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"## A complex (multistep) reaction `A <-> C` derived from 2 coupled elementary reactions: \n",
"## `A <-> B` and `B <-> C` \n",
"We are given the time evolution of the complex reaction, \n",
"and want to determine whether it can be modeled as an elementary reaction. \n",
"\n",
"In PART 1, a time evolution of [A], [B] and [C] is obtained by simulation \n",
"In PART 2, the time functions generated in Part 1 are taken as a _starting point,_ to explore how to model the composite reaction `A <-> C` \n",
"\n",
"**Background**: please see experiments `cascade_1` and `mystery_reaction_1`\n",
"\n",
"LAST REVISED: June 14, 2024 (using v. 1.0 beta33)"
]
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"id": "4d9b4808-b2ec-4b90-a604-f7fa69af39b8",
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{
"name": "stdout",
"output_type": "stream",
"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"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "3924c013",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"from experiments.get_notebook_info import get_notebook_basename\n",
"\n",
"from src.modules.reactions.uniform_compartment import UniformCompartment\n",
"from src.modules.visualization.plotly_helper import PlotlyHelper"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "fe5d6bfa-7e62-491a-a57f-be5105081a9d",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "75411c8b-f0c5-411d-9e12-1eaa423449f9",
"metadata": {},
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"# PART 1 - We'll generate the time evolution of [A] and [C] by simulating coupled elementary reactions of KNOWN rate constants...\n",
"## but pretend you don't see this section! (because we later assume that those time evolutions are just GIVEN to us)"
]
},
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"cell_type": "code",
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"id": "72b4245c-de4e-480d-a501-3495b7ed8bc4",
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"name": "stdout",
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"text": [
"Number of reactions: 2 (at temp. 25 C)\n",
"0: A <-> B (kF = 8 / kR = 2 / delta_G = -3,436.6 / K = 4) | 1st order in all reactants & products\n",
"1: B <-> C (kF = 12 / kR = 1 / delta_G = -6,160 / K = 12) | 1st order in all reactants & products\n",
"Set of chemicals involved in the above reactions: {'A', 'C', 'B'}\n"
]
}
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"# Instantiate the simulator and specify the chemicals\n",
"dynamics = UniformCompartment(names=[\"A\", \"B\", \"C\"], preset=\"mid\")\n",
"\n",
"# Reaction A <-> B (slower, and with a smaller K)\n",
"dynamics.add_reaction(reactants=\"A\", products=\"B\",\n",
" forward_rate=8., reverse_rate=2.) \n",
"\n",
"# Reaction B <-> C (faster, and with a larger K)\n",
"dynamics.add_reaction(reactants=\"B\", products=\"C\",\n",
" forward_rate=12., reverse_rate=1.) \n",
" \n",
"dynamics.describe_reactions()"
]
},
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"cell_type": "markdown",
"id": "98a9fbe5-2090-4d38-9c5f-94fbf7c3eae2",
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"source": [
"### Run the simulation"
]
},
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"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (A). Conc: 50.0\n",
" Species 1 (B). Conc: 0.0\n",
" Species 2 (C). Conc: 0.0\n",
"Set of chemicals involved in reactions: {'A', 'C', 'B'}\n"
]
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"dynamics.set_conc({\"A\": 50.}, snapshot=True) # Set the initial concentrations of all the chemicals, in their index order\n",
"dynamics.describe_state()"
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"cell_type": "code",
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"Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n",
"85 total step(s) taken\n",
"Number of step re-do's because of negative concentrations: 0\n",
"Number of step re-do's because of elective soft aborts: 1\n",
"Norm usage: {'norm_A': 24, 'norm_B': 25, 'norm_C': 23, 'norm_D': 23}\n"
]
}
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"dynamics.single_compartment_react(initial_step=0.01, duration=0.8,\n",
" snapshots={\"initial_caption\": \"1st reaction step\",\n",
" \"final_caption\": \"last reaction step\"},\n",
" variable_steps=True)"
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",
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},
"metadata": {},
"output_type": "display_data"
}
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"text": [
"0: A <-> B\n",
"Final concentrations: [A] = 1.096 ; [B] = 3.898\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.55592\n",
" Formula used: [B] / [A]\n",
"2. Ratio of forward/reverse reaction rates: 4\n",
"Discrepancy between the two values: 11.1 %\n",
"Reaction IS in equilibrium (within 15% tolerance)\n",
"\n",
"1: B <-> C\n",
"Final concentrations: [B] = 3.898 ; [C] = 45.01\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 11.5475\n",
" Formula used: [C] / [B]\n",
"2. Ratio of forward/reverse reaction rates: 12\n",
"Discrepancy between the two values: 3.771 %\n",
"Reaction IS in equilibrium (within 15% tolerance)\n",
"\n"
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"# PART 2 - This is the starting point of fitting the data from part 1. \n",
"### We're given the data of the time evolution of `A` and `C`, and we want to try to model the complex reaction `A <-> C`"
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"source": [
"Let's start by taking stock of the actual data (saved during the simulation of part 1):"
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\n",
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" | \n",
" SYSTEM TIME | \n",
" A | \n",
" C | \n",
" caption | \n",
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\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0.000000 | \n",
" 50.000000 | \n",
" 0.000000 | \n",
" Initialized state | \n",
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\n",
" \n",
" | 1 | \n",
" 0.004000 | \n",
" 48.400000 | \n",
" 0.000000 | \n",
" 1st reaction step | \n",
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\n",
" \n",
" | 2 | \n",
" 0.008000 | \n",
" 46.864000 | \n",
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" | \n",
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\n",
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" | 3 | \n",
" 0.010000 | \n",
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\n",
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" | 4 | \n",
" 0.011000 | \n",
" 45.764849 | \n",
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\n",
" \n",
" | ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
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\n",
" \n",
" | 81 | \n",
" 0.638365 | \n",
" 1.497612 | \n",
" 44.279102 | \n",
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\n",
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\n",
" \n",
" | 85 | \n",
" 0.809862 | \n",
" 1.096061 | \n",
" 45.006431 | \n",
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.estimate_rate_constants(t=t_arr, reactant_conc=A_conc, product_conc=C_conc, reactant_name=\"A\", product_name=\"C\")"
]
},
{
"cell_type": "markdown",
"id": "94af05ee-037a-4223-a1a7-fa681baf5ae1",
"metadata": {},
"source": [
"### The least-square fit is awful : the complex reaction `A <-> C` doesn't seem to be amenable to being modeled as a simple reaction with some suitable rate constants\n",
"Probably not too surprising given our \"secret\" knowledge from Part 1 that the complex reaction originates from 2 elementary reactions where one doesn't dominate the other one in terms of reaction kinetics"
]
},
{
"cell_type": "markdown",
"id": "8951650d-cb8c-4def-99c3-4e465a12b9d4",
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"source": [
"### A glance at the above diagram reveals much-better linear fits, if split into 2 portions, one where A(t) ranges from 0 to about 24, and one from about 24 to 50 \n",
"Indeed, revisiting the early portion of the time plot from Part 1, one can see an inflection in the [C] green curve roughly around time t=0.1, which is when [A] is around 24 (blue). That's shortly after the peak of the mystery intermediate B (orange). \n",
"\n",
"We'll pick time **t=0.1** as the divider between the 2 domains of the `A <-> C` time evolution that we want to model. "
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(colors=['darkturquoise', 'orange', 'green'], xrange=[0, 0.4], \n",
" vertical_lines=[0.1])"
]
},
{
"cell_type": "markdown",
"id": "6d4a4dbd-de22-471c-a1a4-5507941d92e1",
"metadata": {},
"source": [
"#### Let's locate where the t = 0.1 point occurs in the data"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "3795ba32-68ec-4d20-9b6b-c2a117810741",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" search_value | \n",
" SYSTEM TIME | \n",
" A | \n",
" B | \n",
" C | \n",
" caption | \n",
"
\n",
" \n",
" \n",
" \n",
" | 47 | \n",
" 0.1 | \n",
" 0.098644 | \n",
" 24.020441 | \n",
" 14.383519 | \n",
" 11.59604 | \n",
" | \n",
"
\n",
" \n",
"
\n",
"
A(t)=%{x}
value=%{y}",
"legendgroup": "wide_variable_0",
"line": {
"color": "green",
"dash": "solid"
},
"marker": {
"symbol": "circle"
},
"mode": "lines",
"name": "C'(t)",
"orientation": "v",
"showlegend": true,
"type": "scatter",
"x": [
50,
48.4,
46.864,
46.1264128,
45.764848537599995,
45.4068108534784,
45.05225696214661,
44.701144688364984,
44.35343245764235,
44.00907928688937,
43.668044775223194,
43.33028909492093,
42.99577298251945,
42.664457730059134,
42.33630517646926,
42.01127769909257,
41.689338205346836,
41.37045012452115,
41.05457739970469,
40.74168447984581,
40.36974667835801,
40.00199954947228,
39.638384203210805,
39.278842735294916,
38.85221330365549,
38.4312876463126,
38.015970628093214,
37.524208687584405,
37.04025733355494,
36.56396179174412,
36.09517096707712,
35.5414506222978,
34.99811725427435,
34.464927853991476,
33.83698995083985,
33.22298880011996,
32.62253891329065,
31.91781347752384,
31.231546747554717,
30.563137063873327,
29.781780557714825,
29.02450701695829,
28.290395078289695,
27.436200826411618,
26.612888876028055,
25.819079124488056,
24.900345094915533,
24.020440777399745
],
"xaxis": "x",
"y": [
-9.600000000000001,
9.600000000000001,
30.822399999999995,
41.899315200000004,
46.41209925119996,
50.12635364006394,
53.750260495463436,
57.28550409970293,
60.73373957343236,
64.09659336783142,
67.37566374856453,
70.57252127164378,
73.6887092513349,
76.72574422023837,
79.68511638167638,
82.56829005451397,
85.37670411053989,
88.11177240453134,
90.77488419712517,
93.25115170979711,
96.13957259742529,
99.07790484714667,
101.92046438241448,
104.54659440517338,
107.5882355929242,
110.65951435651903,
113.47432857809292,
116.70583563316939,
119.93843550873544,
123.00561986850903,
125.7843600870674,
128.9334704744358,
132.04015897436716,
134.81271347105132,
137.9016042505301,
140.8923754152064,
143.50321860426106,
146.3378372360919,
149.00327850294707,
151.24788504239746,
153.5792410492994,
155.6570928893061,
157.28583223293128,
158.81822392583024,
160.00570033308645,
160.73927115789127,
161.15321666154205,
161.37579227171
],
"yaxis": "y"
},
{
"hovertemplate": "Linear Fit :
A(t)=%{x}
value=%{y}",
"legendgroup": "wide_variable_1",
"line": {
"color": "red",
"dash": "solid"
},
"marker": {
"symbol": "circle"
},
"mode": "lines",
"name": "Linear Fit",
