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"## Coupled pair of reactions: `A <-> B` , and `A + E <-> B + E`\n",
"A direct reaction and the same reaction, catalyzed\n",
"### Enzyme `E` initially zero, and then suddenly added mid-reaction\n",
"\n",
"LAST REVISED: Dec. 3, 2023"
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"text": [
"Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n"
]
}
],
"source": [
"import set_path # Importing this module will add the project's home directory to sys.path"
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"id": "087c0d08",
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"source": [
"from src.modules.chemicals.chem_data import ChemData\n",
"from src.modules.reactions.reaction_dynamics import ReactionDynamics"
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"id": "23c15e66-52e4-495b-aa3d-ecddd8d16942",
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"Number of reactions: 2 (at temp. 25 C)\n",
"0: A <-> B (kF = 1 / kR = 0.2 / delta_G = -3,989.7 / K = 5) | 1st order in all reactants & products\n",
"1: A + E <-> B + E (kF = 10 / kR = 2 / delta_G = -3,989.7 / K = 5) | Enzyme: E | 1st order in all reactants & products\n",
"Set of chemicals involved in the above reactions (not counting enzymes): {'A', 'B'}\n",
"Set of enzymes involved in the above reactions: {'E'}\n"
]
}
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"# Initialize the system\n",
"chem_data = ChemData(names=[\"A\", \"B\", \"E\"])\n",
"\n",
"# Reaction A <-> B , with 1st-order kinetics, favorable thermodynamics in the forward direction, \n",
"# and a forward rate that is much slower than it would be with the enzyme - as seen in the next reaction, below\n",
"chem_data.add_reaction(reactants=\"A\", products=\"B\",\n",
" forward_rate=1., delta_G=-3989.73)\n",
"\n",
"# Reaction A + E <-> B + E , with 1st-order kinetics, and a forward rate that is faster than it was without the enzyme\n",
"# Thermodynamically, there's no change from the reaction without the enzyme\n",
"chem_data.add_reaction(reactants=[\"A\", \"E\"], products=[\"B\", \"E\"],\n",
" forward_rate=10., delta_G=-3989.73)\n",
"\n",
"chem_data.describe_reactions() # Notice how the enzyme `E` is noted in the printout below"
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"### Set the initial concentrations of all the chemicals - starting with no enzyme"
]
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"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (A). Conc: 20.0\n",
" Species 1 (B). Conc: 0.0\n",
" Species 2 (E). Conc: 0.0\n",
"Set of chemicals involved in reactions (not counting enzymes): {'A', 'B'}\n",
"Set of enzymes involved in reactions: {'E'}\n"
]
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"dynamics = ReactionDynamics(chem_data=chem_data)\n",
"dynamics.set_conc(conc={\"A\": 20., \"B\": 0., \"E\": 0.},\n",
" snapshot=True) # Initially, no enzyme `E`\n",
"dynamics.describe_state()"
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"### Advance the reactions (for now without enzyme), but stopping well before equilibrium"
]
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"execution_count": 5,
"id": "76f24d9a-a788-41d8-90a4-db87386f91aa",
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"outputs": [
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"name": "stdout",
"output_type": "stream",
"text": [
"Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n",
"9 total step(s) taken\n"
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}
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"dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n",
"\n",
"# All of these settings are currently close to the default values... but subject to change; set for repeatability\n",
"dynamics.set_thresholds(norm=\"norm_A\", low=0.5, high=0.8, abort=1.44)\n",
"dynamics.set_thresholds(norm=\"norm_B\", low=0.08, high=0.5, abort=1.5)\n",
"dynamics.set_step_factors(upshift=1.2, downshift=0.5, abort=0.4)\n",
"dynamics.set_error_step_factor(0.25)\n",
"\n",
"# Perform the reactions\n",
"dynamics.single_compartment_react(reaction_duration=0.25,\n",
" initial_step=0.05, variable_steps=True, explain_variable_steps=False)"
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"#dynamics.explain_time_advance()"
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[
0.8888888888888888,
"#fdca26"
],
[
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]
]
},
"colorway": [
"#636efa",
"#EF553B",
"#00cc96",
"#ab63fa",
"#FFA15A",
"#19d3f3",
"#FF6692",
"#B6E880",
"#FF97FF",
"#FECB52"
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"font": {
"color": "#2a3f5f"
},
"geo": {
"bgcolor": "white",
"lakecolor": "white",
"landcolor": "#E5ECF6",
"showlakes": true,
"showland": true,
"subunitcolor": "white"
},
"hoverlabel": {
"align": "left"
},
"hovermode": "closest",
"mapbox": {
"style": "light"
},
"paper_bgcolor": "white",
"plot_bgcolor": "#E5ECF6",
"polar": {
"angularaxis": {
"gridcolor": "white",
"linecolor": "white",
"ticks": ""
},
"bgcolor": "#E5ECF6",
"radialaxis": {
"gridcolor": "white",
"linecolor": "white",
"ticks": ""
}
},
"scene": {
"xaxis": {
"backgroundcolor": "#E5ECF6",
"gridcolor": "white",
"gridwidth": 2,
"linecolor": "white",
"showbackground": true,
"ticks": "",
"zerolinecolor": "white"
},
"yaxis": {
"backgroundcolor": "#E5ECF6",
"gridcolor": "white",
"gridwidth": 2,
"linecolor": "white",
"showbackground": true,
"ticks": "",
"zerolinecolor": "white"
},
"zaxis": {
"backgroundcolor": "#E5ECF6",
"gridcolor": "white",
"gridwidth": 2,
"linecolor": "white",
"showbackground": true,
"ticks": "",
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}
},
"shapedefaults": {
"line": {
"color": "#2a3f5f"
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},
"ternary": {
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"linecolor": "white",
"ticks": ""
},
"baxis": {
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},
"bgcolor": "#E5ECF6",
"caxis": {
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},
"title": {
"x": 0.05
},
"xaxis": {
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"gridcolor": "white",
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"title": {
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},
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"ticks": "",
"title": {
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},
