ex16_chemical_evolution_models.ipynb

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    "## Astro 304 \"Galaxies\""
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    "### Chemical evolution models"
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    "# setup notebook for inline figures\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "\n",
    "# import pyplot and set some parameters to make plots prettier\n",
    "import matplotlib.pyplot as plt\n",
    "from code.plot_utils import plot_pretty\n",
    "plot_pretty()"
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    "### Instantaneous recycling approximation\n",
    "\n",
    "$$\n",
    "\\dot{M}_{\\rm g} = \\dot{M}_{\\rm g, in} - (1-\\mathcal{R}+\\eta)\\, \\dot{M}_{\\star},\n",
    "$$\n",
    "\n",
    "Notice thtat in this simplified equation we neglect a time delay between the birth of stars and the time when they affect the ISM. Young massive stars live for $\\leq 40$ Myr and neglecting such time scale compared to the cosmological time scale of Gyrs is a reasonable approximation for the outflow term $\\eta\\, \\dot{M}_{\\star}$, especially if the SFR is evolving smoothly. \n",
    "\n",
    "However, stellar mass loss occurs on a longer time scale and the assumption of *instantaneous recycling* - i.e. return of $\\mathcal{R}$ fraction of mass turned into stars back into the ISM *instantly* is not so obvious. Below we will consider the recycling process and associated time scale in more detail. "
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    "### Lifetime of stars of different mass and metallicity\n",
    "\n",
    "The plot below shows lifetime of stars as a function of their mass for different metallicities (shown by lines of different color) from $0.1Z_\\odot$ (red) to $2Z_\\odot$ (blue), calculated using fitting formulae to the actual results of stellar evolution calculations (<a href=\"http://adsabs.harvard.edu/abs/1996A%26A...315..105R\">Raiteri et al. 1996</a>; see notebook for code that produced this figure). As you can see the main dependence is on mass, dependence of lifetime on metallicity is very weak. \n",
    "\n",
    "Stars that produce energectic winds and explode as supernovae (type II) have masses $\\geq 8\\ M_\\odot$. The figure shows that such stars live for $\\leq 40$ Myrs.\n",
    "\n",
    "<img src=\"http://astro.uchicago.edu/~andrey/classes/a304/fig/tlife_stars.png\" align=\"center\" width=\"500\"></img>"
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    "### The actual recycling of gas into the ISM\n",
    "\n",
    "would be computed as follows: \n",
    "\n",
    "$$\\dot{M}_{\\star,\\rm loss}(t)=\\int\\limits^{m_U}_{m_{\\tau=t}}[m-m_{\\rm rem}(m)]\\dot{M}_\\star (t-\\tau(m))\\phi(m)dm.$$\n",
    "\n",
    "Here $\\phi(m)$ is the initial stellar mass function (IMF) assumed to be constant in time and normalized such that the total mass of the stellar population is $1\\ M_\\odot$:\n",
    "\n",
    "$$\\int\\limits^{m_U}_{m_{\\rm min}}m\\,\\phi(m)\\,dm = 1\\ M_\\odot. $$ \n",
    "\n",
    "$m_{\\rm min}\\approx 0.08$ is the minimum mass of stars in a population, $m_U$ is the maximum mass of stars (can be something large like $150\\ M_\\odot$, $m_{\\tau=t}$ is the mass of stars with lifetime $=t$, where $\\tau(m)$ is lifetime of star of mass $m$, shown above. \n",
    "\n",
    "$m_{\\rm rem}(m)$ is the mass of the long-lived remnant left by a star of initial mass $m$. Predicting this mass from models of stellar evolution is difficult because SNII explosions and violent shedding of envelopes by the stars at the tip of the AGB is not well understood. However, there are observational calibrations of this relation from observations of high-quality color-magnitude diagrams of star clusters in Milky Way and SMC (e.g., <a href=\"http://adsabs.harvard.edu/abs/2008ApJ...676..594K\">Kalirai et al. 2008</a>): $m_{\\rm rem}(m)=(0.109\\pm 0.007)m + 0.394\\pm 0.025$, where masses are in $M_\\odot$. "
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    "### The mass loss computed without IRA\n",
    "\n",
    "The figure below shows the mass loss rate computed for the above equation and $m_{\\rm mem}(m)$ fit for the Salpeter (1955) and Chabrier (2003) IMFs (thick lines) for a stellar population of $1\\ M_\\odot$ per Gyr. So to get the mass loss rate say for $10^{10}\\ M_{\\odot}$ worth of stars multiply the rate in the figure by this mass. \n",
    "\n",
    "The thin lines show a fitting formula for the mass loss proposed by Jungwiert et al. (2001): \n",
    "\n",
    "$$\\dot{f}_{\\rm loss} = \\frac{C_0}{\\lambda\\,(1+t/\\lambda)}$$\n",
    "\n",
    "or cumulative mass loss of \n",
    "\n",
    "$$f_{\\rm loss} = C_0\\,\\log(1+t/\\lambda),$$\n",
    "\n",
    "with $t$ in Myrs, and $C_0=0.046$, $\\lambda=0.276$ Myr for the Chabrier (2003) IMF, and $C_0=0.032$ and $\\lambda=0.51e$ for the Salpeter (1955) IMF. \n",
    "\n",
    "Figure shows that gas recycling is definitely not instant, but $\\approx 3/4$ of the mass loss occurs in the first $100$ Myr. So on cosmological time scales IRA is not a bad approximation and simplifies modeling (even though in principle we could code up non-instantaneous recycling fairly straightforwardly). \n",
    "\n",
    "<img src=\"http://astro.uchicago.edu/~andrey/classes/a304/fig/mass_loss.png\" align=\"center\" width=\"600\"></img>"
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    "### Model for enrichment of heavy elements\n",
    "\n",
    "As  stars form, they form out of gas containing heavy elements present in the ISM. Thus, the gas that goes into stars also takes away heavy elements from the ISM proportionally to the gas *metallicity* $Z=M_{\\rm Z}/M_{\\rm g}$, i.e. star formation decreases mass of heavy elements in the ISM, $M_{\\rm Z}$, at the rate $-Z\\,\\dot{\\tilde{M}}_\\star$.\n",
    "\n",
    "The $\\tilde{}$ in $\\dot{\\tilde{M}}_\\star$ indicates that star formation rate that enters here is the mass *locked into long-lived stars* - i.e., after the stars recycle a fraction of their mass to the ISM via winds and supernovae ejecta from young stars and via AGB envelopes for older less massive stars.  \n",
    "\n",
    "In the *instantaneous recycling approximation* this recycling is supposed to happen instantly, so that  $\\dot{\\tilde{M}}_\\star = (1-\\mathcal{R})\\, \\dot{M}_\\star$, where $\\dot{M}_\\star$ is the actual instantaneous star formation rate. \n",
    "\n",
    "The fraction of mass returned to the ISM instantaneously is by definition\n",
    "$$\\mathcal{R}=\\int\\limits^{m_U}_{m_{\\rm min}}m f_{\\rm ret}(m)\\,\\phi(m)\\,dm = \\int\\limits^{m_U}_{m_{\\rm min}}[m-m_{\\rm rem}(m)]\\,\\phi(m)\\,dm, $$\n",
    "where $f_{\\rm ret}$ fraction of star of initial mass $m$ that is returned to the ISM after its evolution, $m_{\\rm rem}(m)$ is the mass of long-lived remnant such star leaves behind and, as before, $\\phi(m)$ is normalized to give total stellar mass of the population of $1\\ M_\\odot$. "
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    "### Model for enrichment of heavy elements (cont'd)\n",
    "\n",
    "In addition, stars produce new heavy elements in their interiors, which adds mass of the heavy elements equal to $y_{\\rm Z},\\dot{\\tilde{M}}_\\star$, where  *the true yield* $y_{\\rm Z}$ is defined as\n",
    "\n",
    "$$y_{\\rm Z}=\\frac{1}{1-\\mathcal{R}}\\int\\limits_{m_\\tau}^{m_U} mq_{\\rm Z}(m)\\phi(m)dm,$$\n",
    "\n",
    "where $q_z$ is fraction of mass that a star of initial mass $m$ returns to the ISM in the form of *new* heavy elements that were synthesized during its evolution. \n",
    "\n",
    "Obviously, to know $y_{\\rm Z}$ one needs to know or assume the IMF of stars, as well as model of stellar evolution and nucleosynthesis (+ dynamics of SNe remnants). Detailed calculations of these exist, but there are substantial uncertainties due to uncertainties in what happens when stars explode or shed their envelopes. These processes are inherently non-hydrostatic and thus cannot be computed reliably with 1d models.  "
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    "### Closed-box model\n",
    "\n",
    "The change of mass of heavy elements is thus\n",
    "\n",
    "$$\\dot{M}_{\\rm Z} = y_{\\rm Z}\\dot{\\tilde{M}}_{\\rm \\star} - Z\\,\\dot{\\tilde{M}}_{\\rm \\star}$$\n",
    "\n",
    "or \n",
    "\n",
    "$$\n",
    "\\dot{M}_{\\rm Z} = (y_{\\rm Z}-Z)(1-\\mathcal{R})\\,\\dot{M}_{\\rm \\star}.\n",
    "$$\n",
    "\n",
    "If there were no inflows or outflows of gas, i.e. if galaxies were evolving as *closed systems*, this equation would be the equation governing evolution of heavy element mass in galaxies. This corresponds to the so called *closed box model* of chemical evolution (<a href=\"http://adsabs.harvard.edu/abs/1972ApJ...173...25S\">Searle & Sargent 1972)</a>.\n",
    "\n",
    "Given what we know about galaxy formation, this model is clearly unrealistic. First, in this model galaxies are supposed to have their entire gas reservoir in place at the start of the evolution. Second, we can have no accretion of new gas or any outflow due to feedback. So why do we need to even mention this model? The reason is that the above equation can be integrated analytically (see below) and its solution provides a useful and simple *baseline* with which the actual evolution of galaxies can be compared. "
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    "### Closed-box model: solution\n",
    "\n",
    "We have $M_{\\star+\\rm g}=M_\\star+ M_{\\rm g}=\\mathrm{const}$, so $d\\tilde{M}_\\star=-dM_{\\rm g}$ and so multiplying the evolution equation \n",
    "\n",
    "$$\n",
    "\\dot{M}_{\\rm Z} = (y_{\\rm Z}-Z)\\,\\dot{\\tilde{M}}_{\\rm \\star}.\n",
    "$$\n",
    "\n",
    "by $dt$ and dividing by $d\\tilde{M}_\\star$ gives\n",
    "\n",
    "$$\\frac{dM_{\\rm Z}}{d\\tilde{M}_\\star} = y_{\\rm Z} - Z.$$\n",
    "\n",
    "$Z=M_{\\rm Z}/M_{\\rm g}$ so its differential is \n",
    "\n",
    "$$dZ = \\frac{dM_{\\rm Z}}{M_{\\rm g}} - Z\\frac{dM_{\\rm g}}{M_{\\rm g}}. $$\n",
    "\n",
    "Multiplying it by $M_{\\rm g}$ and dividing by $d\\tilde{M}_\\star$ we get \n",
    "\n",
    "$$M_{\\rm g}\\frac{dZ}{d\\tilde{M}_{\\star}} = -M_{\\rm g}\\frac{dZ}{dM_{\\rm g}} = \n",
    "\\frac{dM_{\\rm Z}}{d\\tilde{M}_\\star} - Z\\frac{dM_{\\rm g}}{d\\tilde{M}_{\\star}} = y_{\\rm Z}-Z + Z= y_{\\rm Z},$$\n",
    "\n",
    "where we used equations above in the last step. Thus, we have \n",
    "\n",
    "$$dZ = -y_{\\rm Z}\\frac{dM_{\\rm g}}{M_{\\rm g}},$$\n",
    "\n",
    "which, assuming that $y_{\\rm Z}=\\mathrm{const}$ has the solution\n",
    "\n",
    "$$Z(t) = Z(t_i) - y_{\\rm Z}\\left[\\ln M_{\\rm g}(t) - \\ln M_{\\rm g}(t_i)\\right] = Z(t_i) + y_{\\rm Z}\\ln \\left(\\frac{1}{f_{\\rm g}}\\right), $$\n",
    "\n",
    "where $Z(t_i)$ and $M_{\\rm g}(t_i)$ are the initial metallicity and gas mass at some initial time $t_i$. If we start before any star formation $Z(t_i)=0$ and $M_{\\rm g}(t_i) = M_{\\star +\\rm g}=\\mathrm{const}$ (it's closed box!), so the ratio of final to the initial gas mass is equal to the fraction of mass in gas at any time: $M_{\\rm g}(t)/M_{\\rm g}(t_i) = M_{\\rm g}(t)/[M_{\\rm g}(t)+M_\\star(t)]=f_{\\rm g}(t).$\n",
    "\n",
    "$$Z(t) = y_{\\rm Z}\\ln \\left(\\frac{1}{f_{\\rm g}}\\right), $$\n"
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    "### Effective yield\n",
    "\n",
    "The $Z(t)$ solution for the closed box model motivates the parameter called the *effective yield* for galaxies:\n",
    "\n",
    "$$y_{\\rm eff}=\\frac{Z}{\\ln(1/f_{\\rm g})},$$\n",
    "\n",
    "where $Z$ is observed galaxy metallicity at a given time and $f_{\\rm g}$ is the fraction of galaxy baryon mass in gaseous ISM. \n",
    "\n",
    "If galaxies were closed boxes their effective yields would be approximately equal to the true nucleosynthetic yield, which should not vary galaxy-to-galaxy as long as IMF does not vary: $y_{\\rm eff}=y_{\\rm Z}\\approx \\mathrm{const}$. \n",
    "\n",
    "Thus, by comparing $y_{\\rm eff}$ for real or model galaxy to expected $y_{\\rm Z}$ we can gauge whether they evolved as closed systems or not. "
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    "### Closed box model: post scriptum\n",
    "\n",
    "Note that the formula for $Z(t)$ in the closed box model derived above shows that as gas fraction goes to zero $Z$ can grow indefinitely. However, $Z$ is restricted to be $Z\\leq 1$ by definition. <b>Q</b>: how this should be reconciled?\n",
    "\n",
    "Note also that the closed-box formula for $Z(t)$ derived above is for the instantaneous metallicity of the ISM gas. If we have metallicity determined from a composite spectrum of stellar population of the closed box galaxy with a range of ages and metallicity, the averaged metallicity that will be inferred  is (assume $Z(t_i)=0$ and note that $df_{\\rm g}=dM_{\\rm g}/[M_*(t)+M_{\\rm g}(t)]$ in this model): \n",
    "$$\\langle Z_*\\rangle=\\frac{1}{M_*}\\int\\limits_0^{M_*}Z(M^\\prime_*)dM^\\prime_*=\n",
    "\\frac{y_{\\rm Z}}{M_*}\\int\\ln(f^\\prime_{\\rm g})dM^\\prime_{\\rm g}\n",
    "=\\frac{y_{\\rm Z}}{1-f_{\\rm g}}f^\\prime_{\\rm g}\n",
    "(\\ln f^\\prime_{\\rm g}-1)|_1^{f_{\\rm g}}=y_{\\rm Z}\\left(\\frac{f_{\\rm g}\\ln f_{\\rm \n",
    "g}}{1-f_{\\rm g}}+1\\right)$$\n",
    "\n",
    "Note that the above equation indicates that *average metallicity of stars will approach the value of the true yield $y_{\\rm Z}$ from below as gas fraction becomes small.*"
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    "### Metallicity evolution and inflows and outflows\n",
    "\n",
    "Real galaxies, in general, are not closed systems and heavy elements can be driven out from the galaxy as hot, enriched gas of SN remnants escapes the ISM. \n",
    "This can, in principle, occur effectively even without much of associated total gas mass loss to the wind. In the latter case, this effectively acts as through the nucleosynthetic yield is decreased. So instead of $y_{\\rm Z}(1-\\mathcal{R})\\dot{M}_\\star$, new stars are contributing only $y_{\\rm Z}(1-\\mathcal{R})(1-\\zeta)\\dot{M}_\\star$ in mass of heavy elements to the ISM, while the fraction $\\zeta$ leaves the galaxy. In the case, when heavy elements are assumed to instantly mix with the ISM and  leave only as the ISM gas leaves in an outflow, $\\zeta=0$. \n",
    "\n",
    "In addition, cold and warm gas of the ISM and the associated metals  can be driven by galactic winds at a rate $\\epsilon_{\\rm out}(M_{\\rm Z}/M_{\\rm g})\\dot{M}_{\\star}$.\n",
    "\n",
    "Metallicity of the gas can also be affected by inflow of gas. If the gas accreted by halo from the IGM is already enriched, the accreted gas brings heavy elements with it at the rate  $Z_{\\rm IGM}\\dot{M}_{\\rm g,in}$. If the metallicity of inflowing gas is smaller than that of the ISM, it will dilute the ISM metallicity, while if $Z$ of inflowing matter is larger, it will increase the metallicity. \n",
    "\n"
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    "### Model for enrichment of heavy elements\n",
    "\n",
    "The master equation for the evolution of mass of heavy elements in the model galaxy is\n",
    "\n",
    "$$\\dot{M}_{\\rm Z} = \\, \\left[y_{\\rm Z}(1-\\mathcal{R})(1-\\zeta)-(1-\\mathcal{R}+\\epsilon_{\\rm out})M_{\\rm Z}/M_{\\rm g}\\right]\\dot{M}_{\\star} + Z_{\\rm IGM}\\dot{M}_{\\rm g,in}$$\n",
    "\n",
    "\n",
    "<b>No inflow model</b> is an interesting special case. In the case when there are no inflows, $\\dot{M}_{\\rm g,in}=0$, this equation actually is close in form to the closed box model equation with $y_{\\rm Z}(1-\\zeta)$ being equivalent of yield and $[1+\\epsilon_{\\rm out}/(1-\\mathcal{R})]Z$ being equivalent of metallicity. \n",
    "\n",
    "Moreover, for constant $\\epsilon_{\\rm out}$, we have $M_\\star+M_{\\rm g} + \\epsilon_{\\rm out}M_\\star=\\mathrm{const}$ and $dM_{\\rm g} = - dM_\\star/(1+\\epsilon_{\\rm out})$. \n",
    "\n",
    "From this, we can guess the solution: \n",
    "\n",
    "$$Z(t) = Z(t_i) + \\frac{y_{\\rm Z}}{1+\\epsilon_{\\rm out}}\\,\\ln \\left(\\frac{1}{f_{\\rm g}}\\right), $$\n",
    "\n",
    "which shows that the effect of outflows is to reduce the gas metallicity by a factor of $1+\\epsilon_{\\rm out}$, the decrease which will be reflected in the *reduced effective yield:* \n",
    "\n",
    "$$y_{\\rm eff}=\\frac{Z}{\\ln(1/f_{\\rm g})}\\leq y_{\\rm Z}.$$\n",
    "\n",
    "Thus, *observations showing $y_{\\rm eff}$ significantly smaller than expected $y_{\\rm Z}$ indicate that winds have reduced gas metallicity substantially during galaxy evolution.*\n",
    "\n",
    "Although model with no inflows is no more realistic than closed box, it turns out that inclusion of inflows does not change the above conclusion, as effect of low-metallicity inflows on the yield is suprisingly small (see <a href=\"http://adsabs.harvard.edu/abs/2007ApJ...658..941D\">Dalcanton 2007</a>). "
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    "### Solutions of the simple models\n",
    "\n",
    "for the metallicity-stellar mass relation and effective yield as a function of stellar mass. The models assume that star form at a rate $M_{\\rm g}(t)/\\tau_{\\rm sf}$ with $\\tau_{\\rm sf}=2$ Gyrs. Outflow model assumes constant $\\epsilon_{\\rm out}=5$. Inflow model assumes no outflows and that gas inflows at a rate at which it is lost, so that gas mass stays constant. The figure shows that at large $Z$ models make different predictions, but at low $Z$, $M_\\star-Z$ relation does not discriminate between these very different models. \n",
    "\n",
    "Effective yield can clearly differentiate between the model with outflows and those without. This is because outflows suppress the effective yield by a factor of $(1+\\epsilon_{\\rm out})$. \n",
    "\n",
    "<img src=\"http://astro.uchicago.edu/~andrey/classes/a304/fig/MsZyeff_simplemodels.png\" align=\"center\" width=\"600\"></img>\n"
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    "### Observational tests of winds and chemical evolution of galaxies\n",
    "\n",
    "Direct observations of winds are difficult and often provide a wealth of information that's difficult to interpret. Chemical abundances in galaxies (stars or ISM) and in the gas of the circumgalactic medium (CGM) provide indirect information about flows of gas in and out of galaxies. \n",
    "\n",
    "Observational measurements of *effective yield* in galaxies of different stellar mass is one such source of information. \n",
    "\n",
    "<img src=\"http://astro.uchicago.edu/~andrey/classes/a304/fig/tremonti_etal04_yeff.PNG\" align=\"center\" width=\"500\"></img>\n"
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    "### Retained fraction of heavy elements\n",
    "\n",
    "Another interesting probe of gas inflows and outflows is the fraction of heavy elements ever produced by stars in galaxies that are still observed in stars and the ISM of the galaxies\n",
    "<a href=\"http://adsabs.harvard.edu/abs/2014ApJ...786...54P\">Peeples et al. (2014)</a>. \n",
    "\n",
    "Metals ever produced can be observationally estimated using constant yield and IMF from the stellar mass of galaxies. The observed mass of metals is estimated from metallicities of stars and ISM. The fraction of retained metals can then be studied in galaxies as a function of their mass. \n",
    "\n",
    "<img src=\"http://astro.uchicago.edu/~andrey/classes/a304/fig/peeples_etal14_fZret.PNG\" align=\"center\" width=\"600\"></img>\n",
    "\n",
    "In simulations of galaxy formation both the mass of produced and retained metals can be measured directly and these can be used to assess effects of inflows and outflows on the abundance of heavy elements and comparisons with observations (e.g.,  \n",
    "<a href=\"http://adsabs.harvard.edu/abs/2017MNRAS.468.4170M\">Muratov et al. 2017</a>). \n"
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    "### Distribution of stellar metallicities\n",
    "\n",
    "One way to test evolution models is to compare what they predict for the distribution of metallicities in stars in a given galaxy and the actual distribution of metallicities. \n",
    "\n",
    "When we run the model like the one we are considering, we have solution in the form of $M_{\\rm g}(t)$, $M_\\star(t)$, $M_{\\rm Z}(t)$, where $M_{\\rm Z}$ is mass of heavy elements. Thus for each time step $\\Delta t$ from $t$ to $t+\\Delta t$, we know $\\delta M_\\star$ and we know metallicity $Z(t)=M_{\\rm Z}(t)/M_{\\rm g}(t)$ with which this new mass of stars was formed. Hence, the model predict distribution of metallicities of stars formed by given time $t$. This distribution can be contrasted with data. \n",
    "\n",
    "When people compared simpler chemical evolution models - i.e., without modeling cosmological mass accretion and star formation explicitly - to observed distribution of metallicities of stars in the Milky Way disk, they identified what's known as the *G-dwarf problem* (<a href=\"http://adsabs.harvard.edu/cgi-bin/bib_query?1962AJ.....67..486V\">van den Bergh 1962</a>)."
