\n",
" \n",
"## Introduction\n",
" \n",
"As you know, a new epidemic has overwhelmed the world, COVID-19 jeopardizes people and changes our habits. It is easy to realise that knowing how illnesses spread is vital to our own protection. How can we predict whether a disease will cause an epidemic, how many people it will infect, which people it will infect, and whether or not it is dangerous to society as a whole ? Also, how can we determine which techniques to use in fighting an epidemic once it begins ? One way to answer all of these questions is through **mathematical modeling**.\n",
"\n",
"In this work you will have to review different epidemic modelings relying all on the representation by graphs of a human network called a **contact network**. A vertex in a contact network represents an individual and an edge between two vertices represents a contact between two individuals. The disease only spread from individual to individual if they are in contact, so through the edges. This representation is actually really common in research, and a lot of state-of-the-art modeling are built over it. From these different models you will be asked to draw conclusions from experiments on varying contact networks.\n",
"\n",
"For readability and ease of use, this project will be carried on a Jupyter Notebook, hence code and question answering have to be written in this unique file. This is a **DUO** project, no group of one person will be accepted, the duo has to be composed of same TD group students, if the number of students in the TD group is odd we will accept one group composed of three students.\n",
"\n",
"**BEWARE:**\n",
"- If the code does not provide good results, its readability as well as its comments are essential for the corrector to potentially find some notation points.\n",
"- The specifications of the functions have to be strictly respected.\n",
"- Do not neglect written questions they stand for an important part of the notation, you are not only evaluated on the coding. Also, even so a written question may not ask you directly to code or provide results from code, support your arguments when possible with a runable example is very welcome and sometimes even expected.\n",
"- Any initiatives and additional efforts bringing contents and thoughts out of the question scope may result in bonus points if pertinent.\n",
"\n",
"Deliverable: You will deliver your work on moodle before **23.01.2022** in a **.tar** containing the notebook with your codes and your written answers, and the different graph figures in .png you will generate. The corrector will use the student N7 computers for running your code, so take care of verifying that your work is running as expected on these computers !"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"## Environment and packages installation\n",
"\n",
"**mathematical modeling**: For evaluation, coding questions have to run with no additional packages ! Only the ones present here ! However if you want to use another package to go further in your answer and add bonus contents, take care of separating the cells and precising which packages you are using."
]
},
{
"cell_type": "code",
"execution_count": 97,
"metadata": {},
"outputs": [],
"source": [
"# Import originaux, qui ne fonctionnent pas avec toutes les version de Julia\n",
"# De plus Lightgraph est déprécié, depuis genre 2 ans\n",
"\n",
"# using Pkg\n",
"# Pkg.activate(\".\") # Path to Manifest.toml and Project.toml\n",
"# using LightGraphs\n",
"# using GraphPlot\n",
"# using Colors\n",
"# using CairoMakie\n",
"# using StatsBase\n",
"# using Plots\n",
"# using JLD2\n",
"# using Compose"
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"\u001b[32m\u001b[1m Activating\u001b[22m\u001b[39m project at `~/Documents/Cours/ENSEEIHT/S7 - Graphes/projet`\n",
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/Documents/Cours/ENSEEIHT/S7 - Graphes/projet/Project.toml`\n",
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/Documents/Cours/ENSEEIHT/S7 - Graphes/projet/Manifest.toml`\n"
]
}
],
"source": [
"# Import packages\n",
"# Marche en Julia 1.8.0 et sur les machines de l'enseeiht\n",
"using Pkg\n",
"Pkg.activate(\".\") # Path to Manifest.toml and Project.toml\n",
"Pkg.resolve()\n",
"\n",
"# Remplace LightGraph\n",
"using Graphs\n",
"using Graphs: smallgraph\n",
"using Graphs: stochastic_block_model\n",
"using Graphs: barabasi_albert\n",
"using Graphs: random_regular_graph\n",
"using GraphPlot\n",
"\n",
"using Colors\n",
"using CairoMakie\n",
"using StatsBase\n",
"using Plots\n",
"using JLD2\n",
"using Compose\n",
"using Random"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"## Part 1 - SIS model\n",
"\n",
"SIS is a compartmental model, ie a model where the population is divided into subgroups that represent the disease status of its members. SIS stands for Susceptible $\\rightarrow$ Infected $\\rightarrow$ Susceptible where the susceptible group contains those who remain susceptible to the infection, and the infected group consists of those who not only have the disease but are also in the contagious period of the disease.\n",
"\n",
"\n",
"Combine with a contact network approach, this model can capture contact patterns (family, company, friends). Each vertex represents an individual in the host population, and contacts between two individuals are represented by an edge that connects the two. The probability of transmitting the disease from an infected to a susceptible individual along one of these edges or contacts is $\\beta$ (=**mathematical modeling**).\n",
"\n",
"In order for a disease to begin spreading through a network, the disease must be introduced into the population, either through infecting a proportion of the population or through infecting one individual. As time moves forward, the disease will spread away from those initially infected, and two things may occur simultaneously at each time step $t$. First, each infected individual will spread disease to each of its contacts with a probability $\\beta$. Secondly, each infectious individual will recover at a rate, $\\alpha$, at which point the individual will then no longer infect any of its contacts. After the disease has run its course, we can determine how the disease affected the network by calculating various quantities that help us better understand the outbreak.\n",
"\n",
"###### P. Van Mieghem, J. Omic, R. E. Kooij, _“Virus Spread in Networks”_, IEEE/ACM Transaction on Networking (2009)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
" \n",
"### 1.2 Introduce the infection\n",
" \n",
"We denote by `state` a vector containing the disease status of each vertex where Susceptible=0 and Infected=1. Then `state` is an `Array{Int32,1}` of length the number of vertices. This array in addition of a graph (represented internally by an adjacency matrix or an adjacency list) will be the data structure of our model.\n",
" \n",
"In `Array{Int32,1}`, `Int32` refers to the kind of data in the array, here 32 bits integers, `1` refers to the dimension of the array, here we have a 1-dimensional structure so a vector"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"Question 2 (written): What do you think/predict about the influence of the initial number of infected people and their locations on the evolution of an SIS model epidemic ?\n",
"\n",
"> Plus le nombre initial d'infectés sera élevé, et plus l'épidémie va se propager rapidement. De plus, plus la répartition initial des infectés dans la population est uniforme, plus la propagation de l'épidemie sera rapide."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"### 1.4 Simulate and understand the epidemic\n",
" \n",
"In the SIS model of this project, every disease is characterized by:\n",
"\n",
"* The infection rate $\\beta$ representing the chance of infection when being in contact with an infected individual.\n",
"* The curing rate $\\alpha$ representing the chance of being cured of the disease.\n",
"* The effective spreading rate $\\tau=\\frac{\\beta}{\\alpha}$ representing the capacity of the disease to spread. More the disease infect easily ($\\beta$ high) and less it is cured easily ($\\alpha$ low) more $\\tau$ can be high.\n",
"\n",
"We are now willing to understand what are the influences of these parameters as well as the contact network shape on an epidemic."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"Question 4 (written): The function `SIS` you implemented launches one run of an SIS model on a given contact network. As it makes use of randomness, one run of spreading is stochastic. Then what simple method can you propose to provide a prediction of the disease spreading on a given contact network ?\n",
"\n",
"> Pour obtenir une prédiction d'un modèle SIS, on peut simplement executer la simulation un grand nombre de fois et ensuite tracer la moyenne de ces simulations."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
" \n",
"Question 5 (code): Implement the function `Simulation_SIS` (respect the header and the specifications).\n",
" \n",
"###### The corrector should be able to write `predictions, taus = Simulation_SIS(net, nbinf, betas, alphas, t, nbsimu)` with your code."
]
},
{
"cell_type": "code",
"execution_count": 111,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Simulation_SIS"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"\"\"\"\n",
"Take a contact network, different diseases (defined by different parameters alpha and beta), a number of initial infected people and process nbsimu simulations of SIS over t time steps. You will provide the prediction of the percentage of infected at each time t as well as the spreading rate of each disease.\n",
"\n",
"* PARAMS\n",
" - net (SimpleGraph): graph representing the contact network\n",
" - nbinf (Int32): number of infected at the start of each simulation\n",
" - betas (Array{Float64,1}): array of infection rate on edges\n",
" - alphas (Array{Float64,1}): array of curing rate on vertices\n",
" - time (Int32): number of time step\n",
" - nbsimu (Int32): number of simulations\n",
"\n",
"* RETURNS\n",
" - (Array{Float64,2}): the prediction of the percentage of infected at each time step and for each disease. The first dimension contains the time steps and the second contains the diseases\n",
" - (Array{Float64,1}): effective spreading rate for each disease\n",
"\"\"\"\n",
"function Simulation_SIS(net, nbinf, betas, alphas, t, nbsimu)\n",
" taus = zeros(length(alphas))\n",
" prediction = zeros(t+1, length(taus))\n",
"\n",
" for (i, (beta, alpha)) in enumerate(zip(betas, alphas))\n",
" taus[i] = round(beta / alpha, digits = 2)\n",
" for _ in 1:nbsimu\n",
" state = new_state(net, nbinf)\n",
" _, X = SIS2(net, state, beta, alpha, t)\n",
" prediction[:, i] += X[:, 2] ./ nbsimu ./ length(state)\n",
" end\n",
" end\n",
"\n",
" return prediction, taus\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"Question 6 (written): Run the 2 scripts below and describe what you see. Conclude on the influence of $\\tau$, $\\beta$, and $\\alpha$ on an epidemic we can model with SIS.\n",
" \n",
"> Il semblerait que plus $\\tau$ est élevé, plus la limite du pourcentage d'infectés sera élevé.\n",
"> De même le rapport entre les valeurs de $\\beta$ et $\\alpha$ semblent impacter la forme de la courbe, pour de petites valeurs la courbe sera plus \"douce\" que pour des grandes valeurs (cf les coubes de même $\\tau$, mais de valeurs $\\beta$ et $\\alpha$ différentes)."
]
},
{
"cell_type": "code",
"execution_count": 112,
"metadata": {},
"outputs": [
{
"data": {
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",
"image/svg+xml": "\n\n",
"text/html": [
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Script launching predictions on different diseases on karat7 and printing the precentage of infected at each time step.\n",
"betas = [0.05, 0.1, 0.01, 0.4, 0.04, 0.05, 0.005]\n",
"alphas = [0.05, 0.1, 0.01, 0.1, 0.01, 0.1, 0.01]\n",
"\n",
"predictions, taus = Simulation_SIS(karat7, 2, betas, alphas, 100, 1000)\n",
"plot = Plots.plot(predictions, label = taus', xlabel = \"Time\", ylabel = \"% of infected\")\n",
"png(\"img/q6_1.png\")\n",
"display(plot)"
]
},
{
"cell_type": "code",
"execution_count": 113,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": "\n\n",
"text/html": [
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Same as before but applied on n7_2A.\n",
"betas = [0.05, 0.1, 0.01, 0.4, 0.04, 0.05, 0.005]\n",
"alphas = [0.05, 0.1, 0.01, 0.1, 0.01, 0.1, 0.01]\n",
"\n",
"predictions, taus = Simulation_SIS(n7_2A, 100, betas, alphas, 100, 100)\n",
"plot = Plots.plot(predictions, label = taus', xlabel = \"Time\", ylabel = \"% of infected\")\n",
"png(\"img/q6_2.png\")\n",
"display(plot)"
]
},
{
"cell_type": "code",
"execution_count": 114,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": "\n\n",
"text/html": [
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Same as before but applied on toulouse_neigh. May be a bit long to run.\n",
"betas = [0.05, 0.1, 0.15, 0.25, 0.35, 0.45, 0.55, 0.65, 0.75, 0.85, 0.95]\n",
"alphas = [0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2]\n",
"\n",
"predictions, taus = Simulation_SIS(toulouse_neigh, 100, betas, alphas, 100, 100)\n",
"plot = Plots.plot(predictions, label = taus', xlabel = \"Time\", ylabel = \"% of infected\")\n",
"png(\"img/q6_3.png\")\n",
"display(plot)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"Question 7 (written): Change the initial number of infected in the scripts above, is it in accordance with your answer in Question 2 ?\n",
"\n",
"> On remarque que plus l'on augmente le nombre initial d'infecté, plus le pourcentage d'infectés dans la population converge rapidement. On peut le voir notament avec la tangente à l'origine qui est de pente plus importante pour un nombre d'infecté initial élevé."
]
},
{
"cell_type": "code",
"execution_count": 115,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": "\n\n",
"text/html": [
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Change the initial number of infected\n",
"betas = [0.5]\n",
"alphas = [0.2]\n",
"\n",
"plot = Plots.plot()\n",
"for i in [5 10 50 100]\n",
" predictions, _ = Simulation_SIS(toulouse_neigh, i, betas, alphas, 50, 100)\n",
" Plots.plot!(predictions, label = i, xlabel = \"Time\", ylabel = \"% of infected\")\n",
"end\n",
"\n",
"png(\"img/q7.png\")\n",
"display(plot)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"Question 9 (written): Describe the figure and draw conclusions on the epidemic behavior for different degrees $d$ on regular graphs. Thus, in addition of the inner properties of the disease ($\\alpha$, $\\beta$, $\\tau$) what other parameter is essential in the spreading ? Finally, what analogy can be done with real life from this experiment ?\n",
" \n",
"> Le degré $d$ du graphe représente le nombre de connections par individus. Ainsi plus $d$ est elevé plus individus se connaissent entre eux et plus l'infection est rapide. On l'observe sur le graphique, le taux d'infectés est directement proportionnel à $d$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"## Part 2 - SIR and SAIR model\n",
" \n",
"Unfortunately SIS model is valuable for diseases we can catch back since a cured person can get ill again. This is true for the flu, the cold, etc. However COVID-19 might create immunity for whom already got it and SIS can not take into account immune or dead persons. That is why we propose in this part to consider another model more adapted to COVID-19 called SIR. It stands for Susceptible $\\rightarrow$ Infected $\\rightarrow$ Recovered where the susceptible group contains those who remain susceptible to the infection, the infected group consists of those who not only have the disease but are also in the contagious period of the disease, and the recovered group contains those who were ill, got cured, are not contagious and can not get ill anymore.\n",
"\n",
"###### M. Youssef and C. Scoglio, _\"An individual-based approach to SIR epidemics in contact networks\"_, Journal of Theoretical Biology 283 (2011)\n",
" \n",
"One limitation of SIR is that it does not model the reaction of humans when they feel the presence of the epidemic. Indeed, if feeling threaten or surrounded by infected, an individual may change its behaviors: wear mask, wash its hands, etc. This result in a smaller infection rate. That is why in this part we will also consider a variant of SIR called SAIR which stands for Susceptible $\\rightarrow$ Alert $\\rightarrow$ Infected $\\rightarrow$ Recovered. A susceptible individual becomes infected by the infection rate $\\beta_0$, an infected individual recovers and gets immune by the curing rate $\\alpha$, an individual can observe the states of its neighbors, then a susceptible individual might go to the alert state if surrounded by infected individuals with an alert rate $\\kappa$ on each contact with an infected, an alert inividual becomes infected by the infection rate $\\beta_1$ where $0<\\beta_1<\\beta_0$. In our simple SAIR model, an individual can not go back to a susceptible state when he got into the alert state.\n",
"\n",
"###### F. Darabi Sahneh and C. Scoglio, _\"Epidemic Spread in Human Networks\"_, 50th IEEE Conf. Decision and Contol, Orlando, Florida (2011)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"### 2.1 SIR\n",
" \n",
"The vector containing the disease status `state` has to change a bit since we added a new state. Hence it will be an `Array{Int32,1}` where Susceptible=0, Infected=1, and Recovered=2."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
" \n",
"Question 11 (code): Implement the function `Simulation_SIR` (respect the header and the specifications).\n",
" \n",
"###### The corrector should be able to write `predictions, taus = Simulation_SIR(net,nbinf,betas,alphas,t,nbsimu)` with your code."
]
},
{
"cell_type": "code",
"execution_count": 122,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Simulation_SIR"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"\"\"\"Take a contact network, different diseases (defined by different parameters alpha and beta), a number of initial infected people and process nbsimu simulations of SIR over t time steps. You will provide the prediction of the percentage of infected at each time t as well as the spreading rate of each disease.\n",
"\n",
"* PARAMS\n",
" - net (SimpleGraph): graph representing the contact network\n",
" - nbinf (Int32): number of infected at the start of each simulation\n",
" - betas (Array{Float64,1}): array of infection rate on edges\n",
" - alphas (Array{Float64,1}): array of curing rate on vertices\n",
" - t (Int32): number of time step\n",
" - nbsimu (Int32): number of simulations\n",
"\n",
"* RETURNS\n",
" - (Array{Float64,3}): the prediction of the percentage of infected, the percentage of susceptible and the percentage of recovered at each time step and for each disease. The first dimension contains the time steps,the second contains the diseases, and the third the status(Infected: [:,:,1], Recovered: [:,:,2], Susceptible: [:,:,3])\n",
" - (Array{Float64,1}): effective spreading rate for each disease\n",
"\"\"\"\n",
"function Simulation_SIR(net, nbinf, betas, alphas, t, nbsimu)\n",
" taus = zeros(length(alphas))\n",
" prediction = zeros(t+1, length(taus), 3)\n",
"\n",
" for (i, (beta, alpha)) in enumerate(zip(betas, alphas))\n",
" taus[i] = round(beta / alpha, digits = 2)\n",
" for _ in 1:nbsimu\n",
" state = new_state(net, nbinf)\n",
" _, X = SIR2(net, state, beta, alpha, t)\n",
" prediction[:, i, :] += X ./ nbsimu ./ length(state)\n",
" end\n",
" end\n",
"\n",
" return prediction, taus\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"Question 12 (written): Run the script below and describe what you see. Why the infected curve does not behave the same as for SIS ? \n",
"\n",
"> On observe la présence de la nouvelle coube \"Recovered\" qui vient retirer progressivement des indidividus de la population infectable. Ainsi, on observe que le graph converge vers un état final, et non vers un état stable comme dans le cas du modèle SIS."
]
},
{
"cell_type": "code",
"execution_count": 123,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": "\n\n",
"text/html": [
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Script launching prediction on one disease on n7_2A and plotting the percentage\n",
"# of infected, susceptible and recovered at each time step.\n",
"predictions, taus = Simulation_SIR(n7_2A, 2, [0.3], [0.2], 50, 1000)\n",
"\n",
"plot = Plots.plot(\n",
" [predictions[:, :, 1] predictions[:, :, 2] predictions[:, :, 3]],\n",
" label = [\"Susceptible\" \"Infected\" \"Recovered\"],\n",
" xlabel = \"t\",\n",
" ylabel = \"%\",\n",
" palette=node_colors\n",
")\n",
"png(\"img/q12.png\")\n",
"display(plot)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"Question 13 (written): As for Question 6 script 2 plot the evolution of the percentage of infected for many $\\tau$. Describe what you see.\n",
"\n",
"> Globalement $\\tau$ semble déterminer la hauteur du pic maximal de l'infection, plus $\\tau$ est élevé, plus l'infection est importante. De même, les valeurs de $\\beta$ et $\\alpha$ semblent déterminer la longueur du pic, plus celles-ci sont élevées, plus le pic d'infection sera court dans le temps."