"orientation": "v",
"showlegend": true,
"type": "scatter",
"x": [
50,
48.4,
46.864,
46.1264128,
45.764848537599995,
45.4068108534784,
45.05225696214661,
44.701144688364984,
44.35343245764235,
44.00907928688937,
43.668044775223194,
43.33028909492093,
42.99577298251945,
42.664457730059134,
42.33630517646926,
42.01127769909257,
41.689338205346836,
41.37045012452115,
41.05457739970469,
40.74168447984581,
40.36974667835801,
40.00199954947228,
39.638384203210805,
39.278842735294916,
38.85221330365549,
38.4312876463126,
38.015970628093214,
37.524208687584405,
37.04025733355494,
36.56396179174412,
36.09517096707712,
35.5414506222978,
34.99811725427435,
34.464927853991476,
33.83698995083985,
33.22298880011996,
32.62253891329065,
31.91781347752384,
31.231546747554717,
30.563137063873327,
29.781780557714825,
29.02450701695829,
28.290395078289695,
27.436200826411618,
26.612888876028055,
25.819079124488056,
24.900345094915533,
24.020440777399745
],
"xaxis": "x",
"y": [
27.884687837813658,
37.86653236097197,
47.44910310320398,
52.05065357362378,
54.30632748137833,
56.54000029158675,
58.75193892805845,
60.94240650747139,
63.11166239864258,
65.25996228083812,
67.38755820114,
69.49469863088422,
71.58162852118608,
73.64858935756718,
75.6958192136994,
77.72355280427968,
79.73202153705108,
81.72145356398255,
83.69207383162268,
85.64410413064044,
87.96449494735077,
90.25874161258528,
92.52721152047056,
94.77026591569839,
97.43185882546598,
100.0578678675941,
102.64888655739884,
105.71681857775232,
108.73602306068611,
111.70746558907928,
114.63208879264752,
118.086557786958,
121.4762260393668,
124.80260959875409,
128.72009617341507,
132.550636188119,
136.29663457204285,
140.6931719041299,
144.97455177910996,
149.14452774178562,
154.01913971780584,
158.7435064336392,
163.32337595512934,
168.65239733939342,
173.78875476613527,
178.74105821665978,
184.47272086748956,
189.96213842542602
],
"yaxis": "y"
}
],
"layout": {
"autosize": true,
"legend": {
"title": {
"text": "Curve vs Fit:"
},
"tracegroupgap": 0
},
"margin": {
"t": 60
},
"template": {
"data": {
"bar": [
{
"error_x": {
"color": "#2a3f5f"
},
"error_y": {
"color": "#2a3f5f"
},
"marker": {
"line": {
"color": "#E5ECF6",
"width": 0.5
},
"pattern": {
"fillmode": "overlay",
"size": 10,
"solidity": 0.2
}
},
"type": "bar"
}
],
"barpolar": [
{
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.estimate_rate_constants(t=t_arr_early, reactant_conc=A_conc_early, product_conc=C_conc_early, \n",
" reactant_name=\"A\", product_name=\"C\")"
]
},
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"source": [
"Trying to fit an elementary reaction to that region leads to a **negative** reverse rate constant! \n",
"It's not surprise that an elementary reaction is a good fit, if one observes what happens to the time evolution of the concentrations. Repeating the earlier plot, but only showing `A` and `C` (i.e. hiding the intermediary `B`):"
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""
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"source": [
"dynamics.plot_history(colors=['darkturquoise', 'green'], xrange=[0, 0.4], vertical_lines=[0.1], \n",
" chemicals=['A', 'C'], title=\"Changes in concentration for `A <-> C`\")"
]
},
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"In the zone to the left of the vertical dashed line: \n",
"when the reactant `A` is plentiful, the rate of change (gradient) of the product `C` is low - and vice versa. \n",
"Does that look like an elementary reaction in its kinetics? Nope!"
]
},
{
"cell_type": "markdown",
"id": "652e8cc0-b053-40d1-9d1c-2f2a30f59469",
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"source": [
"### II. And now let's consider the LATE region, when t > 0.1"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "2d61a783-e1e5-473a-9fd8-cba5cb842a85",
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"name": "stdout",
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"text": [
"Total REACTANT + PRODUCT has a median of 42.74, \n",
" with standard deviation 3.695 (ideally should be zero)\n",
"The sum of the time derivatives of reactant and product \n",
" has a median of 16.91 (ideally should be zero)\n",
"Least square fit: Y = 4.132 + 7.995 X\n",
" where X is the array [A] and Y is the time gradient of C\n",
"\n",
"-> ESTIMATED RATE CONSTANTS: kF = 8.091 , kR = -0.09668\n"
]
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CIAACIAACIAACIAACIAACwQhAmoPxwtUgAAIgAAIgAAIgAAIgAAIgAAIJIgBpTlCyESoIgAAIgAAIgAAIgAAIgAAIgEAwApDmYLxwNQiAAAiAAAiAAAiAAAiAAAiAQIIIQJoTlGyECgIgAAIgAAIgAAIgAAIgAAIgEIwApDkYL1wNAiAAAiAAAiAAAiAAAiAAAiCQIAKQ5gQlG6GCAAiAAAiAAAiAAAiAAAiAAAgEIwBpDsYLV4MACIAACIAACIAACIAACIAACCSIAKQ5QclGqCAAAiAAAiAAAiAAAiAAAiAAAsEIQJqD8cLVIAACIAACIAACIAACIAACIAACCSIAaU5QshEqCIAACIAACIAACIAACIAACIBAMAKQ5mC8cDUIgAAIgAAIgAAIgAAIgAAIgECCCECaE5RshAoCIAACIAACIAACIAACIAACIBCMAKQ5GC9cDQIgAAIgAAIgAAIgAAIgAAIgkCACkOYEJRuhggAIgAAIgAAIgAAIgAAIgAAIBCMAaQ7GC1eDAAiAAAiAAAiAAAiAAAiAAAgkiACkOUHJRqggAAIgAAIgAAIgAAIgAAIgAALBCECag/HC1SAAAiAAAiAAAiAAAiAAAiAAAgkiAGlOULIRKgiAAAiAAAiAAAiAAAiAAAiAQDACkOZgvHA1CIAACIAACIAACIAACIAACIBAgghAmjWTfbFvWPMOKM6RQMeUrMhmUuLm0DjH8BATQwLT27MqqlvDOYbRISSOBNBnOWaVd0wzOlpELj8phkbwPmtqphd0t5vaNLQrYgKQZs0EQJo1ATItDmlmmljGYUFAGCeXaWjos0wTyzgsSLP5yYU0m5+jqFoIadYkD2nWBMi0OKSZaWIZhwUBYZxcpqGhzzJNLOOwIM3mJxfSbH6OomohpFmTPKRZEyDT4pBmpollHBYEhHFymYaGPss0sYzDgjSbn1xIs/k5iqqFkGZN8pBmTYBMi0OamSaWcVgQEMbJZRoa+izTxDIOC9JsfnIhzebnKKoWQpo1yUOaNQEyLQ5pZppYxmFBQBgnl2lo6LNME8s4LEiz+cmFNJufo6haCGnWJA9p1gTItDikmWliGYcFAWGcXKahoc8yTSzjsCDN5icX0mx+jqJqIaRZkzykWRMg0+KQZqaJZRwWBIRxcpmGhj7LNLGMw4I0m59cSLP5OYqqhZBmTfKQZk2ATItDmpkmlnFYEBDGyWUaGvos08QyDgvSbH5yw5bmz3zhm2LHzkMlgXfNnC7eePUF82GE1EIvBnRr4vDFZz4lnvvG98TzX/6seOrjjwq6tq9/UPz4pedDqj2820CaNVlCmjUBMi0OaWaaWMZhQUAYJ5dpaOizTBPLOCxIs/nJDVOaNzz+tBLDckEmMZw7e5b48z/5nPlAQmhhEBEOcm0ITQt0C0hzIFx3Xwxp1gTItDikmWliGYcFAWGcXKahoc8yTSzjsCDN5iU3c/aMaHvrddH69psie+yIaH1vRyiNJPk7dvJ8zRHlTzz9nFi/ZmmJQJeLI13T3dWp2mWPWj+4rVd9feC1l0rau/2pZ8WjD2xy7lc+yvvyd74qNvWu8IzxK1//rvjJP7xd8570xwD3Y9WyhVVHhquJ8L5DJ8WnP/81Qe36f/76Z6p+94Pi/MG3v6S+RbHRI6pRekiz5q8GpFkTINPikGamiWUcFgSEcXKZhoY+yzSxjMOCNEec3HxetOzdLVr37BIt9lP+u+QxORlKI0ksn/zYIzVHk/1K8/HTF8Qzf/ikePaPfs9pH9Xh/t6rP31TTXW2RbpcVl/4/o/Eiz/8yV1S7A641j3Lf27LbDWR9SvNJPPVroU0h9I1o7sJpDk69ibXDGk2OTtomxcBCAj6RdwIoM/GLWNoL6S5uX0gNTZmybEUY/XcvVO0HNhX0ojcmnVifPMWMX7PVjF2zxYx+3c/pt1Ie/TUXqdb7YZ+pZlGmu0RV/t+5YJJ/6YHXecewXWPLJN4fvJ3P1Ii3+721XPPWsAqrWmm0WV62CPNtaS5Vj2N/jlGmjUJQ5o1ATItDmlmmljGYUFAGCeXaWjos0wTyzgsSHNjk5saviMluSDIUpZb9+4S2UMHSyW5d72U422WKNNzy1YxOaXduSaMNc3NkubykWUaBbZF3f6ZF/HyEWv3NdXuSdeR5NOoNz38bmgW1khzY3tP7btDmmszqnoFpFkTINPikGamiWUcFgSEcXKZhoY+yzSxjMOCNIeb3NTtW9Z0693F0eTs0cMllYxv3KxGke3RZHqdbG2t2JAwpJluHvb0bK+RZqrHHjlevLBHfOvFV5z1vuXyG4R8pXu672Gvf7a/V7622n0tpDkIfcbXQpoZJ1cjNEizBjwUjYQABCQS7KhUgwD6rAY8FI2EAKRZD3v65k0pyfZ6ZDmiLEeTsyePl0qyS5DHCl+LTMZ3xWFJc62NwEg6afdse5Mv99TrShuBlU/PpqDoPgePnnE2CrOvCTLaXQ6n0j0rQfRa5wxp9t3lknMhpDk5uQ4SKaQ5CC1cawIBCIgJWUAbghBAnw1CC9eaQADSHCwL6f5+KcZyHXJhTTKNKGfOnCreJJsVY/Y0a5pyLdck00iyziMsaaY2eB05ZY8A25uEkaC++e6+u0aI3TtSe4m1HaMtx/Tv8jXU9lpi9ygw1ffgtvXqTORKj0r3pLb/p5f/vmSnbDueartyBxlprrZZGTYC0+nZBpSFNBuQBAObAGk2MCloUlUCEBB0kLgRQJ+NW8bQXkhz9T6QvnZVrUmmtcj2Bl6Zc2edQpOtbZYYu6dbb9gUascKU5qpYV6bYJXLLclg/8AtFQfJMk3F7usfdOS0mjRTGfp5/8Cg51FMXvVXm0ptw6x0z/Ljpuj6asJsM3DH406Y14Zl7nXTOHIq1O4d7c0gzdHyN7V2SLOpmUG7KhGAgKBvxI0A+mzcMob2QppL+0Dm8qXirtaF0eTMRWuTKXpMtk8tkWTawCu3rrehHSlsaW5oY3HzphLARmCauCHNmgCZFoc0M00s47AgIIyTyzQ09FmmiWUcVtKlOXPhvCXJrjOSM1cuFyV52nS5s7XctKswzZpGlHOr1za1R0Cam4o7VpVBmjXTBWnWBMi0OKSZaWIZhwUBYZxcpqGhzzJNLOOwkibNmbNnlCC3qlFkOeVarklO9113Mjwxc6Zcg+za2VrKcm7Fqkh7AKQ5UvxGVw5p1kwPpFkTINPikGamiWUcFgSEcXKZhoY+yzSxjMPiLs3Z0yeVGDujyVKU0zduFCW5u9uS5MKa5DEpyfmly43KOKTZqHQY1RhIs2Y6IM2aAJkWhzQzTSzjsCAgjJPLNDT0WaaJZRwWN2nOHj9aEOTClGuS5MHBoiTP6VFTrWktsjonWT7zi5cYnWFIs9HpibRxkGZN/JBmTYBMi0OamSaWcVgQEMbJZRoa+izTxDIOK+7SnD1ySElyq1qTTFOud4vU0G0nY/l5861RZNfu1vn5C2KVUUhzrNLV1MZCmjVxQ5o1ATItDmlmmljGYUFAGCeXaWjos0wTyzisuElzy8EDJeck09Tr1OhIUZIXLXZGkMe3bFNnJk/0zI11BiHNsU5fQxsPadbEC2nWBMi0OKSZaWIZhwUBYZxcpqGhzzJNLOOwTJfmlv175Zrkna41yXIkeXy8KMlLlylJJjkepynXcur1RPdsVhmDNLNKZ6jBQJo1cUKaNQEyLQ5pZppYxmFBQBgnl2lo6LNME8s4LKOkeXLSOvqpcASUmnItvxYTE04GcstXlpyTTKJMO15zfkCaOWdXLzZIsx4/AWnWBMi0OKSZaWIZhwUBYZxcpqGhzzJNLOOwopRmGjFWguw+J3nfnhLauVVrCmuSrU276MzkyemdjDNyd2hJl+Z9h06KT3/+a+Ll73xVbOpdoQC9+tM3xXPf+J545g+fFM/+0e/dBe2F7/9IvPjDn4jnv/xZ8dTHH2XbXyDNmqmFNGsCZFoc0sw0sYzDgoAwTi7T0NBnmSaWcVjNlGZae6w267JHk+mc5AP7SyV5ba+SZDXdeot1XvLk1A7GGagdWlKkecPjT98F48BrL6nv0c/c0rz9qWfFF5/5lBJiL6m2xfpbL74i3nj1hdqQY3oFpFkzcZBmTYBMi0OamSaWcVgQEMbJZRoa+izTxDIOq5HSnLozZI0iy826WgujybTbtfsxvmGjdU6yWpNMu1xLSW6bwph48NC4S3OlUeOvfP27Ctaf/8nnBEmyLb80ivyzNz4QP37pefXzStJMP/vE08+J39h+r+dodPBMmFcC0qyZE0izJkCmxSHNTBPLOCwICOPkMg0NfZZpYhmHFaY0p24NWkc/KUG2RpTp3OQSSd50T+kRUDSS3NLCmLB+aNylmYT4k7/7Ed9iWy7CVL5/4JYDetWyhY5Qlwu2fjbMugOkWTMfkGZNgEyLQ5qZJpZxWBAQxsllGhr6LNPEMg5LR5rTAwPF458K5yRnT50o0kqnnXXI7nOSRSrFmGj4oYUtze+cf0eM5IrHdIXfYu87PrToITElWzqLoNoocaV2lU/VrnYP+2f2NO9mxdqseiDNmqQhzZoAmRaHNDNNLOOwICCMk8s0NPRZpollHFYQaU73XS+MIO+0plvLZ+bMaYcOjRg706zVmmR5BNTGzYzpNSe0sKV56/+1Vey+LHclb/Jj1/+yS2yZt6WkVntqdhCpJWl2X19LvMuvb3LYDa0O0qyJF9KsCZBpcUgz08QyDgsCwji5TENDn2WaWMZhVZPm9NUrlhzb5ySTJJ8/V5RkufbY3qzLkmUpyes3MKYVTWhhS/Mf/H9/IC7fvtz0YP7iv/8LMW/avJJ6awmvVyMhzUUqkGbNbgxp1gTItDikmWliGYcFAWGcXKahoc8yTSzjsNzSnLl0seScZFqTnLl8qSjJHdMKI8nW0U8kyjm52zUejSUQtjQ3trXB705rkh99YJPa8MvPA9OzIc1++omvayDNvjAl7iJIc+JSHvuAISCxT2HiAkCfTVzKYx1w5txZMePoPpHauUuID95XU6/T1646MU10dlo7Wxd2tVaSLM9NxqO5BLhLc6Xds2kTr4tXrt8l0147YpNIe53JjI3AmttXY1cbpDl2KWtKgyHNTcGMSkIkAAEJESZu1RQC6LNNwYxK6iSQOXNK7m5trUW2zkreJdJ9fUVJnjWrKMmFc5Jzy1bUWRuKhUWAuzQTJ3uatptZ18zpnmcse4kwfe/FH/5EFXfvno0jp8LqhUzvA2lmmljNsCDNmgBRvOkEICBNR44KNQmgz2oCRPFQCWRPHneOflKiTJIsd7y2HxPds8XkvfeKnBxJHlq/WY0o55csDbUNuJk+gSRIc1BKNKX7i898Sjz18UcrFqUR7G+9+IqneAetz9TrsaZZMzOQZk2ATItDmpkmlnFYEBDGyWUaGvos08TGJKzssSOuNcm71ZnJqdvF82vzc+cVd7curEmetma5yOUnxdBILiZRJq+ZkOa7c15pSrd9pT3y7DVlm1MPgjRrZhPSrAmQaXFIM9PEMg4LAsI4uUxDQ59lmlhDw8oePiTFeGdxurWcep0avuO0Nr9goSXJ9vFP8jU/b35JNEGOnDIUg3HNyk3kxKXbF1S7hsaHxI2R6+rrq3euiNHC+cjnb51V3xvNj6rv02NwdEDcHL2pvr5G1+ats5TP/vFp42JEg8wgAGnWzAOkWRMg0+KQZqaJZRwWBIRxcpmGhj7LNLGGhNVyYF/Z7tZSksdGndblFy9xRpLH1AZeW8TEnJ6qrU+qNOfy4+JO7o58Dok7Umzp66Gx2/Jr63vDhe+pn6mn/Pm4/Lm8zvqZfI4Vyttl1b3uiNzEeKg9ZvJfTYZ6P9yMDwFIs2YuIc2aAJkWhzQzTSzjsCAgjJPLNDT0WaaJjSgsa8MuelqjyXRmssgVp1Hnly4XY1uso5/sc5InuroCtdZ0aaZR2+GCyFqCK0VVSuvQWEFcleAW5FV9ryC3bvktlLElWcmxvMogzjQAACAASURBVG48PxaIlZ+Ls+kWMbVlquhomSZfO8TU7FT5lK+t1mt74XvWz+X36N+F71k/65Bl6fpCWfn1tiUr/VSNaxJIANKsmXRIsyZApsUhzUwTyzgsCAjj5DINDX2WaWKbEVY+b4kx7Wqtdra2drh2P3IrVhWPf1JrkreKiRkztFrXaGmmKcZXh64405T7h/vUiC1NX85P5sU5OU2Zpiy7pygPjllTlKmcPUVZK8gqhRd3WhuftWWmiDlT56qvZ7TNEJ1tM9XXPfJ7bZk29fWi6UvUKwlvV3u3+nrWlNlKcukxf9pCkU1nQ28q1jSHjpTNDSHNmqmENGsCZFoc0sw0sYzDgoAwTi7T0NBnmSa2AWGlxsZcRz8VjoDav7ekptyadc4osj2iPDlteqit8SvNg3Kt7U255tZea3tRSu9oblRcHrqghLh/pM9Zk2tfc27wTGhttYU0k8oqObXktUPK62z1tZfctmWnqO/TgyS4s9X6A0NPB4nwlNDa1ugbQZobTTi+94c0a+YO0qwJkGlxSDPTxDIOCwLCOLlMQ0OfZZrYEMJKjQyLlt2FEWQ1orxTZA8dLJXk3vXCWotcmHIt1yRPtk8NofbiLeyR3/O3zogRKb2389el7N4SV25dU+JLAkyjwHSdenWNAtfbEBrNtUdy7VFcW3LndSwUbdk2saAgwlNpFHeKNYpLo7k0qpv0B6Q56T2gcvyQZs2+AWnWBMi0OKSZaWIZhwUBYZxcpqGhzzJNbB1h0VFP1nTrwiiy/Dp79HDJncY3bBLjW7a51iRvFZOtrXXURrs031ajwCS6NApM06CvD19V055pxJd+dvXOZSnI1tTnoA97SjKN1tKorZJeOZK7WE5ZzqQyavTXvsaestyo6cpB2x736yHNcc9g49oPadZkC2nWBMi0OKSZaWIZhwUBYZxcpqGhzzJNrI+w0jdvSkkujCQXRpSzJ46VSjJt2EWjyPI5VhhNFplM1buXyzDJ77U7V5UEkxyTJNPXdJ2fB625JZmlJ011Xtm1TLTKqcqzWueI6VKIaSSYpjzT1Ge6hkaI7enQfu6Pa8InkFRp3nfopPj0578mXv7OV8Wm3hXhgw3xjlG1NTHSXAmwfWB3eS4PvPaS861PPP2cOH7aOgNu1bKF4scvPe/8DNIc4m8Bo1tBmhklMyGhQEASkmhGYaLPMkpmjVDS/f2WJBc27WqVopw5c6pYSsqwLca2KNMO1/SYmJxQo8Akv7TZ1XUSYfq3fF4fsl5JhK/Ln18fvuYL6swps8Sc9rli9tQeuaGV9Zzdbn9d+H7h362Fja3oxn7XNPtqBC5qCAHO0hyVbNaTKLut5WXLPayZMSVCmrc/9azoH7iluJf/BYWk+VsvviLeePUFz5x+5gvfFH39g44ok0B3d3WKH3z7S+p6SHM9vwr8y0Ca+eeYW4QQEG4Z5R8P+izfHKevX1Nrklvt0WQpy5lzZ52AJ1vb5Hrke8Tg+jXiytql4syKOeLYovaCAEv5pdFhkuLCSHHf8HVfsGhdryXAc6UUSwnuqCzDdNxR0AekOSix5l8PaW4+c68a/cqw3+vCiCoR0kygqo00V5NmEu4vPvMp8dTHH1W8yyUb0hxGN+R3D0gzv5xyjwgCwj3D/OJDn+WT08yVy9Yosnxmd38gMvK19fJlJ8DxthYpxrPFoaXTxJ4FGfHO3DHx9owBcWOk3xeEbnlUkSXAUoZJiu0RYinG6nvyZyTJ9P1GHGNkNxLS7CtdkV6UVGl2exIlgKZqP/OHT4oXf/gTJx/Pf/mzjg/RN2lgccfOQ87P3QOTX/n6d8VP/uHtklzaP7frct+/fFCzmgy7f/a/fuXfOQOjVFn5SHSYnQnSLEean/vG90qY2lOzvRJW/j1Ic5jdkc+9IM18cpmUSCAgSck0nzjRZ+OVy7GJUXGtMB36zskDIis37Zp+8JCYc/i0WHziipg1MOIEdEse1btzvhAfyKd6XSDEYeu0o5KHEl0lvAUZLowOWwJsfc+W4XQqHTkwSHPkKajZgNCl+Z13hBgp9u2aDQjrgoceEmJK6VFffkXUlma3gL7w/R8pgbYdiaT4zXf3OTN1a83cdV9vt6Oa4AZtazPWYidemsv7pns6th9pDqtv4z4gAAIgAAIgAAIgEDcCw7lhceX2FXFFrheu9Jo9e14sPHZFrDszJLZdEurZM1SMdEB+ticxJkHeNT8lzqyeLe4sXSjmTpsr5spzftXT/rrsNW680N6EEdi6VYjdu5sf9K5dQmyx1vXbDx0RLS+74fGnRfnIMy1h/Wef/u2S0ejyukm6/UyprrSmmeTYlvryrxu9gRmkuawb20mqlFSMNDf/9z6ONWKkOY5ZS3abMWqX7PzHMXr02eZkjY5QOn3zhDxK6ay4PHRBHatkHalkvdLPyx8r5azpewtyTIJ870V5DvCwS5KntYizch3ylTWLxYBcl0zrk6es3igWTV8qeqQg0y7SHB8YaTY/q6GPNP/BHwjhWmrQNAJ/8RdCzJvXUGn2isUt0u49pexrg0qz1wiy11RyjDSH2LP8/FWDqrN307anH3itaabp3PbPMT07xCQxuhWkmVEyExIKBCQhiWYUJvpsOMmks4RPSSk+L+VXvd46K5/y64GT6jU3katZ0f1DM8Vj1zrkCHJK3HM+J1acviHah0adcuOzu0VOHvuU23Kfc05yfvGSmvfldgGk2fyMhi7NBoUc9khzNVEtH4muNShZjkmnrY1CnviRZpJi987Z5btjY/fsRnU93veFNPPOL8foICAcs8o7JvRZf/kl6XVL8OmbJ8U5KcO2JJM0V3v0yLXBizqXiuUzVqpXWiO89kpOLD/VLxYevyRmHToud7neI1JDxbOL8/PmW3K8ZVtRkhcs9NdgxldBms1PLqS5dPqzPeW5XGLL/YgyS9fYD9pIzD3qbG8MFvZIM7XPa6p4I3paIqS5fHpA18zpjii7z2AmwA9u63WOk7KB45zmRnQ93veENPPOL8foICAcs8o7JvRZK7+5/Li4MHReXLx1TlwoPC/ePi8u3KZ/y1f5vaHxotCW94q5HfPFwumLxYJpi8SC6YvEwmnW1/b3aDOtloMHSs5JbpGbeKVGivOt8wsXCXU+MomyfKUzkyd65vLugHVEB2muA1qTiyRBmsuRkvv88T//fbVjdqV1wl4jv9V2yLY3DrProjpop+1GSLO7Luye3eRfmCDVYXp2EFrJuRbSnJxcc4kUAsIlk8mJI0l99vrwNaFE2BZjKcTq34OWKF+9UzyeqbwHdLbNsAS4oyDFBUG2v7ewc7HIpDIlxVr275XnJO+UorzbesojoFLj4841+SVLLTlWkixHk+/ZIia6Pba3Tk539BUppNkXpkgv4izNkYJlUHkiRpobmSdIcyPpxvfekOb45i6pLU+SgCQ1x9zi5tRnR+QO1CS/jhgXBNktyqN572NrWjKtSoiVBNNIsS3F9ohx5yIxrWV65fRPTjpiTHLcSuclS1EWExNOmdzylUqM7ZHk8c1yJHnWLG5dquHxQJobjli7AkizNkK2N4A0a6YW0qwJkGlxSDPTxDIOi5OAME4TQnMRiGOfpfXDx28cUc8TA8fUK+1MTZtuVZJiCrmjZZpY3LlELJPrihfLdcULpy0Ry2fKNcZyt2n6Pv3c9yOXc8S4Za8U5N3yuW9PSfHcqjWFNcmFKdckyZ2dvqvAhd4EIM3m9wxIs/k5iqqFkGZN8pBmTYBMi0OamSaWcVhxFBDG6UBoPgiY2mdp4y0S4eM3jqrXEwNHxeG+g+rr/uG+ipHZQkwSvLRzhZLjxVKK6ftd7d0+iHhfkhodkdOri9OslSgf2F8qyWt7XdOtrXXJk1M76q4TBSHNce0DkOa4Zq7x7YY0azKGNGsCZFoc0sw0sYzDMlVAGCNHaJoEouyzk2JSnB08Jc7cPCVfT6vXM/LfZ+nft06LmyMDd0WXTWfFks7lYumMZYXX5VKKl8l/L5f/Xiamt4Yzkpu6M2RNt5YjyK1qTfIukT18qKQ94+s3WGuRCxt30dTryTaeZyNrdrNQi2OkOVScDbkZpLkhWFncFNKsmUZIsyZApsUhzUwTyzisKAWEMVaE1kACzeizNDJMEkwyrKRYibL8t3w9J8819nrMbp8jlkgRXioFmV6XyNFiS4yXq/XGYT9StwYtOaa1yIUR5eyxI6WSvOmekt2tSZYnW1rCbgruV4MApNn8LgJpNj9HUbUQ0qxJHtKsCZBpcUgz08QyDqsZAsIYH0KLgEBYfZamU9syfE4KsjV6XBxFvjU2eFd0tPmWkmI5QkxPW5Ct12XB1hgHZJceGJBy7NrZWo4oZ0+dKN4lnXbORh5znZMs5PfxiJYApDla/n5qhzT7oZTMayDNmnmHNGsCZFoc0sw0sYzDCktAGCNCaIYRCNpn6dgmZ8RYTaM+4wgy7Vzt9eiZOrcwWizlWI0e26/LxfxpC5tCJN3XZ40iy2nW9s7WmTOnnbppxLi4q7W1HnlcjizjYR4BSLN5OSlvEaTZ/BxF1UJIsyZ5SLMmQKbFIc1ME8s4rKACwhgFQosJgUp9dmDkhjgpd6Y+efO4fD0uTtFrv/y3/PpObuiu6NoyU4ojxoVp1PZ0alp/3J6d2lQi6atXXNOtreOfMueLUk9rj9XxTyTH9jnJco0yHuYTgDSbnyNIs/k5iqqFkGZN8pBmTYBMi0OamSaWcViQZsbJZRoa9dmzN8+IHed3qqObDl7fp16P9B8UNOW6/EHHMi2bsUKsmrVWPteIlfJJX9P3Ah3ZFDLPzKWLJeckK0mW37MftIu1EmQpymOFjbtycrdrPOJHANJsfs4gzebnKKoWQpo1yUOaNQEyLQ5pZppYxmFBmhknN+ahTU5OWqPFcqT45I3iCPLpm8fEhVsX7opu5pRZYsXM1eq5cuYq6+tZ9O9VYkqmPXIaNGpsTbe2Nu+iKdfpa1eddtF5yOPyXGQ1irzFeqVzk/GIPwFIs/k5hDSbn6OoWghp1iQPadYEyLQ4pJlpYhmHBWlmnNwYhUZri2lq9Sl5prGaYq1E2ZpiXf5oy7TJkeLVcqS4IMa2IEtJ1jnXOGxctP7YXotsr02mdcr2Y2LWLEuSnenWUpKXrwy7GbifAQQgzQYkoUYTIM3m5yiqFkKaNclDmjUBMi0OaWaaWMZhQZoZJ9fA0PpGrlujxvJpC/IJkuWBE2I0P3JXi2lX6hWzbDm2Ro03z+sVizuXiFvDd0/FjjLk7MnjztFPjiTLHa8dSe6eXViTvM2Zbp1fsjTKJqPuJhGANDcJtEY1kGYNeMyLQpo1Ewxp1gTItDikmWliGYcFaWac3AhDuz12qzhqXBBkkmMaRR4cvXlXy+a095RMp7amWVuynE1nS643pc/Smcj2VGs6J5nOTKazkx1J7pkrxtSaZHvjrq0iv3BRhFlB1VERgDRHRd5/vZBm/6ySdiWkWTPjkGZNgEyLQ5qZJpZxWKYICGPErEOjjbfs6dTW+mNr1PiEFOWrdy7fFfu01umWDM8orjdWgiynWk9v6/TFKqo+mz18SE63LpyTLCWZRpNTw3ecNucXLHTOSR4vnJOcnzffV0y4iDcBSLP5+YU0m5+jqFoIadYkD2nWBMi0OKSZaWIZhxWVgDBGyjY0mj59uO+g2Hn5XXFi4Kg4cH2v/PcBz5FjgkBnHW+Ys1ntVL2+e5NY271BrOteL+ioJ51Hs/psy4H9UoxtSZYbeElRTo2NFiV58RJHksfu2aamXk/M6dEJDWWZEoA0m59YSLP5OYqqhZBmTfKQZk2ATItDmpkmlnFYzRIQxghZhuYW5IN9e8WeKzurHum0Vsrwhtmb5a7Va8RGKcpruzY0bFOuRvVZa6q1fO4lQZa7W8t/i1xx3XR+6XI53dp1TrLcxGuiu5tl/hFUuAQgzeHybMTdIM2NoMrjnpBmzTxCmjUBMi0OaWaaWMZhNUpAGCNjF9rQ+G1x4JoU46s7xcG+ffLrPRUFedmMlWr0ePOcrWoEmUR5cWdzN7MKpc/m82o9Molxy+7CaDJJsjzmyn7kVqxyzklWx0DJ0eSJGTPY5R8BNZ4ApLnxjHVrgDTrEuRbHtKsmVtIsyZApsUhzUwTyzisUASEMR9uoZ0fPCuO9h8WxwYOqdej/YfEMfl6a6y4gRXFTOcar+laJ9bIEWT12tWrXpd2rogcST19NjU2Vty0q3BOcsv+vSWx5FavdTbtGiuckzw5bXrk8aIB8ScAaTY/h5Bm83MUVQshzZrkIc2aAJkWhzQzTSzjsOoREMY4WIV2dvC0OHbDEmO3INPIsvvR0TJNrHaJ8ZpZvWL1rHViyYxlRvLw02dTI8PWVGs5zVpNu6Yp1wcPlEpy73p59FNxZ2takzzZPtXImNGoeBOANJufP0iz+TmKqoWQZk3ykGZNgEyLQ5qZJpZxWH4EhHH4bEI7ffNEiRgrUZbCPJIbLomRdqgmKVYjx1KMVxdGkBdOXxwbFl59NjV021qHrNYkW7KcPXq4JKbxDZsK061tUZaS3NoWm7jR0PgSgDSbnztIs/k5iqqFkGZN8pBmTYBMi0OamSaWcViQ5vgl98SNo0qIj7lGkOnf4/mxkmBmTpl1lxyTLM/rWBC/oF0tpj6bujkgRne8bwnybms0OXviWKkkq3XIxXOS6cxkkcnEOnY0Pp4EIM3m5w3SbH6OomohpFmTPKRZEyDT4pBmpollHBak2ezkqunVfTS92ho5ttcg5yfzJQ3vau9WI8hqmrUaSbbWI9OxTxwe6f5+a4q1lOOp+3eLtBTl9MmTxdCkDNNmXSTGblHmEDtiiD8BSLP5OYQ0m5+jqFoIadYkD2nWBMi0OKSZaWIZhwVpNie5tNZ4r9zB+gN5DvKuK++p85Cv3rlyVwPpnGM673jbvAfk+ceb1W7WYZx/bA4JIdLXr6k1ya32OclSljNnzxSb2NpqCTKNJtNzizwnWU6/xgMETCQAaTYxK6VtgjSbn6OoWghp1iQPadYEyLQ4pJlpYhmHBWmOLrnHbxxRYryzIMhH+g+K3ETxXGBqWbkg3zN3mzwDeb3IprPRNbwBNWeuXLY27bI37pKvmYsXnJpogy7aqIsEOXP/fSIvd7e+uXxtA1qCW4JA+AQgzeEzDfuOkOawifK5H6RZM5eQZk2ATItDmpkmlnFYkObmJHdw9GZhBPlddR7yu5feFvS98oc9gry15wE1krxq1hp2gkwxkxA7glw4J5nE2X7QUU9qunXh6Cf6Ordmnfox+mxz+ixqCY8ApDk8lo26E6S5UWTjf19Is2YOIc2aAJkWhzQzTSzjsCAg4SeXzjw+dH2/ONS3Xxy8vk+90r/v5IZKKls1a63onb1R9HZtkK+bRG/3RrG4c2n4DTLgjjS12jr6qTDlWk69pinY9mNixgwpyfZ6ZGsDr9yKVZ4tR581IKFoQiACkOZAuCK5GNIcCfZYVApp1kwTpFkTINPikGamiWUcFgREP7k0zZqk+KCU48MkyPJ5btC1/lZW0T1ltiXGJMndBUmWstySadVvgIF3yJ4+edc5ybSZlyPJXV1SjOU65MKaZBpRzi9d7isS9FlfmHCRQQQgzQYlo0JTIM3m5yiqFkKaNclDmjUBMi0OaWaaWMZhQUCCJffGSL+U4n1yBNmS40NyJJlk2X3cUzqVVqPG1uixFOTC11x2svYiRsc9WWuS7XOSd4r04GBRkuf0qDXJY/ZospTl/OIlweAXrkafrQsbCkVIANIcIXyfVUOafYJK4GWQZs2kQ5o1ATItDmlmmljGYUFAqif3cN8BKcVyirWSZEuWrwxdKim0YNoiJcbrpSSvm02SvElu1tXLuNcIkT162FmT3Fo4Jzk1dNuJOT9vfnFX68Jocn7BwlCYoM+GghE3aSIBSHMTYddZFaS5TnAJKAZp1kwypFkTINPikGamiWUcFgSkmNyrQ5eVFB/ut9YgK1mWo8iTk5PORVNbOuTxThvkUU8b5SuNJktZlpLc2TaDcS8RouXgAeecZHtEOTUyXJTkhYssSbbPSaaR5LnzGsIEfbYhWHHTBhKANDcQbki3hjSHBJLhbSDNmkmFNGsCZFoc0sw0sYzDSqqA0NFO7unVaiRZTrXuG7leku3lM1bJEWRahywlmQRZPpd2rmDcI6zQWvbvLT0CSm7glRobK0rykqVKkMfUKLLcwEuuSZ7ont0ULknts02Bi0oaQgDS3BCsod4U0hwqTlY3gzRrphPSrAmQaXFIM9PEMg4rKQJCkrxXHvX09oXXxS55LjId+dQ/3FeSWTr7mM5AfmDBI2Lr3PvFPT3b5JFPCTgLWI6kq52tC+cktxa+FhMTDp/cshVKjJ3RZCnKE7NmRfKbkZQ+GwlcVNoQApDmhmAN9aaQ5lBxsroZpFkznZBmTYBMi0OamSaWcVicBeRw30HxxrlfiHcuviFffymGxotrbiml86ctVGJ8//yHxba5D4h75m4TbZkpjLNdCC2XE7YYt+yVm3fRmuR9e0rizq1aUxDkwpRrkuTOTiPYcO6zRgBGI0InAGkOHWnoN4Q0h46UzQ0hzZqphDRrAmRaHNLMNLGMw+IkIHTM06/lSPJrZ3+mXq/euVKSORo1fnjhdrF90UfEtnkPKGlOwiM1NmqJceGc5JY9O0XLgf2lkry2V0nymFqTTFOut4jJjmlG4uHUZ40EjEaFTgDSHDrS0G8IaQ4dKZsbQpo1Uwlp1gTItDikmWliGYcVZwE5duOw2HPlA7H7qnzK1z3ydWKyOKWYNujaMu9eOZp8n9jSc6/YOOcexpkshpa6M1SYbr1btNKUazmanD18qCT28fUbSs5JpqnXk23xGGWPc59NRAdEkHcRgDSb3ykgzebnKKoWQpo1yUOaNQEyLQ5pZppYxmHFSUDO3zp7lyS7p1zTpl1b5pIk36skmb5uybQyzp4VWurWYGG6dWFdshxRzh47UirJGzfLNcnbXGuS5UhyS0ss2cSpz8YSMBodOgFIc+hIQ78hpDl0pGxuCGnWTCWkWRMg0+KQZqaJZRyWyQJCO1mrkeQr7zsjydeHrznZmNexoEyS72N/9BMFnx4YsI5/UqPIJMpSkk8eL/bSVMo6+qlwBJSaci2/Fuk0i55scp9lARhBhE4A0hw60tBvCGkOHSmbG0KaNVMJadYEyLQ4pJlpYhmHZZKA3BkfUlOs3dOtaZ2y/ZjRNlNK8n3WSLIcRabR5Lkd8xlnxwot3ddXEGRLkmnKdebMaSduGjFWguw+J3kT36noJvVZ9p0PAYZCANIcCsaG3gTS3FC8sb556NL8la9/V/zkH972hPLkxx4Rf/4nn4s1sPLGQ5pZpTO0YCDNoaHEjZpEIEoBmZRHHZVL8tH+4trb1nRbYU1yUZKXzVjZJDLRVZO+dtVai2w/pShnzp8rSrJce6w267JHk+mc5A0bo2twk2uOss82OVRUx4QApNn8REKazc9RVC0MTZo/84Vvih07rQ85B157yTOeDY8/rb7/4LZe8YNvfymqmEOtF9IcKk42N4M0s0llYgJptoDQMVB7rhanW++RZye7H5vmbHGNJN8nemfzl8HMpYsl5yTTaDJ9z35MTu2wRpHlZl1jhdHknNztOqmPZvfZpHJG3OERgDSHx7JRd4I0N4ps/O8bijSTDHfNnC7eePUFX0S2P/Ws6B+4VVGufd3EkIsgzYYkwrBmQJoNSwiaU5NAowXkzOCpwrpka3dr2uV6JD/stIuOgaJp1vcUplvT1OtMOlOz3XG+gEaNrbXI1mgynZmcvlo8Hmtyeqd19JMSZGtEmc5NxsMi0Og+C84gEDYBSHPYRMO/H6Q5fKZc7hiKNNMoc9CR43rKmAgd0mxiVqJvE6Q5+hygBcEIhC0gdDayLcf2iPKNkX6nUQunL75Lkqe1Tg/W6JhdTeuPraOfpCgXNvCidcr2Y2LmzOLxT4VzknPL+U9DrzeNYffZetuBciDglwCk2S+p6K6DNEfH3vSaQ5Fm04NsZPsgzY2kG997Q5rjm7uktlxXQG6NDTrHQNmyfPH2eQdnV3t3QZKts5JpRHlOew9r3NlTJ0TLbntna+ucZNrx2pHk7tmFEeRt1nRr+cwvXcaaSZjB6fbZMNuCe4GAHwKQZj+Uor0G0hwtf5NrD12aaar281/+rHjq44+WxP3C938k/vJvful7CnfY0PYdOik+/fmviZe/81WxqXdFye0/8fRz4vjpC+p7q5YtFD9+6XnfP4c0h50pHveDNPPIY5KiCCoguYncXZJ8YuCog6w9O7V0JFlK8pJO3kJIZyLbRz/Z063p7GRHknvmWnJsn5NMkrxocZK6WaixBu2zoVaOm4FAHQQgzXVAa3IRSHOTgceouqZJ86s/fVM8943vRbKO2V5DTXkpl2aaJt7XP+iIMgl0d1enM9281s8hzTHq7U1sKqS5ibBRVSgE/AjIwev7CuckWxt47b++p6TukjXJ8kiotV28N6nKHj6kRo+tHa5pyvVukboz5DDJz19Qck4yrUnOz+N/NFYoHdLHTfz0WR+3wSUg0DQCkOamoa67Ikhz3ejYF2yaNNNRVG++u8+4kWYS6i8+8ylnZJzk/lsvvuK0s9bPIc3sf0fqChDSXBc2FIqQgJeAnBo4rs5Ktqdb09fj+TGnlSTF90g5dstyhCE0vOqWA/ulHO8srEmWkiynXqfGRouSvHiJc07y2D3b1NTriTm8p6A3HHqVCiDNUdJH3fUQgDTXQ625ZSDNzeUdp9pCkWZ7FLlW4F7TtmuVCevnXtOza32P6i6f0l1eBtIcVoZ43QfSzCufSYiGBOTirYvirbM7XJL8vhgcvemEv2TGMusYKNcu1zQNm+ujZd+ewprk4u7WIpcrSvLS5XJ3a2stsnVW8lYx0d3NFYdxcUGajUsJGlSDAKTZ/C4CaTY/R1G1MBRpdje+0prmqAK0jgvdHgAAIABJREFU660lyPY6Z/d1fqR5dHwi6tBQv4EEMumUSKWEyOUnDWwdmgQCFoEbwzfEB5feF+9fek/sLLySONuPnmlzxX3z7xP3zrtf3LdAPuXX3VNn88Q3MSFSOz8Q6V1y9HjXTpHeuVO9isni7/DkqtVicqsU4233ytdtYkJ+LWbN4skjBlFl5fssPXITeJ+NQbrQREkgm0mpt5Q8+qyx/aGtJW1s29CwaAmELs3RhlO59kZJc99gcWqeqbGjXc0nMKU1I8+YTYmhkeKoVPNbgRpBoJTAWG5U7JRrkWk98s7L74tdV94XpwZOOBdNa5sutspR5K1yyvXW+dbrInk0FMvH2JjIynXIWbkeObt7p8jsll/LkWX3I79mrcjJTbtycjQ5v0WekSyfk9N4H4sVp1y3t1nneA+P5uPUbLQ1wQRoFhoJ88gY+qyp3aC7s83UpqFdERNItDQTe681y+4Ny2r9HNOzI+7BhlaP6dmGJiaBzaLNukiS7bOSaTMv+5FJZ5zp1g8tfkBsm3efmN/O81zg1MiwtVmX+5zkgwdKekRuXa+cbi3XItvTraUsT7bznX4e918HTM+OewaT135MzzY/55iebX6OomphKNJMO0z/4NtfChRDPWUCVVB2caUjp2rtjl3r55BmnazwLQtp5ptb0yMbGr8tfn3hDfHfTv2NePfir8XxG0dKmtwzda7YvvgJ8eiix8XDCx8TizuXqp9zE5DU0G21YVerfU6y/Dp75FAJi/ENm8p2t5aS3IpRBtP7uN0+bn02LtzRzvoJQJrrZ9eskpDmZpGOXz2hSDOtY+6aOd33ztj2EVAHXnupKcTcR05RheVtxTnNTUlDoiqBNCcq3ZEHe/rmCfHLM/8oRfm/SlF+W4zmR5w2dbRMk5L8EfHQgu3iI0t/U6yatdazvXEXkPTgYHFn68KIcvbEsVJJViPI9LRGk+nMZJHNRp4/NKA+AnHvs/VFjVJxJgBpNj97kGbzcxRVC0ORZmo8jcju2Gn9Fb+SDJNc0+PBbb2BR6ajAlSrXow01yKUzJ9DmpOZ92ZFTVJMcvza2Z+Jn578G0HS7H7c07NN/May3xaPL/lNsVl+nU3XFsO4CUj6xg2XJFvnJGdPnyxiyGQsMaZdrdXO1tYO13jwIRC3PsuHPCKplwCkuV5yzSsHaW4e67jVFJo024G/8P0fiRd/+BNPDs/84ZPi2T/6vbgxqtpeSDOrdIYWDKQ5NJS4UYHA/mt7xAeXd8idrt9Rr2cGTzlsls1YKXe2fkjcN+9B+XxI9M7eGJib6QKSvn7NWpO8d5doLaxLzpw948Q52drqOvqpcATUxs2BOaBAfAiY3mfjQxItbRYBSHOzSNdfD6S5fnbcS4YuzdyBlccHaU5axv3FC2n2xwlXVSZA5yO/T5J8+R1HlEdyw6oAjRzfO1cKshTle0mUFzwkuqfoHQVlmoBkrlxWa5Jb5M7W6lU+MxfOFyV5SrsYl7tZqxFkNaIsd7nuXY8ulSACpvXZBKFHqHUSgDTXCa6JxSDNTYQds6ogzZoJgzRrAmRaHNLMNLENDutY/2FrNFk+6fVof3HjqgXTF1mCLEeSaUR5izwOKsxH1