0VvrRlGu0iLZtsYKerfmbGmzOWJVyjonSOM0s8UR58X7dUjb7l6Y8WAiilU3CIJRQq6PVMJq+1KJP3/IStT9HUUsQuv3oW/w0JOggj7J3pBkGBQgGOX9C7/YN54fmPKh2krLBnmjtXcTQFVYjf/tosXHhP9imzHUQoaFBHHKqm4PgG3JBQg06FwZ6Ja+52Dl6YxbTe+W//lb+/UYqfzyjWLq3bmPgUHpw4D6f9861EKbzVZ6rOEg86xk+wplC9IefJ//CaDOLcyj/5i5mNtSUTn0LYZLKw81ZtaMKaTc2eAU5ao+A0rEdfujE8/1HaeZ2ckOZaJC4Mos0LBV3CMLVSF4vl4X0mSwM6V5i5ZB3GfVKef+aVaUsx4hfPYOLs8gZhWj90wUemk5WAdFToAgGr1jeVOZzjdpZBna76LOba8fKzl5bi5oNWISu/TtwIMO++QPOW0d3TQdvpBfwGfx3687hpGPGLZ7B6Y1PoeYBZVmCnE3PqtrEPxj5O1bK/4TMxzVoanCkgaF7IUx8u8MxtcIjSruKuSZLWIODeCZ/j3c9XuBNgRSjkiFs0eUzUUVZzsaiYj5wJMdb3ME3BuYY/EZeDEwUzcU55/iRTM8GUBas9OVnUc41GhSG3WbWhCQ9Nio4NJxAuuncSzvv3RCxevVEpR/Tt3WIwazWFFiWpGVCaE9Ci2CdOMXTA6crjN7GE+WCc4pUVs0pt+ScPvV+2TS/Y9Of7Oxknzn+VY74IKXdJUwg+5o0Z5emgg8rpdeA7n0sP0u/TOPnmNwKvHdTk/vDsp/odBs76sLks1Von+843ZuMrf39DWY+D8dq0pRifIIFh2rTJeQrRy12WPrew4mh2fQoWYWMMp8NZvKZ8QhUAvPd5sO3SdDCysamIA/8wHrsP6u5uc8pospB8WCf4o/9MxrhPFmPXAd1Cr1EolEbuqpYSK6a+yJ7GfusrMzB98VoUGR7B1GB75Ryn3AfzVmKZL114EN/12Wg/W7SmzPYdaj4K2F6tEMf/TCwXyLo7Bd09amARtr9g4GjWlaM0o9m3j5UJoO49gq8V9k6DJgvWB2wPnCnvDuysSKogyicQpvu+65TU69+4PV2nfFLaqFAI33/uv99xPxeL5XlkTHIfxTUBecuXvOI5HeZGg0Routt8MG8ldurfFfNWWBqOLn5aLR8RKTO+S8fEiqln9mhdQZPeCj77638mztUep+M1X2jkkTe8Enq8v/iliBzfcRlq/UEmMF0ZoqJ+woqdZE1yb0iqXwMrUeliOUG+J2fAUFauwNn/pc9hJtdyrUd/XNI26/ycPJmP2qZQiNivjrKteQpek4xJbne/oy8IvaPO6FQtza7fI/pY/yGfLFiNL934Or5z0HauSt2gmZ2lXpugjgIVM0GMEVWxaDYR0BkNOoKvQ0Od8T1M8DyzoMZfQZhopeg6niIDBZN37TsmNLmevSvpMq7l6VZKekRY1JIJQTPIdfUU8LYljxnLfo+rNjTh2qf1g5DFqze6obela+jLlbRTd06rJFosbdqkUIjTkNUZzW7qantfWL02rSQ6wRK3gqhXiJMAzd94HVPXlC9Wu+kh6jUjMPWsAlFpnV5PAzQuBorMWnNCfYE88dt1vlXOOrRLt/qGCTXXNBLD5JQ2unttbimirhBfOIaV26kXcYIWwq69uaWIFma0r69z32fSoLWgGeS6emqVpVQYtU06m6cuCE5hf/7dk8rmkgTNOUraqTunLV9rZgbNgjbpaI7z/qyQVOtzc5Hx2aI14VkjbUwFz71vf1627GFLWKB3BJvirDTm/+6GGZKrKeg6a9UGWyAlrt3eNm3RGm0kSBDNRdY67f0mgfo6R1OwytaxXbqagglhppHq37t824X/Oym26YKZgx2zKP2mOBlmNzUXsdqeV+Ev50F/eAnDf27VB6duJ53fEtenoD6aZo1QCNJYNjW3YNm6cn+gzixHVD4I/MH97+FSg4WXnPr0xaqNEUdmR5sUCnE0hWafpnDkDa9gpr24zgPvBNu0TTWFWUvX4dy7Jnq2zTRY+zWIeJqC/juhlEhO96h+8vAH7mfLp+CNaz/tn2+VnxTCpqYW7cjRbxKo9030qar5yE/AhK5a+xRenbY0trlxxpK1uP21WYH7ndus2tBkfE01Cs6fksGZDDr4sicxfqoVdTd/5YbYs8wBrzBRhWGgT0F5Ni3Fkv+lNHmtvOY99/FCDP/5M5i7vDxycOpCfZ4qf3v/7+QvQrMC68qXF9qUUFi1vimyIvpHXas2NLkvzp9x05l5qiOOOqk2vvc+X1HRSl6xhAIYd781B0MufxLFIntmajuj8eufCx5RAtYoyWlWzk+Om8N/3eYWbeNsV+/t9F2fQotjPkpZKKiffa+vFFlTpl+lWoYwAp2cBmVQyx01SneOXRrDpGE68FeTxf3ysfgLLaoKgdoRB/sUSseoQRO6+RION40vX6wJCDYdMSf3KVRz8mNS2pRQ2O2q53Dija+HagrNvpf71ZvfcJ3GOrPOYwFrvJo6mgHvKCeJlqA28rAOeerC1W6cOgCArTwrzJbdt5TTidwG9MQHCzRXKlFQpYLdOQWN2oJYt6lZ2zjb+Rr6+3YKAqcBBnUESQl7Z84zPutf/nULUi1CKEEdiFFQgXJMQ8SSgUk6OFPHcZPShtRJiKYERbgF+RTUwZna7sP8gkG+FCc7sQ5/v2FK/kRCG3Q0f7poTaC6vWLdZjTUl1cu1afg55L7J+OYnfujne+8OKNl1U5aaSXRTYZzOPrPr2J43y6ee6l5btyGAvPFWQjlmkJcp9u6Tc3axul/F/fYi/o476EC14sW1Ybu/wVO8Vau95pUau1TMGWhMrEwahnZJE5T06VpPaP1BE9PfUdFj/lIL5Sc0GrrfiXcsHJNxQv6+a+FpF2PMwj0nCeaQj4IGnHtfvXzWvOSP/rIz7wV6z0zbwG4TjcTVCdZEnVSrdZhudwBeHL3M5ein9TQW0tTMOtxC4WST8F1UMY0H63f3KKNwgrSOJz3kHaD2qwxLzjUIvdR2b0MYu7ToCVBbn9jTUG5dpJ+9F1l0qf6/usDpNJZd5Q0O9ZoCtqEfgEPNEgbASrQFPInE9qmUAhTj3Wqo1NJghbCOPSPL+PsO9/xbHNyzJgQ19ziJ0w7CINRCgVVo6yI4k2+82sKcVY7A4B1AbbadgHPJWpFuaRsNpjw54cBNDZk04yC3kkc4cgc/dySCFvTU5qL+pF+EtR2XG9gSvTOWbD+62TZtIB8Wg0h07CTz1PIn1Roc+YjIDxqyD/iB0qT1ppD7BVvzvTmglkTR1OoS898FMRvn5yi3e6M8q1KbWsKMa67uaXoNiJnJNu+vhBrbeCglBw6U55K2g2qKcS0EbzeQ/ykakkJTgMd7xpRpU3yXE07RdX8VqzAQQt4zYcmmgorbzVMUwjC0hTK+4dXPluCO9+YbXwdb5nyR5vUFJaH5FZx1j9WcTqtqPp7v2K6WR0jnC/K8ZcG/3x1Vtk2Zu80e+f3xWkoquPaaaQH7tAnVtmC7LF+R3PZealrCkVsam7RdlTBWVw5u9FeUPRRjPsffP1LuPqJ8Oi2JKaQRM+AOXakWtA9TWqsd8Z6/PIGafQzQ7K6RiHRRzUkaGYjAJw0amv381qNUNhkaFb487hp7mfdEpxBeFTfLKNZ4M2dH6ZSB6E6JV+cugg3jZ8eqlHpCOqE3pkdbhZLX1MOTGXIAAAgAElEQVQoYvjPn8F37p4U67ys2nUamgIAjPskfF1tnVCMTiKZRJCYty0dat0z0hQ0kUtxSp12tBsgPoWaolZ0f52vU0bqOqHw7Mdmi9OrUURJRlsbm1rwYoapc5lL2UmbPfMUzCu/6me5/rnP8IdnP43tU0ieIsA676dHj0h0vh8nO+e4TxaVmRGDYvuZs7MLB85TSPn2ut8TlfIiSX1ncOy6ouKde2F2P3c5TMQPVqiGkTBHefBc2oxQaPYIBe+bUKN/4vgC/KgVM06qCqc4D06ci2c+Dp4QlzbMJQHwxcoN+GyR5RvwJwELQ9cY46RHAOKH8/mzeA7p3THW+Sb4JxAGdQiM7MxH/nQoSiFSRRdQceOL+gldDklCMovFZGGp6vkOJkJB52iOc/tqJK3Lo/mozTiaVaHgV4/VzItxpvb7UWOi44ycnE7FHwOfBc5P/9o/zBar8aMzNcS1EycN53OeW10GPpkgLE0hm3v94rGPtdvTFkradBq+1ON+krzD2cvW4dv/eif6QJsjd+qL55QV/orM+OYdb2OPQd1hMo63NGPruI+/WO1ew5SESWND+TQgbUYtaTuaQsCkF8CrKWwICI80xRnNxYmqcKfch608UgWs+1Z2T51WkERTSDJidB6xSThipYQ5mgHgksO2x7/PHlP1cuhIWyYl6fySaArrN7e4nbMJ/mi0liLjlc+W4M/jpoUu2uNgheN6yxkvD1r6UuGPz3+W+jUrpc0IBe+kGW9FUH0Bldg4AUv1/mj+KsxZZj6Fv1axygyO5VTWsVnzvOKGGVbqU8gieiuo83L6iboCBWbwrDZpmyC0pk/lHsfv2r9sd1JtLw7+eQLqzzbyKWiKGEcA1kKTrwVtRiioUt5vM1WjCiodDRSZcfkjH8Y+B4hvdqmUd2avcDNYJkU3ezlu/1DpxJ8sNAVAb9N3BFqBkq8mVinpawqa6CPlsy47bRYrh/lDQtXBhMlcEZ02msfJY7Wm7QgFRRD4R/GqTTpo1rK6DnIYRY7fOTi3jGt2qZSr/k9vo46DrsxxG1qlq1ZVI1RQR1NzcKdCymJDWaP6stJA1wTUd6pbxyITTcFnPlLLZKKkHXz9S2Wpr7Mod2ujzQgFtfN6e/Zyzz7VpxA0E/ear+xidJ9Drn8JH8xbFatsXCNNIQ30QiHeNdQ89yY4na/TKVSaJsQU3Uhz8WpL0yooa1VnzUk3vZ7q9XT+AfU1N2qEQhaagj/tiVpOk0V7dHUsaSK7LZk2IxTCRgSq+eHRgIUxenduX7UcN07nlrWmkLQ5qKMyvU/B/HdYeZaS+hSs/x1TXpYz6n4q81dao/QCJXPZf330gMoKVQV0bUXtPDs2lD/vLISCf3W1NG5ZDedxa6ftCIUQB7KqDgc5k/ypsdPEqZe6DjaPeB3zuugj89/hrMM8dKvOscvhdFSd2mezLGfYryoQJYoeC8u8WSt0QrolwnxUaQz/wcOjU6PU+cyER/35Ffdz0txDIhPKyV+NrBKDQyY4dWofPdJsV1eoms24VppC0l+jznjWmbzi/I4CEYpFTmQCKmasKYRBCTWFoLWFa4lu1K8KimqYj+oMzD9xZtqbIppCObFbExF1ArCRmZMnLakBYR1HJ4NOpV1doWo245Xrm3DOne/EypdUS1RNQZe7Jo5QqCsQNrcUy7LMhuFPUdAp5WU5A+8bMhpO6lMIWgeglujMR+pP79ulfdn+SoWCiZZlIjjikoXZq7UR2RsSUQHAqQDOALAXgE0A2hPRUgBPAriFmcPnwOccnTrsJ+lI0ISFqzd6VsbKO3WRmoJ5Q6srEP71+uxY92e2UpzPXbEeRNmZYMImWlkhqfFrSFaRU3HQOV+dMNQfHbEDhvfrUra/Usw0hdRvK9FHGkxa03gAQwFcDqAfMw9k5q0A7A/gLQDXEdE3qljGqhNlfqCEDX5LRR3V6Xw1cTWFuBSZ8e0738Yj786vikkhiIvvey9wX6GQzLiY1RyLOCxfX55a3vHbHDS8T1WeuUk9qMaM/9akKfzp+c/w7zdnV/0+Juajw5m5zPvKzMsBPAzgYSJqSL1kGdIxwlGZZceTJUkFndo2dSOtWEIhQRmKDLw1c3lZWWoJESV6nnk0H907oXxJVydLakOVzKgmHX41Qo9bk1B45qMF2K53Z3xzn8FVvU/kU9YJhCTH5Jkon4JTX7c0bSFpegR1sp+uUcUxH0V1BrolOZ9XkqI54/NfnbCT8T2rgUlI6nGa9BB5dDTr2OwKBarKIMnkMVTjWVUj82m1aC5yJqlUIoUCEV1NRA8S0Z1EZDaDS3+dRiJ6m4jeJ6KPiejX9vYhRDSBiKYT0QNE1C7pPZIS5VNwGoHzOq6scQeUFqsTpglX+2ld9EaSZIBBDOrVEbsN6BZ8vu10/uqe2cT7b9O9g3Z7gaI7y1EDymfF5zEkVYeqKdTKfKQes+/QXqnctzVpCsVi5bnKTDCpkR2Y+WsAzgdwUQX32gTgUGbeDcAoAEcT0VgA1wG4gZmHAVgB4JwK7pEIU6HgSAW1IW/bK/1c/nlH7RQqbVNRIYFRfYW7WpzBvbo0Vh66GtSJBOU+6t25FKmj22/qaK61QuFoCvV1haqUxcSMqJqPttJEQCWhNQmF3GgKABqJaA9m3owKAnDYYq39tcH+YwCHAnjI3n4XgJOS3iMpUfMU/O9Bbch9OqdTOVsTaY4UdQn1VKLct06TNilTGqUOilYxMS3qjjGdFFnrvmuTYj6qhhnVpLPbRdEY01pDozUJhWKRM/FvmjzZHwM4lIjuAPBYJTcjojoimgxgMYDnAcwAsJKZHTvGPADbaM47n4gmEtHEJUuWVFIELe01DfPuc0q58f0vwmNTZ8bobXuUnd+/W2OKJcwXaY5WmiIaZVQbYDchnXf79w8dprlW5eUOSuHhNx+N/5+DNceUn+eve8/84ICyY576fvm2rHHmozQUquNoNnk3vTu1x1UnjgSQnn+hNQmF5rwIBWbewMzXM/PZzPx0JTdj5hZmHgVgAIAxAIwW12XmW5l5NDOP7tMnejp8XHQVsl/XRmW//d/+rmoKxSLjtrNGl53fivxXsUmzXjZXOIvbadP+xqJzYKdR7qB0KX7zkW5Cne72jb401Dozyk5bd41VxjT562m7o0CKo7m+Wj6F6GPU8N20Qnlbk1AoMmdiRqyJl4uZV8Ka/7APgO5E5NhvBgDQZ6TLGLXeOx2MIzzUkXILM7p3LPeNV7L2bN5Js1OIapOmo3v/Yboy6q7UvaMVTT2gh96B7CfIfFQ2o1lzM91v8WsKcWPxTxq1dazj4/Kl3bZGXYFc81F9garSMamhuUEZiesLVFqlMKU62Jomr+XJp5AKRNSHiLrbnzsAOALAJ7CEw8n2YWehQhNVUk72Ra+oDdgZvTmb1Ar8pd2q2yjzSJY+T9M24Pc96M7Tdcq9OlkCfdeQCCeVoJElUXRHpdvdvt6rKcQ1ixwyYqtYxydBfW7WPIVqhKSWrtk5wMfnj9RKoxitSVNoKXJVnr0fk5DUyFKYHAOgP4DxRPQBgHcAPM/MTwD4KYBLiWg6gF4Abje4VuqcNmag57tn0Of7ear56LwDttNeL+lI5it7lLlUIunXtRHv//JI7b7x/3Mwrvtq4khiPRXUy2N27hdrTgERjFq/vy/VVUndVZwgA9P3FRQtVaDoGc26/X5Hc9x6k4mNmUr/61LQFHboW54RV71m0E+qK3i1sTR+uyMUDktBuO6yjdnAIiktRTYys1WKUZoLIrqYiAapG4moHREdSkR3wRrhh8LMHzDz7sy8KzPvzMxX2dtnMvMYZh7GzF9j5srWh0yIvxNRv7uT1+zvda45Kdi8QQBGJMgR0ydBqN3C1RvRrWNpUvlvTtrZ/dyxXV2Z3bpSKmmK/bo14rhdyidxBd/L1Hzk1xTMfArOJtMRetDA0iQhnon5KG4/l41QsO7hjNQrvefVJ+6My47xuhNNzCKq+QhIJ0GeM/s+SbtT+d4hwzzRUdUgN45mAEcDaAFwHxF9QURTiGgmgGkATgPwZ2a+s4plzAT/oy6EjEiceOmw10NEuO+8sbHLoZvBGxe1gyMAh+/Yt+JrqlRSMQsxMwua3srfp+j7mOCLVZpXxzpddw11dbDyvX7zUVzzQCaOR7tM7VISCg31hbLovIKnzuqvrzqXieILUB2OT8HkWoND5iQlXWQpDi15EQrMvJGZ/87M+wHYFsBhAPZg5m2Z+TxmDs4S1orwP2y1YvrTXNS7mkL4C+qQIKWzLhdOV9+kq7P3GxJ6Dc+oi8zWi4iDSb0MmhAYtxOLOjwoBYmu8QzsqXEmO8EDFTY2Iq9ZxensR/QrRQ7pylRuPop332okiXP4mu1nc31pdV7fWlIIwKYmrxlOff5B11fbBrP+eZ6Q0MdnMhg7/8ChgfsKhcqXY91tYPg68LkRCirM3MTMC+zooVaN03E+eME+ADRCQdUUfA3PNBwuyQvU1c2dfbbKqMgmz4iqCuMXk9915thtA8+NU6YowRtkGtOddsuZe5ZvtO0Runca5/X5U2d369CA+88fi79/Y4/S9TTn+e+bJ5/CJYdv77mHqyFXKhSIytbhMFpPwXeMzuSUtGjtDUysYXKjQFTxGusNRs+golsY0ToSr1QBJ468NNL07tc5tJxNTuO49IgdAq/PHB4+FuQY1jUOf4RT1BwIdXJdNQaSJiaOoN9OBrZ37/EI/cEdAhqzrrPs1SnYbqw7Pk6HSxpH89jteqFrYwNuPXNPjLv0QO3v9vsyMrAGuRy+Y7hz1XnPThGdTqtSQVQg4Phdt0bPTqVQbo+mYHCNIPNRkqI1NhTM7hlmfiRg7aZkucQcTAabudMUWjuqA1ax9ALQTH7SOZrt/3UFwuxrj8N3DymfNetgOYW828ZdepD7WXUMq/jNGA11hFP2Gohpvz0GvzjeLGrH41OooBIFdRomVwyqvHFtr1HHBmkK2pBUAE9cvL/2eJ0Qi2NSKlDwbz5yZD8M26qLtlPxn+P3MVSTX50wErOvPS5wv1MyV1OoT8enQCD06NQOj160r7vNdASsZvY1nYsSRcd29WazikIuTkRYE5JgcmifTpGXD0oNrppiq2kudO9heiARXWeyLc98Q2PScOqV35QfFvpmEimhiyneqmt0hIP/2u3r60BEdnZKa1tUymv1GpVUoaAU2CZ9QtAjituhJPXbaE0LVG6KCytXnPQ6ZtFH5du6NjbgjcsOdb8HDRaCSJr+PKg8uv1+X5r/0ZqsXKi7rmfg5RnImF0nrYlcHRrqtM/xxBgTA4nCI9iuOG7HyGsEna8boFaTOJrCEZptx6RVkMzxzYwM0xT8ldQkfFE3U9LEmVUeGqt8tv9HdQPqFSoZ1O0/rLd2u1HyuYBjNjW3xNJeoo4M6pC08xRC7qvrYOKZj0yO8R503Vd3QbeODdjal4572FblcfxBVDL3KnKynatFW99LPoXKTF6624a1jcNGbIW7zh5Tdm/TCYpRNDYUyiyUE352GG74+ijvtUOuQSBc+9VdA/eb1CUn5Le3L8mm+jursU61H5PJaxcS0YcARhDRB8rfLAAfVr2EVcKpAyUV2btf/Vp6oeY2Vd1MSadRhc2edcyKO/bvWnYvZzSlVuBTRg/E307b3XMNr0BLXom6dWzATafvUbbdZLQS9IzufGN2rE4k6lk3Bphb4mokQULhuR8eaHS+iabg3GLfob1w+t6D8JU99GtA6Eat4//nYNxy5p6hYZFhXHhweeRM1Epm/hF90PFx65grbJRn7h1oea+3TY8OOGgHK+dZlPkoCR3a1ZUNtBrqCmWmmqjf2bdrI765T3CAhY5xl5bqlzMp1p9OXZ3JncVa7iaawr0AToCVfuIE5W9PZj6jimXLBL+KXNpe+q5OVlO/h6Gb+VpXIDx84b64+5y9A8+rKxBm/O5YN0urL7oUgJUYy+G6k3ctC8PzaBcVthvtTzW4aIGAb4wdVCYAf3jEDvHKFHFso6Ip/F4ZqcUO7dRqFsAOfc0mIJossuPs7tOlPX735V0CO1nd4H9I7044amQ/zT4zVUE3YbB35/D1rPwDpiBH6JDe0fZyz3VdYVPaFnexIUJ6PoXG+royTUE3Ije5dpA1L6hubNur9OyckFv/c1a/BSVkTBOTeQqrmHk2gEcALGfmOQDOBHAbEe0eenKOcUYcQeYjb8dqCwX7e1JNAQD23LYHunUIthsTEeqUmZveOQfxq3ylYynd6MhIUygQfnPSLnj8e17H7ml7DQo4I+D+Efs7NJSq8IE7lDLohr2j4WpHbx+n65OihL+aCTVokR0VZ4Qc6QaI0e5NXQr+dbN3HdAteoTvGzDphNjtZ43Gr+101qa4AzHl7Tb4JqaZ0KOTRqglqPCNDXVlYd7k+6ldG+uNyhUULh50rip8HGHQ4HNmqVFNuXI0A/gFM68hov0BHA4rR9E/qlOs6uN/deUzYoNtl1GhY/27NeLvZ2hi4g2oc01EfgNXCQbw8o8PxkuanP1AuJM8Ltqwv4TnAdZEunjzFLzf7z/fO0tcDUk11ZAeUaJeHHQjwyj7bZfGknC3QlKjjrcmEfbUdWYKccaCpsf6fVznH6jP2aVSMvNY33WrxB22Y9/YjubSQKy0TRU4PTRZh3UELY0KeLXGKNrXl/sU/L/0gyuPCq1Tzr4gIR10qnrNhgBNIYvMqCpxhIIz2+Q4ALcy85MAMl9POW10oxbre4mw2c46/vOdfXDETslSSzgdkROaqK5P7NyV2VI7B/vUdmc+gzoCrNx8VH6BME3HYdqitdrt7eoLsUZz/vv70yOoIalh7yzoHPd4bbSSWSdv3a/UyQXNnTh0xFb43Zd3wU+PDl9GJCyiKGmwkaopNDYUcOzO0fmnTH0KcZ2fVPbBaz4aM6Rn4LlDbSf8yK27aaP53LYZo0imucHC2r3bNs1va52n0xR8z1l958UMsrrGEQrziegWAKcAeIqI2sc8P1f487L767V3tO3dFjWjuBIVzzm3W8cGPHLRvvir4kQulUl//7+cOgqzrjnWG31UoQFJtwjOwJ4d8ZA9EzyIsJjtOPjfS+f29XjxRwe5s5M9IabKsWHLXDqvZ5vuHUozmpV31thQ8BwXRGdVKBTIHY137aBPK0JEOH3vQZHpT2JpCoYH7zW41NGeNmaQUR31m0vVNBP9uja6Se3i1nddSKozMc6f0sXPAdv3wfM/PBBfGz1Am2I7ySDI0hR85qOEo6nA92FwOUcY+P0rqg8xi/Uf4nTqXwfwLICj7DQXPWEt1dkqcTp2t4KGRBq4i+wY2oQr0fbUc/cY1MOTt8hpRIEqKlnr53btoJo1kpcFADY0tWi3jx4cPJoD9I72vvbILk6Z/EKtvlDAdn0646iR/fDoRfvijL0HaY/VLbHqHkeEm8/YAw9dWBJszjsetlVnPPcDa5JhlOmtc3uvpuA06qRaokMcbcB0MaeGuoI7+dH0+uQbMLWrLz2Pt352GC44yIpoih8m6ZiPSueVzKbRZ2/ftwuIyDVbnbv/kPKDDK5zjn1e+wZvXTlm536xBU7UgM0EZ2DiT3ehPpMs1n8wzpTGzOthOZud7wsALKhGoaoJkfWQnQftj8VWj3NwKu+I/l2wcPXG0A4HqCyWOMx+qJqPwthjUGnN6EqFwvrNeqEQha7yTvjZ4QDi+QL95Vd9cLsP6hF4bJimAADH+KJxnGdaryQ2C3oXdQVCS5E9HQcRoU+X9njxRwdhUM9kYaMOxRhSIY4AOWB7a97JsYapy8M0BZW4Nm9/KnqgJIBaYvwg1Zdx8aHD0NTCWLY2OPP+4F4dMXvZeve70wm3r6/zPPNv7jPYuAx+gn0K0c+ozjYf+X0KatmyEAom8xRes/+vIaLVyt8aIlpd9RKmzMQrDserPznEledOBTVJc/G303bHvefujV6dw2cmVzI3wMQxHGepT5PK2L1jg9th+NmQUCj4o108ZarS81H3xE1B7oT6tVOcjkEzmp1OsLNGi9uuT+fY4ZV+bjp9Dxyzcz/tPv+7j9NF7NC3C2Zfe1yozV7FHzoa5FOIbz4q1xScT3E6vY7trOe/bnMLfnTkcM8aDQwuy4rb1ecLc95je9/ktaAqZlJvK1mb3WmrfuGbO/MRM+9v/+/CzF2Vvy7MXLsVxRPSq3N7DFRGcqV5Ct7jdHb5Lo0N2Ddglq9KJdECoZ2e49OIUS9M+t+HL9w3MIIkyHwURVrx1P7nERb55Vk2MkJTcK9vv6uWYmkNYqcRBr0LZ+s2yrrOaQaI7DawO27+hln0WiVpLqJw6v3K9U0AgDnL1mmPi7uEqHO0GvbpPOo4WpITpeTN9WX9ZwYe/643HNpfSuf9lq1p4TvOWSkual4HEB2SqovgijpGvWKc55OUOLmP7iai84goPHSiteA+2/JRi+57HEzbyCMX7YvT9/bG7YcNMl2fRoyymBRlaJ/gtAr+aB9TNodpCiHn+SOb1Nfwuy/vYpwwzrSjcka/zgisvq7gmjCi6kC7+gK2sxOdVSN75b/PHhMYduxgOupPhP2TFq+xTDLdA/Iyxc9n5bm8Z1ucgfDRO/fDj48ajh8fPbx0HaWNlM1j8JXT6WDb1VFgZz7tt8fg6UusWcf7Du2Nf317LxwyvE/ZcSb+xkk/Pxy3n7VX4H6ndH5NU71mLjQFhTtgrbP8NyKaSUQPE9ElVSpX1SlzNIdOXot3bVPzyB6DeuDokV4zQdqaQqWd1cl7DsDVSnZZU84KscuGFenmM6y0GgPsUbh66PaatX1V1FGz39Txw8P1ac4d/5Az52B43y7KxMbQ2xktDFMJB+7Qpyzs2E//bh0iI3aS4v9N5wasRx7fp6AxHzk+BU2nF1Tf6wqE7x4yDF2V+SIN9XofIVA+GFEHAkH3aKgreH7fIcO38qSmL5XfLqv+MiBYVgqdCe74Xft7rhGmTbQErBGeJnEczeOJ6BUAewE4BMAFAEYC+EuVypYJuok0QGVCIU4jiZOB1Wk4sXwKhkUJi2gam2A0+tU9S3l9/vnN0ZETthz2HdYbn/3mGFz28AeYt2K+d85FxLnqT1AbX89O7dwFY/w4x22/VWfcfc4YjBnSE7OXWs7IQPOR6oj2hTZXG917qpbz0f+L0pqn4F5fbWMhx8VxPv/4yBGoLxRw0u7blO3zNy3HxFlfoApihryEtSPAWqPcz19P3R03nDIKfxk3zS5P8Fg9A5kQy3z0AoDXYc1T+BTAXszcak1Jpegj+3/IBLW4sf5xBk7+92/UucTyKWTTWYVxxE59see2SkRUxPNsV19QwoBLRP0UtUGqvoc3Lz9Uc7R9L7uja2op4oDt+6B9fR2G9O6Esdv1xHUnm8+KzUooOIkSVbIwKQDBzvs4KcYBvXa+S0BKc0A/VyaIbh0bcOWXRmrNjESEe88r5R1T/UhJIsYO1piRogZsQ3p3wss/PtizrVCwUuOXNAX9A60vEH4fo04mJc7r/ADAZgA7A9gVwM5EFDzPPOe4SSR8ERbwbfd/NiFOB1HmywiRKE60S3fDNABpEeaET+N6OkoTBr0u/zDUBqnOKg7zQzjCQ/WBtKsv4P7z9/GE9qo4M2A3txTLotiqzZ9PGYUHfKk+qqYp+F5UQ73+RyY1H6mXdyKJdKQVtECwJt2517WfW11dAecFmMa017HLfdoYTR6vQE2h9HnbXp20viDnkCDz0TVf2cUTJFMt4piPfggARNQFwLcA/AtAPwDRK8fkmFIFDXY0J630SY4NU8WPGtkXV584EifvOTBWeSone21D13FEPdb2daXO379GQRDO6DfO+rodG+qwEk3YqCw+n5VG1ql9PfberheA0uzfamkKpuaj5I5mszbWlNLv86+R4gjT+oKVhHKvwT3wzuwVid5lybRrxj3n7l0u7Jz5IAFCIascSMZCgYi+B+AAAHsCmA3L8fxqdYpVffyhfP7nXVcgHLlTXzw3ZVFk3nk/upd39n5DtMeWJ+ILvi4R4cwKJtYkpRYWKK35KOKcbh0b8NAF+2CExsQShDPJLWiVOR1Ouu5NSrhu1s/oye/vjz5d0h+PnX/gdrj1lZkAyn9TkPkofkhquR8vrMNLzblK3jkSTYpPIYVLAwgOEdYJWH/KJeeYtCYJJsVk8pojOBoB/AnACGY+nJl/zcwvVrV0GRAUfQQAe9h28LiVRnf4L0/Qr69cpqFknBHRz4h+5esHmJbIiaKIIp75SD0v+sTRg3tqUxQE0aD4FExx5nRsbGpxO4Gs39rIrbthqy5ep2UaVUdNuOb3/QQ6mu0bm04YLM0NKl0/rOxxBHYYPTo2eNaIcH0KEVmP46ArabcODRiuaVd+nMcR1N/kRigAeBsAmPl6Zp7AzOlkOqsxJVtwuZnCwZXcMStNHPVTp6HUEpNlLIN+342aVdq09zCZ8u+8lyp3t46mEM98ZAmdWpiPwohK7WGC2qn5f1KQrZuIcNkxI/D4xfsZ3UPnxwt7fnEczUH88vidcJ2STptArlkqLNonLjpF4f1fHelJsx5FXcBzNp2jUykmQ6ra1/Yq4EYfaTSFn9iTYUqSO3mlGdCjA+at2BC4P81Jcyp3fGs0Hpv8hfHxruM9lbtXjtNJ1NWlFy6ow1kZLs7qYdv26oi3Zy/HwJ4d8NasapUsPu3qCh5BlYSw6M+wWeJOcjwTHEHvvOOoVOJp+EzOtpPfrdrQZN8baLE1kLB5AXGppKTOz/QvsvOrE3bCmo3NOGzEVhVc3RwTodCHiC4N2snMf0qxPJlTsm+WKsZFBw/z7KvE5jju0oNCK3W5UEh8Kw+HjuiLQ0fEz9apk39pCwoz81G5SaIaAuvEUdtgx/5djZfdBID9t++NL++xDcYM7okHJ82rWtni0q6+DkBlijyD3YR/Zdc3MA/dc+7e+N6972KFnRpDh/r+Z197nGffvkN7lR2f5hKUanv/6p4D8E49t5wAABRdSURBVMzHC7HLgO6VX9f+TRWlHbHP9VsLundswLcDfJLVwEQo1AHojHzU+9QpJcQr3+dqCjFGEtd+ZRfP96gFPPydcK3NR9q1aWMU6aX/ORgbm8PzJZlczul/KhHIT1y8v1GW1zgCAbA6lH2HWjmwMkhFY0waI94u7evxnQO3w99fmlH27E0CLvYb1hs/PmoEfvboh4HHBJXynSsO9yxc5KBLw14pRNb8GVUoJXmXuw3sjvfnrky8yI6K36SNgO/VxkQoLGDmq6peklqhcXr5iZP18lRd7HIIta4AZeiEQozxQFRaBusW0ddz0zUrzz5ug9s5ZEJUJWgXjM/BkKnSIvz8uB3xjbHbon19AT9RTDodGuqwoanFeMAS9SyC6nhQNFWaIbdhgSX+Y6JgtlZGfH/uSmVj6eMd3xqNTiHzL3TXc+5/3Vd3wU8f/tD+nj+hkIPqXj1Cl9izX4Z/0Ys0Ccu5VAvCNKZMy+FGtOSv+qnPKE7KkWpTaecRlNvo/y7eH+/MXm58najmEreYaZqPkpbBc672etZWtT5s26tTaLJJP0Ul55Y6oMnaeGAiFA6reilqSNgDLyoJs7K6f7WjbaLIQlMxuYPzXOrrCrkblWgjtGpYyvvOG4sJs5bhwYnzqnL9YVt1xrCtzDu3qGcR91nFCRf2c//5Y7FgVXmgR1pvy29yUr/HXdOjlGXBN1DMuG5FCgVmNh8itELCRldNVYhjjrp/tfrkrbs14otVGyOPG9SzIybNWWF0zatP2hlPfvAF3poZr4rEcTTHnTiYBR5NIQeKwj5De2Gfob0wac4KzF8ZHOkWxK9O2CldZ27U+41Zx8duV+58Tnquaz5KefhdcjRb/8cM7hk7JYVnoR/lIVWz/9GRvxaXMf7HreZKb0lxxmMQYTmX0uSJ7x8QOqnLqZBHjexXtmJVWe4j+/uZY7fF/efvg2rgmu5yZD5ynl9efQo3nr4Hbj3TbHEelW/vNwTnHWie+yeKKDNWnOb0wo8OwhXH7VhhiUroVn2LyzG7WOnudRPSHPPRt/cbHPu6ajp/tXhZt4E2LxTUyvHuL47AP5RG5Uxu0eVPTwv/HIhqqYo9O7XTzlb2QwTsPcQ/ukp7VFW63mXHjEBjQ/DzrbnjHcChI7bCAdv3xk52+gz1lX1pt60BlC/1WAu6dWjAoRnFsldCnPq0bc+OVdEWdSUw1ZW+vPsAfPqbozGkd6fy5VF9859i4WZu9p6c5uQ6E6qzOkdrQnn+/pz/azdaMd+d20fPJLzjW6MTmRJ6+Zb4q2YfaBI9onWi+b6naTK54KChuOCgoRh82ZOe7UVXINdeKNzxLWu1rFNueROAt1P7nyOH48KDh8aasarj3V8ckXhdApU8zKxO2XqUKs69dc8pTsqSoCU8f3L0cCxeswn7b1+eVjsK1dGsFk/MRxkT1oaWr7OWIezdOTrx2KEj+uKwHeNPFuvkM+lU8/Wrlesf3/CnpCj19MfZOYyc1NG16GdaAiby1BKnLKr2UihQxQIBsAYk3QKWu4xDfp5WMHHqU/paqvU/rWrlHyAN26oL/vvd/WLl3/Jfqzy9iGgKmRJmnli2bjMAaxm9rKhmB+z81t9+eWccvbM+eR0R4ZDhW5XNNM0aVVPIgS8XQL4EVBA5UBRc81qfLu3Rr2sjPpy/yrs/RiGr9XPCipDoGabw4EupZsjraM643mUigohoIBGNJ6IpRPSxs7YzEV1JRPOJaLL9d2wW5fGULWTfwcMt++zwmDNe4+JdGax6FeDUvayJdYcMj2d39ts4s+h4nDQLnnWQq3/bUJzOrJjRSmdJyIP5yDGt7DmoB0ZubZ7GXEfaP8d5dWn5qtKsCaqm4DEfbaE+hWYAP2Lmd+1FeiYR0fP2vhuY+fqMylFGWN04e7/BOGWvgYlUwTj071aK9qlmmz5u1/44btfaagCmOOajHPRxLo6mUK2VzrYUnMABK91JuUmslu/UEeipCQXfsr6VsG6T5cPs0M7rr9gifQrMvICZ37U/rwHwCYDylbVrQPh0d6q6QCi7Z6Z3K5GHeHuVk/ccgK27NWL3gCUxa4GrKeTtYeWMxvrSehM6YpmP8jQqqDKL11jziPzrZGyR5iMVIhoMYHcAE+xN3yOiD4joDiLS9gBEdD4RTSSiiUuWLMmopLWh1o0gL01w5Nbd8Mblh2HPbfMkFKz/IhTCaW8ngdygpPE+amQpCKOWdcyN8Emp59vFTkexXYzU60Est32Yfbu29zyjamZU0JHp3YioM4CHAfyAmVcDuBnAUACjACwA8Efdecx8KzOPZubRffrED/UKL1Oql6uYLIvz7i+OwNs/i5/FpNapOGpFyXxU44LkHMd8tKmpBQN6WKZRdV3xWg580vYpnDZmIJ774YHYd1jviq/1+5N3w2ljBmHk1t0woEdpNnTWmkJmthEiaoAlEO5h5kcAgJkXKfv/CeCJrMrjkIfJUSpZFsc/L0MIx0mN0CKaQigdGkrmowsOGorh/bri8B1LwQ21bHFhcxGSvFUiip16PYjh/brgGjv1fod2dejfrRELVm3MPOotq+gjAnA7gE/URXmISI2L/DKAj7Ioj6dsWd8wgrY6Cm8N1LWC6KM84DhKNzS1oL6ugCN26uvRDmrqaDbSFPLRBpsySLOjIytNYT8AZwL4kIgm29t+BuA0IhoFS0jPBvCdjMrjUmsbvp+cFQdAPstUCyT6yIxenax5PZcctoN2fy3bHOcwqi2IFjch5xYYksrMr0Evfp/K4v5htIL5SLmjVg2q1l2xRB+Z0a6+UPPJj0F0tKMJdcns8sbwfl3w1szlaB+yNnY1aPMzmkVTsMi6m9ttYHecPmZg9IHIizIPHLhDbzz87jyM6FfZhCyhdmzTvQPuPXdv7Daw8nWZq80tZ47G1AWry1LhVJs2LxTyRq2FVFa3f+y7+xkfm5dx+YmjtsFBO/RB947ioG/NBEUK9e/WiPdQcpTXmm4dGrB3BWtJJEWEQs7Iy6g4j+Th2YhA2HK57qu74qiR/bBThak5WjttPktq3siZNUtLKyiiIMSmS2MDThyVi0QLNUWEQs6QkFRBEGqJmI9yRh41hagivX7ZoW6oX1Je+NFBgblyBEHIjjarKThLK+aNHMqESLbp3sEzLT8JQ/t0xsitu2n3HbuLNcexf7dG7X5BENKjzWoK939nLBau2ljrYpRTq5BUg5F+l/b1OG7X/rj4sO0zKFGJ7xy4Hc4cu23moXmtnY9+fRR2/tWztS6G0Mpos62sa2MDuqawjGLa1NqnoDNf9ezUDrts0w0/OnIHd+GhbMtEIhASkHXad2HLQGpNzsijT6G+roD/u3j/WhdDEIQMaLM+hbxSK5mws50X3r/AhyCkRRprDgjVRzSFnFGrGc0/OHwHHLFTX1c4CELaPPrd/bB07aZaF0OIQIRCzqhVgr66AmHXAfnPByO0Xrp1aEC3Dvnz4wlexHyUM2rtaBYEoW0jmkLeEJkgVMjxu/bHgdunu2yt0HYQoZAz8hh9JLQubjx9j1oXQWjFiPkoZ4hMEAShlohQyBm1Xk9BEIS2jQiFnCEiQRCEWiJCIWeIoiCkzc7b5DP5o5BPxNGcMyQkVUiTT646GvV1UqcEc0Qo5AzRFIQ06dAuH+sNC60HMR8JgiAILiIUcoZoCoIg1BIRCjlDfAqCINQSEQo5QzQFQRBqiQiFnCEyQRCEWiJCIWfIjGZBEGqJCIWcISJBEIDdBsraHrVC5inkDFEUBAF48Dv7YHNLsdbFaJOIUMgZYj4SBKBdfQHt6sWQUQvkqQuCIAguIhQEQRAEFxEKgiAIgosIBUEQBMFFhIIgCILgIkJBEARBcBGhIAiCILhkIhSIaCARjSeiKUT0MRFdYm/vSUTPE9E0+3+PLMojCIIg6MlKU2gG8CNm3gnAWADfJaKdAFwG4AVm3h7AC/Z3QRAEoUZkIhSYeQEzv2t/XgPgEwDbADgRwF32YXcBOCmL8giCIAh6MvcpENFgALsDmACgLzMvsHctBNA36/IIgiAIJTIVCkTUGcDDAH7AzKvVfczMADjgvPOJaCIRTVyyZEkGJRUEQWibZCYUiKgBlkC4h5kfsTcvIqL+9v7+ABbrzmXmW5l5NDOP7tOnTzYFFgRBaINkFX1EAG4H8Akz/0nZ9TiAs+zPZwF4LIvyCIIgCHqySp29H4AzAXxIRJPtbT8DcC2A/xDROQDmAPh6RuURBEEQNGQiFJj5NQQvKnZYFmUQBEEQopEZzYIgCIKLCAVBEATBRYSCIAiC4CJCQRAEQXARoSAIgiC4iFAQBEEQXEQoCIIgCC4iFARBEAQXEQqCIAiCiwgFQRAEwUWEgiAIguAiQkEQBEFwySpLqhDBQxfsg5lL1tW6GIIgtHFEKOSE0YN7YvTgnrUuhiAIbRwxHwmCIAguIhQEQRAEFxEKgiAIgosIBUEQBMFFhIIgCILgIkJBEARBcBGhIAiCILiIUBAEQRBciJlrXYZYENESAHMquERvAEtTKk5roK39XkB+c1tBfnM8tmXmPlEHtTqhUClENJGZR9e6HFnR1n4vIL+5rSC/uTqI+UgQBEFwEaEgCIIguLRFoXBrrQuQMW3t9wLym9sK8purQJvzKQiCIAjBtEVNQRAEQQhAhIIgCILg0maEAhEdTUSfEtF0Irqs1uWJCxENJKLxRDSFiD4mokvs7T2J6Hkimmb/72FvJyL6q/17PyCiPZRrnWUfP42IzlK270lEH9rn/JWIKPtf6oWI6ojoPSJ6wv4+hIgm2GV8gIja2dvb29+n2/sHK9e43N7+KREdpWzPXZ0gou5E9BARTSWiT4honzbwjn9o1+mPiOg+Imrc0t4zEd1BRIuJ6CNlW9Xfa9A9QmHmLf4PQB2AGQC2A9AOwPsAdqp1uWL+hv4A9rA/dwHwGYCdAPwewGX29ssAXGd/PhbA0wAIwFgAE+ztPQHMtP/3sD/3sPe9bR9L9rnH5OB3XwrgXgBP2N//A+BU+/M/AFxof74IwD/sz6cCeMD+vJP9vtsDGGLXg7q81gkAdwE41/7cDkD3LfkdA9gGwCwAHZT3+60t7T0DOBDAHgA+UrZV/b0G3SO0rLVuBBm9kH0APKt8vxzA5bUuV4W/6TEARwD4FEB/e1t/AJ/an28BcJpy/Kf2/tMA3KJsv8Xe1h/AVGW757ga/cYBAF4AcCiAJ+wKvxRAvf+9AngWwD7253r7OPK/a+e4PNYJAN3sDpJ827fkd7wNgLl2R1dvv+ejtsT3DGAwvEKh6u816B5hf23FfORUPId59rZWia0y7w5gAoC+zLzA3rUQQF/7c9BvDts+T7O9lvwZwE8AFO3vvQCsZOZm+7taRvd32ftX2cfHfQ61ZAiAJQD+ZZvMbiOiTtiC3zEzzwdwPYDPASyA9d4mYct+zw5ZvNegewTSVoTCFgMRdQbwMIAfMPNqdR9bw4EtIsaYiI4HsJiZJ9W6LBlSD8vEcDMz7w5gHSyV32VLescAYNu4T4QlELcG0AnA0TUtVA3I4r2a3qOtCIX5AAYq3wfY21oVRNQASyDcw8yP2JsXEVF/e39/AIvt7UG/OWz7AM32WrEfgC8R0WwA98MyIf0FQHciqrePUcvo/i57fzcAyxD/OdSSeQDmMfME+/tDsITElvqOAeBwALOYeQkzNwF4BNa735Lfs0MW7zXoHoG0FaHwDoDt7YiGdrAcVI/XuEyxsKMJbgfwCTP/Sdn1OAAnCuEsWL4GZ/s37UiGsQBW2WrkswCOJKIe9ijtSFg21wUAVhPRWPte31SulTnMfDkzD2DmwbDe14vMfAaA8QBOtg/z/17nOZxsH8/29lPtqJUhALaH5ZTLXZ1g5oUA5hLRcHvTYQCmYAt9xzafAxhLRB3tMjm/eYt9zwpZvNegewRTSydTxk6eY2FF7MwAcEWty5Og/PvDUv0+ADDZ/jsWlj31BQDTAIwD0NM+ngDcZP/eDwGMVq51NoDp9t+3le2jAXxkn3MjfA7PGv72g1GKPtoOVmOfDuBBAO3t7Y329+n2/u2U86+wf9OnUKJt8lgnAIwCMNF+z/+FFWWyRb9jAL8GMNUu192wIoi2qPcM4D5YPpMmWBrhOVm816B7hP1JmgtBEATBpa2YjwRBEAQDRCgIgiAILiIUBEEQBBcRCoIgCIKLCAVBEATBRYSC0KYgol5ENNn+W0hE85Xvb1TpnrsT0e0Jzx1nlNlSEFJCQlKFNgsRXQlgLTNfX+X7PAjgN8z8foJzzwIwgJl/m37JBKEc0RQEwYaI1tr/Dyail4noMSKaSUTXEtEZRPS2nbN+qH1cHyJ6mIjesf/201yzC4BdHYFARFcS0d1E9Kad4/48e3t/InrF1lg+IqID7Es8DivrpSBkQn30IYLQJtkNwI4AlsPKW38bM48ha3GjiwH8AFYuphuY+TUiGgQrDcGOvus4M01VdoWV+74TgPeI6ElYHf+zzPxbIqoD0BEAmHmFnbqhFzMvq8ovFQQFEQqCoOcdtlMOE9EMAM/Z2z8EcIj9+XAAO1Fp8bKuRNSZmdcq1+kPKx22ymPMvAHABiIaD2AMrBw9d9hJD//LzJOV4xfDyiAqQkGoOmI+EgQ9m5TPReV7EaXBVAHAWGYeZf9t4xMIALABVr4eFb8jj5n5FVirc80HcCcRfVPZ32hfRxCqjggFQUjOc7BMSQAAIhqlOeYTAMN8204kax3iXrCS/b1DRNsCWMTM/wRwG6yU2U523H4AZqdeekHQIEJBEJLzfQCjyVpcfQqAC/wHMPNUAN1sh7PDB7BSQ78F4Gpm/gKWcHifiN4DcAosfwUA7AngLS6tQiYIVUVCUgWhyhDRDwGsYebb4obBEtFfADzOzC9Us4yC4CCagiBUn5vh9VHE4SMRCEKWiKYgCIIguIimIAiCILiIUBAEQRBcRCgIgiAILiIUBEEQBBcRCoIgCILL/wMPAE+npms86wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3aece2b198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Extracting \"Twist\" of 22nd bp\n",
    "twist_20bp = pdna.data['bps']['22']['twist']\n",
    "\n",
    "#Twist vs Time for 22nd bp\n",
    "plt.title('22nd bp')\n",
    "plt.plot(pdna.time, twist_20bp)\n",
    "plt.xlabel('Time (ps)')\n",
    "plt.ylabel('Twist ( $^o$)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Local base-step parameters as a function of time (manually)\n",
    "\n",
    "* A specific local base-step parameters for the given base-pairs range can be extracted from the DNA obejct using function [dnaMD.DNA.get_parameters(...)](http://do-x3dna.readthedocs.io/en/latest/dna_class_api.html#dnaMD.dnaMD.DNA.get_parameters).\n",
    "\n",
    "\n",
    "* The extracted parameters of the given base-step can be plotted as a function of time\n",
    "\n",
    "\n",
    "* The extracted parameters (average) for the DNA segment can be plotted as a function of time\n",
    "\n",
    "\n",
    "Following example shows **Twist** vs **Time** plots. These example also shows that how to extract the parameters value from the DNA object. Other properties could be extracted and plotted using similar steps.  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3aea808978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3aece55c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3aea781b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Extracting \"Twist\" of 20 to 30 base-steps\n",
    "twist, bp_idx = pdna.get_parameters('twist',[20,30], bp_range=True)\n",
    "\n",
    "# Twist vs Time for 22nd base-step\n",
    "plt.title('22nd bp')\n",
    "plt.plot(pdna.time, twist[2])      # index is 2 for 22nd base-step: (20 + 2)\n",
    "plt.xlabel('Time (ps)')\n",
    "plt.ylabel('Twist ( $^o$)')\n",
    "plt.show()\n",
    "\n",
    "# Average Twist vs Time for segment 20-30 base-step\n",
    "avg_twist = np.mean(twist, axis=0)     # Calculation of mean using mean function of numpy\n",