]
},
{
"cell_type": "code",
"execution_count": 124,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": "\n\n",
"text/html": [
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Equivalent experiment as for Question 6 script 2\n",
"# Script launching predictions on different diseases on karat7 and printing the precentage of infected at each time step.\n",
"betas = [0.05, 0.1, 0.01, 0.4, 0.04, 0.05, 0.005]\n",
"alphas = [0.05, 0.1, 0.01, 0.1, 0.01, 0.1, 0.01]\n",
"\n",
"predictions, taus = Simulation_SIR(karat7, 2, betas, alphas, 100, 1000)\n",
"plot = Plots.plot(predictions[:, :, 2], label = taus', xlabel = \"Time\", ylabel = \"% of infected\")\n",
"png(\"img/q13_1.png\")\n",
"display(plot)"
]
},
{
"cell_type": "code",
"execution_count": 125,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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mzK1bt2pqamCtUSI15LYV7i9HEICr1CQyQqKQrMJ4bpMMelkejitLcvYNmXyI6EBMDpXOC4xZ5xow586NL0tzDwTEfG7rNobooCDIEEVEvGRM/fjx49euXQMAUKnUqVOnHj9+/K233tJHZN0w6USoFKlsIvluU2wBALhKLa2T5/3y0MATYd2jGyyuA9ei269akE6x+a5Rr++rK7uRc+2L4qzdgTFfmAkCiA4Kgjqrbq8tbCrWz3tFCENYlF7UGm1ubhaLxY6Oj/cJcHR0PHeO4OnZJp0IMRmGMh4vFCOREZYtHSCIvFlJ4xvuJJTygmMOPqa+DT3hBI4xo2Zfenj3j+STcwT2UX7Rq5lce6KDgqAnqttrrz5K0s97+Vt69yoRyuVyAACF8vgyS6FQZDKZTiLrMZNOhCoZjtKeGSXlODHaSiVWfB5RIb0YppJWl14KHLqO6EAggCCoS8AsR5/JxVm/Xjk42tZ9nF/0pzTGi/ZggyC9CbUJDLUJJDqKrllZWaEo2tDQoCm6XV9fLxQKiQ3JpCfLYDKMTH+mdAjXiSl6JCEqnpeqKj5rYRtBY1oRHQj0GEpmeEUsHTX7KgDg4r6hhelbVUrD/f2BIEOAomhkZOTVq1c1d69duxYdHU1sSCbdIsRkOEp/tkXowqw/Vk1UPC9VVnDMwRv2ixocOksQOmqTV8T7helbz/020CN0oXtIAkqmER0XBBHjl19+KSkpqaur279/f1pa2rvvvuvk5LRjx45du3ZlZmYCAFauXJmQkICiaGlpaXJy8s6dO4kN2KQToUqGkRnPtAjZ9gxpnRyTd+4yNQRyaWNjVXpkPMG/MVB3WDzH0FGb3ILm5aVsLMnZ6z1wubPvdIRk0n9ikGnicDh8Pn/lypWau2QyGQAwYMCAjs14J06cyGQyjx49yuVyU1NTra2tCYsVAGDiiRB7boyQREaYtvT2cinPvetqCASquH/axmUUmWJwgUFP41n5Rb2+r6k6827yt0UZ232jPrH3HA8AQnRcEKQ/Xa6FCA0NDQ0N7bgbFxcXFxenx6BexODaPfqEybBOXaMAAK6zgQ4Tlhccc4T9okbCXBgWM+VwaOwPD7J/vfj7iIr7p4mOCIKgbpl0IlTJ8E5dowAAjjOz7aHBJUJxa1l7c4nAKYboQKBesLQbMHTaCd+olfdSN904PKmh8hbREUEQ1AWTToSYDHt+LJCrSYQGVnatvPC4ned4WGXbCCF27uNi51x18p2ecf79pGNvNdVkER0SBOlJQ0NDZmZmd8sEi4uLDx8+nJVF/F+ESSdClQxH6Z1bhFQuGaWSpA1yQkLqDuwXNWoIgjr5TY+bl2TrPu7m3++knJrXWp9HdFAQpFs4jr/xxhvh4eFlZWXPP7p3796oqKiTJ09OnDjx//7v//Qf3tNMNxHiKjWCABK5i1kMXBfD6h1tqc/DVDILW7gZvXEjkSiugbNHz0sROEQnHZ956+x74tZHRAcFQbry448/hod3fdVSKBSffvrpH3/8ceDAgevXr//www9VVVV6Du9pppsIMSn2fHNQg+PEFD2U6jmeFyjPP+rg/Qacedg/oGSae0jC6PkpPEufq3+Mu31ppUxcR3RQEKRlpaWlv/322xdffNHlozdv3sRxfMSIEQAAZ2fn8PDwM2fO6DfAZ5ju8gnVc6vpO3BdmLU3m/UcT3fUary88MTgSX8QHQikTWQK0ytiqbP/WwVpWy7+Psw9ZIFH6CIylU10XFA/Ia2Ttz4Q6+e9LIN5nWYdqtXqhQsX/vDDD2x217/SlZWV9vb2CPL4y72Dg0NlZaXOA+2e6SZCTN65vloHli1d1qxQPVeAjRDNtTkUGodr4UV0IJD20RgWQcPWe4Qm5KVsPL832itiqWvgXBJKJTouyOgpxVh7hZ4qWZv7cQHjmSPbt2+3t7ePi4tTqVRdPkWpVKLok6srmUwmdm9e002EKmm3LUKEhLDtGe2PpGZexH9Drym5KHQ1lGWnkC4wuQ4RY7a2Nd7Pv/ldUeZO78gPnf3fQhDiv4RBxovrwuS69GJHCO3asGHDoEGDFi1ahOM4AODzzz9ftmxZVFRUxwlCobC+vr7jbl1dXXejifphwmOEL2zwcZwMZb5MdelFG5dRREcB6RzXwjMy/pcB47aX5R+5tH9kZfE/wNAW8UBQz2zYsCE2NjYsLCwsLAwA4OfnZ2FhAQBQKpWaNmJYWFhdXV1xcTEAQCKRpKSkDBkyhMCATbdF+HzF7adxnZlVSY36jKdL0vZqSVulhTCM6EAgPbGwjRg67URN6eV7qRsL0n70i1pl4zKS6KAgqHfmzJmjuaFSqd59993p06d7enoCAKZOnert7f3tt9+am5svWrRo2rRpS5YsOXLkSHR0dHBwMIEBm24iVMm6nTUKAOA6M+//t0KNqxESkXM1q0su2TgPh4WbTY2Ny0gblxGVxWdzE78quLXFL2qVlQPB+9RAUB+QSKRvv/3W0tJSc3fBggXm5uaa299///3+/fszMjLi4+MTEhKIixEAU06EmBwnd98iJLNQCocsqZWzhHR9RtVJTelFuO+SqULs3MfZuo0pLzxx+9InTJ6Df/RqvnUQ0VFBUC+QSKRVq1Z13B0/fvzTD82dO3fu3LlExNWZSY8RvqBrFGiqbxM6TIipZA0VN22cRxAYA0QsBCE5ek+Km3vd3uO11FPzEo9Ob23IJzooCOpvTDcRdllf7WkcZwaxy+rryhLNBAEUGpfAGCBDgJDILgGzRs9PtXaKSTw6LS9xjURE5KIrCOpnTDcRYjKc/MLddzlOTFE5kS3CmtKLQtdYAgOADApKpnuGvzd6XjKNaXn5QGz21f+TiWuJDgqCXqSysvLSpUsSSdcX0tzc3L1796akpOg5queZciLE0Of2YHoa04Ymb1JiclxvIT1LXV1yCa4ghDqh0LjuYctHz08mUxgX9sXcvrRSLql/+dMgSO9UKtWUKVNiY2MrKiqef3THjh2xsbE3b96cM2fORx99pP/wnma6iVAle9FkGQAAQkKYQrq4Sk/VGTppqctDyQw235WQd4cMHJXO9x+8JnbOdYREvrBv6N2kDXIp8at9IOhpmzZtGjp0aJcPyeXytWvXHj58eMeOHdevX9++fXt5ebmew3ua6SZC7IXLJzTYDvT2cmKGCatLzgvdYHMQehEG2yZkxDcjZ13EVNKL+2Jyrq2VttcQHRQEAQBAYWHhn3/+2d3+Sjdv3kRRdPDgwQAAOzu7AQMG/PPPP/oN8BkmvHzihQvqNdj2jNZiPRWu7aS65FLAEIL36IKMApNjFzTsK6/w9woz/3Np/3AH70leEe8z2DZExwURSdRU3FB5Uz/vZe85odOcPhzHExISNm/eTKd3vfyssrLS1ta2o+i2nZ0dsdswmW4iVElfXlOb7cCovNqgn3ieJhPXiVtLLewG6P+tISNFZ9sEDV3vHbHsfub2S/tHOPlN84p4n8awIDouiBhyaVNzbY5+3kvoGtspEW7ZssXX13fEiBHdFd3GMIxEetIOQVFUqVTqNsoXMt1EiMlx9IWzRgEATGuavEXZkzO1q7r0orXTcBKJos83hfoBGtMyYMhaz/AlRZk7Luwd4hIw0zN8KZXOIzouSN8s7QZYEvdNetOmTTExMb0quj1gAJHf+010jBBT4AgZQdCXlE97PF+mUt/DhDUll2ChbajPaAwL/8FrRs68IJc2XdgbnZ+2WakQER0UZEJ27NgxefLkUaNGjRw5EgAQFRVla2sLABCJRJqlFBEREY2NjQUFBQCA9vb25OTkYcOGERiwqSbCl00Z7cBxYIj0O18GxxT1FSk2LrCgDPRKmFz7sNjvh715WtxSen5PVEHaFpWineigIJMwYcKEqVOnTp06dcqUKQCAMWPGODs7AwBmz569fv16AACPx1u6dOnUqVO3bNny2muvxcbG+vv7ExiwiXaN9mTKqAbbntF8X6+Xj6aaLA7fjUrn6/NNof6KbeYSPvqn9uaS/LQfzu0Z5BGS4Bb8NplK/EabkCkgkUg7d+60trbW3F2yZImZmZnm9jfffBMeHp6RkTFr1izCK46aaCJU9WDKqAbbnl5+Wa8LlusrUizto15+HgT1GJvvGjHmZ1Hzg4KbP5z7baBbyAL34AWweh+kayQSaeHChR134+KeLAlDEGTKlCmaJiPhTLZr9OVTRjUY1jRFqxKT6a++TH15spUDTISQ9nH4bhFjtw1/6x+pqOrcbwNyrq2FVWkgCJhsIux5ixAhISxberu+5svgmKK5NsfSFi6cgHSFxXMMHbVpxIwLmEp2Yd/Q3MSv5RIC1ghBkOEw0a5RTIaRaT1qEQIA2PaM9gopz42l05A0GqszueaecAgH0jVNOvSJXF6Yse3CviFOvtM8w5fQWdZExwX1E21tbadOnVIoFPHx8R1jhB1kMllSUlLHXXd3d81sGqKYaIsQk+Eoo6c/O9uB0V6up4qjDRUpsF8U0hsGxzZ4+L9i51wDAFz8fVj2lc/gBk/Qq2tsbAwODj527FhSUpK/v//9+/c7nVBfXz9mzJhf/icrK4uQODuYaItQ1eNZowAAtgOj/KKehlLqy1O8Ipbq570gSIPOsg4c+qVXxPtFt3dePhArdIvzinifw3cjOi7IWO3cudPb2/vYsWMAgGXLlm3atGnXrl2dzqHRaIcOHSIiui6YbovwxZsRPo0poClESpUU02lIAABMJW+uu2NhG6HrN4Kg59GYlv6D14xdcMvMyu/GkSkpJ+c01RD8PR0yUmfPnn3jjTc0tydOnHj27Nnnz8Fx/MyZMxcuXGhsJH7jFBNtEWIyDLWi9vRsBLCEdHGljOeu22HCpppMnoU3HCCECESmst1DEpz9Z5bmHrh5egHHwtMz7F1rpxgAXlKGCTIod1pbz1brad/md1ydLajPXE41NbU1t+3s7GpqajAMQ9FnOuEcHBz27t1bV1eXm5t78ODBMWPG6CfaLploIlTJcPILd+XthO3AaC+X6joR1pcnWzlE6/QtIKgnyBSmR+hCt6D55YUncm98mQsQt+D5jj5TUTKN6NCgHpFjeLO+ylhjanWnI2q1umNnCQRB1Gq1+tlz7O3tOwYOf/7554SEBGL3IzTRRIjJsF7V0WbbM5rzdV6tsb48xTvyQ12/CwT1EAmlOPlOdfKdUvvw2v3MHfk3f/AIW+wSMItMYRIdGvQSEeb8CHPCqlMJhcLa2sft0draWoFAQCY/k2s60iQAYNKkSe+//35zczOfT1jApjtG2PPJMkDTIqzQ7VJCTCVrqb8LBwghw4NYOw8fMvmvqNd/b6rOPPfbwIK0LUp5G9FRQYZr1KhRHeOCZ8+e1ZTeBgBUV1dLpZ0vpGlpaWZmZh2l1whhoi1ClQzrYdFtDaaAphCpVFKsVx2qvdJUncGz9IHftSGDZSbwj4zfKWp+UJi+9fyeQS4Bs91DE+CWh9DzFi9eHBoaunjxYj6fv3379uvXr2uOR0REbN68eerUqZs3b05LS/P19a2urj548OCmTZuebiPqn4kmwt62CAECWLYMnc6XqS9PsYIlRiGDx+G7hcf9KGmrKMzYdmHvYCffaZ5h79LZNkTHBRkQW1vbrKysP//8Uy6XZ2RkuLu7a45v3bo1LCwMADB9+nQej1deXu7n55eamurr60tovKacCHu8oF6D40AX6XK+TH1Fis/AFTp6cQjSLibXPmTEN74DP3qQs/fSgZHWziN8Bq5gm7kQHRdkKIRC4fLlyzsd7FhTYWtr+/bbb+s9qG6Z5BihGmAKHKX27mdn2zPadbYxIaaSttTBAULIyNCYlr6DPo6de4PBsb36R3zGhQ/bGguJDgqCek2HibClpSUpKenFk2JramoSExOfL8CjU5gCJ1EQhNS7Lmm2A6O9TFeJsLEqw0zgh5IZOnp9CNIdGsPCP3r16PmpHDPXxKPTk0/Mrq9IJTooCOoFXXWNXrx4ccaMGUFBQXfu3Pnwww8/++yzTieo1erPPvtsx2hEBWEAACAASURBVI4d/v7+NTU1q1ateuedd3QUTCcqaS/qq3VgWNFUUkzZrqKwtf+hwT0IIWNHpfO8BizzCFv8KP9w1uVPKFSOZ/h7tu5jEcQku51MXkNDw9GjRxUKxeuvv+7o6NjpUYlEcubMmY67/v7+Pj4++g3wGTpJhGq1+oMPPvjuu+/mzp1bUlISEBAwZ84ce3v7p885cODA4cOH7927JxQKAQAymZ6qWgMAMDneqymjjyGA7cgQlUnNfTlaD6m+PNl30EqtvywE6RkJpbr4z3T2e6u65EJh+s95yd94hi9x9JlKQilEhwbpT11dXVhY2LBhw8zMzIKDg5OSkjpNh2lsbHzrrbcmTZqkuUsmk/thIszLy3v48OH06dMBAK6urtHR0ceOHVu2bNnT5+zevXvFihWaiUMODg50Ol0XkXQJ61OLEADAcWS06yARYippa/09OEAI9RsIQrJ1G2PrNqa+IrUwfeu91O88Qhe6BMyC5QNNxI4dO8LCwvbv3w8AoFKpmzZt2rNnT6dzDKrotk4SYXl5uVAo7Mhtzs7OFRUVnc65f/9+UlLSDz/8QKVSSSTSiRMnOqbYdqJWq4uKii5evKi5a2lpGRQU1PEojuNqtRrHe7GDvFKKkWhIr56iwXZgVCc39uGJL9ZQlcmz9EFIVK2/sk7hOI7jOLGrf0yT5pMnOooesbCNjHo9sqU+ryhjW2H6Vif/mW5Bb9NZAqLj6iMj+uSJdf78+Y5JoePHj58xY8bz5+A4fujQIQqFEhUV9fyGhd3pw+dPIr28/08niVAqlVKfqsFKo9HEYnGnc1pbW+vr6wsKCshk8pIlS5YvX3769OkuXw3H8WvXrpWUlGjuRkZGenh4dDyqUCjUajWG9WJrCEmrBKEAiUTS86dooFZqUZlUIpZot/5wbVkq1yq4D/EQSyqVIggCE6H+SaXSTvWLDRyV5eI39DtZe2XZvYOXD4y0dIhxCVrI5nu8/JkGxmA/efVz1T5VpXXK9GL9vDt9TAjCfWaiX1VVlWbMCwBga2tbW1urUqk6VVnz8fE5e/ZsTU3N3LlzDxw4MGHChJe+kVqt7sN1kslkvjQX6iQR2tjYPL2zRkNDg5+f3/PnTJw4UfPRTJs2TdOP2iUURRMSElatWtXlo5pESKP1ohZwO1DS2Co2u/e9NGxAYdSiMiqj5ztX9CSexlwn3+l9iYdoLBYLJkL9U6vVxvjbwmZ7Wdp86R+1vCRnX+bZ+XzrIK+IpcY1ImCwn/zzf4YIGUVY+hpvem4GvqbQtua2pgB3pwgdHBxu376tub1r167Fixf3JBEiCKKjz18nidDPz08ikRQUFHh7e+M4npycPH/+/E7nDBw4sKMqa01Njbm5uS4i6RImx8h9GiMEALAdGe1lEq0mQnVTdWboyI3ae0EIMlxUupl35AceYYsf3TuUcf4DGtPSK2Kp0DVWW9s8iZWSVnkbAECkaAcAiBUSNXh8RSaTyPT/7Z6BIiiT8rgRgwCETX2mUAaFRKaT9TdrQRdQBwvUgbDqd0KhsKamRnO7pqZGIBC8oCUdHx+/cOHCpqYmfWaBTnSSCHk83oIFC95+++3PPvvs5MmTfD5/1KhRAIBTp059+umn9+7dAwCsWLFi3Lhxbm5uXC53zZo1z9cg0B1MhqN9mDUKAACA48gQlUmtwrRWH1bUXIJSWLBCFWRSUDLNNXC2S8CMyqJ/8m9+fzdpg0fYYkfvSSS026+YMpW8QdrYJG2ulza1yFrbFWKxUtyuELcrxa1yUau8rU3e1ipvo6E0Lo2DAIRDZQMAWFQm8r8Uq8RVcpVccxtTYxLl42XBaqBuVzwzdqPElTKVHACAIiiHymZTWRwqm0NlM0h0AcfSgmFuTjfjM8wsGRZ8uhmfztPFR2TU4uLi/v777wULFgAATp8+HRcXpzleUlIiEAjYbPbT+zQlJiaam5sTuPUE0N06wu++++7nn3/et2+fk5PTxYsXNV20rq6us2bN0pwQHh5+/Pjx3bt3q9XqjRs3Tp48WUeRPA+TYVSzPk7m5jgyGnJatRhMU1WGhTBciy8IQcYCQVB7z/H2nuPrym4UZe7MS/7G3u9NsvOoGpWsXtLQKGlqkrU0SBqb5a0NkkZMjVkwzC0Y5lYMcx6dy6awzRl8R649m8ri0bhcGodH4/JoXApJm9c0FY6JFO3tinaRQtyuaK9tq5MCeZO0ubS1rEna3CBtapa2iJViPt3MimlpzuDbsKyEbGsblrUNW2DDErBMtYb+4sWLw8LC5syZY2ZmduDAgcTERM3xmJgYTdHt77//PjEx0dPTs66u7tixY9u2beufRbcpFMry5cs7tfP8/f39/f077kZHR0dHE7APrUqGM/vcNWrPkFTLcZWaRNbOP1tjdYaFLUyEkGlRA3WjpKmqvaaqvbaqvaa6vaaSadfOkXnlHXbP3N7G9wTOo6ysfDwt3KyYlnwaz5JpQUhSIZNQPp3X0eYTcUQcTufVU0pc1SxrqZc0NEiaasR1FaLqjOrsanFdrbgOAYiAaWnNEghYllZMC2umlTXLSsCysmJYUPr1wkpra+vs7Oxjx44pFIqcnBwHBwfN8d27dwcGBgIA5s6d6+joWFZW5u3t/fnnn7u5uREar0kW3cZkWJ+7RklUEt2KKqmSsR21Uw6tsSrDJWC2Vl4KggyZTCXLbyzKrb+XV194tyGfhlJt2TZCtrWQbRNmEzzBw8aOLTRn8BWy5tI7+4uzfzNrDPCKeM9S4P/ylyYUhUQWMC0FTMvnH2pXiOslDTXi+jpJfZ2kIaMmp1ZcVydpaJA0cmkcIdvalm0jZNvYsm1s2da2HKElg7BBMq2ztLRcuHBhp4NjxozR3LCyspo2bZreg+qWKSZClRTv82QZAADHkSkqk2glESrlbRJRhZkVwVuQQJCONEib7tbn59bfy63Pf9Ra4c539rf0ec097tNBy/j0rgfaqXS+14BlHmHvlheeuH3pE5RMdw9JcPSZhCCGuG7hxdhUFpvKcjFz6nS8U4M4syb7dHtNpahGqpLasm3sOMKn/2vNskKN8Gc3LqaYCDF531uEAACOI6P1gViojUiaam7zBYGIVkc1IIhYrfK2jJqc9Krb2XV3xUqJv6VPoMD3/bAEb3P3nvcHklCKk+9UR5/JVQ/O3U/fVpD2o3vIAie/6WSKrvZB0ycEIJZMC0umRaDgmXVlUpWsUlRd1V5TKaouaiq5XpZSKapulDYLWJZ2HKE9x9aeY+vAsbXn2tqwrElw5ZL2mOIluNe78j6L48iouNqglUgaq9It7IxpHRUEdQlX43kNBTerMtOrsypF1SHWARHCkLd8Jzny7JFXWBeBICQ793F27uOaa+8UZ+26l7rJ0WeKR+hCJtdBi8EbDgaZ7s53cec/s62jEldVt9dWiqrLRZVlbRUplbcq2qpa5K2OXHtnnoMzz9HFzBFT96KiCPQ8U0yEKinWl6Lb/8O0oSvbVCopRma8an9FY3Wme/CCV3wRCCKKRCm9VX07pTL9ZmWGNctqoG340tAFflbeWu/K41sHRozZKhFVPsj+7crBMZb2UR6hC41rMX6fUUhkR66dI9duEHgyq06mkj1qrShpffSotfzE/bON0mYCI+wHTDERYvJXahECBLDs6e1lUjOvV6pxoFbjzTVZcMooZHTqJA2plelJ5Wl5DQX+Vj7R9gMSgmZZdTVbRLuYHLuAIWt9Bn706N5fGec/pNJ57qEL7T1eM8HBBTqZ7mXh7mXxuD7zBeZxYuMxdib3C6TG1bhS3dvt6TvRLKt/xUTY1lhAZ1pR6UQuI4WgnituLkmqSEuuuFUnbhhoFzbeY/T6mE8Zeq/AQqYw3YLmuwbOrSm5WJS1KzfxK/fgBS4Bsyg0rp4jgfoNk0uEmBxHaaRXLOfEdmTWpb9qX0RjVaZ5L5uDlWL178Xq049wHhXYMhEHNrBjIi4cZIQt8ly1PwjSjvK2yiuPEi89vKHCVUMdo5aFJ/hZepOI3m4XQUhCt9FCt9EtdXeLbu8891uko88U95B3WLzOUzRNAZ1O37Jli0Dwom091P/7X0fNOQRoaoAax7VDp9sSmF4ifIX6ah04jowHR6pe8UWaqtMtbCN7cqYcAycf4XuL8LQ69VQX0r8iUJkKVEnU5WJ1Wr16VyEuVYF/hZMmOMGtwCGtESslZx9cvvDwaoOkcbjT4NWDPvC19CI6qC6YCfwjxmyVtdcUZ/929Y9xlvaDPEIXmcjwYYfff//9+PFe9I6qcKxJ2twgbWiQNta014uVYgHLyoYlsGEJrFlWZAPrasYwTK1W8/n877//XkdvYVg/sB6oZBhKe9WRfJoZBSEBebOSxu97eYjGqkzPsCUvPS2tTj3xosqPj8z3JB0dSWI8+Rd78j3uTLn6s3Rs4x38mwh0iI1xfL+DDFalqPpI4elLD68PEIYuDp4XbO1PePvvpehsG//Bn3lHfvj08KGdRzyJ1J8LuHTw9PTsbn+enmhTiO7W5+fW5efW30tszvEydw+1CQy1CfSx8CKTiF/CqFQqMQzT6ebtJpcIMRlOZmjhr5rjxBQ9ktD4fay3K5c2yqUNHAvPF592vVo97Ypqbwx5rMOL0lu8AzLWnnzwAT73OubHBzsHo7ZMmA6hXsusyTlScDq/8f5r7nF74rcaXaGTzsOHN9a7Bb/tEjCbCutivxCXyomyGxBlNwAAIFPJ7tTfu11zZ2vG7gpRlae5m4+Fp6+lp7eFhx7mQxHFBBMh9kpTRv9HM1/GMriPf2BNVRnmNqHIC79on69Qz7mu+nMEebjw5VmNhIBZ7qRprqRvc/ABJ7E/hsOmIdRTckxxsfTa0cLTAIAp3hO+HPIJtftdIAzfk+HD+rzi27+c3zPQwXuSR0gCy8yZ6NCMAJ1MHyAMHSAMBQC0K8T3GgvzG4r+eXD5+1vbUYTkb+UTYh0QbB3gzOtXSzmfJMKDBw8uXbr0pU9oamrSZTw6p5LhKE0LLUK2I7PsXG2fn95YnfHiYYy/y9TvJKqOjyJHWfcin1FJ4PMQUowN8uYVbJkfaVWQofdoQcRqkDYdv3/mTPEFHwuvpWHvhNkEER2RNplZ+YWP3iKX1D/I2Xf1z9fMhaHuIe8IHGOIjstosKmsjqQIAKgV1+XU5WXV5v6Vf0KqkgVb+wcL/IMEfs5mjsYy46Y7TxKhp6dnR41UlUr166+/ksnksWPHCoXCurq6y5cvNzQ0JCQkEBSn1mAyLSyEBwBwHBniSlmft6ForMrwifywu0f/KsGXpWKn48gDrPry4sOEyM3X0SmXsOwm9e4hKMvkmv3QS+BqdWZN9qmic9m1d2Ndhm2L22jH0UrRQENEY1r5DvrYK+K9R3mHsi6vptC4bkHz7L1eR4186139s2YJ4lwEcS7DAQB1kobs2tzs2rtHCk+3ytsCrXyDrP2DBH4efDdjrP325BoZHh4eHv54Nv97770XGRl57NgxJvPx1idKpfKdd955+PCh/kPULpU2Zo0CAFAaiWFDay+TcF17XfwQx5Utdbn8/33P6iS9Xv1hKnZlHNmP3/ffJwcWci2evCQFG3RK9c9o1J5lfL+akC60yFvPPrh8uvg8k8yY4DFm9aAPOzZq799QMsM1aK5L4Ozah1cf5OzNTVzv6DvNNXAO28zl5U+GniNgWsa5DNckxSZpc05dXk5d3pniC03SliBr/1DrwBCbABeeI9Fh9lQXjQWpVPrrr78mJiZ2ZEEAAIVC2bBhg729fXl5ecfmUsYIk2FkbXSNAgB4LqzWkr4kwraGAhbPkULtvLEZAECFg0VJ2PcD0VfJghoMMtgTg266gw87g10ehzqxYS40aQ9byw8XnLxeljLYYeD/RX3ka/mSiVr9EoKQbFxG2riMlLSVl9zZf+2v182s/NxDE6ydhr14wB56AXMGf7jT4OFOgwEATdLm27V3smpzDxecVOKqQXbhUXYDQm0CaYY96txFImxpaZHL5c/vF6w5Ultba+SJEKdYaOefhOvKrEltAsCqt09sqsnm24R0+dCPebgVHcxw09rf5MpAEpcKhv6NXRqHunNhLjRFmTU5f+WfKG4umeg57r8TdvBgBRYAmFwH/8Gf+Q76uOL+qXsp/865ttY9eIGT7zQy9ZXKRUHmDP4o56GjnIcCAMraKlMqb/2Zf3x98qZgQcAA2xDNLBsDHFDsIhEKBAIbG5svvvji6NGjHUs3VCrV2rVrGQyGl5chLqrtOZUMQ7WxfAIAwHVlFf1RqcbVvS3r0lybzbcOfv54Wbt6Yw6WOkHLY3qLvEkoAob+jV0ch/qaGdyvIKQ7qZUZu3MOYGpsmvfr/4r5rH/vit4HJJTq6DPF0WdKY1V6cdbue6nfOfpOcQuaD/tLtcKRa+fIfeNNnzdEivZb1VmZ1dmH8k9KVdIggX+IdUCoTZAj147oGB/r4pqLoujWrVvffPNNJyensWPH2tjYNDQ0XLp06dGjR9u2beNwuujQMyKYDCe/8oJ6DQoLpfLI4mo52653o+7NNVluQfOeP740Bf8oAHXTQbvtHS8Skwxi/8HOjUEDzGEu7P9y6/N3Zu1rV4oTgmZH2UcY4Hdwg2JhG2FhGyFtr36Qs/faXxP4gkC3kAWwv1RbOFT2SKchI52GAADqJQ1ZtblZtbkH7x0lIaQBwtAIYUiYTRCxY9VdNz6mTJmSlJS0cePGGzduVFZWWltbBwQE7Nq1KzY2Vs/xaR0mw7XVIgQAcF1ZbSXiXiVClVIibn3EtfTudPxQCf6wXX10lK7qOGi6W0efU12NJ3vx4GWx33rQ8nB39v6SlkdvB86IdRlujFP4iMJgC/2jV/tErqgoPHEv5d85V9e6Bc1z8psOy3lrkdVTs2wetpbfqso8WXR2Q+pmD75ruDA43CbY28JD/5WMuu2FGzhw4LFjx/QZin6oZJi2WoQAAK4rs+lum+0Qi54/paUul2vp06nyU4sCrEjDj4xEKbr8BZjhRlJgIP48ljKeLDCJqYKmpaq9Zs+dgxk1ObP8pq6PWU0xsIqRxgIl05z8pjv5TW+szijJ3pOf9r2te7xb0DwzQQDRofU3zjwHZ57DNJ+JMpX8Tl1eRk32d2nb6iQNIdYBYTZBQdb+ehtQfNGfCo7jZWVlbW1tgYGBeghFP7RSdLsDz5VVeqqmV09pruligPDTW9jrTshAgc7/yed5kkpE6vjzqmuvkeH6wn6jSdr8+91DVx4lTvYav2LAEv1vjdQvWQjDLYThcmnjw7sHU08voDOtbL2muwdOR8k0okPrb+hk2gDb0AG2oQCAJmlzRk1Odm3u4YJTIkV7oMDX38In0NLHm+alu+6Nrq+FOI6vX79+8+bNbW1tdnZ2FRUVAIBly5YpFIodO3boKBT9wGQYqo0F9Ro0PoVERqT1CoZVT2eiNtdm27iMfPpIfov6VBmeP0VPExm+DENLRdica9jhkSjcvMnYyVSyA3lHThadHes68sD47VyacQ/hGyAaw8Ir4n3P8PdqH14pzNhVlL7J2e9N18A5TK4RT543ZOYMfpzLsDiXYQCARmlzTt3drJrcvx+cFynEYTaB4cKQMJsga1av5+q/WNdto3Xr1n3zzTcLFy7csGFDx8FRo0b997//VSgU2o1Az1QyXFvrCDW4Lqy2EnHPz296bsrolrv4uz4oT1/LbBAAfotBWxXqlbcwPb0lpBvXypJnn15SK67/ddyWJaFvwyyoOwhCsnEZFTpm97Dpp3BceeXgmJRT82ofXVercaJD688sGPwRTkOWhSbsjvtx17jN4cKQjJrsRedWNEi1XOmzixahSqXasmXLN998s2LFiuvXr2/btk1zPCQkpL29vby83M3NTbtB6I0aU6sxNenVtqfvhOfKbCuRmDu1tRzZRmLzUK45yjVHeRYUW1eKnWunkxWyZoW0ic1/crxZDg6X4vf01RzUoJDAsVjy4NOqrXn4+35wXpzxKWur3JKxs0navDb6o0CBH9HhmBC2mUtgzDq/qFVlBcfuJn2tVLS7Bsx28nuTZmw7dRgdAdNynNuocW6j1ECt9YHDLhJhXV1dW1vbmDFjOh03MzMDADQ1NRlvItTuAKEG15VVcbWhuXY73SecYu2ItTVhbU3K2vKWk7uslm6k2DyzX3ZzTTbfOujpOdm7C/HXHEnWep+6wqWAU7Fo9GnMywyJs4M9pEZDppL9nv/X+bJrs/2nTfKKRxHit4szQSiZ4eI/08V/ZlPN7ZI7v5/fM0joMsolcI6lXY+22oZehS6mz3SRCDkcDolEqqmp8fX1ffp4Xl4eAMDGxkbrQeiNSoaRtbEH09OY1jRlu1TF4HDjZoCnxnLFaeeb9m8UrNiCoE8+5E79opgabM/HD40k5lrmzEGOjELfuKhKnUB24cBcaOjUQH3p4fWdWb/7m3vtid9qweATHREEzG1CzW1CFTFflt07dPvSSgDULv4zHX2n0hi9mEkOEa6L5hGHw4mOjl6/fr1YLO4otNbW1rZq1arAwEBjr6+m9RYhJmqiqR6goXPBszOaWJGjyZbCtnMHnj7YXJPNt3mSCE88xO1ZINySsCQ0SICsCkInXcKkKqJCgHqkqLnk/QurD+Wf/GLwxx+FLoFZ0KBQ6Tz30IS4uTfCYn9obSy4sDc67cxCOIJoRLqeNbply5ahQ4d6e3v7+fm1tbUtWLDg7NmzTU1NFy9e1HN82qXS0h5MT2s5so3nFtnexLB+7iH+1PdrNy2he4fR3B6vQGquzQ4Z8U3HCVvy8A+IHqJb7k/KalAvSsJ+HwY72QxRu0K8I2tvcuWtBYEzx7nFkhBEJBIRHRTUNU2FGqVCVF5w/G7Sv5TyNpeAmc5+b9KYWp7lCGlX11fhkJCQjIyMIUOGpKeni0Siv/76KzQ0NDk5eciQIXqOT7swLe3K20F2L11Z/dAqdmBbieT5R0lsntnU95sP/qCWSwEAUlEVAIDBsdU8mtWoftQOXncifq7K9sHo7Ub17kL47dXgpFSmzzvzPkpC97/2n9fc42CZGKNAoXJcA+eMnHkhMn6HuOXRhX1D0s4srCtLBEBNdGhQ17pdU+3p6Xnw4EEAAIZhKNpP2gqYDEO1N0aolkubD/1kPvMjqgtH1lShkmBkZucXZ/gPlOWmtJzcxZ+2rNMA4U95+Hu+JDLxeRCwyOD4KHTw36ogcySiT1sBQ1qnaQhm1GR/NujDUJv+U9HCpPCtg/mxwQFDvyjLP3rnxpeYUuLs/5aT7zQ66/n+I4hIXV+GExISCgsLNbc7suD9+/enTZump7h0A1Nos0XYemYv3TuM5hGMkBCOA7PtYReNQgCA2aR35fezZfduPT1AWC8Dpx7h73gZQBoEAADgwUO2R6PTrmBNcqJDgQBIqkib+/d7VJS6N/5nmAWNHYXKcQuaN2rWpQHj/iNufXTx92Gpp+bXlF5Wq+FCXkPR9YX49OnTjY2NnQ42NjYePnxY9yHpEKbAUap2WjzK2jJpdiJvwgLNXa4rs8veUQAAQmPw31zefOin5prb5v/bhnBnPj7FhWRuSKWaJjmTJjsjb9/AYPcNgdoUoq+Tf9h+e8+6IZ8sC0+gw2pe/QjfOjh01Hdj38kQusbmp20+uzsiL+Xf4tZHRMcFdZMIu1RZWWlhYdxzgnGlmqSlstay3FRGyFAS83EtD802FN2dTHMPINu5NVXd5lsHAQCUONhRgC8jeprM8zZEoFUS9c95cLCQGGlVmQvOfEAn034d92OAle/LnwAZITKF5ew/Y/ibfw+e9Cemkl79c/yNI1PKCo5hKtgbQ5hnxgjPnDmzb98+AEBra+vatWufTntyuTwpKSkqKkrfAWoVJsfJWlo+ISvI5Iyc2nGX68IUV8swebddr+TooeSz+ykoCwBwsVLtwgF+fIMbjaOSwB/D0ajTqiE2SLCFwYXXj4mVku2392TW5KyJWh5sDXc5MAlcC8/AmHX+0WuqSy48vHvwzrW1Dt6TXQJmci2Me/NzY/RMImxtbS0pKQEAYBhWWVnZ2tra8RCDwZg+ffpnn32m7wC1ClfiJI4W9lxQK2SK8qKORREAABIZYTsw2kolfG92l08RIU1cqq047QJ78GuHSvDprgbXHNRw4yI/R6HTrmCZE8kcuJ+5XqRWZnx3a9swx6g98VthX6ipIaEUO494O494SVvFw7sHk469yeQ6uATMtvccj8JdRPTlmawwY8aMGTNmAAAiIyO3b98eGhpKUFS6gitwrRQalRflUJ28EOozv6Y8d1ZrcXt3ibCpJtvKd6zo0l/UAaP/LgMbIgx3D6SpLqRz5eplqdiemH4yW9hgiZWSrZm7c2rvfh79cRAsGWramFx736hPfAauqCm9XJJ74M71z+29Jrr4z4D7IOpB11khLS2t/2VBAACmUGtlsoys8DbdK6zTQTN3VktRt8OEzbXZlt6jKELn2+fP+/ERW6ZBdzz+FIWm1akPFMPBQh1Kr86af+Z9MoL+Fv8TzIKQBkIiC91GR0/cP2r2VQbL+ubf71z+b1xJzj6lvI3o0PqzrhPhd999t3nz5k4H9+3bt3btWt2HpEO4AtfKZBlZQSbdu3Mi5DgxpfVylbSLKdE4rmxryDcTBHDHzWGnHprubOgJhkUGf45AV9zEilrhHFLtk6pk36Vt25S2bdXAZR9Hvgf30YWex2DbeEd+OHp+asDgNfUVKed+G5Bx/oOGyltEx9U/dZEV1Gr1hg0bni+u7ebm9u9//7utzYi/mGAKHH3lrlGsqU4tFVNsXTodR1CE68xsfdBFo7CtoYDFcyJTmMDO4x7ZfmLDpVeMQQ8CzZF1oehbVzE5XOykVYWNxQlnl6vU2J74n8JsgogOBzJoCEISOA2NjN8ZNy+FZ+l7+9LHF/bFFGXulEsaiA6tX+kiKzQ0NDQ3NwcGdl7GGxAQoFQqHz58qI+4dANXamGMUFaQQfMOtPGR1AAAIABJREFUBV0Vu+K5s1qLu0iEzbV3NAsnzlfgF7xmItf/VGNGUOV6iS/Jg4d8mg4zoXaogfpIwelPrn45L+DNTwcuY1GYREcEGQ0aw9wjbFHc3Bthsd+3Nuaf3xudemp+9YPzatwIriSGr4usoNlxorm5udPxpqYmAACOG3q33gtg2pgs0+UAoYaZO7u1q2HClrocM+tAAMDhEnVIiA9FYC9Jv/yKYejH9mj05CP1yUdG/I9uIJplLZ9c/fLyoxvbx2wa5TyU6HAgY2VhGxEe9+O4dzKFbnH3M//zz+6wOze+bGsoIDou49ZFVrC0tHR0dNy9e3en47t372YymV5eRrzGBX/1yTI4Li/KoXmFdPkgy54ub1EqRZ2/ozXX3uELAuUY+Lscf8MZ4Y6ZKbr0J1AbwfCbGRX8OQJdlISVtRtBtAYrpTL97X8+CLDy2Rb3b1u2Ee/oCRkIMpXt7PfW0Gknh049jqK0pBMzrxwcXZy1Wy7tXBEM6omuJ/GvXr363XffbW1tnT9/vqOjY3V19V9//bV///41a9YwGHrfTF17cOWrTpZRlBWi5gKU0/VucAgJ4boyWx+ILYN5T94UU4qainhWfv9U4kHmiC0TAS5+JAZHVpBB94l4lWD0Y4AV8oE/OusadjWejBr0XFdDpMRVv2Ttu16e+nXMaj9Lb6LDgfobNt/VL/pT36hP6suTH907dC91k5V9lL3X60LXWDKFRXR0RqPrRLh48eKWlpavv/76xIkTmiM0Gu3jjz/+4osv9Bib9mHyV50sIyvI7K5fVMPMg91S9EwibG3IZ5m5oGT64RJsqsvjd2dFx4uTzxhFIgQArAokXa3Cv8rC1oXClYW9UCuu+zLpOzM6d/e4zVwqh+hwoH4LQUgCxyECxyEqpbiy6J+y/KNZl1cJHAbbeY6HGbEnul3W/emnny5evDg1NbW+vt7c3HzgwIGWlpb6jEwXXn2yjKwgkxc/9wUn8NxZ1clNTx9pqXvcL3qmHN8Y+bhYCzNseOvpX7GmOtRc8Crx6AcJAfuHkUOPq4YL1UOFsFXYI4nlqT+k75jpO2Wy92sIgB8apA9kCsvJd6qT71SFrLX6wbmy/CNZl1cJHGMcvN+wcR6JwrpF3XhRfRMzM7OxY8fqLRRdU+NqNQ5I5L5fknBpu6rmEdXlRWufWUK6SobJm5U0/uOc11ybY2YdeL4CDzJHbP7Xr4xQqMyw4eK089yxs/scjz5ZM8Ceoejsa1jWJLIF/Gt6IUyNbb+9J6Uy/d/DPvc0dyM6HMgUUek8J7/pTn7TFbLWquIzJTl7b19cIXSNc/B6Q+A4BCEZbmUrQnTbPMrPz1+6dOmIESMGDx6sObJr1y6j3oYJV6hJlFf6Yi6/n0119UPILyzBiQCeK+vp1YTNtTl866DDpeqpz9YXZUXHi1PPGsU6Co04O2SKC5KQCFdTvEiLvHXllXXlbVU7x3wPsyBEOCqd5+w/Y8jkQ7FzbpgJAvNv/nBmV0j2lc8aq9IBgDPgHus6EV67di0sLOzUqVMqlapj4aBYLF69erX+QtM2TPnKA4TdL5x4Gs+D1bGIAscU7c0P6HzfM+X4G87PvDvF2pFsaSvLS3uVkPTsmwi0VKTeVQBXU3StsKl40dmPvMzdvxm2lkPtuuosBBGCzhK4h7wz7M3Tw9/8m84SZF786NxvA/NSvhU1FRMdGvG6TgzvvfdebGzs/fv3169f33Fw9OjRDx48qK6u1ldsWvbqFbflhbefr6z2PDN3VktRu+Z2a0M+28wlsZ7qx3/SL9pBM2XmVULSMxoK/hiOrsnAClrgd8nOThefX3ll3dKwdxaFzCV1VW8BggwBi+fkHflh3NwbA1/7FVPJbxydeuXg2AfZv5ry0osueoobGxvv3bu3Z88eOp2OPPX37ODgAACorq4WCoX6C1B7sFcrNKqqr1TjONna4aVnMgQ0AICsUUG3oDbX3jGzDjpQgY+17+KtGUGDW47vVNVXkq3s+hyYnnmbIV+Ho9OuYFdGAjgXTUOBKTan7yhoLNo+epMdxyj/OiATZCbwNxP4Bwz5v/qypEf5R/JSNlraRTr6TBG6xpnaDlBdXJ1VKhUAgEqldjpeX18PAKDRjHWmBK5Qo7S+f09XPCygufR003De/3aiaKnN4VsHnS1Xj3Xo4q0RMoUVGStOPdvnqAix0Jvka4asz4Xj7QAA0CBp/ODSZzKVHGZByBghCCpwGhoxZuu4hCx7z9cf3v3jn10hmReW15cnq9WmMgjSRSIUCAS2trZHjx4F/yu3prFnzx4ej+fp6am/6LTqFVuEyurS5wttd0ezNyEAoLkuR8YJaFWou9vwnRU1Tnzrolqp6HNghPhPNHqiHL1QaeodpLn19xad/3iIw6DPB39MN7Ev0VA/Q6YwHX0mD570R+yc6zxL3zs3vjy7O/zOjXVN1Zn9flpNF1/qEQRZvXr1hx9+KJFIHB0dVSpVYmLiX3/9tX379vXr11MoxrptOf5qk2WUVaXsmIk9PNnMg/3w71pMKW9vLrkh8RltT+quKUq2EFLt3aU5SczwEX2OTf/MaWD3QOU7iUjWJJLJrqY4XXz+tzsH1wxaHi4MJjoWCNIaOkvgHprgHpogaioqLzyZeXGFSiG28xxv7zne3CYE9MdFsV33bi1dulQkEn399dcSiQQAEBMTQ6FQli9f/umnn+o3PG16xckyyqpSiq1zD0+m8SkUNrk6L4vNdztbRXnL9UW/Oqzo+ParR40rEQIAoqzwqa5IQiJ2bJTJlZtR4qrNt7YXNj3YPnqTDcsISiJAUB9wzD18B33sO+jjtsbCivunMy8sVykl9h7j7b0m8K371Ze/bod5Vq9evXjx4pSUlMrKSnNz8+joaCOdI9MBU+BoX7tG8fZWtUqBmln1/Cnmvpya/HM8QeD1avy3mBc1oxl+kS1HtilryyjWjn0Ljyj/CiNFnsIOFOOz3LWw3bGxaFOIPr/xLRWl/hS7AW6lBJkCroWX7yAv30EftzUUVNw/lX52KY4r7T0n2Hu+bibwJzo6LXhy/dqzZ4+f3+OaKStXrnzw4AGfz4+Pj1+4cOGUKVOMPQsCzYL6vk6WUVaV9HyAUIPvw26qyamjBfqaIS/pPCShzIhRkrQLfYuNQDQUHByOfpyGPTKZvSkqRdXvnV/laub87bDPYRaETA3X0ts36pO4eUmDxv+GIOjNMwkX9g6+l7pJ1FREdGiv5EkipNFoSqVSc3v//v21tbUEhaQrr9IiVFSVUmxde/UUrgtTpsrPEfuMcXj5m7IGjZFkXDaiKjMd/PjIcn909jUMM4FUmFt/b+nFTyd7vbYsPAGuFIRMGc/Kzy/60zHzU8PHbFUpxYlHp186MKrw1k/tLaVEh9YXT7pG3d3dS0pK9u3b5+/vr1QqCwsLu1wpERb28hXlhulVKm6rqkqpPV478fjtcAVGqSordZgf/vIrJtlCSBbYy/JuMQKj+hYhgVYGks5V4D/exT8K6M8dpGdLLu/M2rdu8Mpg6wCiY4EgQ2FuE2JuExIw5PPGqlsV909fP/QGnWVl7zHeznM826x3vWgEepIIBwwY8Oabb86bN09z9+233+7yCWpj2E62S7gCJ7P6uPRNWf2QFR3fq6e0NuTRmK5uNbJwyx41HViRY8Q3zxljIiQhYE8MOuCkKs4OCTDvn+2kg/eOnio691PsBkeuPdGxQJDBQRCSpd1AS7uBQcO+aqy6VXH/7+uHJ9GZlppxRBbP0Gc/PJMYDhw48OWXX5aVlU2ePHndunW+vr1rAxk4TInT+tYixHFlbTnFxqlXT2quvdPKCwotlgBMDXqw5QUjeEjLiZ1YS32vpuQYCGcO8l0kOuMqdut1MqN/rbPH1fiP6Tvv1uf/HPutJdOC6HAgyKA9lRHXN1bdKi88efXP15gcOwev/2fvPAOauto4fu7InoS995KlbBARRXHvUVfVOlpX62hrp1bbarVqW1e31VY77HbviQhuBARBNoSwIUAI5K73A32dAXLDCvH+PsnNOec+wXD/OedZ42zdR/HF7Vfm6hGefmi5urq6urpOmjRp2LBhnp6ePWJTF0E2UzBbn/0KVlGMSEwhzjOlQtuktiwlGeobZ8qty1NJ3duvvwyx2Py+0aobZ8VDp+thZI8z2x0+VUy9eZ3YFWk82RRNeNP6K1uaCc3OuE1MaAwDg+48VMS+gz6uKLpanHX4/K8juQJLG9dhNq7DpRa+BpWPqH2H9N133xmZCoIOdJ/ASmjUlHlIddnd0yo/Wz9RTXq9jlP44cMak06BXnv4/GV/5HgRdajASMoy1TYrV5x9X8KVfDpoHaOCDAz6AUGIhcOAwCFbRr18t9/gTwi8+frxxce/D06+8F55YTxFGkSEYKvHWDk5OUePHi0tLX3KKbhp06aut6pL0DuhHi/JZ1k70ZpC4E31tfkcOy+7ACjzpyLncTrNYtu7Q1xBc3YKxz1ADzt7HAkb/DYYGX8GDzGHbPgG9HVPD0oaSt88vy7WKfol/+lMf3kGho4DQbCpTYipTYjfgPfrq7NLck7cS9jUUJtn5Rxr4zbCymkQgtI7detEtAvhV199tXz5cgzDLCwshMInjvV6rxDqXWtUU5InCBtKa0ptRZqK6xbnwBbaIISGVFdoeOZPFzHXiiAsTpV0qpcKIQAg1Bx6xQuZcYE4PxJttaycwZNbW/D2xQ9n+kwe5z6ip21hYDBCRDI3T9mrniGvNjWUluScyk356dapFRaO0bbuo61dhqKs7m5so0UIKYp67733hg4dunfvXgsL4ykfpXetUUxBO5u+tizlPuQ7yg4GEJB5C2sy6nnmOsVZ8ENi604eIBsbYH5vbeu6ph98UUFuSyXf9O+V2RS3S1M+TNiyImRRjEP/nraFgcHI4QqtXALmuATM0TTVluScKEz/487Z1eb2/W09xli7DGWxRd1jhpZHVUVFRU1Nzdq1a41JBUFLZRn6wTJkk4pU1aOm9ArrlChS0in/UHMIAGDiLarW2U0I84Rcr6DG2xfo2mk4wBDYNxDZmkrcqux9zs4z+Rc/TNj6UfQ7jAoyMHQnbK7UyWd6/wk/D59/w8ZtRHHmvye+C7p6eG5hxp9Yc11X312LEEqlUpFI1NDQ0JF1MQzbsWPH/PnzN2/e3FK5WysURe3evfvgwYMduZeOEBp9doS4Ip9l5QholhEpK0k1tfJHYQAAkHoK6wsbiWZdQ0gE4cNVSSfp2mlQOAqhnRHIzAuEyiAc4bry+/1D3yUf2D5kg5+5USUOMTD0IthciWOfqZHjfhqx4Kad++jiB0fP/hhx4/j8vNSfm1RdVe9MizCw2ey33npr06ZNarVa73UXL178+++/x8bGxsfHT506tbVhe/fuXbt27ffff6/3jXRHv2AZTUmeHpEyZENeXyfvlh8RNixy4Ndm6frFguMeQKkbNUVZtG5qaEx1gcMtoNeTiJ42RFd+Sf/ryINTu+I2OUoMNNWJgeG5gsURO3hPjhy7b8jcJDvPiRXFV8/8FHPh11GZ13d0+h5Re7BMbW1tcnKyh4fHwIEDBYIn/JbffPNNu4sqFIoDBw7k5OTY2tqOHz/ewsIiLS3N1/fpIuUKhWLbtm3Lly+Pj4/X+w3ojn61RrGSPJYtvSqjyop7pYjrINtHBepkfUQ1GfWmfmKd5kOQIHyYKvEk27639kBuYVckEvgv/mceOdnZoJ2FFKC+vPVDcnnazrhPpBxJT5vDwMDwBCy2yNp1lLPPJJLEKouTFLlnILiTk5W1C+Hly5fFYjEAIDExUY9Fb9686ezsbGtrCwDg8/lhYWEJCQnPCuGSJUs2bNhQWFioxy30gMT08RFiJXn8wBhaU/KLU/IQv2Umj+4l8xEVn68AlK4ppPywYWWbFkrHLaSbxW9QCFng5xhk3Bm8vyVsbahpeCRFbrm2q7he8cWQDUyyIAODIQPDLAuHARYOAzp9Ze1CeO3atY4sqlAozMzMHv5obm6uUCieGvPzzz+jKDp+/PgdO3a0vRpBEAcOHLh+/XrLj4GBgStXrnz4qkajoSiKINo5giNxCoKBuonmYS9FYSV5uMSCaN3N+SxZeXdYJv2a1I9N4QGYC1dkVgscuDotgXJQZ5/apNOcEHppG91JY2MjBEFQm95THwGY54rMOt98eDBhgMkUGkKz6cYOnCQ+DH8LwkAjRuN/uQdRq9UIYjzle3oRzG++R8AwjCAIktSzUgeXy4Xhdg6luqQuJJfLfdjRCQDQ3NzM5T4hAJWVlevWrbt48aIuq8Ew7O/vP27cf0np1tbWj68GwzBFUVobZTwOriZgFvyUGe2CV5XCPCFPRq/4Z1N1mkvAS0/dyyxA0pDVbOoh1XERqP+o+pMHJAPG0Lp1d4LjOJfLbVsIAQDrgsGQk+S3OehyH8OSwia8+cPEbRK26J2IlWhnn7R0KRiG0f0kM3QKzG++R0AQhCAIvX/z7aogeFwI1Wq1UqkUiUQCgaCioqK1PZaVlVW7i9ra2hYVFT38saioaNKkSY8PuHjxokKhiI6OBgAolcrGxkYfH5979+5pXQ2CIH9//9YiblqEsN23SmEEzIZ1+Y08DlFawLJxpjWLwJs5TfmB7t5PzTLzl9z/sdB5rK5pGDzvEOWfu4mSPJadKw2LuxEYhmEYblcIYQD2RkPhh/HBtmiAwfSmaMKb3ovfIOOavBu5AoF6kwqC///me9qK5xHmN98j6PiQ79AtHv7rt99+s7a2bjmo9PX1tW4FXRaNiorCMOzChQsAgIyMjIyMjBEjRgAA8vLyWi6OGDEiJSXlzJkzZ86cWbp0aWBg4NGjR7vk/f0f/bLp9agy+qAorQxx8TN7+suL0JYLSNCoaNJ1IQjihw1TJZ2gdXfDxFkEfR6OTDtPNGDtD+4GVFjjqnNrbYRW70Wu6nUqyMDA0Ok82hFGR0fv27evpe/uzp07O5I7weFwtmzZMnXq1IEDByYkJKxfv97U1BQAcPLkyW+++SY5OVkgELi4/BeKaWpqyuPxnJ27toUjoVc2PabI4/nTS6y+k5OCiQO03knmK6pKreNb67rBF0QML9u8SDJ2AcTu9acxM1zh8yXUwivEr4N6WHjqNQ1vnl/nIXNdGbqIKSLKwMAAHhfClgZMLf9uI/NPR+bMmTNo0KC0tLRPPvnE3d295eKMGTNGjhz57MgpU6Z08HbtQuqVTY+V5ImHz6I1pVyRYmbVV+tLpn7ivH8V9nG61utBxDKOc5/GO5cFYXG0bDBMdkUi4YfwfVnkXI8eO1yqaVK+fm5NmE3QK/3m9JQNDAwMhkYXNlF1cHBwcHiiMbFEIpFIns7T0nqx0yEx2hW3KUxD1Fag5ra0ZsHKlICI2VpfkrgINHV4U7WGK9OpADcAQBAxou7Mb8YhhFwE/DIYiTmKh1pAfaQ9sBWrbKxaeW5NrNOAuX69suMjAwNDF/G8OH6JZto7Qqy0ADW3hRAa3xUKlE1mWJ6/UysFuiAg8xFVp+ladxQAwPUOIWorMUW+7lMMmT5SaFMoMvUc0djtpdfKVOWvnX13lNtQRgUZGBie4nkRQhKjXV8NLy1kWTq0P+4x4rPuNfKcUbTVXA5TP3FVKp3iQDAsCB+mSjSGkJkW5nnAQWbQ8sRuLb1WWCdfdvrtSZ6jp3lP6M77MjAw9AqeFyEkNBRCM1gGr5TTPRfNLUzhmLbVSlDiLlSVNGnqaWyIBOHDGm9doDTNtCwxZHZHIvGl1M/Z3dTIPk9ZuOrcmnn+MyZ5Gm5SJgMDQw/ySAirqqpay+QzAvSouI1XyFELekKoqkx1sfdvYwCMQlJPYfU9GqejiNSc7dSn8c4lWpYYMkIW+D0WWZlEpNd2eZ+m+1UPVp59f1nQ/BGuQ7r6XgwMDL2UR9pw+PDhh8GiYWFht2/f7iGTugQ9gmWwcno7wiIVZY2leDq1JYQAADN/mqejAAijRqkSujbPspvxl0GfhyMTzhB1XZlZmFGV9fbFj94Kf41pLsjAYDwQnX+Y9EgbhEKhSqVq+XdBQUFTk86p370BPZoREpUK1IyGEJ4v1tgQeVKzdlrZmXiL6vMaiSYa/5dcr2CysaG3N2Z6iplucJQl9HJ8VzkLM6uz3720YXX4sgjb4C66BQMDQ1dD1auJ3DLiWrb6zyTVzhN17/5Su+hbslbVuXd5FBIZEBBQVFS0aNGigIAAtVp96NChtLS0Zye8/PLLnWtB90BqSJRPI5WbqK8BCALzhbpPuZOXHiFwQtB2kt8RDixy5tfcrzfrq3PSCAQJIoarEo6xp/XuxkxPsbs/0v8I/lUGudi7k33VmdXZb1/86M2wpZG2oZ27MgMDQ1dBkERpLVFURRRVEooasqKOLK8DKAybiYC5GHEwY4W5c61NEGspQLusDZOHh8f27ds3bNjQ0nHw008/1TqhlwohoaFo7QjxCtqRMmUlKeZW7ZyLtmDqJ65MqaMhhAAIwoeXbpgnGbuQljYbOFwEHByM9D+Ch5hDwWadllnIqCADQ6+ArG4g5NVEUSVRXE3Iq8iSGlgmROzNEHtTdoQHYi6BLSUQj93SfaJLy50/kSS3bNmyZcuWqVQqZ2fn/fv3h4Yaz3OEro8Qr5CjFna6j8+vp2w0dx3bjJR5iKmvKP9IKa34HVgg5nqHNN48J4wep7tVho+bGPoyEpl6jrg1HjVpp4OITqRXZr576eN3I1aG2gR2wnIMDAydBFlVTyhqSHkNUVJNlFQT8moIRRA7U8TOFPW04Qz1R2xlELsLa7y0gZa7CgSCtWvX+vr6mpiYdL9BXQRBM2oUryhBzW10H3+5lPIGqSYWM3UZzBKiIkdedTqd01EABP1H1xz8QjhgLGiv4UPvYpIznFBGzbyIH4lDkY69sxa/IKOCDAw9DEkR5UpSXk0oWmSvhlTUQjwWYiODbUwQR3N2hAdiawqJDKWKsnb5XbZsGQAAw7CCgoLi4mJra2tnZ2c2W9fCYAYI3VqjeIWc3zda9/EJJZqhzTkS83YiZR5iHigtv1VLSwg5Lj4QjDTnpHLcdNp39iK2hCFjTuNvXSe2hul/9J9Tm//2xY/eDFvGqCADQzdDKhv/8+3Jq4miKrKkGpIKEDsZYm3C8rbjDPFHrE0gnuEqiHYhpChq69atGzdurK2tbbkiFApfffXVDz/8EEV7ZuvaQUiMglk0tht0fYTZ8owxEicE5ek43tRPnPu3AlcRqIDGo1/Qf3RDwlHjE0IEAj/HoGGHcS8pucBTn8CZwjr56gvrlwUt6G9nPOf5DAwGCkkRihoiv4IoqiSKKomiKgonEQczxM4UdbfmDPZFbGUQh9XTVtJAu6pt27Zt9erVQ4YMmTZtmpWVVUVFxeHDhzdt2tTU1PTZZ591s4mdAr1aoxSFVyp0PxqtbALihjvWzjQ2IggHlnoJK1OUVhEy3WcJQmLrjv9IKKsQianus3oFJhxwJA4ZcAT3kEDRVvROSOX1ilXn1rzSd06s44AuMo+B4TmHLFfiDxR4bjlRUEEUVUISAepsjjiYc4b1RezNYBNBTxvYIbQIIUEQmzdvXrJkye7dux9enDt37saNG9evX79u3TqxWNyNFnYOtGqNEsoqmMuHOLpu7+JLyTBWssw6jJZJ5oGSkktVtIQQ4vB4fQeorp0Wxxlh5WhPCXRgEDrjApE4FrEX6KqFioaylefen+8/I845piutY2B4zsAJvKCSyC7Fs0rwBwoAQ6iHDeJiyQ5xRRzNDfmcUw+0CGF5eXllZeWCBQueur5w4cL33nvvwYMHLc17exe0EurpnoteKaOCNXdkVotomSTzFmUflNPqygQAEPYfXfn9OvGQFwBshHVi42yhlb7w2NPElTGoQIczeHm9YuW5NbN8pjAV1BgYOgpBEooaIq8czysncssIeTVsJUXdrFjBLrzpUbCZqKft60K0PGx4PB4AoKKi4qnr5eXlAAA+n98NZnU6tHIV8Ao5rZDRGyXK/hqFWEYv2x1CIFN/SWVynd1gM91nsWxdEKmZ+t41nl8Erdv1Fl73g9NqqLmXiN9j24khLaqTrzq3ZqbP5LHuw7vJOAYGY4IgCXk1nl9O5FcQ+RVEcRUsEyLOFqiLBTvSE3Ew66lkhu5Hy/uUSqWhoaErV648evSos7Nzy8WysrIlS5Y4ODh4enp2r4WdA4FRiM7BMrR2hCocYFV3ZJb+EEz7Q2MeKMn9R9GaENZheEJVVUJl1d1apS2P5yYUuIuEHkKhVf/RqoSjxiqEAIBvo5BhJ/A1N4mPg1uNJCqsK3793Np5ATNHuMR2p20MDL0YnMALK4n8CqKgAs+vIEuqYXMx4miOOlmww9wRRzOIa1QHnrqj/dm9e/fu2NhYDw+P4OBgGxub8vLymzdvUhR16NAhuDeeyFH0EurxCjnf2UfHwUnlVH/2XVNrfUL2JS4CXE00Kpr41o/yaXJVqh0Pci5WVOY2qIJlJgPMTOc5OyqamrIbVBcqKrMbGkrUTeNg2XsFOd6Ornrc1PBhweCPIWjEYdxTSr7opuV/rUBZ9Pr5DxYGzBrmMrj7zWNg6EWQtSo8u5TILsWzS4nCSthSgjpbII7m7GhvxP452vO1jfbfQnBwcEpKyueff3758uXk5GShUDhnzpzly5d7e3t3s32dAtGigjqHImJ0sunjS8k+1B2ZtV7RKxAw7yupuKN0tOYCAErUTR9n3P+jWL7Y1eXrwL5BJlKWtq8dlc2abScaYm4k95dXvunpHmFKI9ymt2DKAYeHIgOP4fYCKMb6if+57JrcNy+sfy1o4SDHqJ4yj4HBcMEJvKCCyC7Dc0rx7FJKg6OulqibFW9SGOJsCXF7U1ZDt9Hq1wFHR8cvvviiO03pOuhl01MUUV2KmukqhFdKqcWquzKrLfrZZh4oTf+hQBRrsjkza09ewTxnx/vDh5q2WbvAjMP+eGDsgs+wkJIzAAAgAElEQVRWnPRbN+vaTTs+76vAvn3ExubK9pJCB2LQaefxK2NQN/F/WphTm//mhfUrQxZF2xvtyTADA12oejWeXYpnKfAHCqKw8r8glwAn3qQw2FLa09b1Ap6LfTGhIXXPpsery2ChFGLpdFaOkyCvrIiNIjyhlX62CWy5aeKmkcfPTHa0TYmLteHpVHMIMbGQOHjMrc1bNCJuT15BzMX497w9X3N3NaraawAMtYU2BCNjTxNXx6JS9v+z5gPnMyrIwEBW1OGZJXhWCZ6lIGtVqJsV6mbNmxiGuDDbPto8F0JIYjRaT9AKGb1dRYWhd8zN9K/pda265k3bom2E65xAesfOwqhRymP7BGHDXnZxGmJp/uK1m0cVpftCAm15uqY/9grme8J3q6np5/GvIsreOL9mUb85sU40St8xMBgTZFktliHHM+R4phxQAPW0QT2sOUMDEDuZkZUg7maeDyGknTuha8jolVIqFE02seqnn2G3amrHJSTuCehntb+eHE/BKI2PMtcruPbvrzWFmWwHTxeB4PKg6E33s4LOXtje1/8Fexp9Mwyfz8ORsSeLFp784M3QF4c6xfS0OQwM3QpZUYffl2MZxXiGHACAetuxfO15k8JgCxqVihna5rkQwq7Lpo8vpWZqkmXWb+th1d1a5egrid8G9RtrY51mnV+VWmfej84nG4IEESNUV46yZ3gCABAIes/bc7iV5YxrN1KVdR/59jGa74dlqlKe+oMyaFpu08CetoWBoTv4v/jJ8ftyQJColy3qbcsbF8I4/LqI50IIae4IS7ieOh11UgBcK2+eU5cutfCja1JmfcOoK4mf9/Uba2MNALCKNFEkVNMTwpZuvR/PlTQoYeF/E4NMpImDB45LSJp7/db3wf20Bp32LuT1ipXn3p/rP83HcmjUEcJdAsXaGI3EMzA8glJr8PRiLK0QSysCGhz1tkO9bLhjgxErRvy6HJ2EUKlUAgAkkt66Eyc0XZJNn1lLuZKZQqkDi00vYlOuVsdeurLF33fa/88wTX3Fuf8oGsua+ZY0utPCfCHPN0J1/Yxo8OSHF2Vs9qno/tOSro+/eu338FABqn9jox6nuL5k5dn3Z/lOGe0WBwD4bTAy9Rx+eTTqLmG0kMEowAk8pwxLL8LvFRPFVaibFernIIz1Q+yMraq+gdPOjuHKlSs+Pj5SqVQqlfr5+V29erV7zOpcdK+4TRE4oaxETHUKAY0vpQbx7sis6EXKUADMu3F7kavzdIdHnjwIgSxCTMqSamgtBQAQRI1WXT0GKOrxi3wE+Tsy3IbLHXwpvqK5me6aBsJDFRznPqLlygAraGMIMuY0UdNb3xMDAwAUIAorm07cadh6uHbZHvWvVwBO8iaGSXbOF74xljusL6OC3U9b8tDY2DhhwoRx48bdunXr1q1bo0ePnjBhQlNTU7cZ11nofjRKVJchYlMI0WmjfKWM8iKTTazpRcp8nZOnxLC3vZ4uTGoVYVJ+q5bEKa2zWoPt4Anzxeq0xKeuoxD0XXC/4VaWURcuF6vVtNY0BIrq5CueVMEWXvKARzlAk8/hGrKnTGNg0AeyuqH5crrqq9O1r+1R7T5JVtRxBvlKts0RrZvKmxKB9rGDWL348Ka38+iJX1dXl5iYOGzYsIdXsrKyLCwsNm7c2PJjYGDgv//+m5WV5e/fyxrDEhoS0a2+Gl4hRy1oRMpMUd2RWS3W3ZLsBtUH9zLiB0Wjz8Q6c2VsoR236q7SPIieS0A0aFLDhb94fpHPvrTex1vKYsVeunIpZoAVV6cMRUOgsE6+6tya+a3UEd0Sikw7T8y+SPwyCIGZI1IGA4bCCDxTjqcWYqmFZJ2a5WOH+tjzpkbApsZW/qK380geSJKcNWvW5MmTi4qKWq44ODgUFhaeOHGi5cfjx48XFRU5ODj0gJkdg9SQMEdnIdTNQVjSSOHNSkJdKpa562oGRc27cWtNH09PkVDrAKsImSKR9ukoLyCKqKvW5GdofXWlh9uLjg5DLydUNmvortwjtKjgwoBZrVXThiFwYBBS1Uy9mkh0s20MDLpAyKubT91t2HpYuWxP0+GbkIAreHmIdOc8weJhnOg+jAoaII/kQSqVZmZmmpmZ+fj4bNq0SaPRyGSyLVu2TJw4kc/n8/n8SZMmbdu2TSrtfSFMureewCvkOhZXiy+lRotSTCxoNJ3YnPmABcPL3FqtlC3zETVVaRpLaXrAYFgYPb7+wt+tvf6+t+dYG+shl6/UaDB6K3c7xfUlq86tmeP3QtvVtNkw+CMWvaygPktlTkgZDAKqTq1JeqD6/pxyxd6Gz48SihpOjI/ki7midydyxwYjThZMwrsh88RDXCaTff311/Pnz1+yZMmPP/64a9euRYsWjR8//tatWxAEBQYGWlnpWUisZyE1JCzWSa6wcjnXJ1yXkfGlVDCSLDPXNVLmXl3dF1nZN4bEtPHXAMGQZai0NKnaZby1jsu2IAgfXnf6F7xSgZppn7jBtw9GkiOvXD0d3V+EGmjOjLxeseLs+7N9p45xG9buYCkbnBqB9D9CmHHBbPdenyXC0Buh1Br8vhxLL8bTi8maBtTLluVjzxsTDFv21gD75xYtz8SQkJDr16/v379/+vTpYWFhu3fvHjVqVPdb1okQGl17MOGVuvoI40upkcQdE6tpugzWkOTMazc/9fd1aK+tsVWE7M62bKeRlronPgIAIDZHED684fK/0omtOiw3+/suunVnXELSsagIHmJwbvlSVfnr59e+6DtF9y67NnzoaBwSexy3FTDJhQzdBUnheWV4aiGWVkQUVaFulqi3HX/+YNTJAjAu616L9qctBEGzZ8++f/++i4uLr6/vunXrNJre4WHSConpVFmGwjGyvhY1sWh3ZE0zKGigyOpkHXMndmfn2nC5c5zad69ypCyRA78ypU6XZR9HOHB8483zpKrViRAAXwX2teFypyfdwCl6saldTUlD6Wtn3nnRd+pTMaLt4mMC/RGLzriAJ5Ub1jtiMDLIyvrmi/fIPZdql+1p3HeRasZ5E8Oku+cL3xzHHR2EulgyKtireUIeampqWpoOOjk5TZgwQS6Xb9++/fTp04cPHw4MDLx48WIPGdlRSA0Fs9v/mOKVJYiJBYDb3y1dKSOHmhTDsE5NJ2o02Kb7WVsCfHWyFQDrSJniarWOgx+CiEx4fhENV4+1MQaGoL0hgRhFzbtx23B0Q16vWHH2vdm+U0e5DtVj+gAr6EAMOu4MfrvScN4TgzFAaXDsbn7jgfi6t3+u//APPLME8rcXfzJD/NE03guRaB870JurVTA8zhNCOGvWrKSkpFdffXX9+vVCoTA2Nraqqio8PPzGjRuLFy+eOHHirFmzamtre8pWvdGx1qjuIaPxpVQ0+7aO28F16RmT7Wx9xGJdBgMATLyFGiXWUEw7+U8YM1EVf4TC24qIYcHwnxGheSrVO6n36K7fFRTXl6w4+95Mn8mjdfALtsZQW+ibKGT0aTyjltFCho5CVtY3n0tt2HZE+doPTSeTYROBYMkwyfZ5gleGQiEusKQd7wZDb+SRj1CtVl+4cKGiokIgEAAA5syZM2TIkISEhLFjxyIIsnTp0ilTpqxevTo9PT0yUkvKmiGjY0I9Xl7MstCpb8PlUmoNfNPUNqzdkTkNql8Ki9LihuiybAsQDFlHmZbEV3lMp9dEgmXtxLJ1bbx5XhDelqjwEORoVMTAi/FmbPYbnrrmfnQFRXXyVefWzGslX5AW4x3hOg0YfpK4NApxEjGHVAw0IUj8gQK7W4ClFJB1jSx/R/YAb8GSYRBPp76kDL2dR0LI4XBQFM3IyAgODgYAKJXKgoKCx5MlLCws9u3bRxmYe0kXdEyoxyvkbAfPdoc14iC9hmLDN0yDp7Y7+PW7qW96elhyaVQQBQBYhZvc3JClqcfZInoRnqJBk2r//lIQFtd2rLaExToeFRl14ZKMzZ7n7EjrFp1FYZ389XNr5gfMGt5mpoTuzHaH6zEw9ARxeTRqzXxrZ9ABsroBSynAUgvx9GLESor6O/LnDUZdmFSH545Hz1kYhtetWxcREREUFMTlcpOTk8PCwqKiop6aAPXCj4iOtUbxcjk/qP2HcmI5FWLS0FiYLzVvx+13qaLyrlL5W3iIrob+H5SHmPWVlCZWO8S1H7nzOByPvhCLo05N5Pm3s2u34XFPDOg/6GK8DY873MqSroUdJF9Z9Pr5ta/0nR3nPKgTl13aB67VgGEn8QujUFN63z0YnhtaNn8pBVhKAVmrYvk6sINdBHNjIJFRdbRmoMUTG45Vq1YNGDDg3LlzarV6+fLl48aNg3t/Hx/Q0n1Cl2CZCjmqw9FofCkZx0s2sfSHEVYbw0iKeuNu2iY/H65euQq2A01Td+XZDTan1a0XACAaNrPuxH6eX0S732o9RcJD/cPHJCSeHNC/r7T7Mp9yavNXn1+3OPClIU6d31/wvb6wCqOGHMfPj0RNGC1k+D9kdQOWWoinFmLpRbCFhOXvyH9pEOrMRHsyAPBsHmFISEhICO0djIGji4+QbFKRmiZELGt3tcsKagV609QmtO1h+wuKEAhM1bdZPM+cw7fhVt5VWtAsPcrzDa8//Ys6LVFr9dGnCJGZ7OoXMOZK4tXBA+353fGN+EFN7pvn1y0NmtcVKtjCxhBEQxKjTuGnR6DCtr6rMBg7LZu/5HwstZBUqli+Dqx+zvzZAyExs/ljeAIDLTLSuegSNYqXy1Fz23Z3URgJblZSIv4NU49X2himJog199J/Cw/tyLdN22jTghPldIUQACAaOr3u5AGeb/ubQgDAZDvbnAbVuISky4MGCLu46ExmdfbbFz96PXTxAPuILr3RljBk0RVi/Bn86DCUy4S4P2dQag2WWojdycNSChBzMaufM3/+YNSZ8fwxtIoxnHy2DUVSgAIQ0s7fAF5RzNKhpszNSspTQtaXJ8usg9oYtje/IMhEGmna/v6yDUy8RISGrMtvpDuR5xcBIYg6LUnH8W95eQTLpNOSbhBdGQmVWpGx+vz6N0KXdrUKgpbqAf0RSx40/gzezJTmfj4gy5TNp+42fHpIuXKf5sp91NNGvGG6aN1U7rgQ1MWSUUGGNjB+ISQ0pE7Z9OVy1FwXByE1XHSfJ7Jhc1vdqBEU9VlW9mrPpzsO0gYCNlGykstVekwVDZ1ed+oA0FnYvgzsi5Hk4tvJetxLF+6Upa65vHFt1Bv97do5Uu4sYAjsG4hwEWjmRQJjSnMbKwSJZxSrf71S99aB+o1/EyXVnFg/yfaXhKtGc2J8YKmgp+1j6B0YvxCSGkq3bPpiXbLpLyvIQOiGqU1bbtS/iktsuNyIjm0HW7AIMVE+aGiupd01gucbDkE0NoUoBP0REZZUVb0zO4fuvdolUX5z/ZVP1w14K8gqoNMXbwMWDH6PRUgKTDiDNzH7QiOCatJormervj5T+9oP6oNXIQFHsHiY5IuX+C8NYgW5QBzGM8xAD+P3EZKYThW3sXK5MKYdISQpcLWcelN609S1rQTwz7IevN/Hi56VrYBwYItgqSKh2mkUzQwHCBLFTas7dYDnG67joZCYhR6Jiog4d8lFIBhl3WltRs4XxO+4+e3Gge/3MWs/R7PTYcPgj1hkziViwhn87yEoz/g/78YMWavCbudht3Px7FLUw5rVz5k3LZLZ9jF0HOPfEXZifbXUGsqKB6nKbpi1viM8X16hxPCRnZeZZx1lWnathtDQPt3j+UZAEKK+d033KY58/p+RYS/duH2vjnbVb62czruw+/YP22I/6hEVbAGBwI8DEQseNOIU3mDoDRkZtECU1DQdvVW//o+6937FsxXsgX0kX7wkXDWGM8iXUUGGTsH4vyHrkjtBKKsgFgfmaW8c/5DLCipOVkJWYQKpU2tjtmQ+WO3lDneeZ55rypa4CUqvVtvGmNGbCUGiodPqTu7n+YTpHikQaSrbGuA79krStdgYM06H6kv9nXnsYMY/24dssBPp1Ou460Ag8EM08nI8MeIUfnwYKmJOznoDRHGV5kY2diOHUmtYQa68KRGopw1AjP+7O0P3Y/yfKkJDtptNj1eU6BIyGl9KhaE329gOpirrUpV1Mx3saVvZJg5xFvKLlST9kA+eXwQEweqUBFqzZjs6TLSzmZR4TUPqH2SyN+XXf7KO7Yrb1OMq2AICge8GIH2k0IiTeD2zLzRgiMJK9V9JdW8daPj8GGjG+fMGSz6by581AO1jx6ggQxdh/B8sUkO1uyPEy4t0qSlzpYy0U7eVSr8l88Fyd1d2Z5fj4VtxRA78sms1tGdCkGTcQuXRvRSB05q32c9HymIt0SuIlALUzlvfXZVf3xn3iTmf5i62K4Eh8HUU0tcUGs5ooeFBFFX9p387jgOCFCyKk2ybzZvWH3WzAkziA0MX8xwIoQ7BMro4CB8oKTYMaSqum9pq3xEWNaqPK0pfdnHSz862sR9mUXy+kiJo5/lx3PxRUytV0klas2AIOhAWfK26Zld2Lq2JJEVuSdqVVZ37xZANUk73lW3TEQiAnZGInwk0kvEXGgIkhd+Xq39LUK7e37D9GMBJwaI4ydbZvKmRiDO9KrsMDB3B+H2ERHP7wTJYuVzg7NP2mEul1GBzVUNGvtTcT+uAzx9kz3d2lLC6xAEltOXyrThlN2qtwk3ozpWMXVD59buC4FiIQ6OylAhFj/SPiDx/yVnA1zGIFCPxjxO21WsaPh30AQ/l0rWze4AA+CoKWXSFGHkKPz6MqcHWA1DNGJZS0FL5BTYTs/s5C5eNQBwM6PCA4Xnj+dgRtns0WlGMtucjvFBCDeLekVr4aa21XYthP+UXvubuqr+h7eEwzKL4XAVF0t4UsmycOZ6B9Rf+ojvRScD/IyJ0/s3bGXX17Q5uwpvfvfgxQRGbY9YarAq2AAHwdRTiJ2POSLsVSq3RJGY27DiuXL5XczEddbcWfzRdvG4qd1wIo4IMPYvxC2H7wTIkQdSUo6bWba9zUUG54DdMbbU7CL/PzR9pbWXL68JiviJHPseEVXFbqcdcyYg5DfGHiTraXsb+ZqZb/H3HJCRWNmvaGFavaVh1bo2FwOzDAW+z2mzKYSBAAOyMQLyl0MhTeG1b74yho5CV9c1nUxu2Hlau3Ke5ls0OcpFsmyN8cyxnkC9swiQ/MBgExi+EJEa17SPEq0oRsQxitZUqkKWkEAiQldpDRgmK+jIn91U3l47a2h72Qy2KzpTrsSlEZBaC0KH1p3/W46YvOjq8YG834WpScytBpDVNtSvOvu9p6vZG2FIY6jWfKBgC3w5Aws2hqCO4XNX72k0bNBTAc8rUfybVvf9r3brf8byy/5L/Voxi9/eCBEx/LAbDotc8tvSGaC+PUJdImQsKKtaGrCm9I7MOfvbVwyUKay43REbbe0cXqbuAJUSrUvTJdhcNnd6YfAUrK9Rj7se+fex4vFdu3Xn2pTJV+atn3gm17rc8+GWot4X3QQBsCUNedIMHHCUeKBkt7DA4gaUWNv54Ublib+Oec4Ci+HNipDvnCRYOYYe4QdxecFTA8Hxi/MEypIZE2t4Rlhe3mztxUUGNEN7nCq201trelZ27zK0LvYOPYz/UIv9IqVmAhK7owHyhaNCkuuP7TV96j+5NIQD2hARGX7i86X7W216PiokX1hW/eWHdZK+xU73G0V3TcHgrALbig0HHiSNxSD/TXqblhgCl1mApBditXCytELGVsQJdRO9OhC0NLmaYgaE1ngchpGBOW083vKIEtXJoe5FLCnKF01W2vZZWt/fq6u7X10+y66a0cRMvYeFpuPxWrUUw7T6FwuhxpRsXaPLS2c596M7lI0hLJVIHPm+Ggz0AILs278PrWxf1mxvnPIjuaobGHHdYxALDT+J/xKLRVowW6sQTlT89bViBLvxZ0UzPW4beiPELIdHejhArL+b6tdUh734txUEgvPyKnc/0Z1/d8SBnkYtzpyfRt4HLOOv7Pxaa+YvbjYZ9CojFlox+qeav3Zav79KjPZs1l3tsQMSQSwnOAgEPl3+QtPmNsGUD7MPprmOYTHSCpWxoyjl8ZwQy1cX4XQZ6Q1bUYXfyNNezCUUNq48dO8JDsHQ4xOtQNT4Ghp7F+IWw3fQJvKKdo9ELCmqwFVF170bwsB1PvVSjwf4sLkkfNqQTDNUZkSNP5Mgria+yizWnO5cfGKNKOKa6fkYQFqfHrX3E4r0hgWPir/TFT3wQuDTKLkyPRQyWwTbQ+ZHoqFNEei21LpBpbP8YFMDzyrAbOZpbuYAgWP1ceBPDmMqfDEaD8Qth290nKE0TqapDpW0pykUFNUZwWyh14vCebjH4XV7+GBsrS253R8E5jba6+0WOZagJS0TzfxCCpBMXVX67lhcQBXP5etwaVqfb4zfz+GOcTbz1mG7g+JhAiWPRUadwuYr4qj+CPufPeQrguaXY9WzNzRyIhbJC3IRLhyGOtL9+MTAYOMb/h9529wm8Qo6a2YDWDzYpAC4pSNemKxYO0U+9RFDU1zm5S127PGviWbimbPMgaeGZcj3msuzcuF5B9WcP6jH3z/tHfkj55VDcK2Nt7KffTu5IVW6DxZoPLo9G5Y3U5HNEI70SrcYCReFZisaf45Wr9jXuOQ+4LOHK0eJNM3mTwhgVZDBKjF8ICQ2FsFr1h+Hl7eROZNRSAhTSlF2xsI966qUjJaVW3ZI1oRWHYRaVyXWNZc16zBWPmadKOolXyHWfQlLUl7d/OJp9atfQTQ5i260BviIUWXYnRY+7Gz5CFjg0FDXhgJhjeEnjc5NWQVJ4RnHj/kvKFfsaf7oIC7jCN8aKN87gTQhD7Ex72jgGhi7E+IWw7R0hViFv20F4sYQaYtVYW35P9kwq/Y7snC6tqdY2KA+xG2RWcKxMj7mIyEQUM1F5ZI+O45vwprXxn2RWZe+I+8SMbwoAQCBob1//GzU127Ie6GGA4cOCwd5oZKYrHHaIuF5hzFpIaXDsdp7q+3O1r+1pPHgVNhEK35kg/ng6d3wIYvu0L4CBwSh5DnyEWFs+QrxCznHzb2P6RQU1gXfNxKovynrCo5amrMuqb5hk25PN9myiTRVXq2sfqKTutEtVCQdNKtv0StP9W1yvoLZHVqqr3730sYvU6YOo1Sz40QdGgCCHI8MjL1x2FwrH2rRToK6XstwX9pBAY07jW0KR2e5G9a2RasKw5DzNjRz8XhHqYskKdOFNDINl7fSmZmAwSozqb1sr7fkIi9s4GqUAuFxKOjResbAf8NRLX+bkvuzixOrGrIlngRDIcaRl/rFSQH/HAiGoZMx85aHvQJt+vuyavCWnVkfYhLwd/trjKtiCPZ93qH/4/Ju3b1TT75XYSxhhD10ejW5MJpcnEvRr2xkcVBOmSXrQsPOEcsVezdUsdj9nybY5wtXjOEP8GBVkeG55DoQQo+A2fYRt9KZPr6FELEituGLh+IQQNuD4wSL5fGfHzjRUL8z7SiAYKrupjw7x/CNhkUlD/KHWBsQXJb5+bu2rQfNf8teSQNlCkIn068B+E69eK1ar9bChV+Apga6MQVOqqfFniF7arYJSazRXMxt2HFeu2Ku5ep/dz1ny2RzhqtHsKKbyJwNDVwrh2rVrTUxMxGLxwoULMezp58fly5cHDhwoEAjEYvGkSZNKS0u7wgYSpyAYQLB2ISQblICiYGGrJVouKKg4s6rG+mITiyeOT/cXFMVamHdprwldgYDrROuCY2W4mtBjtsnUV+tO/4pXa3E0Hsz4d8fN77YMXjfAvq1qAwCASXY2i1ydJ169pib0saFXYMYFp0eg9kIQfgjPrus1G0Oqvqn5cnrDZ0eUK/dprv+/88OqMewoL4jP6B8Dw390lRAePXp03759aWlpxcXFd+/e3b1791MDGhoa3njjjbKysqKiIhzHlyxZ0hVmtH8u2nakjIIagCaY20VCT54KfpWTu9jVudOs7BhCO57MR1x0Wp9UCtTMRhg9vvbPXY9fJCnyixvfnMw9tytus4dMp2igd709vUSi2ddv9RqJoA8LBrsjkRW+cMRh/EihQeeNkJV1zafu1n/yj3L1fjy1kB3pJfliLtP5gYGhNbpKCPfu3btgwQJbW1uxWLxy5cp9+/Y9NWDkyJFjxowRCoUSiWTevHnJycldYUbb2fRYeVshoxQAlxWkrSrBwuGJxInLFZU4RcVYGFBCldMoy/LbSpWiSY+5oiFTieoydcrVlh/VeNO7lz4uri/ZFbfZUqDre4QA+D64X2Vz8/tp6XrY0ItY6AX/OxRdnEBuvmtwWkgUVTX9e6Nu7cG69X8Q8iruyH6SHfMES4ezw90hLlMCjYGhVboqajQrK2vGjBkt//bx8cnKympj8LFjxyIjtdSzfohara6p+c8NxmKxhEJdvfrt5E6U5LGsnVp7Na2aMuFAKsUVi7BFj1//KidviauLQRVmRvmIw1CLnL8U/kud6XalgBBUOnV59Y8bOR4B1WTT2xc/8jR1WxW6GIHo1Rhjw/CfkWER5y458fkLXZzoGdGr6G8JJY5Fxp8h7tVQX0ch/J6NvKYo/EEpdjtXczMHAMAOduXPHIC6W4NW3AEMDAzP0lV/xLW1tQ/lSiQSqdVqtVrN0+ZUO3jw4OHDh2/fvt3aUjiOf/rpp9u3b2/5cejQoXv2PEqA02g0FEVpNNq7jKtrNQAm6+vrtb7aVJzNcfJp7dUjuehwcSFe0wxYlg/HVGo0p0vLtnq6tTarpxD4oSWJWNG1UqkP/a7f5g6IW99r/362hZ0z0XXUOJfhjQ2N7U5SqVQkSUKPFe9mA/BrP78R127ZwFC0qTGnoEkBOBEDrbiJhv9L7O+vcRF265FwQ0MDICnqQSmVXEDdLQRiHuTvAC2IgWxNcABwAICqoTvteX5oaGB+sT0AhmEEQTwbaKIjfD4fQdr5Wt9VQmhqaqpUKlv+3SKKWlXwyItkd84AACAASURBVJEjy5cvP3XqlI1Nqwl5KIp+8MEHb731ltZXW4SQw9Hu+aAqG1k8lkgk0vpqfVmR2LUP0sqr58rx1wTXLR0GiETihxe3Z2ROsbezNemZajJt4z4FzfypyCbQoo3T4NZIHxC58dKnr7nNGBowRccpEAQJBALoyS4WQSLRH5Fh05JuXB40wF3njXtvRATAL0PATw/IYeehXZHIZOduCcAmSCyjmEzIIFKLEDMxO8SNPSaU6fzXnbT2MGHoOlqEkMvldt0tukoIvb29U1JSpk6dCgBISUnx9tZSoPn06dMLFy48cuRIQEBAF5nRxtEo2VALKBIRa9+4NGDgZgVlRlyxcI19eJGgqO9y8w/1N9DGQ2InvsRVUHy2wnGkJa2JR7NP7Un5Za3rVIeLl0HgZAB3qPHCQHOz9T7eY64kJg6OMWEbeVPy2e6wrwk05RwRX0ptDWu731cHIEgsoxi7nq25nYdYSkCAvXhSJGzGPJEZGDqHrvoau3Dhwu+//z4lJaWwsPDTTz9dsGBBy/V58+YlJCQAAC5dujRhwoQ1a9bAMHzr1q07d+50hRltBMu07SA8IycjLUGNPMHC4VEG4VFFqR2P21dquF/AncZYlSbV6F6AlALU3pRff0n/e+fQT0KiZiIik7qzv3fcjJddnMbaWI9JSGw03oSKhwSaQdfHow/qqCHH8cKGzjwjpZowzc0c1bdna5f/0PTPddhWJv7wBdGayfCgPowKMjB0Il21Ixw8ePD7778/efLk5ubm2bNnPxTC2traFn/evXv3vL299+7du3fvXgAAh8NpEcjOpY0doaYkj2XTagrEiWJqjDiDzZXyhI+Kh32ZnbvErQd6TegOW4w6DLd48Fux/6surWVPPqQRU29M/KJe0/DN8G0ithAAYDJtZfnWZVyvILaDRwct2ezvu/Dm7XEJSUejIjg9Wn+nGzDlgKNx6NZUMuQQ/lkYMtOtQ++XqldrbuVit3PxLAXqZsUKdOFNDmfKvjAwdB0QRRl66tfbb79tYmKin4+wNKmmobDRbaqW2jE1v2xju/gIwodrnej4G/6L9S4hVR0Q82HLlewGVdSFSwWjhhv6Y50CqV/lyfqIbGPM2hhVoCxaE7/J37zP8pBXHq+dpk5JUB770fKNXRCrnYD7hoaGZ32Ej4NT1KSr10Qo+lNoENz6MGMirYaaeYHwkEDfRCEymgl7VH2T5lYOdj0bzytn+TuyglxYfg5aO7/X19cznqoegfnN9wjd4CM07Gd6h8FVOCrQvuvFFPmtHY2mVFNsGDTLT9m4PZLJL3NyX3JyNHQVBABAwH2abfG5ijYOSK8UX1t+9r2pXuPeCFv6VAVRnn9/tq2z8ujejhuCQtBv4SHFavWK5NSOr9Yr8DWBksai1nzQ7x/8fIlOXzFJZWPzhbSGLYeVq/fjGcWcwb6S7S8JFsexQ920qiADA0OnY/CP9Y6hqcfZWnu4kyRWVsSy0l4s9HgRNcGyTKUsMLMJbbnSSBD7CwpfcTGUajJtw5Wx7eMsHhyUU89UiSYo4ps7P+64+e0nMe+PdovTOl065VV1SkLT/Vsdt4SHIIf7RyRUVX2Yfr/jq/UKeCjYEYF8G4XMuUS8fo1oasVJSlbUNZ1Mrt/wV907P+OZJexBPpLtLwkWD2MFu0Js4+8Jw8BgUBj5nxxWj4sc+c9exytLELEJxNFeLPR4EbladNbSefDDymoHCoqizEydBFqWMkxsokyrUuoUCdU2Ax61VK1pUq678ikHYX8/8gsxu9UTHpgnlE1fWf3LZ5arv4L5HXVNiVno8ajIARcui1noCne3Dq7WWxhmB6VOQl+9SgT9g++PQQLNIAAAIEg8qwRLKcTu5pP1anagC3dMMKuPHUA7FKbLwMDQQYxcCFvbEWKKPJa19u2dUgPuVlFizWlr32kPL+7Ozv2sr19XWdkVQMB9mu3d7bkybxHXjA0AuF/1YG38puEug+f6zWjXY8fx6Mfzi6j95yvZzDc7bosll3NuYNTgS/GNOPGut2fHF+wVSNlgfwzyRx4560j9elbRiJpCPL0YsZKyAhz5C2JRZwvwfPhNGRgMHyMXQqweZ2kXwgKWjZPWKafl5CCLxtrcG5ajv265cqmiEqPIwYZUXFQXuKZsu8FmD36X+y12Pp1/8cvbe1aFLolur5XEQyRj5pdtXdp46wI/aFDHjbHn8+IHRcdeukIC8P7zoYWEvBq7kzc8OT+2uPqamd1mK4cZ7w70tu81hwoMDM8PRi6Ere4IS3Jbe74fL6LGcONlNsGs/x8e7s7OXWpgxUV1xCbatDJV+dfPJ/+RHPp8yAZniYPucyE2x/Sl9yt2v82ydWnNmUoLKy73/MABsZeuEBT1QR+vji9oiOAEdr8ES87HkvMARbH6OnHHh4i8bIejSOF9cuAlYp4nsbZfT5cnZWBgeBJjDpYhcYrUkChPiwMGK9F+NEoBcKqYdFGdtnEZ1nKlRN10rrziRUcaEmI4VDXXHHA8IE03+8zzY1oq2ALL2kk6cVHVng/JJlWn2GPJ5ZyPifqrWP526r1OWdBAoFRNmoRM1c4Ttcv2NP1zDZbwhMtHSbbN4b84kOXrAFAEAuAVLzh1EqtEBTz/wP/ON7jOFQwMzzPG/NX0v3PRZ7ZylKaJqKtBzbRUN71dScnYpKr4vHXMOy1XvsnNm+5gJ2b1vl/UnbLUjxO2TfAcHejt+eCXEukqifYA2jbhB8ZoctJqft5qOm9tp/i0LDicswOjhly6AgOw0c+n4wv2IGRlPXYnV3M7j8grR33s2f2c+XNjIFGr7ZoteeCnGOSMnFqSQPyaQ30RDtsKeuNBAwODsWHMO8JWHYSlBSxLe6AtI/BEETVFcpMvtm0pKKMhyW9z8w2nB6+OUID68/6RjxK2vhOxYpbPZBN3kWWINOtA0bPZFLogmbiIaFDWX/qns8yz4HAuxUSfL69YcjuZNPh6Ds9CFFc1HbpR98HBunW/E4VV3LgAyY55wldHsKO82lDBhwy1hVInoX2koO8/+GepJM5sDhkYehpjFsLWHYStVhk9XkQGYWes/38u+mex3Fci9hGLtQ42TFRY4wfxmy8WJnw74vNg674tFx1HWAIAFZ+v1GNBCEFN57zTcP7P5pxOy4s3YbPODozKrG+Yff0W3iu0kCDx+3L1wavK1fsbPj9Gqpr4MwZId8zjzx/M6udMN/OPi4D1QUjSWPRsCen7F35Ot9R7BgaGLuK5FEJFAapNCKuaQXothZadsXH9TwhbwmS61MjOJbM6e8HxFZYCiy+GbDDjPdZYAwKes+wUCdW1Wfo0VEOk5iYzXq/ev5moq+4sU4UoeiQqokqjmXT1WjNpoNsisqKu+Xxaw47jtUu/Vx+8CtiocOlwybbZ/BkDUE+bDja/dRVDx4ehHwfDL10iXrpMlKo7y2oGBgZ6GLMQYg04S0hjR3iskJwgy6aIZol5HwDAndraYnXTGBurrrazszj84OTq8+tf6TdnaeA89JlWSiwR6jHdNutXuaYO12NxrleQsP/oqu/XURpdW1u0Cx9B/u0fjkLQhIQkteH0qSApPLNEffBq3Ts/13/0J55Tyg51l2yZLfpgCm9CKOLYyVk0k53h9MmoBRf4/YVtuku2VomGgYGh6zBqIWw1iTCPZaNln/drDjkSPW3tOhwACACwLTP7VTcXpDdkPWsIzadJO//MPLJ96MYYh/6tDZN6CG2iZOk/FJCYPjsw0dBpLDu36gOfgs47zOTA8MGIUHMOJ+5yQrVG01nL6gFV36RJeqD69kzta3saf44HLIT/8lDJ9nmChUPY4e6QqAsL/gpZYHMocnsCml5DefyO//RAL18uAwODvhizEGrqMLb46cawRF01oChE/HSL+comkFROyWr+OxctVqtPlpYtdHHqHlM7QlGdfNHJNzAS+3b4NieJfduD7WLN+RacrJ+LgV7PWumkJWSTqlNKcj8EhaB9oUGxFuZRFy4XNjZ24srtQ5B4Zon6r2v1635Xrt6vuf4AdbMWfzhN/OELvIlhqLPFsyHHXYe9APopBvkxBvkslYw5iidXMWrIwNBN9L6sAN3R1BNs0dMnhFiJ9u3gX/nkOOvqxuxsM9twAMBnWdnznR0lLENvsH4i5+w3yT8uCJg12m2YjlPcX7BN+zq/8HS5wzALureDENR07nvlX6xEZZYgYCDd6a0uC8A6H29TDjvy/OWjURFd3fqY0uB4aqHmdi52Nx82FbP8HHjTo1A3K4D0/PfCQdbQrQnonkxy+El8vCP8cTBi1oV7UQYGBgCMWwixeowlelrJMEW+1n68v2STqwQnrJxiYYRVh+H7CwpvDxncLWbqSYNG9dmNr3Jr8rcOXu9mQiOiB0Igr7kOd7/I4ZmzzQOldO8L80Vmr3xUseMNntAE+OtasE0XXnVztePx4i4nHAgLjrOkLdLtQiobW2q+4Bly1NWSFejCm2SIDW8RCLzsBU91gTfdJXz+wlb5Iiv9WmsvzcDA0AkYsxBq6rREjeKKfLbL03ncchV1r4YS1f/uEPEmAOCrnNxR1lb2/PZzwnqKW6V3P0ncHm0f8d2Iz1kI7W0rS4D0WeCY+mUe15SttTtH26Cm1rI571T98DHfwobdSiKKfkywtZGx2S8kXf88wH+6g12nrEkUVmLJ+didPKKsluVjzw51EywcAvFpts3tdqRssCkEedENXpFE7M8mt4Uhw+x6gbuagaE3YrRCSGIkRQKE+/QXaUyRL+g/6qmLB3OpmVZ5TfkKC8doDUnuzM49MSCyuyylRxPe/E3yvoTi6+9FruxnqX9DDL4lx/0F24x9RQGvuXBMaEspx8WXO2JO1bdrLV7biph05u5toLnZ2eiosQmJmfX1H/h46/fsp5ox/F4xdjcfSykAKMLq58SbEoF62hjC4SctfEygMyPQQwXk8kTCSQS2hCJ+MkYOGRg6GaMVQu1JhC39eJ/ZxPyaQ37A+d3BewoEIQfyC/wlYj+JISbRp1dmfpL4hafM/YeRO4RsQQdXk/UR2ceapX2d7/+qs9Y8k7ZhBwxgkXjFl+9YLN8GC2kfsbaBr0R8Y8igiVevpSde3xcaxEd0bddHyKuxtEI8pQDPLkNdLdEAR+Hwvoj104FRvY5xjvAoe/iHLHLYSXyIDbymDyRqtZskAwMDbYxWCLE6nCV+5ly0Qo5ITCH2E+EH2XVUiQqHK/52nHSQAuCzrOyd/fy70VKdwEni9/v//nX/yGvBLw906LTdqnWUKaYi0r7O91vqrLU6edsIo0aTysrKb9eaL93cWpdj/TBls09H93/55p3BF+P/7R9uxW01YoRqaMLSi/G0Qiy1ECAwy8+BM9hP8OpIiGvogU60QGHwshf8ggv8yV0i/CR7cR/iDX9Eyu5psxgYjAKjFUKtO0JMkc+yfrqj0K851MuyeB5iI5K5H1OUchF4kIG1HsyrLdiY+IWMa/LNiM+eqBfTGTgMsyCayHvfFfguckLoh2RIRs2taait2rfBdME6COnMjxMHhveFBm3IyAw/d+nf/uGPh5JSGhzPKsHvFWPpRWSZEvW0Yfk5cEcFwpaduTE1QCRssCkEmevQ+PkDvucf2Cpf5DUfmGe0f8QMDN2E0f4Nac2mb867x3b0furibznkFvhPxz5TAQBbMx+84eneTSbqAE4SP9/745+sY4v7vTTMpauiWJ3HWj34XZ7xQ6HPQkcIoemCgiCTqcurftxY8/NW2YtvdW7XdQiA9709PUXCuMsJn/n0mYaxsAw5fl9O5JcjjuasPnb8mdGoq2Wv8/x1EFs++CYKWekLr7lFevyBv98PfsmDCStlYNAfo/3r0bojbM5O5bg9EWCSUk1RmBIvvWjnMe56dU1+Y+NkO9tuNLMtsmvyFp96I70y69sRn3edCgIAAATcptjALCjrN7k+ifYwLJu1mlBW1Rzc3olFZwAAACfw+/LRN+QpKY2DPzl+b99ZAsO5o4MkO+aJ3p3IHR+Kelg/byr4EC8p9Ecs8s9Q5N980vUg/kUaqdKndh4DA4PxCuGzO0KysYGoUrDs3B6/+GsOuUBwyMppMJsr+eBexmpPD9QAaqppCM3elF/fOL92rPvwzYPWWvDNuvqOEAx5zbbXKLHMX4opgraYQSy22SsfEzXl1fs3AbJj5TJxAs9SNB2+Ub/539qle9S/JwKcMB0XKvz8pfVjvYaaYWVu5hDHqPx/HSHYDDoxHD02DLldSbkexNbdJqo7rRYsA8PzgtEK4bM7wuacVLaT9+N+LAqAg7mUp/JPxz5TEyqr7tfXz3d+2oPY/dxQ3Jl/fHlBXdHeUbvG6FwvpuPALNjnZScSIzP2FpIa2sVIITbHdOF6CtNU7vmIwjF6k3ECzyxpOvSf+DX+Ek81arjD+0m2zxWtncybEsHycxCLeH9Fhk2wtQk9e/F8eQVd84wbfxn0UwxyaTRa2AA8fsfeuk6UMb0sGBh0xmh9hFqFkOP2RDhoUjllTz4ATQoLx+jplxPX9vFia+vW220U15fsvvVDYV3x0qB5kbah3W8AjEJes+2z/yhJ/SrPZ4ETKqAXRwqhLNnc96p/2lS150PTeWsgVptBjRQg5FVYWhGeVog/KEVsTFAvW+7wvqiHDcTTPhECYLWne7CJdNa1m8vdXVd7efT85t2Q8JRAP0QjRSp4awrp8yc2zRV+0x92FDK/JAaGdjDaHeGz6ROanFSO6xMOwm/vky9y/nT0nnK+orq4Uf2io0P32viIJrxpb8qvi0+96SFz3TdqZ4+oYAsQDLlPtRW7CFJ25+rRsKmliy/MF1Z+t5bSND07gCyrbb6Urvr6jHL5Dw07jpNltZwYH8nnc0QfTOG9EMkKcGpNBR8y2ML8xpCYwyWKcQmJtRjNredzgL0A2h6BZExhSdgg+F987iWCqd/NwNA2RrsjfKoZIdmkwivkLAePh1cqm8CRAmyi+m/HmN+X3M1Y5+PVI95BkqJO5J7dc/dAuE3wT6N3m3ANIAEAAs5jrFAukrIr1/cVJ64pzWw1GJHNfLPmj50Vu1abLlyPCE0IRQ2eVYJnluAZxQCCUG9btI8tb1IYbK5n1QJbHu/SoOj309JDz178KzLMMKsf9CzmXLAhGFntj3yVQY49TTgIwbI+8ERnJriUgUELximERDMJIPB4VpwmJ43t6PW4g/D7THKh5JKQZRvfLKrWFE6z75zKlrRIrcjYefM7NsL6JGaNp8yt/QndiP1Qc5YQSdmZ6zXXQexEsx4pBUSh01UnTtW8vRulLCEeB/W0Rr1teRNCYYvO6SyBQtAmPx9fsTj20pWtAb6ze243b8hI2ODtAPhNf/hQAbk7nVx1jVjoCS/yRqxp15dlYDBmjFMINXU4W/xMpMxjiRMEBb7OIHcTX7sGzZt4L+NDX2+4e7eDlerqb+78eLss5eWAF+NcBkHd2fhOZ6wiZFxTdsYPhS7jrMyD2tmqUhqcyCnFMxV4VgmeUwabiVieDki0pOHu3ybzVj3lne0sZjna95VKZly7cUiu+DqorznH0Etp9wgIBCY6wROd4PRaanc66fsXNtIeXu4LB5sZ4qeOgaH7MU4hfLYBU/ODFMmEVx7+eLiADELvII0lN4QhFMieYGvTbbap8aZf0//+N+v4eI8RP4d+zUUN+tkt9RD6LXFO/75A/b/27jw8qur+H/jn3G32fcm+kwSSsCNgVMSwo1AsuH37A7e2arUuj21dam2rttVqtYsibb8oar/WiqK1sbJjURYNa4CQjeyZJJOZzL7d7fz+GBqjghDIZD2vJw/PnTs3M4ebO+c999xzz3HxmQu/OlEtjvJiXadY4xBrHFKLi860MvkpigWTNHenIM3pQdG4mXnuDb82LLtdPSMht0KWGPQH51/1q5M1k7fufGna5MH8U444RUb0Uin9qxn0+hr5uh1SmhruK6FWZFEsaS8lxrbRGYR8UOK0X/R4lKNhwdnK9blA+GKVfKfw4rhpP7i2qvbpicWD88VYxnhb466/HHm9xDbhz4t/l6JNGpS3vVjqZMWk+3Kr1jfHeoRx16finoBY3yHWd4m17X5ngM61s4WpqpWz6LxkxJ3hcOJyiq13/dr9l8dFl0O/6DsDO/RMHEtRvyiesDA56ebPD7zf3vGHqZOMw35G5SFk5ODBidT9JdQ/m+U/nZDv3SvdXEDdXkDlG8gJIjFGjc4g/EqXUb7xBJdZiJjTlWOVF3td9arokT36x3U9bVenJA9Ckfa2V/z58AazyvSbuT8rMOcNwjsOFMyLlMNZmOv17m7s2eGhVTRbmErnJ9NTMrTjMxB77kOITc6yPfD7ntd+7WqtM6/+CaW82HkzzqjUYj6yYN5Dx45P3LLjT1Mnr0hLScS7jBq97aW1Pvy/NfKccnG8Ed1eSK3MJoOXEmPO6Dzk+YDA9WkajdVX9h1Z7cUT8l3Mi2mTv3dnVd1bsy9JdGEqnSf+evRvAT5417RbZ6fOSPTbDQjZGxKrHWKdQ6zrlDu9dIaFzkuyXDfZ41fWfxLKm5NqnaQXg0FgzvdGQ1pnsv3gad+Hrzl/d6/ltp99fSasAaFh6BenTr4pI/17Bw+vb2x6efqUdNXwnV15mCgwoN/OpH81g/6gWV5fK9+3T7ohl7q1gLrERk4QibFidAahEBC1mV90jIvVHzMsvz2+7ONhW337otDOtxS3ldnx5VZL4orR6G3ecOytk+661SXXXZ23gELD+lKM1OGR6juFGodY68BhnilIYQvTuNJCJsvWG3hJAJrxkerXW/2nQrYybf/egKINy25j03K7X3rYtPIHqqlzBv7/AAAAl1ktRxeUPV9bP33brkcnFP5wXO4g94QaiVgKVuZQK3OothDeUItv2iWpaLi9kLopj0oi3yWI0W50BmHfYWVwLCJ0NnOZhfGHr9XJ36XWcUW3vdLScXTBvAQVoNHXsqHy78dd1WtKrv/ZZT9iqH5P9TcYJFlscoq1HWKtQ6zrRAqGyU9lClOUS6bSqeaz9WPVZqgm359X+2bbqde6JqxRKPo5J5562lw2KdP96pOxpirDstt726sHFktRD40vWJqS/L0Dhza1O16aOrmE3Gt4ftI16LGp6KdTqd0d+JVa+ZeHhNl2dFMedW02pSMXXolRanQGYd8Rt2ONVVzGuPhwXxjgtWPOx/ybXqLW/aggNVV11uleL1i9p/GN429XdlfdMGHFo6UPKOjhNXcqFiSpoUusbhdrHGJDF2U3MAUp3KwC9eorKfP5nuGxGrr4u1kNm9uPvtAw7oY0c1H/pktn03LtD/7J89YfnC/cZ17zMJuUqFsAJxr0e8uu/FtL64Lde67PSHuyuEh/Hlc0CQBAAFemoCtT6LBIf9Asv3kK37tPWJxO3ZCLFqeTi4jEaDM6j2je/8UZYay+UjFucnx5cyu+MvJK17g11SH+3YIBvoH9lLfp9WP/OOo8cf2Ebz1y6f3D5b4ISZba3GJTt9ToFBudsqOHzrQyBamKRZM1Zx/V89wQ2K8wWItMtX9r89YEs5clU0w/mh8pldZy60/DFdu7//gj/cL/0V654gKLcc43QmhNVuY1Kcm/rKou2rL91xOLVmdlknbS86dm4MY86sY8cMfodxrll6rkW3dLi9Op63LQkgxKPTrrD2LMGY0HMgYh2OeM8NQxw9KbAQADPFnhuz/898el3z4/ZaJi4MbXrnLVvn78rVOeppuKVv609AFuaM8CZSx1eKQmp9jYLTU5pVY3ZdHS2TYm286VFtLZtjPe5HBhdJmqKQ/m1b/tqPxjQ+HqDJWtn82kl8znMgvdbzwdO3XMdOP9lLp/Z5bnz8xxf5gy6YaM9B8cOvJaU8sLUyZOMgzMADdjh0UBd4yn7hhPdUfhvSb5z9Xy7Z9ISzKoG3PR4nRKMSzb/gniPI3CIBSjEsVS8RMUzEcFRyOXPQEA/nFKnuX/333p/y9bZ1ieOjB960+4qv92fOMpb9P141c8ccXDQxOBkiw5PFKTU2zqlpqcUpubMmnpHDuTY+dmjqOzrAmdvY9R0uPXZHTs6an8U0PWEnvy7LNeXDzzrydl2O//vb/81a5n7jRd/0Nl8eyElRRKLeaD86/6a0PTot17l6UmP1lclKQcHmftI4pNCd8fT31/POWOwbuN8u+Py7ftlr6VRd2YR5WlIGZYdwgjiDMbhUHY9wIh33SSS8tDLMfL8NznbfdE3/4xPP7JlInf/Arn42Dn0Ter3m3zO/5fyXVPzHmEpQZxT0qy1OoWm7ulJqfU1C2191BmLZ1tp7Nt3CV5dJbtwhs8L1TKZWZDrrp+o8N5wDtuVao6pR8XXxHDGlZ8XznpMs/fn+eOfGK89i5K3c/+qOeNRujOvJybMtN/dbKmZOv2Bwvy78/PU9LkdOZCWBSnE9ERxm834McPSt/x429lUSuzqXlpiIzuTYwgCOPhPkXLww8/bDKZHnrooTM+y/M8xljRZ5BJX32oZatz4g9yAMD7zou00aabf8OLVXJ03/d2Jl81MWPKM5NKLrgwvMRva/rPO9UfIEDXjV++IOeqwegRikHq9EiNTrGhS2roklrdlN1AZ9mYbBudbaczrUg5BP35gsGgRqNBfe9MwOA86G38V6dtiiFraRKt6F9diPmY78MNkSO7E31qGHcqGPpJ5fEDHu/Pigpvyc4akrlHLkwgENDpEtWMfDGag3hTE363UT7pxVdnUMuz0Pw0qp/dioe1YbvnRzdBECRJUioHvm9jr9F4RvjfCZiwwIcP70760YsBAd757D/TGGimkzYVT7iwl3VFej6o++iDui0TLPn3TP/u9OTJA1rqL4tf52vplppdYlO31NyNNAomL4nOSeJm5g/sdb6BhMA+w2gs1Da813H4ufq8b6eYJvSj1kCcwnjtHarJl3ve/B17YKdx+Xdpkz1xhc3Tat4tnfVZj+epqupfnax59pF8XwAAIABJREFUZHzh7TlZ9MiJw2EoS4seKEEPlFCOMH6/CW+olW/fLZWY0eJ0alE6mm5FNNm7xLA0Cs8IHbvdUTefe21K+PB/wvu3WO/69S8PxrQHr3vadtu2q66aYux3L4lj3Sffqymv6DgyL3vOqvHL0nUDP6wzjgpSm1tqcZ3+aXcjg5rJstFZNjrbxmTZkS6B34YuzBnOCPvwVAcb3u9QWbmcb6X0txMNFvjAjreDn3ygvWK5bt7155jpfiDscnY/drzKL4q/KJpwbVrKML8BfwSdl8Qk+KQTb2mTt7Tj9hAuS6UWpKEFaShHN6z38NmMoD0/mgzCGeEoDMKmD7sYJZU+z+Za91P1zAWBCXPve+OlGhNzw8SrHh5fcMYXOfMrS/yOpt2baj+MiNFrC5Yuzp2nYQdsGjcsSFJLt9ToFBucUpNTdgWoVBOTZaMzrHSmlc6wDP51vv765iAEACzhjj09rductmnGrCVJtLJ/LaWSz+0rfyVWd9Rw9S3qGfMSMVr3V3zY0fnUyZoenv9xYf7qrMwB7Fc8sEZoddwRhm3t8rZ2vL1d1rJoXiqal4auSqGsw+473lmN0D0/0pEgBOh/ENa91a7PUVsLpa5nf5Dyi789uLfHVf94XeaqT+cvOM+GrwZv87/qt2xv+k+xtfDbBdfMSJl6sacIGGSXX2p1S+1uqdUttbnlbj+VamZy7XS2ncmx02lmoIdptXs25wzCOCEgNn3Y5akOZC5OSpppRFT/9mTs1DHvpnWIUxquuUWRNwC9nM7pU5f7meraCo/nztyc+/LHmbhhN57KSK+OMcDxHrzDgXc68O5OOVuL5qWheanUnGSkHXY7+0tG+p4foUgQAvQ/CE/8tTn1cjPT9qHo7XYvuufXf3/4feslBxYvydWcY9KDqBjd0fxJef1WV9i9NG/B0rz5SRrbhZUZh6JSi0tq65Ha3PH8Q1olnWam0y10hoVOs9CppvMfsXp4Os8gPL1xS6TxX51CUMy+Jtlc3M+qBOPI0U99H26gTXbDNbf2nU4rcY75/M/W1P27o/O2nKz78vPShtPg3aOpOhZlOODCOx14e7tc4cLTLGhBGjU/Dc2wDsc7MUbTnh9BSGeZCyH4BVZLBz/fZvzOjx/ftvdzfeZvJ0/65hSs7Tn1r/otHzfvmWQvWlNyw6zUaf0bIFuSpU6v1N5z+gpfqwtHeDrDQqdb6Cwbd9n4EdHUmVDaTNXEu3O8tcHGf3W2bu/OWZakzz3vyZgQUk25Qjnx0vBnW92vPMllFuiXrE7Q/BW9Jhr0r8+c3hmNrjvVOHXbrsXJST8pzCcDlg44hoLZdjTbjh6dQoVF2N2Jt7fLd34qNwbwJTZUmoRKk6hL7cgwpj89RMKNwiDkgxLyNiKa/ovH0h14Y1zq7O+OO/M5REgI72jaXV6/1c8Hrs5b8Oo1f7KqzOd+A0mWnD6pvUdu65Ha3ZLDIzt9lFlLp1voDKviyiI600rZSI15BsYC7ZQH8pwHvDV/a9OkKTMW2HWZ53umhWhGU7pUfcn80J5y18uPshn5+vk3cDlFCS1wslL5i+IJ9xeMW3eqceHuPVOMhrvH5S5JThrmvWlGKDUDi9PR4nQaADwx2OfE+5zyb49KB1w4S4suS4rnIhqnJzufGGCjrmkUw56fnJgwbZtbn/pAZ+UJU8mRZSsNX56vXMb4YOeRLQ279jkqZiRPuWbcwunJU85atWEsd/uleOa1uaX2HrnLh0waOt1Cp5rpdDOdah4F7ZwXoF9No1+BJdx92Ney1cnpmPQyW38bS7EkRg597N/6d0pr1M+/Tlk0axC60sRk+a2WtpdPNThjsTtyc27LybIphmZgmrHWQCfKcKQH7+3Ce7vwni4syPhSO3VpEpptRzOsaDDHOx1re36YINcIAfoZhEJIOvR0TYb0+IMFszar0w4uXZar/eLAbfS1bGv8eGvjx2aVcXHOvPnZc/SKLx3WWJDkTq/U4ZE7vVKnR3Z4JIcH6VR0mplON9PpFjrNTKWaETvmYu/rLiYI47CEnQe9bTu6WR2bXmY1T9D1a3g2kKXw4f8Etr8NFK27aqVq6hxED0aleNDjfflUw6Z2x9Lk5Ftzsq6yWQf5BHGMV8etIby3C+934v1OXNmDJxjRTBuaZkXTrajEhNhEXlkc43t+qJAgBOhnEIY7olV/qa40rX8gadY/Ly+dm5YLAG0Bx87mT3Y2fxoWwmVZVyzKLcsxZIIky66A1OWVO7xSl1fu9EpdXuwLU3YDlWykk41UspFOM9Op5jF+ee9sLj4I47CMXUf8jk9cQkBKLjUlzTKzmv59z4g1nAjseFtordOULtXOWZG4Edr68vDCG80tG5paenj+luzMm7OzcjQDdnfNNyPVca+YBAdduKIbH3Ljgy7cEMBFRjTNiqZa0BQLmmRGmgH9akT2/JAgQQjQzyD01gX3/d+HN48PPpw/7tvjcj9t++w/LXu8Yc/VhtLLVMUZMT3u8kmdXrnTK7sDyKihk4xUsoFONp0OP4sO+tm/f8waqCD84gXbIh17etyVfnOxLvlSsz5b3a8TRKGtPrDznWjNIfWMMs3MhWxa7kAV7Jsd8fpebWr+e0tbsV73nayMlWlpib7jglTHZxMW4WgPPuzCR3rwYReu8uIMDZpmRTOsaIYNTbNc7O0ZZM8PCRKEAP0Mwupt1fc0bp8mxPL5HqufLRTttiDH+AXKpKHtBspuoOx6OslIJRvpJMMYvLA3gAY8COPEiNT1uafrM48sYPslRvsMo9LcjzNyqccZ+mxLqGIbpdJpZs5XTy+jtIMx4xIvy//u6Pq/ltZtXc6r7NbvZGZck5KcoOG8SXV8nkQZTnrxYTc+4MIHXbiyB2dq0DQrmmJBk81oqhVZ+nmRl+z5IUGCEKCfQXigopLZsFNlUesyUyyZmfHAo6z6EXe7+vCXoCD84vXbIs4Kb/dhnzpJYZtmsEwy9KPJFONYfWXo823R4/u53BL11DnKktmUcjCaLn2CsKnd8WZL24Eez4Ik+/LUlCUpSRZuIFvXSXV8YUQZqrz4oAsfceOjPfiIG+tYNNkMJWZUYkLFJjTBiJTfeIiRPT8kSBAC9P+GemJwJDoI47CEPdXB7sNez8mgNkNlnay3TNTHB1U/r1+PRSLH90UO747VH1PkT1ZNnaMqnoUUg3F3fHcs9mFH178cHTuc3VOMhmWpyUuTkyfoB6AaJdXxQGkM4MoefMIDxzy4yoPr/Dhdg4qMaLwRxhtQkQkVGr50CyPZ80OCBCEACcLhanCCsJcsYs/JgOuo33MyoElTWkr05hLd+beaytFQ9Ni+8OHdfMNxLqdYVTJbWTKbNlgSWua4qCTt6nb9y9Hx744uhGBJctLSlOQyu019oQ2npDpOEFGGej+u8uIaH5z04JNeXO3DGgYmGFGBARUYULYiOiVZla0j02gMKhKEACQIh6tBDsJesoi9tcGe4/6eEwFWx5iLdeYivTZDeZ6jmOJYJFp9IHJ8f7SqgjEnKYtnKYtmchn5g3AnIgBU+QP/7uj8qLOrosczzWS8ym67ymadbTFz/RngmwThYGoL4Rof1PpwtRefcAsNIaYzgsfpUaEBFRggT49ydShPD2nq/g6jS5wvEoQAJAiHq6EKwi9gCDSH3ccDnupAzCMY8jWmAq2xUKu0nN9poizHGk9ET3wWrfpcDgWUE2Yoi2Yqxk+jlOc99ttFCInSpy7Xrm7XLmf3SX9glsU8x2qZY7PONJtU5zpTJEE4VOJ7PiJCrR/XeHGND075cUMANwTAFcXZWpSnhzw9GqdHeXqUq4NsLVKNwsG7BhsJQgAShMPV0AdhH3xA9NYGvbVBb02QYih9ntowTmPI05xn26no7oyerIie+DzWcJxNylTkT1KMm6zIK0HcYEwR5BOET1zuT7pdn7rclT7/ZKPhcqul1GKebTHbz3RgkyAcKt+w56MSNARwvQ+fCsApPz7lxw0BaAliPQeZGpSpRZlayNaiDC1kaFCmFiUNo1HchzsShAAkCIerYRWEfUWcMd+pkO9UyFcfQjTS52r0WSpdtlqTeu7mUyyJfHN1rPZIrP4o31rPpmQrcoq43GJFThGlNQ5C4cOS9Jm75xOXe5+7Z7+7x6LgLrWYZ5vNl5hNk42G+BSJJAiHygXs+c4ItARxSxC3BKElhJsD0BrCrSHs5yFZjVLVkKRCaWpIUqFMLWRqUboGMjRIQW7s6oMEIQAJwuFq2AZhX5Fu3t8YCjSF/U2RmIfXpqt0WWptpkqXoVKYznFzNRZ4vrk61nCCb6riG09SWgOXPZ5NzWVTc7i03EHIRQxw0h/Y7+7Z39NT0eOpDQSL9PoZZmOJSjUzyV5s0F9wdxviwgzgV5CoBJ1h7AhDVwS3h6EzfDopW4PQFsJmBWRoUYYGZWghS4syNJCiRqlqSFGf4waPUYkEIQAJwuFqRARhX2JUCjZHAi2RQEs42BrBGHQZKm26SpOm1KQpz9GIirHQ2cy31AiORsHRKLQ3IJphU3PYtFw2JZtNyWFSshI90mlUko54fRUez35nd3U4Uu0PpKqUEw2GEoN+okFfotfn67TMyPlzjESDcy6OATrD0BLErSHcGoLmIG4LQUcYO8LQGcYqBlJUKEkFqRpkU0KyCiWrwa5EyWpIUoFNmdjRVocECUIAEoTD1YgLwq/gfUKgJRJsi4TaoyFHVIrJmlSlJlWpSlKobAp1koLTf1OwSV6X4GgUOhqF9gaho0l0ORhLCpOcySZlnv7Xno6YhIy1Fq+OJYzrg6FjPt8xn/+E31/p9bdFIoU6bbFeP16vy9dqCnTafK1Wy5DeGgNmODRK98SgI4y7ItARxt3R08vOKO4MQ1cEuqNYz4JViaxKsCiRVQE2FdiUyKIAixIsCmRVgk2JTCOqviQT8xJEonAG1jKRtUw8PXOkEJJC7ZFwZyzUHnUd8UW6YpIgq2ynQ1Fl41Q2hcrOUf/9vk0brbTRqiy6JP4QS6LY2SI4W8XO5siRTwNdzaK7kzZY2eRMJimDsWewSZmMLZXSDNhElTRChTptoU67Kj0tviYiSVX+wHGfvyYQ2NjWXhcI1QaDFo7L1ahzNJocjTpXq4kvpCqVZErFEcqsALMCFZsAzjIUrysKrih2RcEVw64oOCPgCONjPeCKYncM3DFwRnBIBKvidF7G/zUrwKJAZgWYFWBRxheQRQHMqDu/PCMShAQBAMBqaGOB1ljwxcwVYkSKOPmIMxZ2xlxHfGFnLOriGTWtMHNKM6c0s0oLpzCxChOrMHEUw7BpuV8a6VuWRFeH0NkiOltj9ZWhPeWiywEYGGsqY01hrKm0NZkxJ9HmJNpoG5BmVRVNTzcZp5u+uHiJAVrD4cZQ/Ce0vau7IdTUGAq5Y3y2Rp2j0eRqNJlqVZpKlalWpatVaSqVoj93NBLDUDzbAOBsSQkAvAyuKHZHwRWD7gh2x6AnBm0hXNkD7hjuiUFPDHpi2B0FNQMmBTJxYFSAiUMGDvQc6FjQs8ioAD0LRg4ZOPjvD9IldsD5RCFBSBBnxqhoXZZKl9WnnzsGPiBG3Xy0h4+5eX9jOHZIiHn5mEdgVLTCxHIGVmFkOQPDGViFgeX0Nq4wVTWptPcF5JBfdHeI3Q7R5eBPHQ9X7BB7OmW/h9KZGJONNtpoo5U22mijjdabaKON0hkvJiMRQKZanalWX2n70vqoJDWGwg2hUGMo3BoOH/P5W8LhtkikPRLVs0ySQmlXKlKVSptCYVcqkhQKm0JhVXDJSmWSUkF66IwCHAWpapR6evDdb2ob8AvgiWFPDLw8eGLYx0NAAL8AHh43BMAvgDcm+3jw8eDlwS/gkABGBRg4pGdBx4KaASOHtCxoGNCwYOKQloX4w6+sVzMwhH1lExiENTU1e/fuzczMLCsrO+OVJK/X+9FHH9E0vXjxYr1+wJqMCCJREHB6htMz+pwvj9+NgQ+IMY/A+4WYV+B9QrgjFvMKfEDkvQIAcEaW0zGcnmF1DKczc/okNnMGM4FRqWlGQ9MclnxuyeuSPE7J5xZdjljdUSnQI3m65aCP0ugonZnWGSmNgdLqKY1BYBQRaxKl1lNaPaXWUxpdf8NSSdMT9LozDnzqivFdsWhXNNYRjTqjsc5otDYQcMX47lisKxZzRmMIQYpSmaRU2hScLZ6RHGdRcFaOsygUZo61cJx5QAcZJ4aQngU9i7JON5ScuzldxvFQxH4BggKERPDxOCBASICQCB4et4QgJEBQBB8vx9eHRfDwOCSAIINRAWoGKWkwcqBiQEWDkUMKCpQUZVFLvU99Zxw1sDNNJioI33nnnTvvvHPVqlUvvPBCSUnJm2+++ZUN2traZs2aVVpaKgjCQw899Nlnn9nt9gQVhiAS678BCXCG26QlXubjoegThaDI+8VwV1AIikJYEkOSGJLEmMSqaUbNMepMRp3LqGnGRDMpFK2iGQWiqCglhZAYACEoCz454pP8beGm43LQL4f9cigghfyI5SiVhlJpKZUGKTWUWkupdZRaR6m0lFpLqbVIpY0/S6m03zzmuFXBWRVc8dm/l4ZEqSMa7YpGu2N8ZzTq4vmWcOSQ1+uO8W6ed/O8O8b7BMGi4Iwsa+Li/7LxZQPL6hnGwLIGljWwvQuskWPJFcvRgUJgUoBJ0ffveb5/23iIhkUckeILEJHAx+NADEI8DmMUFrFLgFN+uDFvgIudkCDEGD/66KPr1q1btWqVz+fLzc09ePDg9OnT+27z+9//vqys7I033gCAlStXrl279he/+EUiCkMQQ4vmKJVdobKftaMelrEYlk7/RCQhLIlhSYrKQlCMdktiRBYjnBQzSlG9FEuWorIYlWgFRSsoWkHTJopJpWkOU5RE0RJFCTTFA46iQJQKhEEIg9AMQhD4EIr55WgAoj4QQ5RSRSsZSqFCShXiVJRaSylUSKFCChWlVCNWgRiWUmmBYSiFCrEcMBylUAFNUyqtCtA4rXac9psGopMw7uF5ryB4eMErCB6e9wqClxe8gtAaDvsF0ScIPkHwCaJPEPyi4OEFPctoaEbLMHqW0bOshqbVDG1kWS3DqGlayzBKmlbRtJqmFTSlZRgWIQPLUgiZOJZGSM+wLIVIF9kR7UwhCgBIECRJwkplAq9eJ+S4qampaW5uXrZsGQAYDIb58+eXl5d/JQjLy8ufeeaZ+PLKlSuff/55EoTE2IQoxGqZ859bKhAIqFmNxMtSVJJ4WQxLUkz+748khmVZkGVBFiOyDLKMsChLQIFEyViJJUrGIsaSLPkwADAcwoBpVkYIU5QEICGQKErEGCMsUBDBshewSEEMSyJgTIkBAMAij0CiOAyAKJahkIBYBUIypaABALEczUqIplUMp6bkDJZCDIcA0yoKMSwAQko1ACCGYY0cAAcAQNEBjovIOEzLAcQEEBWS5LAs+wGHZCEsxtxhKSLLMUBhGWKyHBQlAWO/KEoIeXlBxDggCrwsh0RJSdMqmlJStIqmFTSlpmkaIT3LAgCDkI5hAEBF00qaQoCMHAsACoqKX/hUM7SCOn2dysSd7vWBAIzs6eVIJJIqSr1/iK9Er45hGPSlypqjKA2Z/XskSEgQOhwOq9Xae29fWlqaw+H4yjbt7e1paWm9G7S3t5/t1WRZ3r9//8svvxx/mJmZuXDhwt5nBUHAGFOkq9ugEwRBEISRex/hyCUIgqyUkAoYFcUApbiIT7EYkQBAjmEsY4mXsYSxhKWYDABYwrKAAQBLIMWkvtsDgCxgOcIDYJnnZR5kSZRFLMdEAABZlsIAGGMsYQnJIgIsYxxfAADAWAYAwCCLvSXHACADg2UaANQA8WuwFIrFnwKgAWjoc88zhWIIEMYyQLyeUQIghJCAeJ6SoxTmacwjKcbIIoIwFQMACUGYxogSYzTiEcgAQRoDgJeCGAWAUBQBT8kIyQDg761REPL/t5gY42CfXBMRDvepeEI0lr78aRAQRL68BgHo5DP8IdQYWBmdbQoUFQb2XPd7qwB9fRuETq9SYlAAdd6NlKexGA3IkKjcxb1O/Gb3vlXNk4svNRnP94ZOhmHOWU0lJAglSer7xjRNi6L4lW1kWe7d5owb9NXe3n7w4MH4Ms/z8+bN6/teGGNJks7yq0SiSJL0lT80MTjie35AXgpxAAA0hwAQA8Pu26QUPVNo/PcpLH+54scYx6JYxLL4xXqZjwDu8yIYSREJC7GvvZyEJQEAEIDIf/3NZJAEAOB5nuvTD0gSKOhbBhxPdx7ks6YWBvDHU19GWP7isxMGLCIMkghwht+NAPDn+pxFAAvoq78ri6dzO4pQDAtneu1vIiAcHojPt4BwZABe5ovS4/58BGiaHpogTElJcbvdkiTRNA0AXV1dWVlZX9+mu7s7vtzV1ZWamnq2V6MoauXKlWcbWYaiKDKyzJAQRVGpVJIgHHyCICR0lI1hpN//y8R2Ph8OI8uMQYMwskxCvgMWFhaaTKbdu3cDgCAIu3btmjt3bny5p6cnvs3cuXO3bNkSX96yZUt8A4IgCIIYZAk5I2RZ9qGHHrr11lvvvffenTt3ZmVllZWVAcD27dv/53/+x+PxAMADDzxQWlqqVqtFUXznnXcqKioSURKCIAiC+GaJuipw3333rVu3zu12L126dOvWrfEGtIkTJ/7xj3+Mb1BcXFxRUaFUKnU63cGDB/PyBvrGEIIgCII4DyN+9onf/e53Pp/viSeeGORSEStXrrzjjjv69uAlBkd6enpNTY1G80138hEDrrKy8u677/7kk0+GuiBjztq1axsbG5999tnEvcWw6yfWX5FIJBb7Wh8wIvFCoZAgCENdirHI6/UO/++vo48kSX6/f6hLMRZFo9FoNJrQtxjxQUgQBEEQF4MEIUEQBDGmjYBrhC+88ML69etTUlLO+KzD4RBFMTMzc5BLRVRXVycnJxuNxnNvSgyoAwcOTJ06lSbTIQ2ucDh86tSpiRMnDnVBxpzOzs5oNJqdnX1hv75u3bpzdsYcAUEoy/LOnTuHuhQEQRDEyDNr1qxzDoMwAoKQIAiCIBKHXCMkCIIgxjQShARBEMSYRoKQIAiCGNNIEBIEQRBjWkIG3R40gUBg8+bNkiQtXryY9ONPKFmWKyoqampqrFZrWVlZ75Qoe/fuDYfD8WWz2Txt2rShK+PoVFFR4fP54ss6nW7WrFnxZVEUt2/f3tXVNXfu3K9Pc0ZcJK/Xe+DAgb5rJk2aZLfbHQ5HVVVV78qZM2fq9Ymd+2mMkCTp5MmTnZ2dZWVlfSdab29v37Fjh8ViWbhwIcuy8ZUY448//ripqam0tLSwsPDi330E9xp1Op2zZ88uKSlRKBT79+/ft29fenr6UBdq1Fq+fHljY+P06dPr6uocDseePXviU0gWFhYaDAaDwQAAU6dO/e1vfzvUJR1tSktLI5GI1WoFgLy8vHXr1gGALMtLlizxeDyTJk167733Nm7cGJ/ghRgoJ06cuP/+++PLkUhkz549+/btmz179iuvvPLwww9Pnjw5/tSLL744IBXxGHf8+PHZs2erVCqXyxUOh1Wq0xPa79+//+qrr/7Wt75VW1tLUdSOHTviWbhmzZpDhw5ddtllmzZteumll66//vqLLQEesX7+85+vWLEivrx69eoHH3xwaMszutXX1/cuz58//5FHHokvFxQU7N27d4gKNSZceuml5eXlX1m5efPm7OzscDiMMV67dm1paelQFG2s2LBhQ0FBgSzLGOP169f3VjvEQAkGgw6Ho6mpCQDiR3XcokWLnn76aYwxz/PFxcUbN27EGB89etRoNPb09GCM33vvvby8PEmSLrIAI/gaYXl5+apVq+LLq1atKi8vH9ryjG59h2ZISUnheb734bFjx7Zt29bR0TEU5RoTqqurt2zZ0tra2rumvLx86dKl8S/Oq1at2rt3r9vtHroCjnLr16+//fbb43PJAYDP59u8efOhQ4ckSRrago0aGo3m62OHxWKxbdu2rVy5EgBYll2+fHm8ki8vLy8rKzOZTABw9dVXOxyOkydPXmQBRnAQtre3p6WlxZfT0tLa29uHtjxjxIkTJz744IM1a9bEH+r1+nffffeZZ57Jz89/7rnnhrZso5JGo9m8efPzzz9fVFT02GOPxVf2PfhtNhvHceT4T5Da2tr9+/evXr06/hAh5PF41q5du2rVqhkzZnR2dg5t8Uaxjo4OWZZ7L3j1VvLt7e29K1mWtdlsF3/wj+DOMpIk9V5TpWlaFMWhLc9Y4HA4VqxY8dRTT02aNCm+Zv/+/fFBLysqKq644orly5cXFBQMaRlHm82bN8f3cHV19fTp05cvXz5z5sy+Bz+Q4z+RXn311aVLl/aer6xZs+bWW28FAEEQrr322p/97Gd//etfh7SAo1b8hLv3RLz3IJckqbfXDAAwDHPxB/8IPiNMSUlxOp3x5a6urnjfDSJxnE7n/Pnzb7/99nvuuad3Ze/Qz5dccklOTk5lZeUQlW7U6t3D48ePnzJlyuHDh+HLB7/f749EIuT4TwRRFF9//fXbbrutd03vn4Nl2euuu+7IkSNDVLTRLzk5GQC6u7vjD3sr+b4HvyzLTqfz4g/+ERyEc+fO3bJlS3x569atc+fOHdLijHIul2v+/Pk33njjww8/fMYNuru7W1tbMzIyBrlgY0cgEKirq4tPtDJ37tzt27fLsgwAW7dunTBhQlJS0lAXcBT66KOPJElasmTJGZ89ePAgOeATR6PRzJw5c+vWrfGHvZX83Llzd+3aFe+msHfvXo1GU1RUdJHvNYKbRu+9994ZM2aYzWaO49avX79nz56hLtFotnr1aofD0d7efscddwDAlClT7rrrrgMHDvzyl7+cNWuWLMtvvPHGggULZs6cOdQlHVUaGhruvPPOyy+/nKbpt956q6SkZOHChQDw7W9/+8knn7zppptmzpz53HPPPffX7rGLAAAEO0lEQVTcc70tSMQAWr9+/S233NK3Ie7WW281m80pKSmHDh0qLy/ftWvXEBZv1BAE4Z577gkGgwBwzz33aLXaP/zhDwDw05/+9LbbbnO5XFVVVZ2dnTfddBMAzJkzJz8/f8WKFQsWLHjxxRd//OMfcxx3kQUYwfcRAkBDQ8Obb74py/INN9xA7uZJqE2bNrlcrt6H2dnZCxcuDAaD77//fk1NDcMw06ZNu+aaa0h1PLBisdh7770X7xQ3adKkFStW9DbNeb3eDRs2uFyuBQsWXHnllUNazFHr1VdfXbhwYW+/JACoqKjYtWtXT09Penr6ypUrzzZPKtEvkiStX7++9yHHcbfcckt8ed++fR9++KHRaLzlllvid9MCQCQSefXVV9va2i6//PKlS5defAFGdhASBEEQxEUawdcICYIgCOLikSAkCIIgxjQShARBEMSYRoKQIAiCGNNIEBIEQRBjGglCgiAIYkwjQUgQI8M//vGPgwcPDnUpCGIUIvcREsSwMHHixFAodLZnP/vss6KioptvvplM8UEQA24ED7FGEKPJ6tWre2d5jA8Z86Mf/aj3WZVK9eijj/ZO+kEQxAAiZ4QEMezMnz+/rq6uubn5fDZ2u91qtTo+SS8AYIxdLpfVaj3jcHeBQCAUCtnt9r6zOBHEGEc+DAQxMpSUlDzxxBPx5bVr15rN5s8//3zy5MlWq1Wn0919992SJL399tvp6el2u91kMm3YsKHvr3/88cczZszQ6/UpKSkpKSkvv/zyEPwfCGJYIk2jBDEydHV1+f3++HI0GvV4PGvWrHnwwQenTp36z3/+86mnnopGo/v371+7dm1ycvIzzzzzve9978orr8zJyQGAPXv2LFq0aPHixS+88ILBYHj77bfvvvtutVp98803D+n/iSCGBRKEBDFSPfLII/EkmzFjxsaNG1977bWqqqqCggIA+POf//z++++Xl5f/8Ic/BICHHnqouLj43XffZRgGACZNmlRXV/fss8+SICQIIEFIECPXokWLepfz8/NFUYynIADYbDaTydTa2goAgUBg3759N95448cff9y7vd1u37RpE8/zFz+XG0GMdCQICWKkMplMvcsKhaLvQwDgOC7eDbW7u1uW5ffff/+jjz7qu4FOp3O73WRGPYIgQUgQo5xerweAn/zkJz//+c+HuiwEMRyRXqMEMcpZrdbi4uL33ntPFMWhLgtBDEckCAli9PvNb35TWVl5/fXXV1ZWRiKRlpaWjRs3PvbYY0NdLoIYFkgQEsTot2zZsnfeeefw4cOTJ09Wq9VZWVnf//73yWAaBBFHRpYhiGFHlmUA+MrgL7IsI4TOOF7MecIY19XVeb1eq9WamZkZv5WCIAgShARBEMSYRppGCYIgiDGNBCFBEAQxppEgJAiCIMY0EoQEQRDEmEaCkCAIghjTSBASBEEQY9r/BwukHZsc/0ttAAAAAElFTkSuQmCC",
"image/svg+xml": "\n\n",
"text/html": [
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"betas = [0.05, 0.1, 0.01, 0.4, 0.04, 0.05, 0.005]\n",
"alphas = [0.05, 0.1, 0.01, 0.1, 0.01, 0.1, 0.01]\n",
"\n",
"predictions, taus = Simulation_SIR(n7_2A, 10, betas, alphas, 100, 1000)\n",
"plot = Plots.plot(predictions[:, :, 2], label = taus', xlabel = \"Time\", ylabel = \"% of infected\")\n",
"png(\"img/q13_2.png\")\n",
"display(plot)"
]
},
{
"cell_type": "code",
"execution_count": 126,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": "\n\n",
"text/html": [
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Same as before but applied on toulouse_neigh. May be a bit long to run.\n",
"betas = [0.05, 0.1, 0.15, 0.25, 0.35, 0.45, 0.55, 0.65, 0.75, 0.85, 0.95]\n",
"alphas = [0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2]\n",
"\n",
"predictions, taus = Simulation_SIR(toulouse_neigh, 100, betas, alphas, 100, 1000)\n",
"plot = Plots.plot(predictions[:, :, 2], label = taus', xlabel = \"Time\", ylabel = \"% of infected\")\n",
"png(\"img/q13_3.png\")\n",
"display(plot)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"Question 14 (code): Implement a script plotting the number of infected over 75 time steps for $\\beta=0.3$ and $\\alpha=0.2$ fixed and on 3 contact networks:\n",
" \n",
"* A regular graph of 200 vertices with degree 2.\n",
"* A regular graph of 200 vertices with degree 5.\n",
"* A regular graph of 200 vertices with degree 10."
]
},
{
"cell_type": "code",
"execution_count": 127,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": "\n\n",
"text/html": [
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Plots of the number of infected people according to tau over 75 time steps for 3 contact networks.\n",
"n = 200\n",
"Plots.plot()\n",
"betas = [0.3]\n",
"alphas = [0.2]\n",
"\n",
"plot = Plots.plot()\n",
"for d in [2 5 10]\n",
" net = random_regular_graph(n, d)\n",
" predictions, taus = Simulation_SIR(net, 1, betas, alphas, 75, 1000)\n",
" Plots.plot!(predictions[:, :, 2], label = d, xlabel = \"Time\", ylabel = \"% of infected\")\n",
"end\n",
"Plots.plot!()\n",
"\n",
"png(\"img/q14.png\")\n",
"display(plot)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"Question 15 (written): From the previous figure, explain why lockdown can be interesting when hospital places are lacking ?\n",
"\n",
"> On observe qu'en diminuant le nombre de contacts potentiels entre les personnes d'un réseau, le nombre maximal d'infecté à un temps donné diminue. Ainsi par la mise en place d'un confinement les hopitaux peuvent être capable de supporter plus facilement la charge d'infectés."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"### 2.2 SAIR\n",
" \n",
"The vector containing the disease status `state` has to change a bit since we added a new state. Hence it will be an `Array{Int32,1}` where Susceptible=0, Infected=1, Recovered=2, and Alert=3."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
" \n",
"Question 17 (code): Implement the function `Simulation_SAIR` (respect the header and the specifications).\n",
" \n",
"###### The corrector should be able to write `predictions, taus = Simulation_SAIR(net,nbinf,betas0,betas1,alphas,kappas,t,nbsimu)` with your code."
]
},
{
"cell_type": "code",
"execution_count": 132,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Simulation_SAIR"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"\"\"\"\n",
"Take a contact network, different diseases (defined by different parameters alpha and beta), a number of initial infected people and process nbsimu simulations of SAIR over t time steps. You will provide the prediction of the percentage of infected at each time t as well as the spreading rate of each disease.\n",
"\n",
"* PARAMS\n",
" - net (SimpleGraph): graph representing the contact network\n",
" - nbinf (Int32): number of infected at the start of each simulation\n",
" - betas0 (Array{Float64,1}): array of infection rate when not alert on edges\n",
" - betas1 (Array{Float64,1}): array of infection rate when alert on edges\n",
" - alphas (Array{Float64,1}): array of curing rate on vertices\n",
" - kappas (Array{Float64,1}): array of alerting rate on edges\n",
" - t (Int32): number of time step\n",
" - nbsimu (Int32): number of simulations\n",
"\n",
"* RETURNS\n",
" - (Array{Float64,3}): the prediction of the percentage of infected, the percentage of susceptible and the percentage of recovered at each time step and for each disease. The first dimension contains the time steps, the second contains the diseases, and the third the status (Infected: [:,:,1], Recovered: [:,:,2], Susceptible: [:,:,3])\n",
" - (Array{Float64,1}): effective spreading rate for each disease\n",
"\"\"\"\n",
"function Simulation_SAIR(net, nbinf, betas0, betas1, alphas, kappas, t, nbsimu)\n",
" taus = zeros(length(alphas))\n",
" prediction = zeros(t+1, length(taus), 4)\n",
"\n",
" for (i, (beta0, beta1, alpha, kappa)) in enumerate(zip(betas0, betas1, alphas, kappas))\n",
" taus[i] = round(beta0 / alpha, digits = 2)\n",
" for _ in 1:nbsimu\n",
" state = new_state(net, nbinf)\n",
" _, X = SAIR2(net, state, beta0, beta1, alpha, kappa, t)\n",
" prediction[:, i, :] += X ./ nbsimu ./ length(state)\n",
" end\n",
" end\n",
"\n",
" return prediction, taus\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"Question 18 (written): Run the script below comparing the number of infected of SAIR and SIR and comment what you see.\n",
"\n",
"> On observe que le pic d'infection maximal de l'épidemie est moins important."
]
},
{
"cell_type": "code",
"execution_count": 133,
"metadata": {},
"outputs": [
{
"data": {
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",
"image/svg+xml": "\n\n",
"text/html": [
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Script launching prediction on one disease on toulouse_neigh and plotting the percentage\n",
"# of infected at each time step for SIR and SAIR.\n",
"predictions1, _ = Simulation_SAIR(toulouse_neigh, 2, [0.2], [0.1], [0.1], [0.5], 100, 1000)\n",
"predictions2, _ = Simulation_SIR( toulouse_neigh, 2, [0.2], [0.1], 100, 1000)\n",
"\n",
"plot = Plots.plot(\n",
" [predictions1[:, :, 2] predictions2[:, :, 2]],\n",
" label = [\"SAIR\" \"SIR\"],\n",
" xlabel = \"t\",\n",
" ylabel = \"%\"\n",
")\n",
"png(\"img/q18.png\")\n",
"display(plot)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"Question 19 (written): Of course the presented SIS, SIR, and SAIR models are limitated in their modelization of the reality. Formulate few of these limitations (at least 2). Propose few algorithm addons/ideas (at least 2) which would make the models more complex and more accurate in regards to the reality.\n",
"\n",
"> Pour rendre la simulation plus précise, nous pourrions faire en sorte que les personnes dans l'état \"recovered\" puissent repasser dans un état \"suceptible\" après un certain moment. Il serait aussi possible de rajouter une dynamique dans les relations du graphe (i.e. quand les individus vont au travail, chez eux, au cinéma...)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"## Part 3 - Discover patient zero\n",
" \n",
"In the two previous parts you may have realised that understanding and controlling the spread of epidemics on contact networks is an important task. However, information about the origin of the epidemic could be also extremely useful to reduce or prevent future outbreaks. Thus, in this part we will focus on algorithm solutions to answer this issue.\n",
" \n",
"The stochastic nature of infection propagation makes the estimation of the epidemic origin intrinsically hard: indeed, different initial conditions can lead to the same configuration at the observation time. Methods such as the distance centrality or the Jordan center try to approximate it. They both rely on spatial information by stating that the first infected is probably at the center of the cluster of infection. Mathematically:\n",
" \n",
"* The jordan center is expressed as $\\min_{v\\in \\mathcal{I}}\\max_{n\\in \\mathcal{I}}d(v,n)$ where $\\mathcal{I}$ is a connected component of the original contact network containing all infected and recovered vertices, and where $d(\\cdot,\\cdot)$ is the distance (= the shortest path) between 2 vertices (if not weighted graph each edge accounts for 1 unit). \n",
"* The distance centrality is expressed as $\\min_{v\\in \\mathcal{I}}\\sum_{n\\in \\mathcal{I}}d(v,n)(\\delta_{n,I} + \\delta_{n,R}/\\alpha)$, where $\\delta_{n,I}=1$ if the vertex n is infected ($=0$ otherwise), and where $\\delta_{n,R}=1$ if the vertex n is recovered ($=0$ otherwise). You may note that in distance centrality we increase the weight of the recovered vertices by a factor $1/\\alpha$, it translates the fact that recovered vertices tend to be closer to the origin of the epidemic since they probably got ill before.\n",
" \n",
" \n",
"We formulate the problem as follow: given a contact network and a snapshot of epidemic spread at a certain time, determine the infection source. A snapshot is a given `state` array for a contact network.\n",
"\n",
"###### A. Y. Lokhov, M. Mézard, H. Ohta, and L. Zdeborová, _\"Inferring the origin of an epidemic with a dynamic message-passing algorithm\"_, Physical Review (2014)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
" \n",
"Question 20 (code): Implement the function `jordan` (respect the header and the specifications). You will need to use the function `dijkstra_shortest_paths` of the LighGraphs library, refer to the doc for more information. If there are multiple minimal vertices, then return the first one.\n",
" \n",
"###### The corrector should be able to write `zero = jordan(g,state,alpha)` with your code."
]
},
{
"cell_type": "code",
"execution_count": 134,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"jordan"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"\"\"\"\n",
"Find patient zero by mean of the jordan center method.\n",
"\n",
"* PARAMS\n",
" - g (SimpleGraph): graph representing the contact network\n",
" - state (Array{Int32,1}): disease status of each vertex\n",
"\n",
"* RETURNS\n",
" - (Int32): the patient zero vertex number \n",
"\"\"\"\n",
"function jordan(g, state)\n",
" n = nv(g)\n",
" d = zeros(n, n)\n",
" for i in 1:n \n",
" d[i,:] = dijkstra_shortest_paths(g, i).dists\n",
" end\n",
"\n",
" _, min_index = findmin(maximum(d, dims = 1))\n",
" _, jordan_center = min_index.I\n",
"\n",
" return jordan_center\n",
"end\n",
"\n",
"# karat7_state = new_state(karat7, 1)\n",
"# println(jordan(karat7, karat7_state))\n",
"\n",
"# nodefillc = node_colors[karat7_state.+1]\n",
"# gplot(karat7, nodefillc = nodefillc, nodelabel=1:nv(karat7))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
" \n",
"Question 21 (code): Implement the function `distance` (respect the header and the specifications). You will need to use the function `dijkstra_shortest_paths` of the LighGraphs library, refer to the doc for more information. If there are multiple minimal vertices, then return the first one.\n",
" \n",
"###### The corrector should be able to write `zero = distance(g,state,alpha)` with your code."
]
},
{
"cell_type": "code",
"execution_count": 135,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"distance"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"\"\"\"Find patient zero by mean of the distance centrality method.\n",
"\n",
"* PARAMS\n",
" - g (SimpleGraph): graph representing the contact network\n",
" - state (Array{Int32,1}): disease status of each vertex\n",
" - alpha (Float64): curing rate\n",
"\n",
"* RETURNS\n",
" - (Int32): the patient zero vertex number \n",
"\"\"\"\n",
"function distance(g, state, alpha = 1.0)\n",
"\n",
" n = nv(g)\n",
" \n",
" d = zeros(n, n)\n",
" for i in 1:n \n",
" d[i,:] = dijkstra_shortest_paths(g, i).dists\n",
" end\n",
"\n",
" delta_infected = (state .== 1)\n",
" delta_recovered = (state .== 2)\n",
"\n",
" _, distance_centrality = findmin(\n",
" sum(\n",
" d[:,i] .* (delta_infected + delta_recovered / alpha)\n",
" )\n",
" for i in 1:n\n",
" )\n",
"\n",
" return distance_centrality\n",
"end\n",
"\n",
"# karat7_state = new_state(karat7, 0)\n",
"# karat7_state[1] = 1\n",
"# karat7_state[3] = 1\n",
"# karat7_state[8] = 2\n",
"# distance(karat7, karat7_state, 0.1)\n",
"\n",
"# nodefillc = node_colors[karat7_state.+1]\n",
"# display(gplot(karat7, nodefillc = nodefillc, nodelabel=1:nv(karat7)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"