AKSuXihuLM1jSTLJ4mz/aCjniw5Lowiy69za9aFiQD3ihmBqPtszHChuQYQgDQbkIQaTYA0m5+jqFoIadYkD2nWBMi0OKSZaWJDDovWJtvTrd+jaddXdoibIwNOLSTG9pRrEmYS50Y9mi0gmXNnHUlu3SNHk+XUa5qCbT8mZsyQklwYSS6MKOdWrm5U+LhvDAk0u8/GEBGabBgBSLNhCfFoDqTZ/BxF1cJQpNne4MsOolm7YkcFzV0vpNmELJjXBkizeTkxpUVnB087okzCTOco2w+aYn3vfNe0azmq7GcTrzBia7SA0CZd1ppk+6zkXSLd31+U5K4uS5ILm3aNSVHOL10eRmi4B1MCje6zTLEhrAgJQJojhO+zakizT1AJvCwUaU4gNydkSHOSs185dkgz+oWbgBpNlqPI9ErPq3euOD+mTbtoffL9hfXJy2euigRe2AJCxz1Za5LlVGu1JllK8s2bRUmePUetSR6zR5OlLOcXL4kkdlQaTwJh99l4UkCr40QA0mx+tiDN5ucoqhZCmjXJQ5o1ATItDmlmmlifYeUmcmLn5XfVucleR0Jtm/eA+Ig8Duqj8lgoOh7KhIeugGSPHnZNt7ZGk1NDt53Q8nPnWaPIriOg8gsWmhA62hBTArp9NqZho9kxJgBpNj95kGbzcxRVC0OTZvuoKa9jpar9LKrAw6oX0hwWSV73gTTzyqefaGh98i/P/KP4+Zm/V6LcP9znFOtsmyEl+WPy3OTfkOcn/47oau/2c8umXhNUQLKHDsqjnwo7W6uNu3aL1Ii1uzc98gsXOTtbj2/Zpr4mccYDBMIiELTPhlUv7gMC9RKANNdLrnnlIM3NYx23mkKT5k88/Zzo7uoUP/j2lzwZfOYL3xR9/YPixy89HzdGVdsLaWaVztCCgTSHhtLoGx3uOyjeu/S2ePfi22LHpbfEhVvnVHuz6Rbx4IIPqecD8x8WDyx4RLRlphgdSy0Badm/t3R3aznlOjU2VpTkJUsLu1vT5l00orxFTMgp2HiAQKMI1OqzjaoX9wWBeglAmusl17xykObmsY5bTaFJM20G9vyXPyue+vijngxe/emb4rlvfE9w2yQM0hy3Lt+c9kKam8M5ilpoTfK7LlGm85TpMXPKLPHgfCnJUpBJlrfOvT+K5tVdZ7mA0PRq+5zk1sI5ySKfd+6fW7ai5JzkcXlO8sSsWXXXj4IgEJQApDkoMVwfNQFIc9QZqF0/pLk2o6ReAWnWzDykWRMg0+KQZj6JvZMbEjsuyNFkKcrvyRHldy+/LfITljwu7lwqR5IfsZ5Sltd09cYz8FxOzDyyT6R37RQTH3zg7HLtDoaOe7LWI9vnJG8VE52d8YwXrWZBANLMIo2JCgLSbH66Ic3m5yiqFoYmzdufelZ88ZlPVR1p/taLr4g3Xn0hqlgbUi+kuSFYY39TSHO8U3j1zmUpym85I8ruY6HWda+XklwcUV4wrXFnJzeKYmps1BJjezSZXg/sK6kut7bXWZNMxz/RmuTJjmmNahLuCwKBCUCaAyNDgYgJQJojToCP6iHNPiAl9JLQpPkrX/+uOHj0TMU1y7XWPMeVP6Q5rplrbLshzY3l24i7nxg46owo0xrlM4MnnWrunfdgYX2yNfWaNvaK0yM1fMcS5MI5ybSBV/bwoZIQJjZsFHkpx3c2ypFkKcg0ojw5pT1OYaKtCSMAaU5YwhmEC2k2P4mQZvNzFFULQ5NmCoBGm+lRPppM3+8fuMVuPTPFCmmOquuaXS+k2ez82K3bffUD8a5rRLlv5Lr6UXt2qrU2uTDtmkaWM+lMPIKSrUzdGhRqHbJrNDl77EhJ+8c3bpZrkq1drenZ9pBcg93SIm4N52ITJxqabAKQ5mTnP47RQ5rNzxqk2fwcRdXCUKWZgqAR55/8w9sl8Ty4rbfirtpRBR5WvZDmsEjyug+k2cx8juVHi5t40fpk+RybGFWNndPeo0T5AbXj9SNic89WM4PwaFV6YEBu2lXYuKswopw9ebx4ZSpVGD22zkkeo7XJUpRFOu1cAwGJTbrR0AIB9Fl0hbgRgDSbnzFIs/k5iqqFoUtzVIFEVS+kOSryZtcLaTYnP33D1y1RpqccVabRZfuxbMbKkhHlFTNXm9PwKi1J9/VZklxYk9wqR5QzZ04VS2Szjhir459oTfKme6rGBgGJRerRSBcB9Fl0h7gRgDSbnzFIs/k5iqqFkGZN8pBmTYBMi0Oao03smZsnHVGmna9pvbL92Dj7HudYKBpR7umYF21jfdSevnZVtKoR5OJocua8dSY0PSbbpli7Wqu1yIVzkuUa5SAPCEgQWrjWBALosyZkAW0IQgDSHIRWNNdCmqPhHodaIc2aWYI0awJkWhzS3PzE7r+2xyXKbwnaAZseKfkfbd5lHQtFu14/LDpazN4FOnP5UmHjrqIoZy5dLEry1A5LkOUI8phak7xV5NbpHXcFAWl+n0WNegTQZ/X4oXTzCUCam888aI2Q5qDEknM9pFkz15BmTYBMi0OaG5/YickJsePSW9bZyTT1+uKvxdD4bVXx9NZO5+xkEub75z/c+AZp1ECjxi20cRc9d+9Um3ilr14pSvL0TkuO7XOS5de51Ws1ary7KAQkVJy4WRMIoM82ATKqCJUApDlUnA25GaS5IVhZ3BTSrJlGSLMmQKbFIc2NSezg6E2x42Lh/GQpyu9fesepaF7HgpJjoXpnB5ue3JgWe981c+a0EmQ15VqtTZaS3Gft3E2PiZkzpSAXd7amEeXc8pUNbSIEpKF4cfMGEECfbQBU3LKhBCDNDcUbys0hzaFgZHkTSLNmWiHNmgCZFoc0h5fYC7fOqRFl2un6PSnKh/sOOjdfNWtt8VgoOaK8pHNZeBWHeKfsqRNyBLmwHlkdBbVT0I7XjiR3dztrke2drfNLmxsLBCTEhONWTSGAPtsUzKgkRAKQ5hBhNuhWkOYGgWVwW0izZhIhzZoAmRaHNOsllsT4XdeIMomz/djSc694YKFcmzxPnqMsRbmrvVuvsgaUzh4/WliTTIK8S023prOTHUnumeuabm0d/5RftLgBLfF/SwiIf1a40gwC6LNm5AGt8E8A0uyfVVRXQpqjIm9+vZBmzRxBmjUBMi0OaQ6e2H3Xdot3Lrwhfk3Pi28ImopNj5ZMq1qfbG3m9bB4UApza7oteAUNLJE9fEhNsyY5tkeUU3eGnBrz8xeUnJOsJFl+z6QHBMSkbKAtfgigz/qhhGtMIgBpNikb3m2BNJufo6haCGnWJA9p1gTItDik2V9iL92+IP7r8b8Wf3fyVTX92n5k01m5edcj4reW/xPx8RW/KxZ3LvV3wyZd1XJgf8k5ybQmOTU6UpRkOWpsHf1kbd5FU64n5vQ0qXX1VQMBqY8bSkVHAH02OvaouT4CkOb6uDWzFKS5mbTjVRekWTNfkGZNgEyLQ5orJ3bXlfes0eQLr8vnm2I4d0dd3DN1rnho4Xbx0IJH1evaLr0jlMLsWi379hSPgCps4CVyuaIky/XH9lpk+5zkCblOOU4PCEicsoW2EgH0WfSDuBGANJufMUiz+TmKqoWQZk3ykGZNgEyLQ5pLE0u7XNOU63fk89fn3xSjeWtUdv60heLhBVKUF8nn/A+JlbPWRN8jJiaKO1vT7tZqh+vdQkxOOm3LrVglR5DpfOTCMVDynGTa8TrODwhInLOXzLajzyYz73GOGtJsfvYgzebnKKoWQpo1yUOaNQEyLQ5pFmrH63fO0/rkN9XIcm5iXGV7yYxlcsfrR8XDC60R5aWdyyPtBanxcUeM7XOSW/bvLWkTnYnsCLKUZTozeVKenczpAQHhlM1kxII+m4w8c4oS0mx+NiHN5ucoqhZCmjXJQ5o1ATItnkRpnpQjsWokWU29flN9PTE5oTK8fMYq8fCiRwuyvF0snB7dTtG09tg5/sk+J/nggVJJXtcrp1sXzkmmEWW5JnmyfSrT3mqFBQFhnV6WwaHPskwr66AgzeanF9Jsfo6iaiGkWZM8pFkTINPiSZHm/GTe2vFajibbO1/bKV0j1yTTjtcPy9FkevZMnRdJtlNDt9X0atqsq7Uw1Tp75FBJW8Y3bJRibEuy3MBLivJkq1k7dDcaHgSk0YRx/7AJoM+GTRT3azQBSHOjCevfH9Ksz5DrHSDNmpmFNGsCZFqcuzQfuL5X/O2JV8WPj/6VOH3zhJNFOjOZdrt+ctX/IEX5MUG7YDf7kR4cLO5sLUWZhJnOTXY/rKnWtCaZBFnubi3/LbLNb2uz2VSrDwJiUjbQFj8E0Gf9UMI1JhGANJuUDe+2QJrNz1FULYQ0a5KHNGsCZFqcozSTHJMkkyyTNNsP2szrn6z679TxUHRMVLNFOX3jhhxF3mmNJhfOSc6ePlnsWZmMWo9MYjy+pTCaTJKcSjHtffWFBQGpjxtKRUcAfTY69qi5PgKQ5vq4NbMUpLmZtONVF6RZM1+QZk2ATItzkWY6R/nHx/5K/OjIyyWi7B5R3r74iaZmMd13vbAmeZcz3Tpz9ozThsnWVteu1oXdrTdubmob41gZBCSOWUt2m9Fnk53/OEYPaTY/a5Bm83MUVQshzZrkIc2aAJkWj7M00yjyW+deE29d+JV4+/zr4k5uSGWJjoN6RE65/tDCD4tHFn1YdLfPbkr2MlcuF9YkF49/ylw4X5TkKe3WVGs5zVpNu6Yp1+s3NKVtnCqBgHDKZjJiQZ9NRp45RQlpNj+bkGbzcxRVCyHNmuQhzZoAmRaPmzQf6T8kBVlKshRlkuWbIwMqM0s6lylB/hA9pSzP7Zjf8IxlLl64W5IvXypKcsc0ax2y65zk3Jp1DW8X9wogINwzzC8+9Fl+OeUeEaTZ/AxDms3PUVQthDRrkoc0awJkWjwO0nzq5nHxlhxJfuv8a0qYrw9fU9mgNcrWaPJjcmT5w2Jx59KGZilz7qxzTnLrXjmavHuXSF+32kKPiRkzrNFjtSbZes2tXN3QNiXx5hCQJGY93jGjz8Y7f0lsPaTZ/KxDms3PUVQthDRrkoc0awJkWtxUaT43eEaNJtO0axpRpjXL9JjdPkeOJj9eGFV+TJ2r3KhH5swp0SrF2DoGil6lJPf3FyW5q6soyTTlWo4o55ataFRzcN8CAQgIukLcCKDPxi1jaC+k2fw+AGk2P0dRtRDSrEke0qwJkGlxk6T5ytAlJchv0fRr+Tw7eFpRn9E2U027ptFkeq7t7m1INrInjjnnJDuSfPNmUZJnz1FiPGafkyxHkvNLGju63ZBAY35TCEjME5jA5qPPJjDpMQ8Z0mx+AiHN5ucoqhZCmjXJQ5o1ATItHrU09w1fV4KsNvO68Lo4ccM6p7ijZZq1mRfJsnxumB3+rtLZo4edUeTWwjnJqdu3nEzn586zNu2yN+6Sr/kFC5n2hPiEBQGJT67QUosA+ix6QtwIQJrNzxik2fwcRdVCSLMmeUizJkCmxaOQ5ltjg9ZoshpVfk0c7juo6LZkWuUaZbk+WW3o9bjY0nNvqNSzhw7Ko59Kz0lOjQwXJVkKsSPIhXOSSZzxMIsABMSsfKA1tQmgz9ZmhCvMIgBpNisfXq2BNJufo6haCGnWJA9p1gTItHizpHk4d0eNJL91zpLlfdd2K6KpVEpNubZl+f75D4dGuuXAPrlZl0uS5brk1NhYUZLl1Grr6KfClGs59XpCTsHGw2wCEBCz84PW3U0AfRa9Im4EIM3mZwzSbH6OomohpFmTPKRZEyDT4o2U5txEztnM6005orzrynsOxQcWPKJGk0mWH5bPMB7WOmRr067Wwtcin3duTZt0lZ+TPCE388IjXgQgIPHKF1qL6dnoA/EjAGk2P2eQZvNzFFULIc2a5CHNmgCZFm+ENP+aRpTl8205qrzj0lsOua1z7y9s6CXXKsvR5WympX6qUoZtMW6hKdeFNcnuG9JxT9aaZGs0eVxu4DXR2Vl/nShpBAFIsxFpQCMCEECfDQALlxpBANJsRBqqNgLSbH6OomohpFmTPKRZEyDT4mFJ8/uX3rHWKKsp2K+JSfkfPTbN2WJNv15MO18/JtqzU+simRobdcRYjSjTU06/LpHkNeucNcljhXOSJzum1VUfCplLAAJibm7QMm8C6LPoGXEjAGk2P2OQZvNzFFULEy/Nr/70TfHcN753F/8Dr73kfO8TTz8njp+2zrNdtWyh+PFLzzs/gzRH1XXNrldHmndf+cCafq029HpdjOVHVbDrutdbokzTr+WmXtNbg4/upobvWJJcmGbdKs9Ipo283I/x9RvuOid5ckq72cDROm0CEBBthLhBkwmgzzYZOKrTJgBp1kbY8BtAmhuOOLYVQJqlNH/rxVfEG6++4JnEz3zhm6Kvf9ARZRLo7q5O8YNvf0ldD2mObd9vaMODSvPBvn3OZl60sdftMeuIppWz1lhHRNFZylKUu9tnB2o3HfWkplsXplmTLGePHSmV5I2bS4+AklOuJ1tbA9WDi+NPAAIS/xwmLQL02aRlPP7xQprNzyGk2fwcRdVCSHMNad7+1LPii898Sjz18UdVjmhk2i3ZkOaouq7Z9fqR5mM3DltHRBXOUx4YuaGCWtK5TE67ftyR5bkd830Hm755UwpyYWfrgixnTx4vlpe7alvrkK1zkscKX4t02ncduJAnAQgIz7xyjgp9lnN2ecYGaTY/r5Bm83MUVQshzR7Ts+2p2fsOnRSf/vzXxMvf+arY1LtC5aj8e5DmqLqu2fVWkubTN084m3nR9Ourd66oQOZPW1gYTZbnKctR5cWdS30FmO7rkztbu3e33i0yZ04Vy2azjhiPb5aiTGuSN93j6964KFkEICDJyjeHaNFnOWQxWTFAms3PN6TZ/BxF1cLES3M5ePd0bD/SfOvOeFS5Q70GE2jJpuXgbUqMjuXF+cFz4ldnfyleP/uaeEM+z986r1re0zFXPLbkw2K7HFV+bMnjcir2qpoRpa5eEZndu0R6107rlZ5nzxbLtbWJ/NZtIi/leEI+6euJjZtq3hcXgEBrizXbYGx8AjBAIBYE0GdjkSY00kWgrTUjJiYmxXgO77OmdozpUzVOIDE1KLQrFAKQ5jKMtijTaDOkOZQ+lsib9I1ckZL8K/GLU78Qr8tdr0/dOKk4zGybJR5b+mHxmBTl7VKUe2evr8ondemSyEhBTu+2JJm+Tl286JSZ7Oiw5Jgk2Zbl3ur3TGRCEHRNAhCQmohwgWEE0GcNSwiaU5MApLkmosgvgDRHngJjGwBpLkuNvZu2PUXba00z7bZt/xzTs43t201v2I2RfrU++c3zr4l3Lr4ujvZbG251tEyz1ifLjbxoM68NszdXbFvmwnlnZ+sWKcqte3eLtBxdth+T0zsL060L65LlmuTc6rVNjxUV8iOAqa78cso9IvRZ7hnmFx+mZ5ufU0zPNj9HUbUw8dJMUuzeObt8d2zsnh1V14xHvbfGBuXRUK87m3kdur5fNbw106qmXD84X65RlqK8pedez4AyZ07LNcm7lRyrDbzkLtfpvuvOtRMzZ1rHP9HGXWrTLinJK2pP444HPbTSJAIQEJOygbb4IYA+64cSrjGJAKTZpGx4twXSbH6Oomph4qXZfQYzJeHBbb3OcVJ2UnBOc1Td08x6R/Mj6vzkt+SIMo0s7722SzU0Jf8jQf6QHFV+YsUT4tElHxI3h0rXvGdPnSg5J5k28UrfsHbNpsdEd3dBkC1JHpOynF+6zEwQaBUrAhAQVulMRDDos4lIM6sgIc3mpxPSbH6Oomph4qVZFzymZ+sSjEf5/ERejijL46HkqDIdE/XB5R1Owx9c8CFHlh+WwkwPe/fsoT0HrOnWhXOS6czk1K3BoiTP6VFibB8BRaKcX7Q4HlDQSlYEICCs0pmIYNBnE5FmVkFCms1PJ6TZ/BxF1UJIsyZ5SLMmQMOLv3PxTWvqtXzS1/Zj69z7rTXKaq3y4yKbzqofZY8cUpI89cBekZWv6Z1y4647Q065/PwFJeckK0mW38MDBKImAAGJOgOoPygB9NmgxHB91AQgzVFnoHb9kObajJJ6BaRZM/OQZk2ABhb/4NIOeZayNapMo8s0ykyPTXO2qDOUP7TYkuX27FTRcmB/yTnJNKKcGh0pSrIcNbbWIlujyWPy64meuQZGjSYlnQAEJOk9IH7xo8/GL2dJbzGk2fweAGk2P0dRtRDSrEke0qwJ0JDitC7ZHlGmUWVat0yPdd3r1UiykmU5stx15FRhurWcck2bd8lnary4bpnWH9N069S2bULI58DazWqdMh4gYDoBCIjpGUL7ygmgz6JPxI0ApNn8jEGazc9RVC2ENGuShzRrAoywOO10rUaUpSTTqDLthE2PlTPXyDXKj4lH5c7XTwx0idlHTotWefyTkmQ55VpMTjqtzi1fKcblGcnOaLLc6Zp2vLbXNJdvBBZhuKgaBKoSgICgg8SNAPps3DKG9kKaze8DkGbzcxRVCyHNmuQhzZoAm1z8+I0j1mZeUpbfOveaoLOV6bG0c7nYPn+7ePL2EvHQ5RbRbY8o79tT0kI6E9k++smebk1nJ5c/IM1NTiyq0yYAAdFGiBs0mQD6bJOBozptApBmbYQNvwGkueGIY1sBpFkzdZBmTYBNKH7m5kl1RBStT6ap11fvXFa1LpuyQPyPIxvEEze6xMYLY2LmwaOi5eCBUkle16vOSbZ2uJZrk+Wa5MmpHTVbDWmuiQgXGEYAAmJYQtCcmgTQZ2siwgWGEYA0G5YQj+ZAms3PUVQthDRrkoc0awJsUPGLt89ba5QLm3mdHzwrOsaE+Gj/LPHk0FLx0JUWsfxkv5h6/ERJC8Y3bJRyvM0aTaannHo92doWuJWQ5sDIUCBiAhCQiBOA6gMTQJ8NjAwFIiYAaY44AT6qhzT7gJTQSyDNmomHNGsCDLH4teGrasq1Lcs3rpwQ2y4J8ci1dvGbN7rFxvNjovvc1VJJ3nRPYU1ycXdrkbWOj9J5QJp16KFsFAQgIFFQR506BNBndeihbBQEIM1RUA9WJ6Q5GK8kXQ1p1sw2pFkToGbx3EROvHHul+LvTv612LH/J2L5qX5x70W5cbWS5Sli0dXi8U8inXaOfbKPgKLRZJFKabbi7uKQ5tCR4oYNJgABaTBg3D50AuizoSPFDRtMANLcYMAh3B7SHAJEpreANGsmFtKsCbDO4of7Doq/3/F/i4uv/79i2ak+Jckky8sGijecbG0tTrMunJM8vnFznTUGKwZpDsYLV0dPAAISfQ7QgmAE0GeD8cLV0ROANEefg1otgDTXIpTcn0OaNXMPadYEGKD4jTP7xZ6ffkf0v/13YvGJK0qUF98s3mBiSpvI0XpkEmSo0kNJAAAauklEQVS1Jlm+rt8QoIbwLoU0h8cSd2oOAQhIczijlvAIoM+GxxJ3ag4BSHNzOOvUAmnWoce7LKRZM7+QZk2AVYpnLl4Qt3b8TFx/+29FVp6TvOjEZTFvcMIpMTqlRQysXy3a739c5Lfcq0Q5t7a3cQ0KcGdIcwBYuNQIAhAQI9KARgQggD4bABYuNYIApNmINFRtBKTZ/BxF1UJIsyZ5SLMmQFfxzLmzomXvbpHa9a648+4vxfSDh0XnwLBzxeCUlDi7skeMSTnufuR3RPsDj4vcytXhNSDEO0GaQ4SJWzWFAASkKZhRSYgE0GdDhIlbNYUApLkpmLUqgTRr4WNdGNKsmV5Ic/0AM2dOidbdu5Qo27LcOjDo3LC/XYidC1Li+tplInPvI2LRY78vlm79WP0VNrEkpLmJsFFVKAQgIKFgxE2aSAB9tomwUVUoBCDNoWBs6E0gzQ3FG+ubQ5o10wdp9g8we/K4aNkjJXmPlGR63btLpG8WFyVf7ZCSPN96nlzRJZZ8+FPi8e2fE6tmrfVfiSFXQpoNSQSa4ZsABMQ3KlxoCAH0WUMSgWb4JgBp9o0qsgshzZGhN75iSLNmiiDNlQFmjx52RpHtEeXU7VtOgYFZU5Ugvznnjnq9smaRWLXpY+KxJb8hHlv8hJje2qmZneiKQ5qjY4+a6yMAAamPG0pFRwB9Njr2qLk+ApDm+rg1sxSkuZm041UXpFkzX5DmIsDsoYOiVY4eW6PINJos1ycP33EuGJ47R5xYPlNJ8t9OvyA+kKI82DVNCfJjSz6qXpfNWKmZETOKQ5rNyANa4Z8ABMQ/K1xpBgH0WTPygFb4JwBp9s8qqishzVGRN79eSLNmjpIszS0H9hWmW9uSvEukxsYcovnFS8SN3tVi/6I28Y9d18UPW/aKc20j6uf3z3/YkuXFHxX3zX9IMwvmFYc0m5cTtKg6AQgIekjcCKDPxi1jaC+k2fw+AGk2P0dRtRDSrEk+SdJsjR4XR5Jb5dcin3cI5patkGckbxG31q8T783Li59MPyv+buAtcX7wrLpmxczVJaPK7dmpmvTNLQ5pNjc3aJk3AQgIekbcCKDPxi1jaC+k2fw+AGk2P0dRtRDSrEmerTRLGSYpLhdlNy467onORh7fslW9viWnXf984F3x+tmfi91XP1CXdrbNUKPJavr1oifE4s6lmsTjURzSHI88oZVFAhAQ9Ia4EUCfjVvG0F5Is/l9ANJsfo6iaiGkWZM8F2mmadXFtciF0WQ5/bpEkteskyPJliCPyRFl+vrI6Dnx+rlfKFF+/fwvxHjemp798MLHnFHlLT33alKOX3FIc/xylvQWQ0CS3gPiFz/6bPxylvQWQ5rN7wGQZvNzFFULIc2a5OMqzbRBlzr6qTDlmjbwoo28SiS5d72U423WaDLJshTlySnton+4TwqylOSzUpbP/Vxcun1BFVvT1Vucfi1HlVsyrZp041sc0hzf3CW15RCQpGY+vnGjz8Y3d0ltOaTZ/MxDms3PUVQthDRrko+LNNNRTyTI9tFP9DUdCeV+jG/c7Iwk2yPKk61F8X3z/C8dUd53bbcq2tXeLaddf1R8mKZfy+e8jgWaRHkUhzTzyGOSooCAJCnbPGJFn+WRxyRFAWk2P9uQZvNzFFULIc2a5E2V5vTNm3Ikeadz9BNNvc6ePF4qyYWp1uNbtokxGk2WT5HJlFxzuO9AYer1z8Wv5BTsickJ9fPtaudr66iojbPv0aTIrzikmV9OuUcEAeGeYX7xoc/yyyn3iCDN5mcY0mx+jqJqIaRZk7wp0pzu73dJ8i65iddukTlzqhhdNmuJsRJla6q1kmSPx7Xhq5Yoq7XKPxNX71xRV/XO3lgyqpwSKU16fItDmvnmlmtkEBCumeUbF/os39xyjQzSbH5mIc3m5yiqFkKaNclHJc3pa1fVmmRai2xv4JU5Zx3tRI/J1jZLjO3RZHrdsKlitJOTk2p9Monyr879TBy6vl9d29Mxz9r9ujCqPKe9R5NYMopDmpORZ05RQkA4ZTMZsaDPJiPPnKKENJufTUiz+TmKqoWQZk3yzZLmzOVL1lTr3YUp1/LrzEVrAy4lye1Tnc26rN2tt4ncut6a0R24vlfJMk29fkMKMz0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""