"zerolinecolor": "white",
"zerolinewidth": 2
}
}
},
"title": {
"text": "WITH zero enzyme.
Changes in concentration for `A <-> B` and `A + E <-> B + E` (time steps shown in dashed lines)"
},
"xaxis": {
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"autorange": true,
"domain": [
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],
"range": [
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"title": {
"text": "SYSTEM TIME"
},
"type": "linear"
},
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"autorange": true,
"domain": [
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"range": [
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"title": {
"text": "concentration"
},
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},
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(colors=['darkorange', 'green', 'violet'], show_intervals=True, title_prefix=\"WITH zero enzyme\")"
]
},
{
"cell_type": "markdown",
"id": "9a793ebf-f544-43ad-a1d3-059f74f3c02b",
"metadata": {},
"source": [
"### The reactions, lacking enzyme, are proceeding slowly towards equilibrium, just like the reaction that was discussed in part 1 of the experiment \"enzyme_1\""
]
},
{
"cell_type": "markdown",
"id": "27401e5d-8f3e-4c27-8438-129d3e3408a2",
"metadata": {},
"source": [
"# Now suddently add a lot of enzyme"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "713dae1e-1c51-4d95-8439-c79d9dcce2e3",
"metadata": {},
"outputs": [],
"source": [
"dynamics.set_single_conc(30., species_name=\"E\", snapshot=True) # Plenty of enzyme `E`"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "e80645d6-eb5b-4c78-8b46-ae126d2cb2cf",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0.275:\n",
"3 species:\n",
" Species 0 (A). Conc: 15.232227244425584\n",
" Species 1 (B). Conc: 4.767772755574415\n",
" Species 2 (E). Conc: 30.0\n",
"Set of chemicals involved in reactions (not counting enzymes): {'A', 'B'}\n",
"Set of enzymes involved in reactions: {'E'}\n"
]
}
],
"source": [
"dynamics.describe_state()"
]
},
{
"cell_type": "markdown",
"id": "0b46b395-3f68-4dbd-b0c5-d67a0e623726",
"metadata": {
"tags": []
},
"source": [
"### Take the system to equilibrium"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "dde62826-d170-4b39-b027-c0d56fb21387",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"*** CAUTION: negative concentration in chemical `A` in step starting at t=0.275. It will be AUTOMATICALLY CORRECTED with a reduction in time step size, as follows:\n",
" INFO: the tentative time step (0.005) leads to a NEGATIVE concentration of `A` from reaction A + E <-> B + E (rxn # 1): \n",
" Baseline value: 15.232 ; delta conc: -21.418\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.25 (set to 0.00125) [Step started at t=0.275, and will rewind there]\n",
"* INFO: the tentative time step (0.00125) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.0005) [Step started at t=0.275, and will rewind there]\n",
"* INFO: the tentative time step (0.0005) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.0002) [Step started at t=0.275, and will rewind there]\n",
"Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n",
"30 total step(s) taken\n"
]
}
],
"source": [
"dynamics.single_compartment_react(reaction_duration=0.04, \n",
" initial_step=0.005, variable_steps=True, explain_variable_steps=False)"
]
},
{
"cell_type": "markdown",
"id": "b4f7e3b5-e4b5-4dd8-a8c3-4e0c231ecdb9",
"metadata": {},
"source": [
"#### Note how the (proposed) initial step - in spite of having been reduced from the earlier run - is now appearing _large_, given the much-faster reaction dynamics. However, the variable-step engine intercepts and automatically corrects the problem!"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "b0543cac-f3cd-453c-ae9b-c00f01e61fa8",
"metadata": {},
"outputs": [],
"source": [
"#dynamics.explain_time_advance()"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "8cc14786-cc9f-4399-9203-290526d3a326",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
{
"hovertemplate": "Chemical=A
SYSTEM TIME=%{x}
concentration=%{y}",
"legendgroup": "A",
"line": {
"color": "darkorange",
"dash": "solid"
},
"marker": {
"symbol": "circle"
},
"mode": "lines",
"name": "A",
"orientation": "v",
"showlegend": true,
"type": "scatter",
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+ZJotn223ynSu1ygEV2c/u93Ot7Px24bDhw/G9bfOtarJV4KzjUW7IAzoX+/KzM/Poy7ZttcZNJQnl3BkEyQ/x+yWViU0UeRT/S7JOuwsxHvi+1SIOyWyPt3joxTFXZds28eBLNP5m6g6rrzE3e0iVKXsMIl7LpFVPbfIEEq5puO7s6bh7jkLse69jRnnrJ2796XPQW7nMslW5bfbz3lfnq9aWlut86Fsl9s5T/5e2L3M6TJ2ZmedekL6vCHyuk1OODmqjlcVr5L+5GSezb+c501nOrfvRLYx4nQ3t7aUrLhLEKoLOrKdIN1izASwOd9/GrNuuTZ91e8G0U+Z2S403K6s3WbKnHcM3E7Yfq5qs4m7MxY4Wwye2xc42zGKMoSgTRjf6HrnI9fxqrRHpV4VpvYfD/vMVDY58rqdKX6onF9QUdb8R57FtVecj9EjhlsY/fal290jt/eCcs0lxG6x0fm0QbesOwVDLiCqrKjA7PnJi3W/saGFEHYn23wFPtvYLOQMohhXb7z154x4a7cTj/yNVvkuuY3VQh6D4G///gYZH07xmXLppLw2QPDzW+slsoUQdmed+Qp8NnEPeqEZJnH3Olavc4t97ZP8nmWbQHF737l2SvX86DbuVM5fudwk250WJwP7hYX9vOF23nHmVf0tUTkW+dvx6DNLMib0VEXb7XjdLvpln9j7z239jtv3sKTF3W1RR7YftGyhMn5mSZy7FfgpM9stX2eZuRZW2QejvIp2zrqK/CtWrsWFk07J+duea8bdvuuOKh+VL0auNM6TlipbP/W6LWZ0csh28nQ7Kfj5cfU60TrLV4lxl31fCK652uvGQkcbvBj5+dyNn9fJ0lm+fealkBcY9nrtAq8yKeE2O2Qvz1S73X63VL9LXr95fneVURknOsaHsx7V38ps7dOxOFWO8SAhMSr8nBfIQmJU7/Zmu2MjygzSbh3iLu+wujFQ+T6qsvO6SPNzbsm2i5Lq+17fP6/dU7Kdq+0ukut8lq3fnOV63aWQ7RR9IO94Ozd2+OWytzGxaXzWRb0qx+K86LeHdDmZZzvnuB2L0xHl3yJ07I7pUzImPufMmmb9na0tfUbc3XbvcLtlZb/68ZJLWWauAZftYsDeMfLHwD7AZTiGmNXN5wfFr7i78bH/SKmctHKlcQ5wv2xzzXLJsryYihnwXLIhQjrsrP38uDp/0N1O0vaTlh9xLwRXv+Kuow2qJz2VdH5uPWYrLx9xzxbmpPodzVfcxTE47yTItojP8okZzsU523HaLxRUv0vZvuvypFQIcdcxPrxEW/JTvUXvJXN+xr0fAXY7DlUJl32Uj7i7fSdkW7zWZXhdsPq9eFWZAFLhr5omm1TL/H7OLaqCLsvO1znkHeJsF6y5XMRLut2+484LCi+PkhO5w4cMsu6uioswr3GUz7F4ibt9Qjlb37iNN3taefEhhF3c3RQvcRGiOoFY0uIu4qH8nhCzxQXbxVSeSAYNaMg44fmdcZdl5joxZbtCy/YD4CZ39tgx1ZOEbnHPdYzyWHKlcX6mKu4q9eaa4RFtszNVlY1cX95cPzDys+0792Ts0BBkxr0QXP2Ku442qJ70VNK5XXT7FSnnuBVhW4WawdYdKiPb7vcugwpbKVd2Fn5n3O0XwbnamO1OpUo7c6XROT5kPSqTF7napEPc7eInZNqPwPtlqjtURtQfRKB1zLiLNvgNpfPLTaQvJXH3c37MdqxuF/IqIToqF2Dyd8bPrL1buarfBa9j8SPu2S7A3MqwTzCKz+9bsMjyzw/+9vf0///292uwcvX6jDHqVkfJinu2uOZsA0tVBL06xf7gF9Uyc/2g+7n69fqBkF9AldkS3eKuctLSMSvr/PKq1Jtrxt3JtNDirho+wBl3r9Ge/fNcFxFBRLYQse75Crs8ei/RcYtdzZ9s9t0hgoh7ru9nIcS9UOND5bfIlLgXUuDzFXaVi8ls8c4qYzZs4p4r1LdUZtxVuLulcbqIXKCaLbJB5a6a6oy7252