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    "### The G-dwarf problem\n",
    "\n",
    "However, for the Milky Way the closed-box and simple outflow model *predict metallicity distribution that overpredicts number of low-metallicity long-lived stars (G dwarfs) by a lot*, which is known as the *G-dwarf problem*. In other words, there are way fewer low-metallicity stars in the Milky Way disk than the closed box model predicts. This problem was pointed out by <a href=\"http://adsabs.harvard.edu/cgi-bin/bib_query?1962AJ.....67..486V\">van den Bergh (1962)</a>. \n",
    "\n",
    "Another way to state the problem is that observed *distribution of metallicities of low-mass stars in the Milky Way disk is too peaked near solar metallicity.* The closed box model, however, predicts a significant tail of low-$Z$ stars. This is shown in the figure below (you can find code that produced it in the notebook):\n",
    "\n",
    "<img src=\"http://astro.uchicago.edu/~andrey/classes/a304/fig/Zsdist_dwarf_problem.png\" align=\"center\" width=\"600\"></img>\n",
    "\n",
    "The figure actually shows recent measurements of M-dwarf metallicity-distribution from <a href=\"http://adsabs.harvard.edu/abs/2012MNRAS.422.1489W\">Woolf & West (2012)</a> (see their Fig 2 and Table 2). It has noe been shown that <a href=\"http://astrobites.org/2012/02/15/and-now-theres-a-problem-with-m-dwarfs-too/\">similar problem exists for K- and M-dwarfs</a>, which are longer lived stars so probe earlier stages of enrichment. The \"problem\" also exist in other galaxies (e.g., <a href=\"http://adsabs.harvard.edu/cgi-bin/bib_query?1996AJ....112..948W\">Worthey et al. 1996</a>). \n",
    "\n",
    "A number of different explanations were developed for this discrepancy. They are related to the fact that real galaxies have inflows and outflows. We know that models with just outflows of constant loading factor behave like closed box models, but with lower metallicity. Thus, constant mass loading factor outflows cannot change the distribution of metallicities. Thus, a combination of inflows and mass-dependent loading factors is required to explain the distribution of metallicities of stars. "
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    "### Gas recycling by galaxies and deuterium abundance\n",
    "\n",
    "Deuterium or D (nucleous of proton and neutron + electron if it is neutral) is synthesized during the Big Bang nucleosynthesis. D is the first element that ignites when stars form and star nuclear fusion in their centers. Because stars at this stage are still fully convective, D is burned not only in the center, but throughout the star (convection brings outer layers to the center, so there is nowhere for deuterium to hide). Thus, D that ends up in stars is completely destroyed. \n",
    "\n",
    "Yet, deuterium is observed via its absorption lines in the ISM of our galaxy, in other galaxies, and in the intergalactic medium in spectra of quasars. The fact that D is not fully destroyed in galaxy ISM, means that the ISM gas was not fully cycled through the stars. Given that gas consumption time scale is $\\sim$ few Gyrs, this by itself indicates that there must have been inflows. Measurements of deuterium abundance thus give us an idea bout the relative role of outflows in galaxies. \n",
    "\n",
    "Recent analysis by <a href=\"https://arxiv.org/abs/1604.07434\">Weinberg (2016)</a> shows in the Milky Way deuterium abundance is $\\approx 0.87$ of the primordial value. I.e., $\\approx 90\\%$ of the gas in our Galaxy is pristine - i.e., 90\\% of atoms in the ISM came straight from the Big Bang and have not been inside stars. \n",
    "\n",
    "Similar results are obtained in modern galaxy formation simulations <a href=\"http://adsabs.harvard.edu/abs/2017arXiv170408254V\">van de Voort et al. (2017)</a>. "
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      "C:\\Users\\h2_sf\\AppData\\Local\\Enthought\\Canopy\\User\\lib\\site-packages\\ipykernel\\__main__.py:32: RuntimeWarning: divide by zero encountered in divide\n",
      "C:\\Users\\h2_sf\\AppData\\Local\\Enthought\\Canopy\\User\\lib\\site-packages\\ipykernel\\__main__.py:34: RuntimeWarning: divide by zero encountered in divide\n",
      "C:\\Users\\h2_sf\\AppData\\Local\\Enthought\\Canopy\\User\\lib\\site-packages\\ipykernel\\__main__.py:34: RuntimeWarning: invalid value encountered in divide\n",
      "C:\\Users\\h2_sf\\AppData\\Local\\Enthought\\Canopy\\User\\lib\\site-packages\\ipykernel\\__main__.py:41: RuntimeWarning: divide by zero encountered in divide\n",
      "C:\\Users\\h2_sf\\AppData\\Local\\Enthought\\Canopy\\User\\lib\\site-packages\\ipykernel\\__main__.py:47: RuntimeWarning: divide by zero encountered in divide\n"
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TiTfCuOs0dTp2DMIaGbazH6zp1qZprjZNc4lhGL8xDON5rKR5EDCnI7tdixzO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\nAOiaYAwAAEDXBGMAAAC6JhgDAADQtX8BZhVmVVK8xtQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb717358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.integrate import odeint\n",
    "from scipy.integrate import quad\n",
    "from scipy.interpolate import UnivariateSpline\n",
    "\n",
    "def M_gas(mg,t, sfr, a, Rloss, tdep):\n",
    "    # chemical evolution model with no inflow, but with outflow dMout/dt = a*dM*/dt\n",
    "    Mgas = -(1.0+a)*(1.0-Rloss)*sfr(t,mg, tdep)\n",
    "    #print Mgas, mg, Rloss, a, sfr(t,mg)\n",
    "    return Mgas\n",
    "\n",
    "def sfr_ks(t, mg, tdep):\n",
    "    # SFR via simple KS-like relation\n",
    "    return mg/tdep\n",
    "\n",
    "tu = 13.65\n",
    "t_output = np.arange(0., tu, 0.01)\n",
    "#t_output = [0.,1.6]\n",
    "y0 = np.array([1.])\n",
    "\n",
    "sfr = sfr_ks\n",
    "a = 5.0; Rloss = 0.25; tdep = 2.0\n",
    "Mgasout = odeint(M_gas, y0, t_output, args=(sfr, a, Rloss, tdep))\n",
    "Mgasout = np.clip(Mgasout[:,0],0.0,1.e100)\n",
    "sfr = UnivariateSpline(t_output,Mgasout/tdep,s=0)\n",
    "\n",
    "msmout = []\n",
    "for t in t_output: \n",
    "    msmout.append(sfr.integral(0.,t))\n",
    "msmout = np.array(msmout)\n",
    "\n",
    "ytrue = 1.0; \n",
    "Zout = 1.e-3 + ytrue/(1.+a)*np.log(y0[0]/Mgasout)\n",
    "fgout = Mgasout/(Mgasout+msmout)\n",
    "yeffout = Zout/np.log(1./fgout)\n",
    "\n",
    "a = 0.; \n",
    "Mgascl = odeint(M_gas, y0, t_output, args=(sfr_ks, a, Rloss, tdep))\n",
    "msmcl = y0[0] - Mgascl\n",
    "fgcl = Mgascl/(Mgascl+msmcl)\n",
    "Zcl = 1.e-3 + ytrue/(1.+a)*np.log(y0[0]/Mgascl)\n",
    "yeffcl = Zcl/np.log(1./fgcl)\n",
    "\n",
    "Mgasin = y0[0]*np.ones(len(t_output))\n",
    "msmin = y0[0]/tdep*t_output\n",
    "fgasin = Mgasin/(Mgasin+msmin)\n",
    "Zin = 1.e-3 + ytrue*(1.0-np.exp(1.0-(msmin+y0[0])/y0[0]))\n",
    "yeffin = Zin/np.log(1.0/fgasin)\n",
    "#\n",
    "# plot\n",
    "#\n",
    "fig,ax = plt.subplots(1,2, figsize=(6, 3))\n",
    "\n",
    "ax[0].set_xlabel(r'$M_*$'); ax[0].set_ylabel(r'$Z/Z_\\odot$')\n",
    "ax[0].set_xscale('log'); ax[0].set_yscale('log')\n",
    "ax[0].set_xlim(0.001, 5.); ax[0].set_ylim(1.e-3, 3.0)\n",
    "\n",
    "ax[0].plot(msmout, Zout, c='r', lw=2.5, label=r'outflow only')\n",
    "ax[0].plot(msmcl, Zcl,'--', c='m', lw=2.5, label=r'closed')\n",
    "ax[0].plot(msmin, Zin, '-.', c='darkorange', lw=2.5, label=r'inflow')\n",
    "ax[0].legend(frameon=False, loc='lower right',fontsize=9)\n",
    "\n",
    "ax[1].set_xlabel(r'$M_*$'); ax[1].set_ylabel(r'$y_{\\rm eff}$')\n",
    "ax[1].set_xscale('log'); ax[1].set_yscale('log')\n",
    "ax[1].set_xlim(0.001, 5.); ax[1].set_ylim(1.e-1, 2.)\n",
    "ax[1].yaxis.set_label_position('right')\n",
    "\n",
    "ax[1].plot(msmout, yeffout,  c='r', lw=2.5, label=r'outflow only')\n",
    "ax[1].plot(msmcl, yeffcl, '--', c='m', lw=2.5, label=r'closed')\n",
    "ax[1].plot(msmin, yeffin, '-.', c='darkorange', lw=2.5, label=r'inflow')\n",
    "\n",
    "#ax[1].legend(frameon=False, loc='lower left',fontsize=9)\n",
    "plt.savefig('fig/MsZyeff_simplemodels.png', bbox_inches='tight')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
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KQkujpr3ZhmdXiOCX9bDlS8basjlrRivNozMN73ur7Au8Hn/M4lq9ejWrV6+O2fWF6CC5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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9fa5860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#\n",
    "# This script computes lifetimes of stars using fitting \n",
    "# formulae of Raiteri et al. (1996) describing results of stellar evolution\n",
    "# calculations\n",
    "#\n",