]
},
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}
],
"source": [
"dynamics.estimate_rate_constants(t=t_arr_late, reactant_conc=A_conc_late, product_conc=C_conc_late, \n",
" reactant_name=\"A\", product_name=\"C\")"
]
},
{
"cell_type": "markdown",
"id": "222e6b40-5f4f-45eb-bab8-7fa208675f7d",
"metadata": {},
"source": [
"This time we have an adequate linear fit AND meaningful rate constants : kF of about 8 and kR of about 0. Do those numbers sound familiar? A definite resemblance to the kF=8, kR=2 of the SLOWER elementary reaction `A <-> B`! \n",
"\n",
"#### The slower `A <-> B` reaction dominates the kinetics from about t=0.1 \n",
"\n",
"Let's see the graph again:"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "0c1a9e04-5622-480c-beca-525857353618",
"metadata": {},
"outputs": [
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"title": {
"standoff": 15
},
"zerolinecolor": "white",
"zerolinewidth": 2
},
"yaxis": {
"automargin": true,
"gridcolor": "white",
"linecolor": "white",
"ticks": "",
"title": {
"standoff": 15
},
"zerolinecolor": "white",
"zerolinewidth": 2
}
}
},
"title": {
"text": "Changes in concentration for `A <-> B` and `B <-> C`"
},
"xaxis": {
"anchor": "y",
"domain": [
0,
1
],
"range": [
0,
0.4
],
"title": {
"text": "SYSTEM TIME"
},
"type": "linear"
},
"yaxis": {
"anchor": "x",
"autorange": true,
"domain": [
0,
1
],
"range": [
-2.7777777777777777,
52.77777777777778
],
"title": {
"text": "Concentration"
},
"type": "linear"
}
}
},
"image/png": 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Q5qoMOy4aBEAABEAABEAABEAABEAABEDACwFIsxdK2AcEQAAEQAAEQAAEQAAEQAAEQKAqCUCaqzLsuGgQAAEQAAEQAAEQAAEQAAEQAAEvBCDNXihhHxAAARAAARAAARAAARAAARAAgaokAGmuyrDjokEABEAABEAABEAABEAABEAABLwQgDR7oYR9QAAEQAAEQAAEQAAEQAAEQAAEqpIApLkqw46LBgEQAAEQAAEQAAEQAAEQAAEQ8EIA0uyFEvYBARAAARAAARAAARAAARAAARCoSgKQ5qoMOy4aBEAABEAABEAABEAABEAABEDACwFIsxdK2AcEQAAEQAAEQAAEQAAEQAAEQKAqCUCaqzLsuGgQAAEQAAEQAAEQAAEQAAEQAAEvBCDNXihhHxAAARAAARAAARAAARAAARAAgaokAGmuyrDjokEABEAABEAABEAABEAABEAABLwQgDR7oYR9QAAEQAAEQAAEQAAEQAAEQAAEqpIApLkqw46LBgEQAAEQAAEQAAEQAAEQAAEQ8EIA0uyFEvYBARAAARAAARAAARAAARAAARCoSgKQ5qoMOy4aBEAABEAABEAABEAABEAABEDACwFIsxdK2AcEQAAEQAAEQAAEQAAEQAAEQKAqCUCaqzLsuGgQAAEQAAEQAAEQAAEQAAEQAAEvBCDNXihhHxAAARAAARAAARAAARAAARAAgaokAGmuyrDjokEABEAABEAABEAABEAABEAABLwQgDR7oYR9QAAEQAAEQAAEQAAEQAAEQAAEqpIApLkqw46LBgEQAAEQAAEQAAEQAAEQAAEQ8EIA0uyFEvYBARAAARAAARAAARAAARAAARCoSgKQ5qoMOy4aBEAABEAABEAABEAABEAABEDACwFIsxdK2AcEQAAEQAAEQAAEQAAEQAAEQKAqCUCaqzLsuGgQAAEQAAEQAAEQAAEQAAEQAAEvBCDNXihhHxAAARAAARAAARAAARAAARAAgaokAGmuyrDjokEABEAABEAABEAABEAABEAABLwQgDR7oYR9QAAEQAAEQAAEQAAEQAAEQAAEqpIApLkqw46LBgEQAAEQAAEQAAEQAAEQAAEQ8EIA0uyFEvYBARAAARAAARAAARAAARAAARCoSgKQ5qoMOy4aBEAABEAABEAABEAABEAABEDACwFIsxdK2AcEQAAEQAAEQAAEQAAEQAAEQKAqCUCaqzLsuGgQAAEQAAEQAAEQAAEQAAEQAAEvBCDNXihhHxAAARAAARAAARAAARAAARAAgaokAGmuyrDjokEABEAABEAABEAABEAABEAABLwQgDR7oYR9QAAEQAAEQAAEQAAEQAAEQAAEqpIApLkqw46LBgEQAAEQAAEQAAEQAAEQAAEQ8EIA0uyFEvYBARAAARAAARAAARAAARAAARCoSgKQ5qoMOy4aBEAABEAABEAABEAABEAABEDACwFIsxdKJfY53T9poBZUEYZAbU0NLe9K0tmBqTDV4FhDBHrakzQ2OUOpmVlDNaKaoAQaG+qoOVlHA6PTQavAcQYJrO5pIvyfYRBoiKo6WuopnZmj8al0iFpwqAkCyfpaam2qp/6RlInqUEdIAss6kjQ0PkMzafwfHhKlkcPl/w2U8hOANBuIAf4AMgAxZBWQ5pAADR8OaTYMNER1kOYQ8CI4FNIcAdSAVUKaA4KL4DBIcwRQQ1QJaQ4BL4JDIc0RQA1QJaQ5ALT8QyDNBiCGrALSHBKg4cMhzYaBhqgO0hwCXgSHQpojgBqwSkhzQHARHAZpjgBqiCohzSHgRXAopDkCqAGqhDQHgAZpNgDNcBWQZsNAQ1b30yceput33kq9K9aGrAmHhyUAaQ5L0OzxkGazPMPUBmkOQ8/ssZBmszzD1gZpDkvQ7PGQZrM8g9YGaQ5KznUcMs0GIIasAtIcEqDhwyHNhoGGqA7SHAJeBIdCmiOAGrBKSHNAcBEcBmmOAGqIKiHNIeBFcCikOQKoAaqENAeAln8IpNkAxJBVQJpDAjR8OKTZMNAQ1UGaQ8CL4FBIcwRQA1YJaQ4ILoLDIM0RQA1RJaQ5BLwIDoU0RwA1QJWQ5gDQIM0GoBmuAtJsGGjI6jCmOSRAg4dDmg3CNFAVpNkARENVQJoNgTRQDaTZAESDVUCaDcI0UBWk2QBEA1VAmg1ARKbZAMSQVUCaQwI0fDik2TDQENVBmkPAi+BQSHMEUANWCWkOCC6CwyDNEUANUSWkOQS8CA4thzR/+J4vUk93O33vm5+L4IqirXL/oaN092e+TA9960u0bfOlxk4GaQ6J8o/PnqNrMvW0sxFrqIVEGepwSHMofMYPhjQbRxq4QkhzYHSRHAhpjgRroEohzYGwRXIQpDkSrIErhTQHRhfJgVFI8+9+9uv0m72HFrS3u7ONdj92v3qvHNL82E+epi9+7Tt03+c/RXfdeVtglpDmwOiiPbDmpX3qBP+4rZ3+z45l1F5bG+0JUXtBApBmu24MjGm2Jx6QZntiIS2BNNsTD0izPbGANNsTC2kJpNmueJiW5q3vvofcgqyvVkR6RW8XffWPfq8s0myKOqTZFEnD9fzxmXP0nQsDdDI9Q9saknR3awd9rKWNmmogz4ZRL1odpDlO2qXPBWkuzSiuPSDNcZH2dh5IszdOcewFaY6DsrdzQJq9cYprL0hzXKS9ncekNIsYv3H0ZC6jXKwFOtMsn+uMdDHRdmes3V2id911L922cxs9vWc/DQyNqlN9+hMfonVrlquMsi76mEKym58Rl+Pv/eRHqFCm/MBTD6oqIc3e7quy7PXIqX56aGyE/uuEc0N8uLlNifO7mlrK0p5qPCmk2a6oQ5rtiQek2Z5YSEsgzfbEA9JsTywgzfbEQloCabYrHialWbLMH3r/LSqbvFgRaX7z2CkluSKpUkSCL790bW6cs4hr/8AI/fDB+9Tn93/3UXrg+4+TllfZX2RZS7H+PL8buBwrdeTLbr7gy+d/8v/9tTq/fPYH//M/yo1ZlvYWq8dUNDGm2QBJmQhsmuaUOD80NkyvTKdoVV2C7m7jrDML9LpEvYGzoIrFCECa7bo/MKbZnnhAmu2JBaTZrlhAmu2JB6TZnlhAmu2Khf5/w0SrtJR6GTNcaEzzF77ybTr4+vGCgqvbJ6L80Q/erkRbZ5q1oBfKAEudkomWsdTuz6U+mczLS1u1sD/yxJMX1YOJwEzcOQbrcM+e/drMND00PkwPjY7Q6Nws3drYrLLO/6Cl3eAZUVU+AUizXfcEpNmeeECa7YkFpNmuWECa7YkHpNmeWECa7YqFrdKsJ+0qREtnp4tJs1uEJftcSHaPHD+tunDrrHWh8+hMtvsz2R/ds+27h3MtKrTk1N9NjKms8y+mJqi+pkZlnD/OmedrGxotvpLKbRqk2a7YQZrtiQek2Z5YQJrtigWk2Z54QJrtiQWk2a5YmJRmqctP9+z8JafcmWYtzaWkVsY052eaTUizXMc7dmzOdRV3dw2HNNt3Dy8qzfJhXyZND49Ll+0ROsYThV3V0MDy3K4mC8Ms22YDCmk2yzNsbRjTHJagueMhzeZYmqgJY5pNUDRTB6TZDEcTtUCaTVA0VwfGNJtjaaImk2OaS00EJmJcbPbsQt2zF+s+HSbTLNyKdc8uJOyQZhN3Wgx1FMo0u0/7XGqS5XmUHuHMs5QP8ARhIs53YKIwY9GBNBtDaaQiSLMRjEYqgTQbwWisEkizMZShK4I0h0ZorAJIszGURiqCNBvBaKwSk9IsjSq05JQWUT1JWKkxzVKPnsHanW0WsX7Hji1qneUw0ixjkaUNA0MjuZm+9URgMgFYvlDLNUlB92xjt100FZWSZjnrLD9knPPDEyP0Akt0D6/nLOJ8d2s7XZpoiKZhVVQrpNmuYEOa7YkHpNmeWEhLIM32xAPSbE8sIM32xEJaAmm2Kx6mpdktvO4rdWeNvUhzsXrcs2cH7Z6tJ/DSs3jrduo2ipw//rNncs2XcdR65m50z7br/l3QGi/SrA94UyYK4+7aIs8DmQzdmGyku3mSsI/xo4bHPqMEIwBpDsYtqqMwpjkqsv7rhTT7ZxblEZDmKOn6qxvS7I9XlHtDmqOk679uSLN/ZlEeEYU0R9nepVo3lpwyEFk/0qxP97PJcTVR2E95K+VjnHG+u6WDdrJEo/gnAGn2zyzKIyDNUdL1Vzek2R+vqPeGNEdN2Hv9kGbvrKLeE9IcNWF/9UOa/fGKem9Ic9SEvdUPafbGadG9gkizVDg0O+ssT8WZ5zc4A30Jd9OW7tqSdV5WV2egZdVTBaTZrlhDmu2JB6TZnlhISyDN9sQD0mxPLCDN9sRCWgJptisekGY74gFpNhCHoNKsT713eorHO7M880zbGX7zvY0tKvP8O82tBlpXHVVAmu2KM8Y02xMPSLM9sYA02xULSLM98YA02xMLSLNdsdD/b9jXquprEaTZQMzDSrNuwt9kl6d6licKa9MThfESVbJUFcriBCDNdt0hkGZ74gFpticWkGa7YgFpticekGZ7YgFptisWkGZ74gFpNhALU9IsTTme5onCxsfUeGdZ5/nahkZnvDM/GggThRULF6TZwI1ssApIs0GYIauCNIcEaPhwdM82DDREdZDmEPAMHwppNgw0ZHXonh0SoOHD0T3bMNCA1UGaA4JzH2ZSmnW9r01P0xeG+mjP1KR66+ZkM/1xdy9trU8aaPHSqwLSbFdMMabZnnhAmu2JhbQE0mxPPCDN9sQC0mxPLKQlkGa74gFptiMekGYDcYhCmnWz/orXdv6/hs/TCE8aluAlqT7Ok4R9tqOHlmOisAWRgzQbuJENVgFpNggzZFWQ5pAADR8OaTYMNER1kOYQ8AwfCmk2DDRkdZDmkAANHw5pNgw0YHWQ5oDg3IdFKc1yHhHm/3u4n77PXbbTc3OUZHn+l+1d9Km2Lmrnsc8oRJBmu+4CSLM98YA02xMLaQmk2Z54QJrtiQWk2Z5YSEsgzXbFA9JsRzwgzQbiELU06yb+emqCHpsYpcd4zPPE3Kzqqn1XS5t6rK5LGLiSyq0C0mxX7DCm2Z54QJrtiQWk2a5YQJrtiQek2Z5YQJrtioX+f8O+VlVfiyDNBmIelzTrpv5scpzFeZR+yAItZWdjE93VzPLMj44qzTxDmg3cyAargDQbhBmyKkhzSICGD0em2TDQENVBmkPAM3wopNkw0JDVIdMcEqDhw6sp07z13ffQZRvX0A8fvM8wxfDVQZrDM6S4pVmaPMcPEefHeJmqn3MGWsrtTc05eZbxz9VUIM12RRvSbE88IM32xEJaAmm2Jx6QZntiAWm2JxbSEkizXfGoFmm+/7uP0s93v0gDQyP0Z1/9A9q2+VKrAgFpNhCOckizbvbYbIa7bI8pgZb1naX8TnMrfZizzrKtlgJptivSGNNsTzwgzfbEAtJsVywgzfbEA9JsTywgzXbFQv+/YV+rzLfow/d8ke7YdT29dOANWtHbRV/9o98zf5IQNUKaQ8DTh5ZTmnUbZE3nH2bl+eXpKarnTLPusv1uzkAv9QJptivCkGZ74gFpticWkGa7YgFpticekGZ7YgFptisWUUjzFE8w/Ny400s1ztLIQ0hvainsJPsPHaW7P/NleuhbX6Ijx0/TNx54mHY/dn+czSt5LkhzSUSld7BBmnUrj6VnnG7bLNBvzKSok29QJc88WdiNyabSF1Ohe0Ca7QocpNmeeECa7YkFpNmuWECa7YkHpNmeWECa7YpFFNI8lMlQ174DsV9oJy+XO7h9a8Hz6q7ZeiyzjG0Wgbapizak2cAtY5M068s5MDOtxjvLbNun02lak0iwPLcred5S32Dgqu2qAtJsVzwwptmeeECa7YkFpNmuWECa7YkHpNmeWECa7YpFFNJ8diZNHz/2duwXurI+QT/YuL7geXXX7Hs/+RH1+e9+9uvWddGGNBu4ZWyUZn1Ze3ics5N5HqVh7o5xhSxTxWOdRZ43JOoNXL0dVUCa7V9L9I0AACAASURBVIiDbgWk2Z54QJrtiQWk2a5YQJrtiQek2Z5YQJrtikUU0mzbFequ2fnt6u5ss6qLNqTZwJ1jszTry3tyMrvGM8tzem6Ork025rptL6utM0ChvFVAmsvLP//skGZ74gFpticWkGa7YgFpticekGZ7YgFptisW1SDN+V2zdQSki/Z9n/8U3XXnbVYEBdJsIAyVIM36Mv9OJgtjcf4Rb6Xc2ugsU/Xh5hZqqWB5hjQbuJENVoExzQZhhqwK0hwSoOHDseSUYaAhqoM0h4Bn+FBIs2GgIavDklMhARo+fKkvObXrrnvpox+8nXTXbI1PumhL+d43P2eYaLDqIM0ubl/4yrfp8Z89c9HAc+ln/+axU2rPQgtuV5I0yzVMc6bZGe88Rr/MrvH8vsYWuquVJwxjga7EAmm2K2qQZnviAWm2JxbSEkizPfGANNsTC0izPbGQlkCa7YrHUpdmu2gXbw2kOcvmsZ88Tf/poR8rOXbP1ibfcvQPjJCezU0Euqe7fcG3HpUmzfp2GOTZ8yTrLI8XUlPqbT3T9vuaWirlHlbthDTbFS5Isz3xgDTbEwtIs12xgDTbEw9Isz2xgDTbFQv9/4Z9raq+FkGaszHXU5vrNcL0FOfSZeAPP/2xXH96kev8tcMqVZr17Z6am6W/GB2mb44M0AhPFiblTp4s7LMd3bSVJw6rhAJptitKGNNsTzwgzfbEAtJsVywgzfbEA9JsTywgzXbFAtJsTzwgzRwLyR7/87s/QJs2rM4trC3S7F5oW0t0offODTpZ2kovMrv2AyOD9GfDA5TiLtxSPtDSSn/Y0UNXN9gtzyLNPR0NdH4oVelhWBLt/9EPH6Ib3nEbLV+5dklcTyVfRLKhjpoaamlobKaSL2PJtH1FVyMtlf8zKj0obc31lMnM0UQqXemXUvHtb6ivpZbGBA2OTlf8tSyFC+hpb6CRiTTNpJ1ECooZAgOT/TQ+M0Z6K7X2TZyjVNrxiBOjzjJQmbk0nR5zhoWOT4/RE//kUTMNQC2hCFS9NMs45nMXBlV363wh9irNmVlHMJdKkfXb/v35C/Tn/RdoKntt72J5/qOVvfReHvdsa6mrraGlFgtbWZdq119+/y/one98J63fsLHUrvg8YgI1XH8Nf6k0m/0iLOLTofoSBPB7yp5bhP/LIPnfGz8a5Y8Jfk+VPwbuFkgiAv9nXByToakhksewbFPO89x7qWF+f1i9vjBxgcZYdi9MXlDSq18HjfLcv1lanhGUQ7mPK4s0S5fngaHRgtd+4KkHY2OS39U6qDRXevfsYsD7eMzzg2PD9J9GB3PdtqW79u9zt+3f4jHPCf6laktB92xbIuG0A2Oa7YkHumfbEwtpCSYCsyce6J5tTyzQPdueWEhLlupEYPNZ3nEanGKhnRnnrK+zHZzqp5FpFl+W3xEWYr113hvi94ZDB6k92UEdyU5qb+igdt5K6W7qoZb6VvV8Vesa/tvaWQZ2bdt6tU0mGukzN/2z0OdGBeEJxC7NhSbSCn8ZwWoQaf7i175T8OBPf+JDaurzQmOa5Ri33C9VadZgjqZneImqUfrxxDi9PO10Ibk52UQf4HHPH2hqpdWJRLAAGDwK0mwQpoGqIM0GIBqqAtJsCKShaiDNhkAaqAbSbACioSogzYZAGqqmEqT5xMjxrOxeUF2cx6fH6ez4qZz4nuHuzSLJ5+WzbJfosHhEbh3JbaGuxl617W7Kbht7qFle81aEuIMFWbYiyEqU+XXQgtmzg5Ize1zs0mzbQtVunIW6Yy/l2bP93kpn0mn68eQYP8bpmexSVdfwWOc7WZx/mwX6svoGv1Ua2x/SbAylkYogzUYwGqkE0mwEo7FKIM3GUIauCNIcGqGxCiDNxlAaqShuafYjwO7xwH4vNlnXSMtbVpBslzWvoMZEkrcr+XWSlvNrLb1ajptFklmC9Wu/5zO1P6TZFMlw9UCaXfwKSbN8vNTWaQ53yxDJhGE/lswzy/PP+SHlchZmyTrLxGHbyzDjNqQ5bFTNHo/Zs83yDFMbpDkMPfPHQprNMw1aI6Q5KDnzx0GazTMNU2MYaY5LgKUrs8isyK/u4ryOuzRr8RUZlkyw7CddnEWKK7VAmu2IXOzSLAJ6x67rVdfnpVKWevfsYnGa4dlTfjwxRj/KZp/T/HpNop7luYWXrGrhLtzNsYUY0hwbak8ngjR7whTLTpDmWDB7Pgmk2TOqyHeENEeO2PMJIM2eUcWyo0jzicF+Oj/Wz2N9B3jSK35MDfJ2kAZ5BuhB3qrX8tm0vCefy36DlJ71Nxt9c4K7Ojd1U2eyizobedvYRV38vIszvPJcv+/s083vO+81cHa4Wgqk2Y5Ixy7NhdY5tgNF8FZUqzS7if2cu2v/aFyyz2Nq0rCuujolzx9obqP3NEYvz5Dm4PdvFEdCmqOgGqxOSHMwblEdBWmOiqz/eiHN/plFdQSkOSqyTr2j0yOO2LLgKrktIcAjvN8A7w8BjjYuXmtf6tKse/rm87jv85+iu+68zSumyPeLXZplTPNiJc7Zs03RhTTPk/w1y7Ma98yThp3NpKmBatR4Z5k07M4IZ9yGNJu6m83UgzHNZjiaqAXSbIKiuTogzeZYhq0J0hyWoLnjIc3eWY6mWICzGV4twOo1P3IZYM4MO+9lJRkZYO+ALdyzWqT5oW99ibZtvlRFQJYEfnrPftr92P3WRCR2abbmyg02BNJ8McyXUlNqzLMI9NGZabXD+xpb6Ld5zLOMfW6rrTUYASJIs1GcoSuDNIdGaKwCSLMxlEYqgjQbwWikEkizEYxGKqlWac4XYLfoagGWpZCk23OcArxp2Qqqy7Rx2qPeSHxRSTgC1SjNeoUjm5KpkOZw97E6GtJcHOJr09P0ExZnWbLqQFaeb+Wxzo48t9CKOjPLVUGaDdzIBquANBuEGbIqSHNIgIYPhzQbBhqiOkhzCHiGD11K0pzKTFHf+DmSJY9kuaMBll7ZnuHlkOR9/TrMLNB+JsEKstxRmInADN8aqI4JGJdmvkfpwnPxs+VZy6n3povOW2z1Itnxe9/8XPztLHLGskhzofWRbeu37idCkObStN7mtZ5/wl22ZdKw51OT6oDrko1KnH+bxz1fwhOIhSmQ5jD0zB+LMc3mmQatEdIclFw0x0Gao+EapFZIcxBq0RxTCdIsEizCK+J7fuKsI8WTfTz2l98TKc5KsqwJ7KdELcB+2qL3hTQHoRbdMcaleXqI6G+6omtwsZobOon+4WBRac7/4NOf+JBVE0fHLs33f/dReuD7j5O737r+hsE2OF7vJkizV1L8xdZsRs24LWOefznlLFd1VUODWutZum1fzes+BymQ5iDUojsG0hwdW781Q5r9Eot2f0hztHz91A5p9kMr2n3LJc0jqWEW3rMqE3xapJgF+AKLsJbggckL6jN57aesa9/gLIXEM0B3N/WSLIWkX8tWRDlIBthPG8LsC2kOQ8/8scalefIs0TMfN9/QUjU2riS69QdFpdnthuiezZh23XUvffSDt1/0zYHI9CNPPGnVgO9SsdefQ5q9klq4309Ynv98bIj2TDmZ52RNDX20pZ3uae1UIu2nQJr90Ip+X0hz9Iy9ngHS7JVUPPtBmuPh7OUskGYvlOLZx7Q0S7a3b/wsnWMhVlt+iBzn3ps4o96TccJeSpK7lfY2L6PepmXUw4/e5uXZ573ZLb/Ofi771Nf5+xvGSxvi3AfSHCft0ucyLs2lTxnrHoW6Z0sDZPJot0jH2qgCJ4s90ywACnXFtvEbBa/BgTR7JVV4v2d5xu3vjA1z9+35Lk27eJmqe1o7eL3nVk+VQ5o9YYptJ4xpjg11yRNBmksiinUHSHOsuBc9GaTZnlj4leYTI8dVd2gZJyzbs+OnVaZYjR3mrXzupbTUt3ImuIfWtm2g5ZIZ5ueSHV6rMsMrc68lc1xNBdJsV7SrUZp1z+SqnggMmWa7fhBtas2x9DR9Z3SYHhkbofG5WdW0dTzW+Z+2tnMGuoOW89rPxQqk2aZIEkGa7YkHpNmeWEhLIM32xAPSbE8stDS/ce50Nht8RmWGdYZ4wZYzxJPpiUUb31CXpBUtK1mEVy7YrmhZxe+tohWtzmeSFUa5mACk2a67olqkOZ+6TcIsbYs904wxzXb9INrYmpHZWforzjx/Z3SIzvBaz1IS3HX7t3jSsI+zPN/e1HxRsyHNdkUS0mxPPCDN9sQC0mxXLCDN8cZDxgVL92hHhlmKXd2nz/MYS2cc8RmayTjLVBYrzfUtjgzzYznLr9qyIMtWSTE/5HlnYxkmOooXaWRngzRHhjZQxUtdmgNBKcNBsUuzXCNmzy5DpCvwlCOzc/T3U2P0C5407Bc8adgQy7SUm5JN9B4W6PdwF+7N2YnDIM12BRhjmu2JB6TZnlhAmu2KBaTZTDxmuWeYSHBu3LDOELve02OLZd/FSluynYVXssGuDHE2K7xSCbGTIW5raDfTeNRSkACk2a4bA9JsRzzKIs12XLq5VmBMszmWxWram5picZ6gX/CSVa9Mp9RuqxIJeg+v+fweHvd8Bwv02p4mOjvAa8+hlJ0ApLnsIcg1ANJsTywgzXbFAtJcOh6S9RXhPccZYCW+ri7TfS4pPj/RV7KyrqZuJyssUpzNDOvt2o41dGnvWmqY7aamxMW9yUpWjh2MEoA0G8UZujJIc2iERiqANBvACGk2ANFjFf28ZNUvJiXzzALNGeix7LfWMnHYh7rb6ca5JF1eX9mzVnpEYfVukGZ7wgNpticWkGa7YgFpJrXE0onR7KRa2Qm1ZCItmVTrZPb99KwzTGqxIhNqyTJKspySTJolz1e1rHa26vkaNalWseJ3IrBS7cHn4QhAmsPxM300pNk00WD1xSbNMmu2rMMsazQvVmwb9O0FK6TZCyXz++xJTbJAszxz1+0D2ezz+vp6up2zz+/l7PPtLNK15k+LGj0QwJhmD5Bi2gXSHBNoj6fBRGAeQcWwWzVIs6xDLFIss0nL49TY2/TW0BElxCdG3iZZmqlUaU920Oqs/MqM0rLm8EqWYC3E8pnsE6ZAmsPQM38spNk80zA1QprD0DN3bGzSbK7J9tUEaS5vTM7xZGFPcub56cwU/Xh4lKay2WeZMOz2xhZ6L49/3sizcKPERwDSHB/rUmeCNJciFO/nkOZ4eS92tqUgzSK9Ir/Hho/kpFgLssiySPNiRTLE69rXqyWXLsoOZ0VZ9om6QJqjJuyvfkizP15R7w1pjpqwt/pjl+Zi6zTLrNqPPPEk7X7sfm8tt2gvSHP5g6EnAnv0zAD9/cQES/Q4HZ5xZuC8hIVZxFkE+t0FZt4uf+uXXgsgzfbEFNJsTyykJZBme+JRCdJ8frKPTo+eVGsPnx47Of98PPuc1ynO8LClYkVmkxYZlmzw6ta1C7pLq/fb1lJdTfHlHOOKFqQ5LtLezgNp9sYprr0gzXGRXvw81kiznlEb3bPtuDEqrRX5s2efTM+o7PPf8/hn2abn5vgPgxruut2U67ota0CjREMAY5qj4RqkVkhzEGrRHQNpjo6t35ptkWbJEr81dFR1mT45+rbTlVqe81aWYVqsSLfodZwl1uOI13LXaXm9lscVy3axccR+eUW5P6Q5Srr+64Y0+2cW5RGQ5ijpeq/bGmn+wle+TU/v2Y9Ms/fYYU8XgcWWnPqliHOKBZoz0EfTTvb5ivokZ55ZoDkDfSuPfUYxSwDSbJZnmNogzWHomT8W0myeadAa45RmEeE3B19X3aiPjxxV44qPDR9VrxebaMstxSLGa1pZikWIs1IcdixxUHamj4M0myYarj5Iczh+po+GNJsmGqy+WKS50LrMhZp73+c/RXfdeVuwKynjUeieXUb42VN7Waf5eGaGxdnJPMsM3FKSNbVqvWe17jN33V5Zlyj/xSyBFkCa7QkipNmeWEhLIM32xMO0NEsX6jcHD2dl2BFinUVO8ZwbhUqiNkEbOzbx41K6pHPTkpXiUlGHNJciFO/nkOZ4eZc6G6S5FKF4Po9Fmt2XUmxMczyXG81ZIM3RcPVTqxdpdtf3yvQU/eX4MP3t2CiluOu2lO66OvpoSzt9orWdJw7DslV++OfvizHNYeiZPRbSbJZn2NogzWEJmjverzRPpSezXaffzs4+7XSjliyydKW+MHm+YOPaGtq5u7TTbdrJEG9cktniMJGBNIehZ/5YSLN5pmFqrCZpFk/ML7YM3Y1dmsPcNLYeC2kuf2T8SrNu8cjsLP3t+IgS6Nemna7bUnYkG5VA/05Tq5JpFH8EIM3+eEW5N6Q5Srr+64Y0+2cW1RGFpHl6NpVdnsklxtkxxieGj5FMzFWoNCWaaX0HjyVudcR4fcdGNSO1kmR+r6upO6rLWBL1QprtCiOk2a54VIM0617JsjzxvZ/8SC4AMnxXylf/6PfKHhRIs4EQQJoNQAxZRVBpdp92b2qKfjAxTD8cG6Px7LJVSZ487A7uuv2R5ja1TfBrlNIEIM2lGcW1B6Q5LtLezgNp9sYpyr3SszMqQ9yfOklvDR6jIwNv5Sbfkqxx38TZgqdvqE0qGdZLNCk5zmaNZeKt3qZlUTZ7SdcNabYrvJBmu+JRDdK866576aMfvH2BMNsVBaLYpXn/oaN092e+XJSDLSl4P4GCNPuhFc2+JqRZtyzFwvwTHvP815yB3j01qWbeliIZ5zubWaCb2uhmTB62aCAxpjma+zxIrZDmINSiOwbSHB1bd80yuZbMRu2sWcwzUmdno1bdqflxdux0wYbIGGPJECs55km31CzUIsftTpfq5c0r47mAKjsLpNmugEOa7YqHaWmeSk/Rcyefi/0iGxONdNPamy46r3bDh771Jdq2+dLY2+X1hLFLs3yTcNvObfSOHVvoGw88nJst+8P3fJHu2HW91d8wFIMKafZ6u0W3n0lpdreyL5OhR1meHxwbphO8jJUuq3jCsA+3tNFH+LGVZ+JGWUgA0mzPHQFpticW0hJIs7l4zPIXnDkZVl2oZbmmY7lxxjIxV6FSwz2GZHzxxs6NSo5XNa9TcqyzxrJ+MUq8BCDN8fIudTZIcylC8X5uWpqHpoao6+td8V4En62zsZMGPzd40XkrZdnh2KVZTwS2acNq+l+/8Cc5aRZgbomOPZIhTghpDgHP0KFRSbNu3iT/cfZrzjr/OsWPyQk6MJPKtfzmZDMvW9VIt/J2Jy9jhUIEabbnLoA02xMLSLP/WMxxTx810VY2Q+yIsTPxlgjzqdETRStd07bOmXxLssaylTWMVeZYxhuvJ78TgflvPY7wSgDS7JVUPPtBmuPh7PUspqX57NhZ+vjfftzr6Y3tt7J1Jf3gH/zgovqQaS6C2D17tjzX3bEr5VuGQpcFaTb28xS4oqil2d2wIZ487Ne8bNXT/HiGJfrNGWcCsXrOXuzibtu3sjiLQG9rqN4MNMY0B76VjR8IaTaONFSFyDQXxifdqWUd4yO8ZNPhgYO5NY3f4mWbRlLDRZm31Leq5Zo28nJNl/DSTVd0b1ZbWcapu6ln0VhBmkPdykYPhjQbxRm6MkhzaIRGKzAtzUYbZ6gy3RPZhgm/il1S7Jlm6Ya95YoNahY093OZHe3pPftzmWdDMYilGkhzLJgXPUmc0uxuyLlMWsmzk4WeoJPptPq4vbaWbks20W08editvL2svrqWsII0l/9nQrcA0mxPLKQl1S7N+XL8GguyiLIIs3xWqCTrGnkN40tpU9eVSog3tF9Kl3VdoUR5efOKwAGGNAdGZ/xASLNxpKEqhDSHwmf84GqQ5mKzZ9//3Ufp9LkLmD1b7ir3ely2DwAv9lMAaTb++8F3heWSZndDj2dmuOs2y7OS6Ak6P5tRH6/g8c+OQHMWmjPQaxIJ39dXaQdAmu2JGKTZnlhUkzQHkWMZS3xVzxYW4itpUydLMWeQ5XlUY4whzfb8bECa7YmFtATSbFc8qkGahXihyaK7O9usSajGnmm26zY00xpIsxmOYWqxQZrd7T/Maz4/M+0ItGSiR7lLt5SNifoFGeilugY0xjSHuZvNHgtpNsszbG1LLdN8YfI8HRs6Qm8NvUlvjRxVz49xl+pi3aqlO/WG9ks4c+x0oXYel6jt6ra1YfH6Oh7S7AtXpDtDmiPF67tySLNvZJEeUC3SHClEA5XHLs3uMc0G2m9FFZDm8ofBNml2E9k3nVLyLOOfn+Zu3NPZNaA3NzSwQDdnu3A3UlNNbflBGmoBpNkQSAPVQJoNQDRYRaVKc9/EOZcQH2UpfjP7+iiNTo9cRKg92ZEbW7yBM8aXyLhjEeSQXaoNhgITgZmEGbIuSHNIgIYPhzQbBhqyOkhzSICGDoc0GwAJaTYAMWQVNkuz+9Kel9m3VfZ5kp7l57rsSDZmBdqZRKzSC6TZnghCmu2JhbSkEqT5tf6DPBnXATp4YT+PNXbGG8u2UHGPN76qewtdyQ8ZeyxjjmXNY5sLMs32RAfSbE8spCWQZrviAWm2Ix6xS3Mlr8dcLGSQ5vLfzJUizW5SsmzV302M0yO8BvQZnlBMF1n3+XeaW9Q60BsTlTmBGMY0l/9nQrcA0mxPLGyT5vGZMTpwfh8duLCPDvbzlp+LMKcyUxdB07NUyxjjLb3b1FhjEWPZVmqBNNsTOUizPbGANNsVC/3/hn2tqr4WxS7NMsjbvT7zUkAOaS5/FCtRmt3U9nDm+UdT4/S34yM0kHEmEJMi0izyLBItMl0pBdJsT6QgzfbEopzSLGsbixwf7j9A+86/pORYxh4XKjIZl2SLd6y4UUmxZI9lfeOlViDN9kQU0mxPLCDNdsUC0mxPPGKXZvds2YUw6HWb7UFUuiWQ5tKMot6j0qVZ80nPzXG37Ql6fHKMfs5Z6D6XQK/jScTubG6l325soZ28FrTNBdJsT3QgzfbEIg5p7p+6sKBL9ZsDh3lJp9fp+MhbF4FY2bJaSfHl3ZI1ns8cy/vVUCDN9kQZ0mxPLCDNdsUC0mxPPGKXZnsu3VxLIM3mWAataalIc/716wz0fxsfXdCFexUvY3UHrwEtj10s0EnLJhHDmOagd7L54yDN5pmGqdHkmGaZsVqPNz4y/EZWlg/T4OTAgibWUA2L8VW57tSbst2qL+NlnVob2sJcTkUfC2m2J3yQZntiAWm2KxaQZnviEbs0F5s9WxavfuSJJ61Zi8tPiCDNfmhFs+9SlWY3LT0G+ocs0MfS07mPkjU1dAuL8281tdK7G5tJMtLlLpDmckdg/vyQZntiof/48ft/how91nIs2yNqci5ngq7M3PxwDqlfZq12ssbzmWORYxFllIUEIM323BGQZntiAWm2KxaQZnviYY00P/aTp+mLX/sOoXu2PTdHJbWkGqTZHY9Xpqfop5MT9NTkOMlzd7mKl7K6o7GV3ssCLbNyJ1iq4y6Q5riJFz8fpNmeWHiR5rPjpxd2r87OXH1m7NRFF7Kmbd1FcnwZZ5SXN6+w66ItbQ2k2Z7AQJrtiQWk2a5YQJrtiYc10vyFr3ybnt6zH5lme+6NimpJtUmzOzgHZqbpBV6+6oXUlNq+nZ7JfXxZfQPdkGyiGxoa6fpkkq6IaTIxjGm258cH0mxPLNzSnJnNONnjIRlzPL+s05GhN2hsenRBo2XpJpmpWi3l1LlwDHJTovKXqCtXhCDN5SJ/8XkhzfbEAtJsVywgzfbEIxZp1lnkUpd93+c/RXfdeVup3az73G9XO+suYAk0qJql2R0+mThM1oJ+gbPPItB7WaR1aa+tVfJ8o0g0Z6Bv4C7dDTzWMYoCaY6CarA6Ic3BuJk8amhqMDfe+OzUUXr59AElzG8Nv3nRaTobu7KTc/EYZO5WrbtZb+zYZLJJqIsJQJrtuQ0gzfbEAtJsVywgzfbEIxZpdl9usTHN9iDx3xJIs39mpo+ANF9MdJbfeoGXstICLRLdPyvvOmV7Q9LJQotANzTRmkTCWFggzcZQhq4I0hwaoa8KZJbqI4NvLBh3LOOPL0yev6ie9R0blRirDLJrDHJv0zJf58TOwQhAmoNxi+IoSHMUVIPXuawjSUPjMzSTnv+bIXhtODIsAZlAEqX8BGKX5vJfsvkWQJrNM/VbI6S5NLG3ePKwF6acDPQLM1P02vT8ZGIyG7dkniUTLSJ9LQt1mIIxzWHomT0W0myWp65tKj3JXau5e7Wra7V+PpOZ/9mS/Rvqkk7WmJd2um71VlrReGlOkpN1jdE0ELWWJABpLokoth0gzbGh9nQiSLMnTLHtBGmODfWiJ4I0G4gDpNkAxJBVQJr9ARybm2V5TmXHQjvjoSf5PSkycdiNnHm+oZHHQYtE86Orrs7XCSDNvnBFujOkOTzeVIa/ZOo/SAfO76OD/fvowAV+8HOZ1Tq/yPjjK7u30NZl19CWnm109bLttLX3GjWrtRSTS06Fv7LqrgHSbE/8Ic32xEJaAmm2Kx6QZjviURZp3nXXvTQwtHCiE40Ds2fbcWNUWisgzeEiJstZqYnEst253ZOJbUrIZGJOBvoGj5OJQZrDxcPk0ZBm/zRFil85t1cJ8p7Tz9DhgYOUnk1fVJGI8DXLr6ererbQtmXX8XarEmYR52IF0uw/HlEdAWmOiqz/eiHN/plFeQSkOUq6/uuGNPtnFsURsUvzh+/5IvV0t9P3vvm5KK6nLHUi01wW7AtOCmk2F4O+TJonE2OBnuYMNHfn3uta0mrBZGKciRaRLjSZGMY0m4tH2JogzYsTPDZ8RGWNnz/7LL3St7doBlkm4hI53s5yfCXL8TXLd9Cq1jW+wwNp9o0ssgMgzZGh9V0xpNk3skgPgDRHitd35ZBm38giOSB2acZEYJHEseorhTRHcwvMzs05GWgW6Benne7cF3iGbl0WTCbGAr2Gx0ZLgTRHE48gtUKa56kd7j9Eh/sP0GucOX598KDqcv3W0MIZrGt4Rvkre7fQlV1blCRfwZlj2ZqavRrSHOQulnNxwAAAIABJREFUjuYYSHM0XIPUCmkOQi26YyDN0bENUjOkOQg188dAmg0wRabZAMSQVUCaQwL0ePg4j3v++eQ4PcXduH8+OUYDLoFO8ljoW3gysduSzfQ/9HbQprkEpWYw86ZHtJHtVq3SLLNYH2Ypfo0lWW0HnO0c/3OXSzsvV1Is2eMruzbzVkR5c2TxgDRHhtZ3xZBm38giOwDSHBnaQBVDmgNhi+wgSHNkaH1VHLs0S/fsO3ZdT/d+8iO+GmrzzpDm8kcH0lyeGMg60D+fmqCnWKRfcXXjvueZ3fTy5q20Yc0GJdG7mppoXaK+PI2s8rNWgzSfGz/jkuODTjaZBXkqM7kg+uvaN6gxx+ohoixZZBmDXBffvQlptucHEtJsTywgzfbEQloCabYrHpBmO+IRuzQ/9pOn6RsPPEy7H7vfDgIGWgFpNgAxZBWQ5pAADRx+Jp2m3VPj9Cx34+78739HP7v8KjrW25ureSNPKLaLM9G7Glmi+SHjo1GiJ7AUpVnGIb94dg+9dO75ohN1yVJO16zYocYeyyRdMoO1ZJTLXSDN5Y7A/PkhzfbEAtJsTywgzXbFQloDabYjJrFLs4xpXqxg9mw7boxKawWk2a6IyezZK67bSS91dNHTPA76Gc5Gj8wu7Kp9DS9lJfJ8E4+Fvp5n54ZERxPDSpdmWdZpH0/QlZPkM8/QwGT/Alh6maedq2/hZZ62K1kuNYt1NLRL1wppLs0orj0gzXGRLn0eSHNpRnHugUxznLRLnwvSXJpRHHvELs1xXFTc50CmOW7iF58P0lz+GLhbkD8RWJonFNvHGWjJRO9WM3JPUorfc5et9Um6pamZrmtI0s3cpXu5z7Wh7SJgT2sqTZq9ZJFl1uodK3fSjStvput5u5XXQpbMciUUSLM9UYI02xMLSLM9sZCWQJrtigek2Y54QJoNxAHSbABiyCogzSEBGj681OzZKZ5Q7BmW5+d5HPQenlSskERfVt9AOzgLfTNL9E7u1i3du1H8E7BZms+Onea1kF+lg7wu8qELvO3fT68PHFpwkT2NvbSFpXhLzzba0nu1er65+2qq4YnnKrFAmu2JGqTZnlhAmu2JBaTZrlhIayDNdsSkLNIsk4G9eeyUInDf5z9Fd915G0m37Xfs2FyR6zdDmst/M0Oayx8DdwtKSXN+a8/PZmh/KkWvzkzRq5yRlsfx9MyC3a5iid7G3biv5oz01SzSV/Pr1to6uy7cwtbYIs0ZjvGhARZjXhPZEeX9dIglOb+rtYw73qwEeZvabl22jZY3r7SQbLAmQZqDcYviKEhzFFSD1QlpDsYtqqOQaY6KbLB6Ic3BuJk+KnZpFmHu6W5XcrzrrnvpDz/9MSXN93/3UXrkiScrcoIwSLPp29J/fZBm/8yiPELGNF+/81bqXbE20Glk/LMI9H4l0NO8naI3ZqYX1LWRZ+N2JLqBH7xlke5Fl+6LeJdLmvvGz+ZlkfepGa3dpauxm+WYs8gsyFt65rPIdUv4yxBIc6BfCZEcBGmOBGugSiHNgbBFdhCkOTK0gSqGNAfCZvyg2KVZMsoPfetLtG3zpQukWWbV/uLXvkOYCMx4jKuiQkizXWEOK835V5PitXX38/JWWqBVNnomtWC3VYlENgudFWmW6LVY5orikOY5Hp+eyyJnu1kf4kzyhcnzC2Ik6x9vFjkWSc4+Vrastuvmjbg1kOaIAfuoHtLsA1bEu0KaIwbss3pIs09gEe8OaY4YsMfqY5dmyS7/2Vf/4CJpLlem+Xc/+3X6zd6FY+jyxd3dnfyyjWvohw/etwAvMs0e77YId4M0Rwg3QNWmpblQE5wsdDYbzQIt3bunWa516eKss+rKLY9kkraxRG+qwnHRUUjz+Yk+1bXa6WL9Kh3Ijkl2x6mzscvpXq26WTtZ5C08FjnONZED3LqRHwJpjhyx5xNAmj2jinxHSHPkiH2dANLsC1fkO0OaI0fs6QSxS/MXvvJtenrPftUNW3fP3rRhNd39mS/Th95/C331j37PU8NN7SRtcK8Z7W6fnEOkun9gJCfK7u7lug2QZlPRCF4PpDk4uyiO9Dum2UQbXufu29KN+1XZSlaaRXrUtcxVU02tMxa6Qbpzs0TzJGNbuWv3Ui8mpPm1/gM5MZbJuiSL3DdxbgG6y7qupM0yUVd2PLJkkle3Buuev5RjAmm2J7qQZntiAWm2JxbSEkizXfGANNsRj9ilWS5bd8V2I/j0Jz5E937yI2Wnsv/QUSXwhbqQ67Z/44GHF4g2pLnsYSNIc/lj4G5BOaQ5n8Dx9LTqzi3yrGSaM9PnM5ncbjL3siPRTnfubbLljHSSKnNW5mJ3gF9p7p+84GSRz++nA1lBlozynCuL357syMmxmrSLJ+uSMckNdUm7bkQLWwNpticokGZ7YgFpticWkGa7YiGtgTTbEZOySLMdl164Fe5u4vkCLUcUeg/SXP6IQprLHwPbpDmfyNlMOpuFnnS2LNKn0ukFu12uJhWTLLQeF91IHbW1dsH12ZpS0iwZ4+dPP0N7zz3Pjz30yrm9lMpMLTiLSPLOVbfQjhU3qvWR5dFS3+qzJdhd//GD/zPsuBcgzXbEQVoBabYnFpBmu2IBabYnHrFLsx5DnD9u2IYlp7QQ62WwvEpz/8jCCYnsCW/1tETWbO1qraeB0YUzLFcPAbuu9IlHH6KdN99KK1ats6thrtakefKql3kc9G8mJ+g3LNC/npigYV4WyV1auEv3TU1NvE50I93Aa0VfyzLdUWEzOzck6ijZUEujE84SXm8NHaHnTj1Dz5z6Fb1wZg+9MXD4ohhdvewaumHVTrqe5Vi2l3dfaW0cK61h0gsD/2fYEbWWxgRlZudoanrhz70drauuVtQnaqmpIUEjE/g/3IbId7Q00NhUmjKZWRuaU/VtkP83UMpPIHZpljHEH/3g7Rd1xS7XRGA6BFqQ3d3EvUpzaga/VMp9K0uH2vr6WppGLModCnX+H/zV9+m2295J69ZvsKI9XhvxytQk7ZmYpN3j4/TLiXE6N7MwEy31bGWB3sEivYO3t7Q001YW6QR/aWNr2X/+Zdp9/Jf03Mnf0C/f/iWdGzu7oKmtDa10y7pb6eY1t9I71txEO9e8g+Q9lGgISEYN/2dEw9ZvrYm6GuLvzpQ4o5SXQC3/Cq3jeMykEYvyRsI5e0OihtKZOcKPhg3RcHpioJSfQOzSLBllncl1X345l5zS59bjmN3tcq8lLe8Xaie62pX/Rkb37PLHwN2COGbPjuOKj/G46D0s0s/zmtGvTKXoML+WDLW7JFmYr2FxvobHRN/Ij+08TnpdmZa6kq7Wr/a9Qq9eeJkfvOXnx0eOLmivLPt0de81dPVyfsi291rqaOyMAyfOwQQwptme2wDds+2JBbpn2xMLaQkmArMrHhjTbEc8Ypdm2zLNIsH5E3u5Q4PZs+24UUu1AtJcilC8n9swEVgUV3yGx0Uf4snFDqdT9BpPLPYaP3+NJxrLz0dfweOir+JZujfzEldXsURfxWOl10cg0m+PHKNXz4sk84MzyvL83PiZ3KUnahO0bfm1tGPVdXR5hyz/tJ2k6zUm7Iri7vBWJ6TZG6c49oI0x0HZ2zkgzd44xbUXpDku0t7OA2n2xinqvWKXZumG/cD3H8/NTi0XWKhrdNQX7j5voXO5s+FYpzmOaIQ7B6Q5HD/TRy9VaS7EaYBn5N7LY6L3skQf4O2e1CSNuJa60seIRO/gjPSWRJKXuuIHz9QtY6b9lJHUMO0+8Qt6/uyz9MzJX6lloPKLiPEta99J1/GkXTeveSet71xNzck6jPf3AzrCfSHNEcL1WTWk2SewCHeHNEcIN0DVkOYA0CI8BNIcIVwfVccuzdK2QktOFeqy7eM6yrorumeXFb86OaS5/DFwt6CapLkQeenW/SKvFb2fZ+l+kSX6AAt1Kq9btxx3GWegr+THDu7WLc9l211Xl6tSJFkm7Hru9O6Ckpys427hK3aoma1vWr1LTdwlM127S6nZs+26c5Z+ayDN9sQY0mxPLCDN9sRCWgJptisekGY74lEWabbj0s21AtJsjmXQmiDNQclFc9xSGdNsio6Mg5bx0DIu+iB37d7LQv0mC/X4XN4kgukJ6hx6hToHX6bxc7vp/MCBBU0QSZblnt69/g4lyPJc3lusQJpNRdFMPZBmMxxN1AJpNkHRTB2QZjMcTdUCaTZF0kw9kGYzHMPWAmkOS5CPhzQbgBiyCkhzSICGD4c0lwY6ysL83NAx+iUv+/RK3146zpN3DQ6+SrOpofmDk71EnVuoo3sbbeBJu7Yvv56uaVtDl/H4aFlTusuVlS52Rkhz6VjEuQekOU7ai58L0mxPLCDN9sRCWgJptisekGY74lEWaZbJwAaGRgsSyF+/2Q5Mi7cC0lz+KEGayx8DdwsgzYXjIZN07Tv/kpLkV869SPv5+fmJvtzO3Y09tGnZddTbs40SXVfTRNtVdLK+m97grHT+wna9vF60iLN0676cx0hflkio7Wreuguk2a6fDUizPfGANNsTC0izPbGANNsVC2kNpNmOmMQuzTKpVk93O33vm5+zg4CBVkCaDUAMWQWkOSRAw4dX+5hmjfPC5Hna1/cSP150RJkf7tmtZamn7ct20DXLd3AW2dmubVt/UTSOcNfuN2Zm+JHibt0z9DqPkX4jPUOTed27ZWKxeZFmoeaM9NXNTbS9rQkTgRm+x4NWB2kOSs78cZBm80yD1ghpDkoumuOQaY6Ga9BaIc1ByZk9LnZpLrZOs9nLirc2SHO8vAudDdJc/hi4W1Ct0jw0Nchi/KLKJu/LSvKp0RM5NK31bbSdJ+7aztlkEWSZxGtD+6WBgneSpVlEWsZGv8HjpEWiJSM9yLN5u4vMz30Vz9R9SZ106U7yo55lWrLT9ZT0OXt3oIbioAUEIM323BCQZntiAWm2JxbSEkizXfGANNsRD0izgThAmg1ADFkFpDkkQMOHV4s0j06P5ORYifI5Hps88laOZmNdk5NFZjlWW5blTV1XGKY9X12KM8+vsTgfSE0vPuEYH9JeW8tLXzXS1SzU27iLt6wnLZlpiHRk4VEVQ5qj5eundkizH1rR7gtpjpav39ohzX6JRbs/pDlavl5rj12apXv2Hbuup3s/+RGvbbR+P0hz+UMEaS5/DNwtWKpjmid5dmvpYi1yrMcmHx16I3fp9XUN81nkbJfrK7o3lzU4Mqb5rbk0PcPzSBwUoeau3a/wetKF1pKWhuplsK5Sy2ElaRNnpS/jrHSipqas17FUTg5ptieSkGZ7YgFpticW0hJIs13xgDTbEY/YpVnWaP7GAw/T7sfut4OAgVZAmg1ADFkFpDkkQMOHLxVpnsnwMlHZbtbS3VpE+fWBQzlatdy9WcYi57pb8+zWm3uvNkwzXHXFJgI7wd25RaD3KZGeosO8lfcKFRHmK5U8N9CWBhkr7TyXB4o/ApBmf7yi3BvSHCVdf3VDmv3xinpvSHPUhP3VD2n2xyuqvWOXZhnTvFjB7NlRhXpp1wtptiu+lSrNmdmMmtFai7KMT36tf+FayduWXau6Wm/LTtwlr20ufmbPPp1O01s86dhbLM9Heby089x5T9aazi/LeQbvTZyNvqQ+QZewSF/C3btleym/bsB46YK3BaTZnp8WSLM9sYA02xMLaQmk2a54QJrtiEfs0mzHZZttBTLNZnkGqQ3SHIRadMdU0pjm/edfzna5dma4fvXCKwvASOb4GlkfOZtRlsyyZJgrpfiR5mLXJF25X+Os9AGevfsIC/Vr09N0mCcfG8ibdEwfL+OlJQu9lYV6I4u0POS1bKu9mzek2Z6fHEizPbGANNsTC0izXbGQ1kCa7YgJpNlAHCDNBiCGrALSHBKg4cNtluaDF/bPT96V7Xo9R/NZ1Ct7NtO27DJQaoZrfiRq6w0Tiq86E9JcrLUizYdZpF9loRaZFqmW2byLjZcWYc6XaJl8TLLVy+vq4oNSxjNBmssIP+/UkGZ7YgFpticWkGa7YgFpticeZZFmGdf8xa99ZwGF+z7/KbrrztvsIeOjJZBmH7Ai2hXSHBHYgNXaJM2H+w+pdZL1xF2STU7Pzo/d3dR5RXad5Otys1zLrNdLpUQpzcUY9bFMy3jpN7OZ6WMs1CLX8n6xImtM62z0lTzx2MbsmGmRbPlsqRRIsz2RhDTbEwtIsz2xgDTbFQtIsz3xiF2a7//uo/TA9x+nh771Jdq22VmfdP+ho3T3Z75Mn/7EhypyVm1Ic/lvaEhz8BjUzgxTTXpIVVCXOkc1s1PO88njalszm6Jaft9bESmqo799oZ5uvixDqztnvR2mTlRHmcY13vfP23OurpVmG3rozdGT9HL/6/TywBu85cfg6zTFY3J12di6hq5Ztp0f3O26Zytvr6Wm9uiWgQp8QYYOLIc0F2v6OZbm45yJfjszQ2/zmOm3M2mefCxNxzk+Z/h5odJANbSexXl9IqG2G3jM9Lrsc3ndxl3BK6lAmu2JFqTZnlhAmu2JhbQEY5rtige6Z9sRj9ileddd99JHP3j7RXIsMv3IE09W5KzakOby38zVIM210/1UkxlzhHbqFNXwMkLED3meL7e1GRZhlmG17/RZokxKPU9oEc5MUe20VxH2H9//fPIeelfPU7Sx6Zj/g30ecYSTxi/w5b3Arv9idjvqcvWN3LP6+iTRDfJodJ53legJnGnasKAVmeQKmqvlg7noz+ZqkyzpK9R7s4kOmqvvcJ439NJcXYuzL38JMFeT4C8EEqG+EPCJZMHuNklzseuQScaOczb6bRboEyzUx1mo9VYEu1h37y4WZi3Rzpblmrt5b+As9bq6BI89t2+ZLEhzmLvZ7LGQZrM8w9QGaQ5Dz/yxkGbzTMPUCGkOQ8/csbFLs8yeXagrtu6yjdmzzQW3mmqqJGmWDK6Ibu1MPz+GHAGenVDZXBHcmvT4vAizJIssR1l0hlYJX30PC2CrI39a+HiG5EyDvwxwkExzzZy3jPbbqXHaO9pPe0f4wduXxvppiLOXuqxpSNL1La10XUub2l7f2kY9LFO6CPPatPOFgpSaiL9AyI+dH95KzFnYndh00hzLuZRCEl/sHqkEaV7s/h7mSchEqGU5LMlIz4u1I9iFZvWW+tZxF+91dU6GegPHX4Rab5fxPV2uAmkuF/mLzwtpticWkGZ7YiEtgTTbFQ9Isx3xiF2akWm2I/BLrRW2SLMIsH7UyvPUaX7tSLJ+BGU/y5nMuURnUWmyKfNpckzzmbFTufHIMjZZxiQPTM5/kbC8eYVaK1nNbp19yHthiu6aruvIZfb5jULd1sud2Zd2SiY8J9gs1yLZUmqaVlJdfROlZmaz2W4WRldXeLfEp7MZdtVNXjLklpdTkp1WXbxFqEWsna7eItZ9Rbp7N/H46A28JJYI9YacWItcO4LdHPH4aUizPTcVpNmeWECa7YkFpNmuWEhrIM12xCR2acaYZjsCv9RaEYc0q0ywEuGsAE++nffaGQNcqkiXXpESyRZKV14RnbnaZvWe7tqr5cUtQqXqtenzMNLcN3HOWSv5nCPI+/gh7+nS3dSTFeT5ZaBW8TjlSinFxpDLlyyqyz2vFS33mBLezLjqkSCldvqCei2lUPf8KK5f7tW5OpbxbA8EyXSrjDd3P5f3dCZcuqBLzwQpNoh3imdDl7HTJ1xjqLVQn0hnaIwZFyrLuEu3Gi8tGWoW6vX8Wnf1lky1iQJpNkHRTB2QZjMcTdQCaTZB0VwdyDSbY2miJkizCYrh64hdmqXJmD07fOBQw0ICoaWZZSUxcYQS469nRVgyxNyFmh8yDliNGxahKVFkIqpMkoVYpFgkOLlaSYQIhWwrJYNX6jpLfe5HmiVrLHK8//xetZWHZJd16WjsVOskb1/Gs1tnM8pr29aXakLVfS7j3XVXftnWZse/JzPnKVk7TeNTPP6dv+iR4u4KL93Va7i7ugi7Hh+fn2kPA9OveIuA6wnh8seWh2mHPjY1N0tvzaTpGGek3+THce7iLetOywzfxdadlmO7eay0ZKdlNm8R6LUs1xv5oZ7z+17Xn4Y0m4iimTogzWY4mqgF0myCork6IM3mWJqoCdJsgmL4OsoizeGbbVcNmAis/PHwLM0sBvVjB6l+aC/VTxykunFHlEWYSxXpHi3yq4U4k1zvPM/KsJr0KTtZVKm6lvrnP33iYbp+563Uu2LtRZc6khpmMc5mkTmjLJnkEyPzWfrW+jZXd+vr6JoVO2hDuzPTPop/AmHGNOsvi/Ss6noyOplkTsaF60y4HhcelXjrL5v0WG75ckq6lcvka7N1Mmwhm/nOzqAuP4eyr98J2N6WLt5qIjI9Idn8GOoLiyyX1cpdutdwl+/VnJlewwIt29Us2Ws4W63fq89OSgZp9n8PR3UEpDkqsv7rhTT7ZxblEZDmKOn6rxvS7J9ZFEdAmg1QhTQbgBiyikLSLN1gE2MHqH7YEWQRZRFkvaRS/inlD/N0y5WUaWYZ5omvMk1ZKc6KsvyRjuKNgFuax2fGlBjrLPK+vpfo2PD8lxSyJrIaj8xyrLacUd7UtXSXgPJG0NxeYaTZRCsCi7cr822iHTprrWc0z2XAZXhEjcyELiIu8u1MuDbrEvDxhuV0irPSp3ms9GkeK6223MX7NEu2fj3OGexiRSYeW8MZ6dWcmb6itZE6eN469Vokm8V6eRknJjPBtlLrgDTbEzlIsz2xkJZAmu2KB6TZjnjEJs16LHOhtZgX+8wOTIu3AtJc/ijV84RbvZl9NHbmZaofeYll+WDh7DF3/Uy3XkEzbdfQTMtmFuRNLMr8aL5UZa5QwhNI8WzUjz/6FzS6copemnxZTeL15uDhXMX1dQ1KjEWQ9eRdV3RvDn9i1FCQQLml2URYdHdxPZZblktT2W0e7y2zzeuJ2HRX89o0d1WXz0zOjJ7tNl6o+/gED8MYma2h8zzOu5/q6WRtB52mRnqLWuhITRMdnUvSGX6vUJFu3U42Opup1tlpkepafl+tRW3f0lkm4lruOiDN5Y7A/PkhzfbEAtJsVyykNZBmO2ISmzR/+J4vUk93O33vm58reOW/+9mvU//ACP3wwfvsIOOjFZBmH7BC7irdQxPjh50u1WqbfT5x9KKaM43rVOY43caPZn6ILPNrvbZuyKbgcBcBkeJnT+3OPn61YOIu2W1d+wbate52um3t7XTzmndS2NmtAd87gaUgzd6vtsCecxnuSj7Kcj2S3XLX8kz29cwIizU/+PNa/ryGX9fq19xTRb2ffV2TmQjXjJp6mk60UYofIzWtNMhf0vXXNFMfP/prW2iYX8v7I5ztHq6TfVpopLZVvd/S0MmPDmrj2fN7G5pJMterOGu9iqVatqYmKQt1gRV4MKTZnqBBmu2JBaTZrlhAmu2JR2zSXGx9Zo0C6zTbc1PY0hLpXl0/+golRvbxOOT9nEF+RY1HLjQhl3S5rO25jsYar2Y53kYz7dtZlDfZcilLrh0yUdfuE7+gZ08/rbbuibvkYjd0bKRb1u6inStvU5Is0oxSHgJVL82GsMuwDplBPzdue8HEac4Ea3XTPIGdzH7O661TJkV1MzzjOWfCa9K8Njj/PjNRhlioh2rbaKyumS7UddIUdy2/kOil+tp6Gm1YRS08vnqqaR2187ameSN1sWA38VCTnvoGam1chXkXXEGANJu4I83UAWk2w9FULeiebYqkmXqQaTbDMWwtkOawBPl4ZJoNQOQqJGvcMLSHGoafVdvEKAtyfuEukjOtWzh7vJWm267j7RbV1ZqSvbS8K0lnB6bMNAa1LCAgk3c9c+pX9NTb/11lk93drWVHWQZq19r3qEyyZJSvXXsFjU3OqLWBUcpLANJcXv7us8sM56taxqnvfL8SaiXWItiuZcbqprICnp2xvzZ1lj+eonrukl47mzJyMSOJLprm7Pa0TKTG47drEq1Uw8vfJTkL3sBbW5cSM3LxkGbTGI3UB2k2gtFYJZBmYyiNVARpNoIxdCWxSfOuu+6lP/z0x+iuO28r2GjJNH/jgYdp92P3h76ouCuANAcjLuMTk/2/oOTAU5S88AteLmd+LV6pUcYYS8Z4pmMHzTSzHHfu4O7WVxTMlHiePTtYU6vuKJm8a8/pZ+m507tVJlkm8XKXlvpW2rn6ZnrXuvdxRvmdtLV3+4LPF5s9u+pglvmCIc1lDkDe6cPOnq1nMJfZy9UYbl67e47X8B6bmaAUC/bE7IxaKm+KJyZrTZ2gmbk56p06SfL11aqZs8QLehkBoidSKz2jOa/zLet9R7yUWJCLQqY5CLVojoE0R8M1aK2Q5qDkojkO0hwNV7+1xibNX/jKt+ng68eLjlkuNebZ74XFuT+k2RttybIk+5/MPSSz7C7SxXq68xaa7riRpnveqTLKsmSMlwJp9kKp+D4yedfes3to98mnlCTLbNfp2fl1qZN1jbRj5U66Zc0uevf696kloRI8nrJYgTSHi4fJoyHNJmmGryusNAdtgUjzOZ71+xxntUcnT9MgdxufnLpAEzyOe3pmgGa5+3iGJ1Br4OetcxM8seIQNXJme2XmAiX4mLVp50vNjTOngzbhouOKzmjOE6qpmcw5Cy7LiskXqDK7uXtG81lZUixkgTSHBGjwcEizQZgGqoI0G4BosApIs0GYIaqKTZqljZJtlpKfTZb3B4ZG6cBTD4a4lPIdCmkuzL6Wux82DL/ASz29QA0jvOXntdMDuZ0zTZewIN/AmeQbeHu92s7VNgQKJKTZHzYRYpHkp08+yd2ud6vnIs66iBCLGN/C45FvWr1LjU8WcfZaIM1eSUW/H6Q5esZ+zlAuafbSxjnOSvexIJ/jNanP8dJa8uiTbVa2+/j9s7yO9SSLdjt/Cdo+O86PMergR/7r5bMTtHxunHp5ny7etnNGvJX3a+LJ1ZKzo5RgQQ9Xanl5sHZeHqyd5brNWbPZqZpsAAAgAElEQVSbx3rL6zl+rYRbbfk17zdbp9/Pvub329q6Kc2zm49PzX9BGK5NODooAUhzUHLRHAdpjoZr0FohzUHJmT0uVmmWpkvG+fGfPbPgKt6xY3PRWbXNXm40tUGaHa4yUU79yIvzosySrJeKkc9neazcdLsjx5JNnum8gf/o6TYSFEjz4hiHp4a4i/WL9Mr5vbk1k0+Nnsgd1FrfpiQ5twwUr5m8of2SwLHpaU9iTHNgemYPhDSb5Rm2Npul2eu1yZrUZ1ikz7BAy/Yki/UZ/iLOec9Zx3pktvh8BjU0Rx0s3d0s05fWTNGlNEXrObu9kh8i2iLcnUrGWbR5pvOEmu1cz4Aus51nZ0JnEQ9VePI0Jd08uZqSay3galv4tRJxlf2eF3JZ5xslHAFIczh+po+GNJsmGq4+SHM4fqaOjl2aTTXcpnqqWZrrR3lma5ZjlVGWx+irudDIHxIixiqL3C7bG3hd5I2RhA7SvBCrjEmWLtYyFlk9zu2l4yPzy3JJ1vgaFmO9TvI1y3bQpq4rjMUG0mwMZeiKIM2hERqtYClIsxcgItbnRaZZoE+kWa7lOWeq1VbkmiV7gF97KTIjeHddHa2tq6flvJXnvTVzLNuTtJwfks3uZclexrKd4Cx2rSwlJkuI6SXDZCkx/ZrHguslxmTpMcpMemlC0X1k0jS3QCvZZqFWmW/JgGelfMHrBULuCPgcC3w1F0izXdGHNNsVD0izHfGANBuIQ7VJs8xq3dT3ODX2/TfOLC+cIEomfJla9n6a7rqNpnrfTybGnXkJUbVL8zTPwitiLIK8/8JLavvGwGs5dHU1dQszycuvp6t6eMx4RAXSHBHYANVCmgNAi/CQapFmLwhTkrEuItbnWagHuKu4CLef0l7Lgi3rV9cllGAv53Wsu2pq1OtlLN3ddfJ5nVrbWsY0Z6ZHaXKElxLjnlJ1vKSYLGkok1RKqZvMW0osO6O57KeWIJvu54nYwnYzd65OxmyrsdvcrXy2vtMZ061nMuf/V4l/h8u8H1L0WPB0k7OUn3rf4/wffljGuS+kOU7apc8FaS7NKM49IM1x0i5+LkizgThUgzQnJo5Q05m/pqbT/4XkuS7yn3yqexc/bqfUsvfx7NZXGiDqv4pqk+ZZ/mPTnUnex92uD12Yz/ILwW3LrnUyySuuJ8kkX72Ml+aKqWBMc0ygPZwG0uwBUoy7QJr9w5aMtAi0ZK5P80NeD/L4axHu89xFfCAzq8Zey2s/pYdFuocluoeFczXLtcpgs3QvZ6lu50cHP1/F7yfJ2RYrsga3rMUta3IXXkqM1+7OifhxVY28ljW/1drfLOAmip7RfJYnUpvlZcTm3AIuk6slWMTVJGv2zWgOaTZxB5irA9JsjqWJmiDNJiiGrwPSHJ7hkl2nWb5FbzrLonz2b6hhcH4cunyrPbXsAzS14i6W5Xda8Q13NUjzgQv7nGzy+ReVMO/re2nB3XtVz1aWZBbk7NhkGaNcy90ay1EgzeWgXvickGZ7YiEtgTRHGw+ZrExJNXf/liz1AI+tHuSHTHB2Rl5nBdyvYEurJYvdwTLtiDRnryVbze+1cyZ7JXevTvKv29Us4u0s3+38u1ey2wn+zEu5aCkx15Ji6rO5lCPYItpZAU9Mzgu4ZMhNFD1TudSl5Vue6+y2yoCzeKvPVXa8RT3Xn+sZztXnPMP5XK23CSQhzSaiZ64OSLM5liZqgjSboBi+DkhzeIZLSpqlq1njuSeo+exDvHbyk6qrmvOfZwdNrfwfaXLl3Y4oW1aWojQfHjjEYsyTd2XHJecvA3VZ15ULxiTLGOWGOjsmpIE02/MDAmm2JxbSEkizPfEY48Ua+mbSdGoypcZZi1iLYItoD3DWenx2jic5myHpRi4yHqSINIs8i0RL9lq6jLfU8XvchbyN3xPplm7jLbIfy7hIuch5kKKz1vndx2s4Ey7resua3rUz0qVcupY7Aq4y4K4u6UHO6+WYnHRztjtT35uVbpbq7KoMNU0rqb6hmSZT6dxSY7KTzorrc+gu6ervkmyXdi/nxz7+CECa/fGKem9Ic9SEvdUPafbGadG9Kr57Nv+HKYIsoizCrMdoyTfEqd730cSaf6q2Xr8xNoDUdxVLQZqPDr2xQJBFlqfS85PUbGi/NDd5l57Aq6W+1TerOA7AmOY4KHs7B6TZG6e49oI0x0W69Hn8rNOc4hm/hySDzV3Bh/j/zGEWank9NMcP9R5vWbbVeyzf8rlkuxebRbxYC5tZpju523iHbFmiu1i0OyXLzeOa5f1OFu4ulfV2PpfPOnmfVgM9i+T/f8lsS9Hy7ZZqJd7Zz5V481re7ux3LS8lJmIuxWTX81LRdGfI57i7vR7/reSae8fJe+p5dg1wea67q6vn/Lnsp0vGlSWfS3SqxEE1FUizXdGGNNsRD0izgThUqjRLl+umvsd4nPIPcv8JCg7JJEtGWTLLlfIfRSVK89sjxxaOS2ZJHp0eyd2Ra9rWLcwkc9frjsZOA3ds9FVAmqNn7PUMkGavpOLZD9IcD2cvZ/EjzV7qy99HFt3KSTRnq5Vws0iLXA+LYLNcy/NBzmoP8xht9Tor4uk5f2cUJVQCrQQ7K9K5rUg1Z7E5m62EW4k3j9lWcl7HI7YjLq5Mdm7cN59SSTdnvaU0pPuooTatMs21Gc6Kc3Zcis6K6xbqLunyOk4p1+eX5IF7gtOFme/5zLmaLb3OEW2ZYd19jM66y2eSdRd5V/vJRHCcPbehQJptiMJ8GyDNdsQD0mwgDpUkzQ2DT1Oy/ylKDjzJ45SfzV19qocn8up+N03zVpaGqrRSCdJ8ZuzUfCaZxyVLJnlwciCHennzytx45Gt48i4Zk9zbtKzSQqHaC2m2J2yQZntiIS2BNNsTj6ilOeiVjmYz1U4WO/tQmW4W7mxWW6RbZ73lPXk9wWLut0hX8K7spGfz0s0ynctqOxKustr8nhJuFm0Z022yBB/TPMfZ7kmehI0fss1MqInVangpsdzztLwnn8v72eey1JjaP/tQdWSPdT+fy9bDci/HxlFkuc65RBPLdvahn9c1c/q/0Xmfn8/V8PMEb9V+rud18nn2WL2V/WR/2Vcdw8+lPo5poQJpjiPS3s8BafbOKso9Ic0G6NouzTJmqfHsf6XmMw8tWCJKui9Nrv44Z5X/Ic20bTdAonxV2CjN5yf7nEzyOUeQ5XnfBC9pki3dTT3ZTHJ28i6e4Xpl6+ryQTR4ZoxpNggzZFWQ5pAADR8OaTYMNER1tkpzkEuadnUfH2Z5drLYjnDLOO1h3Y1cvy/dyznrLbLttzSyMKuMNgt0F3dr7qiV1wmWaqdbuZLvbBZb9uvgXLZ0MW9bZKx2cGn22/pw+7u7r+fGhGerdGfO9Thy+UhP4qbPXJedwE1e57rAy348A7vMxB53WZD5znZLb0jU0HRNB2V4BnYpKlsuS59lS6Zpfe65WhotOyGceyI4WQbN3U0+7utaSueDNNsRTUizgTjYKs3S/brl7T/n9ZR5nHJ2SQvbJ/QKGg4bpHloapDlOCvIvASUiPLp0ZO5S2praL9odut17c46m0utQJrtiSik2Z5YSEsgzfbEYylJc1CqepKzERbtERZsWdJrgruKy/JeI7wVqZZZx8f5c1k7e5ilO8g4bWlfC4u0LOsl62TLuO119c4EaN0yAzm/v7qpgWZSGbXkV5I/XyYZbd7K5GnVVtQ64LJueLYs6JbuWh/cPcacO3vnljaTw/Qkb+r5zAW1JJoUt/jHyTV/PXH3uHFph14yTbfJPf5cfc4CL93e5z/n9cyzUq8+z+vent+VPs5rNX0uSLNposHqgzQH47bgKKukmccONZ7/MbUd+fp8Vpm/7ZMloiphQq+g4SiHNI/NjC4ck8zLQR0feSt3CU3cBcpZJ3mH0+2aM8mXdF4W9BIr6jhIsz3hgjTbEwtpCaTZnnhAmoPHQmYbd0TayVaPyJJe/JynBVNbeT3M3cbVe7xfkCW+3K3Ts5DXyVJfaikvUkt+SVmXleq1/L56nX1fZiOf399sd/Lg5Cw7Mm/mdJ357mhpoImxCzTLyQApMuGbW+Lrpt7OXUjd9Fn29ZR6XTvD2XKeqV0dk52l3bIrvkjO3e0TMZ+tLzJ3DK9OkmlYWfhy+IueTMP8RHL5O2WS/BnvU6ioOousfCJtkTatWHuVbRirsj2QZgNht0Ga5VvJ5lN/SS3H/l9KTBxRVyXf2o2v/19ofO0/XzAJhYFLtq6KOKQ5xf8BqHWSs12tX+Fs8pHB13MsErxOp14jWc9ufUX3ZutYxdEgjGmOg7K3c0CavXGKay9Ic1ykS58H0lyakck9JEMtmWoR7hRJBtsR7lGW6nF22vGaORpIyVrazvjsAd5XxFzW1jZR9LrZKoPNXcYlg53kLHeCzytLgEmR8d2S/Zai5buZ95HsuBR1jIFZyk1cT5R1RDGm2d0tXdoumXDp4q6Lu3u7vOdM9ObIuHqtlktzsuXO6yHOns93Z3cLu3xerox6JHH5xz5nBoykEagU0mzgHiinNCfGDvEM2I/zUlGPc2b5JXU1Mvv11PIP0tSKD/F4knUGrtD+KqKS5jcHD9Ozp3ZnH79aMCZZqEj36pvXvJNuW/tu2rXuPbS8eX7Mj/3UomshpDk6tn5rhjT7JRbt/pDmaPn6qR3S7IdWtPuWGtOsu5Gnsl3Hp9ghzvMa2um5Gjo7y9tshjvDn59mGZcia2xLOcHdy02XJIv18mxmW3c3V38TcJdzKTJxWntWvlfyF+oi5iLo0vVcyjI+VupISOacM+K2lSikuXzXKJPF8T0ggs6PGh7LT3LHyGt+X23d78u+eh91XIajlN03+37uOO4SXyP3mRyv6snWJ/vlvyev1T3Jx2TPrdoh+0o75BxyLjmnvJ+tV57Xf/DV8uHDmXMEIM0GboZySHPD0B4lyo3nn6DE+BvqKqaW/bYS5anlHyrevcTA9dpYhQlpTvMvrgMX9tGe08/Qc6d3054zz9DApLPepC4ixSLHIskiy0t1THLYGEOawxI0dzyk2RxLEzVBmk1QNFMHpNkMRxO1lJJmE+fQ8iwZ7gxPnCbjt0WyJZcp3cylDHDme5zfk3JixpFt6WouY76lSDfzdPZzE21y1yEzmXdkpVp1LecvBFp4krXurJw7Y705Q8sHSdZcinymM+Nrs93S9djxMO1bWtIchoQdx2JMsx1xgDQbiEOc0py88HM1sVcTC7N0ZZmrbc6K8gdpkoW52PIBBi7T6iqCSLMIsYjxS+eepxfP7lHjk8dnxhZcp0jxjhU7WZB3qcdlXVdazcGWxmFMsy2RIII02xMLaQmk2Z54QJrtiUUc0mzqaqdZmsfVEl+85czgBM9EPsESLu9Jd/Jxec3biayAj7N0y2JVapv93HnO7+X2m+UazBXpYC7yLF3L1ZbfaOGu5SLYzTIRG+c1RchbeMkp2crr5uznLfz5Kh7TPDedoeQsv8/HSB0tPDN6g+Glxsxd8dKuCdJsR3whzQbiEL00z6qschPLsmxlTMcsLwswme2Cneq5w8BVVHYVpaRZZ5H3shxrST427Iz9dheR4h0rWZJX34ZMcohbAtIcAp7hQyHNhoGGrA7SHBKgwcMhzQZhhqyqkqQ55KUWPVzGbotESzmZ7VIuWe+BbBZcstwyujvFdt3H0i1FPhNJV8dku6OHmeG81LXpCdlkv3YW6fZsZny1ZMaVXDuzoUtRXdB5K++vzmbG3ePDq3Vm9FKMC30OaQ5CzfwxkGYDTCOT5gIzYc/xlPoT6+6hsQ2/j/XvXLHLl+bX+g/Sof79dOjCq2p7sP9VOjt2ekG0JYu8uedq2tK7nbbwdnPv1XRp5+UG7ghUAWm25x6ANNsTC2kJpNmeeECa7YkFpDmaWEhX9DTnsPVYcDmLCHeKs+B6PLi8p5cXk+eyxFhtXQ0Np2epPyvsfWoWdJO58IXX6x4jrmc8lz3cs6TLaz1TujzXs6XLc+nOLuPD9XOpQ8pSmbgN0hzNz4ffWiHNfokV2N+0NC86E/b6z/B45fl16gw0v+KrOD/RR6+xFJ+YOES/OfEyizLLMr+ezX5jKxfYmGhyBFkey7YrQd7Ss41k7WQU8wQwptk806A1QpqDkovmOEhzNFyD1AppDkItmmMgzdFwDVprsTHNMp5bLx8ms5tLF3Qpery4ZMYHs1nwMzxPjIi5CHpfdgZ0PSu6HGNyZnSv16lnUNf7uwVdv+ceR67fk+y5Hjuu39MTvOXqcmXU9XvuzLp+L4jIQ5q9Rjja/SDNBviakubamWFqOf6n1PL2n/JU+s40+unmTTS+8ffVGsuyUHu1lzn+xlSE+KCIscoi84Of902cW4AGWeTy3imQ5vLyd58d0mxPLKQlkGZ74gFpticWkGZ7YiEtiXMisBT/XTfJXcwnOdHhPNyvs++zeE9yojv3eW7f7Hvqc72vbF31cd3TRkeMm4mVdGJv4C7u9TKzOi+BVs/S3aAfnClv4LHmMoZc9vnV5k1mTopaQhGANIfC5xxsQpqbzv41dRz6P9TkXlJm2nfQ6KbP8YzYH+DJvexbjsAANk9VnBs/w4LsdLEWST7I29f6Dyw4VrLIkkHeseZauqRtC7LInshGuxOkOVq+fmqHNPuhFf2+kOboGXs9A6TZK6no94M0R8/YzxnilGY/7Qqyr+TCp1myZ1i6pYv5DAu0TOamHvzceX/W2YclVTLjM9nPpvkz2U+OUfuwgMuc6vJcttO87zT3BHfe531kq17Pus4lddfwuXQbnK2c2+tM7HPXbQ9y6TjGMAFIswGgYaT5/2/v/mLsqO47gB8K2MbYZr0mgDEtrnGghhIqVw1SBCLtQ0RUFSz6AA8lohBV8MALPJDUElJRofAAfeABlBJqCmpJq6aGPhShqEGyGzWRmqq1iAsYQxqbQAAbTPCfxpDeM2aW6+u7e+/MnNl77PlcaeX13nPOnPn8Znb3u/PvlA9f6oXlO8PCd//1SFhe+rmw76L7wqEVv5dgZsfXEPFmXeWR4xiOy7A8+NinYUeR1y6/MJy1fGF4c8/B42ulT9DZuqY5n8IKzfnUIs5EaM6nHkJzPrUQmvOpRZzJiRSa85L9dDZlmC+CeQzyReCOwftIeD8SyI98/fpVK3JdjU7NS2hOUO46ofmU/TvDaW88FRbvfjKcfHB378jyb4X9594Y9p93Y4g3++rCKz7eKT7mKT7uKd7RethzkaNDeUfr9Wf/TnFn60t6N+4afI26e3YXPHNaR6E5n2oIzfnUQmjOqxZCcz71EJrzqYXQnFctyp8b+c2qezMSmhPUvFpo/mURlBfvfios2Lu1uKnXgRiWV32ld5T5NxPMJs8h4tHiF9/5r96p1T8K297+z5nPB2d7+qlLimBcfPRC8udXfiEsWzj6xmdCc151F5rzqYfQnE8thOa8aiE051MPoTmfWgjNedVCaM6nHkJzglqMG5oX7N1ShOUYmuPr4Gd+v3dk+SvhYO95yyfKKx493rH35eII8qvvvVyE5BiWB0+xLtf3N1ZcHD531m8XAXm2o8jj2AjN4yjNXxvXNM+f9aglCc2jhOb3fadnz6/3XEsTmvOphdCcTy2E5rxqITTnUw+hOUEtRoXmkw/uCot3/U1Y/NOnwsn7Xw+Hl1xcHFmOp2N/vGB5ghnM/xDx+uMYjl/a82JxJ+sde1/qheP/Dj/Z9+Ohk4lHkON1xxetuKR41NNlZ60Pl/Qe/RS/nuIlNKdQTDeG0JzOsulIQnNTwbT9hea0nk1GE5qb6KXtKzSn9Ww6mmuamwqm7e+RU2k9644mNNeV6+s3V2g+7Y2/C4t71y4vfPe7vUdGLS6uWY5h+RdnrE+w5PaHOHB4f3jt/VfDzr2vhJ3vvdI7eryj+Pe193eEvQf2HDOB5Yumw5rlnw2/fsbasOaMC8Kaqd7ny9f2/n9BsoA8bK2F5va3hSpLEJqraLXbVmhu17fq6EJzVbH22gvN7dlWHVlorirWbnuhuV3fqqMLzVXF2mkvNCdwHRaaF+z9915YfrK42ddJH/8iHPrMl8L+lTeGAyv/MMES2xkihuGdvVD8Wu/j1U8+j1/76c93H7PAJacu7YXjGIZ7H1NHQvEFn4TlqUXzf/RcaG5nm6g7qmua68ql7yc0pzdtMqLQ3EQvbV+hOa1nk9GE5iZ66fsKzelNm4woNDfRS9dXaB7D8tqbNoYdrx8JjmtXrwrPbLr3qF79oflXDr1VhOV47fIpH74cDp9+Ye/I8h8V1y5/vOCsMZbWXpN4SvWuD35chOB4GnX89+0DPyuuO46nWc923XF8xNNF0xcXd7G+aHpd77Tqy4pTrReevKi9yVYcWWiuCNZyc6G5ZeAKwwvNFbDmoanQPA/IYy5CaB4Tah6aCc3zgFxhEUJzBax5aCo0zwPyGIsQmkcg3XzHA+HdPftmgnIM0Cuml4XHH7prpmcZmk978x+LwLzw7ed7p2Kf2juqfCQs/9/U5WOUonmTGILLj5/0wvGbH74R3uh9bdcnAfln+9+acyHTp63oPc7pshBvznXB1IXFo51iUB7n7tXNZ99sBKG5mV/q3kJzatH64wnN9e3a6Ck0t6Fab0yhuZ5bG72E5jZU648pNNe3a6On0NyGavUxheYRZlduuD3ceev1YcPVVxQtNz+3NTz46LfCls0Pz/R8+7V/O/IYqV1P9k7F3h8OTf9uce3ygZU3VK/ILD32HXo/xCBchuJdH/xv8XkRintfn+0GXIPDrVyyKsQjxytPXxXi5+ct/bWwundqdbwxVwzNx+tLaM6rcq5pzqceQnM+tYgzEZrzqYfQnE8thOZ8ahFnIjTnVQ+hOY96CM1z1GHb9p3hhtvuCU8/cne4dN2aouUxX9v+YDj8yuPhlJ//KHx02urwP9N/EA6cfV34aOE5RfsYaMtXPD26//rgwx9/1Dsa/On1wod/+dHM+4cOHwzxyPDbvY/YJz7KadQrht4yDMdgfM7p5xbB+FeX9kLyJ2F51BjH6/tCc16VE5rzqYfQnE8thOa8aiE051MPoTmfWgjNedWi/LmR36y6NyOhuWFoPunPTpqXrWbRKYvC6qnV4bxl5xUf8fPzzzj/qP/HNl4ECBAgQIAAAQIECBAgkE5AaE4Ums9Zck7oD61LFiwJZy4+86jRY9Dtf8X3Y7vytfDkhSGOU75i+6lFU0UwHhwr3SZgJALpBZ544olw1VVXhdWrj97m0y/JiAQIECBAgAABAgTaFRCaR/gOu6Z54/2PhRdf2DTTc67nNLdbPqOXAk7PzmtbcCOwfOrh9Ox8ahFn4prmfOrh9Ox8auH07HxqEWfimua86uGa5jzqITSPqEOVu2fnUdJuzkJozqvuQnM+9RCa86mF0JxXLYTmfOohNOdTC6E5r1qUPzfym1X3ZiQ0j1HzKs9pHmM4TVoQEJpbQG0wpBuBNcBL3FVoTgzacDhHmhsCJuwuNCfEbDiU0NwQMHF3R5oTgzYczpHmhoCJugvNCSCdnp0AseEQQnNDwMTdhebEoA2GE5ob4LXQVWhuAbXmkEJzTbgWugnNLaA2GFJoboDXQlehuQXUGkMKzTXQBrsIzQkQGw4hNDcETNxdaE4M2mA4obkBXgtdheYWUGsOKTTXhGuhm9DcAmqDIYXmBngtdBWaW0CtMaTQXANNaE6AlngIoTkxaMPhXNPcEDBhd6E5IWaCoYTmBIiJhhCaE0EmGEZoToCYcAihOSFmgqGE5gSICYYQmhMgOtKcALHhEEJzQ8DE3YXmxKANhhOaG+C10FVobgG15pBCc024FroJzS2gNhhSaG6A10JXobkF1BpDCs010Aa7CM0JEBsOITQ3BEzcXWhODNpgOKG5AV4LXYXmFlBrDik014RroZvQ3AJqgyGF5gZ4LXQVmltArTGk0FwDTRcCBAgQIECAAAECBAgQ6IaA0NyNOltLAgQIECBAgAABAgQIEKghIDTXQNOFAAECBAgQIECAAAECBLohIDR3o87WkgABAgQIECBAgAABAgRqCAjNNdBil2tv2hh2vL676L129arwzKZ7a46k22wCVY3nar/5ua1h4/2PHbOoF1/YpAA1BarWJy5m2/ad4Ybb7glPP3J3uHTdmppL1i2lvX0j/fZUpT433/FA+P4Ptx81Cd+X6tckpb19o34dhvWsUpuv3/eN8Ozz37NfJCxBSn/7RsLCNMgU5X7id6q09ZhtNKG5hnP8JefdPftmgnL8RrRiell4/KG7aoymyzCBqsaj2sdv8A8++q2wZfPDwBMIjPIetogrN9we9rz3QfGWb/D1i5Da3r5RvxYpvnfF/aL/+1L8JWjrD7b5XlWjLFX3jVH29o0aRZilS9XaxN+r/vyuW2b+uPrwN78d/v6fv2u/qFmS1P72jZqFGNKtam3KIWIN/vrpfykO4PmdKl095hpJaK7hHH/Q3nnr9WHD1VcUvX3zqIE4oktV41Ht1ShtjUZ5z7Y0R5qb1yG1vX2jeU36R6hbn3IM+0j9eqS2t2/Ur8Vgz9S1STezboyU2t++kW67qVubS754UxGWnb2XrhajRhKaRwkNvD/sFxq/5FREHNG8qvE47YedSuQUyHp1G8dbaK5nO6pXG/b2jVHq47/fpD7lUhxRG9+7v2Ub9vaNerUY7JWiNvFo3Cs7dznSXKMkbfjbN2oUYkiXurWJZ2L88Q1fDhecf67QnKYUY40iNI/F9Gmjuht4xcV0unlV46rtI+7g6TCdBq+48nW8y0X4A1NF7IR/tBvX3r5Rv0ZN9o241LL/vV/76syZTPVn062e82Fv36i3TTWpTf9lPf7Qna+/fWP+ahMv4Xnrnb3FJaHj/lyvNzu9BgWE5orbRJNv/hUX1dnmVY2rtu//5dQP4eqbWR1vobm687Ae82FfLsO+Ub1mKepz643XhNtvua76wjveYz7s7Rv1NrImta+YYfkAAAmXSURBVCmXGM/AePTJZ4PvS9VrMB/+9o3qden/XbT/muS5gvDgafFCcz33ur2E5hpyw64/iHdm9s28BuYsXaoaV21fnlqkZvVqVtVbaK7nPKxX2/b2jWa1qlOf0tzNXPK2t2/Ur0+d/WJwaeU1nJ68UL0ObfvbN6rXpOxRpTaz3bU8juUPrvVrMG5PoXlcqb52de90V2NRne0yyjhezxFf5aO+RrUfvEuqO54327RGeQ/WR2hu5t3fO7W9fSNdbeJIVevjhjrp/FPb2zcmV5tRdzZPN7NujFR13xjlb99It91UrU3/kh1pTleHcUYSmsdRGtKmyvPuai6i893mMh4Wyka1L5+rHWEvX7/OI8IabmGjvPv/qBE/7782Lf5/emqpm7rUrEFK+/6x7Bs1CzLQbdz6lL/wDFuq65rr1SKlvX2jXg1m6zVubWL/Qfv4NWeGNatHSn/7RrNaDPauUhuhOa19ldGE5ipa2hIgQIAAAQIECBAgQIBApwSE5k6V28oSIECAAAECBAgQIECAQBUBobmKlrYECBAgQIAAAQIECBAg0CkBoblT5bayBAgQIECAAAECBAgQIFBFQGiuoqUtAQIECBAgQIAAAQIECHRKQGjuVLmtLAECBAgQIECAAAECBAhUERCaq2hpS4AAAQIECBAgQIAAAQKdEhCaO1VuK0uAAAECBAgQIECAAAECVQSE5ipa2hIgQIAAAQIECBAgQIBApwSE5k6V28oSIECAAAECBAgQIECAQBUBobmKlrYECBAgQIAAAQIECBAg0CkBoblT5bayBAgQIECAAAECBAgQIFBFQGiuoqUtAQIECBAgQIAAAQIECHRKQGjuVLmtLAECBAgQIECAAAECBAhUERCaq2hpS4AAAQIECBAgQIAAAQKdEhCaO1VuK0uAAAECBAgQIECAAAECVQSE5ipa2hIgQIAAAQIECBAgQIBApwSE5k6V28oSIECAAAECBAgQIECAQBUBobmKlrYECBAgQIAAAQIECBAg0CkBoblT5bayBAgQODEEHv7mt8OjTz57zMrceuM14fZbrgtXbri9eG/L5oePaRPfm55aFp7ZdG/x3qixLvniTXOiTU8tLZZz8x0PhO//cPvQtvd+7athw9VXhGtv2hh2vL47lP8vG29+bmvYeP9jYe3qVTPzGhxonHlc8flLw7PPf2+m6zVf+kL4iz/9k0rLHWc9ToytyFoQIECAAIHxBITm8Zy0IkCAAIFMBMpQ9/Qjd4dL162ZmVUMv9/Z8h8zoTOGzMvXrwuPP3TXTJuv3/eNsPUH22bC9LhjDYbbwdAb349jvbtn36yhN7YpQ/PgvMqvzxWa+/nLkD1sHsPeq7LccdYjk03BNAgQIECAwLwICM3zwmwhBAgQIJBKIIbh8gjqXGMOhsdt23eGG26756ijvOOOlTI0r5heVhyRLkN/Oa8YpEeF7nHmMVtoHne5QnOqLdU4BAgQIHCiCAjNJ0olrQcBAgQ6IhBPr/7smvOOOoI826rHAPjKzl3FkeV4tDUGx/4jz1XGisuY6wjvOGEzzuHiC88Pb72zN5x95vLi1Ol49Du+4tfaDM3jLnec9ejIpmY1CRAgQIBAISA02xAIECBA4LgSKINrOenymuLZVqL/WuAXX9h0VLOqY40KzeNc0xzD6+XrLy6uYY7zifOLR53/8q/+ofXQPM5yXdN8XO0OJkuAAAEC8yAgNM8DskUQIECAQDsC5anN5ejDTtsug255k7DZZlJlrCbXNMfQXN6cK86lPPpd5QhvnWuax11ulXm0U1WjEiBAgACBvASE5rzqYTYECBAgUFMgnuYc7xw9eDR52LXMoxYx21ijjjSPOr26PD07hubyrt1lAK8SVpuE5lHLrTKPUY7eJ0CAAAECJ4KA0HwiVNE6ECBAoCMCMQD/7T99pzhSO/gqw+DgXbVnC811xkoZmuP84zXV5WOxqoTVJqF51HKrzKMjm53VJECAAIGOCwjNHd8ArD4BAgSOJ4H+U6j7jyj334G6/0Zfcd3mCs3xbtrxNe5YqUNzv32VsNo0NM+13CrzOJ62HXMlQIAAAQJ1BYTmunL6ESBAgMDEBPpv7lVOYrZrlkednl1lrFGhedwbgQ07Ul4lrM42j/K08tKkvMa7/7TwwaINLteNwCa2WVswAQIECGQqIDRnWhjTIkCAAAECBAgQIECAAIHJCwjNk6+BGRAgQIAAAQIECBAgQIBApgJCc6aFMS0CBAgQIECAAAECBAgQmLyA0Dz5GpgBAQIECBAgQIAAAQIECGQqIDRnWhjTIkCAAAECBAgQIECAAIHJCwjNk6+BGRAgQIAAAQIECBAgQIBApgJCc6aFMS0CBAgQIECAAAECBAgQmLyA0Dz5GpgBAQIECBAgQIAAAQIECGQqIDRnWhjTIkCAAAECBAgQIECAAIHJCwjNk6+BGRAgQIAAAQIECBAgQIBApgJCc6aFMS0CBAgQIECAAAECBAgQmLyA0Dz5GpgBAQIECBAgQIAAAQIECGQqIDRnWhjTIkCAAAECBAgQIECAAIHJCwjNk6+BGRAgQIAAAQIECBAgQIBApgJCc6aFMS0CBAgQIECAAAECBAgQmLyA0Dz5GpgBAQIECBAgQIAAAQIECGQqIDRnWhjTIkCAAAECBAgQIECAAIHJCwjNk6+BGRAgQIAAAQIECBAgQIBApgJCc6aFMS0CBAgQIECAAAECBAgQmLyA0Dz5GpgBAQIECBAgQIAAAQIECGQqIDRnWhjTIkCAAAECBAgQIECAAIHJCwjNk6+BGRAgQIAAAQIECBAgQIBApgJCc6aFMS0CBAgQIECAAAECBAgQmLyA0Dz5GpgBAQIECBAgQIAAAQIECGQqIDRnWhjTIkCAAAECBAgQIECAAIHJCwjNk6+BGRAgQIAAAQIECBAgQIBApgJCc6aFMS0CBAgQIECAAAECBAgQmLyA0Dz5GpgBAQIECBAgQIAAAQIECGQqIDRnWhjTIkCAAAECBAgQIECAAIHJCwjNk6+BGRAgQIAAAQIECBAgQIBApgJCc6aFMS0CBAgQIECAAAECBAgQmLyA0Dz5GpgBAQIECBAgQIAAAQIECGQqIDRnWhjTIkCAAAECBAgQIECAAIHJCwjNk6+BGRAgQIAAAQIECBAgQIBApgJCc6aFMS0CBAgQIECAAAECBAgQmLyA0Dz5GpgBAQIECBAgQIAAAQIECGQqIDRnWhjTIkCAAAECBAgQIECAAIHJCwjNk6+BGRAgQIAAAQIECBAgQIBApgL/D/JuGKa8AcT9AAAAAElFTkSuQmCC",
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""
]
},
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}
],
"source": [
"dynamics.plot_history(colors=['darkturquoise', 'orange', 'green'], xrange=[0, 0.4], \n",
" vertical_lines=[0.1])"
]
},
{
"cell_type": "markdown",
"id": "57e7c2b9-c693-4e16-92f6-6e0a94b18a2b",
"metadata": {},
"source": [
"A possible conclusion to draw is that, in this case, the earlier part of the complex (compound) reaction `A <-> C` cannot be modeled by an elementary reaction, while the later part can indeed be modeled by a 1st order elementary reaction, with kinetics similar to the slower `A <-> B` reaction"
]
},
{
"cell_type": "markdown",
"id": "e9069c36-6852-4530-bd51-7a18aaeb4eb7",
"metadata": {},
"source": [
"**The intuition:** imagine `A <-> B <-> C` as a supply line. \n",
"`A <-> B` is slow, but the moment something arrives in B, it's very quickly moved to C. \n",
"The slow link (`A <-> B`) largely determines the kinetics of the supply line."
]
},
{
"cell_type": "markdown",
"id": "18171c4e-eb73-42c7-a5b7-c74c61357b20",
"metadata": {},
"source": [
"### While it's a well-known Chemistry notion that the slower reaction is the rate-determining step in a chain, we saw in this experiment that the complex reaction could be roughly modeled with the rate constants of the slower reaction only after some time. "
]
},
{
"cell_type": "markdown",
"id": "106971a6-169a-41e8-98a5-7d74fead715c",
"metadata": {},
"source": [
"If we were interested in early transients (for example, if diffusion quickly intervened), we couldn't use that model."
]
},
{
"cell_type": "markdown",
"id": "43c44071-8633-4a25-a236-3ce6f8295de5",
"metadata": {},
"source": [
"#### In the continuation experiment, `cascade_2_b`, we explore the scenario where the 2 elementary reactions are much more different from each other"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a485900d-f5ef-4bd3-9c4b-3896ad3de241",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
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"name": "python",
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