BbJOxKsfn5lXZ+sd5fvcz427//di0eavVNDHLLt8Xk84v//pNOEN+QyXuUrBzPUTIHmOlKtlesbr5iLufMnMNTvsgE8dzsKUVxx19ZMbYy3WFZ0+oW9xzHaNs6+gRh2ZdIOg3xl3+AKjUe+jQQVlj3oKIe7YvpddtQbeYQedJJ1fcoXMse40v+wlC9XuQ6wet1GPcc81cyr4J8gATHQKvowyVGcogFypuYyDb+Aki7l7fF5WTusoJWKYp1PgoRXHXKfBS2FVnLrP1Sa4x6XUh6vd3SXVcBKlXtQ57Oq/vpZ9zS9BQGVXnyHacKi4iF3+7rTNTvdOk+jshLhJEFMLEphMzmqxSj8qxiJh2VXH3E+MunfbtNe9h+669cMaxi99Be7y7/bvtdIqSnXG3n7RELJMzZEYC83oAk9tgcOtgeXs4nxh30Va3DpTvOcNbnG2XHSTaKne7cVuc6ucLqFvcRRvd7oI4Z9Pc0rjNCvoRTJV6VZiKL6SfGXe/X0qvceA8IWb7cXBjUwiuuU68uXaVsT/R1U/f5nMCdOZROQGr/ICrtMXvXT9ZZraxqFKnn+OV7fvicUdpu/3vxjfbWgA/36Vcv7kqdxBV2RVyfJSyuNtP8n6fmC2ZFfoBTFJcRIiPagisU4bzfRKwyrhQHWMq6bzO1X7OLUHF3X5ecoYC2p0j2776bucjt+PLdj7LNb7EsYmX2DAjGzPpZnLMuKVT7d+gx+L2OyaO2/6dy3VXycsJ3UKhQzfj7jwROr8w9i+/HxEU5cjBIMsUixzEK58Z92ztFF8S8WAYe5l2SXfb+9S+2MItNk11MUYhxF203S0+zNkmtzTOH2q//ZVvvaLN9vb5kQ3nOHHbx925qt3+Iyn7WowDsS+t86TjjNPTvY+72+5BXouQZfuznSCD9K3KCc8rjUpoSK5QCa/yS+1zrxhR1d8DP8flrFOMe/ncA/uMWpDvkvxeilvGOmfcCzk+dIi7fR9rZ58Uan2Fn77XkTZXTLXqGi23dugIlTG1q4y8SMm1Y4vdQXKdW3SIe7Zzt/P8mK3/VVwk2/msqjJuFet0LvGe1zNCRBq3O0D2O5r286zb+dh5TCrHojrjLst2Hlu2yYhsk0G57hSHVtx1/JgUq4xCxHAW61hYLwmQAAmQAAmQgDeB3jSB4H20wVN43aUIXkPvKaGkQ2XChFl8SZ9+/nXMnHF1eg/RXIuywnRsbCsJkAAJkAAJkIA/ArrC9vzVGs7UFHf1fqO4q7PKmdLt1k3QRT6amsZiSIAESIAESIAEDBOwh4/kE9dvuLlFrY7iro6f4q7OiilJgARIgARIgARIgARIoGgEKO5FQ8+KSYAESIAESIAESIAESECdAMVdnRVTkgAJkAAJkAAJkAAJkEDRCFDci4aeFZMACZAACZAACZAACZCAOgGKuzorpiQBEiABEiABEiABEiCBohGguBcNPSsmARIgARIgARIgARIgAXUCFHd1VkxJAiRAAiRAAiRAAiRAAkUjQHEvGnpWTAIkQAIkQAIkQAIkQALqBCju6qyYkgRIgARIgARIgARIgASKRoDiXjT0rJgESIAESIAESIAESIAE1AlQ3NVZMSUJkAAJkAAJkAAJkAAJFI0Axb1o6FkxCZAACZAACZAACZAACagToLirs2JKEiABEiABEiABEiABEigaAYp70dCzYhIgARIgARIgARIgARJQJ0BxV2fFlCRAAiRAAiRAAiRAAiRQNAIU96KhZ8UkQAIkQAIkQAIkQAIkoE6A4q7OiilJgARIgARIgARIgARIoGgEKO5FQ8+KSYAESIAESIAESIAESECdAMVdnRVTkgAJkAAJkAAJkAAJkEDRCFDci4aeFZMACZAACZAACZAACZCAOgGKuzorpiQBEiABEiABEiABEiCBohGguBcNPSsmARIgARIgARIgARIgAXUCFHd1VkxJAiRAAiRAAiRAAiRAAkUjQHEvGnpWTAIkQAIkQAIkQAIkQALqBCju6qyYkgRIgARIgARIgARIgASKRoDirgH9voMd2HegXUNJLCIXgYaacrR3JnCgpYOgCkygLBZB/7oKfL67pcA1sXhBYFBDBfbsb0d7RxeBFJhAdUUM8fIYdje3FbgmFi8IDBtQha07DyJBHAUnUF9djq5EAs0HzZ4jhw+sKvixsYJuAhR3DaNBSLuQd74KS4DiXli+9tIp7uZYU9zNsqa4m+VNcTfHm+JujnUxa6K4a6BPcdcAUaEIirsCJE1JKO6aQCoWwxl3RVAaklHcNUD0UQTF3QesgEkp7gEBhiQ7xT1gR9177724febdnHEPyFEl+6rfv47+AwdjTOMJKsmZJgCBPbs+x7LXl+Cyq64LUIr5rGveeRMdHR2Y0HSW+coD1LjkhZ/i1DPPwcBDhgUoxWzWtrZWPPPED3Hdjf9mtuKAtX30wXr8/e8f4/SzLwpYktnsv/nVYowYOQajx44zW3HA2n78Xw/i2utvQlk8HrAkc9nf/dNqvPnGUkQiEavSaDSK8vJytLd3oKa2FvF4BTq7OlFdXYNoLIa6ugbs2L4NNTW1OHJMI9atXYWmM8/F5o82IhaN4gsTTseLi57EGZO+hEMGD8WqN1egPB7H+JOarPKXL30Vw4YfhrHjjk8f5FOPPoSrrpmKyqrq9Hsfb/oQ699di4suubIHDFFmXU0VTj71NNdQmfXr1mDXzu044+wLcoL89ZIXcFTjcRg56igl4AsfmofZs2crpWUiPQQo7gDuX7AIjz6zJE30iQfvwoTxjem/n1+yAvfMe8z6++LzmnDvzKmoqkz+CFHc9QxElVIo7iqU9KShuOvhqFoKxV2VVPB0FPfgDP2UQHGnuPsZL0zrTaDPi/uuPfvw+LOvYsZ1l1sy/uFHW/DNOQvxnVnTMHrEcKxauwH3LViER+behv4NdZbki9ft06dQ3L3Hl9YUFHetOHMWRnE3x1rURHE3x5vibo61qIniTnE3O+J6f219XtydXSxEfsZdD+CO6VOsWXch6iMPH4orJk+0kjpFXrzHGHczXxTGuJvhLGphjLs51qImxrib480Yd3OsRU2McTfHmzHu5lgXsyaKu4O+EPNZcxZiwbw7MHzIIMye/xiaTjomLe7OGXmKu7nhS3E3x5ribo41xd0sa4q7Wd4Ud3O8e6u4i3DllavXZ4Qpm6OqrybnxHC+JVPcU+SEkE+/8z58+tkOyBj3gy1tlrhfdemkdMy7m7i3tnehjfsv5zsGlfNVlkfRmQD3ulYmln/CaASoqijDfu6Znz9EHzmFTIrfkc4u7nbtA1teSctjEcRiUbS0deaVn5n8EairKrMWS4ZpZHc+dwCJzRwfKj0dPT2OhvNqVJJmTWP3L5lo2JCB1gSqCFkupriLuhctXpYOlw5yoBT3IPRy5LWDPa5xlOeMu1icetfd/wdt7XxwSoG6JF3ssqW/xKBDBuO4E75Q6Kr6fPlih4TXlizGtf98Q6hYvLXy9+ho78AZZ50dqnYveuZJTJx0PoYOGx6adre2tuJHCx7CzbfcEZo2i4b+5b138fHHm3DBhZeEqt1LXn4Ro0aPReO4Y0LV7of+43u4ccYtiIdoV5nVP/oDlu9ahghSu8oginKUox3tqEMd4oijE52oRjViiKE+Uo/PE5+jNlKLMRiDNYk1OCtyFj7CR4giilMip+C5rucwKTIJQyJD8IfEH6wyTo6cbPXl64nXMRzDcUyku28Xdi3E1yJfQ1Wk++FGmxKb8OfEn/EP0X/oMQacZToTiHw7EzsxKTop5/h5JfEKGtGI0ZHRSuPs+13fD7SrjNz8w7kpiIh++NniZdYs+6u/WckZd1tvcMbdZWja49q9Yty5q4zSd1tLIi5O1YJRqRAuTlXCpC0RF6dqQ+lZEBeneiLSmiCMi1M3/OQtvLF7ObeDVBgJQbaDlDPtc2ZNy9jJz1mtnHG/5ILTrDWI4mWfkZfpnTP3N3x1cnojEbk+8ev/dBFNxMgiAAAgAElEQVRu/9bDGWX86X8+SO8cePy4URmz626z/fadBkVBsh63OwffvnNqOtSaM+4KA0oliQC99I3VuPFrl1rJnQOJu8qoUDSThuJuhrOoheJujrWoieJujjfF3RxrURPFnbvKZBtxqmEoUpTtIi4mVbdu25mOe3eGMctQ56GDB1jyLlzu+lvnpiVbtEluBe4sV3wmdw50iruzzaKeX7yyHFdefDa2fLY9p09S3DX99sjOfWXpynSJfvZxF5m4q4ymzvAohotTzXAWtXBxqjnWoibuKmOONxenmmNtzYwOqMLWnQdDFeNe8WIbolu60HpZHF2HRs0CC1Bb2BanOuU7l+A7F6e6TaradwAUZdnTfPC3v2ds7e38XGz37faeXdxbWlszdh1U6Sp71AbFXYWYoTQUdzOgKe5mOFPczXGWNVHczTGnuJtjTXE3y7qvintlRYW1HtE+ASvJy9AXHeIuZtTnP/ws5tw9zXquj9tLzuzbP5Mz+hR3s9+HnLVR3M10BsXdDGeKuznOFHfzrCnuZplzxt0c77CJu59QmVwz7lLc7Vt3O6m7PYNH5T37jLuXuIvZ9SW/eSu9G45og/2hnRR3c9+FnDVxcaq5jmCMuznWjHE3x1rUxBh3c7wZ426OtaiJMe6Mcc824nItTrXHjrvtKuO1/rAQ4p4rVMZt+3CKu9nfGuXaKO7KqAInpLgHRqhcAMVdGZWWhBR3LRiVCqG4K2HSlojiTnHPNZjctoOUM9NHDB+cdTtIp7jLEBXnLi6PP/sqZlx3Od7dsDFwjHtVZdyaQX977Yb0zjPyAmPyeadh7n/+BHIxrDhm54JYzrhr+1kJVhDFPRg/P7kp7n5oBUtLcQ/Gz29uirtfYvmnp7jnzy6fnBR3irvXuHHbRtG+04vbloxuYS65tmNUCYuRsn3fgkVpMXerW+5GI4/LGcO+7r2N1kfiffkSu9RQ3L1GgsHPGeNuBjZj3M1wFrVwVxlzrEVNXJxqjjdj3M2xFjUxxt0c77DFuJsj07tq4gOYNPQnxV0DRIUiKO4KkDQlobhrAqlYDMVdEZSGZBR3DRB9FEFx9wErYFKKe0CAIclOcdfQURR3DRAViqC4K0DSlITirgmkYjEUd0VQGpJR3DVA9FEExd0HrIBJKe4BAYYkO8U9YEcxxj0gQB/ZGePuA1bApIxxDwjQZ3bGuPsEFiA5Y9wDwMsjK2PcGeOex7BhlhwEKO4BhwfFPSBAH9kp7j5gBUxKcQ8I0Gd2irtPYAGSU9wDwMsjK8Wd4p7HsGEWinvhxgDFvXBsnSVT3M2xpribYy1qorib401xN8da1ERxp7ibHXG9vzbOuGvoY8a4a4CoUARj3BUgaUrCGHdNIBWLYYy7IigNyRjjrgGijyIY4+4DVsCkjHEPCDAk2SnuGjqK4q4BokIRFHcFSJqSUNw1gVQshuKuCEpDMoq7Bog+iqC4+4AVMCnFPSDAkGSnuGvoKIq7BogKRVDcFSBpSkJx1wRSsRiKuyIoDcko7hog+iiC4u4DVsCkFPeAAEOSneIesKMY4x4QoI/sjHH3AStgUsa4BwToMztj3H0CC5CcMe4B4OWRlTHujHHPY9gwSw4CFPeAw4PiHhCgj+wUdx+wAialuAcE6DM7xd0nsADJKe4B4OWRleJOcc9j2JREllVrN+D6W+fi23dOxRWTJ5ZEm0QjKO4Bu4LiHhCgj+wUdx+wAialuAcE6DM7xd0nsADJKe4B4OWRleJOcc9j2JRElvsXLLLasXXbTtw7cyqqKuMl0S6Ku4ZuYIy7BogKRTDGXQGSpiSMcdcEUrEYxrgrgtKQjDHuGiD6KIIx7j5gBUzKGPeAAG3Zd+3ZhznffxrfuO4yzPvBM5h509UYPWK4vgoClERxDwBPZqW4a4CoUATFXQGSpiQUd00gFYuhuCuC0pCM4q4Boo8iKO4+YAVMGlpx3/cJsPuDgEefR/a6w4B+Y1wzijCZN976M26fPgVi5n3k4UNLJlyG4p5HXzuzUNw1QFQoguKuAElTEoq7JpCKxVDcFUFpSEZx1wDRRxEUdx+wAiYNrbivfgBYdnvAo88j+0m3AZPud80oZP2sU0/AhPGNEBJ/34JFeGTubejfUJdHRXqzUNwD8mSMe0CAPrIzxt0HrIBJGeMeEKDP7Ixx9wksQHLGuAeAl0dWxrgzxt1z2Pz158DaH3gm055g7FeA8Tf3KPbDj7Zg/sPPYs7d0yxRF2EzM+56AHdMn2KJfLFfFPeAPUBxDwjQR3aKuw9YAZNS3AMC9Jmd4u4TWIDkFPcA8PLISnGnuOcxbIqa5fklK3DPvMd6tOGGr062QmeK/aK4B+wBintAgD6yU9x9wAqYlOIeEKDP7