    "plt.title('20-30 bp segment')\n",
    "plt.plot(pdna.time, avg_twist)\n",
    "plt.xlabel('Time (ps)')\n",
    "plt.ylabel('Twist ( $^o$)')\n",
    "plt.show()\n",
    "\n",
    "# Average Twist vs Time for segment 24-28 base-step\n",
    "# index of 24th base-step is 4 (20 + 4). index of 28th base-step is 8 (20 + 8)\n",
    "avg_twist = np.mean(twist[4:8], axis=0)     \n",
    "plt.title('24-28 bp segment')\n",
    "plt.plot(pdna.time, avg_twist)\n",
    "plt.xlabel('Time (ps)')\n",
    "plt.ylabel('Twist ( $^o$)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Local base-step parameters as a function of time (using provided functions)\n",
    "\n",
    "Above examples show the method to extract the values from the DNA object. However, [dnaMD.DNA.time_vs_parameter(...)](http://do-x3dna.readthedocs.io/en/latest/dna_class_api.html#dnaMD.dnaMD.DNA.time_vs_parameter) function could be use to get parameter values as a function of time for the given base-pairs/step or segment\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3aea7132e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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gpJOKWxYVylVyKEebw8svAxUVwBdflLokeqjIwQ8pOaTIgQ/AYgdMihxsOzm/7qefvOdWlN9+Sb6oLR2u3CSHcq43Lul99FE86U2blhw5M6avy2K6spYBUnIIgjglh82bgbffDpYXh0qtdPzx3usqK+3KVI4oxxmwiGJKDrV9EOJ9Iw5CnTkT6NEDuP76gsOJGKT9zpXyvRQh7/pLDmEq10QOFRXB07j6au95m0FRJIfNm/XX1WZyKHcUgxyCEGQ5kynvG3HYHbi75/TpABIwSMsegKb3XEo7SkoOCSApg3SYdG0JJSxqIzkk3eiffDKedMotfEY5SxdxSg4SQkkMNTXADz8UHlP13zFjgIYNTZkHzzsupORQZojb5mAiBxu10r33mvOqjeTAkdRM+Pe/jycdPqO0fe9RUNslCN7OEyTUQBLEzTcDHToACxZEy7SU5FAEqSUlhyCI21tJRQ5B1EriQr727b3XNW5sV6ZyQjnPgEVs2uR8N2pU2nLUBhSBHAJh8mTne8kS7zmTQVp1bamQSg4JIm6bQ1zkEPalH32091htlhz+8Q/vsXIZXICUHIIgTpuDpn8EUi+FWdNgU5bvvnPSmTQpeFq6NHV1lpJDAogidqvUSvwlhSEH0z1BvSeyWW+DadDArkzlBP4MP//sPff888UtiwmcHEw66aTw1VfOinzxfZezxJWEzcHtA6EM0iZyCBKVVR64P/jA+Y4St03O45JL7K5LAPWPHKJUajEkB1NeHKoOUVNT9/2w16wpdQnyKCU5HHcccOedap15OdscymWVdFBysHVl5WNAlOeU03zoIfV1RajLWji1LCHKxeaggkpyqI3kEGTmFhZbbum4REZRuwVVK337rRNU8dBDw+fJwWfgqpl4Ob3zc85xvjt0cL7LRS3I+6qqrqJ4iMUR5yybLRwXSrjGov5JDnXBlVWnVpIbZZIN6IknnHKo1D9JIa7Z0sqV0eNOBZUcdtkF6N1be5oxhtV8P2M/lMrAO3my886//tru+meecT6i5LBunXltTjGgGsRt+++8efnfOnJQ9buaGuDXX/3TL8VeEhrUP3LgCFO5cbuymu4JWr5iSw6jRjnfc+cml4eMOEXpqIvYYjZIDxs2DC1btsSPNjH9TeRA5AzA338fvjA33qiObMvDl7//frD0RJtD06bAQQeFL5sGkQ3S+YTM/eaQQwqvFWGSSAYNAlq08CdG2zaekkOZ4N13gfXr8y9EtY9CKVxZRSRhc9iwwenIH3/sPcdnzHHPAk1lLkdymD07lo763HPPAQAWLVrkf7GKHMQyHHss0LFjuIJUVwO33w707Ok9F7Stc8g2h08+CVe2uBDFW0mMYSa3R5PNgRup1683p6+THH74oTBwYbrOoQzw7beOOuCii8rHldXWWynqoDVzpjNLVHlMJEUOJogdIuqzxUUOgLOnRxLQPaOf4fPdd6PnrZJKwqpQE1whzRHIaylMBFYVghikuTOF2G5UkO/lZe3QAdhjD33eCaD+kUPQhs31hDNmJKtW+uIL4JFH7NIoB5sDJ4e4YwzZSg5xksPYsd6IoX7pi+ofORRDCPDBTakekd93kjYHG4eAc88F9tnHPk3b8vbvH93bas0aR+I1IYpB2mavabkfijYav8lUGdkc6q+3Eq/c228HevXSGwv5WoHq6mQlBz4rmDbNPw3VYKRSK8Uleqqem9dLqSSHbDZa6ApxoOK7vanUhSosWeKEYOCIoaMayUGGn80hCmzJ2Q18ZwVbchg92j8tv/pp3txRqX33nf6asAZpP8lcJ5GIqqRaRA71T3KQceONwGGHFRx655138CuXGPzIIegiOBFhvZVUEkYSaiVThym1zSFptZJpIFu4sPB/sd1HSy05BEUS6xyktkk1NcABBzh/5s+3u1e3ziHsAG2SSDjCqpX8rksA9ZccNJW+bNkyHHbYYTjzzDOdA7xh+0kOtjM2P5tD2JeeBDmY7g8iOcQ1eMqSQxREIQc576Q7qlx/tYEcVOrTOMvrps8lrhYbNwIffmh3b9gV0jJsDdLi2OBHDltsUaiy1CGVHBKEpnLXrl0LAPiCewbwF1tdXZyorHzQCuPKmpTNQUV8XHI49VRg/Hj9vYcealc3q1Y5G7ioBu2XX3bK8OWX+WN+z2ZSKwD+pBaEHJLqqLoJhy05hClXXN5iGzfmf8dJZnGsAFfM8PtfcIHnmC+Eax966CH0Pe4454+pnlTksHx54X+R5FK1UhHh07iYNCPJvWgbm8PixcCSJZg+fbped+xHDmHVNEmGz1ClIy7++s9/9Pf+97/Kw5MnT8ZNN92UPzB4MHDHHcC//+29mB8TO43fs/Xtaz4fJznowJjj5aZaMxAFqhlq2NW+jBXaD+KSHFSDYIKhPQK1dIXNIXe/uMhNxsiRhfYDoT4ef/zxfBomtZRcLz/+CGy9deExcYKUqpXKB3xQz8gdcPNmZedY57qo/bhsmRM2u1077LPPPhgzZowug/xv1YzaNGitWwd06aI+V2ybQ8Sgfn369MFtt92WP8A7nUpyUKkl/DqHKwFq4SfexyE5LFnixMbxIyrEaJAWIZdz1Srg9dcLj40Z43gevfACxowZgyOPOMI+Pdu8izDL9eTw7bfeaxjDCy+8oBzEcy1dM5lRZ1qYa1ZzvKAfiRIVoF6pL77X+iQ5ENF8IppJRJ8R0VT32C1EtMg99hkRHVvscnFk3UatlBwUaqXv3BXCb0u+5bNnz1ZnEEVymDVLH7pARQ5RZxemBhh3wDlTXry+dYu+wqRdDLUSJ1ALdUoi5MDT2mEHYOBA4IwznNDuy5blr5k1y/n++muce+65+NCktw9LDlFjDWWzwDXXOPp4Wzz4YMHfp556CsOHD8d9p5wC4vs52Ej3JgjXMcby5BBEraQY/Efcc0+gvJNCqVxZD2OMrZCODWeMWdRKTNBUrketxK9TqW0AkHssGzW2UkWFk4fJUGrKo1TrHGwR1fUUCCY5+D17nJKDriyiM0OcsHVl5XWwYAHw8MMOSQBGqcrYisMaa23WgaxaVZgPf47dd3dUPfKMOwCWLl2K888/HwDwhHhCJTmoYKnaYZrjRrWSIu1Pp071z7sOk0PpELPNgXxIRnEi/1tFDroZ7VdfFe78JkNncxg8GDCpCkywcWW1xbp1QLNm3uMPPGBeWCSWI07JIU5ymDoV+N3vnBAJIgHycv/yi105beEXPkNXzqiGYb86r652FrINHgy0bZs/Pny4f9qiVCBGJpUlcE0ZPNOO++7D31u3RuPWrXGE0P4LaiQqOYSRPOQFeoq0G/icB1BnbQ4MwGQimkZEA4TjfyKiz4noCSLaUnUjEQ0goqlENHW5bOGPCVyt5LE5iGolEW5DsB6qVO5zQOF6Cvk6AOjaFTjqKFPB1eRw771OrB1PMRieffZZ1IQdKIJKAWvXAlOmeNcIXHop8Kc/2amVxP0L/AYq8bzNwClDrJdhw8z3vvKKs3Pd4sX6Mvig58qVuBjAb/r1y6evu99WItG5wBqe3ThI+tXZokWODeOoo6KrknS4+GLnW17noKir6dddhwEDBmCTMBEouEpHDi+/bFdOKc9cGqby8w2BDLAih7pocwDQizG2N4C+AC4hokMAPAhgJwDdASwBcK/qRsbYI4yxHoyxHm3atEmkcEZy4C9EfGGal1fht2gO8EoOPJ8wsDRIb9q0CdlsFk8//TT69euHv//97+Hys2mcouvp2rVORMsuXYBRo7BVkLx04UKiwK/8Ijlce22wvPl2kW+8YVeWbBZ/+/prjARQ9f33XulRfn7eNv28WnSLtGzIIYz3E5/gLFsW7f2YJiwabyIVOfAjWnLQlfGVV8zlyyWmIQeTQVpew+AnOVjmnQSKTg6MsUXu9zIALwDYjzG2lDFWwxjLAngUwH7FLpdQPgABXFnzN+Z+Hglg6L33OuK14bqChsE7blhXVpXNQREBcvvKSvTv3z8XGnqJapP1uNCtW/43H8jWrQMuuQRj5WttJAfb6+V7wgx0YVxZeZrc4+XJJ815+KWnQ1i1kmkx2jXXoAIRJQehDP8aN858bZR8BFB1Ne4D0FwRT4mXZrEg0VlJDrYIIzmYiMNFATlENZpHQFHJgYiaElFz/hvA0QC+IKJthctOBvCF6v5YYWuQtnTJE19xzlnwiSe8F/qpleJc56AwPC6F47lRdEgDklbuUxFBGMlh0SLHTgPETw62gfZsO3BYclBJmSZS9LE5HI/4yOGVl14yl82EAKrO7T/6CFcA+N2nn3qL437/aeBAHCAdc/5EHGCl+zOa4wWQ61CxBqbAh1FX53XQ5tAWwP+IaAaAjwG8yhibCOAu1731cwCHAbiiyOXKQbvOQf4tQdnsq6rMmYl6e95x/QylOqjUSjxMsCGGU5d585wG2qKFXT4jRwKHHx68Y0kd3tPw4pYcAODPf9afi0IOf/yjXZohXCIB+Hd8SxXkVVdeidNPP917nyb9LRHRW0k4Xx22HQPBJAf32oaKe3hp/rh0Kd4H0BN6cjA+t24Ro5SnVnLQETZj+aCPAgokBz8pNUEU1VuJMTYPwJ6K478rZjlM0K5zAKzVSjmoyEEnOfCOG0WtpJMcmjRRblHYAED/554D3I1mtGAMePppYP/9HeMxAOy2W7DySQNZIDE+LDlwaSxuyUGHkOSwds0aNA1yH6+PJ590vKQ0eOThh7FKPOAT48iXHAJIDpHIwaLuFy1ejPbID/YZg82ho9undgK0NgfjLPnRR9XHpXUORnuNIk/ddeVCDvVvhXRYV1bnpD5Z1UHVKuKkyOGnnwoXNwF5ctBIMIFiwp53XuFmI0EhdXjtWzC5soqwmV0WmxxkWJTxvffeQ+vWrQPfBwB46638b5WbtXzAR61UVMlBN+ACVs/PY5+ZyIFjpfu8zSC5skbZShXQk4ONzWHZMq2Ls5WTeB1UK5UPwtgcgr4Qv0HJpFYKOjNYvNi7AQtXK2nIwXr2zutC1+GnTwd+/tmchh85BH3eIJJDkPvHjwfOOadoksP777+vVrH973/OqmDA2ePjyCPzC8FEspR3oRPOBSWHFqp75HJZnq/xI4cBA/TnAvSzLO+vBslhtfvdXDgGoMBhJFGDtCpQZ9u2QLt2ymRvDZF3Eqh/5BCH5GCr5jCsi9Cmk8SMIKrk4Edyn3/uv9DOz+ZgQth64oNhEMnht78FnnkmmuQQoOMSkWdgytbUOKEuON580/nMnMlvyp/joeUV8NSxj82B4OPKGlWtJKfZr586Hdu6f+01HPrwwwDUkgMvLVeotgC065EikQNjmDRzJv4gH1dBrMMoqreUHBKGarYhGqQnTCjcCMig8lCulA5CDqpVwHFBQw6xvny/yKNRJIdysTn85z/Ae+/p7wlqWIaaHDbrQkUEHBA8teZjc7gMwGRTgn75C89bo1KPyvc/+6xvOtqiAGA33pj7b7I5cHLwSA4CdvDNUQEhKGeb6mqcKB93sWr16vyfuAb1lBwShmq2IRqkZZHd8ELOEOKhzOc/jjnGnL9qlXES5NCkifKwUXL48stgBni/Xe1sbQ4qIlDVU9LkoJrVnXqqs6WsDrJkqRrkpEVQKnLw9W23dAnVSg7iFqcSupsSDCA5WJGDDm5b+VJcROlTHpNaibe8DPTkcJVdyaQM3NTkZ5XK8qP4zuPSDKQ2h4RhIIdMJuONH6SIyqrCHP6jVStnRi2GVSgjtZL25Y8f7yxgG+tZqpaHXE4NAeXgp1Yy7Z0d1SCtgt9AFSHQmzHtbbct+EtE3rrw81CxJAetzeGdd7xp2iAAOWRV5GDbtrNZTJgwAd3ERZQqCG3KZJDOFQ96cggFHTmIz/noo9gu5v3GY03HgPpLDowpK7jxN9/gEABPzJoFPP649x4L5ObQjAF77eVseO6XhkqttGaNE8wtakPQDNzal8912zNm6NOUO7rfmg4/cjBtsqJC0pJDnz7ByqNK06KMKsmBxeS+qCWHsJDznzMHGDcOaNTICSjnIzkssPUOymb1Ie/F4oiuqAbJwe9YWFTzZzRJDgMGoKmoco1r8lfX1jmUHRQV3P3cc/EuoA5rbPlCPCslxcYjpqFKTxxEL7nEWV+w885W+WoR1CDNy8A9kGz6NfLZAAAgAElEQVTsKSIBrV/vPW+rVuLEVHBxSMnhwQeBUaPCkYOMIC7GbnlrqqutjP5KcjCV2dIG4yFgST23du1aNNi4EZUWZVTmseuuwHbbOXWzfLkvOazn3nN+qKnJL0I1wZIcSHEsDmzauNEZQGUVZJDwGWGRSg4JI2gFW6qVCiSHoHmKETm5OkqxgC0QNOoV7cvnAzmXHFat8l4jS1UiAXXs6A3PbUsOKlgOhtkk9bATJ/pfI3ivAMBmC2+UTCbjJQcfu1ON6TklV9aCtEXJgTE0a9YM9//tb75lzMHkYCFJ4qS4Vum0MWOG0pBPNqozH7WSqqfF2UI28XhOPjaHwgIELEE9C9ldWvgFZDMhjFrJlIbK/qAaGKLOEjT3+0oOHDYqn9mzgX33dVZCy4vxFGlGdmVVPFO1LpyE6vl/+KFw72Q//Pa3+d86FZqUj049NH/+/Nxvpc1Bo/Lkxz4w7dYmgCDVs0gOtrvI+R0Tz4nkYOu91727N0BhTY0vOTQAkBF2RSyFWilH/iabg6cALB/zywZ+zgkJov6RA4euA/rdYwGrAFy687zTMhafe6umHL6SQ1BMneoNSaxJM5DkoFJHKDqgcm8KnYrmzju9iwZt0amT1WVVimBwAPDTTz/lfoexOSxR7TusQAZSPYuqmjAzT9U9vI3Ke6wrrs3o8vz888L/u+/uSw5HymlbkEPcBumN3GlBlhD9JIeuXaNnnpJDgkiQHEKplWT3xy++yG8GH/PeBQ0BVK1Zo5ccImxr+e6pp6pPRCEHWYUFKOtRSQ5xb9HpZKQ+3rlzYUgLCyjJQZd+CG+lgg4ubpAVZgJgaoebNhVKDqprdG1fTpcxO5uDgFJIDlq1Upw2h1StVAKEIIdcp/XZ7Cc36PqpiPwM0hwxk8PfAFx2++1oqbs+woB66McfW6UZakWqCFvJQbP3d9x55/Daa763i1vINtqwAfJSsKyuzLrn+OEHQLEvh4cc3n9fyCREmzLV46ZNBWmqJh46yWGOwjPJyuYgpl0Cg3QotVIt8laqf+QgztADVvDkSZOsrst1DL8QApbk8JHF1oJGSPnwoAXNddcnsRBPIofIDU8lOahIzW+TpjAQdN2hIJRn9/few6HyaR/JwTNwdujgrN6WkIFZdfgIAi7+CiA5qPJtLK4UFvD26697jgWVHEyL4BLzVuKbaakM0pMmqQNV1iJvpfrryipLDm+95fWwkTDPNSSxigrjzDfXrG3iy3AY7AvrVO6dQSDl6fvS6xo5BJyFJg6hnIHULzZqJcG465EcRGSz+VhAtjB5X23a5Kx3cKHKt92cOYqj6iikgSUHxTEVOcSpjMlu3uz0lbvvlk5kgQsv9O6Xzs/FgZQcEoDG9c43cByAGe4q3jUbNuhn3RAkh+++yx+srvb4glutHwBw2IQJvmUzIig5JKGnL4ZaSbUWYc0aX9KPFTYL33zWTPgugjMNnMJKcz9yCIx16/TnLCQHHWIhB0O987LEbZBm1dXOOqQXX5ROGFTWQet940bHeSJqOiFQ/9RKvFJDqJV4I67xcYfNkYMoLl96qROi1y8IVxIvXUqTk4O2+9UGcpDrbto0ZFULFw891N8FM07MnOm7LqXx3Lk547BqEPQ1SFvCT60UGCpy4GWSyCHIWuy9FcfiNEhnFMfiAKuudlaGy8hm9f147tzgGV13nSLzVHKIHzrJwQK5GY7gL64a5JTN+uWXnW+N3jWHJFQ6Cm8lIMA6hzggzZYjz0qyWZx88snYbbfdMPTCC4EePdBC5SklSm8qxN3JXn+9cFKgQLf+/YHmzbVtIdQKaQVilxxU5MsRQXJQbSElk2bWJ01TyO6kbA6suhqjHnsMF3tOMH39LloUU+ZlbJAmoqZEFDFYSwnAKzWbBXbYIdCtfFBlPjFqlGdV4ZJ5WRYtAr79Nl+umPG5JkZSEq6sWiQgObz44ou44447cmE+GmnWFVhLDkXocDkYpIuqv/9dHa4jTnIIMgFgzFFvcANsQSbCRlAhyUEFWXLwG1JLIjls3owPVAsp169Ppg8VZF5G5EBEGSI6i4heJaJlcIKPLiGiL4nobiKKGACoSBAlB1VYCANy5MDDUbz8MnZUeBIZyUFsNLwsRx+dP5bArH2eZoWzVmysJeSQT8wQIlu+1jbNIkGlVqoaM0a9s57bNshS5WJSKyntMzrcfDPQuLH5GmkRXFRykOslTHpBvJUUtOeffnU1lCb6n392tu1NEmVmc3gbzh7d1wLYhjG2PWNsawC9AHwI4K9EdE4CZYwXYuyigMiplXjnPPFEVCr0sNaSA4eo+kiAHHQDcVHVSkkapN2BpJEQlqIA5Sg5hAEPJ295uUlyuHvYMPt8R4/Wn+MeORFsDirI5BBF/21jkA5TXlZToyaHYqDMbA5HMsY80w3G2M8AngfwPBFZ7Y1dUoiSQ0Dwh2slbOyjgrJDclWUSnIQxfUEZgTHao5rX34S5CDtj5CEK2vkdMpEctCCSw62aUNfz+9NmWKfrw3OPx944onc37glhygDi1iWwBMlA1h1NSLs+hEN5UQOKmLgIKItGGMrTdeUDWIgBwD4ee5ctNJcZ5QcVHtSi0hgYNZ1rKKqlSRjZhKSgxblLDkEIQcuOQTYCU43SNtsjhMYjz1WkHcUyDaHMJLDyQC6Id/WPFFqBYSSdDZvRskGvHIgByLaB8DxcKIuVMOpb/GzO4CmALZIrpgxIgI5iJVVY/D5DmyQFhF005sIOEF3IuoKYBWk4Hlx2RzaAWYvGuFa33N+nk0JQBm9VAcuOcRgkA6UbwhEJYfGUnsJQw4D3G++SsBooA8Bv9DqiaJMbA4PA3gFwAIAXwG4Dc5Ws9/C8ULbizFWO4gBiGRzuEL4nTFsI6ncu5eH6fUzBMoRKhPEeboTmpWskSB558SlVloEOGsZIqYDAOjSJVKRguKKK64IplaK0eaQ9AKnqDaH/7voIowT/kexOfCyGNd9hEF1dekWipWJt9L7AK4EMB1OX3yUMXYpY2wUgI2MMUXw/jJGBMlBhIkcPA1ZnGHodoWr65BmgrHaHMLsTWBzLmGMGDEimFopoOTQHcCBmnOJqJXE9GNI4wzh98oI6fD4USa1Uhiw6upY0wuWeRmQA2PsMgD9GWOHAugDYH8i+oCI+iJet+HiICZyUPp8u9jSdF9KDgCid9KPLDe8AVC25AAA+zwrx2Q1IKDkMBrAM5pzVmqlL7+0zIknmn+rcc+oDbuZWyNutZIoOczxc/WNG2WiVgJjbJ37/TNj7M9wSP0sAG2J6LAEyxc/eKeIqC9kpjgzJgTxL69LiJkcBg8eHM+srTYRdEDJwQQrySFsG4d61XNYTEHefuCHXwznMgA6Ri6NgJqaXBvcXOzgjuUgOajAGPueMfY7AAcBuJqI3o23WAmC7+Jlsb+vEbabpcu4777876Re8CWXJJNuFMTsrUQI4N4YQXKYZjxbZASUHEzo7mfEj4g/x5jWqwDmA7BxF+hgOEcoVFVFRk1N7l1Ux0AO1tbGwYOd7VUTRqR2xhj7jDF2DIBb4ilOEfCXvwAtWkSewTcfMiTcjStW5H8nRQ6nneY8Zzkh5pDdBKDS5sIWLcparRQIMUoO19rE+CmTuuEKlN0AKMLc5TATgGnKFvfcnglqpZoY3sl+theeeiqwzTaR8/NDLCo4xtjbcaRTNBCFJgc+tDcMskm4DsOHAyedFD0dGUSF+wWXAxIgh0a+VwFo0sR4+ttvvvHNp2zgSg5lVaYigJPDBgCmsJV+VBZ7jxDUSnGsDNoIoCfMBAegaH27zEaQIoEotFrJuxljRLz0UtwpOs9XZhvcbJDUcDaujv90v1WdxVpy8AnNfkyfPjaplAdcyaFonTao5JCQpCFaB005+O3aEXuPECSHDTGtefgYjo3FiCL17SCB93xLZHNNWaCcyCEJZDJlJzms+PFHz7HLfO7hga9VMl53WEoOPqHZ14a1HcWAwG+ISw7F6mZLlgAffWR/vbhHdYyw9cvp5HM+SclhXVQbppis3wXlRg4A3iaiS4mowOZDRI2I6HAiegqGdVVlhbpODmWoVlItYtrH5x7ToDAcgNWw5ePy93ufGV+S3bAq6A3FlhxOOgnYf/9i5aZFXE6bsb9LwSC9UWhnM7aItibYV0VVhuRwDBxSG0dEi91Q3fMAfAPgTAAjGGNPJlDG+BHB5rA85qIkgjIkB5Xm/1yfe3h30z3J1jYZ+0gOdxjaQdKe5F5Zygf11OZgq1byQxLkoLI5jN/aqmVqUS7kECTw3gYAowCMcqOvtgawnjEWaPEiEc0H8Cucd17NGOshnPsLgHsAtGGMrVCnEAMiSA4b4Ly8st5CrwxtDi1C3ONHDnaJBN8OloMh2YE48M7WpYzlU0LERdJJqJV4muIUY2PEwJW1jhxEuNFXo2hYDpMHfyLaHsDRcGI4JYsI5JCFszFI81gLFDPKUHIIg1jIIcR2sGL+ZUWx2SywaRMOXlJk5WaJJxrFVivVwDI2lEZyiEoOtdHmkDSGwwmDkrxzdQRyYAi3a1