    "import matplotlib.cm as cm\n",
    "import matplotlib.colors as colors\n",
    "\n",
    "Z = np.arange(0.002,0.04, 0.002)\n",
    "M = np.arange(0.5,120.,0.1)\n",
    "\n",
    "# lifetime of stars using fitting formulae from Raiteri et al. (1996)\n",
    "lM = np.log10(M); lM2 = lM * lM \n",
    "\n",
    "fig1 = plt.figure(figsize=(3,3))\n",
    "#plt.xlim(0.9*np.min(M), 1.1*np.max(M))\n",
    "plt.xscale('log'); plt.yscale('log')\n",
    "cNorm  = colors.Normalize(vmin=0, vmax=len(Z)-1)\n",
    "scalarMap = cm.ScalarMappable(norm=cNorm, cmap=cm.Spectral)\n",
    "\n",
    "curline = 0 \n",
    "for zd in Z: \n",
    "    lz = np.log10(zd); lz2 = lz*lz\n",
    "    a0 = 10.13  + 0.07547 * lz - 0.008084 * lz2\n",
    "    a1 = -4.424 - 0.7939  * lz - 0.1187   * lz2\n",
    "    a2 =  1.262 + 0.3385  * lz + 0.05417  * lz2\n",
    "    logt = a0 + a1 * lM + a2 * lM2\n",
    "    curline += 1 \n",
    "    colorVal = scalarMap.to_rgba(curline)\n",
    "\n",
    "    plt.plot(M,10.**logt,linewidth=1.5,c=colorVal,label='zd')\n",
    "\n",
    "plt.xlabel(r'$M_* (M_{\\odot})$')\n",
    "plt.ylabel(r'$t_{\\rm life}\\ \\rm(yrs)$')\n",
    "plt.grid(linestyle=':')\n",
    "\n",
    "#plt.savefig('fig/tlife_stars.png', bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tlmin, tlmax= 6.52805289708 14.5431837098\n"
     ]
    }
   ],
   "source": [
    "#\n",
    "# routines to compute stellar mass loss \n",
    "# without instantaneous recycling approximation\n",
    "#\n",
    "from scipy.integrate import quad\n",
    "\n",
    "def psi_tau(t, tau=1.0, tU=13.6):\n",
    "    \"\"\"\n",
    "    input: t,tau in Gyrs\n",
    "    output: SFR in Msun/yr normalized to 1 Msun\n",
    "    \"\"\"\n",
    "    if t < 0:\n",
    "        return 0.0\n",
    "    else: \n",
    "        A_tau = 1.0/(1.0-np.exp(-tU/tau))/tau\n",
    "        psi_tau = A_tau*np.exp(-t/tau)\n",
    "        psi_tau = np.clip(psi_tau, 0.0, 1.e9)\n",
    "        return psi_tau\n",
    "    \n",
    "def imf_salpeter(m):\n",
    "    m_max = 150.; m_min = 0.1\n",
    "    Asalp = -0.35/(m_max**(-0.35)-m_min**(-0.35))\n",
    "    return Asalp*np.power(m,-2.35)\n",
    "\n",
    "def imf_chabrier03(m):\n",
    "    # Chabrier 2003, PASP review\n",
    "    if m < 1.0:\n",
    "        A = 0.158; mc = 0.079; sig = 0.69\n",
    "        dummy = A*np.exp(-0.5*(np.log10(m/mc))**2/sig/sig)/m\n",
    "    else:\n",
    "        dummy = 4.43e-2 * np.power(m,-2.3)\n",
    "    return dummy\n",
    "\n",
    "def ch03_int(m):\n",
    "    return m*imf_chabrier03(m)\n",
    "\n",
    "def mfinal(m):\n",
    "    # based on the fit of Kalirai et al. 2008\n",
    "    return 0.109*m+0.394\n",
    "    \n",
    "def tlife(m, Z=0.02):\n",
    "    \"\"\"\n",
    "    input: star mass, metallicity\n",
    "    output: lifetime on main sequence in log(yrs)\n",
    "    based on approximations of Raitieri et al. 1996\n",
    "    \"\"\"\n",
    "    lz = np.log10(Z); lz2 = lz*lz\n",
    "    lM = np.log10(m); lM2 = lM*lM\n",
    "    a0 = 10.13  + 0.07547 * lz - 0.008084 * lz2\n",
    "    a1 = -4.424 - 0.7939  * lz - 0.1187   * lz2\n",
    "    a2 =  1.262 + 0.3385  * lz + 0.05417  * lz2\n",
    "    logt = a0 + a1 * lM + a2 * lM2\n",
    "    return logt\n",
    "    \n",
    "def mloss_int(m, t, tau, imf='chabrier03', Z=0.01, tU=13.6):\n",
    "    if imf == 'salpeter':\n",
    "        phim = imf_salpeter(m)\n",
    "    elif imf == 'chabrier03':\n",
    "        phim = imf_chabrier03(m)\n",
    "    else:\n",
    "        print \"error in mloss_int: imf %s is not implemented\"%imf\n",
    "    dummy = (m-mfinal(m))*psi_tau(t-10.**(tlife(m, Z)-9.0),tau,tU)*phim\n",
    "\n",
    "    #if imf == 'chabrier03' and t>0.2:\n",
    "    #    print t, m, t-10.**(tlife(m, Z)-9.0), psi_tau(t-10.**(tlife(m, Z)-9.0),tau,tU), phim\n",
    "\n",
    "    return dummy\n",
    "    \n",
    "Z = 0.01\n",
    "mmax = 150.; tau = .1; tU = 13.6\n",
    "\n",
    "#t = np.arange(0.0,13.,0.005)\n",
    "lt = np.linspace(-4.,np.log10(tU),200)\n",
    "t = 10.**lt\n",
    "# grid of masses from H-burning limit to some reasonable max. mass\n",
    "m = np.arange(0.08,150.,0.01)\n",
    "# tabulate lifetimes for m(t) interpolation\n",
    "tl = tlife(m,Z)\n",
    "print \"tlmin, tlmax=\", np.min(tl), np.max(tl)\n",
    "\n",
    "from scipy import interpolate\n",
    "tl_sp = interpolate.interp1d(tl, m)\n",
    "\n",
    "def tlsp(t):\n",
    "    if t < 6.6 : md = 150.\n",
    "    else: \n",
    "        #print t\n",
    "        md = tl_sp(t)\n",
    "    return md \n",
    "\n",
    "def mloss(t, imf='salpeter'):\n",
    "    mlrate = np.zeros_like(t)\n",
    "\n",
    "    for i, td in enumerate(t):\n",
    "        ltd = np.log10(td*1.e9)\n",
    "        mmin = tlsp(ltd)\n",
    "        mlrate[i] = quad(mloss_int, mmin, mmax, args = (td, tau, imf, Z, tU))[0]\n",
    "        #print td, mmin, mlrate[i]\n",
    "\n",
    "    mlsp = interpolate.splrep(t,mlrate)\n",
    "\n",
    "    mlcum = np.zeros_like(t)\n",
    "    for i, td in enumerate(t):\n",
    "        mlcum[i] = interpolate.splint(0., td, mlsp)\n",
    "\n",
    "    return mlrate, mlcum\n",
    "\n",
    "# compute mass loss for Salpeter IMF\n",
    "mlrates, mlcums = mloss(t, 'salpeter')\n",
    "\n",
    "# now Chabrier 2003 IMF\n",
    "mlratech, mlcumch = mloss(t, 'chabrier03')\n",
    "\n",
    "# normalize the rates properly (i.e, normalize IMF to 1 Msun)\n",
    "Ach = quad(ch03_int,0.1,mmax)[0]\n",
    "mlratech /= Ach; mlcumch /= Ach\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cTmfNCT0hhDQTJcptSqFQ4KmnnipYNjg4iB5ND6KPRJEJZZD4eQKpiyl0m7uh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\n5cUn6T1D5Zn1N1Iod49b9+qO2sjPAo8A847b9QjwjRDiWV9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rKoiJ15GQFExCcjCGsL4t\nmtvtDq655Omj1uROnnzhWnJGx7s95qsv8nj4wXVMnJTC5GnpnDQljZzR8dJaLBmyBPJ450+hvBNn\nveSlQohCv1x0mDKUY7YCjaI8I/FJwf2yNFv2WTC+bzwak6adoCV0YSiKrv8Tps6sglpt15ihpsY2\n1qzYyTurdmG19OzmpdGouPzqmVx+zalotb37vzlsgs03lHU76QhNcVqWI0cF3LtuUPF0XyWBzUDu\nayBPHPyJL8Y7YRPOmsXFtqPiWJyQ2DD8tnDUsa7vTofJgUovrcUDZaDvxKodbXx8RSnNeT0ktFJg\n0rIYTv1rAtoQFTu/qGfN62U0Nfa88BwUrCIhOZjE5GDOXZRIQnLfYplbW9r5dMtBWpvbuezqmR7b\nPfn3DXywtmvO2utuns1PrjnVbXubzY4Q9Hps9zdyvBuejNTxzp9C+WkhxK09tFkhhLjcLx0KYIZr\nXUl/U1dj5pHfHSDUoOGm5dmkpOt7PugE7LV2Wle14qh1unyp4lQYLjWgjunfALZ3714AJkyY4HZ/\nVWUTLz37OZ9s3N+r82XlxPGr3y7wuDJ9IsIh+GxZBd8/Ve+xjSFVw0Vbs4nIlgm+ektP91USmAzk\nvgbyxMGfeGO8E2bhFMSdwrjMBh7WG1WRTmtx8OzhUa94qNLfZ0c4BLsfq+Wr+6pwHBeVZNcKzBEC\nc6Tzt1BgTL2es/+bSvKPjuVy+f6bRp5+PL/LOQ3hGpJSgo+K4sQU5+/IaG2/vMSOHKpi3TvfsmXD\nfiwWG8F6LW+8c5vHHCLf7irmN79Y2WXb+InJPP5/V/b52kMBOd4NT0bqeOfPNMj3KIryEM6M2Fs8\ntJnmx/5IRjg7vmjA2GrH2Grn0fsPcMUN6cw8o/fuygDqWDXhN4ZjfN+IdZ8VR42D5uebCb0wFN04\n7wvJhMQI7vnD+Vx4yVSee/IT9u8t77Z9QV4Ny5e+xhXXnsrl18zs0TVLUSmc8e8k1HoV3z5W67ZN\na6mNtWcWsHhrFuGZUixLJJKhi+VQR04JdzYBBdSJajRpmqM/MrZ46GKstPLRNSUUfNOKOU3QHnlM\nHNtOCMfVoHDZ06MIOqHkU2pGCD+eH0diSjBJKXoSU/ruLu0Oq9XOtq2HeH/Nbvb90HVcbjdZ+Xzr\nIeYtmOj22JMmpxIRqaep0URmViyz5oxm5qwct20lEol/8adF+X9ANMfE8In+nZEAQgi5hNsDnSvs\nW7Z0XW+QMcp9QwjBF1vqWPlyCTab8zmYfXYsS65JdZt0o6dzmb82Y9pogo58IkGnBaE/S9+n2LWm\nJmft54iIiF5d87MtB3nh6U+prmzusf3YCUnc+4eFJCT17tzbflXJnn/UeWwTlqnlok+yZOmoXtCX\n+yoJHAZyXwN5hd2f9Mb12mF0YCu1oRvj+i6yN9pp/nfH+1GDM7Y4TYMm3RljPJBQGUn/6cuzs3N7\nPds+qKVorxGzXkAPt8ygV5OaE8KNy7IICfWtPaih3si6td/y4Xt7XOKMj2fS1DQeecKzw+TX2/NI\nSo7sU26RoYoc74YnI3W886dQrgfyO37cEQWcJYVyzwylLKDDgaJ8I88/UXA0iUd6dgg3LcsiJq7v\nz7OtxEbr6lZEq/O50mRonCWkDL6zUrSbLLz+0nbWrNyJw+75edbrtTz5wrUkp0b16rxCCD6/s5Lv\n/uVZLEeM0nHxtmxC4kdOjW6JxBsE8sTBn7gTyg6jA1uRDVuRDWuh9WjoS/jPw1FHdp1CCCEw7zA7\ns1InqVHUUhgPNVqarZQVm1CpFHLHh3XZJ4Tghbvz2F3huhisboegJsX506iQOSGU8/6VSkz6wOoi\n94aqiiZWv7mDj9f/0OvKFC+tuLlXC9USyXAjkMc7fwrlI8A0IYRH05eiKDuFENP90qEAZijVlRwu\nGFttvPR/hezb4/x6hhrUXHd7JhMm931Qc7Q6MK4xYityDp4h54cQNM3374b8I9U88bePOXSg0u3+\nX/7mXI+uX54QQvDZz7uPWY6frmfRlkx0BrnGJZH0lkCeOPiTzvGu5bsWbIU2bIU27NXuA4xDFoUQ\nNEl+nEMVu01QWd5OWYmJsqI2yopNlJWYaG50jpW5E8JY/tvRR9tbWuxsuamMb75opHaCneBGpyAO\nalQIblJQt4OCgjpI4fTHEjnpjmivV544kcL8Gla9sYNPNu3vdmHaHdfeOIsrrjvNRz2TSIYugTze\n+VMony2E2NRDm6lCiN1+6VAAI7Ne+waHQ/C/dyv54O0KhABFgQWLk1iwOBFVH0t/CIezhJRoFYQs\nCvH54N2J3ebg7bd28Op/v8BmPTaZ/NFZY7j3/oX96ocQgq23V7D3ac9iOX2+gfPez0CtldYaiaQ3\nBPLEwZ8oimLWqXW6yvtdFwAVvYImQ4MmQ4M2Q4sqXuW3d62ke9qMNsqKTZQWmSjtEMUVpe1Hw5zc\nERau4eH/TAKgfn87H11cQsOB7uc5UeOCOOetNGIn+daKfOhAJW+8tJ2vvsjr87FTp2dwzvkncdrs\nHIKCZCZoycgjkMc7fwrlKUKIb/1ysWGOFMq+Zf/3zfz3yQKMrU6hOX5SONfdntmvhB9CiEGZuBUV\n1PLYXz7kyKEq4hPCeOrF6zCE9X8iIRyCT24tZ99zDR7bjLk2krNfSpETVYmkFwTyxMGfHC+UlaAO\nYZzp/FHHq+X7Zojyr78e5uDeFo/79SFqUjP0pKR3/KTpSUrVowtSkfd2ExuvK8NmdHR7jfE3RTH7\niSS0Ib4LbSoqrOXV57ex7dPDfTouJFTHvAUTWbh4Cqlp0T7qnUQSGATyeOdPoXxYCDG655aSnpBC\n2ffU11p4/l/5FOU5k3NExei47a6cfpWQcoejzYHKzeDe3Ox0/Q4PDx/wNaxWO688/zkzT89h4uRU\nj+2EEHy1LY8Zp+d0azkXDsHG60o59FqTxzbT7o3ltIcSB9Tv4Yg376tk6DCQ+xrIEwd/oiiKWafV\n6YyFRtSJ6j4lR5R4F4dDUFNlprSwjZJCEyWFbYw9KZx5CxNc2q55vZRN66sBiEsIIiVdT2qGvkMc\nh6DWmlAUpcuzIxyCHX+qYccD1d32Qx2sMOc/yYy7vnf5NvpDZXkjr/33C7Zs2I/D0ft5cmZWLAsv\nnsJZ88Z7LAc13JHj3fBkpI53/szAk9OR+foWIUShH687LPHXAsdIJTpWxy9+n8ua18v4dEMNwiEI\nj/DO42I5YMH4rtFtCamSkhLAO/UHtVo1N942p8d2H7y7h6f+vpHTZo/irt+dR4iHwV1RKZz1Qgqm\najslH7e6bfPNw7WEJmuZ9PPAz9zpTbx5XyVDB3lf/YNAoEmWCQP9icMhqCpvp7jgmCguLWyjvb2r\nlVetUdwK5VlnxjLllEiS0/QE613zV+zd67TQdj471jYHm64vJW9V9xUcwrO1nPt2OnFTvLNofSL1\ndUbefHk7H637Dpute4v28Uw7JZNLr5zB5GlpI97LQb4Xhycj9b76c+RpBP4G3KooShbwjBBicw/H\nSCSDhlar4vLr08geHUpMvI6wiIHHFgmLoG1dG1jAuNqI7TRbn0tIeZMf9pTy9BPOx3D750e46443\nefDhxcQluF8xVOtUnLs6jbVnFlCzq91tm8+WVxCSqGHUpTK7p0QikQQKu7bXk3/YSHFBG6VFJixm\nz0IxWK8iLTOErFGhbvcnJPc+1KelxML6RcXU7nY/pnSSuTCMs19JJTjK+4kjLRYba1ft4q1XvsRk\nsvbqGEWBWXNyueyqGYweIz2pJJLhiD9dr7OEEAXH/X0JcDnwNfBsd9mwJV2RdZQDG1uJjda3WxEt\nriWkrFbnAK3V+j7hR01VM8uWvkZjQ9fajzGxBp555aeEGjx7yLRV2Xh7Vj7NeRa3+9VBChd9kkXi\nqSFe7XOg4s/7KvEfA7mvgeyK5k9kqJF3EUJgswm0WtfQn8ceOEjBYaPLdkOYhrRMPWmZIaRlhZCW\nGUJMnK7PSS6Pp/PZqdtlZf1FxZiqPJdYUlQw40/xnHxvnNcXlYUQfPl5Hs/93ydUlDX26hiNRsXZ\n8yew5MpTZPyxG+R4NzwZqeOd34Syxw4oylRgI7ACp2CWCb96QNZRHhq0NFkpzDNy0rTIPh97Ygkp\nxaBgWGJAk+YfJw+z2cpdd7zFkUNVLvuuuXEWV/aihEVTnpm3T8/H5KFUiz5Bw2U7czCkysFSIjmR\nQJ44+BMplAdGU4OVonwjRXltFOY5rcVnn5/AuYtcLaArXy5h15cNpGeGkJ7lFMXpWSFExWh94k58\n8PVGNt9QhsPieR6qi1Axf0Ua6fPDPLbpL0UFtTzz7y3s3lnUq/YqlcK8BRO58vrTiPfgdSWRSFwJ\n5PFu0IJ+FEXJBO4BlgIKcA6gUhQlClghhFgzWH0LBNRqNVu3bu2yLS0tbZB6M/Kw2wUvPlXIob0t\nzFuYwAWXJaNW934ioTKoMFxtwLTZhHm7GdEqaHmlBf1cPUEzgnwe49TcaMLc7upedvb88Vxx7am9\nOkdEThAL12fyzpwCt9lJTVU21i8qYvFn2T7NSiqRSCQSaG+3U1LQRuERI4Udwrix3vU9X5zvajUG\nWHxFCpdem+rz8UcIwa6/1vDV77pP2hWZq+O89zKIGuP9ubXd5uD3d79NTbXnzNzH86Mzx3DNjbNI\nTZcWZIlkJOFP1+v/CSHmK4pyFk6BPBenQN4IPHJ8jWVFUW4GpgH3SJdsV+QK++BTU2XmH388RFOj\ncxIyepyBn/4si4jIvltPLfstGN8zQocXs3aCltCFoSg6305WjEYzf/vjB3y9PR+ASVPT+PNjS9Bq\n+xb/VfxxCx+cX4TDg+dczqXhzF8hE5xIJMcTyCvs/kSOd93z1Wd15B1spTCvjfISE56mdLogFWmZ\nejKyQ8kdb+iXJ5Q3sFsFn95ezr7nPZcaBEibF8o5K9J9Eo/cycaP9vL4Xz/sts30mVlcd9NsRo1x\nTVgmkUh6RyCPd/4Uyg6gAYgEmoBncSb0KvDQPgJ4WAhxm186GEDIicPQoKnRyn+fLODwfmcG6IhI\nLTcsy2LUGEOfz2WvtdO6uhVHjdMyq4pVYbjUgDrWd5MEALvdwbNPbmHX14X84z9XEhbev0yie5+r\n55Ol5R73z3gwnlP+EN/fbkokw45Anjj4EzneORFCuF1sfOi3+yktMnXZpiiQnKYnMyeEjJxQMnNC\nSEzR98nryRdYWuz879ISiv/nvmpCJ5OWxzDrsURUGt/21+EQ/PK21zm4v9JlX/aoOG75+ZlMmirz\nvkgkAyWQxzt/C+VvcIrj53poGw5E47QoS6F8AnLiMHSw2wXvrShj4wdOFzKVChZfmcKZ58b32YIq\nLIK61XWo8zrEsQ63JaR8gbHV3G3yLoD62laiYkI9/r8+W17Bd/+q83j8uavTyLlkZGbCrqx0TsQS\nE2Vm1OHEQO5rIE8c/MlIHO8cDkF1pZn8Q60UHDaSf8jI7LNjOfNc18XGN18s5odvmsgcFer8yXHG\nFQcF+3aRta8Yy62sO7+I2m89Z7ZWaRXm/F8S42/yn3vz/r3l/PK2N47+HR6h57qbZzP//JNQq2XI\nUH+Q493wZKSOd/6MUc4XQkzvZdvngUuA1T7sT0Az2EnYJE7UaoXFV6aSNTqUV58uor3dwduvlZF/\n2MjVN2e4rR/pCUWnUDWpitDQUCJ+iAALmL81ox3rm0Qqx9OTSC4raeDXy97itDNGcfudc91mO531\neCIN+9sp2eA+/m3jtaWEZ+uIm+qb+pdDmbo65wKCnDgML+R99Q/DfbyzWBwU5TkFcf6hVgqOGDG2\ndk2SmH+o1a1QvvTaVK64YWhbPet+aGfdeUW0lnguuxQUqWLBO+mk/LjvHlmeKC9tYNUbX3PHL+ei\n0bgfi8dNSObs+eP5ZOMBLrh4KlddfxqGsN6XtpK4It+Lw5ORel/9KZQf6UPbh4AdON2zJZIhz5RT\nokhK1fP8P/MpL21n91eNlBebuPnObJJSey8MNVoN5rFmwqaFYdpkIvQizxZcf1FR3si9d66kvs7I\nB2v3YLc5+Pld57iIZZVG4ZwV6bx9ah6Nh1zLRtnaBOsvLOLSXaMIiR+0PIKDgkYzsv6/IwV5XyX9\nobXFRt7BVvIOtpJ/yJmJ2m53vxgQGa0lJ9fA+MnusyxrNEPb6lmxzcgHC4swN3quyRyWoWXh+gyi\nx3tHoAohWP/eHp576hPM7TaSUiK57KqZHtvfcMuPuOyqmaRnxnjl+iMd+V4cnozU+zro5aEkfWck\nuqIFCuZ2O2++WMyObc5EJbogFVfdnM700/ruSuYpJs2fVFU08etlb1Fd1TUz6NxzJ3DnPfPduqY1\nHDSzemYelib3E6PUs0O54H+ZqAY5Xk4iGUwC2RWtJxRFyQZWAZcKIfIHeK5hN949eNdeqitc/z8q\nFaRmhJCdG0p2roHs0aFExfg+9MZXFK5v4X9LirGZPM8z46YFc/66DEKTvFNGsK62lX8+8hE7vyo8\nuk2n0/Cfl68nOWVwEphJJCOdQB7vBmV5QFGUs4QQmwfj2sOJbdu2dfk7LS2N9PSh7YI13AkKVnPd\nbZlkjzaw+tVSLGYH/32ykMqydhYuSe7TuTyJZEezAyVM8bmIrqlq5t47V7qIZHBmC7XZHNz12wWo\nT7BoRI0JYv7KNNYtKEK40cqlm4x8fX81p/5ZZhGVSIYTHQL5ESAfZ+WKEadMhBBUV5g5cqCVuMQg\ncse71v/NyTVQXWEmOFhFVq6BnA5hnJkz9GKL+8uhNxrZdF2px2oIABnnGThnRRo6g/f+z62t7ezZ\nXdJlm8Vi48nHN/CXx5cM+uKzRCIJLAbFoqwoyg4hxCl+v/AwQVEUs1qt1tntXWOY7r//fh544IHB\n6ZTEhYIjRp5/Ip+mBiu33Z3DhMkDT2TlaHHQ/FwzmkyNz0tIVZQ3cu/yFW6Fcic/njuWu+47z61l\nec8TtXx+p2s20U7Ofz+dzIXu3QklkuFOIK+w9wZFUQRwshDimwGeZ0hblIUQVJa1c3h/K4f3t3Dk\nYCvNjU51OPOMaK69NdPlmIpSEzabICVd7zbfQ6Dz3ZN1fPbzim7bjF8axZynkn2S2fqdlTt59slP\nXLbfdd8Czp4/wevXk0gk3RPI451PLMqKonwMnHzcpnrgluOsyFGKotiBxhMO3SiEuNwXfRpuqNVq\ntm7d2mVbWlraIPVG4o6sUaHc+5ex7P++xSsiGcC0xYQwCqx7rTRXNfu0hFRSciR/+9dPuPfOlVRW\nNLlt88nGA4SEBvGzX851WamftCyG2m/bOfDSiY+5k43XlHLprlFEZAeua6FEIhlZCCGoqjBzaF8L\nh/e1cHh/Ky3N7s2m9bWuuRqAPuWtCCSEEOx4sJodD9Z0227mn+M5+bdxPrPuLlpyMts/P8L335Ye\n3aZSKdRUe170lUgkEnf4zKLcIZanA/cAK4UQTcftOwJkn3DII0KI3/ikM8OMob7CLvEdwiIwrjNi\n3duRPdQPJaRqqpq5586VVJS5F7wAl18zk+tvPsNlu7XNwdun51O3x31JkNipwVyyLRuNfmgnpJFI\nvI2vVtgVRckeaFywl/oxrCzKu7bX8903TRza13LUYnwi8UlBjB5rYNS4MEaPNQR0fHFfEQ7BZ8sr\n+P7Jes+NFPjx08lMWOr78k9VFU3c9tOXMbVZSEyO4K77zmPCSSk+v65EInElkC3KvhTKT+MUvwVu\n9h0BLsUZxwQwD7hZCDHfJ50ZZgyViYOk/wgh2LS+mllnxqIPOWYRLihwPi5ZWVndHmveYca0wQQd\nMcBBpwWhP0uP4iM3vtqaFu69cyVlJQ0e29x0+xwu+YlrREXjETOrpntO7jXuxijOen54T2B6c18l\ngcdA7qu3Jw6KoswFnsHpmXVLN+2W4hxz64FonKUb7/FGH064zrASyi/+u4BdX3Z9/8UnBZE7LozR\n4w2MHhtGRJR3ElIFGg674JOlZex/0fNiqkqnMO/1VEYtcXpXDeTZaWpsY8OHe7nkJ9O7tUp/vP57\nDu6r5Kbb56APGTmLFoONHO+GJ0NpvPMnvnK9vgnY4E4kd9AohNh93N+rFUVpUBTlIWlV7h0yW3lg\ns2l9Ne+8Ucbnm2q5+c4sUtJDAGhra+vxWEVRCJ4RjCZJQ+vqVkSrwLzdjL3cTujFoagM3rfOxsaF\nOd2wl6+gpNi9xeD5/9uKISyY+eef1GV75Kggzn45lQ8vKnZ73P4XGkg8Tc/4G31vZRgsenNfJYHH\nULiviqJswBnGtANXT60T2z4DZAsh5h2/TVGUDcdvG2r4erxrb7dz5EArB75vISJSw7wLXOuE5k4I\noyjfSO74MEaPDyN3vIHIKCm+HDbBputLOfS6+/AcAE2oivPWppM291iN5P4+O999W8Lf/vgBdbWt\nhITqOO/CyR7bnnPeSZxz3kke90t8w1B4L0q8z0i9r77Kej2vh1jjnSduEEJsUhTF4yq4pCsyc2Pg\nIoSgptJpHampMvPo/Qe58sZ0ZsyOITy898mtNGkawm8Ox7jGiK3Ihq3IRvPzzRguMaBJ8/6jHR0T\nyl8eX8JdP3vTY4Kvfz36MQZDELPm5HbZnr0onGn3xvLNw7Vuj/v0jgriTtYTN2V4xu715b5KAoeh\ncF87Ba6iKJE4M067RVGUacBSIOeE429RFEUoirJUCPHsce034LQ4d0e9PwS2t8c7h0NQUtDGvu+a\nOfBDCwWHjUfrGCckB7kVyqf/OIbZZ8V6tR+Bjt3iYMNVpeStbvbYJjhGzcL1GSTMCOmyva/PjhCC\nVa9/zcvPf47D4bxXz/xrC+MmJJOVE9f3zkt8xlB4L0q8z0i9rz5xvVYUZUV/knL197iRxlBxRZMM\njC8+qWXFSyXYrM5n8Iy5sVxydSpabd8swsIhMG02Yd7e8X1QgX6enqBTgnyyoFJaUs9dd7xJU6PJ\n7X6NVs0f/3YxU0/O6LLdYRO8d04hZVuMbo+LHKPj0p05Xi0VIpEMVXzgeh0JNADPunO97rAmLxVC\nuLwUFEXZhZdF71BzvW6os7D/+2b2f9fMwb0tGFvtLm2Cg1WMHh/Gjcuy+vweHmnYzQ4+urSEwvc9\nJ8gypGq44ONMoscFD+habW0W/v7Qh2zbethlX1p6NP967mqC9dK6L5EMVQLZ9dpXQrlf5Z9k2aje\nIYXy8KG4oI3nn8inrsaZHTUjJ4SblmUTHdv3Qd+yz4LxfSN0JFrVTtD6rITUkUNV3LN8BW1G91ld\n9Xotjz11Bdmj4rtsb6uysXLaEYzl7pPhjL0ukrNfSvV6fyWSocYgCOU8ACFEjpt9q4Al7kT0APsy\nqEK5KN/Izi8a2P99MxWlrgkFVSrIHBXK2InhjDspjIzsUNQ+KFc03LC2Ofjo4mKK/9fqsU14tpZF\nm7IIzxyYgC0tqedP971LcWGdxzbzFkzgl79ZMKDrSCQS3xHIQtlXS6Z9HmkURYnoz3ESSSCTnhXC\nPX8ey4QpTpeWorw2Hr5vP/u/9+zK5gndeB3hN4ajinU+1rZCG6LdN7F9o3ITeOChxeh07l28TSYr\n99/zDnW1XSdSIQka5q9MQ+XBM/zAy40cfNVzwjCJRNJvsnEtydhJPRx1z+43iqJEdliuV3Vseq4j\nBrrb2GlfcWhfK5s/rO4ikmMTgjhjbixLf5HN356ZzK/uH8P5lySRnWuQIrkXWI0OPlhY1K1IjszV\nsfjT7AGL5C8/P8Lypa91K5LB6Upvt7lPFimRSCQDwVcW5YcBhxDit3045iEgUghxm9cM3MtEAAAg\nAElEQVQ7NMyQFuXhh8Mh+GhtJevXVCAEKAosXJLEORcmoupjJmthEbR90IZuqg5tpm+zsH71RR5/\nvG8tDrv798io3AQe/fflLm5xux+r5Yu7K90eowlVcfk3OUTmBtzCo0TSa/xpUT5u3zdCiJPdHPsM\nzvjlAVuAvU13453N5iDvoJGKUhM/nh/vsr+s2MRjDxxkzIQwxk8KZ9ykcOIS5Hulv1jbnCLZU/gM\nQPSEIC7cmEloYv/HHodD8PpLX/DGS9u7bRcUrOGOX8xl3oKJ/b6WRCLxPYFsUfaVUM4GjgBThRB7\netF+Ks4EXzlCiEKvd2iY0Tlx2Lx5c5ftaWlppKenD1KvJN5g33fNvPRUwdH4uYlTw7nutkxCQn2V\nd2/gbP54H4/+eb3H/afNHsV9f7oQtfqYA4twCNYtLKL4Q/dWidipwSzZno06SMYJSoYnQ1QozxNC\nbPRGf7yFoihmQKfVap0Z/4OiSEs8jfSkWaQkzESnDcXhsHHTr0IYPyEHvf5YQkAhBFVVtdTVVQMw\nYcIEl/OXlJTQ3NxMSEiI27InBw8exGazERMTQ2Ji1yRfVquVQ4cOAc7x98RkN01NTZSWlgKQm5uL\nVttVPFZWVlJXV4dWqyU3t2sCRID8/HxMJhPh4eGkpaW57N+7dy8AiYmJxMTEdNnX1tZ2tJxLdnZ2\nl88FoLa2lqqqKqB3n4vN5OCDC4so3ehZJMdOCebCDZloIkS/PxdTm4U//m4N3+4s9XgdgNj4EH72\nqx8x8zRXkezPz+VE5PdFfi7HIz8X5+cSyELZJ7NQIUQ+8CjwjaIoN3bXtqOU1E6cg3uhL/ozHLHZ\nbMyePbvLz4svvjjY3ZIMEKEu4eLr1KRnOzOE/rC7mYfvO0Cb0X1Mb19xmBw4jN51UTvrnPHcdPsc\nj/u3f36EF/6ztcs2RaUw9+VUQpLcLwDU7m7ni19XebWfg8nevXuPDjqS4cMwuq+d2a3d134bdBSm\njL2OC858lqsWrmPOKb8nK/UsdNpQAOwOK/U1rov+iqKgke7UA8bW7mD9RcXdiuT4U/Qs2pyFPrZ3\ni7pCCJeyXzVVzdz1szd7FMkTJyey/J7TSU6N6NW1JP5lGL0XJccxUu+rTyzKR0/uLC9xFs64qI1A\nPlAHxOCMl1rS0XSTEOIcn3VkmKEoilmr1eq2bNnSZbu0KAc+nS+h3NxxrH6llM831zLnnDguu851\nta+vCCEwrjBiq7RhWGJAk+o9K7UQgicf38j69zw7kNzxy7ksvGhKl22lW1p59+xC8PAaWrA2nexF\ngV+SoPO+ultxlgQuA7mvg5DMSwD5HpJ5bQDm4vTqyvdGf7yFoihmlUqru/UnX3bZHhOnY+LUCCZO\njWD0WANanfQ+8QW2dgcfLi6m+CPPMclJs0JYuD4DXXjvKxac+Owc3F/Bg79ZS0O9ZzEOcPVPT+eK\n607rc0iSxH/I8W54MpTGO3/iU39OIcQ8RVEeAe4GLqXrdLjzLfc3IcS9vuzHcERRFGbNmjXY3ZB4\nmYSEBAC0WhVX3JjOhCnhjJ/sHaFoK7BhPWwFoOXlFvTn6Ama7p0SUoqicNudZ1FZ0cQ3OwrdtvnP\nE5tITIpg+sxj7kepZxqY/rs4dv6pxu0xm39aRtyeYMLSArv0R+d9lQwvAuy+NtJDXeShJpKPR1Eg\na3QoJ02L4KSpESSmBPuk/J3kGHazg48u6YVI/jADXVjfyvod/+x8tuUgj/3lQywWz55ToYYg7v7d\necw83WWdRzLECLD3oqSXjNT76lOL8tGLODNa3wJMByJxDtg7cK58N/m8A8MMmcxL0l9OLCGlm6gj\n5PwQr5WQMraa+dUdb1BU4D5LqT5Exz+evpKMzNij2xw2wdqzCqj4rM3tMck/CmHR5ixUajkplgwf\nBsGi7LEEVEcdZdzFLw82Tg8qna6+zoghbOjmahhu2C0OPrqkhMJ1nuskJ56m54KPMvtkST4eIQRv\nvfIlr7ywrdt26Zkx/OEvF5GSFtWv60gkksElkC3KfvFVEkI0CSH+JoS4TAhxTsfvR6VIlkj6x84v\n6tm7p++Pj268jvAbjpWQsvxgofnFZux1dq/0K9QQxIOPXExUdIjb/aY2C3/67bu0thwr16LSKMx7\nPZWgaPeTrfJP2/jmYfcWZ4lE0mueAdcSUB0Ce1rn/qGIoiBFsh9x2AQbrirtViTHz9Cz8MP+i2Sb\nzc7jf/2wR5E8fWYWf//PlVIkSySSQcEvFmWJd5EW5ZFNSWEbjz9wEJtNsGBxEgsW96OElFlgXGfE\nus/pik0QhC4KRTfGOy7OB/dVcM/yFZjN7l3pZpyWzf0PLe7S74L3mlm/qNhte0UNF3+eTeKp7gW4\nRBJo+NCivFoIcamHNs8A2UKIeSdsmz4Urckgqzz4G+EQbL6xjAMveSq5DfHT9Vy4IZOgyP6J5LY2\nC3/5/Xsew3Q6WXTJNG6+48eoNTL+XCIJZKRFuQNFUS5RFGWHoig3KYoS+Bl4JJIhSLvJTlCwGiFg\n/ZoK/vNYHsbWvmXFVoIUQi8ORT9P78wWYAbjSiOmTSaEY+CLZ2PGJ3HXfefhKYTw6+35bP/8SJdt\nWReGM2lZjNv2wg4brizB0uwdy7dEMlxQFOWRjmRcBR2bliiKsktRlFWKosw9vm2HS/YGRVGe6Thu\nFdA4VEVyJ3a7XVZ58ANCCD5bXtGtSI6bFswFH/dfJNfXGbln2YpuRbJKrXDHL+dy6/KzpEiWSCSD\nitctyh01kW8BLgM2ACuEEGu8epERjrQoD19MJhOAS026E2mos/DcE/kU5TnjemPidNy0PJv0rL5b\nXK1FVoxrjIhW57tAk6UhdHEoqtCBT1DefOVLXnn+8y7b1GoVty47k/MvmuKSjMfW7mD1jDzqvnf/\n3c69OoJ5rw48A7i/6e19lQQWA7mvgbzC7k9klQf/8eV9Vez6q+cwl9gpwSzalElwdP/c4EtL6vn9\nXW9TWeE5bCjUEMRvH7yAaadk9usaksFHjnfDk5E63vm6PNQlwOXA2cBK4BkhxLc+u+AIoXPiYLFY\nBrsrEi/Tl/T7VquDNa+V8unGWgA0WoXLr0/j9B/H9nCkK44WB8a3jdhKnJZpJVxxlpBKGVhcoBCC\nv/zhPbZtPQxAZFQI9/3xQiZOTvV4TN3edlZNz8Pe7v7dNPfVVMZcHTmgfvkbWS5jeDJSy2X4Ezne\n+YddD9fw5W88166PGh/E4q29r5N8Igf2VXD/PWtobjJ5bJOYHMGDD19MeqZ7zyJJYCDHu+HJSB3v\nfOrTIoR4WwhxGc6ayd8AzyuKclhRlIcURcn05bUlkuGOVqvi8p+mc91tGWh1Cjar4PXninnt2SIs\nFkefzqUKU2G4xkDQTOc7TDQLHM19O4c7FEXhV79ZQEZWDLljE/nXc9d0K5IBYiYEM/vviR73b729\nnKZ8OWmWSCQSb/Ddk3XdiuTwHB2LNmb2WyR/vT2Pe5ev6FYkjx6bwD/+c6UUyRKJZEjh92ReHaWi\nluJ0z24AVuAsZ9Hs144EMNL1evjS1uZ0pQ4J6ZsLdVlxG8/9s4CaKud3Ii1Tz03Ls4mN7/vinWWv\nBXutHf0c77lN1VS3EBGhRxfUu4mWEIIPFxdT8K77rKsJM/Us/iwbtTYwSkb1975KhjYDua+BvMLu\nT+R451sOvtbIxmtKPe43pGpY/Fk24Zn9S/S4+eN9PP7Qhzjsnuea02dm8dsHL0Af4p1kkpLBRY53\nw5OROt4NatZrRVGycArmpTjrKj8j45l7Rk4cJO5oM9p49ZkivtvljP8KCVVz3e2ZTJwSMcg96x+m\nWhsrJh/BWO4+UdnJ98Vx6p8T/NwricQ7BPLEwZ/IrNe+o3B9Cx8uKsLhIRekPl7N4k+ziRrTv6+o\n3ebgF7e9zuGDnq3V886byLK75qHR9C85mEQiGfoE8ng3ZMpDKYpyNnApx5KAPSOE2Nz9USMTKZQl\nnnA4BBvXVfHeynKEcNYfvWl5FlNOGXgNSiEE9ko7miTf1DM9uL8Cc7uVSVOPTX5LNrXy3rxCcPea\nUuCiLVmkzAn1SX8kEl8SyBMHf6IoilmtVuvs9q4Z7++//34eeOCBwenUMKByexvvnl2AzeR+DhgU\nqeKiT7KInTwwz6LGBiN3/3wFpcX1LvuuuO5UrrlhlktSR4lEMrzw9XinKMoUnBUcCr1+7qEilI+n\nIwnYLcDJyCRgLkihLOmJAz8089+nCjGEabj7j2MIDh74ar15l5m29W0Ezw4meE4wSh9rN3tCCMH7\na3bz3FOfEGoI4skXriU2Luzo/u33VvLNI7VujzWkarh8z6h+Z2GVSAYLKZR7h7Qoe5/6fe2smV2A\nucF9uT1NqIpFmzJJnOkd19maqmbu+tmbVFc5Q2lUKoU7fjGX8xZN9sr5JRLJ0Mbb452iKB/jDN+9\np+NnHrAL2CCEeN4b1zh6raEolDvpiGe+DJgrhLh8sPszVJBCWdIbGuosWK0O4hODB3wuYRM0PdWE\naO4oIZXdUUIqZGD5ANvaLDzxt//x6eaDR7dNmJTCw/+87Kgrnt3iYM2sAqp3uk8Ek31xOOeuTpNW\nCUlAIYVy75DjnXdpKbawZlY+raXu/a1VOoULPswg9SyDV69bVtLA3T9/k5YWM/fev5BZPxrt1fNL\nJJKhiw+E8tNCiFs7dGI9kCOEKFQU5SEhxG+8cY2j1xrKQlniHllXcvhSV1cHQEzM0Mv86Wh20Pp2\nK/ZSpxVCFaEidEkomuT+WXML8mr4yx/eo6ykwWXfkitO4cbb5hz9u/GwmRVT87AZ3WfiPvO5ZMbf\nFN2vfviDoXxfJf1nIPdVCuXeIYWy9zDV2njnjAIaDnj4LBU4d1UaOZf4Jq9FQV4NjQ1tTJ2eId+J\nwxh5b4cnQ2m8UxTlLiHEYx0eyA8LIUZ3bH9YCHGvN67RiU/LQ0l8h91uZ/bs2V1+XnzxxcHulmSA\nVFZWUllZ6dNrVFe2s/Llkr6XkApXEXZtGEEznO85R5ODlpdaMO8y058Ft+LCOrciGaC2phWH49g5\nI0cH8aMnkzye67PlFZ4nf0MAf9xXif+R99U/yAX9gWM1OvhgYVG378k5/0nul0i22eyseuNrLBYP\nWcE6yMqJY+r0DEA+O8MZeW+HJ0P0vs4DNh73t9cHCxnYF6Co1Wo+/fTTLtvS0tIGqTeSQMFidvD8\nEwWUFZvIO9jKzXf2rYSUolYImR+CJkWDcZ0RrNC2vg1bmY2QBSEofSjXNOfssez9rpT33zmWfkCj\nVXPrsjM578LJLq7UY6+LpPijVo6saHI5l61N8PGVJSzZno06SK7/SSTDjW3btnX5W3pQ9R6HTfC/\ny4qp+spzHeMZf4xn4i1998qxWv+fvfsOj6pYHzj+nd1seg8lQBKSUCxYaRbACiICgtIs167oT694\n9SrYwS7qtTfALiJFsYEiICAINooFlJoACRBCQnrf3fn9sQkYcjak7GZL3s/z8NzLzu7ZWcaz57w7\nM+9rY+ojC1i9chsbf8/kgccuJjBQbi2FEG5VoJSaC4wGelYnhJ6GIxm0S3nF0mul1KnAQCAWR5mo\npVJX2TlZiiaaqqzUxgdv7jxUQiok1My1tyZzwqmNn0WwZdsonleM/aBjZtrc3kzYmDDMMQ1PHFZZ\naeWef89m6+Ys2sdH8sBjF9PtmHinz6/ItzHnlO0U7aoybD/5rjj6/8/5zLMQ3kKWXjeMZL1uHq01\nK27Zy1/TjVfvAJx4WywDXunQ6DwPVVU2npr8FT/+sP3QY2f078p9jwzHYpFyT0IIB3dc76pLDB/U\nWhdU//9oAK31Ble9B3hHHeVJODJbr/vHhx0NaK31cx7rnBeTQFk0x5ElpACGXBLPRZd2wNTITNa6\nQlPyRQlVWxyBqwpWhI0Mw9LN0uBj7N9XwIfvrObmCecREXH0xGP7Vpfw2VnpaCcrx4cv6kzS4Ajj\nRiG8hATKDSNZr5tn7ZPZ/PxAttP2rmMjGTQrEZO58ckQn338a5Yt/qvO4/3O6sa9U4ZJbWQhBCDl\noZr2xo6AeLyz7GRHa2/NJFAWrrBlUxHvvJpOcaFjX9lxJ0Zw7W0phEc0btmc1pqKHysoW1Z2aHdI\n8IDqElJuykT9yyPZ/DrF+OYvpH0Al/3RldB2svxPeC8JlBtGrndNt2VmPkuvynTanjAwjGELOjd5\nu8qWv/dx/13zKC2prNN2ZEJGIUTr5cvloTy5mW9ifUGw1jodWKuUurQF+yREq3FMjwjuffxYUrqG\nAfD3n0U8/cBmdqWVNOo4SimCzwwm/MpwVKgjMLYXNi5RWGP1fqAtHfoZ1/gs229l2XWZkgBICNFq\nZS4rZtn1e5y2tzklmCHzk5qV0+GY4zrw+HOjCQkNrPV4ckobRl3Wu8nHFUKIo0irLhucB4zncBnh\nLq5+I48EytWzxUuP9jyt9adAH/f3SIjWKSYukP881I2zBrUFHLWXn39kK6uX5TQ60LSkWIi8KZLA\nUwMdib1cOJu86c89PPrA54eyqpoCFAM/SiAwyvgrbNfXxfz56kGXvb8QQviK3D/L+eaS3dirjL/D\nw5MsDFvYmcCI5i+NPq5HRx5/dhQhIY7tNild2vLUS2OJjglr9rGFEMKJmsQIA3EEzTur/+7yZYye\nmlE+H8cU+SFKqTeVUtbqdea1mlquW0J4VkZGBhkZGS36ngEBJsZdm8g1tyZjCVRYrZpZb+9m5ozd\nTSohFTYsrFHZr+tjt2vmzvyZiRNm8+Oq7bzzxuFM75GdAznnzY5OX7vmnixy/ih3ST+ayxPjKtxP\nxlV4m+I9VSy4aCeVTlb1BEaZGPZ1Z8I6NjyPxNEcf2InHn1mFD1O6sTTL44lOtp4tc8/ybnjv2Rs\n/ZOXjqvby0N5KlA2uouOw7g/sn7SgCwr9U+FhYUUFnom4XvffrHc88ixtG3v2ELy0/e5vPdausuO\nb91jRVsb/t9tfn4pkyd9yrvTV2G3OV73xafrWb1y26HndLssmmOvjTZ8va1Cs/jyDKxl7l0G3hCe\nHFfhPjKuLUOudw1TWWxj4bBdFGca1zM2WRRDPksirsfRkyb+U0P+/U84OYFnX7mMyKiQBh1Tzh3/\nJWPrn7xsXGvKQ40HpimlzldKbac687UreSrbzVKgJ7Cz5gGt9RilVJTW+sgiqTKjbMBdSZKEZ4WE\nNOwmw106JYUw6fFj+XDaTjb9VsjgEc5LNTWG7YCNoplFmGOrS0hF17/kb29mHhMnzCE3p7hO24tP\nL6Jrt3a07+AoaTXg5Q7s+6GUgu11E8rk/VXB6ruzOPs15zPPLcHT4yrcQ8a15Ugd5frZbZolV2aS\n85vzVTTnv9eJhHPDG3Vcm83O808tIiEplsuvPr3e5zbmvkTOHf8lY+ufvGlctdYzlFJLgZv+UTFp\njDvey5NZr9/UWt9ylOecB8RU71UW1SQLqHA3rTV7dpeR0PnoS+gaonRxKRU/O/57VSHVJaS6Ol/6\nZ7PamXjHHP760zgZzTHHxfPsq5cfqtW5/9dS5p+Zht14IoWLvkgi5eLI5n0IIVxIsl43jNRRbpjV\n92Tx23M5TttPf6o9ve5t26hj2u2al575lsVfbwTg8mtO56rr+8kP9UKIRnHn9U4pFam1dttUt7eX\nh5p0tGC6NZJAWfgarTXlq8spX1F+uITUWcEEn+W8hNSB/YXcdsMHFBUaz5BcOq43N912zqG/r596\ngB/v3W/43OA4M5f90dWl+/KEaA4JlBtG6igf3V9vHWT5TXudtve4JZazX+/QqABXa81rLyxl4ee/\n13p89OV9uP6WsyRYFkI0mDuud0qpUcAMIKr6ofFa67dddfxD7+PJvT9KqVOpXl+utf6t+rFkHNPn\nsVJD2ZgEysJTbFbNh9N3cu6F7eic2visplVpVZR8VoIudXzvBHQNIGxkGKYQ43QJv/y4g8mTPnN6\nvClPX8JpZzqqAWi75otBO9mzzLi8VcL5YVy8OBllkhs84XkSKDeMXO/ql/FdMQsu3Ol0NU3SheEM\n/aozpoDGBcnvvLmSTz7+1bB9xOie3Hz7uRIsCyEaxA11lM/HUT95GpAPxAD3Ak9qree74j1qeLKO\nMlrrDVrr/wO6KKWeVko9hSPV9ycSJAvhfT6fvYdfV+c5Skgtd77MzxlLqoXIGyMxd3QsmbZut1L0\nVhHWfcZ3eX3P6FJvPc7/PfkNB/Y7Vtwok2LgBwkExxnvf878roQN9SxNFEIIX5K3uYJvR+92GiTH\n9gjigtmJjQqSAeZ+9IvTIBlg7c/pFBfLDxdCCI8ZrbW+QGv9qdb6O631J1rr3sA4V7+RRwPlGtUf\n9F6t9X1a67e01q5LtSuEcJnElNDDJaTe2s3M6bsaX0IqykTENREE9gwEwJ5vp+i9Iip+M77xunb8\nAI7t0cGwraiwnKcfWYDV6ti/GN7Jwrlvd3L63j8/sJ/stWWN6q8QQnibshwrC4btoiLf+Ps3pJ2Z\noQs6ExTVuFrJC7/4jfemr3LaHt8xiqdeGEtEROMyZwshhAsdmfi5Rp6r38grAuXWQCmVqpRap5RK\ndcXxpFyGf9q6dStbt271dDecOrKE1I/f5/L8I1vIyW7c7IIKUIQNDSP04lBH7n0rlH5VSsnCkjol\npAICzNz78DDCw41X7Py1cS8fvHU4I27qiEhO+L9Yw+farbD48gwqi22G7e7i7eMqmkbGtWXI9a42\nW5Vm0ejdFO6om+kfwBykuOjzzkQmBzbquCuW/s1rzy912t6ufQRPvziWtu0iGnVcI3Lu+C8ZW//k\nZePq7KIQ4+o3ckugrJS6sYmvu9TVffG06gB5HnAzjpJYLq/xJfxHVVUVVVVVnu5GvWpKSJ3Uy5E/\nIWNnGVMf3Mym35z9wOdc0MlBRFwXgSna8VVUub6SoveKsBfWniVp3yGKO++70Olx5s36hV9/Sjv0\n9zOfiyfmeOPAumB7JStv3deiN9++MK6i8WRchSf8cMc+9n5f6rT9/Pc6EX9G4yoW/PLjDp574huc\nfS3GxIby1AtjaR8fZfyERpJzx3/J2PonLxvXNKXUG0qpzkqpSKXUKUqpNwDne0aayF0zyjc38XV+\nty9Za52mtR6jtZ7kyuNKEg3/FBcXR1xcnKe7cVQhoWZu+k8qI8Z1RCkoLbHxxnM7WPjpXuz2xgWg\nAfEBRNwYgaWbIyO1rtBgMBFy5oBujBjd0+lxnnviG3IOFAFgCTVxwceJmIOMz5MtH+bz1wyXr9Bx\nylfGVTSOjGvLkOvdYRvfPMjGNw46be/7SDu6Xda43+P//C2DJx76CpvNeBl3eHgQT/xvDB0TXDdZ\nI+eO/5Kx9U/eNK5a6xlAIZCOY7n1uurHn3P1e7kl67VSyg7cROPWisfiyH7duA01PkQppYFeWuv1\nzTyOZAEVXmPzxkLefXUnxUWOjDLHnxTJNbcmEx4R0KjjaK0p/6EcS3cLAe2NX1tVZeO/t81i22bj\nMlAnnJzA0y+MxRzg+A3w95dz+eGOfYbPNQUqRq1OpV3vkEb1UwhXkKzXDSPloQ7b830JXw5Md5q8\nq/uVUQz8MKFRPyxs37qfSXfMobTEeBl3UHAATz0/luNO6NiULgshhNuud0qpKCAVSNNaN35ZY0Pe\nw42BcmMPrADtjkBZKZWqtU47+jPdSwJl4a/ycit566U0du5wLAeMbRPITf9JJSmlccv/GmLf3nz+\nfcMHTm/sLr/6dK6+sT/gCL4XDtvFrq+LDZ8b0dnC2PVdCI5tXFAvRHNJoNwwSqkKs9kcaLPVzisw\nefJkpkyZ4plOeUDhzkrm9dlBeY5xfoX2p4UwckUKAcENXyiYtTefu26dRd5B42XcAQEmHpl6KT37\nJDely0IIAbTc9U4pdUpNuWGXHdNNgfIOHNPgjVkr3ga425WBslJqII4aW0u11k6XgyulxgODgIM4\nZrbTXL1Uuvp9JFAWfquqys78mZmsXOoowRQYZOKRF3oQGWVp9rHtBXbsZXYC4h0B7Q8rtvLEw18a\nPlcpeOJ/Yzi1d2fAkR127qnbKc40noZJGhLOsAWdpb6yaFESKDeMzChDZbGN+f3Syf2j3LA9rGMA\nY9Z2IaxDw79r8/NLufvWj9mTabzwz2RS3DdlOP3P6d6kPgshRI3mXu+UUqc08KkztNZ9mvIeTt/b\nXQltqotBDwJygOla68IGvGZtdR2s5r73EhwFqH8Fpla/v2GgrJSaBqRqrQfV95grSKAsWoNffshl\n1tu7GTKyA4NHxDf7eNqqKXq/CFu2jdChoQSd5Pieff2FpXz1mfEPh9Exobz29tXEtgkHIOunUj47\nKx17lfH3Xd9H29HnoXbN7qsQDSWBcsO09uudtmu+HZvBjk+Nb6HMQYpLVqXQvk/DV++UlVZy73/m\nsnVzltPn/GfSYAYPPbHR/RVCiCO5IFCuWal8tOXVUa5emey2QPnQGzjWj4/HMVO7RGu9rJ7n3qO1\nftaF7x2NY5+0YaCslOqJY+a7y5FLs6uD2pu11tP/8dgSHJ+jPgedBdgSKIujqckoaLE0fxbWk7Kz\nymnTLgiTC2ZprRlWij4sguoVh0G9gwi5IIQqq427bp3Fjm3Zhq87+dREnnh+DGazYynin6/lsvLf\nxvuVUTB8UWeSLmh+2RMj/jKuorbmjKsEyg3T2q93vz6azS+Tjb/jAAbOTOCYKxuevMtqtfHIfZ+z\n9ud0p8+56bZzuHRcs+cs6iXfif5LxtY/uft6p5SKdDap2tCJVKXUXK312EZ3sL5jtmSJlKbMMjfz\n/Y4WKE8Dxmut69zNK6XWUU/Q28T+uCxQtlgsgZWVxns0he/atGkTAD169PBwT7yLdZ+Vknkl2Asc\nWVnNncyEjw5nX0EBt9/4AWVlxiUL/nXdmVx53ZmAY7/ykn9lsm2W8Q+SwXFmxq7vQkRS42qPNoSM\nq39qzrhKoNwwrfl6t3NBIQuH73bafuo9bTjzmYav2tFa8/xTi1i6aJPT54y+vASNHYwAACAASURB\nVA83/N/ZjepnU8h3ov+SsfVP7rzeKaVSgB044q42zemnq7mrPJQhrfV3Wut7gRnAOKXUU0qp81qy\nD0cYCDhL8pVW3e4S1UG7EK3a4q+yWPjpvsaXkOrgKCEV0MWxR9m2x0bhjELaWcOZMHGw09d99N4a\nfl/vuNFUSnHu9E5O6yuX59pYNCoDa5lxiRQhhGgp+dsqWPKvTKftSUPCOf2p9o065vszfqg3SD53\n0HFcd/NZjTqmEEK4wEAcpYVrTSQqpe72THcOa9FAuYbWukBrPUNrfR+QV100+kmlVHILdyUVx15m\nIwfh0PLsJlNKRVfPXM+rfmiGUmqaUiq1mcdtzsuFl0pISCAhIcHT3XCLLZuK+HLOXr6ev483nttB\nSbGTGidOmEJNhF8WTvCAYAB0qab4o2JOD05myLCTDF+jNUx9dCH5eSUAWMJMDPk0CUu48Vdf9toy\nlt2wB1evtPHncW3NZFxbRmu73lUW2/jmkt1UFhj/aBd9TCAXfJyIydzwf5cFn21gzsyfnbaf2rsz\nd957oUu2yzSEnDv+S8bWP7l5XNNw5Ia64IjHXZorqik8EijXUEpdCjyN41eEezkcTLbEe7fIDK/W\nOl9rfbPWepDWWmmte1X/3ePlqoT3iYqKIioqytPdcIt28UEkpToSzvz1eyFTH9zM7nTjsiTOKJMi\n5JwQwi8LRwUr0FC2rIxrk07n2K4dDF+Td7CEZx//5tAsdsyxQZz3Tien77Ht4wLWP53TqH4djT+P\na2sm4ypcTWvN8hv2cHCT8Z7swEgTF33RmaCohuer+XnNDt54yWl6GLp2b8+Dj4/AYnF5dU6n5Nzx\nXzK2/smd46q1/g7orZSyKaV+VUq9Xh0jelyL7lEGqJ41vhlHgq+Y6oenA9O01htc/F5O9yj/o229\n1rqXwWunVfdxkNZ6qSv71VxKqQog0GKxOP2lXWvNhg0bSE1NJSQkpFZbTk4O+/fvB4z3GmRkZFBY\nWEhoaCgpKSl12rds2YLVaiUuLo74+Nr7o6qqqti6dSvgKN8RGRlZq72goIDMTMdysu7du9dJCpCV\nlUVubi4Wi4Xu3euWpUhLS6OsrIzIyEgSExPrtNfsoYiPjycuLq5WW2lpKenpjgQm8u9yWEv+u8TF\ntePTmZmsqi4hFRCgGDDYzHEnmxv972LLs5H/cT6mXMfvffZIzeQVX7Ej90CdPgBcc1N/Lrvq9EN/\n/+Guffz+Qq7hc1Fw/pz22I7PbpF/F/nv5bDW8u8ie5QbprUl89rwXA5r7nGejfqiL5NIGR7ptP1I\n27fs554Jsyl3kschvmMUz79+BTGxYY3uqxBCNERDr3fV5XrHAzWreWuC1PXAWhwJmNe6ulZyfVps\nRlkpdalS6lscm7UnAek4skqbtNa3uDpIdoGa7NYHPdoLIfyIxWLisuuSuPqWzlgsCqtVs3yhleVf\nV1FV1bi9weYYM1UXV1Ga5JiVNhUqpvQeRp92yYbP//Dt1Wz8/fCevzOmxhPd18nBNXx/fTbFW1v2\nh0QhROuVuayYHyc5D5J7P9y2UUHygf2FTL53vtMgOSo6hCeeGy1BshDCK2itp2ute2utTUBXHLHi\nszgmNsfhmFhdVz3zvE0pNUcpdYM7t+66dUb5iNnjaBz1r2pmj53XJnDd+x8t67UG0rTWXQzaluDY\nXF6ndJSntbZf2IV/ytxVyowX08jJdmSzTUoJ5cY7Uohr27gJNq01lRsqKV1UCnb42vQXMxf9aPjc\ncwcdx8SHhh76e3mulXmnpVG4wzijbkSyhTG/diGkTUCj+iTE0ciMcsPUXO+WLau9dDgxMZGkpCQP\n9cr1inZXMrfXDspzbIbtnS8KZ+hXnVEN3ENcUlLB3bd9zM40420kQcEBTH1pHMccZ7xlRQghXKWp\n1zul1OJ/7luuLjncG8eMc5/q/03FMfO8HrhRa/2763ruphnl6tnjXzk8e7wOGKu1jtVa3+ssSK6e\ncW5J+RylLrK3BcnCvxUWFlJY6NaqaV4joXMokx4/lhNOdcyQ7E4vZeqDm/nrj8Z9fqUUQT2DiLg2\ngtBhoYy6sw9JyXFHPMdRKuq/9w+p9XhwXABDv0zCEmH8VVi0s4pFo3djq2xeJuzWNK6tiYxry7DZ\nbPTv37/Wn3feecfT3XIZW4WdRaMynAbJkV0CGTgzscFBMsBbr3/vNEhWCiY9NMyjQbKcO/5LxtY/\neWhcp/7zL9XJoL/TWj+rtR6rte5aPfs8GFgGfKqUusSVHXDLjLJSyk71TC6O2eOdDXhNFI76WS7L\nJtGAGeV5wOh66ihjtH/Z02rqSi5fvrzW4/72C3tr1BrrD9rtmsVfZrHgk31o7biJGzqqA4NHxDc5\nA+uu9BzuGD+TigorMbFhTHp4KCf3dH5u7FxYxMLhuw7vhjnC8TfFcM60jk3Ovtsax7U1kDrK7tca\nrnff37qXjW8Y7/IKCFWM+rELbU4KbtQx8/NLeez+z/lr4946bbdMOI8Ro5tV0KPZ5DvRf8nY+idv\nv94ppSK11oVKqTla63GuOq471xOmA12Aqf+4uVQY34oqXFizuBGmAaOVUj211odqd1UH2D1xLBv3\nSjW/sP/T5MmTmTJlimc6JEQTmUyKC0d2oHNqGO++lk5JsY0Fn+wjMtpCv3ObVne+c0obbr3zfFYs\n3cw99w8hbH8gWmungW7y0AjOeLo9P07ab9j+14w8IlMC6XVf2yb1RwjRPP369fN0F9xi66x8p0Ey\nwLlvdWp0kAwQHR3KUy+M5X9PfsPK5VsOPT5iVE+PB8lCCOEGy5RSKcBcVx7UXTPK27XWXRv5mmgg\n100zyp9orcc4ec40HLW7Bh3xWG9vnE2G1vELe2tVVeVIunJktt7WIvdABW+9nI7Forjj/u6YA5pe\n01NrjdZQsbKc8lXlWI6zEDY8DBXkPFP8d9fsYcuHzkqrw8APOnHMVTFO251p7ePqr5ozrjKj3DD+\nnJPj4N/lzOuThrXEeGvHyXfG0f/55i2Ptts1701fxbxZv3B6vy48+PgIzGaPVgYF5DvRn8nY+idv\nv94ppUbjKDU8UWvtvB5eY4/rpkC51uZrd7/O4DhTccwI98aRRAwcm7zTcCwFX3rE8yfimP3Ox7Ep\nPE1rPam5/XAXf75xEKKqyk5FuZ3wiOYveNFWTdE7Rdj2O/b+meJMhI8Jx9zW+Pc4a7mdz89JZ//P\nZYbtpgAYtiiZxPPDm9030bpJoNww/nq9qyy28UnfNPL+Nv5cHQaEMuK7FMyWpv9Y+E+rlm+hz+kp\nBIcEuuR4QgjRUL58vWvxOsqi+fz1xkGIo6lv+bTT11RpSheWUvlndWbrQAgbHkbg8YH8+VsGq1Zs\n5f/uOO/QcUv2VfHJaWkUZxiXVAmMNHHJqtQmLYcUooYv3zi0JH+83mmtWXpVJls/KjBsD2lnZtyG\nroR1lBk5IYTv8+XrnefX34gmW716da0/u3fv9nSXhHCbXTtKeOGxbRzMMS7l5IyyKEJHhBIyJMTx\njVcJJZ+W8OdrO3nwrk/4av4G5s9Ze+j5YR0sDPumM4FRxl+PlYV2Fly0k+JM40BaCCHqs2l6ntMg\nWZlg0KzEBgfJlRVW3p/xA+VljfteFEIIcXQSKPsofy+XIcQ/lZZYmfFSOju2FPP0A3+zeWPjS0gF\n9w4m4poIVLhj5jjhYBSTThlMVGAI77y5kg1rdx16flyPYC76PAlToPHsdckeK18N2UlFgXE5FyGE\nMJK9roxVE/Y5be/7SLsGb+3QWvPC1G+Z/eFP/PffszmwX0ryCCGEK8nSax8kybz8V1ZWFgDx8fEe\n7ol3sds1336RxcJPD5eQGjamIxcMb9+oElI5B4r430NfMzTkBHrEdgQgr6KEl/9Yzl57Aa+8dRXt\n46MOPX/rx/ksuSLT6fE6nRPGsG86ExBc/2+OMq7+qTnj6stL0VqSPy29rsi3MbfndgrTjVejJA0J\nZ9iCzg2ulzz7w594f8YPh/4eExvGw0+O5NjjPVcfuaHkO9F/ydj6p9Z6vZMZZR/Wr1+/Wn8kSPZ9\nubm55ObmerobXsdkUgy5pAP/d08XwsLNaA1fzd3L9BfSKC2xNvg4QUEBZOUX8tT6RXyZ/jsAMUFh\nPNDrIm44sz/RMaG1nt/98mjOmNre6fH2rCjh23EZ2Krq/8FRxtU/ybi2DH/4QV9rzfLxe5wGyeGJ\nFgZ9mNDgIHn191trBckAeQdLmDhhNiuW/t3s/rqbnDv+S8bWP7XWcZVAWQgvEhAQQECAO8ub+7Ye\nJ0cx6fFjSUpxBLR/ri9g6kNb2LO7tEGvj4gM4eEnRmIJMjN7+1qe/20pZdZKAkwm+to6U7Wwos5N\n+an3tOHE22KdHnPnl0Usuy4TbXd+My/j6p9kXEVD/TUjjx3zjJdGmyyKwXMTCY5r+H9L0bFhxMSG\n1nm8qtLGN1/9gb2e7yNvIOeO/5Kx9U+tdVy9aum1Uuo8V9a+8lc1S9GWLav9TyVLr0VrUVVpZ+77\nGaxZ4fh10xKouOKGJPr2j2vQ61cu28xTUxYQExvG5EkjiP89DPsBO8H9gwk5N6TO8+02zaJRu0n/\nosjpMU/4v1jOeq1Do7Nyi9bJl5eitSR/WHqd+2c58/ruwFZufL/V/6UOnDyhYd9d/3Qgu4jHH/yC\nrZuzDj3WoVM0L755JZFRdb/HhBDCE3z5eudtgfIcrfU4T/fD2ymlKsxmc6DNVjuR0OTJk5kyZYpn\nOiWEB6xZkcOc9zKwVi99PmtgG0ZdlUBAwNEXy3z9xe+c1q8LcW3C0ZWail8rCDojyOnSx6pSO18O\n2knWGuez1z3va8MZT8q+LHF0vnzj0JJ8PVCuKrEzr88Op/WSUy+J5MJPE5v8A1tlhZWXn1vMd9/+\nRWhYIC+8cSVJyY0PuoUQwl18+XrnbYHyr1rrPp7uh7eTGWUhDtudXspbL6WRe8BRHiW5Syg33pFK\nTFygy9+rIt/G5+emk/NbudPnnPF0e3pOauvy9xb+xZdvHFqSr1/vlt24h7/fzjNsi+hsYeyGrgTH\nmJv1HlprvvhkPQlJsfQ+LaVZxxJCCFfz5eudywNlpVQKMLEJL40FRmutm3fFaAV8/Rd2IVytuMjK\n+6/v5K8/HHsAjz0hgtvv69bs427bkkVoVgAdesdiCnPMUpdmW/lsQBr5W53XLT37jY6ccIvzfc1C\n+PKNQ0vy5RVU9WXNV2a4dFUq8WfU3WcshBD+xJevd26ZUVZKbQdSm/BSLYHy0UmgLERddrvmm8/2\nseLbA9zz6DG0iw9u1vHWrNrG/Jd+4d6TLsQcbiJibAQBCY5EFkW7K5nfP53iDOMMtgDnvt2J46+P\naVYfhP/y5RuHluSrM8r52yuY23MHVUV2w/bTn2pPr3sbtvLkYE4xMXFhkv9ACOGTfPl6565A+Xyg\nJzC9MS8D0rTWMg1zFBIo+6/09HQAUlJk+VxTFRdZCY9oemZGrTWfzv6Vd95cycWdT2Zct96OBhOE\nXBBCUO8glFLkb61g/oA0yrJtxgdScP67nTj2mhgZVz/VnHH15RuHluSL1ztbpZ1Pz0zjwDrjLRqJ\ng8IYvii5QaWg8vNKmHDTTI4/sRP/mTSY4GCLq7vrEfKd6L9kbP1Ta73euSXPt9b6O6XUeK31s415\nnVJqrTv644+8aW+5cJ3S0oaVORLOOQuS7XaN6Sg3plarjdeeX8qiBX8C8MXO38kqLeDmHmcRHGCh\nbFEZtj02QoeGEt09iIsXJ/PZ2elUFhjMGmn47ro9KLPCeqqMqz+S87Vl+Nr17ueHsp0GySHtAxj4\nYWKDgmSr1cYTD3/Fgewivv9uMxm7D/Lw4yNo3yHK1V1ucXLu+C8ZW//UWsfVnXWUm7LmcL3Le+HH\nVq9eXevP7t27Pd0l0UyRkZFERkZ6uht+p6Lcxv+mbGHtmoP1Pm/lsi2HguQaP2fv5MFfvmBPcT4A\nlX9WUvROEbaDNtqcHMKwr5MJCHVy06vhu2syKVwWLOPqh+R8bRm+tOQ4c3kxG57NMW5UMGhmAqHt\nGzZH8e6bK9n4++E9zmnbspkwfiZ/bPD9a72cO/5LxtY/tdZx9aqs16JhfDm5iRCe8MGbO/l5lSNI\nPmdwWy65opNhCSmtNS9M/ZYlX2+s0xZstjD++P6cHu9Iv6CCFKEjQgk8JpDMZcUsGLrLaZ1UZYJB\nsxLpNs73Z4KEa/jyUrSW5EtLr8sPWpl90nZK9lgN23vd35bTn2jfoGOtWr6FJyd/ZdhmMitefetq\nUrpIdn0hhPfz5eudW5ZeC/czm818//33tR5LTEz0UG+E8G5nD2rL1r+KycutZMW3B9idVsoNd6QQ\nHVO7hJRSitv/O4ic7CI2rN1Vq63cVsXLfy5ne8EBrjimL6YKKJlbgq2fjU7nhDH0q84sHG4cLGs7\nLLkyA2WCrmMkWBbC32itWXHzXqdBcvvTQ+gzpV2DjrV7Zy7PP73Iafv5g3uQnNqmSf0UQgjRcDKj\n7IN86Rd2IbxFcZGVd19NZ/PGIgAiogK44fYUuh0XUee5paWV3HvHHLZt2W94rGNj4rnv9AuxWB1J\n+gNSAgi7NIzMH0r4+uLd2CqczCybHUsvu10W7aJPJXyVL//C3pJ85Xr393t5LLtuj2GbJdzEuN+7\nEpV69NrupaWV/Gf8TDJ2G28T6XZse5575XICg2SeQwjhG3z5eufSPcpKqWSllMsXsCulTnH1MYUQ\nrUt4RAC3TerKhSPjASgqsPLyk9tYunB/nWRBoaGBPPrMpXTsZBzQbs7L4q4V8yiPdsweWdOtFM4o\npFOvUIZ8noQp0HhPpbbBkisz2fx+ngs/mRDCk/K3V7Dq9n1O2896rUODgmStNS88vchpkBwZFcKD\nj42QIFkIIVqIq5N55QGfKKVOdtUBlVJ3AwNddTwhROtlMimGj+nILf9NJSTUjN0On83aw9svp1Ne\nVnvPf3RMGI//bzQxsaGGx8otK+HfCz6mOMVRS9kUbsIUZaLzhREMmZ+EyeIkWLY7smFvml5/YjEh\nhPezVWmW/iuTqmLjesldx0VxzFUNW0Hy2dx1/LBiq2GbUjDp4aG0a9/6kukIIYSnuDRQ1loXALcA\nnyql/tucY1XPTi8G4rTWz7mkg35Elsz7p02bNrFp0yZPd8PvndgzmomPHUOnpBAANvySzzMPbWZf\nZlmt53XoGM2jz4wiJNR4Nqi0rJI7Zs6moG8l4aPDUQGO4Dh5aAQXfpLoNFhGw4qb9/LHK7mu+1