BR3n8ACJKe4B4CXR1aKO8U9j2FTtCwHW9owe/5jaDrpmIyYducsfNEayO0g9aBnjLsejl6lMMbdi5C+zxnjro+lSkmMcVehpCcNY9z1cFQthTHuqqSCpwttjHvwQ9dWghD0b85ZiO/Mmpaxi4wU+qsunVT0cBnOuGvoboq7BogKRVDcFSBpSkJx1wRSsRiKuyIoDcko7hog+iiC4u4DVsCkFPeAAEOSneKuoaMo7hogKhRBcVeApCkJxV0TSMViKO6KoDQko7hrgOijCIq7D1gBk1LcAwIMSXaKe8COYox7QIA+sjPG3QesgEkZ4x4QoM/sjHH3CSxAcsa4B4CXR1bGuDPGPY9hwyw5CFDcAw4PintAgD6yU9x9wAqYlOIeEKDP7BR3n8ACJKe4B4CXR1aKO8U9j2HDLBT3wo0Binvh2DpLpribY01xN8da1ERxN8eb4m6OtaiJ4k5xNzvien9tnHHX0MeMcdcAUaEIxrgrQNKUhDHumkAqFsMYd0VQGpIxxl0DRB9FMMbdB6yASRnjHhBgSLIXVdzl06jWvbexB67jx40qmcfLevUlxd2LkJ7PKe56OKqUQnFXoaQvDcVdH0uvkijuXoT0fk5x18szV2kUd3Osi1lTUcX9/gWLrGMvhSdRBekEinsQeup5Ke7qrIKmpLgHJegvP8XdH68gqSnuQej5z0tx988s3xwU93zJhStf0cRdzLbP+u5CzLzp6oxN7sOFD2CMu7keY4y7OdaMcTfHWtTEGHdzvBnjbo61qIkx7oxxNzvien9tFPeAfUxxDwjQR3aKuw9YAZNS3AMC9Jmd4u4TWIDkFPcA8PLISnGnuOcxbJglB4GiibtokwiVGXn4UFwxeWJoO4nibq7rKO7mWFPczbHmjLtZ1hR3s7wp7hR3syMueG2r1m7A9bfOzSjohq9OLpmw7qKK+4cfbcHTz7+OmTOuRlVlPDjtIpXAGHcz4BnjboazqIUx7uZYi5oY426ON2PczbEWNTHG3RxvxrjrYS3E/b4Fi9IbpMiNVO6YPgUTxjfqqSRAKUUT91w7yojj4a4yAXq1l2aluJvrWIq7OdYUd7OsKe5meVPczfGmuOth7RT3gy1tmD3/MTSddExJRIgUTdz14C2NUjjjbqYfKO5mOHPG3RxnWRNn3M0xp7ibY80Zd7Oswyrun+z9BB/s/MAsLACH1R+GMQPG9KjXbca9lDZTobgHHCqMcQ8I0Ed2xrj7gBUwKWPcAwL0mZ2LU30CC5CcMe4B4OWRlTHujHH3GjYPrHwAt//ydq9k2j+/rek23H/h/a7i7oxxHzZkIBbMu6MkdkEsuri7LQJ44sG7SiKOSGWUUNxVKOlJQ3HXw1GlFIq7CiV9aSju+lh6lURx9yKk93OKO8Xda0T9fP3P8YNVP/BKpv3zrxzzFdw84WbPGXeRwDkLr70xPgosqri7gRALVqffeR9uuu6ykogl8mJJcfcipO9zirs+ll4lUdy9COn9nOKul2eu0iju5liLmijuFHezIy54bW5uWkrPHiqauMtg/6sundRjdl1A+9niZbh35tRQ7DbDGPfgXxSVEhjjrkJJTxouTtXDUbUUxrirkgqejjHuwRn6KYGLU/3QCpY2rDHuwY5af243ceeMO4BcVy9i1n3+w89izt3T0L+hTn+vaC6R4q4ZaJbiKO5mOItaKO7mWIuaKO7meFPczbEWNVHczfGmuOth7RbCXUo7HXLGXUM/U9w1QFQoguKuAElTEoq7JpCKxVDcFUFpSEZx1wDRRxEUdx+wAialuAcEGJLsRRN3wef5JSuwaPGy9Cb34j3GuIdk5BShmYxxNwedMe7mWIuaGONujjdj3M2xFjUxxp0x7mZHXO+vrajiLvAWe1cZGWv/ytKV6d527mojLjDumfeY9fnF5zVlxN5zcaq5LwnF3Rxrirs51hR3s6wp7mZ5U9wp7mZHXO+vrejiXmzEItb+8WdfxYzrLrcWwooLiVlzFqb363QuSLh/wSKrybdPn2L9S3E314MUd3OsKe7mWFPczbKmuJvlTXGnuJsdcb2/tj4v7s4uFiI/464HcMf0KdZuN0LURx4+NL01pdvKYsa4m/miMMbdDGdRC2PczbEWNTHG3RxvxribYy1qYoy7Od6McTfHupg1Udwd9EWM/TfnLMR3Zk3D8CGDMHv+Y2g66Zi0uNs/Hz1iuJWb4m5mCFPczXCmuJvjLGuiuJtjTnE3x5ribpY1xd0s72LVZlzc5Yz21//pIjz+3GtY995G12MvxtY7Mt5dirrbXvM9xP2tOcBbc5CI1yERb0AiXo9EeT0SFXVAeQMSFcm/UZH8DOJzW1pYaUWa0t/2sliDVNZbWR5FZwJo7+gqdlN6ff3RCFBVUYb9LR29/lhL4QCFTLa2d6GzK1EKzenVbSiPRRCLRdHS1tmrj7NUDq6uqgzNBzsQppHd+dwBJDZ3IjalGpEjYqWC0rMdFeVRJBJAm+FzpOhjvswRMC7u8tBy7eNejAcwSUkfOnhAOn7dKfKi7U5xFzHus2u/paHHIpa8C6mHvAAQgi+lX4i9Jf/iP5EmdYFgXQgk/4O4ACir1dCW0ixi2dJfYtAhg3HcCV8ozQb2olbt2L4Nry1ZjGv/+YZQHdVbK3+PjvYOnHHW2aFq96JnnsTESedj6LDkXbwwvFpbW/GjBQ/h5lvuCENz0238y3vv4uOPN+GCCy8JVbuXvPwiRo0ei8Zxx4Sq3Q/9x/dw44xbEI/HQ9Pu1T/6A5bvWoZIJGK1ORqNoby8HO0d7airrUNFRQU6OztRXVODWKwMDfUN2Pb5Z6itrcPYoxux+p23Memc8/G3jR8iGoui6bQz8dOnHse5F1yEoUOH4XcrliFeEccpp55ulf/LV1/GYYcfgWOPOyHN6JEfPIjrv34jqqqr0+/9beMHWLvmj/jHK5Nr7OwvUWZ1VSWaTj8dbe09J7fWrlmNnTu249zzL8zZD//94i9wzLHHYcxRRyv11/3zv4vZs2crpWUiPQRKUtxNP4DJTdolXq8YdyHud/zbzdi/dxei7fsQaduLaPteRNrFv+LvPdZ7kbZ9tvfl3+Iz8f4+RDqa9fQoougqr7VEvkvM5peLf5N3A5L/dou+9XlZHbpSFwPJ9OJv8X6NpvboK4aLU/Wx9CqJi1O9COn9nNtB6uWZqzQuTjXHWtTExalcnGp2xPX+2kpS3MX2iytXr8/YdrFQXeE2q26vy9yuMglELcFPCX/7nqTQiwuAtuQFgXUR0C5EP/WveE/8Ld8X6Tr360EViaUuABrQVZac+e+y7gA0pP6tQ6Kin030UxcAQvzFBUA8dQEQ654tCNowintQgur5Ke7qrHSkpLjroKhWBsVdjZOuVBR3iruuscRykgSMi7t8wNKnn+3I2gfDhgxMb8dY6I7K1p4bvjo5HTKTax930b7SWpyaQLRViP1eRDuSM/7ddwJsFwBipr9DzvjLCwDbhUPnAT3oI2WZFwDWnQD7HQDx//2SFwNlcsZf3h3ovhhIxKrAxal6ukSlFO4qo0JJXxouTtXH0qskLk71IqT3c+4qo5dnrtK4OFUPa7fnC4mSv33n1PRGJXpqyq8U4+Ium5krxj2/QylertISd00cEl3JmfwOOeNvvwOQFP1Iq3zPfnFgDwsSdwAO6mlQpCy98LdTiL91B8AW2iPeq+hnuzuQDAmyLhKs8J+G5BqCWKWe9vTyUijuZjuY4m6ON8XdHGtRE8XdHG+Kux7Wbtt+6ylZTylFE3c9zS+NUnqluOtCKy4AWnenLgBk/L+Y+U+G+Ii7AbD+Ta0LEOE+VniQ7S6AuEjoatHSokS0PBX3b5d+GQaUFH3IOwDpiwN5l8B2ARCt0NKeUi2E4m62Zyju5nhT3M2xpribZU1x18Ob4q6HY8mWwienGuqaRCdWvfEqBjZU4+jDByZFXy7sdV4ApNcJpOL/bQuDI11tWhqciMa7LwBEPL8V1y8FP7kwWOwOlJzxT90dyEgn3usHREpzqzHGuGsZJsqFMMZdGVXghIxxD4zQVwGMcWeMu9eA6drbha5d5rd5jtZFER0Q7dE8inuOHssV716Mfdy9Bpfb5xT3fKjll0fH4tRIV2tqQa99IbCc4U+GBUEsDLZm/FNhQvY7AKk7A5Gu9vwOwpErEa1wCfux3wGwXQCICwMZHiQvBsrq0VUhLgB6/vgEaSDFPQg9/3kp7v6Z5ZuD4p4vufzyUdwp7l4jp2VlCw7+WlNYrVdlts8rTq1A9Zd6bqDBGPcsEO27uZx47Bg8/fzrmDnjalRVxiG2YDzr1BMwYXyjjy4oTlKKuznuOsRdV2sjnS2ZO/rIrUCl8HfsA6w1AM6wn9TFgLV2YC+Q0POAo0S0snsLUOcdAGtLUPGgr2Scf1L+bXcHrO0/xUVBQ/oCgOKua6SolUNxV+OkIxXFXQdF9TIo7hR3r9HS/l47WlbpCYf1qsv+eXxcHBUTeoa9csY9C0X74lSRZP7Dz2LO3dPQv6EOxXgAk5/OdqZljHsQeup5e+OuMmLxbnpLTxn6I2U/vTB4ty0sKLVOQIQDpXcNatZ3ARCrTsX51yNa2YC2WG339p5lyYd/WQ8BkxcA9l2C0tuG1mu/A6A+SsKZkjHu5vqNMe7mWIuauDjVHG/GuOthTXFXEPcB/eow5/tPY9Yt11ribvoBTEG7muIelKBa/t4o7mpH7p0q0nkgvd9/cqFvKr6/Q/wrdwHanXpfLAAW4UCphcAZFwB6HgOfiNWk9/uXO/p0h/mkdviRD/6y3wEQzwlIPShMpAeSTy7s7S+Ku7kepribY01xN8ua4q6HN8U9C0fng4/sTyg1+QAmHd1McddB0bsMirs3o6ApxBN8hdCXd+5FfXkL9uzajWjbzu51AaltQGX8v/UwsI4DiLQlnxwsHwYWtB0yv/oFQObOQNZCYXkHQKwBKPEXxd1cB1HczbGmuJtlTXHXw5sx7oocRejMjLsewLr3NsLkA5gUm5c1GWPcgxJUz19KMe7qrQ5nyqAx7skLgMw9/TOf+LsXkdbuBcDyM7kVaPKugXgKsL+dBt5om4j2RBnOrfhNBvjMC4DUVqCpJ/xa8f3WcwBSIUDyfftTgK3FwIXbBYgx7ua+J4xxN8da1MQYd8a4mx1xvb827uMesI8p7gEB+shOcfcBK2DSoOIesPp0dhnyI5/+K9YERFt3pJ8GLJ4MnNwWNBkOtPKzBnS0t+Oc2ne67xJ0NOtqjlVOV8Wg7rh/Ee5TVpsKC0o9B6CiwfYgsNRTgstqk+sDrAsA8SCwzJ0MKO5auyhnYRR3c6wp7hsRi1LczY643l9b0cS9tzw5leJu7ktCcTfHulTE3e8Rr3nnTXR0dGBC01kZWZMXAKnYfyH5HWJNwC5bCFAzkhcBYvGvfAiYfQ2A2AVot9/m5EwvZvBlSM+T27+Ec4dswtDaBBJl1UiU1yJRVpN82m/q7y4h/xmfiYXD1daFg5XW8FOB29pa8cwTP8R1N/6bVi6FLoziXmjCmeVzxp3ibnbE9f7aKO4a+pgx7hogKhTBGHcFSJqS8Mmp7iC7dwGSFwHiKcCZsm89B0BuD2pdBNguGuRCYU1PAs68OilDl13sy2rQJS8AhNhbFwJC9msA8X55DTIvBmrRlU4n0qcuFGJxTaOqNIphjLvZfuCuMuZ4M8bdHOti1lQ0cRcHHab92nN1EsXdzBCmuJvhLGqhuBeedTLkJ7kOoH+8Ffubd6GrZR8iHfut/6Jt+wHx/yIUqKM5uQi4Xfy7P/X3fmsdQHI9wZ6CNtjaGcg242+tCYiJ2X5xMZC6AIjXAdYdAHnBkLobID6PJS8a0hcP4pkBRXpR3M2Cp7ib401xN8e6mDUVVdzFto/2By8VE0SQuinuQeip56W4q7MKmpLiHpSgv/w6dpURT/OVIp/8Vwh+UuyTwn8gKfxi0a+4CyDSpNJZ8p/+f/F+c/piAQk9W4Q6iSSfGizvBMjZf9udAdvsP6yFwsmLBEv+xboCZ9hQ6o6C1xaiFHd/YzNoaoo7cKBjP97f+Re8v3MD3t+1AX/ZsR7bDmzFntY92Nu6GztbdgTFXLT8M5v+X8y78N6i1d8XKy6auNt3kXEDf/y4UXhk7m3Wvu6l/GKMu7neYYy7Oda9LcbdHLn8airlxanWU4JTFwDR9u5Z//YDe/H4r/+Km84dkL4TIMKCMu4MiAsGkSd1wZC+c9AhdgxK5AfLI1ciVmVbFyBn+pOz/0L+1+8bgo/31+KCoxLdawjE3QRxZyB9IZG6O2DdPUheLHhdEBTkYGyF/uZXizFi5BiMHjuu0FVpLb+vxrhXHdWAt/5nBTY3f4RX2l7GjbgRL+NlbMEWnI/z0YIW/A6/