RRUYYG6TCIhRw2b/bsJWGLpCWHwKipAWbNKnUpAuH9rl0jpxFUraTZLNZ6JmwbqoM0ksPmiBKeL7XUYVdWBmAyEU0jogEAQEQnAljEGIsjhIo/ItgcgFpADqnkkMe6dUDIAao8loAJyGYB3W53ZYoHOnaMnEZQyeEszfGzoxZEQmbzZqXkEJUc/O5eGyGsSRCUQnXeizG2iIi2BvA6Ec0BcB0clZIRLpkMAIAOHUwL5X0TiiQ5mFZplgXK0OYQBryTlIrmyo4camqAlVHikxYfi5cujZxG0KG2WO8tU12Nm9zfIjmsMQTltIFf+X/+5Rc0jZSDHQL3O3JwDhHd5P7vQETWK78ZY4vc72UAXgBwKIAdAcxwjdXbAZhORJ714YyxRxhjPRhjPdq0aRO06OJDRCKH5OMhRkQqOcSCslMrRTCuR0KEPFdJ+3iEgdjfbEpSTHLo7P4WyWH5qlWR0vUrf7ZIbSBMvxsF4AA47quA43k00uZGImpKRM35bzjSwieMsa0ZYx0ZYx0BLASwN2MssKdfIIRUK9UKcqgjNgfeBaJuHBM1/7JBTQ0eHGnV1WLPNyw2hLT3iAja36K+N9sJQUYwPIujSdTxwa/81UXyWgujVurJGNubiD4FAMbYL0RktVgVQFsAL7grPBsAGMsYmxiiDNEQ0eZQdoOGjDoiOZQa5eit9Nn06SXJNyw2xRCivlwdeDPCIM1pYjOSnzwWS3IIQw6biagC7hhJRG1gWR+MsXkA9vS5pmOIMgUDUWgPFiAlh2KBIYBbYUL5lxVqakqzvibCTHVjDGEliq1Wsr2fBOLjv9aHzP+cAPlXF2GjHyCcWulvcGwFWxPRUAD/A3BHrKVKGgFtDm+fdlrud21QK63fsAHTZxTH8StJMJR2gGZQx3UqGW67DbeVIt8V4dejymqldSFCTRebHGylxQrh2fivTSHzXyj89ru/plzJgTH2DJz1CHcCWAzgRMbYv+MuWKIISA5f7VMYBajsZpQS7hg2DE+OGVPqYkRGqckhC/2KzD8WsyACWpUo37CQJQemkWhNJtyg6xyK1WbWCHti8K2TahBu8lgh1Itf+T+ZOjVEDsERxlvpNDhrEkbCaat3ENHesZcsSRCBBSAHJr24cieHRYsXl0y66QjgNL+LLFHqus4CmKQ5p5Mo5iRUltqKjZLNQUcOptl6sQ3SthD3iufkUB0y/4oGeYWh3/1D77wzRA7BEUatdCNj7Fci6gXgcACPA3gw3mIliyxjoACiGZPWDJQ7OXzw0UeJG/F0y3C+BxBX4GaVCu/bCOndBeBfAa7PwmnYKlWOrg2Uq/G0VJDrKVuhtiCVihx2RT40vKks9yuOtRR+i5JDVHLwQ9FcdUPcw9v/cQAeZYy9CsvQ+uWCoI0tqM6z1OCG3CRh2mgnLqmFAWgsHbsxQnoLEGwPYf4c/1Oc+9jnnhQO5P4iT7RswNvyxRdfHLtaaQ4AeVmhalD8QnFMjDTMJ0txkIPf/eVMDouI6GEA/QC8RkSVIdMpGX4MuGpTbNClWhgVZFPSLJInB5MHUZKNN8rg2zDg9fw5ZBXSuwC+1NyTkkMhbMlBdZQrfnkahx56aKg8deArd+XrVYOZKt6RuB+HqFYK0wYaBCCHYrWxMIP66XBUsX3ccN2tAFwZa6kSRlD3Op2etJgIMuAWQ3IwIU7JIc60w7qBygODqW7jIMbn4OhrawtUs2oODzlorlP1MB6mhhNHhUYlFRafaMqkKovqnYulWS9cV28lB8bYOsbYfxhj37j/lzDGJsdftOQQtHLlASmy5BBiIVNQcijlDDZIWa8ImE4U0gsqOagibgLm54uj3k8D8DZ8FgSVEY40nIsiOXBy4INwRUVFIt5KrVq39i2LX7vj94Qlh4xAfLWOHIjof+73r0S0Wvj8SkSrkyti/AhcuZJaKTL22iuOVLSIIjlcEuKeXxT528I0mKrSiVL/QclBFXHTrwxRyUE0uH8eMa1iIUgkIV3d3as4xtcO8GEzk8ngAZ/0Z86cidtvvz1AiYB99ysMDWerVhLxg/s9CuHaAAXQTpQdOTDGernfzRljLfgHwBYALk6qgOWA5csLNwcthc0h6IAblhyWhbjnBEX+togqxenQB05HFRFUrcTfcxDJIWrHvSri/aVAoLbJGJ5WHL8RgLw8jtc7H6QqKipwj0/6u+++O849L9hW9hlpYLZVK4lYAae9jEJItVItlxxaENG1RPQAER3lRmf9E5zJTlyu7UVB0Mq94478AvBSGaSLZXOwzUdcf22rV1bBNNirNMzFtDnwzhFWcjgWwK9bbqm71IMecEIP1DYEeSdzv/tOe06uV5XkYIWAHlEZyZYRRnJgmt+2qO02hzEAugCYCeAPcNSipwE4mTF2YgJlSwxRKjfqi7nw8HhNjQ8BeF46ZiIH3aIu8V4/3A+gl+GeoESmQxRymAsviYeVHIKQAz+XBTABwLPXX2+dX7m7Sc/UHA86GdAN3fK75W4j/L1ZG6QDkgNJ6Yp3T3G/5f70+p6FFqGs5rctgtgcDj744BA5BEcQcujEGDufMfYwnHDdu8HxWPosmaIlh1J2wmVN492m4yJ4N/M2GaT9FpHxujFtKTMfwBrhv5xXXGqlMOQwCs7K1bmKc0FtDhzywGAjOfBrGsS0uCnarsTxQFf3Qd+3buiWn1+lVrJCjJID90KS679auieq5EAKctDZnMKsFQmDIOSQU70yxmoALGSMlf2maCpElRzKTa0kl8dkc/DryOLM1xZJqZXC6H4Z8sQm10tYg7RcRlvJAfAOPCaY0i12NNb/KI7p3lWQ923qO3I6XHIQvZXsMokmOWQUv+V2t1lScUVdKNtAQQ5PQv3eyzHw3p6ihxKA39RVb6V5PuejkMP48eMxZMgQ3+vkSIamMssv0aRWataihTFfnk8QX/5yUiuR5jcQ3uYQhBxkyaGioT0lldMCOlVZ4iCHIIsn+VJV/h6tbQ4BYTJI68ihRrpHLLuunuRx5RoA3NUlU1GB3r17F6RFinzlvJJEEG+lCsFLqTljrIHw2zzilBEYY76VG2R2EwY333yz7zWy2S4ucmixxRbGfG0kBz8yCDLIBTVIi+/m73DUajqUUnLIqZV8yEF0HQ4SHry1/yWRkNSg1BN2NodOcAyb3xx5ZC4eVmJqJUn1J96tI4fqEJKD3KdJuDZTUYEzzjij4P5OHTsq0ynnbUJrNaKSQxTMDnCtPCA9ZbhWLq9RcmjZUnOmMN8g5GAaPH8PwESFJklF1TjFIF6XQR9SW4VxAa4FwpGDXH9+AdVEG1AQcvgpwLVhUAopRqzX7+A8Y4dXXkGNSwpJeSuZ1Er8jFwf1YZgnGEk54qKCgwYMAB///vf8+XQPG9KDgnBhhz8BsZGAVQFIoLENZfLMAH5FaMy5PlUVnE/x+FHmtazxq9WehL6OER++anmiXLAP1M5xe77KYA3DNeqwDvHUvfDF3vFKTmI76kcjM4cqnpNmjBU9ZrJZHKDJNkO+kElhxBqpTCSg2lRZ6aiAkSEli1b5gkjJYfiQiQHnUeOX+dv3qyZ5/iZNnlbXMOh8gDS3R9ErdSwsRzn1HuvKn/VNbr/8r1HGAjJJKnI5DAehfslbLvttp4BNU6pT1wEtw2cmEdAvJJDuZKD6hl1baJHjx6J5UlEmDhxIk477TRUVppiARfcZDx9L4CdxcsN5KCVHAxSjK1tRixlw0aOTCyGCNFJDtUpOSSDbDbrOzv2q3qV7lPnA16Qt8U1umtN95rUSj8C+K14UmpwcgjCOMjB0wkMumJTfvJdv0VheRs3bmwtOYRyL5T+y1KBCh5X1kaF0ezlUBN+5PCO4pjfKmEVOga8XjWFiEtysF3nADjkcPjhh+PZZ5+NTa30A4CeZ52VP6Aghz8CuPPII5VOCVvATA5b+Nj1RPB0q5o4AcBFctBJDiwlh2QgVmxYd8+ws9NSSA6/IO/1AQCQBmrdAi8b1YlYNtN5OU/VvTbkIKftRw5RYeuPrzqX6+CC5FAFr++6HzkcAaD3AQcUHFuuuM4PKwGs3HVX6+u9srFBXRLTYKWTHDjiIgcG4DwxxIZ0PQF4BMCX22yT61uPPPZY7vwqeG0OHFtuuSUeFa6V89Uda6Ighwaa5y3Wvub1khz8JAfVQPURvx9q3afNrCopcrgPwM/StfzZNsv3SQO1Lm5QEHKQ/++8yy6F5936UoXuNUkOqsYpk0OSqpgp0v8gkgP/Fm0OGxT3+pFDFkCDJk0UZwoxy+d8FsCH993nmw6Hihy0i+AC+t0HIV2xr8Vlc/D0Yel63u4YY7kJSiNJHauTHBo3bqx1XzaplRpXObtDiFoJHRluVB6NH/WaHIL4bb/jfldD3UhtBn7TNcdJ/4OQwwwAWyE/0DPh2s1wjLE5SA1ORw4b4BiTVR4+fuQw56vCrYl+duMLmcihicKOE1VyiGp/OEmTd1jJwXQ9oJ8R2uja/Z41C/tBfDKAlxTHdc8dhBx028vq0reSHAIaoMV82rVrpyUH8TdJ71FHDplMxro8oisrVytlMpl829GkUyzbVL0jhz//+c+hbA63w5mhPwJ1R4xKDn6qGhM5qNLiTXkznMaUW6UYQHL4PZxdz/zK6imX1KiXt26N7aEOy5ybYSsGUblxNmjQoCCvysrKRA3Sa6T/oWwOMXgrNbTwjouTHI6F99l5GirYqpW2hGPY52WVnTj8UtFKDrLa0kJy4HXRrVs3pc0hlzRPUu43Qh53/O53+XszGe2qePn5GsBLDqnNoYRYv369r+SgOr4GwF/giHSkeDktfVYeA9FUNUHJgQ8nfPDPdSxLycFUR77kIIGIsFBzLndvI+825HIX22OPPQryqqqqUhL8Aw84Uf/jXq9iQw7c4KxSK6nutSGHRoq6kTHzmGOM54OQg27DmqiSw0oAv0rpPQjHaYKX0QQtOciDaAByUM30+T/GWH6AlAZ8cYX0GmHtUCaT8ZZHgwJycNVKROTvylqG4TPqDMLYHDieeuopZSf56GPdlvN2kPNUxUuyhSg5eAYcS3IwGYplJUfoTi3eW1GBPaRzcgiRyZMno6XQESsrK5Xv8JJLwmxZ5A8bclgmXRNEctC6H/sQzAYAc/Y2r6JRkYMqYiZ7+21PucQ0VIgyk70YwLYAmjZt6jvJsFYr+ZBDt27djOTAc9lzzz31koNYFkHqNUkOMkRyqBRsGvxYRvMcU6dO9ewxkwRSchAgz/pUOPfcc9UnIkZKlDuGamGb7wzd/f74k0+8kkMuYb1aaSa8A6AqTzmubBh1wNMAThTvJfIQ4iLpf+vWrXFQr3ywcJVaqSBfn3KpkFMQHHSQ51wQcuBz/SDkIGLYsGG53zZhI/xUT3y2vPbqq3PHxiuuIym+j4g/atKOayYbWq0UUHK4+JJLCslBoVYaNmwYBg8erJUcCryVBHIgIu2ubvLziW+soUI65GR4V/PmOFk6N23aNGUecaLekYMotulm675NXTVT0jTI+y3LJaeock+1nZ+1btMmt1iM77qVK53UcDlB/nG33bAfvAPgB4r0ZckhzIxvCICXxXszGbvBXKhnlVopqippMYCTDj4YeMO7ntqGHLjXGJdv5IHdz7YEAC1btsTVwiDu56VD8I/+Wg1nEF8jSFU87zcUBm/VM+oCUgaVHMK4CAMGySEgOYAoV2YiUkoO+++/PzKZTH6SJkvcoqFcIGaTWslkc+DkoFIrPbDFFnhRutc6zlQE1DtyAPSSA5+F+qpJAnSGVy2vk/O0kRx0G2lkKiqwAE4nfIYf5I1ZalQ835YdOhS4WvLv2XBmwZcAeNwNBBaWHDp37uy5J/fcCslBBXGgVK2QLrjWIj0V1jRqBChWkvMhQLfGfDS8ajy//RxUdbfVVlv5lLAQts+ZzWax+te81j+3FsbCNftmOGV9Z+BAXKBIF4Yd3jhOOOEEnHrqqTj99NMBmG1Xd955JxpL7yCy5HDBBbnrTWqlGci/NxtvpQqJHPyIerH7LZIDz08kB65WUpFiUhFqC/JIPIcyBG8K8pIgvvo2lAZV0yBNrnsi5DxlIVMmh8UXXYS9NGlVKgY2nVqJp9nc3YRINTveDHfjdHd2E9TmcMghh2DXXXfFnXfe6cnXpFZSQqjnLbbYIpFFcLqZ8AD3W7ftYX9468KPHOQO2KtXLzz33HMFx+RBcQ68sGmz2WwWXbt1y/83XCun9777/fNRR+EJAMdL6foaYXfZBS+//DKee+45tbefVOfXXHMN1q9fX3AssuQgHNeRw9Fw9h/n721gRQWmAahu27YgKVGtJM7ibdRKXJXbEF7JQbyOSw4qUkwlhwRARNjN/S0/PCcH0a9c3qQegFqtpGkQ65VHFUlK/+XhXSYHlQ80P1Jl2m1OKOc3yG/q8qvrSnfiSdJXD3UAACAASURBVCcpywMAcOslqOTQsmVLfPnllwUxeDzkYDkTkjtekHUOn376qfI6AHhTc09QBCUH+eyUKVOw11462ncISLYV2G6mcuaZZxa8KxM56FSuvG+85XrXAO7AblLlzJ0LfPKJZSn1sJYcdODXMVaoVhLu/y8c1SB/b+80aIAeAEiyCTQU+pi8cE1HDhxcuhQlh0bCmCOTAyfFQS1bor+QT9Kod+QAqFd/AnlyyAqNUBUSmouNBVppTcO1JQe5M6pm52LH1nkyiOUToZIcvoWj+7/49NOx2iWHHTt10hcyJDlkpEYu3uOnVjpd+i93vCDrHLp37648Pu6IIwrTiOBccNbZZxf8l8lBpXfm6NChQ8G5oUOHetKfrsjzQEW6OtiSgy497lYrzvR9JYdOnQAxVLx7b1AJPTbJgTGt5KBS84jfAHDTTTfh+ltvVZYrk8nkPJtWAFgovH+etoocuOOCqFbieXLyGdeoEUYr8kwK9ZIcdMiplYSGr2pmLZo3BwCMsEgzrFpJlhxkg7TKB1pU0WihUCutb9Ik1xCNRldXXRWWHEjRCcUyy0HpAK87q/xscayQ/mqHHTzlCgs5zIKN5JB16+f7778vONfcbWdivame9xuEcyc11Z1OchDJYdVZZ+EjWEgOMjTk8O235h3OI9scLMiBQyaHTCYDTJ8OTJmCW2+9FS3btMldq5McNgEY3qqVJ+2gaiVels2b876FqVopAZhmhbY2B6VXU8ySg7xCtVoqV2NTSAWDykk1wyMiK3IgDTnYrnPwkxzmATjMJy352WTJ4WDB1dV2uBR92AnmNuKHMOTw9JAhgELlFSSGVxhSCyI5yOTQsGFD/DJ0KPaHKznEsOn9TjvtZDwfeZ0Dvz+bzZGpn+SQT5KAvfYCePsSBvNVq/LTmoceeqhQulWkLZIDRyOFt1JGkhxWrsxvMpBKDglA7nCiJpQHtBI7jbKZuQ2roHNJM4QV7ncYm0MXSJFU4Z3lNWncGF9//XXBsV9sMlKpnBTkoAyfHFFyUJGDbHN4B8APV1yBu909IEaPHo0C+EgOu3btmvt9JQDuDS6W8WIAeEmIHiR0yKhoKJG2jbfS+latAIXKKwg5hNkAhted0kCsuYcPYpWVlbn3GVhyUOVnUX4taduSg0JykG0ONmolADkVKwDU1ORb4YEHHpi/B4X1aKNWEsElB5WUkEoORcBByO/FYO2tpCKHFi0Agdl3yGRQhXDk8DW8rqyekAaMYRcp+ukBALIPPFCwKMcDlTpK6JgmyWHZ9tsDAMbI97vfuoFLpVbi2yGqVGE/nXsuPtt6awCKGZyfQdp9lhYtWmA58h5GYtd+EAB+m9/l4uj/+798+ogmOcj7N8jll73Q3rHIj4istm9VYR6AjzWzzDv/+lftfXI+N15/PaZMmVJADrzcVt5KIkKuqI4cW0mQHHr27AkAOOecc6zUSp68hTyrqwvl14JJkCJtlVqJCQsJZclBGXesLkoORDSfiGYS0WdENNU9dhsRfe4em0xE7YpVns3ISw98X17bDuhp4oLRbYP7sY2g6LfOQUUOMuYCyLiLnG6++WZ1RopZEiA0foOxcOPWW4OQ93CS09HpsFVqpZbuhiiiWilfxEyuwzVo0AC45hqAezoJ1xGRtn5XrVqFHQRbggkHHHkkDlKsiD7wwAO19zRr1gzXw+tW2sBHcpDnhwz6QS8OtdJOAI7UeK+ZvNrk9A466CD06tUrtxK7UaNGaNu2LVq2bIl77rknlOSgLHOHDkCA0OIAQtkcdtppJzDGcNxxxxVczydcPNaRzRalMjnIUjiHSXKodu0JBWqleio5HMYY684Y476NdzPGfsMY6w7gFQA3JZWx+JLvdr8vAdALjmEPMBvqAKglB88lwWZHJi8W5TU+6ctbN+rWOQBSwzeQQ5XgviiC14Ou3lRqJT7IqFxZKyoqcsa3hg0bAnfemXOFFMtaUVFhJF+VGksJxSpZAHjttdcMtxDugHetTFDJgaely0OGNpKwoT1oZ5ldugAApitUGp62zQc8N5/Kyko0atQIK1euxBlnnBGLzQEA8P33wBVXBLsnqCurHO5DKPv48ePxyiuvYGtXctVKDgKy2SxOOukkTJgwofAeqCWH/8KJdjwY+XYpagF0NofCR6mDkoMKjDHRVbspojuNWKHVXXcBcGb47wEYCkfl8Iywt4CySbg6xpzvwHbbRS4LA/D9Y4/hT+5/v70Mwormuo6Um+24HUeVurxiVS6XjixVHWzbdu0K75EHfVFyKEws93PgwIEYMHCgJtfCDqR8j4IBVDzPyykG+TvppMLdHXSdU7Y5yNepyEGXlqrexDo+AsCl7m9Ta9AOJAceCHz1FZ5USBBiejN79wakfcC32WYbubCGEsiJ51Pn6yZsJlPaa0LYHAog1M9OO+/sSBO5W/zJYfPmzXjhhRdwjBsZV7fOgafQ45BDsGTcOHwBYZ2DS9CdO3e2UivVVcmBAZhMRNOIiKuEQURDiegHAGdDIzkQ0QAimkpEU+OISlglbTCzCo6xcp1fQ3UHrs1wjbNz53ouCSo5ZAFs6NULI93/yxTXxEIOmkYlznbEvIYMGZK7Jiw5qCSH7V2Vj8rmkMlkCiUHsZxCGk2aNMGDDz6IOe4sT5eviL333ht78wims2cDfBWuz+DWqVOnggWRusFClhzk61Th8WwkB1UdvwXgAXVxC2BcH9C5s3JdDM/nFwAfnnVWzo7VtWtXDB8+HP/617+8aQXE2LFj8fnn8sapISDn7bcewiA5yLAlBx1UksMxffpgjz2cGMS59u+WqWPHjp7r643NAUAvxtjeAPoCuISIDgEAxtj1jLHt4YQD+pPqRsbYI4yxHoyxHm0EP+MgKNh2UGO4LdDFqy5wX2Q1XCO2Rbx9wCEMnaqCofCF3w/gHFNiPpEwPY2Zk4kwEOSMYaJBWlArDRgwADvuuGPunB85BFErNaqqQmVlpVatdP3116N58+bYf//9C59L0Snu6NMHF+YfwJOvWMZp06blI1o2bJhbu6GSHCAdu0rxTDJkyUFGWLWS0n1aQCi1ktsWVOd5anLJiAiXX3452krhJMJIDo0aNbLaq8IXIWwOWkj3hiEH3bsQU8h5eimu41Iqf6p6Y3NgjC1yv5cBeAHAftIlzwA4tRhlyej2evVZBMfVStXQvyRdY+KNYi84xsyN7nXjx48v6KQ1EILmwYkSGURWOPzww9GnTx9cddVVhSd8VBgQ1EryM+jIwc/moOxgmQyGDBmiVSv16tULq1evRit5EZFm4FbVTSaTyaVvuym7bgiQjd+69+tHDmElBz67D0MO2oFEQdq59HgZfNLOIYzNQXChjoQQ4TMKYHi+yOTgMw6oytDTnRDxO+uFzYGImhJRc/4bTpyrL4hI9Mk8EerYYvGXR7edn9RYPIZYgRzat2/vuX869Lt38Zf6GRxj5hI37XbbbWecDeyyyy6B1EpVVVWYOHFiLmSEyiD9vHC9yltJ7hA6g7Q4qx0xwrtuXCU5oKICgwcPxrhx43gBhFOGWZGGHFRo2LAhZgAYBqCfPkUAheK/SEh/dd09TZ5RIip8ZsKtFPp90U9eBZ3NwRZ+5KA6L+ZjtV+DUMbXd9/dfK04+ZIM3SZwG9DI/v0LT9gOlNIEyHiNVD7TYLxp06aC/6EkBwWh1CtyANAWwP+IaAaAjwG8yhibCGAYEX1BRJ/DIYxBSRWgYCDRdJqVkji/5ZZbFl7gduZbb78d//3vfwtONYQjCvmRA0duUCIyvnDGWCE5uA38lVdewX0G1z/PbN995jlALk6LlJGTPNwZudBoxdg/hx12WO43L3UWyBnlRCg7WEUFMpkMtnEN07LNQQdl3CgNOTRq1AgMwLVQx8jSYdSovHVBDNAmDuG6AaBCUFWqNuDJKIhg9Wpz6Dy/8Bmm8gD+K4tNkoNf2nJaADBR8pQz3RNEcmjSpAk2bNiAix97TJu3X34AzJJDDGqlBq7Ke6ihbEHIQfV+6pxaiTE2jzG2p/vpxhgb6h4/lTG2u+vOegJXPSUNnc3hwwYNACG0sadzuB38lH79PL701XA6MB8Y5Jcov+is0GADkYNbpuOOOw6HHHKI8zyKhpgboPgzuHlsFK4RV0iTQXLgM7dWrVpht912yx3nT1ijKYPSV5zXi0COcj5K+EkOwrsKpM9272uz1VbYwl2D4RwOZvgXY/vLM0pATQ5ByhlGcvCbZarO83wIlpKDZDOyRVC1krj4LjB0BumQaqXv+/bFw/CSQ6t27TDgD3/ASOi9yGzIQSlxS/cnibJwZS0VKkwriU85BYBG58o7uOF+PijLM2ktOWSzxhdeYLwFChpTU1dVobrfM3t1O67K0OgkW0gO4rNXVFTgm2++waxZs5TG0rWaMiifSyaHTCbnqdGsmS5uLrTkoOqEsRg7hTxEaCUHnzxfv/pq4PR8rNkPP/wQAwYMMNyRKwAALzm0aNECd911Vzibg+F8FMnBdg/lwtsj2B7ilBw8t+jT3jhiBAYC6N27t+dc3759PWWzNUjL19cLyaEcUGDk0wzGcqyYIOTw5JNPYtKkSbmBSc5Du21kTY2RHO6+++7CA0KZmrjhto2SA4cmfAZXnTUR7ApyehUVFdh55509Pu6LAdwIZ5MU1TPwdApc8ng98OuJ8Pnnn+Pnn3+GCSpvJV0HrvQxDqszUJOANTn47OW8fJddgMcfz/3v2bNnJMnhwgsvxJVXXhlOrWQ4H1hyCEIOIW0OofCXv+R/RyAHVfk6d+6MhQsXYvDgwdr7amJQK5mk8SRhjgpWB2FDDmJnUEoO/LyCHM477zwA6rj3qjx5uGbU1BhnA61atSoMaR2RHOQrr7rqKrRo0QLHdOkCjBjhca0FColNfq7b3W9TQy54PoVaiYeoNiHIDDMIOfCQyedI+zHETQ5uYlZlUuXtCaVtMbiGIYcokkMHy7AlsXkrmdK4+27g3nsLrwtADgXBBRVQOaQ4WTl5rRXGiMAGaYNNKJUcEsYBBxygPO4rORjIgYMPyrI+0kat1KJFC3z00UeYP39+YblUZUCeHExqJZW3kojKykoMGjQoFwlSZXMQG6RKnw7FPbpjHltDUNWALv2QNocKNxBbX8kTRnz3Z511FiYDGCgdvx/A39zfGb8orAEimNqQgw7Tnn8eH95/v1OmItscBvzxj5aljKhOyididy6CK6tVHQjgdfqrpr+ZXFlxxhlA+/aYe/TRBWUw3p8A6jU5iIZHEfI6B+3MyTBLPPVUZ6mG7Kev9VYS1EqMMey3334eY7fO5lBVVYXLLrvM4znlFNFfcuDkIqarsjmIaiHTqlAZxoYsGcr9oFMrqd6Q0bAtY8gQYNo04De/kYrH3OJl8Mwzz6APgIdR2CYuR969zo8c3ALbl0u6RzZn84CBchvd55RT0NT1KCtnm0Pi5KC6LoRBOqjai9+32i9cjaoM7doBCxdinUYqAVLJIRHIgdtUEGd3RnIwDARDhgzBjz/+iAsuuKDguC05KMtVWMjcTyLC/fffj/32k9cT6iUHW3IQIdZXEHIwDgC8o8YlOQi45557cO2119qlW1EB8LAaAoKqlfxIjojCkQPPV/p/8sknm8sD/wE4k8mgGYCpb7+tzCeozcH3+XhZBbVSLDaHP/zBfF4nORgQlRzWqNRKRGa1kgt+jar+U8khYeg6jdwQwpBDJpNB27ZtcYS0P7HW5pDN+nZiHTmYoPNWEtFUXJjl463EEUStZCU5WA6YHYVwHqY8AUcyvOOOO6zS1UFL1Apb0vPPP+9LDoyxUHGIOHElYbbNZDJYC6BaWBMTxSDtCwU5RAKRk+Yjj/hfB3glB4NtKio5rJd2GeTgfSLXOjt39qRhIodUckgYQchh6tSp+OGHHwovtFEhSJAHyjlc7dS2bWjJwYSwaiW+CE6ELDk8AGCGFK00NDlYDpgXXXyx55jO5hAH/CQHvgBxhx12wCmnnGL3HGEGxNdew8bXX9eGAYky85YHoW+++Sa3A59Rci5MBDjkEOA//wn0fLGQgx+OPhp45hm9QVps/xKeeOIJ9OjRA+3aBdtiJrc+IpPBbJd8HoazkRfOPTdX5y/w8ihUoOJ78VNPJ4F6Rw42jVFlkN5nn32wnRyaO8QLkhn/2d12A2bOBLp18zV+RSGH3NP4kcPOOwMAXoPZW2nTpk24FMCcM87wLUOcaqUgK6TjgB859BL2rAYQKzkUDMqtWoHJeQW53wD+Xnm723nnnbGjG868QUUFLlYQsgdEwLvvAiefXFxyuPhi4LnnzNdMmgScdZZ+EZxh06MjjzwSn3zyiXK1uwmq3eC+h7MFMNq3txrcRXI42jVOq9JPCvWOHGzg68qaOxm8YXteakUF4Mai8RNhw5AD99iZz/NVNKqCdQudO+Ppe+/FSACtW7fWqpW4zUH2CEparRRkEVyc0JEDrxNmKQH17NkztLeS3wp6nfmdyImkqgNPtyDGk5tno4YNrVyMpQzN5+Nc5zBypFIlYyyXnJeBHMLCxs7jB5EcRo4ciVtvvTV3LlUrlQi+rqzS3s1BIDcKsRE1btwYVVVVuN91QfQppFV+uZXajRsDzz+vNEif4q4G5zh70CA88sgjuOKKKwrEabHs3OZgs5bA2FECqpWCGKTjgDxAX3nlldhjjz1yx7kHV66NGDotYwxdu3YNPKmwJQdThKaBFpsiFUisIYy3OQQg+qKolTh0z2RQK4WFKuyGyuZggqxWuummmzznkkS9IwdrtRK/HgpyeP994OOPQ+Uvv1TxfyaTwbp167ThFKKolRYDTkgQwQuLQ2Vb+MMf/oCGDRuiT58+ynS55CCTQ2DJIQZvpSQhk8Ndd92Fzz//XE8OSdkcYK7HSy+9NBeBl0Nst8ZghipyiFLP5WZzyGfmfMtqJR6u5YQTYszKSw4igpKDLv0kUe9WSNvAV3Jo3dr5hICJHJT4xz9yZdEtgjOBk0M26CDsgyCSQ6xqJQWICBv4n5hVBH7eSsUkB9OA0KFDB3z66afKdktEBWqIowA8e9NN4LGGZZtDlDIGvbcsJIejjnJsF9dcE1tWBeSgmJBFJYdioN5JDjawXgQXAia1khJnn+0Y0xBOcuCD107CfslAvqHOmDHDKh0ZF110EQDHeCnCszkPLNVKEW0O/wbw/rHHAsOG2aUTEDqbg6eTxyjuy+0u7EBKVBgO/g0A6wTpVGlziKJW8kOcNgcdevXy7u1+1FHO94knFh5v2NCxXWy/fWzZi5GI+ZP9/vzz8dFHHxWct0lDJIcrr7wytjL65l+0nMoENh0sm80WsH2cDVc2JAXp8GEN0i+99BLeeOMNniEAoE2bNujYsSN+I60ItkX//v3BGMNWW20lFIkVej65iNOVVUcOWQAfH3UUENR46gOdt9LDDz+MNm3a5CSzQJJDQMQxuzZJrNdddx0aNmyIfffdV8w0fGblYHOYMgWQXc9/8xunvR18cDJ5ClDZGo444ojcQtWw5OAXgTdO1DtyAFBguJs4caL6IpNaKSiEENSB1UoCeClWAcCNN1rf99vf/tYTSXXLli3x3XffWaehg035Y10hrUAQFVdQ6Mihf//+WLZsmVclo6uPFi1C5x0HTG7Jhx56KDZt2lRA9IkapBWSQ12D6rmYMMinaqUyBBFhewCP3u7EEd1zzz0918hqpdYh7Qs5LFwILF0KIBo5cBwMAJ06hSuLzp3PgGOPPdaQnH/nNj4jH9Dl3fYCYMMGx+Kg2+M6CvwGaB6f69xzz3UOqJ516VJgwYLQZZDrOKjPPWAmB02mgfNQ3btixQrveR7TrHHjOk8ORFSwBa183oRSk0O9NEivBrDeVT+oXpKoVurbty/OFLaNDAVh9aPcST0L6wzgw1Sk7hSiM7788svaWEq6Rv4VAL6dn5EcevcG7rkHkGJQBQEnh2JKDhzNmjXD2rVr88Sketatt46tPE899RR69uyJww8/HPvss4/xWpO3ku+kJCbJoUAa4Rg5EthrL+CII0Dr1nnKWhcgksPiykp0W7cONcLkJSWHMoap0zPGnLC5Q4ag+/DhQMeOseXLX3jTpk3x6KOP5qK32uBqAGMAfBtHQQJ0xoqKCu1MU9fIu1pc454s3JAlBIohOZieocDOEkQS3GOPwOXhEsqiRf476Xbu3BlbbbUVhg0b5nl/vpKDbjWxDfwGvi22ANwNcuqq5CAapCtGj8Z555yDkQYJ3JRGSg5FgtwYtY1zxx2B9etjz19sNGeeeWageycCaBO1ACHUSmFw22234UbXLpL0gp1Sk0MBuCutZq+QHGbMADp0sMo7LJo2bZpT6/z0008F53zfCVddxUgOmzdvxsKFC3Pvy0k+iwkTJgAAZs+ebZ+Hew+C3FNENG3aFBMmTECjRo2w7bbb4pqPP/bEZvN77qqqqlwagerGRePGjbHddtuFUkMC9ZAcZBRjpaEqv5KJ0UWaqd1www05ckh6dlhW5LDFFsCsWcC225qvC+AlloS3kq/kkICKbuHChWjevDk6duyYe6ZsNov169eDiLDrrrvaJ7Z2rfMd5J4iYs2aNaiurkbTpk21z7XWfQbT+erqajRp0iRY3cBptz/99BMWLlyIHRWRjG1Q7wzSHIE7fUzwxOIpFYqYf8HA1LdvoIHRBmVFDgCw226RDOxy3nEgsM0hAXLYsGEDttpqK70qN0VsICJstdVWBVJaUNQ7crBWKyWEYksqHhRJrVSYpVDHr73mqFSiYO+9gcceE/46ex3I7rpxoGtXx3oiL/YrJuJoo7JqwVdyCLDFahDUVRtDEoi6QDBqXdd7tVK9JYfajGnTCv7ed999uOCCC9AprHuvAf3790e3bt2w//77x552MVFVVVXwvxSSQ31ElPGlqqoKrVq1SmTSY4N6JzlwlEqtVHKbA58RxtjgRowYgc8++yy29IKisrIyJz3EDSIqGTHE2Ubkdl4fyWH+/PnY3Q2PnzT4u3vggQdwzz33eM7fcsstOPbYY3HWWWdhl112wSmnnIIvv/wyd753797Yd9990alTJzRp0gRTp05F7969C9K4/PLL0b59+8S8meodOZx99tkA8gu7ik0OJRer27UDnnwSeOml2JIcNGiQcjFhingQqM0ccQRw2GHRM01IrSSj5P2hhDjzzDMxduxYfPPNN+jXrx8OP/xwLF++PHd+2bJlOY8mGdlsFi+88AK23357vPvuu4mUr96plfbdd9/CFdAlapwlNcCdd17p8k6RLHgMrahIuF9cfvnlOWnz119/BYBgmwq594ixtLp3744RI0YYb6uursbZZ5+N6dOno1u3bnj66afRpEkTvPnmmxg8eDCqq6ux77774sEHH0RlZSU6duyIqVOnonXr1pg6dSoGDx6Md955B7fccgsWLFiAefPmYcGCBbj88stx2WWXAQCGDh2K0aNHo1mzZmjfvj06WqyT6tevH1599VWMHTsWgwYNAuAE2Rs6dCj69u3ruf6dd95Bt27d0K9fP4wbNw6HxTEhkFDvJAcZxbYB8J3TzrDYXjNFiiRQzMietgjrix8UX331FS6++GLMnj0bLVq0wKhRo7Bhwwacf/75+Ne//oWZM2eiuroaDz74oG9ac+bMwaRJk/Dxxx/j1ltvxebNmzFt2jT885//xHvvvYcRI0bgiy++MKbRTIi7tvfee2POnDm5/wcccAAaNWqEt99+23PfuHHjcOaZZ+Lkk0/Gq6++qo1gEAX1TnKQUWzJoUGDBlixYgVaKjYUt8XkyZNjLFGKckVS0uVdd92VSLpBIM7wq6urkclkgk3UvvkGWLUK6NEjUL7bb789DjroIADAOeecg7/97W846qijsOOOO6Kzu93oeeedh5EjRxq3VgWA4447DpWVlaisrMTWW2+NpUuXYsqUKTj55JPRpEkTNGvWzDijb9++fS5PQP2+b7jhBtx+++3461//mju2adMmvPbaa7jvvvvQvHlz9OzZE5MmTcLxxx8fqC78kJJDCdRKyngzAXAUj0ufol4grjb6wQcflOV6Ar7nSCCE3Ko3qCt7gwYNcgZfec2AGMuroqIC1dXVgcoiE+Knn36KHhLZHX744bjhhhvw4Ycf5o5NmjQJK1euxB5u+JV169ahqqoqdnKo92olEYceemipi5AiRQ5xD+T7778/DvAL6yHinHOcIHnhMwx/b0JYsGABPvjgAwDA2LFj0atXL3Tp0gXz58/Ht986UcvGjBmTGws6duyIaa7r9PPPP++b/iGHHIIXX3wR69evx9q1a5UqIRWef/55TJ48WRlS54YbbiiQ9saNG4fHHnsM8+fPx/z58/Hdd9/h9ddfxzo3iGFcSMnBRePGjfHOO+/gxhtvxPvvv1/q4qRIkUPJPHrGjHG2zwyDuXOB11+PtzwxoEuXLhg5ciR23XVX/PLLL7jooovQuHFjjB49Gqeddhr22GMPZDIZDBw4EABw8803Y9CgQejRo4f/wkE4doN+/frhwAMPxKBBg3KzexWGDx+O7t27Y5dddsE//vEPvPXWW2jTxhs97dhjj80dX7duHSZOnIjjjjsud75p06bo1asXxo8fH7Q6jKByFDNt0KNHDzZ16tTI6axfvx5NmjRB48aNsT6BQHtxIrEtFRNCuZR3m222wfbbb49PPvmkpOUIihEjRuCKK67AoEGDfL1wagNmz54dOEZQbcXq1avx9ddfo3nz5ujSpUvJyqGqcyKaxhjzNdbUe5tDZWUlmjZtiuHDh5e6KCkSwo8//ljqIqRIUetQ78khk8lgzZo1pS5GihQelFriSlG/UXRyIKL5/9/e/QdXVd55HH9/KmooVEQNLG1AwrasMEMLlFGUli1um4jTgozMrB1ntKVaWX+s0j8wkZFBbWe2a8cVWOVHLasWSRVa0KFTSdAoMlWgHRVYEC+kWQurBaIE4kgs5ds/znOvJ7lJDJDck9z7s+ujeAAAC7pJREFUfc3cyTnP+fU8eQ58c57z3OcBjgF/A06Y2QRJDwLfAT4G9gHfN7Mjuc6b61ovv/wyW7ZsSTobvVZSQ7w4B8k9OUwxs/jksjVApZmdkPRToJJo4jPXi02ePJnJkycnnY1ez4ODS0KP6K1kZtVmlu4k/BrQ+YmVnXPOdbkknhwMqJZkwDIzW95q+yzg6bYOlPRD4IcAwz5lisV89NBDD/HBBx8knQ3nXCf15qe+JJ4cvmZm44GpwG2SMu0OkuYBJ4Cn2jrQzJab2QQzm9BWf+B8N2fOHO6///6ks+Fcr7Vo0SJGjRqVGZ25Kw0fPpwxY8YwZswYJk6cyJNPPpmZi6G+vh5JLF68OLP/7bffzuOPP55ZP3HiBMXFxVRUVHR53k5HzoODmR0IPw8Ca4FLASR9D/g2cL15Nw3nXDd49NFHqamp4amnWv79eapDX7SntraWHTt2sHXrVg4fPswdd9yR2TZo0CAWLlzIxx9/3OaxNTU1jBw5ktWrV/eInmo5bVaS1A/4jJkdC8tlwP2SrgLmAv9sZl37HXDneqm87q10113Q1RNEjR0LHXxZcPbs2dTV1TF16lRmzZpFY2Mj+/bto66ujmHDhrFy5UoqKip46aWXaG5u5rbbbuOWW24B4MEHH+SZZ56hubmZGTNmcN9993WYlf79+7N06VKGDh3K+++/D0BxcTGTJk3iiSee4Oabb846pqqqijvvvJMlS5bw6quvcsUVV5zBL+PM5fqdw2BgbbjZ+wCrzOx5SXuBc4GasO01M5ud47w516PkdXBIwNKlS3n++eepra3loosuYsGCBezatYvNmzfTt29fli9fzoABA9i2bRvNzc1MmjSJsrIyUqkUqVSKrVu3YmZMmzaNTZs2fWpPvPPOO4/S0lJSqRSDBw8G4O67784Ep7jjx4+zceNGli1bxpEjR6iqqiqs4GBmdUDWlGFmltzs7c653Oshw4FMmzYtM792dXU127dvZ82aNQA0NjaSSqWorq6murqacePGAdDU1EQqlepUN+3WzUMjRozgsssuY9WqVS3S169fz5QpU+jbty/XXnstDzzwAA8//HCnxnPqLgX/DWnnXOHq169fZtnMWLx4MeXl5S322bBhA5WVlZkmps46duwY9fX1jBw5ksbGxkz6Pffcw8yZM1uMAl1VVcXmzZszs8Y1NDTw4osvJjo8f4/4noNzziWtvLycJUuWZGZVe/vtt/nwww8pLy9nxYoVmWF2Dhw4wMGDBzs8V1NTE7feeivXXHMNAwcObLHtkksuYfTo0ZlRVI8ePcorr7zCO++8kxmG+5FHHqGqqqobStl5/uTgXA+VnjozPbWs61433XQT9fX1jB8/HjOjuLiYdevWUVZWxu7duzNzYfTv35+VK1cyaNCgrHNMmTIFM+PkyZPMmDGDe++9t81rzZs3L9NMtXbtWq688soWkwdNnz6duXPn0tzc3CI9lwp+yG7neqrjx48zf/585s+f32Ku4d6qkIbs7il8yG7n8lBRUVGPmO/ZFSZ/5+Cccy6LBwfnXM701mbs3uhMf9ceHJxzOVFUVERDQ4MHiBwwMxoaGigqKjrtc/g7B+dcTpSUlLB//34OHTqUdFYKQlFRESUlpz/7gQcH51xOnH322ZSWliadDddJ3qzknHMuiwcH55xzWTw4OOecy9JrvyEt6RDwf6d5+EXA4S7MTm/gZS4MXubCcCZlvtjMPnUqzV4bHM6EpD905uvj+cTLXBi8zIUhF2X2ZiXnnHNZPDg455zLUqjBYXnSGUiAl7kweJkLQ7eXuSDfOTjnnOtYoT45OOec64AHB+ecc1kKLjhIukrSHkl7JVUknZ9TIWmopFpJuyT9r6Q7Q/oFkmokpcLPgSFdkhaFsm6XND52rhvD/ilJN8bSvyppRzhmkSTlvqTZJJ0l6XVJ68N6qaQtIZ9PSzonpJ8b1veG7cNj56gM6XsklcfSe9w9Iel8SWskvSVpt6TL872eJc0J9/VOSVWSivKtniWtkHRQ0s5YWrfXa3vX6JCZFcwHOAvYB4wAzgHeBEYnna9TyP8QYHxY/hzwNjAa+E+gIqRXAD8Ny1cDvwMETAS2hPQLgLrwc2BYHhi2bQ37Khw7Nelyh3z9CFgFrA/rzwDXheWlwL+F5VuBpWH5OuDpsDw61Pe5QGm4D87qqfcE8ARwU1g+Bzg/n+sZ+ALwJ6BvrH6/l2/1DEwGxgM7Y2ndXq/tXaPDvCb9jyDHFXM5sCG2XglUJp2vMyjPs8C3gD3AkJA2BNgTlpcB343tvyds/y6wLJa+LKQNAd6KpbfYL8FylgAvAFcC68ONfxjo07pegQ3A5WG5T9hPres6vV9PvCeAAeE/SrVKz9t6JgoOfw7/4fUJ9Vyej/UMDKdlcOj2em3vGh19Cq1ZKX0Dpu0Pab1OeIweB2wBBpvZu2HTe8DgsNxeeTtK399GetIeBuYCJ8P6hcARMzsR1uP5zJQtbG8M+5/q7yJJpcAh4H9CU9pjkvqRx/VsZgeAnwHvAO8S1dsfye96TstFvbZ3jXYVWnDIC5L6A78G7jKzo/FtFv1pkDf9kyV9GzhoZn9MOi851Ieo6WGJmY0DPiRqCsjIw3oeCEwnCoyfB/oBVyWaqQTkol47e41CCw4HgKGx9ZKQ1mtIOpsoMDxlZr8JyX+RNCRsHwIcDOntlbej9JI20pM0CZgmqR74FVHT0kLgfEnpyari+cyULWwfADRw6r+LJO0H9pvZlrC+hihY5HM9fxP4k5kdMrO/Ar8hqvt8rue0XNRre9doV6EFh23Al0IPiHOIXmQ9l3CeOi30PPgFsNvMHopteg5I91i4kehdRDr9htDrYSLQGB4tNwBlkgaGv9jKiNpj3wWOSpoYrnVD7FyJMLNKMysxs+FE9fWimV0P1AIzw26ty5z+XcwM+1tIvy70cikFvkT08q7H3RNm9h7wZ0n/FJL+BdhFHtczUXPSREmfDXlKlzlv6zkmF/Xa3jXal+RLqIReBl1N1MtnHzAv6fycYt6/RvQ4uB14I3yuJmprfQFIARuBC8L+Ah4JZd0BTIidaxawN3y+H0ufAOwMx/w3rV6KJlz+b/BJb6URRP/o9wKrgXNDelFY3xu2j4gdPy+Uaw+x3jk98Z4AxgJ/CHW9jqhXSl7XM3Af8FbI1y+JehzlVT0DVUTvVP5K9IT4g1zUa3vX6Ojjw2c455zLUmjNSs455zrBg4NzzrksHhycc85l8eDgnHMuiwcH55xzWTw4uIIk6UJJb4TPe5IOxNZ/303XHCfpF6d57MZOjaTpXBfxrqyu4ElaADSZ2c+6+TqrgR+b2ZunceyNQImZ/aTrc+ZcNn9ycK4VSU3h5zckvSzpWUl1kv5D0vWStoYx8/8x7Fcs6deStoXPpDbO+Tngy+nAIGmBpF9KejWMsX9zSB8iaVN4gtkp6evhFM8RjbLpXE70+fRdnCtoXwFGAe8TjZv/mJldqmiipTuAu4jGevovM9ssaRjR8AajWp0n/c3VuC8Tjb3fD3hd0m+JAsAGM/uJpLOAzwKY2QdhSIgLzayhW0rqXIwHB+c6ts3CUMeS9gHVIX0HMCUsfxMYrU8mUztPUn8za4qdZwjRMNxxz5rZR8BHkmqBS4nGAFoRBlhcZ2ZvxPY/SDRiqQcH1+28Wcm5jjXHlk/G1k/yyR9XnwEmmtnY8PlCq8AA8BHReEBxrV/4mZltIpot7ADwuKQbYtuLwnmc63YeHJw7c9VETUwASBrbxj67gS+2SpuuaJ7kC4kGFdwm6WLgL2b2c+AxoqG60yPy/gNQ3+W5d64NHhycO3P/DkxQNAn8LmB26x3M7C1gQHgxnbadaEjq14AHzOz/iYLEm5JeB/6V6H0GwFeB1+yTWdGc61beldW5HJE0BzhmZo+davdZSQuB58zshe7Mo3Np/uTgXO4soeU7jFOx0wODyyV/cnDOOZfFnxycc85l8eDgnHMuiwcH55xzWTw4OOecy+LBwTnnXJa/A2WLxPz9r9SKAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3aea75b1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Slide vs Time for 22nd bp\n",
    "plt.title('Slide for 22nd bp')\n",
    "time, value = pdna.time_vs_parameter('slide', [22])\n",
    "plt.plot(time, value)\n",
    "plt.xlabel('Time (ps)')\n",
    "plt.ylabel('Slide ($\\AA$)')\n",
    "plt.show()\n",
    "\n",
    "# Rise vs Time for 25-40 bp segment\n",
    "plt.title('Rise for 25-40 bp segment')\n",
    "# Bound DNA\n",
    "# Rise is the distance between two base-pairs, so for a given segment it is sum over the base-steps\n",
    "time, value = pdna.time_vs_parameter('rise', [25, 40], merge=True, merge_method='sum')\n",
    "plt.plot(time, value, label='bound DNA', c='k')     # balck color => bound DNA\n",
    "# Free DNA\n",
    "time, value = fdna.time_vs_parameter('rise', [25, 40], merge=True, merge_method='sum')\n",
    "plt.plot(time, value, label='free DNA', c='r')    # red color => free DNA\n",
    "\n",
    "plt.xlabel('Time (ps)')\n",
    "plt.ylabel('Rise ( $\\AA$)')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Distribution of local base-steps parameters during MD simulations\n",
    "\n",
    "* As shown in above plot of Time vs Rise, comparison between bound and free DNA is very difficult. Therefore, to compare the parameters of either different DNAs or same DNAs in different environment or different segment of same DNAs, the distribution of parameters over the MD trajectory are sometime useful.\n",
    "\n",
    "\n",
    "* The distribution could be calculated using the function [dnaMD.DNA.parameter_distribution(...)](http://do-x3dna.readthedocs.io/en/latest/dna_class_api.html#dnaMD.dnaMD.DNA.parameter_distribution) as shown in the following examples.\n",
    "\n",
    "\n",
    "* The normalized distribution is calculated using [numpy.histogram(...)](http://docs.scipy.org/doc/numpy/reference/generated/numpy.histogram.html).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3aea808a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3aea792f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### Rise distribution for 20-45 bp segment\n",
    "plt.title('Rise distribution for 20-45 bp segment')\n",
    "\n",
    "### Bound DNA ###\n",
    "\n",