s1hfjsuxCZuwFmvT7O/EnXgID+EADqTfG4uxOBkn46f4aY8+cpbpTHAKTsEgDMISLMnZv1fjaqsdG7BBaRx8C9/C7NmzldIykR4CRRN3Pc0vfikUd3N9QHE3x5ribo61qKmUxT0biaCLU9MhQeKiIBXyE2mTdwmSs/5WmoyLAbc7A7Y7B50HPTvuTx3j8beOkbi88kXPtN0JIqnQIPFkYRnyYwsTSt8JqEnuHmSFBqXuDGR8llw3YK0tEO87dhfK1SCKu4/uCph0w0/ewhu7lyMSST4ALhqNory8HO3tHaiprUU8XoHOrk5UV9cgGouhrq4BO7ZvQ01NLWKDK/GHt17HS50vQYh2BzqwAivwr7H/hU8Gf4rDhx+Jw3YOx4CagRh74gloqGjA+jf/iGHDD8PYccenW/7Uow/hqmumorKqeweqjzd9iPXvrsVFl1zZ4whXvbkCdTVVOPnU09B8sKPH5+vXrcGundtxxtkX5KTz6yUv4KjG4zBy1FFKFBc+NI/irkRKX6KiiXuuXWXE5vc/W7wM986ciqrK0l4YRXHXNxi9SqK4exHS9znFXR9LlZL6orircPGfJpEK87GLvwj7SYYOif/e/2Q3Nu9owQUjbWsEbCFDVohRKrRI3imIdLX5b4pSjmhK5DPvDCRn/zN3EXrlw3qMOiSOsYeJ7UYdOwyJOwNxuaDY/A5DuQ61L824707sxlNbH8fpOB3r6zfgkoGXYXDNMHx50hV4cdGTOGPSl3DI4KEQkl0ej2P8SU0WuuVLX6W4K31fmEgQKElxF7Hv8x9+FnPunlbyoTICImPczXyZGONuhrOohTHu5liLmnTEuJttcXhryyvGPdGZlPn0XQD7xUBy3YAMA4L1XAF54ZAKE0pfDKQuIKw1BPtRqPUDiMRsM/spyU+FCskFxTJ0yNphSO44JNYNWHcDku917zIk3quGWJfg99UXYtwTSOC7f7gHD//xfpRFy/GtM/8vvn7CN/yiCpyei1MDIwxFASUp7s8vWYGVq9eHYsad4m5unFPczbGmuJtjTXE3yzovcS9QEyNdrRDhQdbiYCssKLV7UMaagNSdAStkSIp/6q5AjwXF4nMRE+3vicPKhxcpS8X8d8/4p2f/5ToB699qQIQMldWgvqEfdrfF0+FBGTsMWXcK6iAuNErpVfFiG6JbutB6WRxdh0Y9m/avv7oeL/x1EQ6pGowfXfwsTh6anEk3/aK4myZenPqMi7uYTZ9+53349LPsq6iHDRmIBfPuwOgRw4tDxWetnHH3CSzP5BT3PMHlkY3inge0AFk44x4Ans+spSTuPpuunDzSKRYRp+4C2HYPSoYAdct/cv1A5l2A9MWDuCsg1x6IrUg7uxdJKjdEMWEiGrftGOR8/kByUXFyN6Ea64LAuhOQ3mXIsW4g9UAyEWqEiLd0uzXRj7h/f/U8/N83v4W6eD1WfG0tBlcPVTxq/cko7vqZlmKJxsVdQuCTU0txOJR2mxjjbq5/GONujrWoiTHu5njzyan5s7YeJmbJf/dzBdJbjgq5b0uFALWldhfqaMb3/3wEbh69GhVdyYsE+8VDtHVX/o1RzNlV0T8V/uO25Wj3swasLUdFqFC8FmtXDMfy/e94Lk6NxKN469PfYxd24az+k3DowMNx5JhGrFu7Ck1nnovNH21ELMonpyp2FZMpEiiauCu2r+STcXGquS6iuJtjTXE3x5ribpY1xd0sb5XFqdHW3ZkXA532xcXddw4g7wLY7xyI5xM47xy07w10kCsO/Ai/7frEU9w3t3yMT/f/HQP7HYJxVcdau8pQ3AOhZ2YFAhR3BUi5klDcAwL0kZ3i7gNWwKQU94AAfWbnjLtPYAGSU9wDwMsjq4q451GsZ5b08weskKHUhUDnweT2oukwInnnIBUylFpj8PZfLseyjk05xb21vQV/3r3W2u7xnLEXon1fK8Xds1eYQAeBoop7rocwheUBTKITGOOuYyh6l8EYd29GulIwxl0XSbVyGOOuxklHqr4Q466Dk64ywrirTM2P30XX/jGIfHEpDjRd7Ipi5m9vxk//53FcMuYfseCip3XhClQOY9wD4QtN5qKK+/0LFlmgbp8+JTTA3BpKcTfTfRR3M5xFLRR3c6xFTRR3c7wp7uZYi5rCKO7VT21AYt9IRI97HvsnXtMD2Gf7P8WEJ8aiM9GJpV9dhcaBx4YzmDEAACAASURBVJqFmqU2intJdEPBG1E0ce8ti1NFD1HcCz5OrQoo7mY4U9zNcZY1UdzNMae4m2MdWnF/+kMk9hyK8qOfwN7zeu7HfvfyW/Hjdf+Fc0Z8CT+51M8TeAvLnuJeWL6lUjrFPWBPMMY9IEAf2Rnj7gNWwKSMcQ8I0Gd2xrj7BBYgOWPcA8DLI2uxYtzzaGo6y18fX4rl+1cjIt6JRBCNRlFeXo729g5U1VTj/b1/QQwxjBo8Fv2rB6CurgE7tm9jjHsQ6MyrTKBo4i5aKEJlRh4+FFdMnqjc4FJLSHE31yMUd3OsKe7mWIuaKO7meFPczbEWNYVR3P/y42VYse9tV3FPVAB/P7AZtWW1aBx2HKKxGMV99myzg6qP11ZUcRcPY3r6+dcxc8bVqKqMh7IrKO7muo3ibo41xd0ca4q7WdYUd7O8QynuT/4OK/b+AREkrIc42Wfcm6PN2N2+C8NrDsPwAYdR3B+ah9kUd6NfqqKJe64dZQQB7ipjdByEojLGuJvrJi5ONcda1MQYd3O8GeNujrWoKYyLUyteOIjopxHUVl6Bz6cuyQB26EPV1t/r/mUzBlQONAvTozbGuJdUdxSsMUUT94IdUREK5uJUM9Ap7mY4i1oo7uZYU9zNsqa4m+UdSnF/sQ3RLV2oq7gc2699Gl0pQV+99W38w88n4egBx+A317xjFqRCbRR3BUi9IAnFXUMnUtw1QFQoguKuAElTEoq7JpCKxXDGXRGUhmQUdw0QfRQRdnHf+Y/z0THgeOuIf/SnH2D2GzPx1WOux/fOfdgHBTNJKe5mOBe7lqKK+8GWNsye/xheWboSw4YMxIJ5d2D4kEHWe00nHROKRauMcTc3hBnjbo41Y9zNsRY1cXGqOd6McTfHWtQUxhj3DT95C2/sXp6McUfEimMXu8ocaD2A3YndGFQ3GA3xfqiurmGMO2PczX6hxIhMJBJiZBblJXeV+fK5TZj/yLO49orzMXrEcKxauwE/W7wM986cWvKLVinu5oYOxd0ca4q7OdYUd7OsKe5mefcmcd/fsh97sAdH9B+J8mic4g5gIcXd7BeqmOJufwCTmGW3i7vYbWb+w89izt3T0L+hzjgUPxVS3P3QCpaW4h6Mn5/cFHc/tIKn5Yx7cIaqJVDcVUnpSddbxL2svBzNLfvQjGYcdUgjOrs6Ke4Udz1fEp+lFG3GPZe4h2nGXfBmjLvPUZdncsa45wkuj2yMcc8DWoAsjHEPAM9nVsa4+wQWMHnYY9zbGkdh9xkPY+mm1/DPL1+B0w+diJ/942sBqRQmO2PcC8O11EotmrgLEM8vWYGVq9dj1i3X4j8fe8EKlRnQrw4z7noAUy6dFIoYd4q7uSFNcTfHmuJujrWoieJujjfF3RxrUVPYxb3ziErsuOBF3Pf2d3D/29/Bv570vzHrtH83C1GxNoq7IqiQJyuquAt2Ynb9+lvnZmB84sG7MGF8Y2jQcsbdTFdR3M1wFrVQ3M2xpribZU1xN8s77OKOgTuw7fJV+Nriy/Hbj36FRyc/h4tGXWoWomJtFHdFUCFPVnRxDzk/MMbdXA8yxt0ca8a4m2MtamKMuznejHE3x1rUFP4YdyAaK8P+zv2IIYZ+9QNRVVHFGPfUMOLiVLPfJ1FbUcVd7CqzddvOjN1j5BaR3A7S/GAo9Rop7uZ6iOJujjXF3SxrirtZ3r1B3COxmCXu5SjHgIZBiMcrKO4Ud7NfJFttRRN3KehXXTqpR1hMmBancsbd3NiluJtjTXE3x5ribpY1xd0s794g7ohGcKDrICoiFehXP4DibhtCnHE3+30q6oy7fVcZsXe7/RWm7SBFuxnjbmbgMsbdDGdRC2PczbEWNXFxqjnejHE3x1rUFOYY98qh30TV3kcwbehl+NEHL2H2GXNx4xduMQvQR22McfcBK8RJOeOuofMo7hogKhRBcVeApCkJxV0TSMViKO6KoDQko7hrgOijiDCLe3zkA6jZ9m1MKBuFd3ZvxItXLsWEYaf5OHqzSSnuZnkXq7aiibs4YBESM2vOQiyYd4f1xFTxErPt0++8Dzdddxm3gyzWqCjReinu5jqG4m6ONWfczbKmuJvlHWZxLzv6SdRtvhVVB8rQ0tWBjTN2oiJWaRagj9oo7j5ghThpUcXdLuqffrYjjTFM20Eyxt3c6GeMuznWjHE3x1rUxF1lzPFmjLs51qKmcMe4Awkk0IFOdEQ6UBOtRU1tLWPcbUOIMe5mv0+itqKLu/lDzl6j2OVm5OFDe8z0iwdF3TPvMSvjxec1ZeyCQ3E314MUd3OsKe7mWFPczbKmuJvlHWpxj0SQSHRZ4p6IJlAZqaK4O4YPxd3s94ninuJtF/Nv3zk1Q9xFOM99Cxbhkbm3oX9DHYTci9ft06dY/1LczQ1airs51hR3c6wp7mZZU9zN8u4t4h4piyKeiFPcKe5mv0AutRV1xl3sLDPjrgew7r2NPZp2/LhRaVk2Rcltxt35nlPkRdu4ONVMDzHG3QxnUQtj3M2xFjVxcao53oxxN8da1BTmGPeOL+3B/7f0SHy/Hfj3ifNxwwk3m4XnszbGuPsEFtLkRRV35+x1sRk6Jd3tYVBi8ew35yzEd2ZNSy+opbib6TmKuxnOFHdznGVNFHdzzCnu5liHXdxbL43hppcb8EIn8MMLn8KlR11pFp7P2ijuPoGFNHnRxD3XPu7FYplN3O0PiXIT99b2LrR1dBWr2X2m3sryKDoTQDtZF7zPoxGgqqIM+1s6Cl4XKwCETIrfkc6uBHEUmEB5LIJYLIqWts4C18TiBYG6qjI0H+xAmEZ253MHkNjcidiUapz/81qs6ujA61c+j1NGX1rSnVpRHkUiAeM+IvqYL3MEKO421vnMuIsY97vu/j9oa6e4F3rYLlv6Sww6ZDCOO+ELha6qz5e/Y/s2vLZkMa795xtCxeKtlb9HR3sHzjjr7FC1e9EzT2LipPMxdFjmw+hK+SBaW1vxowUP4eZb7ijlZvZo21/eexcff7wJF1x4SajaveTlFzFq9Fg0jjsmVO1+6D++hxtn3IJ4PB6adq/+0R+wfNcyRCIRdCW60IlO1FRUoqMTqKutQ0VFBTo7O1FdU4NYrAwN9Q3Y9vlnqK2tw9ijG7H6nbcx6Zzz8beNHyIai6LptDPx06cex7kXXIShQ4fhdyuWIV4Rxymnnm4x+eWrL+Oww4/AscedkGb0yA8exPVfvxFV1dXp9/628QOsXfNH/OOVyTV29pcos7qqEk2nn+7qI2vXrMbOHdtx7vkX5uyH/37xFzjm2OMw5qijlfrr/vnfxezZs5XSMpEeAkUTd9H8bLu46Dk0/6XkE+POxan+Oeebg4tT8yXnPx8Xp/pnFiQHt4MMQs9fXi5O9ccraOqwL06V4l4br0B7Z4SLUx0DgrvKBP2G+M9fVHEXYSdPP/86Zs64GlWVxb8adxN37irjf1AVKgfFvVBke5ZLcTfHWtREcTfHm+JujrWoqfeIexztnVGKO8Xd7BfIpbaiiXuuHWVEO03uKmPfDlLUPWzIwIynuebax12k5+JUM+OYi1PNcBa1cFcZc6xFTVycao43F6eaY22dTwdUYevOg6GKca94sQ3RLV1496yNmLj8ZJwcBZZ94V+w57Tvm4XnszYuTvUJLKTJiybuIeXl2myKu5nepLib4UxxN8dZ1kRxN8ec4m6OddjFfcWEVbj8rQtxWQx4btQ52HHhK2bh+ayN4u4TWEiTU9w1dBzFXQNEhSIo7gqQNCXhjLsmkIrFUNwVQWlIRnHXANFHEWGecX/huFdxw5+vxc3lwH8MOAyfXfVXH0duPinF3TzzYtRYdHEXMeTX3zo349ifePAuTBjfWAwevuvk4lTfyPLOwBj3vNH5zsgYd9/IAmVgjHsgfL4yM8bdF67AicMc4y4OPoEEIuhEVbQDbZFaxrg7RgQXpwb+ivguoKji7vYUUrFgdfqd9+Gm6y7DFZMn+j4g0xko7uaIU9zNsaa4m2MtaqK4m+NNcTfHWtTUG8Q9GulCJdrQFq1BTW094vEKdHZ1orq6BtFYDHV1DRBb6NbU1OLIMY1Yt3YVms48F5s/2ohYNIovTDgdLy56EmdM+hIOGTwUq95cgfJ4HONParI6Y/nSVzFs+GEYO+74dOc89ehDuOqaqais6t4O8uNNH2L9u2tx0SU9HwQlyqyrqcLJp55m7ZvvfK1ftwa7dm7HGWdfkHMA/HrJCziq8TiMHHWU0kChuCth0pqoaOIun0pqf7iRPDIh9D9bvAz3zpxaErvN5CJOcdc6HnMWRnE3x5ribo41xd0sa4q7Wd69QdxjkQQq0Iq2SBVq6vpR3G1DiOJu9vskaiuauOd6cqqYdZ//8LOYc/c09G+oM0/FZ42McfcJLM/kjHHPE1we2Rjjnge0AFkY4x4Ans+sjHH3CSxg8jDHuE+v/gZ+1rwIb589BxNWz0LLiMux85yfBiRSuOyMcS8c21IquWji3ltm3EVnUtzNDGmKuxnOohaKuznWoiaKuzneFHdzrEVNYRb3KxJXYFliGTZe8zaO/O9T0Fl9KD6b8r5ZgD5qo7j7gBXipEUTd8FM7I++aPEyPDL3tvTMethi3Cnu5kY/xd0ca4q7OdYUd7OsKe5meYdZ3C9PXI4/xf+M9dO2YOjTQxBt34etV3+MrspBZiEq1kZxVwQV8mRFFXfBjrvKhHwEGWw+Y9zNwWaMuznWoiYuTjXHmzHu5liLmsIc4y52lEnegSxDOVrQ0QnU1lSjrHoAF6emhhFj3M1+n0RtRRd384est0YuTtXLM1dpFHdzrCnu5lhT3M2yprib5d1rxD3agY72DtRWxlBWN4ziTnE3+0Wy1VZUcb9/wSJs3bYzY/cYGfvedNIx3A6yaMOiNCumuJvrF4q7OdYUd7OsKe5meYdd3COIIBaLoTwWQUfbQdSVtyPW70iKO8Xd7BepFMSdi1OL1uehrZgx7ua6jjHu5liLmrg41RxvxribYy1qCnuM+0kTzsT/PuX/INK2F8N+OhSJWCU+/dp2IBI1C1KhNsa4K0DqBUmKNuPO7SB7wegxfAgUd3PAKe7mWFPczbKmuJvlHXZxv2TSFFx77FQL2pBfHIvYvr9h2z+8hY4B3Q9LMks0e20U91LpicK2o2jizhn3wnZsbyyd4m6uVynu5lhT3M2yprib5R12cf+Xi2/FeSMvsqD1X34dqv72M+w+7SEcODop86X0oriXUm8Uri1FE3dxSGJHmVlzFmLBvDswesRw6yjDth0kF6cWbnA6S2aMuznWjHE3x1rUxF1lzPFmjLs51qKmXhPjXl6O9rYWNCR2oryyBm3Vh6K6ugbRWAx1dQ3YsX0bampqceSYRqxbuwpNZ56LzR9tRCwaxRcmnI4XFz2JMyZ9CYcMHopVb65AeTyO8Sc1WZ2xfOmrGDb8MIwd1z2L/9SjD+Gqa6aisqo63WEfb/oQ699di4suubJHJ4oy62qqcPKpp6H5YEePz9evW4NdO7fjjLMvyDkAfr3kBRzVeBxGjjpKaaBwVxklTFoTFVXc7aL+6Wc70gf2xIN3YcL4Rq0HWqjCKO6FItuzXIq7OdYUd3OsKe5mWVPczfIOvbhHopZ8lwtxb29DQ9d2xMsiaK0/iuIOgOJu9vskaiu6uJs/ZL01Utz18sxVGsXdHGuKuznWFHezrCnuZnmHUdzfe2olfrdnBcQ+7tFIFNG0uLejoetzxMsSaKsdg6raes64PzQPs2fPNjuo+nhtFHcNA2DfgXbsc7k1paFoFmEjwBh3c8OBMe7mWIuauKuMOd6McTfHWtQUxhj3rp/vRs22SkyvnoEHr388A9iA17+Cyk+WYPdp/4kDR99gFqZHbYxxL6nuKFhjKO4a0FLcNUBUKILirgBJUxKKuyaQisVQ3BVBaUhGcdcA0UcRYRT3g899hgE7GnD3wHtwzz/Nzzja6g+eRL/ffQPt/cbh88tX+yBR+KQU98IzLoUaKO4aeoHirgGiQhEUdwVImpJQ3DWBVCyG4q4ISkMyirsGiD6KCKO47/npZgzdfQi+d+iDuPmyuzKONtq6A0OfOdx6b/uXf422IWf4oFHYpBT3wvItldIp7gF7gjHuAQH6yM4Ydx+wAiZljHtAgD6zc1cZn8ACJGeMewB4eWQNY4z7W4/+En8++CfraCORiC3GvQM1tbWoav8ciZZdqK6Mo3PwF7mrDGPc8/hm5J+F4p4/OysnxT0gQB/ZKe4+YAVMSnEPCNBndoq7T2ABklPcA8DLI2sYxf3NH72Kd1vWZRX3eFkU0V0bUBtpRufQJtQMOJTbQeYxNpglPwIU9/y4pXNR3AMC9JGd4u4DVsCkFPeAAH1mp7j7BBYgOcU9ALw8soZR3H+38GW817o+u7jHK4DmT1DfthmoPgSVIydS3PMYG8ySHwGKe37cMnIxxl0DRIUiGOOuAElTEsa4awKpWAxj3BVBaUjGGHcNEH0UUawY99bOFuxv348Dqf/2tzen/06+L/5uxoGOA+jszHxg0UVrz8HJnSfh96f8EV88+XTXo401b8bgnyefN7PtK++hs/YIH1QKk5Qx7oXhWmqlUtw19AjFXQNEhSIo7gqQNCWhuGsCqVgMxV0RlIZkFHcNEH0UoSLue1p3JyW6/UDq3/0pqRb/Ssnej5b2g9jXutf6zHq/Q3wm8uyzSXkz9rXt9dHCnklfiryEsyJnYd1ZH2LM8cdmLavfG/+C6g9/ioMjrsSuc54KVKeOzBR3HRRLvwyKu4Y+orhrgKhQBMVdAZKmJBR3TSAVi6G4K4LSkIzinj/EfW37Mmaqk7Kdkmwh0G3Jv8V/zakZ7a5IC3bs35NK1y3hQrp3t+zKvzGKOftV9kdNeS1qymtQXV6L6rLq1N+1qCpP/n+t+DxeiyrxWbwWX15zDgbvGoi9l3Sh/IjqrDWV7X0fg58/0fp85/m/QMthX1ZsVWGSUdwLw7XUSqW4B+wRxrgHBOgjO2PcfcAKmJQx7gEB+szOGHefwAIk7wsx7gc7xCy0TZItue759/621Ex1h5TvnhIuw0lEmfm87sbd+B6+hza0Zc1eHosnxbqsJi3YSdEWf9da/8rPauN1yb/jybTW52XVlpSn/069L556ms9rw0/ewhu7l1s7yohX95NTk7vKxOMV6OzqRHV1DeL7P8KgfW9ja+IwlB9+Oo48+kSsW7sKTWeei80fbUQsGsUXJpyOFxc9iTMmfQmHDB6KVW+uQHk8jvEnNVnlL1/6KoYNPwxjxx2fbu5Tjz6Eq66Zisqq7guHjzd9iPXvrsVFl1zZ47BEmXU1VTj51NPQ7PJAyPXr1mDXzu044+wLciL59ZIXcFTjcRg56igldAv55FQlTjoTUdwD0qS4BwToIzvF3QesgEkp7gEB+sxOcfcJLEDyUhJ3EYfdIzwkFS4iRVvMTIv/j/2lE3tr9+Hzmh1JCW/rDhcRf8vZbyHYXYmuAISyZy2LlnXLdGrm2prFTs1cp2e1y6shBFv83fWH/Thk0gjUVtVbf1dZci5nwGusdLFIrCDtzbdQP+IejcUwaO872L67GXVlbTj85EuxZuMeinu+8JnPkwDF3RNR7gQU94AAfWSnuPuAFTApxT0gQJ/ZKe4+gQVIno+4dyY60WyFiSQlWkpyUqrlosdkjLaVrk3GaCdjttMS7sgvylV9fQVfwQZswLt41zOLEGEh08lZ6O7wEGumWsxGW7PVyZlsKdHiXxk6It9LSnYqbbwa8WiFZ93OBGHcVcavuNfV1WP3pnfQ7+BfcUz5e/h9fAomXPBVzrj7Hi3MoEKA4q5CySMNY9w1QFQogjHuCpA0JWGMuyaQisUwxl0RlEeyBBJotuKsxW4hDslOSXN71wG0dB3AjuY9mRKeEvLume5u6W7vzB7mEaTlIpRDxFWnQ0LS8dciFKTnTHZ3KIjjszIZOpKcya6IVQZplta8KotTtVaoobCKF9sQ3dKF1svi6DpUPdym6m+L0H/59VYLOupGo/nEmWgfMB7tA07Q0CrvIhjj7s2oN6SguGvoRYq7BogKRVDcFSBpSkJx1wRSsZi+KO5SrC3JluEhbck4bLFFn5ypFnHY6c9TiyF7SLk1w70fLZ0HFYn7SxZBJCXY3bHUSdlOLnjsjscWs9l16XjsdHx2Kq1Y+GiPxxbS3ttffUncRV+W71iD/sv+GWX7Pszo2o7aUejo14j2/sehs/84HBj1T9q7nuKuHWlJFkhx19AtFHcNEBWKoLgrQNKUhOKuCaRiMaUs7nI/bCs8RIi160x2MhzEkmybdFsS3uYIF+k4YIWciNnxQrwqY1XJmGtrxrp78aKU6PrKWtRX1KEMVSnJlruM1KDKtuBRLpaU4SVC3vnyT6CvibskVLHlt6j+6xOIf74Ssf2b/YMLSY59X5yNunO+FZLW9o5mUtwD9iNj3AMC9JGdMe4+YAVMyhj3gAB9ZtcR4y7COXpIc3qhY2qbvpR0y3jtZCy2M2Zb/p2cCc8Wh12JStyKWzEXc30ebTK5iJcWsdY9Zq5TixfT8djlyQWM9r8z47GTci7isWvjtfAS7Hxi3PM6QM2ZfvOrxRgxcgxGjx2nueTCFtc3Ytwbcj459YtfOBEvLnoK5x5dieGJD/CH9/ejsnMXzqhajWjbbizeexZGRDdhfPnadGfM338nbq5+CNWR7t183u8Yi1XtJ+Oaqp/26LSlbeejAi04M/471w5d1X4KPu8ahMkVS3J2+HMtV+PEsrVoLNugNDDubf4WZs+erZSWifQQoLgH5EhxDwjQR3aKuw9YAZNS3AMCVMi+s2UHmtv2QuyN/e7SP6Bh3BC0V3fZFjImFzp2L2xMPZxGzGhbM9vd0r23dY9Cjfknqa9oyFjkKMJB6qN1mPD3L+KDoz9K7o9t20nEvtOI2CO70ha7LSRblFesF8XdLHmKO7eDNDvien9tFPeAfUxxDwjQR3aKuw9YAZNS3N0BihhqIdpSuIVYi6c02v/d27Yn4+/M9ElRF+En9te/4F/wGl7DJ/gk754TW/VZD5CxxVyn468zdgcRcdjuD6RxzmqLeGyxx7bbq62tFc888UNcd+O/5d3mYmSkuJulTnGnuJsdcb2/Noq7hj5mjLsGiApFMMZdAZKmJL0txt0pzyKkZE/rrgwJF49St0u4iMMWj2Jvbk/Kufh/na+Gin6oi9ejtrwOA2v6Ix6tssI97HtiJxc6JmVczmKLPFVlVcnwENv+2aW0k4hOTrrL4pNTdRPNXV5fjXE3SzlZGxenFoO6+Top7hqYU9w1QFQoguKuAElTklIRdyHc+2wz2PuERLd2z2gL2d5rzXgnZ7JFWqeki0ev63wNrByE2ng96uJ1tn/rkhIuQkgqGiwZt/8tJFukl+85dxMp5cWpOtmVQlkUd7O9QHE3x5vibo51MWuiuGugT3HXAFGhCIq7AiRNSYKKu9iBRMxS2yXaLtVCtjNmuFv3wJJyK09SxEVst64nQIrHpQupzpTtpHzXlSeFu66iIeNzZ1oxQ16oJzxS3DUNXIViKO4KkDQmobhrhOlRFMXdHOti1kRxD0ifMe4BAfrIzhh3H7DyTCqEW8Rrb9u+Ge/+fjUOPevoHrPYYiFkOqSkdY+1k8nu1l2puO7kjLeul124e4h1eQMaxKJJa5Y7Kd8dHx1EWaIMY794QnrWWwh3qb907Cpj+hgZ426WOHeVMcfb/5NTc+8q84UJp+PFRU/ijElfwiGDh2LVmytQHo9j/ElN1kEtX/oqhg0/DGPHHZ8+yKcefQhXXTMVlVXde/1/vOlDrH93LS665MoeMESZdTVVOPnU09B8sKPH5+vXrcGundtxxtkX5AT56yUv4KjG4zBy1FFKwBc+NI+7yiiR0peI4h6QJcU9IEAf2Snu2WEd7EjuQJIRNpKaxZZhJHtbd6dmwFMz2zKmu13k24P9bc3prf+GYigux+X4IX7oo4e6kzpnuJNiLWe4kzPbUsTrKsT7qTCT8obUzHg9xPteW/s5G7fmnTfR0dGBCU1n5dXuYmWiuJsjz8Wp5liLmrg4lYtTzY643l8bxT1gH1PcAwL0kb03irvcpUTEbSfDSrrDRfa1J3cr2dviEG4ZTiKEu1U8tr0ZHV09Z1h8oE0nFbHXYuZ6RGwEzjp4BlYNXdMt3HGHcFsi3jOuW7wnHuVejBfF3Rx1zribYy1q4oy7Od6cceeMu7nR5r8mirt/Zj1yMMZdA0SFIkopxl1s55e5GNJlFjsdUpJaOGnftaQ9GcutS7jFjiL1lkSnZrVts9hCpEUct9sMt/VZ6nOxqFIKd9AYd4XuZBIbAca4mxsOjHE3x1rUxBh3c7wZ426OdTFrorhroE9x1wBRoQgd4t7W1ZpeMLm3tXv/7e5FkcmwEfvCSXv4iQg7EX93dLUrtNg7iXh6ZEYYiW0WW0q1tUtJakeS5Hup3UyEnJfXQ8Rw657hprh7953OFBR3nTRzl0VxN8ea4m6WNcXdLO9i1UZx10Ce4q4BokcR4rHriVgzdh7ci237dmY8AEeEiyTju5OLJrv34k5uHSh3NtnbvhfisfA6XuKhNPXWbiTdIi0XSKaFO54Zry2FW86MF3KXkqDHSHEPStBffoq7P15BUlPcg9Dzn5cz7v6Z5ZuD4p4vuXDlo7gH7C/GuOcGKLbzEw+uEfHaYha7e7/t7v255S4l9offOLcSFKEpl+ASbMVWvIN38u61smh5RkiJEO+kSHfvsS2EOnOGW37evaBSzJT35hefnGq2d7k41RxvLk41x1rUxMWpXJxqdsT1/too7gp9/PySFbhn3mNWyovPa8K9M6eiqjL5GPDeKu5CuC2hlgsk7Q/BsWK1ux+Es7c984E49r27xeJLHS/xOPd/iFyG5vJmfFKzJRmXbcVxdz8Ep14Id+rBN/adSpIPvkkurOTTJdV6g+KuxklXKoq7LpLegzdrnAAAEZVJREFU5VDcvRnpTEFxp7jrHE8sC6C4e4yCVWs34L4Fi/DI3NvQv6EO9y9YZOW4ffqUkhT3BBJJ4RYPsUntOiJ3KpHbBcrwEedTJu1hJmJ7QR0vIdziqZE9niaZDiOpQ31laoZbLKBMSbZ8WI5cUFkZq0Jv3FVGB+NClEFxLwTV7GVS3M3xpribY80Z942IRSnuZkdc76+N4u7Rx0LURx4+FFdMnmildIq8eE9HjLsQ7owFkbZZbEu4xSx3Kl57X3vmY93tWwke6NivZdSKJ0TWxGtRLwTb8fh2KdVihjs94y3S9HjyZD2cj3YP0jgdi1OD1N+X8jLG3WxvM8bdHG/GuJtjLWpijLs53oxxN8e6mDVR3HPQP9jShtnzH0PTScekxf3Dj7bgm3MW4juzpmH0iOEQwr1l9w58ukc+OTK5OFLGa3fvUCL26E7uSNId5929d7fYi1vHS+wuIma406Ekqce5WwIudyapqO/eycSScsej3ivqIR6gU2oviru5HqG4m2MtaqK4m+NNcTfHmuJuljXF3SzvYtVGcVcQ96sunYQJ4xutlE5xX/z4Ypz5yZnF6j/WSwIkQAIkQAIkUAACdf9PHcpGlhWgZBZJAvkToLgriHuuGXexOPWW6C359wBzKhP4beK3GIRBOD5yvHIeJsyPwHZsx6+6foVrotfkV0CRcq1KrEJHogOnRU8rUgvyq3ZR1yKcFTkLwyLD8iugCLna0IbHuh7DN6LfKELt+Vf5XuI9fJL4BBdEL8i/kCLkfC3xGkZhFMZGxhah9vyr/GHXDzE1MhXxSHJDhzC8/oQ/YXnXckQiEau5sVgM5eXlaG9vR319PSoqKtDZ2Yna2lrrs379+mHr1q2oq6vDscceizfffBMXXngh3n//fevziRMnYuHChbj44osxfPhwLF261CrjzDOTk34vvfQSRowYgfHjx6fxzJ8/HzfffDOqq6vT74nyVq1ahWuu6fm77CzTyVnk+/zzzzF58uScXfDcc8/hxBNPRGNjcrLS6yUcaPbs2V7J+LlGAhR3D5heMe69dVcZjWNMW1FcnKoNpWdBXJzqiUhrAi5O1YozZ2FcnGqOtagpjLvKvPun1XjzjaVpcY9Goylx70BNbS3i8Qp0dnWiuroG0VgMdXUN2LF9G2pqanHkmEasW7sKTWeei80fcXGq2dHWN2qjuHv0c9h2lenNw5bibq53Ke7mWIuaKO7meFPczbGmuFPczY62vlEbxV2hn3Pt4y6y69hVRqEZfT4JF6eaGwJcnGqOtaiJi1PN8ebiVHOsRU1h3FXGLCF9tXFxqj6WpVwSxV1D71DcNUBUKILirgBJUxKKuyaQisVQ3BVBaUhGcdcA0UcRFHcfsAImpbgHBBiS7BR3DR1FcdcAUaEIirsCJE1JKO6aQCoWQ3FXBKUhGcVdA0QfRVDcfcAKmJTiHhBgSLJT3AN2FBenBgToIztj3H3ACpiUMe4BAfrMzhh3n8ACJGeMewB4eWTl4lQ+OTWPYcMsOQhQ3AMOD4p7QIA+slPcfcAKmJTiHhCgz+wUd5/AAiSnuAeAl0dWijvFPY9hwywU98KNAUvc7/ymtUCVr8ISoLgXlq+9dIq7OdaiJoq7Od4Ud3OsRU0Ud4q72RHX+2vjjHvv72MeIQmQAAmQAAmQAAmQQC8gQHHvBZ3IQyABEiABEiABEiABEuj9BCjuvb+PeYQkQAIkQAIkQAIkQAK9gADFvRd0Ig+BBEiABEiABEiABEig9xOguOfZx7v27MOMux7Auvc2WiU88eBdmDC+Mc/S+m42r6fSOsnkSm//TOa74auTcfv0KX0XcI4jX7V2A66/da6V4vhxo/DI3NvQv6EuJysx7md9dyFm3nQ1Ro8YTq5ZCBxsacPs+Y/hlaUrrRTfvnMqrpg80ZOXGMObNm/tMWbvX7AIjz6zJCO/apmelfbCBH5+V+zfA4Hi4vOacO/MqaiqjPdCMsEPye/Ydo5d+7h1nkdF64YNGYgF8+7g70uWrvIztj/8aAum33kfPv1sh1Uax3bw8V8KJVDc8+gF+cPVdNIx1slYfDm+OWchvjNrGn9sfPAUJ8z7FixKC6P4gRevbKLtlV78oK1cvZ4nXYU+cI5ZL3b2kzVPrN6A7WNZyskd06dkvbi3y6PbxabXd8O7RX0nhdfvhNtkwOHDB1t9I8f50MEDeMGfZcj4GduC5yM/fhFfv/rL1qSAFMk5s6ZZvFW+G31n5HofaZCxLUrn74g34zCkoLjn0Uvix2f+w89izt3TrB8jp8jnUWSfzCJ+REYePjQ9E+n8UXJC8UrvJZ99EnKOWRv7zK7qxSdn3L1HkRsj1RNmrhn3XBe13q3qOym8fie8SPB3JDuhIGNblOo8V1LcvUZj5ucc2/549dbUFPc8etZNMFVPzHlU1yuzuF3s5JJHlfTOUBmGyWQfOs7xqnoCpbh7fx3dxrGqDKqGyjBMxr0fVH4nvHqQv+XZCQUZ26JU5++MM1SGd/Oysw86tnk3yeubH57PKe559JUQ958tXpYRksEfe38g5Y/IVZdOSocPqIi7anp5Qphy6SSl2GJ/rQ9/aufMDcVdX58678iJkoOKu711znADfS0Pf0l+f1ecR+x11y/8hIIdQZCxLWr2Ok+K78mixcuU1tsEO5Lw5Q4ytuU6A8a4h6/f3VpMcc+jHznjngc0Rxa/swd+00tZclvoF7z14S+BM+6F68Mgs5LZZtydrXVeeBXuaMJVcj6/E/IIxe/6rDkLuTAyR5cHGdtizG7dtjPnGiTe0SvcjLufCYRwfev7Xmsp7nn0OWPc84DmksVvvJ7f9KoSpOdowlWKkw1j3PX1X5A4YNUxS3HP3l9+fydESZR2tfGf79hWkXbRAop77n7IZ2zbS3S7Y6LW80xVSgQo7nn0BneVyQOaSxavFfLO26a50os++cUry3HlxWdb27iphn7oOZLwleK1q0y2cAyeWNX62mvnjWwi4ybugvmSpStx7RUXWJWrXmSptbT3pQr6u9L7iOg9olxj2y1EMVd4jOgr8ZJbKauGlOk9ovCU5jW2nb8r//WTxTjvrJPSu92pXkCFh0jfbCnFPc9+5z7ueYJzZPPal90Z75grvYzjk1VwAV/uPsq1j7tT3J17N4uSGS+Zna/XXtfOE6hzL3FRsnw2hBt7Pjci99j287vi/N0QJXORZH5j2ynubvu02387tny2PWOfcdXnSeg5+4SzFK9zoD0cic8oCGcfe7Wa4u5FiJ+TAAmQAAmQAAmQAAmQQAkQoLiXQCewCSRAAiRAAiRAAiRAAiTgRYDi7kWIn5MACZAACZAACZAACZBACRCguJdAJ7AJJEACJEACJEACJEACJOBFgOLuRYifkwAJkAAJkAAJkAAJkEAJEKC4l0AnsAkkQAIkQAIkQAIkQAIk4EWA4u5FiJ+TAAmQAAmQAAmQAAmQQAkQoLiXQCewCSRAAiRAAiRAAiRAAiTgRYDi7kWIn5MACZAACZAACZAACZBACRCguJdAJ7AJJEACJEACJEACJEACJOBFgOLuRYifkwAJkAAJkAAJkAAJkEAJEKC4l0AnsAkkQAIkQAIkQAIkQAIk4EWA4u5FiJ+TAAmQAAmQAAmQAAmQQAkQoLiXQCewCSRAAiRAAiRAAiRAAiTgRYDi7kWIn5MACZAACZAACZAACZBACRCguJdAJ7AJJEACJEACJEACJEACJOBFgOLuRYifkwAJkAAJkAAJkAAJkEAJEKC4l0AnsAkkQAIkQAIkQAIkQAIk4EWA4u5FiJ+TAAn0egK79uzDjLsewLr3NmYc67fvnIovn9uE2fMfs96/d+ZUVFXG02k+/GgLpt95H2667jJcMXkicpUjPr9/wSI8+sySrDyPHzcK93/rZjz4Xz/DK0tX9kh38XlNVhvES7RJpHniwbswYXxjOu3Blrasn8lEzy9ZgXvmJY/J7TVsyEDMu+cbmPeDZ9JMRNsemXsb+jfUpY9D8BHHZX/JY5Sf2dvjrEsej51prx9sPEASIAESCECA4h4AHrOSAAmEn4BTvuURifeffv51zJxxNVpaWy2xn3LppAxRFZIqXrdPnwKVcuyCKiX/julTXMV76OABVrluL7sM3/DVyRnpVq3dgOtvnWtlc0p9rrKaTjqmh4TLepxtkXLuFG/J4NPPdsAp7rmOJ/yjiEdAAiRAAmYIUNzNcGYtJEACJUpAzD4vWrwsPZucrZlCiGfNWYgF8+7A6BHDIf6+b8GidD7VcmT5OsR9zJGH4o/r3sfMm6622iRF+4RjRuOJRa9hzqxpGRcFOsW9+UALmpsP4KpLJ6XrEEJfW1OF3/x+TfoiJ5v8l+hwYLNIgARIoKQJUNxLunvYOBIggUITcAp5rvqEmG7dthO33XgVbvvWDzJm4P2UI+rQIe5ilnzT5q1Wk+Ws//yHn4WYhRcXGYUUd1HnyMOHYuXq9Vb4jrgrMeu7C626xQWNvDtBcS/0CGb5JEACfYkAxb0v9TaPlQRIoAcBtxhst9htkdEeCuIME/FTjoq4q8S4C3E/8dgx+OachfjOrGl46bXfWTIt3hOx94UW969f/WUrhEiE+2zess26iJDvOcU91/Ewxp1fTBIgARJQI0BxV+PEVCRAAn2AgD0+XByuM35cvCdCYh7+8UvpkBk3LCrl6Jpxl4te317zHvo11GHO3dOwc/c+I+IuZvmtEKH//q2FQVw8DOhXl7EegDPufeCLw0MkARIwRoDibgw1KyIBEggTgWyhL87Ydq9jylaOTnF3LoyVfxd6xl2IuzyOU8Y3WuE68m+GyniNDH5OAiRAAv4JUNz9M2MOEiCBXkRgxf/f3t2jNBBGURjOQmwEF2Fv5z5t7cXGUuzckXyBgTBO1OHMGYJ50nvv5ImBV5mf98/DuNXhuM3h6WvE73QKyrjwc3qdC/e1c7YM93FsT8+vh8eH++P72DPcx+6Xt4/D3e3N8QJZ4f6PvhzeCgECFycg3C/uI3FABAjsKTDd0/z01onT6R3jOOb3bj8X7mvnbB3u8z869jjHfel2lcJ9z99euwgQuDYB4X5tn7j3S4DAN4GlBxItnd8+fvCnU2XWzPkt3P96cer8AUjjGLf4j/v8YVLzBzCNPWvC3cWpvngECBDIBYR7bmgCAQIECBAgQIAAgbqAcK8TW0CAAAECBAgQIEAgFxDuuaEJBAgQIECAAAECBOoCwr1ObAEBAgQIECBAgACBXEC454YmECBAgAABAgQIEKgLCPc6sQUECBAgQIAAAQIEcgHhnhuaQIAAAQIECBAgQKAuINzrxBYQIECAAAECBAgQyAWEe25oAgECBAgQIECAAIG6gHCvE1tAgAABAgQIECBAIBcQ7rmhCQQIECBAgAABAgTqAsK9TmwBAQIECBAgQIAAgVxAuOeGJhAgQIAAAQIECBCoCwj3OrEFBAgQIECAAAECBHIB4Z4bmkCAAAECBAgQIECgLiDc68QWECBAgAABAgQIEMgFhHtuaAIBAgQIECBAgACBuoBwrxNbQIAAAQIECBAgQCAXEO65oQkECBAgQIAAAQIE6gLCvU5sAQECBAgQIECAAIFcQLjnhiYQIECAAAECBAgQqAsI9zqxBQQIECBAgAABAgRyAeGeG5pAgAABAgQIECBAoC4g3OvEFhAgQIAAAQIECBDIBYR7bmgCAQIECBAgQIAAgbqAcK8TW0CAAAECBAgQIEAgFxDuuaEJBAgQIECAAAECBOoCwr1ObAEBAgQIECBAgACBXEC454YmECBAgAABAgQIEKgLCPc6sQUECBAgQIAAAQIEcgHhnhuaQIAAAQIECBAgQKAuINzrxBYQIECAAAECBAgQyAWEe25oAgECBAgQIECAAIG6gHCvE1tAgAABAgQIECBAIBcQ7rmhCQQIECBAgAABAgTqAsK9TmwBAQIECBAgQIAAgVxAuOeGJhAgQIAAAQIECBCoCwj3OrEFBAgQIECAAAECBHIB4Z4bmkCAAAECBAgQIECgLvAFffsAQt/95ksAAAAASUVORK5CYII=",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(colors=['darkorange', 'green', 'violet'], show_intervals=True, title_prefix=\"WITH enzyme added mid-reaction\")"