    "## calculation of parameter distribution for the segment\n",
    "values, density = pdna.parameter_distribution('rise', [20, 45], bins=20, merge=True, merge_method='sum')\n",
    "\n",
    "## plot distribution\n",
    "plt.plot(values, density, label='bound DNA', c='k')     # balck color => bound DNA\n",
    "\n",
    "### Free DNA ###\n",
    "\n",
    "## calculation of parameter distribution for the segment\n",
    "values, density = fdna.parameter_distribution('rise', [20, 45], bins=20, merge=True, merge_method='sum')\n",
    "\n",
    "## plot distribution\n",
    "plt.plot(values, density, label='free DNA', c='r')    # red color => free DNA\n",
    "\n",
    "plt.xlabel('Rise ( $\\AA$)')\n",
    "plt.ylabel('Density')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "\n",
    "#### Twist distribution for 25-40 bp segment\n",
    "plt.title('Twist distribution for 25-40 bp segment')\n",
    "\n",
    "### Bound DNA ###\n",
    "\n",
    "## calculation of parameter distribution for the segment\n",
    "# Twist is the twist angle between two base-pairs, so for overall twist of a given segment \n",
    "# it is considered here as sum over the base-steps\n",
    "values, density = pdna.parameter_distribution('twist', [25, 40], bins=20, merge=True, merge_method='sum')\n",
    "\n",
    "## plot distribution\n",
    "plt.plot(values, density, label='bound DNA', c='k')     # balck color => bound DNA\n",
    "\n",
    "### Free DNA ###\n",
    "\n",
    "## calculation of parameter distribution for the segment\n",
    "values, density = fdna.parameter_distribution('twist', [25, 40], bins=20, merge=True, merge_method='sum')\n",
    "\n",
    "## plot distribution\n",
    "plt.plot(values, density, label='free DNA', c='r')    # red color => free DNA\n",
    "\n",
    "plt.xlabel('Twist ( $^o$)')\n",
    "plt.ylabel('Density')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Local base-step parameters as a function of base-steps\n",
    "\n",
    "* What is the average values of a given parameter for either each base-step or a DNA segment?\n",
    "\n",
    "\n",
    "* To address this question, average values of a given parameter with its error could be calculated for either each base-step or a DNA segment using a function [dnaMD.DNA.get_mean_error(...)](http://do-x3dna.readthedocs.io/en/latest/dna_class_api.html#dnaMD.dnaMD.DNA.get_mean_error).\n",
    "\n",
    "\n",
    "* This average values could be also use to compare two DNA.\n",
    "\n",
    "\n",
    "* Standard error could be calculated using block averaging method as derived in this [publication](http://scitation.aip.org/content/aip/journal/jcp/116/1/10.1063/1.1421362). To use this method, [g_analyze](http://manual.gromacs.org/programs/gmx-analyze.html) of GROMACS package should be present in ``$PATH`` environment variable.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3aea88df60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3aea6b36a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "######## Average Rise values as a function of base-steps ########\n",
    "\n",
    "plt.title('Average Rise for each base-pairs')\n",
    "\n",
    "### Calculating Average Rise values for 5 to 56 base-steps DNA bound with protein\n",
    "bp, rise, error = pdna.get_mean_error([5, 56], 'rise', err_type='block', bp_range=True)\n",
    "\n",
    "# plot these values\n",
    "plt.errorbar(bp, rise, yerr=error, ecolor='k', elinewidth=1, color='k', lw=0, marker='o', mfc='k', mew=1, ms=4, label='bound DNA' )\n",
    "\n",
    "### Calculating Average Rise values for 5 to 56 base-steps DNA\n",
    "bp, rise, error = fdna.get_mean_error([5, 56], 'rise', err_type='block', bp_range=True)\n",
    "\n",
    "# plot these values\n",
    "plt.errorbar(bp, rise, yerr=error, ecolor='r', elinewidth=1, color='r', lw=0, marker='x', mfc='r', mew=1, ms=4, label='free DNA' )\n",
    "\n",
    "plt.ylabel('Rise ($\\AA$)')\n",
    "plt.xlabel('base-step number')\n",
    "plt.xlim(0,61)\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "######## Average Rise values as a function of DNA segments ########\n",
    "\n",
    "plt.title('Average Rise for DNA segments')\n",
    "\n",
    "### Calculating Average Rise values for 5 to 56 base-steps DNA bound with protein\n",
    "### DNA segments are assumed to made up of 4 base-steps (merge_bp=4)\n",
    "bp, rise, error = pdna.get_mean_error([5,56], 'rise', err_type='block', bp_range=True, merge_bp=4, merge_method='sum')\n",
    "\n",
    "# plot these values\n",
    "plt.errorbar(bp, rise,yerr=error, ecolor='k', elinewidth=1, color='k', lw=1, marker='o', mfc='k', mew=1, ms=4, label='bound DNA' )\n",
    "\n",
    "### Calculating Average Rise values for 5 to 56 base-steps DNA\n",
    "### DNA segments are assumed to made up of 5 base-steps (merge_bp=4)\n",
    "bp, rise, error = fdna.get_mean_error([5,56], 'rise', err_type='block', bp_range=True, merge_bp=4, merge_method='sum')\n",
    "\n",
    "# plot these values\n",
    "plt.errorbar(bp, rise, yerr=error, ecolor='r', elinewidth=1, color='r', lw=1, marker='x', mfc='r', mew=1, ms=4, label='free DNA' )\n",
    "\n",
    "plt.ylabel('Rise ( $\\AA$)')\n",
    "plt.xlabel('base-step number')\n",
    "plt.xlim(0,61)\n",
    "plt.ylim(13.0, 14.0)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Deviation in parameters of bound DNA with respect to free DNA\n",
    "\n",
    "As discussed in the above section, average parameters with standard error can be calculated for both bound and free DNA. Additionally, deviation in bound DNA with respect to the free DNA could be calculated using function [dnaMD.localDeformationVsBPS(...)](http://do-x3dna.readthedocs.io/en/latest/dnaMD_api.html#dnaMD.dnaMD.localDeformationVsBPS) as shown in the following example.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3aea65f6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3aea654b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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PPcbvfve7uKgpVemPf/wjaWlp3H333WHZ3zvvvMNpp53GqaeGPPJBTLnnnnt44oknYnrgMJOYLJEkkS1btpCfnx9TTVr+SElJYerUqcyaNYvXXgt9lIJE6WSvrk+fPvzkJz/hrbfecjsUk2QCTiTidaWI3O/MnywivcMfmgm3J598kuuvv560tPgrjZaWlsa///1v7rjjDlatWhX0foqLi1m3bh0XX3xxGKOLHYEWc4xFVmAy/gRzRfIc0BcY6czvBZ4NW0QmInbt2sXUqVO5/fbb3Q4laKeddhpPP/00l1xyCd9++21Q+5g8eTLXXHMNDRs2DHN0sWHw4MEcOnSIuXPnuh1K0KzAZPwJJpH0UdVbgQMAqvotkJi/lQnkb3/7G5deeint27d3O5SQjBw5kosuuogrrriCioqKgN574MAB/vGPf/Db3/42QtG5LyUlhTFjxjBx4kS3QzFJJJhEckhE6gEKICKtgcB+o01U7d27l+eff961UvHh9thjj1FWVhbwX67Tp0+ne/funHLKKRGKLDaMHDmS9evXU1hY6HYoJkkEk0ieBt4BThSRPwMLgYfDGpUJqylTpnDeeeclzF1KDRo04M033+Sll14iPz/f7/claid7dVbM0USdPyWCq7+ALOBW55UVzD6i+UrGMvLjx49XVdUDBw7oSSedpIWFhe4GVAeCKHO+ePFibd26tW7YsKHObYuKirRt27Z68ODBYMKLO3v27NGWLVvqpk2bVDW+ysjHU6yJjnCWkfclIsOAL1T1WbzjkzwsIj3CldhMeFQ2+7z++uvk5OTQo0fi/RedeeaZPPjgg1xyySWUlZXVuk3lHUCTJ0/muuuuo0GDBlGM0D1WzNFEU8AlUkRktaqeLiL98A67+zhwv6r2iUSA4ZCMJVJEhMOHD5OTk8Pzzz/PgAGxPWxMsCU8VJXrrruOAwcOMG3atBpFKEWEffv20bFjRwoKClwZl94tO3fuJDs7m+LiYk488cS4uSXYyrnEjkiWSCl3fv4C77C7/4vdtRWTZsyYwfHHH8+5557rdigRIyI899xzbNiwgaeeeqrWbd566y169eqVVEkEvMUcf/7zn5OTkwNATk5O1AYMM8klmETyhYi8AFwGzBKRRkHux0RYLJeKD6fU1FSmT5/OxIkTmT9/fo31ydLJXpuCgoKq8vLr168nLy/P5YhMIgomAQwHZgMXqrdoYwtgTFijMmGxZ8+ehH2Cu7r09HSmTp3KyJEj2bZt2xHrNm/ezNChQ12KzF2bN2+umq6oqKC4uNi9YEzCCjiRqOo+Vf23qm505neo6v+FPzQTqrFjx5KSkjwXixdccAGjR49m2LBh/PDDD1XLr7/+eurXr+9iZO7xHf0xJSUlrkeDNLErkKF2Fzo/94rIHp/XXhHZE7kQTSBKS0urxu6eNGlS0rWJjxs3jnbt2nH77bezb98+AG644QaXo3KPx+OhTZs2AGRlZeHxeFyOyCQivxOJqvZzfjZT1eY+r2aq2jxcAYnIIBEpFpESERlXy/pzRGS5iBwWkUvDddxEkZeXx2effQZ4CxQmW5u4iPDKK68we/bsqi/QwYMHJ11CrZSRkVFVDbioqKjqjwxjwinkdg8RSRGRK8IRjFN65VlgMJANjBSR7GqbfQ5cA0wLxzETjW8beLK2iTdv3pyUlBT++9//AtbJ3K1bNwAbp8RETCBNW81F5A8i8oyI/NwpJz8aKMXbAR8OvYESVS1V1YPAG8ARvcWqullVV2P1vWrVoUOHqulkbhO3TuYfNWvWDPAmVGMiIZArkqlAJvApcAPwH+BS4JeqGq5bg04CtvrMb3OWGT+dc845nHjiiUB8tYmPHz8+rPvLzMysutEgmROqr+XLl7sdgklQgSSSDFW9RlVfwDsWSTbeW4BXRia00IjIKBEpEJGCyvvoE52qMn/+fObNmwfEV5t4uAcz8ng8ZGVlAfGVUCPJEomJlEDuiTxUOaGq5SKyTVUPhDmeL4COPvMdnGUBU9XJwGTwlkgJPbTYt3r1aurVq1f1JHMyy8jIoKioCBGhqKjI7XBigiUSEymBJJIzfG7zFSDVmRe81TrDcefWMqCziHTCm0BGAJeHYb9JYebMmVx00UUJ/yS7Cc7KlSupqKhIqmeLTHQEcvtvvWq3/NYP9+2/qnoYuA3vk/PrgDdVtUhEHhSRiwBEpJeIbAOGAS+IiP256ahMJMbUpmXLlpSUlLgdhklAMfe4r6rOAmZVW3a/z/QyvE1exsf27dvZtGkT/fv3dzsUE6N69OjB8uXL6dKli9uhmARj17gJIj8/n0GDBiXNeBsmcD179rR+EhMRlkgSRPVmrXDfTmviX+UViTHhZokkAZSVlbFgwQIGDRpUtSzct9PGK0uoP+revTvLly+3QaNM2AXcR+KMP/JrIN33/ar6YPjCMoGYM2cOvXv3Ji0tze1QYo4l1B+1adOGJk2asGXLlqQb5MtEVjBXJDPwli05DJT5vIxL7G4t468ePXpQWFjodhi1Ki0ttdEc41QwiaSDql6mqo+p6hOVr7BHZvxSXl5Ofn5+UhclNP6L5X6SvLy8qnpg69ats890HAkmkSwSkdPCHokJytKlS2nbti2dOnVyOxQTB2I5kRQXF1NR4a3FqqqsW7eOsjJr7IgHwSSSfsByZ8yQ1SLyqYisDndgxj/WrGUCUdm0FYsd7pmZmVVVGVJSUmjevLndshwngkkkg4BTgQuAocAvnJ/GBTNnzrQmAOO3k07yFtPevn27y5HU5PF4SE1NBbyFNpcvX86ECRMYNGgQjz/+eNXViok9AQ+1CxThLSW/xnkVOT9NlJWUlLB792569erldigmTohIzDZvdezYsaoOWGXl6hEjRvDJJ5/w7rvvcuGFF8ZkAjQxONSu8Z/H4yEvL8+K8Jk6+T5PE6uJZMWKFbUOe5Cens6HH35I//796dGjBzNmzHAhOnMs9g0Ux6x/xPjL93maWE0kH3/8MWeffXat6+rXr8/999/PO++8wx133MHNN9/Mvn37ohyhORpLJHFq9+7dFBYWMnDgQLdDMXEmVhPJwoUL6dev3zG36du3LytWrGDv3r3k5uaycqX/4+rZw6mRY4kkTr333nsMGDCAJk2auB2KiTOdOnVi7969fPXVV26HUkVVj3lF4uv444/ntdde47777uOCCy7gySef9Ksj/oEHHghHqKYWlkjilDVrmWBVdrivWLHC7VCqbNq0ifr163PyySf7/Z4rrriCpUuX8vbbbzN48GB27NgRwQjNsQScSESkkYhcLiL3isj9la9IBGdqd/DgQWbPns3QoXbXtQlOrDVvffzxx/Tr1y/g0T0zMjJYsGABZ555Jj169CA/Pz9CEZpjsVpbcWj+/Pl07dqVNm3auB2KiVOxlkgWLlzoV7NWberXr88DDzzAW2+9xW233catt97K/v37wxyhORartRWHrFnLhCrWnhivvCIJRb9+/Vi5ciW7d+8mNzeX1aut4Ea0WK2tOKOqlkhMyDp37syuXbv49ttv3Q6Fb775hm3btnHaaaF/raSlpTFt2jTGjh3LwIED+etf/xqT5WASTbC1tgqt1pY7Vq9eTf369cnOznY7FBPHUlJSOOOMMwK6fTZSFi1axJlnnkn9+gEPj1QrEeE3v/kNS5YsYdq0aZx77rlkZmYCVp4+UoL5nxsc9iiM3yprawXaKWlMdZX9JAMGDHA1Dn9v+w3UKaecwsKFC2nfvj1ff/01AOvXrycvL4+ioqKwHy+ZBXxFoqpbgDQgz3mlOctMFHg8HmvWMmERKx3u/jyIGKwGDRoc0XxXUVFBcXFxRI6VzIK5/ff3wOvAic7rNREZHe7ATE3bt2+npKSE/v37ux2KSQCxMFrigQMHWLlyJX369InYMTIzM6vq0VVeyd9yyy0x9UBmvAumj+R6oI+q3q+q9wNnAr8Nb1imNvn5+QwaNIgGDRq4HYpJAF27dmXr1q3s3bvXtRgKCwvJysriuOOOi9gxPB4PWVlZgPecly5dSsOGDcnOzuaRRx6xW4XDIJhEIkC5z3y5s8xEmN2tZcKpfv36/PSnP2XVqlWuxRCp/hFfGRkZVX0iRUVF9OzZk6eeeorFixdTUFBAZmYmU6dOtfFOQhBMInkZWCoiE0RkArAEeDGsUZkaysrKWLBgAYMGDXI7FJNA3O4niWT/SF06d+7M9OnTmTZtGs888wy9evXiww8/DHg/VgwyuM72J4HrgN3O61pVfSrcgZkjzZkzh969e5OWluZ2KCaBuJlIKioqWLRoUcSvSOrSr18/Fi9ezJgxY7j22mu5+OKLWb9+vd/vj1QxyHhKUEEVbVTVQlV92nnFTuW3BGbNWiYS3EwkxcXFNGvWjPbt27tyfF8pKSmMGDGCdevW0a9fP/r168dtt93Grl27XIspnqoVBzzUrojsFZE9Pq+9IrInXAGJyCDnYccSERlXy/pGIvIvZ/1SEUkP17FjVXl5Ofn5+TY2uwm7n/70p5SUlLjS4RyOsijh1rhxY8aMGcP69etJSUmha9euTJw4kQMHDrgdWkyLqaF2RaQe8Czehx6zgZEiUv0R7uuBb1X1VOAvwMRwHDuWLV26lLZt29KpUye3QzEJplGjRmRmZvLpp59G/dihFGqMtFatWvH000+zaNEilixZQlZWFtOmTbMO+aOQQOvQiMhEVR1b17KgghHpC0xQ1Qud+T8AqOojPtvMdrZZLCL1gZ1Aaz3GiTRr1kx79ux5xLLhw4dzyy23sG/fPoYMGVLjPddccw3XXHMNX3/9NZdeemmN9TfffDOXXXYZW7du5aqrrqqx/q677iIvL4/i4mJuvPHGGuv/+Mc/cv7557Ny5Upuv/32GusffvhhzjrrLBYtWsSIESMQkSMSyVNPPUW3bt2YO3cu//M//1Pj/S+88AKZmZl4PB6eeKJmTc2pU6fSsWNH/vWvf/H888/XWP/222/TqlUrXnnlFV555ZUa62fNmkWTJk147rnnePPNN2usr+y0fPzxx2uU9k5NTeW9994D4KGHHmLevHlHrG/ZsiXTp08H4A9/+AOLFy8+Yn2HDh147bXXALj99ttrlPno0qULkydPBmDUqFFs2LDhiPXdunXjqae83XpXXnkl27ZtO2J93759eeQR70fu17/+Nd98880R6wcOHMif/vQnAAYPHlzjr/mhQ4dy9913A3DuuedSXax99qo3Mfl+9u69994a7w/XZ69du3Z06NCBpk2bHrF+/vz5qGrYP3ubN2+ma9euQX32vvvuO0pLS2nYsCHvvPMO/fv3r/rszZ8/n5/97GdAeD97IlK130rR/uzNnz+/UFVza2xYTTB9JBfUsixcZVNOArb6zG9zltW6jaoeBr4HWlbfkYiMEpECESk4dOhQmMJzxzfffEPLljVO0ZiwOO644/jvf/8b1WN++eWX7N27N6ojfKanpwf93rS0NLp3705mZiZXXnkll1xyCZ9//jnLli0DYNmyZcn9PIqq+vUCbgY+xTv2yGqf12fA6/7up45jXAr83Wf+KuCZatuswVvKvnJ+E9DqWPvt2bOnxquNGzdq27Zttby83O1QTIJatGiRRvt3ZPr06TpkyJBa13m/lmLXvn379NFHH9WUlBQVEQU0JSVFs7Ozw7L/TZs2aXZ2tgKanZ2tmzZtCst+gwEUqB/f3YEUbZwGvAc8Avh2gu9V1d3BJLFafAF09Jnv4CyrbZttTtPW8cA3JCiPx8PQoUOrSjwYE26nn346a9eu5eDBgzRs2DAqxzxW/8j48eOjEkOwUlNTGTt2LPfdd19Vn0lFRQVr167lpJNOokmTJqSmptKkSZMjXv4uu+mmm/j888+B+Cky6XciUdXv8TYjjRSRE4DOQGPwtuWp6oIwxLMM6CwinfAmjBHA5dW2mQlcDSzGewXzgZM5E9LMmTO588473Q7DJLCmTZvSqVMn1q5dS7du3aJyzI8//phJkybVui5enp/IzMxk/fr1VFRUkJKSQufOnZk7dy779+9n3759R7yqL9u/fz979uxh586dNbbZsuXHGrjxUmQy4DLyInID8Hu8Vwsr8dbaWgycF2owqnpYRG4DZgP1gJdUtUhEHsR7iTUT71P0U0UUgOHLAAASjUlEQVSkBO8DkSNCPW6s2r17N4WFhQwcONDtUEyCqxwxMRqJZN++faxZs4ZevXpF/FiR5PF4yMvLY+3atWRlZeHxeOjQoUPI+83JyTkiQVWOpRLLgmkv+T3QC9iiqgOA7sB34QpIVWepahdVPUVV/+wsu99JIqjqAVUdpqqnqmpvVU3YUWree+89BgwYENUOSZOcovlg4ieffMLpp59OampqVI4XKdVreGVkZIRlv75FJisTVKwLJpEcUNUD4H04UFXXA7GfMuOQPc1uoiWaiSQahRrjWaQSVCQFk0i2iUga8C4wR0RmADawVZgdPHiQ2bNnM3ToULdDMUmgW7durF69mvLy8ro3DpGbhRpNZARTtPFXqvqdqk4A/oS3z+KX4Q4s2c2fP5+uXbvSpk0bt0MxSaB58+a0b98+4h275eXlLF68mLPOOiuixzHRFdI9pao6X1VnqurBcAVkvKxZy0RbNEZMLCoq4sQTT+TEE0+M6HFMdMVc0UbjfUjUEomJtmj0k8RioUYTupgq2mi8Vq9eTf369cnOrl6v0pjIiUYiieVCjcGK1AOUsf5gpq+Am7ZE5E4RcX8AgQTm8Xi46KKLELERjE30dO/enRUrVkS0wm0iXpFE6gHKeHkwE4LrI2mG926tj0TkNhGx3uAws2Yt44aWLVvSokULNm3aFJH9b9u2jbKyMrp06RKR/Rv3BHPX1gOqmgPcCrQD5ovI3LBHlqS2b99OSUlJwv3VZuJDJJu3Kp8fsSvtxBPKXVtf4R0L5BvAbsEIk/z8fAYNGkSDBg3cDsUkoUgmkkTsHzFewfSR3CIiHwLz8I4D8ltVPT3cgSUra9Yybor0FYldaSemgIs24i3hfruqrqxzSxOQsrIyFixYUDX6nzHRVplIVDWsTVB79+5lw4YN9OjRI2z7NLEjmKat+4CfisifAETkZBHpHd6wktOcOXPo3bs3aWlpbodiklTbtm1p1KhR1XgY4bJkyRJ69OhBo0aNwrpfExuCSSTPAn35cZyQvc4yEyJr1jKxIBLNW1aoMbEFk0j6qOqtwAEAVf0WiM6wagmsvLyc/Px88vLy3A7FJLlIJBIr1JjYgkkkh0SkHqAAItIaiNwTTEli6dKltG3blk6dOrkdiklylYNchcvhw4f55JNP6Nu3b9j2aWJLMInkaeAdoI2I/BlYCDwc1qiSkDVrmVgR7iuSVatWcfLJJ9OiRYuw7dPEloDv2lLV10VkK3Au3mdIfqmq68IdWLLxeDy8/PLLbodhDB06dODw4cPs2LGDdu3ahbw/6x9JfIFU/xURmSAiX+Md1OoOYAIwLEKxJYUJEyZQUlLC7t27yc3NdTscYxCRsF6V2IOIiS+Qpq07gLOBXqraQlVPAPoAZ4vIHRGJLgk88MADeDwe8vLySEkJaXgYY8ImXIlEVe1BxCQQyDfXVcBIVf2scoGqlgJXAr8Jd2DJxPpHTKwJVyLZvHkzFRUVdhNJggskkTRQ1a+rL1TVXYAVhgpBYWEhAwcOdDsMY6qEa7TEyqsRK9SY2AJJJMcaTteG2g3BgAEDSE1NdTsMY6pkZGSwZ88edu3aFdJ+rH8kOQSSSM6oNsRu1VC7wGmRCjAZWLOWiTUiUjXQVSisfyQ5BDLUbr1qQ+z6DrVrTVtBOHjQeyE3dOhQlyMxpqZQ+0m+/fZbNm/ezBlnnBHGqEwsstuEXFJaWlo1Utx5551HaWmpyxEZc6RQE8nixYvp3bu3ja2TBCyRuCQvL6+qwur69eutxpaJOaEmEnsQMXlYInFJcXExqgpARUUFxcXFLkdkzJG6dOnCzp07+e6774J6vxVqTB4xk0hEpIWIzBGRjc7PE46y3fsi8p2I5Ec7xnDKzMysegAxJSWFzMxMlyMy5kj16tXjjDPOYOXKwMewO3jwIIWFhZx55pkRiMzEmphJJMA4YJ6qdsY7jO+4o2w3Ce/DkXHN4/GQlZUFQFZWFh6Px+WIjKkp2Oat5cuX07lzZ5o3bx6BqEysiaVEcjHwqjP9KvDL2jZS1Xl4B9OKaxkZGRQVFQFQVFRERkaGyxEZU1OwicT6R5JLLCWSNqq6w5neCbQJZWciMkpECkSkINSHqoxJVsEmEnsQMblENZGIyFwRWVPL62Lf7dTbC62hHEtVJ6tqrqrmtm7dOqS4jUlW2dnZbNmyhbKyMr/fY4Uak0/A45GEQlXPP9o6EflSRNqp6g4RaQd8FcXQjDG1aNCgATk5OaxatYqzzjrLr/ds3LiRxo0b07FjxwhHZ2JFLDVtzQSudqavBma4GIsxxhFo85ZdjSSfWEokjwIXiMhG4HxnHhHJFZG/V24kIh8BbwEDRWSbiFzoSrTGJIlAE4n1jySfmEkkqvqNqg5U1c6qer6q7naWF6jqDT7b9VfV1qqaqqodVHW2e1GHbvz48W6HYMwx2RWJqYtUPl2dyHJzc7WgoMDtMIyJSwcOHKBFixbs3r2bxo0bH3PbXbt2ceqpp7J7927q1asXpQhNpIhIoarWOQZ4zFyRGGNiU+PGjenSpQtr1qypc9tFixbRt29fSyJJxhKJMaZO/o6YaP0jyckSiTGmTv72k1j/SHKyRGKMqZM/iWT//v2sWrWK3r17RykqEysskRhj6nTGGWdQVFTEoUOHjrpNQUEBOTk5NG3aNIqRmVhgicQYU6emTZuSnp7O2rVrj7qNFWpMXpZIjDF+qat5yzrak5clEmOMX46VSCoqKli0aJElkiRlicQY45djJZJ169Zxwgkn0K5duyhHZWKBJRJjjF+6devGqlWrKC8vr7HObvtNbpZIjDF+SUtLo23btmzYsKHGOusfSW6WSIwxfjta85ZdkSQ3SyTGGL/17NmzRiLZsWMH3377LVlZWS5FZdxmicQY47farkgqnx9JSbGvk2Rl//PGGL91796dFStWUFFRUbXM+keMJRJjjN9atWrF8ccfz2effVa1zPpHjCUSY0xAfJu37r33XtauXUtubp1jH5kEZonEGBMQ30TyyCOP0K1btzpHTjSJzRKJMSYg1Qe5sv4RY4nEGBOQyisSVQUskRhLJMaYALVr144GDRqwefNmAM466yx3AzKus0RijAlYjx49ePXVVwFo3bq1y9EYt1kiMcYErEePHrzwwgtuh2FihCUSY0zA2rdvz86dOwHIycmhtLTU5YiMmyyRGGMC9pe//KVqev369eTl5bkYjXGbJRJjTMB8r0AqKiooLi52MRrjNkskxpiAZWZmVhVpTElJITMz0+WIjJtiJpGISAsRmSMiG52fJ9SyTTcRWSwiRSKyWkQucyNWY5Kdx+OpKhuflZWFx+NxOSLjJql8qMhtIvIYsFtVHxWRccAJqjq22jZdAFXVjSLSHigEuqrqd8fad25urhYUFEQsdmOSlYgQK98hJvxEpFBV6yykFjNXJMDFwKvO9KvAL6tvoKobVHWjM70d+Aqwm9iNMcZFsZRI2qjqDmd6J9DmWBuLSG+gIbDpKOtHiUiBiBTs2rUrvJEaY4ypUj+aBxORuUDbWlbd5zujqioiR71eFpF2wFTgalWtqG0bVZ0MTAZv01bQQRtjjDmmqCYSVT3/aOtE5EsRaaeqO5xE8dVRtmsO/C9wn6ouiVCoxhhj/BRLTVszgaud6auBGdU3EJGGwDvAP1T17SjGZowx5ihiKZE8ClwgIhuB8515RCRXRP7ubDMcOAe4RkRWOq9u7oRrjBk/frzbIZgYEDO3/0aS3f5rjDGBi8fbf40xxsQhSyTGGGNCYonEGGNMSCyRGGOMCYklEmOMMSGxRGKMMSYklkiMMcaExBKJMcaYkCTFA4kishdI1LFAWwFfux1EhNi5xSc7t/hU27n9RFXrHKojqkUbXVTsz9OZ8UhECuzc4o+dW3yyc6udNW0ZY4wJiSUSY4wxIUmWRDLZ7QAiyM4tPtm5xSc7t1okRWe7McaYyEmWKxJjjDERkvCJREQGiUixiJSIyDi34wmFiLwkIl+JyBqfZS1EZI6IbHR+nuBmjMESkY4i8h8RWSsiRSLye2d53J+fiDQWkU9EZJVzbg84yzuJyFLns/kvZwTQuCMi9URkhYjkO/OJcl6bReRTZwC9AmdZ3H8eAUQkTUTeFpH1IrJORPqGcm4JnUhEpB7wLDAYyAZGiki2u1GF5BVgULVl44B5qtoZmOfMx6PDwF2qmg2cCdzq/F8lwvn9AJynqmcA3YBBInImMBH4i6qeCnwLXO9ijKH4PbDOZz5RzgtggKp287ktNhE+jwB/Bd5X1SzgDLz/f8Gfm6om7AvoC8z2mf8D8Ae34wrxnNKBNT7zxUA7Z7od3mdmXI8zDOc5A7gg0c4PaAIsB/rgffirvrP8iM9qvLyADs6XznlAPiCJcF5O7JuBVtWWxf3nETge+Aynjzwc55bQVyTAScBWn/ltzrJE0kZVdzjTO4E2bgYTDiKSDnQHlpIg5+c0/6wEvgLmAJuA71T1sLNJvH42nwLuASqc+ZYkxnkBKPB/IlIoIqOcZYnweewE7AJedpok/y4iTQnh3BI9kSQV9f4pEde34YnIccB04HZV3eO7Lp7PT1XLVbUb3r/gewNZLocUMhEZCnylqoVuxxIh/VS1B96m8VtF5BzflXH8eawP9ACeV9XuQBnVmrECPbdETyRfAB195js4yxLJlyLSDsD5+ZXL8QRNRBrgTSKvq+q/ncUJc34Aqvod8B+8TT5pIlJZpigeP5tnAxeJyGbgDbzNW38l/s8LAFX9wvn5FfAO3j8AEuHzuA3YpqpLnfm38SaWoM8t0RPJMqCzcxdJQ2AEMNPlmMJtJnC1M3013r6FuCMiArwIrFPVJ31Wxf35iUhrEUlzplPx9v2sw5tQLnU2i7tzU9U/qGoHVU3H+7v1gapeQZyfF4CINBWRZpXTwM+BNSTA51FVdwJbRSTTWTQQWEsI55bwDySKyBC87bj1gJdU9c8uhxQ0EfkncC7eKp1fAuOBd4E3gZOBLcBwVd3tVozBEpF+wEfAp/zY3n4v3n6SuD4/ETkdeBXvZzAFeFNVHxSRDLx/ybcAVgBXquoP7kUaPBE5F7hbVYcmwnk55/COM1sfmKaqfxaRlsT55xFARLoBfwcaAqXAtTifTYI4t4RPJMYYYyIr0Zu2jDHGRJglEmOMMSGxRGKMMSYklkiMMcaExBKJMcaYkFgiMQlDRNJ9KyO7FMO5InKWmzH4Q0Q+FJGEHHvcRJ8lEmPC61wg5hNJKHyeWjcGsERiEk99EXndGWPhbRFpAiAi94vIMhFZIyKTnSfpEZHfOWOgrBaRN5xlTZ2xXz5xitpdXNuBqr/XKTZ5E3CHM4ZFf+ep9unOsZeJyNnOeyeIyFQRWeyM//DbWvaf7pzHFPGOY/J/zpPxR1xRiEgrp0wJInKNiLzrjCexWURuE5E7nfNYIiItfA5xlRPnGhHpfaxzd/Y7U0Q+wFvt15gfuV3S2F72CtcLb4l9Bc525l/C+7Q1QAuf7aYCec70dqCRM53m/HwY79PYAGnABqBpLcer7b0TKo/pzE/DW/wPvE8Mr/PZbhWQirdSwVagfS3ncxjo5sy/6RPXh0CuM90K2OxMXwOUAM2A1sD3wE3Our/gLYZZ+f4pzvQ5OEMTHO3cnf1u8/13tJe9Kl92RWISzVZV/diZfg3o50wPEO+ofZ/iLS6Y4yxfDbwuIlfi/dIGb12lcU7Z9w+BxniTQHW1vbe684FnnH3NBJo7FY4BZqjqflX9Gm99qt61vP8zVV3pTBfiTS51+Y+q7lXVXXgTicdZ/mm19/8TQFUXOHGlcexzn6NxWA7ERJ61dZpEU73mj4pIY+A5vH/BbxWRCXi/IAF+gfcv8jzgPhE5De/gTL9W1WLfHYnIy3jHSdmuqkOO8t7qUoAzVfVAtX3VGmst7/etUVWO9woGvImr8g/BxhzJ9z0VPvMVHPk7X9vxj3buffCWGzemBrsiMYnmZBHp60xfDizkxy/ar52rgUsBRCQF6Kiq/wHG4h057jhgNjDapx+lO4CqXqveYVeHHOO9e/E2K1X6P2B05YxTLK/SxeIdz70l3k76ZQGc52agpzN96TG2O5bLnJj6Ad+r6vcc5dyNORZLJCbRFOMdhGgdcALewXu+A6bgLQM+mx+/sOsBrznNXSuAp51tHwIaAKtFpMiZr+5o7/UAv6rsbAd+B+Q6HfJr8XbGV1qNt0lrCfCQqm4P4DwfB24WkRV4+0iCccB5///jx3HV/Tl3Y45g1X+NcYHTvPZfVX3c7ViMCZVdkRhjjAmJXZEYY4wJiV2RGGOMCYklEmOMMSGxRGKMMSYklkiMMcaExBKJMcaYkFgiMcYYE5L/D8coCtQGZii9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3aea69e6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3aea5b2438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3aea6aa518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Ytm0bBw4ccDqKIbDO8clAA+DfIpIlInNF5PchymUi2JQpU8p0tpGve/fu3HDDDTz00ENlDxVD9u3bx86dO0lKSnI6StBUqFCBHj16FDsDgQmvQDrHFwPjgJHAi0AiMDxEuUyEysnJ4cMPP2TAgAFB2d7f//53Fi5caNNrByAjI4PevXtH7Gjx4lg/h3sE0lS1CFiGZxxHJtBRVa3ZypxhxowZpKSkUL16cLq/qlevzoQJExg2bBhHjx4Nyjaj3VNPPRVVzVT5kpOT+eCDD8jNzXU6SswLpKnqC+BH4DKgDXCZiFQJSapCRGSXiGwQkfUiYtfkuViwmql89enTh+7du/PII48EdbvR6IcffmDbtm0RPVq8OA0bNuTiiy9m5cqVTkeJeYE0VT2oqt2Bm4BvgSlAOHstr1XVtqqaGMZ9mgDkL/V57bXXBn3bTz/9NHPmzGHZsmVB33a0yMrKIj4+HoBu3bqRlZXlcKLgs+Yqdwikqeo+EZkFrAN+gaez3BZyMgWmTJnCbbfdRlxc8GeiqV27Nv/+97+54447OHHiRNC3Hw1SUlLYs2cPAFu3bo3K5iq7LNcdpKQ5gUSkvKrmisgfgaXAGlUNayOjd9Go7wAFJqjqxCLeMwwYBtC4ceMOu3fvDmfEmPfjjz/SqFEjVqxYEdI1Nfr370/z5s15/PHHQ7aPSFW+fPkzpuUoV65c1PUH5ObmcsEFF7Bx40YaNmzodJyoIiJr/G3R8edPw1UAqjpeVVeGu2h4dVPV9njOcO4Vke6F36CqE1U1UVUT69WrF/6EMS4jI4NWrVqFfCGm5557jsmTJ7N27dqzXstfkjZWNWrUqOB+XFxcQbNVNClfvjy9evVi/vz5TkeJaf4UDgl5ihKo6l7vz4PAm0AnZxOZwqZMmcLQoUNDvp8LL7yQJ598kt/+9recOnXqjNfS0tJCvn8369ChA/Xr1wcgISGB9PR0hxOFhvVzOM+fpqps4J/Fva6qxb4WDCJSFYjzLiJVFVgAjFHVYv/kSExMVJsQLXy+/vprWrZsyZ49ezj//PNDvj9VpW/fviQlJfHYY48VPC8iMTsd+w8//EDDhg3ZvHkzDRs2jOr/DgcOHCAhIYGDBw8WuY69KZ1gN1WVA84HqhVzC7X6wCci8jmeZrN3z1U0TPi9+uqr3HjjjWEpGuApEBMmTOBf//oXmzdvDss+3S4jI4PExEQaNGjA6NGjnY4TUvXr1+fSSy/l008/dTpKzPJnaOl+VR0T8iTFUNUs4Aqn9m/OTVWZMmUKL7wQ3lWEGzduzJgxY/jtb3/LsmXLSjULbzSZPn06v/nNb4DY6OtJTk5m3rx5XH311U5HiUkR0cdh3Gv16tWcPHmSbt26hX3fd911F5UqVeLZZ58N+77d5LvvvmPx4sXcdNNNTkcJG+vncJY/haNHyFOYiJU/Ulwk/H9fxMXF8dJLLzFu3Dh27NgR9v27xZw5c7juuuuCNs1LJOjYsSP79+8vGLdiwsuf9TgOhSOIiTwnTpxg1qxZDBkyxLEMzZs3584776RNmzYAtG7dOipHTJ/LjBkzCpqpYkW5cuXo3bu3nXU4JPhDfE3MePvtt2nfvj2NGzd2PMfx48eB6B0xXZzs7Gy++OILkpNjbxKH/H4OE35WOEyphWvsRkm2bdtWcD8vL4/MzEwH04TXzJkzuemmm6hUqZLTUcKud+/eLF68mJMnTzodJeYEMldVJREZJCKPiMio/Fsowxn3ys7OZtWqVfzyl790Ogrx8fEFfSzROmK6OLHYTJWvbt26tGrVik8++cTpKDEnkDOOt/FMbpgLHPO5mRj0yiuvcMstt3Deeec5HYX09HQSEjxLw7Ro0SJqR0wXtnnzZnJycuje/awZeGKGTXrojECWCGukqtE3yb8JWP7YjWnTpjkdBYCmTZuyefNmRIT//Oc/IZ8vyy2mT5/OwIEDQzIbcaRITk5m8ODBPPXUU05HiSmBfOM+FZHLQ5bERIxPP/2UuLg4Onfu7HSUs8TKeh2qGtPNVPnat2/PoUOH2Llzp9NRYkoghaMbsFZEMkXkC++KfF+EKphxr6lTpzJ06FBHxm6UJFYKx/Lly6lSpQpXXBHbkyrExcWRnJxsl+WGWSCFow9wKdALuB7o5/1pYsixY8eYM2cOgwcPdjpKkVasWEFeXp7TMUIu/2zDjcU73Irr54iFqVecUmLhEJH8SxY2ARuAjd7bJu9PE0PefPNNunTp4tpFdOrVq8emTZucjhFSp06dYvbs2QwcONDpKK7Qq1cvlixZctbKkJE0zX6kFTl/Ro538/6spqrVfW7VVDV25jgwgHvGbhQnKSkp6purFixYwKWXXhozFwGUpFatWlxxxRV8/PHHTkcptUgqcmADAE0Adu3axeeff84NN9zgdJQijR49OiYKh3WKn80uyw0vKxzGb9OmTePXv/61a0cpp6amRn3hOHbsGBkZGdxyyy1OR3EVKxzhZYXD+CUvL6/gaio3S0hI4PDhw+zfv9/pKCHx9ttv07VrVy644AKno7hKmzZtOH78OF9++aXTUWKCFQ7jlyVLllC1alXat2/vdJRziouLo2vXrlF71jFjxgwGDRrkdAzXERG7LDeMbK4q4xc3j90orGvXrlG5rOg333zDJ5984or5wdzImqvCx+aqMiU6cuQIb731FrfeeqvTUfwSrf0cr7/+On379g3b2u6RpmfPnixbtoxjx+zXUqjZXFWmRK+//jpXX311xLSrd+zYkY0bN3L8+HFXTMIYLNOnT+cvf/mL0zFcq3r16iQmJrJ48WKuv97GJoeSzVVlShQJneK+zjvvPC677DI+++wzp6MEza5du8jMzKR3795OR3E1W4s8PAKdq2qNzVXlPqEadZqamsr27dvJzMykX79+IdlHqERbc9XMmTO55ZZbqFChgtNRXC2/n0NVnY7il6ysLFq3bg1E1rLHgTRVxd7alBEiLS0tJMUjLS2N3NxcBg0aFHG/sJKSkpg8ebLTMYJCVZk+fTovvPCC01Fcr1WrVuTl5bF161ano5xFVTlw4ADbtm3jyy+/ZNu2bTz//PMcOXIE+GnZ40iYMsfvwqGqu0XkCuAq71NLVfXz0MQybjFt2jQyMjKcjhGwrl27cuedd5KXlxfx61Vs2LCBo0eP0rVrV6ejuF7+ZbmhvLoqNTX1nH+offfddwWFIf9n/v2KFSvSokULWrRoQfPmzc/oyI+kZY/9Lhwi8nvgTuAN71OvishEVf13SJIZV6hXrx5t2rRxOkbAGjRoQM2aNdm6dSutWrVyOk6Z2IJNgWnfvj1/+MMfAE/zT3p6elDm9crKyiIlJYXNmzcza9YsnnrqKY4fP35WgThx4kRBYWjRogX9+vXjgQceoHnz5tSuXfuMbc6YMYOtW7cW/IETKcsei79tgd7+jC6qesz7uCqwXFVD/ltFRPoA/wLKAS+p6t/P9f7ExERdvXp1qGM5zveL3KpVq6D9A8knIjz77LOMGDEiaNsMp8GDB9O9e3fuvPNOp6OUWl5eHk2aNGHevHlcdtllTseJCC1btjyjqapy5cq0bt0aESm4AWc89uf5VatWcfz48YLtVqxYkb59+xYUiPxiceGFF/o93inU/4YDISJrVDXRr/cGUDg2AB1V9YT3cWXgM1UN6ZVWIlIO2IZnHZBs4DNgoKpuLu4zsVI44uPj+fLLL1FVRITatWvz0EMPUb16dapXr06NGjUK7vveKleufM7tZmVl0bdvXzIzM4mPj2fevHkRORPrCy+8wIoVK5g6darTUUptyZIljBgxgs8/t1Zhf5UvX57Tp08XPI6Li2PlypWoapE3wK/XevXqdcZaL+XKlSM3NzcomUXE8Q79QApHIJ3jU4CVIvKm9/EvgUmBhiuFTsB2Vc0CEJHX8AxELLZwZGZmcs0115zx3K9+9Svuuecejh8/Tt++fc/6zO23387tt9/ON998Q//+/c96ffjw4QwYMIA9e/YUuYjRQw89REpKCpmZmdx1111nvf7YY4/Rs2dP1q9fzwMPPHDW63/7298KRjw/8sgjZ73+zDPP0LZtWxYsWMCf/vQn9u7dS05OTsHrqsqhQ4dYs2YNy5cvJzc3l9OnTxf8rF27NsePH+e7774jLy+P8uXLU65cuYKfnTt3pl69euzbt4+lS5cW/IPIzMzk8ssvJycnh/POO4///ve/zJ49+6x8H330EQDjx48/q0+kSpUqBZdIjh07lkWLFp3xep06dZg7dy4ADz/8MMuXLz/j9UaNGvHqq68C8MADD7B+/fozXm/RogUTJ04EYNiwYWzbtg2Ao0ePsnnzZmrWrMkzzzwDwK233kp2dvYZn+/SpQuPP/44ADfffDPffvvtGa/36NGDkSNHAp41rn/44YczXr/++uv54x//CHDW9w7K9t3btm1bwTad/u4tXLiQv/71r2e9PmHCBOLj40lPTy9y7e9XXnmFiy++mFmzZvH888+f9fqcOXOoW7cuU6dOLbLIz5s3L6DvXqVKlc44M0hISCAxMbHM372aNWty6NChgtcqVarEsGHDivzu5Wvbtm3EfPcCEUjn+D9F5GMgyfvUUFVdF9DeSuciYI/P42zgrMWuRWQYMAxw7eytZXHy5Elefvllxo0bx549e7jooos4evRowRcpLi6OhIQEbrvttiK/BL7/eP/zn/+cVVjyfyG9//77Z/0V5fuPMJJUrVqVH3/8MWJHEufl5ZGTk0NSUlLJbzYFLrvssoIBoFWrViU9PT0o273hhhuYPXt2wcDSmG46LO4UzS03oD+efo38x4OB5871mQ4dOmi0yM7O1kcffVQvuOAC7d27t2ZkZOjp06dVVXXHjh3aqlUrBbRVq1a6Y8eOoOyzVatWGhcXp4DGxcVpq1atgrJdJ/Tp00ffeOMNp2OUyttvv61XXXWV0zEilufXW/CNHj066NsMVdYAM6xWP38v+710rIgcEZH/+dyOiMj/QlTPfO0FLvZ53Mj7XMTxd6yFqrJs2TIGDBjA5Zdfzvfff8+SJUuYP38+/fr1K7i6pmnTpgXXfG/atClo/RDp6ekkJCQAntP8YP3F5oRIHgg4ffp0W7DJhSJtmddQ8Ltz3CkiUh5P53gPPAXjM2CQqhY7SsatneMldYCdOHGC1157jWeffZYjR44wYsQIbr/9dqpXP/cKvaHqWHNDh11Zffjhhzz22GMRN1vukSNHaNSoEVlZWdSpU8fpOBEpkr6/bsgaSOd4INOqP+HPc8GmqrnAfcD7wBZg9rmKRiTKzs7m0UcfpXHjxsyaNYtx48aRmZnJ/fffX2LRAM+SqaZonTt35vPPP+fEiRNORwnIm2++ydVXX21Fw7hSICOKehXxXFimIVHVearaQlWbqeq4cOwz1FSVpUuX8qtf/Yo2bdpw5MgRli5dynvvvUdycnJAg73s1Ll4VatWpWXLlrjxDPRcrJnKuFmJV1WJyHDgHqBpoUkNqwGRdf7vkPxBPuCZS+e2227jtdde49ixY4wYMYKXXnrJrzMLUzr5/RzdunVzOopfDhw4wKpVq3jzzTdLfrOJCpHWauDP5bgzgPeAxwHfxQCOqOqhoj9ifKWkpBSMZN2yZQtjx45lzpw5XHfdda6eRiLSvszFSUpKKrgWPxLMmjWLlJSUqFpLxJxbpLUaBNQ5LiK1gOZAwdBjVV0Sglxl4rbO8cIjWYM54tSUbO/evVxxxRXk5ORExNK3nTt3ZsyYMbb2Rhm5ocM5koSqc/x3wBI8ndRp3p+ppQkYa+Lj4wvOLCJpIrNocdFFF3H++edHxMyj27dvZ9euXfTo0cPpKMYUK5B2kt8DHYHdqnot0A44HJJUUSaaxkVEqqSkpIi4JHfGjBkMGDCA8uUDmQ3ImPAKpHCc0J8mOKykqlsB+9PZD6EaqGf817VrV9cPBFRVZsyYYVdTGdcLpHBki0hN4C1ggYi8DewOTSxjgisSRpCvXbuW3NxcOnXq5HQUY84pkEkOb/TeTRWRxUANYH5IUhkTZJdffjn79+/nm2++oW7duk7HKdL06dMZNGhQRHTgR4JouSrQjUp1Laiqfqyq76jqj8EOFM3si+yc/Knj3drPcfr0aV577TUGDRrkdJSoEWmXuEZe7fXPAAAQz0lEQVSSSJjkMGrYF9lZbm6u+uijj2jQoEHBRRTGuFmJhUNVu3l/VlPV6j63aqpqw51NxHBz4bApRkwkCWQcxx9EpGEowxgTSp07d2bdunWcPHnS6SjAT2egJ06c4K233mLAgAHOBjLGT4H0cVTDczXVUhG5T0TqhyqUMaFQrVo1WrRowdq1a52OAkBaWhoA7777Lu3ateOiiy5yOJEx/vG7cKhqmqq2Bu4FGgAfi8jCkCUzJgTc2FxlYzdMpCnNVVUHga+Bb4ELghvHmNByW+E4fPgwCxcu5KabbnI6ijF+C6SP4x4R+QhYBNQB7lTVNqEKZkwo5BcOt0x+N3fuXHr27EnNmjWdjmKM3wKZEOdi4AFVXR+qMMaEWuPGjalUqRLbt2+nefPmTsdhxowZ3HPPPU7HMCYggTRVPQpcJiIjAUSksYjY3Agm4ripuWrdunX069fP6RjGBCSQwvEfoAuQP7T1iPc5YyKKm2bKvfHGG6lcuXLJbzTGRQIpHJ1V9V7gBICqfgdUDEkqY0LITTPl2hQjJhIFUjhOiUg5QAFEpB6QF5JUxoTQFVdcwVdffcWhQ86sfJyVlcWll14KwIgRI8jKynIkhzGlFUjheBZ4E6gvIuOAT4C/hSSVMSFUvnx5OnXqxPLlyx3Zf0pKSkGxyMzMJCUlxZEcxpRWIAMApwPjgQnAPuCXqvp6qIIZE0pOdpBnZmYWXA6cl5cXEUvaGuPLn9lxRURSReQbPIs4PYhnrfFbQpzNmJBxsnD4rgdia9CbSOTPGceDQBLQUVVrq2otoDOQJCIPhjSdMSFy5ZVXsmbNGn78MbxLyhw9epTc3NyC5YNtDXoTifwpHIOBgaq6M/8JVc0CbgWGhCoYgPdMZ6+IrPfe+oZyfyZ21KhRg2bNmrF+fXjHsz733HP07NmTHTt2ALYGvYlM/owcr6Cq3xR+UlVzRKRCCDIV9rSqjg/DfkyMyb8sN1xrfH///ff885//ZMmSJWHZnzGh4s8Zx7nO5W3pWBOxwt3P8cwzz5CcnGyr/JmI588ZxxXFLBErQDiGvN4nIkOA1cBD3oGHxpRZUlIS//d//4eqIiIh3dehQ4f497//zcqVK0O6H2PCwZ+lY8sVWjLWd+nYMjdVichCEdlYxO0XwPNAM6AtsB946hzbGSYiq0VkdU5OTlljmRjQpEkTRISdO3eW/OYyGj9+PDfddBPNmjUL+b6MCbVAZscNCVXt6c/7RORFIOMc25kITARITEx0x5zZxtVEpKC5KpQd1AcPHmTChAmsW7cuZPswJpxKs5BT2IhIA5+HNwIbncpiolM4+jmeeOIJBg0aROPGjUO6H2PCxfEzjhL8Q0Ta4pkfaxdwl7NxTLRJSkpi8uTJIdv+vn37mDp1Khs32t88Jnq4unCo6mCnM5jo1rZtW7Kysjh8+HBIVuF7/PHHGTp0KA0aNDjrtdGjRwd9f8aEg6sLhzGhVqFCBRITE1mxYgV9+vQJ6ra/+uorZsyYwdatW4t8PTU1Naj7MyZcXN3HYUw4hKqf469//St333039erVC/q2jXGSnXGYmJeUlMT48cGdnGDHjh288cYbbNu2LajbNcYN7IzDxLwuXbrw2WefcerUqaBtc8yYMdx///3Url07aNs0xi3sjMPEvFq1anHJJZfw+eefk5iYWObtbd26lffee4/t27cHIZ0x7mNnHMbgaa769NNPg7Kt1NRU/vCHP1C9evWgbM8Yt7HCYQzB6yD/4osv+PjjjxkxYkQQUhnjTlY4jOGnKdbzl3QtrdGjR/OnP/2JqlWrBimZMe5jhcMYoFmzZpw6dYqvvvqq1NtYs2YNn332GXfffXcQkxnjPlY4jOHMCQ9La+TIkTzyyCNUqVIliMmMcR8rHMZ4laVwfPrpp2zevJk77rgjyKmMcR8rHMZ4laVwjBw5kpEjR1KpUqUgpzLGfaxwGOPVvn17tm/fzv/+V9SCl8VbvHgxu3fvZsiQISFKZoy7WOEwxqtixYq0b98+oOVdVZWRI0eSmppKhQplXhDTmIhghcMYH/mX5frrgw8+4NChQwwcODCEqYxxFyscxvgIpJ8j/2wjLS2NcuXKhTiZMe5hhcMYH127dmXlypXk5uaW+N709HROnjzJzTffHIZkxriHFQ5jfNSpU4eLLrqIDRs2nPN9eXl5jBo1irFjxxIXZ/+MTGyxb7wxhfjTXDV37lwqVqxISkpKmFIZ4x5WOIwppKSZck+fPs3o0aMZM2YMIhLGZMa4gxUOYwop6Yxj5syZ1K5dm969e4cxlTHuYYXDmEKaN2/O8ePHyc7OPuu13Nxc0tLSGDt2rJ1tmJhlhcOYQkTkjPEcqampBa9NmzaNxo0bc+211zqUzhjnWeEwpgi+zVVpaWkA/Pjjj4wZM4axY8c6Gc0Yx1nhMKYIRfVzTJo0iZYtW9K1a1eHUhnjDq4oHCJyi4hsEpE8EUks9NrDIrJdRDJFxHojTVh06NCBrVu3cvToUQB++OEHxo0bZ2cbxgDlnQ7gtRG4CZjg+6SItAJ+DbQGGgILRaSFqp4Of0QTSypXrkzbtm1ZtWoVABMmTCAxMZHExMQSPmlM9HNF4VDVLUBRV6n8AnhNVU8CO0VkO9AJWB7ehCYW+TZXPfHEE7z//vsOJzLGHVzRVHUOFwF7fB5ne58zJuR8r6zq3r07bdq0cTiRMe4QtsIhIgtFZGMRt18EafvDRGS1iKzOyckJxiZNjGvYsCELFiwAYM2aNWRlZTmcyBh3CFtTlar2LMXH9gIX+zxu5H2uqO1PBCYCJCYmain2ZcwZhg4dSl5eHgA7d+4kJSWFTZs2OZzKGOe5vanqHeDXIlJJRH4GNAdWOZzJxIjMzMyC+3l5eWc8NiaWuaJwiMiNIpINdAHeFZH3AVR1EzAb2AzMB+61K6pMuMTHxxdMmR4XF0d8fLzDiYxxB1cUDlV9U1UbqWolVa2vqr19Xhunqs1UNV5V33Myp4kt6enpJCQkAJCQkEB6errDiYxxB1dcjmuMGzVt2pRNmzYhIta3YYwPV5xxGGOMiRxWOIwxxgTECocxxpiAWOEwxhgTECscxhhjAmKFw5gSjB492ukIxriKFQ5jSuC7dKwxxgqHMcaYAFnhMMYYExArHMYYYwJihcMYY0xArHAYY4wJiBUOY4wxAbHCYYwxJiBWOIwxxgREVKNveW4ROQJE4zqfdYFvnA4RInZskcmOLTIVdWyXqGo9fz4crQs5ZapqotMhgk1EVkfjcYEdW6SyY4tMZT02a6oyxhgTECscxhhjAhKthWOi0wFCJFqPC+zYIpUdW2Qq07FFZee4McaY0InWMw5jjDEhElWFQ0T6iEimiGwXkb84nacsRGSyiBwUkY0+z9UWkQUi8qX3Zy0nM5aWiFwsIotFZLOIbBKR33ufj/jjE5HKIrJKRD73Hlua9/mfichK73dzlohUdDpraYhIORFZJyIZ3sdRcVwAIrJLRDaIyHoRWe19Lhq+kzVFZI6IbBWRLSLSpazHFTWFQ0TKAf8BkoFWwEARaeVsqjKZCvQp9NxfgEWq2hxY5H0ciXKBh1S1FXAlcK/3/1U0HN9J4OeqegXQFugjIlcCTwBPq+qlwHfAHQ5mLIvfA1t8HkfLceW7VlXb+lyqGg3fyX8B81U1AbgCz/+/sh2XqkbFDegCvO/z+GHgYadzlfGYmgAbfR5nAg289xvgGa/ieM4gHOfbQK9oOz7gPGAt0BnPYKvy3ufP+K5Gyg1o5P0l83MgA5BoOC6f49sF1C30XER/J4EawE68/dnBOq6oOeMALgL2+DzO9j4XTeqr6n7v/a+B+k6GCQYRaQK0A1YSJcfnbc5ZDxwEFgA7gMOqmut9S6R+N58B/gTkeR/XITqOK58CH4jIGhEZ5n0u0r+TPwNygCneJsaXRKQqZTyuaCocMUU9fypE9CVxInI+MBd4QFX/5/taJB+fqp5W1bZ4/kLvBCQ4HKnMROR64KCqrnE6Swh1U9X2eJq77xWR7r4vRuh3sjzQHnheVdsBxyjULFWa44qmwrEXuNjncSPvc9HkgIg0APD+POhwnlITkQp4isZ0VX3D+3TUHB+Aqh4GFuNpwqkpIvlT/ETidzMJuEFEdgGv4Wmu+heRf1wFVHWv9+dB4E08RT/Sv5PZQLaqrvQ+noOnkJTpuKKpcHwGNPde5VER+DXwjsOZgu0d4Dbv/dvw9A1EHBERYBKwRVX/6fNSxB+fiNQTkZre+1Xw9N1swVNA+nvfFnHHpqoPq2ojVW2C59/Wh6r6GyL8uPKJSFURqZZ/H7gO2EiEfydV9Wtgj4jEe5/qAWymjMcVVQMARaQvnnbYcsBkVR3ncKRSE5GZwDV4ZrE8AIwG3gJmA42B3cCvVPWQUxlLS0S6AUuBDfzUXv4Inn6OiD4+EWkDvIznOxgHzFbVMSLSFM9f6rWBdcCtqnrSuaSlJyLXAH9U1euj5bi8x/Gm92F5YIaqjhOROkT+d7It8BJQEcgChuL9blLK44qqwmGMMSb0oqmpyhhjTBhY4TDGGBMQKxzGGGMCYoXDGGNMQKxwGGOMCYgVDhOxRKSJ7+zBDmW4RkS6OpnBHyLykYhE5frZJvyscBhTNtcAri8cZeEzMtwYwAqHiXzlRWS6d52BOSJyHoCIjBKRz0Rko4hM9I5WR0Tu964D8oWIvOZ9rqp3/ZNV3ongflHUjgp/1jtB493Ag941HK7yjhyf6933ZyKS5P1sqoi8IiLLvWsg3FnE9pt4j+NF8azl8YF39PkZZwwiUtc79QcicruIvOVdU2GXiNwnIn/wHscKEants4vB3pwbRaTTuY7du913RORDPDPiGvMTp6f9tZvdSnvDM+28Aknex5PxjGgGqO3zvleAFO/9fUAl7/2a3p9/wzPiGaAmsA2oWsT+ivpsav4+vY9n4JksDzyjcrf4vO9zoAqe2QD2AA2LOJ5coK338WyfXB8Bid77dYFd3vu3A9uBakA94Hvgbu9rT+OZQDL/8y9673fHO11/ccfu3W62739Hu9kt/2ZnHCbS7VHVZd77rwLdvPevFc/KdBvwTMjX2vv8F8B0EbkVzy9p8MxL9BfvVOgfAZXx/NIvrKjPFtYTeM67rXeA6t5ZgAHeVtUfVPUbPHM8dSri8ztVdb33/ho8xaQki1X1iKrm4Ckc6d7nNxT6/EwAVV3izVWTcx/7Ao2w6TVMeFjbpYl0hefMURGpDPwXz1/oe0QkFc8vRIB+eP7iTgEeFZHL8SxIdLOqZvpuSESm4FkrZJ+q9i3ms4XFAVeq6olC2yoyaxGf953n6TSeMxTwFKr8P/Qqcybfz+T5PM7jzH/jRe2/uGPvjGcKbmPOYmccJtI1FpEu3vuDgE/46RfrN96/9vsDiEgccLGqLgb+jGd1tPOB94ERPv0g7QBUdah6lhHte47PHsHTTJTvA2BE/gPvBHP5fiGeNcnr4OlU/yyA49wFdPDe73+O953LAG+mbsD3qvo9xRy7MedihcNEukw8i+5sAWrhWbDmMPAinmmx3+enX9DlgFe9zVfrgGe97x0LVAC+EJFN3seFFffZdODG/M5x4H4g0duBvhlP53m+L/A0Ua0AxqrqvgCOczwwXETW4enjKI0T3s+/wE9rg/tz7MacwWbHNSYMvM1lR1V1vNNZjCkrO+MwxhgTEDvjMMYYExA74zDGGBMQKxzGGGMCYoXDGGNMQKxwGGOMCYgVDmOMMQGxwmGMMSYg/w+pCoicexFuGgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3aea7b0a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### Deviation in shift, slide, rise, tilt, roll and twist\n",
    "#### Deviation = Bound DNA(parameter) - Free DNA(parameter) \n",
    "\n",
    "### Deviation in Shift\n",
    "fdna_bp, pdna_bp, deviation, error = dnaMD.localDeformationVsBPS(fdna, [5,56], pdna, [5,56], \n",
    "                                                                'shift', err_type='block', bp_range=True, \n",
    "                                                                merge_bp=4, merge_method='sum')\n",
    "\n",
    "# plot these values\n",
    "plt.errorbar(pdna_bp, deviation, yerr=error, ecolor='k', elinewidth=1, color='k', lw=1, marker='o', mfc='k', mew=1, ms=4)\n",
    "\n",
    "# plot line at zero\n",
    "plt.plot([0,61], [0.0, 0.0], '--k')\n",
    "\n",
    "plt.ylabel('Deviation in Shift ($\\AA$)')\n",
    "plt.xlabel('base-step number')\n",
    "plt.xlim(0,61)\n",
    "plt.show()\n",
    "\n",
    "### Deviation in Slide\n",
    "fdna_bp, pdna_bp, deviation, error = dnaMD.localDeformationVsBPS(fdna, [5,56], pdna, [5,56], \n",
    "                                                              'slide', err_type='block', bp_range=True, \n",
    "                                                              merge_bp=4, merge_method='sum')\n",
    "\n",
    "# plot these values\n",
    "plt.errorbar(pdna_bp, deviation, yerr=error, ecolor='k', elinewidth=1, color='k', lw=1, marker='o', mfc='k', mew=1, ms=4)\n",
    "\n",
    "# plot line at zero\n",
    "plt.plot([0,61], [0.0, 0.0], '--k')\n",
    "\n",
    "plt.ylabel('Deviation in Slide ($\\AA$)')\n",
    "plt.xlabel('base-step number')\n",
    "plt.xlim(0,61)\n",
    "plt.show()\n",
    "\n",
    "### Deviation in Rise\n",
    "fdna_bp, pdna_bp, deviation, error = dnaMD.localDeformationVsBPS(fdna, [5,56], pdna, [5,56], \n",
    "                                                              'rise', err_type='block', bp_range=True, \n",
    "                                                              merge_bp=4, merge_method='sum')\n",
    "\n",
    "# plot these values\n",
    "plt.errorbar(pdna_bp, deviation, yerr=error, ecolor='k', elinewidth=1, color='k', lw=1, marker='o', mfc='k', mew=1, ms=4)\n",
    "\n",
    "# plot line at zero\n",
    "plt.plot([0,61], [0.0, 0.0], '--k')\n",
    "\n",
    "plt.ylabel('Deviation in Rise ($\\AA$)')\n",
    "plt.xlabel('base-step number')\n",
    "plt.xlim(0,61)\n",
    "plt.show()\n",
    "\n",
    "### Deviation in Tilt\n",
    "fdna_bp, pdna_bp, deviation, error = dnaMD.localDeformationVsBPS(fdna, [5,56], pdna, [5,56], \n",
    "                                                              'tilt', err_type='block', bp_range=True, \n",
    "                                                              merge_bp=4, merge_method='sum')\n",
    "\n",
    "# plot these values\n",
    "plt.errorbar(pdna_bp, deviation, yerr=error, ecolor='k', elinewidth=1, color='k', lw=1, marker='o', mfc='k', mew=1, ms=4)\n",
    "\n",
    "# plot line at zero\n",
    "plt.plot([0,61], [0.0, 0.0], '--k')\n",
    "\n",
    "plt.ylabel('Deviation in Tilt ( $^o$)')\n",
    "plt.xlabel('base-step number')\n",
    "plt.xlim(0,61)\n",
    "plt.show()\n",
    "\n",
    "### Deviation in Roll\n",
    "fdna_bp, pdna_bp, deviation, error = dnaMD.localDeformationVsBPS(fdna, [5,56], pdna, [5,56], \n",
    "                                                              'roll', err_type='block', bp_range=True, \n",
    "                                                              merge_bp=4, merge_method='sum')\n",
    "\n",
    "# plot these values\n",
    "plt.errorbar(pdna_bp, deviation, yerr=error, ecolor='k', elinewidth=1, color='k', lw=1, marker='o', mfc='k', mew=1, ms=4)\n",
    "\n",
    "# plot line at zero\n",
    "plt.plot([0,61], [0.0, 0.0], '--k')\n",
    "\n",
    "plt.ylabel('Deviation in Roll ( $^o$)')\n",
    "plt.xlabel('base-pair number')\n",
    "plt.xlim(0,61)\n",
    "plt.show()\n",
    "\n",
    "### Deviation in Twist\n",
    "fdna_bp, pdna_bp, deviation, error = dnaMD.localDeformationVsBPS(fdna, [5,56], pdna, [5,56], \n",
    "                                                              'twist', err_type='block', bp_range=True, \n",
    "                                                              merge_bp=4, merge_method='sum')\n",
    "\n",
    "# plot these values\n",
    "plt.errorbar(pdna_bp, deviation, yerr=error, ecolor='k', elinewidth=1, color='k', lw=1, marker='o', mfc='k', mew=1, ms=4)\n",
    "\n",
    "# plot line at zero\n",
    "plt.plot([0,61], [0.0, 0.0], '--k')\n",
    "\n",
    "plt.ylabel('Deviation in Twist ( $^o$)')\n",
    "plt.xlabel('base-step number')\n",
    "plt.xlim(0,61)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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