]
},
{
"cell_type": "markdown",
"id": "3171fd78-a103-4523-8c43-6e29695f49d2",
"metadata": {},
"source": [
"## Notice the dramatic acceleration of the reaction as soon as the enzyme `E` is added at t = 0.275!\n",
"The reactions simulator automatically switches to small time steps is in order to handle the rapid amount of change"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "c3afbcc8-bdae-4938-a3f1-ce00d62816f2",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0: A <-> B\n",
"Final concentrations: [A] = 3.333 ; [B] = 16.67\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 5.00003\n",
" Formula used: [B] / [A]\n",
"2. Ratio of forward/reverse reaction rates: 5.00000519021548\n",
"Discrepancy between the two values: 0.0005779 %\n",
"Reaction IS in equilibrium (within 1% tolerance)\n",
"\n",
"1: A + E <-> B + E\n",
"Final concentrations: [A] = 3.333 ; [B] = 16.67 ; [E] = 30\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 5.00003\n",
" Formula used: ([B][E]) / ([A][E])\n",
"2. Ratio of forward/reverse reaction rates: 5.00000519021548\n",
"Discrepancy between the two values: 0.0005779 %\n",
"Reaction IS in equilibrium (within 1% tolerance)\n",
"\n"
]
},
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Verify that the reaction has reached equilibrium\n",
"dynamics.is_in_equilibrium()"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "47c6d97b-a778-47c1-9cad-e75433a32f66",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" A | \n",
" B | \n",
" E | \n",
" caption | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0.000000 | \n",
" 20.000000 | \n",
" 0.000000 | \n",
" 0.0 | \n",
" Initial state | \n",
"
\n",
" \n",
" | 1 | \n",
" 0.050000 | \n",
" 19.000000 | \n",
" 1.000000 | \n",
" 0.0 | \n",
" | \n",
"
\n",
" \n",
" | 2 | \n",
" 0.100000 | \n",
" 18.060000 | \n",
" 1.940000 | \n",
" 0.0 | \n",
" | \n",
"
\n",
" \n",
" | 3 | \n",
" 0.125000 | \n",
" 17.618200 | \n",
" 2.381800 | \n",
" 0.0 | \n",
" | \n",
"
\n",
" \n",
" | 4 | \n",
" 0.150000 | \n",
" 17.189654 | \n",
" 2.810346 | \n",
" 0.0 | \n",
" | \n",
"
\n",
" \n",
" | 5 | \n",
" 0.175000 | \n",
" 16.773964 | \n",
" 3.226036 | \n",
" 0.0 | \n",
" | \n",
"
\n",
" \n",
" | 6 | \n",
" 0.200000 | \n",
" 16.370745 | \n",
" 3.629255 | \n",
" 0.0 | \n",
" | \n",
"
\n",
" \n",
" | 7 | \n",
" 0.225000 | \n",
" 15.979623 | \n",
" 4.020377 | \n",
" 0.0 | \n",
" | \n",
"
\n",
" \n",
" | 8 | \n",
" 0.250000 | \n",
" 15.600234 | \n",
" 4.399766 | \n",
" 0.0 | \n",
" | \n",
"
\n",
" \n",
" | 9 | \n",
" 0.275000 | \n",
" 15.232227 | \n",
" 4.767773 | \n",
" 0.0 | \n",
" | \n",
"
\n",
" \n",
" | 10 | \n",
" 0.275000 | \n",
" 15.232227 | \n",
" 4.767773 | \n",
" 30.0 | \n",
" Set concentration of `E` | \n",
"
\n",
" \n",
" | 11 | \n",
" 0.275200 | \n",
" 14.372651 | \n",
" 5.627349 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 12 | \n",
" 0.275400 | \n",
" 13.575171 | \n",
" 6.424829 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 13 | \n",
" 0.275600 | \n",
" 12.835300 | \n",
" 7.164700 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 14 | \n",
" 0.275800 | \n",
" 12.148878 | \n",
" 7.851122 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 15 | \n",
" 0.276000 | \n",
" 11.512043 | \n",
" 8.487957 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 16 | \n",
" 0.276200 | \n",
" 10.921213 | \n",
" 9.078787 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 17 | \n",
" 0.276440 | \n",
" 10.263435 | \n",
" 9.736565 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 18 | \n",
" 0.276728 | \n",
" 9.542527 | \n",
" 10.457473 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 19 | \n",
" 0.277074 | \n",
" 8.767428 | \n",
" 11.232572 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 20 | \n",
" 0.277419 | \n",
" 8.089086 | \n",
" 11.910914 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 21 | \n",
" 0.277834 | \n",
" 7.376689 | \n",
" 12.623311 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 22 | \n",
" 0.278249 | \n",
" 6.771007 | \n",
" 13.228993 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 23 | \n",
" 0.278663 | \n",
" 6.256054 | \n",
" 13.743946 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 24 | \n",
" 0.279161 | \n",
" 5.730676 | \n",
" 14.269324 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 25 | \n",
" 0.279659 | \n",
" 5.299738 | \n",
" 14.700262 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 26 | \n",
" 0.280256 | \n",
" 4.875569 | \n",
" 15.124431 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 27 | \n",
" 0.280853 | \n",
" 4.542897 | \n",
" 15.457103 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 28 | \n",
" 0.281570 | \n",
" 4.229802 | \n",
" 15.770198 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 29 | \n",
" 0.282430 | \n",
" 3.951341 | \n",
" 16.048659 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 30 | \n",
" 0.283462 | \n",
" 3.720982 | \n",
" 16.279018 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 31 | \n",
" 0.284700 | \n",
" 3.547589 | \n",
" 16.452411 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 32 | \n",
" 0.286186 | \n",
" 3.432586 | \n",
" 16.567414 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 33 | \n",
" 0.287969 | \n",
" 3.368656 | \n",
" 16.631344 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 34 | \n",
" 0.290109 | \n",
" 3.341352 | \n",
" 16.658648 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 35 | \n",
" 0.292677 | \n",
" 3.333912 | \n",
" 16.666088 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 36 | \n",
" 0.295758 | \n",
" 3.333265 | \n",
" 16.666735 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 37 | \n",
" 0.299456 | \n",
" 3.333353 | \n",
" 16.666647 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 38 | \n",
" 0.303893 | \n",
" 3.333317 | \n",
" 16.666683 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 39 | \n",
" 0.309218 | \n",
" 3.333343 | \n",
" 16.666657 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 40 | \n",
" 0.315608 | \n",
" 3.333314 | \n",
" 16.666686 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
"
\n",
"