Ci\nxcn52jK8+Xq39rFs9v9cZtgWnmjh7Dc6Nihr95+/ZfD2m987bb/qhv707JPc1G56HTl3/JeMrX9q\nrePq8vJQWus0oBfQTSmVq5R6o6EzzEqpSKXUpdUB8hJgqtb6Plf30V9IeSghmq5dfDB3TzmGvv1j\nAdi/r4JnHt7Cuh9rz/R27d6eh58YSYDFbHicstJK7nlpLunZtUvCpFwc6QiWnSzDBlg1YR/rnz3Q\nzE8ihPCEfWtKWfeEk/NXwcAPEwiOMf7e+KeDuSU8NeUr7DbjHwROO7ML4/51WnO6KoQQogncmsxL\nKZUKjK/+EwWkVf/JB2ruRmOBaKB39f+mAc9orWe4rWM+TspD+a+cHEew1aaNZDRtKVprVn2Xwycf\nZGKzaSwWxZQXetTJiL1y2WaefmQBzr4yI6NCeOaVcXROPjx2tmwbWcuK+eq6DGzlzvvQ99F29Hmo\nYRlxhfdozvnqy8lNWpK3JvOqKrEz++TtFO6oNGzveW8bzngq/qjHsdnsPHDXPH7fkGHY3qFTNC9P\n/xfhEcHN6q+3kWud/5Kx9U+t9XrXYlmvlVIDgVOBLjiC41QcwXJN0LwOWKq1Tm+RDvmwmhuHZcuW\n1Xo8MTGRpKQkD/VKCN+Wvq2Et15OY/iYjpx+Vpzhc7756g9efnax02PExoXx7CuX0TEhBl2uKXy7\nEPtBO5UJJj7/dybWUufft70eaMtpj7Vr0DJN4ft8+cahJXlroPz9bXvZ+LpxnoG2vYIZtSYVc+DR\nF+19+M5qZr33o2FbUFAAz79xBald5Uc0IYTv8uXrnZSH8kHeeuMghK8rL7MRHFL/UsnP561j2ivL\nnba3ax/Bs69eTqw9lOJZxejq4NgWq/hqyj5Kc2xOX3vKf+M489l4CZZbAV++cWhJ3ni9y1hSzJcX\n7DRsCwhVjF3flZhjjj6s63/dyYN3f+J0lcrdDwzh/ME9mtFTIYTwPF++3rl8j7IQQvgqZ0GyzaYP\nJRQaOaYX144f4PQY2fuLmHTHHPJMpUTeFIm5k+OY5oOaERPjadfNeZmY3/6Xy6rb96Ht8gOmEN6o\nIt/Gsusznbaf+Wx8g4Lk3JxinnlsodMg+cLhJ0mQLIQQHiaBshBCHMWnMzN599WdlJc7ZoPH/es0\nLr/6dKfPz9pbwMQ75pBTVkzE1REE9XbcOKtyOP+atnTvH+70tX++dpBl1+/BbpVgWQhvs+qOfRRn\nWg3bEgeFccL/xR71GDarnacfWUBBvnG27NSubbllwrnN6qcQQojmk0BZCC9SVlZGWZnxzZPwjN/X\n5vP94gOs+ymPZx/aQtZeR1auq27ox6Vjezl9XdbeAiZNmEN2TiHqHIVliAUCQNmh9wVRnDE2BlOA\n8Ws3v5/PojG7sVUY12YV3kHO19Yl7fNCtnyQb9gWGGXivHcSGrRtYua7a9j4u/GsdEiIhfseGU5Q\nkKVZffV2cu74Lxlb/9Rax1UCZR8le8v9U1paGmlpaZ7uhviHY0+IoPeZMQBk7S3nmYc2s+GXPJRS\n3HjbOVw0wnn1u6x9BUycMIe1v25kV8guIq6LwBTj+NpNOSGUwbe0IzTKeLl3+udFLBi2i8pi53ua\nhWfJ+doyvOF6V5ptZcX4PU7bz3qlA+EJRw9u1/2SzpyZPzltv2PiYBISjz4r7evk3PFfMrb+qbWO\nqwTKQghRj6BgM9femsyYqxMwmaGi3M5bL6Uzf1YmdjvcdudABl10gtPXZ2cV8vrzP5ObU0pAfAAR\nN0Rg6ea4oY5pZ+Gi29oR38V4T2Pm0hK+HLST8oPGSz2FaC1Wr15d68/u3btb7L211nx/y17KDhj/\naJV6SSTd/xV91OM49iV/7XRf8tCRJ3P2+cc2p6tCCCFcSLJe+yClVIXFYglcvrx25l0pD+X7SktL\nAQgNDfVwT4SRHVuKefuVdAryqgDodlw419+eQnhEAC8/u5hvF/7p9LVt2obzzCuX0aFjNFpryn8o\np3yFYxm31ppfvsxnx7pSw9fGnRjE8MXJhMX793JMX9Oc89WXs4C2JKVUhdlsDrTZagepkydPZsqU\nKS3Shy0f5bP0X06WSrc1c9nGboS2c7KPotrR6iV36daO51+/gsCg+o/jL+Ra579kbP1Ta73eSaDs\ng7zhxkGI1qogv4p3X01n29/FAETFWLhxQgrJXcN45bnFLFrgPFi+aMTJ3P7fQYf+XrWjipLPStBV\nmh8W5LF7jXGgDBDZJZARS5OJTHaeNVv4Dl++cWhJNeWhli1bVuvxlvphuHS/lVnHb6PioPFs8pD5\nSaReEnnU48yZ+TPvTV9l2BYSGsirb11Fx4SYZvVVCCG8kS9f7yRQ9kGevnEQorWz2TRfzNnDdwuz\nATCZYdSVCQwY2IbXnl/KN1/9Uec1PfskM/mpkQQG1p4xsuXbsOfYscUqFgzdxf6fnCfLCOsUwMVL\nkok9Lti1H0i0OF++cWhJnq6jvGjMbnZ8UmjYdsxV0Qz8IOGox/h7017u/vfH2G3G91v3PzKcAece\n06x+CiGEt/Ll650Eyj7I0zcOQgiH9T/nMXP6LirKHdmpe58Zw2XXJfLWG8v5+ovfDz3vhJMSeOy5\nUQQH1790urLYxjcjd5P5XYnT5wTHmRn+bTLteoW45kMIj/DlG4eW5Mnr3fZPCvh2jPFS6bBOAVy+\nsRtB0cbJ+GqUFFdw2/Xvsz/LONg+cpWJEEL4G1++3kkyLyGEaKKep8Uw8bFjie/omOFduyaP9T/n\nc9udAxk60pENu/ux8UyZeslRg2SAwHAzwxZ2JvWSSEwBcFz/cExH3IeX59r4/Nx09q50HkwLIZqn\nPNfKytv2Om0/Z3qnowbJWmtefm6x0yC5c0oc4/99TnO6KYQQwo1kRtkHyYyy/8rNzQUgLi7Owz0R\njVFebuOj6buw2+HGO1JQSqG15pOPf+XCYSdSWeXYe9zQcbVbNTvuO0CbSAs5GZWsmpNLWWHtmsrm\nYMWFnySRPDTC5Z9HNExzzldf/oW9JXnqerfkqgy2ziwwbGvokmutNV98sp6331yJtar2HufAwABe\nmn4lyaltXdJfXyPXOv8lY+ufWuv1zitmlJVSo5RS51X//zc83R9fID9w+KesrCyysrI83Q3RSMHB\nZq6/PYVrb01GKQWAUooxV/QlIjKk3nHN3l/ILz/uqPWYAuJPdSytbpMYyJBb2tE+pXYSL1u55puR\nu9g2O9/1H0g0iJyvLaOlr3c7FxQ6DZJD2gfQ/8X4Bh1HKcXIMb144Y0r6JRYO1HX+NvPabVBMsi5\n489kbP1Tax1XrwiUgfXAJKXUKYD8BCWE8DlKKSyBxl+pNqvxjf7BnGLu+89cHrn/c5Yv+fvwsQIU\n4ZeHEzQgCK01weFmzr2mDcf1D6/1ersVFl+RycY3cl33QYRoxSoKbKy4xfmS67Nf70BwbONKOHXt\n3p5XZlzFBdX11s8c0I2LLj65Wf0UQgjhfh5feq2UitRaFyqlngZSgJsAtNbGm3qELL0Wwods+r2A\nj9/O4IYJKaR0DTv0eGFBGRMnzGZXuiPIVQpuv/sChgw/qdbrq7ZVUTi7CBOOmeqMv8r46bM8qipq\nf3f3mdKOPg+3PTSjLbybLy9Fa0ktfb1bPn4Pf83IM2zrMiaSC+c2r7LEqhVbOKVnEhGRkoxPCNE6\n+PL1zhsC5TdxBMgK6A0sAVKBm7TWv3myb95KAmUhfENpiZUpd22ipNiGEosrlQAAIABJREFU2awY\nc3UC/c9vQ2lJJffdOZdtW/bXec09D17EeRccX+sxW56N3GmFWKocfy/MsbJqdi4F2dZazzvxtlgG\nvNwBZZJg2dv58o1DS2rJ613Gd8V8OXCnYVtQrJkr/upGaPvGzSYLIURr58vXO48HyjWUUnOBNGC2\nBMj1k0BZCN+x7seDzJyxm8oKRzKuvv1j2fT3L/z52+46z01KjuOZl8cRFR1ap01Xafa/kU9Q9dZJ\na6Wdn7/IZ9eftesudx0XxcAPOmF2sgxceAdfvnFoSS11vbOW2fn4xO0U7qg0bB84M4Fjrox2ax+E\nEMIf+fL1zisCZaXUKGAsMB5YqrXu4+EuebWaG4dly5bVejwxMZGkpOYtCxNCuN7ezDJmvJhG9j7H\nzX50nIm/Nv9IefnhEk8dOkXz7CuXEdcm3Nlh0FqT9VEhlm02zAGOWeMtPxazYXEB9n8k1U0cFMaF\n85MIDK+/fI3wHF++cWhJLRUo//TAftY9ecCwLXlYBBd9mXTUbQ0vTv2W1K5tGX7pqbIFQgghqvny\n9a7ZgbJSKllrvfOIxyIbs8dYKZUCoLVOV0qdr7X+rlmd8nNKqQqz2Rxos9UuNzF58mSmTJnimU4J\nIepVVmpj5vRd/ParI0t1YKBiX/afFBRl07ZdBM++ehnt46MadKz9i4uxLiknNNIRCO9Pr+C793Lg\nH1/n7fqGMGxhZ0LayFJRb+TLNw4tqSUC5dxN5cw9ZTt2a922wEgTl//VjfBO9ddBX77kb555bCEA\nvU9L5s5JFxJbz49eQgjRWvjy9a5ZgbJSajuQDPSuWS5dHfTuAA5qrdu4opOiNqVUhcViCVy+fHmt\nx2VG2fdlZGQAjrEU/qNmXBMSEli6MJsvZu+h5qvXyj4eePJ0kjo3LuH/wd/KOPBGAe0Sgvh1QT7b\nfimp85zoYwK5eHEyEUmBBkcQzdWc89WXbxxakrsDZW3XzB+QTtaaUsP2s9/oyAm3xNZ7jOz9hdx6\n3fuUFB/uY2RUCBPuHkS/s7u7tL/+Qq51/kvG1j+11utdczexbQAKgX8W8hwI3Iyj5NMhSqm7m/le\n4gj9+vWr9UeCZN9XWFhIYaEkfPc3NeOqlGLQsPZMuK8bEZGOmd4AOvDl7DyKiwyms2peX1BGYUHt\nvcixp4TQ4b4YNvxQaBgkA+RvqWR+vzQO/l3uug8jDpHztWW4c4vYX2/lOQ2S488Mpcf4GMO2Gna7\n5n9PflMrSAbHOfv4Q1/y9Re/u6yv/kTOHf8lY+ufWuu4NitQ1lqP0VrHHrH0Og1I1VpfcMTTBzXn\nvURtsv/JP4WEhBASImVD/M2R49q9RwT3PnEsKd0c5aL+/qOQqQ9uZlda3YC3rLSShyd+yt3//pgD\n2UW12iKTgzjjo0606+v8v5niTCvz+6eT9bNxMCCaTs7XluGu611JVhVrJmYZtpkC4JxpHY+aQV4p\nGHBOdwID625xiI0Lo/85MqNsRM4d/yVj659a67i6JZmXUmoJcB6OWeVfgaXAzVrrwS5/s1ZIsl4L\n4R+sVjvzP9rD94sdSYSOPzmS2yZ2PdReWWllyr2fsWHtLgDatY/giefHkJBYeyloZbGNRaMyyFhc\nfOix7qeFkbWjgsIcx0x1QKhiyPwkkgZHuPtjiQbw5aVoLcmd17vFl2ewbXaBYVvP+9pwxpPxDT5W\nxq5cnnnsa7ZvPVzy7fHnRtOrb3JzuymEED7Nl693bst6rZQajyOLdc/qh2reaD2wFlgHrJVSUI0n\ngbIQ/uWX1Qf55rN93PVQdyKiHEmDbDY7zzy6kJXLt9R6blR0CI89O4pux9S+ibdV2ll69R62zykg\n4dhgzroijqoKOz99nkfGJsfSa1MAnP9BAt0vlzI3nubLNw4tyV3Xu12LilgwZJdhW2SXQC7/sysB\nIY1bdFdVZeOj99Yw76NfGH7Jqdxyx3mu6KoQQvg0X77etUh5KKVUKrAY+ARH4NwbiOZw8JyGI4Be\nDHx3ZBZtUZsEykL4H5tVHyr5pLXm1eeXOt3fGBIayOQnR3Jyz9p5CbRds+qOfZSuKaf3sOhDx/t7\ndRG/LSlE2wEFA17qwEm3Ny55mHAtX75xaEnuuN5Vldr5uMc2inZWGbZfvDiZxEFNz1j996a9pHZt\nS1BQ/ZmyhRCiNfDl611zk3k1iNY6DUjTWt+rtb5Aax0LxAAXAPfiSArWC5gB7FBK/aqUOrkl+iaE\nEN6gJqgFsNs0RYWO5F1K1a2FXFZayYP3fMrqldtqPa5MigEvdyBuRDhL3zlAaYGjhNxx/SI479o2\nBIebQMOqCfv4+eH9bk2SJIS3WvtottMgufuVUc0KkgGO69FRgmQhhPADLTKjDNDQ+shKqYE4En+N\nAu7RWn/m9s75GJlRFsL/2Wx2Xn5mGX//FkpRyV7yC3fWeY7JpJhw9wUMHnZinbaNb+Ty08T99Bsd\nS3yq40fc0kIbP8w9SM7uSgB63BzDWa91xGSW5IAtzZd/YW9Jrr7e5W2uYPaJ2wxrJgfFmLliczdC\n20ntcSGEcBVfvt61yIwyQEOC5OrnLQWe0Fp3BS5zb698l8wE+aetW7eydetWT3dDuFhTxtVsNhER\nmoolIJjYqFTi25yESdW+gbfbNS8+8y2zP/ypznfCCf8XxznvdOL7Wbn8tcqRLTs00szA69rQ/TRH\ntu1N0/JYfFkGtgp7Mz5d6yXna11KqYlKqXnVf5ZU//jdLK663mmtWXn7XsMgGeDMZ9sfNUj+6N01\nfDZ3LXa7XIObQ84d/yVj659a67i2WKDcSMuUUrnAQU93RIiWVFVVRVWV8ZJA4buaOq6XXplA59RQ\nAEJD2tApvg+BlrrLQt+f8QNvvLQMm612wNt1TBRDF3Zm45piVn6cS1W5HZNZ0XtoNGeOjsFsUez4\npJCvLtpFZZGtaR+uFZPztTal1EQc26zGaK3HAFOBJUqpnkd5aYtIm19I5lLjmuMdBoRy3PX110z+\ne9NeZr3/I9NfXcGkCXPYuyffHd1sFeTc8V8ytv6ptY6rtwbKTwPpwDxPd8RbSR1l/xQXF0dcnCRZ\n8jdNHdfYNoHc+XB3+p/fBgBLQAgd2/UiPLRu2Zqv5m9g6qMLqKysPV2WODCckcuTyTlQxaJpB8jP\ndlzokk8KZfD4tkTEBbBnWQmfn5tOabaTqTZhSM7XOsbhSM4JHFohth64rzkHdcX1rqrEzg93GtdM\nVmY4+7WO9b5PRUUVzz+16NBM8sY/Mrn1uvdY8NkGmV1uAjl3/JeMrX9qrePaYnuUhevIHmUhWp+f\nVuYy661d2KonfguL95CTt5XDxQMcTjo1kYefGElYeO2tQHlbKvjygp2UZ1k5bUQ0nU90zFRXldv5\ndsYBCg9Yie4eyPBvk4lMDmyJj9Sq+fKeLWeUUkuAeVrr6Uc8htZ6UBOP6ZLr3U8P7GfdkwcM2066\nI44BL3ao9/UzXl3O/LnrDNsuHdebm247p1n9E0IIf+XL1ztvnVEWQgjxD6efFcc9jx5LRJTjazsy\nvBMd2/XCbK593fljQwb33D6b3JziWo/HHBPEqDWpRHQNZPW8PNZ9nY/dpsneXUlhjmMmOX9rJfP7\npZG7sbxlPpRwuepyjB6htR70zyC52kAcs8oek7+tgg3P5Ri2hbQPoO8j7ep9/cY/MvlsnnGQHBQU\nwJCLT2p2H4UQQngfCZSFEMJHJCaH8vCzJ5DaPRiA4KBIEtr3ISSo9t7K9B0HuOvWWWTurp3mIbyT\nhUtXpRB/Rghbfiph6bs5/PjpwVqT0iV7rXw2II19a0rd/nmE6yilBiqldgCTjvK88dWJtqZV/+9U\nN/ZpIpAPPOWu9zgarTWrJuzDXmm8eu7MZ9oTFFW3BFuNygorL079FmeL764dP4CExFhXdFUIIYSX\nkUBZCCF8SGhYAHc+dBznXBiLRmM2BxLf9hSiIzrXel52ViH/ve1jNv+1r9bjwbEBXLwkhaQh4eTs\nrqSyrG4EUJFv58uB6excWOTWzyKarzqz9DygJ1DvbLJSahowpjrZ1s3VCbeia5ZHu7hfPYGbgV5a\na49lvUr/sojdi4oN2zr0C+WYq6Lrff2s939kT0aeYduJpyRw8SivyFMmhBDCDWSPsg9SSlVYLJbA\n5cuX13o8MTGRpKQkD/VKuEJNRkGLxeLhnghXcte4rvvpAO+8uhO0GZutisysn7HZK2s9Jyg4gPsf\nuZi+Z9SOoWxVmmXXZ7J1ZkGd47btHEhUOws71pdw3judOPbq+rMBt1bNGVdX79lSSkUDecB0rfXN\nBu09gXVAF6112hFtGrjZYG/x0aZKDxrtPa5+rxnA+c0NkpuzR9laZmfW8dso2lk3U6sywdj1XWhz\ncojT12/fup87bp6J3Vb3Pik4xMLr715Dh471B9rCmFzr/JeMrX/yputdS6q/YKDwWjabjf79+9d6\nbPLkyUyZMsUzHRIuUVOjrkePHh7uiXAld41rr9Pb0iEhlKkP/cG+PX/XCZIBKsqtPHL/Z/xn4mAG\nDTnh0ONmi2Lg+wmEtAng9xdzDz0eEmGi/9hYQiLMtEkIZMWNeynLtnHq3W1c2nd/4GPn680ARwbJ\n1dYDY4BDgXIzkm+l4igLdShIVkpNMwreG6qpP+ive/qAYZAMcMKtsfUGyVarjRemfmsYJANcf/NZ\nEiQ3g4+dO6IRZGz9U2sdVwmUfZTZbGblypW1HktMTPRQb4QQntIxIYznpvXl9RcLWbTAuPS83aZ5\n/qlF5OWWMObKvofK4CiTot/z8YS0C+Cn+/cDEBBoorLcTkiEmdRTQ4npYGHVkwcoy7ZyxtT2UprO\ndw3kH6WbjpAGjG7uG1QHyUuAacDY6v9WujT3uE1RtLuSDc84SeDV1kzfR9vX+/r5s9eSti3bsO34\nEzsxdOQpze6jEEII7yaBso9SStGvXz9Pd0O4WEJCgqe7INzA3eNqCTQz4Z4LiIkL4+P3fzr0uFKm\n6tk4x6zYu9NXcTC3hPG3n4vJVB0sK0Wv+9oS0tbMipv3UpRr5dvpBzh9ZAxJPUKIibdw4S3tWPNp\nHssOWDl3RidMARIsg8+dr6k4zz59EBxLprXWzclQPa/6fY5MENbk2WRoWh3ln+7fj63ceDb49Kfj\nCY5xnsArM+MgM99bY9gWYDHzn4kXHDp/RNP42LkjGkHG1j+11nGVZF5CeJGoqCiioqI83Q3hYi0x\nrkoprr6hP7fdNZCauKJt7PF0bNezVgmpLz5dz9RHFlBZaa31+uNvjOXCT5IwBymsFZof5hxk/bcF\n2O2awBAT5/wrjsDdNr65ZDdVpXa3fhZf4Svna/X+ZbfTWvfSWiuDP0eWjHKr/b+UsvWjunvvAdqf\nFsJx1zr/57DbNS9NXUxVpc2w/cprzyCxc5xL+tma+cq5IxpPxtY/tdZxlRllIYTwI8NGnkJMTCgv\nP/ML4aGO+rAJ7fuwP3cj5RWOvEorl2+hIL+Uh54YSVj44SA69ZJIhn+bzNcX76Ky0M7m1cUc3FtJ\nvzGxhISbOeGcSPZtL2fR0F0Mmp9U76yc8EleWeeosrKSwMBApzPLWms2bNhAamoqwcHB/HBnltNj\n9X+pA+ofs8EZGRkUFhYSGhpKSkoKX3/5Oxv/yDR8bWrXtoy+vM+hv1dVVR3at5eYmEhkZGSt5xcU\nFJCZ6ThW9+7d6yTBycrKIjc3F4vFQvfu3eu8X1paGmVlZURGRhpurdq0aRMA8fHxxMXVDt5LS0tJ\nT0939Ds1lZCQ2vuxc3Jy2L/fsd3CaM/hkf8uR9qyZQtWq5W4uDji4+Nrtcm/i/y7HEn+XeTfxVfJ\njLIQQviZfmd35/7HzqK4LAMAszmQDm1PJSricFb8P//IZOvmugFFp7PDGPl9CiHtHb+jZqdXsuiN\nbA7sdmQd7tA1mFN7hvPdiN0U7zFOlCR8Tk2AbLzJ3Ydsn1dIlpMa4N2uiCL+tFCnr83eX8g7b3xv\n2KaU4j+TBhMQID8OCSFEayHloXxQc8plCCFaj/QdB3jk3u8IDkjBbHL82lxSmk32wb+5456BDB52\notPXFuyo4MvBuyjc4cikbTLDqYOjOOb0cABsVs3GH4s45dV4orv7XMUHj/NAeSgNpGmt6yTXqi4F\nNRCD0lGe1pjrnbXczqzjjMtBmYMVV27pRkRSoOFrtdY8ct/n/Lxmh2H76Mv7cMP/nd24zgshhPDp\n8lAyoyyEFyksLKSwsNDT3RAu5qlxTenSlmdevQi7aRsVlUUAhIW24/juAzjxlK71vjaqSxCX/pBC\nm1OCAbDbYN3XBaz55CDWSjvmAMXJAyL54/YssteWuf2zeCMfO1/zOcrSam8Lkhvrj5dynZaDOuW/\nbZwGyQA//rDdaZDcsVM0/7r+TJf0UTj42LkjGkHG1j+11nGVQNlHyUoA/5SRkUFGRoanuyFczJPj\n2q59JM+9PoqIuL0UlewDoKzUxLMPb2Htj/WvtA2LtzByRQqdzgk79NjOP8pYPOMARblWyottbP+p\nhM/PTSdjabFbP4c38rHzdSngLItVLM4zYntcQ653pfutrH3igGFbaHwAPe91Xge8tLSSN15c5rT9\njkmDCQqyOG0Xjedj545oBBlb/9Rax1UCZSGE8HORUSE89eJoho9ty9hrEzCbFZUVdt59dSeffJiB\nzeo8EAmKMjPsm86kXno4kUj+fiuLpmWz/MNcygrtVBXbWXDRLrbNNc40LLzCNHCUgPrng9VLtnvW\ntPuqXybvp6rIOBv7aU+0JzDc+d7ime+sJudAkWHbhcNP4qRT6ia6EUII4f9kj7IPkj3K/quqyrFs\n8MjshcK3edu4pm8v4a2X0sg/6OhXavcwbpyQSlSMhYVf/EZJUQVjruxbK8uw3ab5/ta9/DU9z/mB\nFZz1SgdOvK11lM9pzri6cY/yJ1rrMU6eMw1I1VoPOuKx3lrrXq7oh6sppSosFkvg8uXLaz2emJhI\nUpIjOV3un+XMOWU72iBObnNKMGPWdsFkNs6YvX3rfu4YPxO7ve69UFR0CDNmXk9EZIjBK0VzeNt3\nonAdGVv/5E3Xu5Yk5aGE8CJyYfFP3jauKV3DuPeJY3n31Z1s2VRE2tYStm8uorwyh9eeX4rWcDC3\nhPG3n4upupSOyaw4582OhLYLYO3jxktc0fDj3VmE52iS7onBHOrfGYK9YVyVUlNxzAj3rn5otFJq\nHZAGTNNaL615rtb6ZqXUxOrgOB9IxZHgyyuD5Bp2u53+/fvXemzy5MlMmTIFgNV3ZxkGyQD9no93\nGiTbbHZe/d8SwyAZYPy/z5Ug2U284dwR7iFj659a67hKoCyEEK1QRKSFf9/bla/m7aWi3E5gSAmP\nPLSQmkVGX3y6nry8Ev57/xACAx2XCqUUpz3WnpB2AayasK/uQRWcOSqWaJOZA1PziRsfiaVT67y4\nthSt9aRGPv8Zd/XFXcxmM99/X7tsU03dz4zvislYbLw/PmVEBAnnhjs97jdf/s6Wv41rLp/cM4lz\nBx3XxB4LIYTwBxIoCyFEK2UyKUaM60Ta9mwmTphDVaWtVvvKZVvof3Z3Bpx7TK3HT7o9juA2Zr67\nZg/2qsOzcUpBaYEVgKAAE4VvFRE6NJSQ3sHu/zDCr/Xr16/OY1prfrpvv+HzTQFw5jPxTo93MLeE\nd6evMmwLsJj5910Da209EEII0fpIMq8WUL3UbV71nyVKqYGe7pMQQgDY7ZpnHltISXHdnAcjRvWt\nEyTX6H55NEMXJBEQdvgyou3w64ICfpyfh7VKYzIpyr8po+izYnQ9CcOEaIq0zwrJ/tW4NNkJt8XV\nW997+qvLKS2pNGwbd2VfEpLqraQlhBCiFZBA2c2UUhNx7AEbU51gZSqw5MjMo0IAZGVlkZVlvBRQ\n+C5vHleTSTHp4WHEtam9RLXvab3Y+kckG35xnrwr6YIIRi5LJjiu9l7k9N9KWTzjAMUHHbPL1o1V\nFLxViL3AyUZSH+XN4+rv7FbNzw9kG7ZZwk30fqCt09eu+2Un33+32bCtU0IMY688zSV9FM7JueO/\nZGz9U2sdVwmU3W8cjqQqAFQnVlkP3Necg0q2cv+Um5tLbm6up7shXMzbxzWlS1v+9/rlh2bRevZJ\npTgvhopyO2+9lM78WZnYbMbfOe37hnLpD6mEJ9Xei5yfVcU3b2azZ0s5APqAnYJpBVSlVbn3w7Qg\nbx9Xf6G1ZvXq1bX+rHlhB3mbjSs/nHJ3G0LaGu8s01rz1usrnL7XbXcNJDBIdqW5m5w7/kvG1j+1\n1nGVQNn9DnI4G+k/H4v2QF+ElwsICOD/27vz+Ljqev/j7+9MMtnTdF9T2hQqUlRs2bRFEVpUREFp\nRfwhKkLrVR+oVwX8ibe9Lj8p6lWvXL0pinJFUYtXEVA0LVikAkrLZlkKTaELXZOm2beZ7++POWln\nkplkJpntnPN6Ph55tDnbfJNPznzn8z3fpaiID2le44a4Tp02Tt/+r8t14cVv0I1fvUifvO5EjRsf\nTX433ndQ3//Gi2o9mjjJHX9yiS7dXKfxp8R3de3rttr0iyY9vbFVNmKlHqnt5+3qerjLE419boir\nF4TDYS1ZsuTY17lLztPWrzUnPLZ0UlCn/Wvy5cmMMfry1y7WmW+qG7LvbcteqzeefkLGyo3kuHe8\ni9h6k1/j6ot1lI0xddbaxpGPzA1jjJV0c7qzlcaczzrKALLuaEuffnLLTr34XHRW4XHji3X1tXPV\nfOSQjjR3aNk7T407vru5X/dd9Ir2PzJ03Oj0E0v05uUTVFIebZ8tnl+s8ovLFSj1Z3utm9eVzKWB\n+u6BBx44tu3gL0N69ZbEyzYt+e40veHTk1K69t8f2aH6/3xQr+5tUWVlidbdcZXGT6jISLkBAFFu\nru88nSg7k2bVS9pgrV01zHErJS1T9EnvBEXHFI8qiU2hTNcp2u16rrW2ZZTXIFEGkBPhsNXdv9qr\njfdFx4MGAlJz60tqPrJLH111jlZ88My42YH7OiP604pdeuUPQ5fsqagJ6pwPTNCEGSFJUnBaUFVX\nV/lydmE3f3DIpcH1Xc/RsO6Yt13dTeEhx1bOLtYV209SsCT1xpfe3n799tdbVFNTrrdf9LqMlRsA\nEOXm+s6TTfnOzNLrJS2UNLR/Vfyx9ZJWOJNtrXIm3KoxxjRkoVwLJa2StGi0STIA5FIwaPS+D87S\nx66dq1DIKBKRaipP1OQJp+in6zar/j8fVCRyvMG1uDygd/7uBL3mQ0NHl3S0hPXnHx3SS1s6JEmH\ne8O+TJIxek9++3DCJFmSzvrKlLSSZEkKhYp02RVnkSQDAIbwZGdza+0ySTLG1Cg6y3RCTuK6UtK8\nQeevMsZYY8xKa+26mOMbFH3iPJzmgddP8Fq3iiQZgAvNOTGko53PKGjnKlRcoaqKaSoprtR9dz+j\nI80d+tyX3qlQKFqlBIuNzv/pTJVNCerJb8dP/hHpl/5+d4t2PN6hpr19OrutXwuvn0TCjBF1HujX\nk/+ReDKZ8aeUaP4VTP0BAMgcTz5RTsMqSUoyfnmrpBWxG6y1y6y1i0b4SpQk1ymasJ8/kCQ7T7IB\noOBZa/W1G+/Wvn0HtffA42rvPCBJCoUqNWvqGXr8kSb92xd+E7cWswkYLf7WdL3p5qkJr9m0Nzox\n2KNfPKDN/7o/OtkXkMTmzZt1z6eeUn9H4iXGzv76VAWCNLYAADLH74nyUsUs3TRIo7N/TJwkucH5\ner8xZqUxJulTbvjbzp07tXPnznwXAxnm9rgaY/SRVeeovCIka8M62LRNTUdelLURBQJFqiyfoqee\n2K3rrv2lmg/Hj01e+IXJOu+2mTLBJBeX9NR3m7Thyj3q742os6FTfS+7Ywkpt8fVLfr7+/XuJcu1\n/67EH1mmnlWmuRdXJdx3tKVTX/7CXdr+vP/W/yxk3DveRWy9ya9x9XuiXCcpWTfoZulYl+mxWO+8\nzlpFJxarl3SdpC1juaiXJ2Hzs87OTnV2dua7GMgwL8T19afV6lu3XK6JkyolSUfbd2vfwSfU2d2s\nQ0dekCQ1vnRI//qJX2jPrvile1770fF6529nK1ia/Inf9p8f1RMr96vn0R6139Gu7r91F/z7nBfi\n6gbBYFA/fO+9KlJxwv1vumlq0q77t9/6sB5/7GV9ZtUd+t43/6yWFuJVCLh3vIvYepNf4+rbRNkZ\nv5x1Tndsk+Br3chnJ8d4Pm+qrq5WdXV1vouBDPNKXOfOm6xv/+By1c6OTtXQ3XtU+w89KWuPT650\nYH+rPvfJO/X8s/viz313td7TMEehccmrnT2PdKqvLyJZqWtjlzru6pDtKdxk2StxLXxGzfeVJtxT\ne0GlZp5bmXDfiy/s1/33Pi1Jsla6/56ndc0Hf6zf/2arwv2Ju3AjN7h3vIvYepNf4+r15aFqJB2R\ntG7w8lAx+7ZaaxclOLde0Ym+lllrN+SivKkyxvRIChUXFydNmK21euKJJ1RXV6eysvj1Jg8fPqwD\nB6JjDBcsWDDk3N27d6u1tVXl5eWaO3fukP0vvPCC+vv7NXHiRE2bNi1uX19fn7Zv3y5Jqq2tHXJT\nHT16VHv27JEkzZ8/X8XF8U8I9u/fr6amJhUXF2v+/PlDXruxsVFdXV2qrq5WbW3tkP3btm2TJE2b\nNk0TJ06M29fZ2Xms2wi/l+P4vfB7GWyk38s/n3lBt/1gi17ZmXxewtLSct2w5u06681xcyVqW8PL\n+tv/aVfvocTnVU4I6q1XTtS4CdGfKTAxoMoVlQpODhb87yWdvxc3L5eRS8aYnuJAKPSdSOJOWMsf\nq9PUM8uHbLfW6vOfvFPP/vPVhOfd9N336w0LZ2e0rACAodxc3/n2iXIKBma3bh72KADwmYrKkFZ9\n5kydftachPuLiso0deIi/eCbz+v+e56J21d9clBvvEMqn5O4ka+9Oaz7/+uQdr0Q7eIVaYqo9cet\n6t3Wm9GfAe6RbKK32e+oTJgkS1JHe4+KixMPjD978TySZADAiHwBeOyCAAAgAElEQVT7RNnZbyU1\nWmvnJdjXoOhkXvOSzIqdN8aYnlAoFOrp6Rn5YADIknB/RN//doP+dF98Mjxl4qmqLJ8iSerpbdM5\ny0p15TVnxvWA6TzYr3svfFmHtnQnvf5rz63UaeePk3GqqZKzSlR2fpmMB2Y3dnMLey4ZY3qKVBz6\nrrYO2Xfp3+o07U2JE2Up+lT5sc079KMfbtLe3UckScWhoOr/56OaPoOlpAAgF9xc3/n9iXKLRlgX\nudCSZAAoFMGigD593QW6/Mqz47Yfan5OHZ0HJUkloSo98qD0za88pEjMk8HyKUW65MG5mnV+RdLr\nP/eXdm386SFFnB7UPY9FJ/qKtDG+1O9ql1UMmyRL0bk8zl5yov779o/oXz59nqrHlel9l51OkgwA\nSInfE+UNkpLVmBOkBE3YAIBjjDG68uol+uRnz9fAA2NrwzrQ9E81tbwka62CgWK9sr1K//faTeru\nPr70U6gqqIvuO0HzViSfIOTgjl7d/Y196nXmcurf1a/WH7Wqf1d/Nn8sFLjaVan3hisqCuo9ly7U\nbXdercv+z1lZLBUAwEv8nijXS0OXgHK6bC8c2F+IrLXavHlz3NeuXbvyXSyM0bZt245NGATv8ENc\nL3rvG/Wlr7xHxaHj40KPtu3SvkNPKByOji9uO1Kt6z7+qA7u7zh2TLAkoAvurNWpn0jeuaerNaLf\nfHGv+mqjVZZtt2r7WZvCB8NJz8kFP8S1EL2gR3X3M/+T9nkVlSUqKw9loURIF/eOdxFbb/JrXP2S\nKCf8BObMZr1O0TWOY61VdDbsMS3hlE3hcFhLliyJ+7rtttvyXSwAPrb4rfP19W8tV0Xl8WFI3T0t\n2nPgH+ruOSpJCvdVaM3nntEzTxw+dkwgaPSWW6brjDVTkl7bhqW/39WiihUVUokUel1Igcl+qcIQ\n613fP1VXXXVVvosBAPA4T07mZYxZq+gT4dN1vGv1VkmNkuoHL/dkjLlO0jxFxyzXKTrB1/W5K3F6\njDE9xcXFoQcffDBue21trWbPZiZPNzt8OJo8TJo0Kc8lQSb5La47dxzSl6/7jZoOtcdsNZpYc5LG\nVc2SJFkb0YWXTtZFl54Qd+4/f9ikTZ/cJyWomsadGNIVL85XuDmsQFVApji/k3qNJa5untwklwZP\n5jXjreV671/qEh576GCbJk+pymXxMEp+e0/0E2LrTX6t7zyZKHsds14DKHQHD7Tqxs/dpd274lfY\nqyyfqknjT1YgEO2ifcobyrTyM69Rcej40+Ft65r1l1VD17+tnlusDzW+JrsFzxE3f3DIpcGJ8sUb\n52jWeZVDjnv6yd364md/rXe++/W64qNvVs345JPEAQByx831Hf3WXIwxygAK1ZSp1frWf12u1y6Y\nEbe9vfOAXj34uPr6ouskP731iB55eEfcMZMXliW85kjtur3P9qpzQ2fSdXfhbtOXlGvm24YmwJGI\n1a23/EWRsNV9v3tKV13+Y/3654+pt4cJ3wAAo0ei7FKMUQZQ6KrHlen/fWeFzl4cv1R9b1+H9h54\nXO2dB3Tg8DNa+9Xf689/iFmLOUmPajvMqlDhw2F13NOhnkd61P7zdkU6WELKa874tylxa3EPeLDh\nWb20/cCx77s6e/WT+r/qmit+rOe2De2ZAABAKoryXQCMTjAY1KZNm+K21dbW5qk0AJBYaWmxbvzq\nxbrlPxp0/73Hk+GI7dfBpuMzaH7npj/JRqS3X/Q6mWRNuMM8KDalRkXTitS/q1/9L/er9dZWVS6v\nVNEsqjkvmHp2mWYtHfo0ubenX7ff+nDCc9pauzV12rhsFw0A4FF8gnCxxYsX57sIyLCuri5JUllZ\n4q6ncCe/xzVYFNC1X7hAEyZV6hc/fSThMZOnVGnRWXMkSe2d/QoXWwX74p8eDtelOlAZUOUVlep6\noEs9j/bItlm13d6msgvKVHJ6ScInkWPl97jm0uk3Jn6afN/dT+rQwbaE56z44JmaMJGxyoWIe8e7\niK03+TWuJMouxSRs3tTY2ChJWrBgQZ5LgkwirpIxRh+6arEmTKzQD76zUZGYpLequlRf+9ZyTZpc\npXC/1fp79urVd/Sp9q9FKm05/nh5uK7XkmSCRuXLylU0s0gdv++Q+qSu+7sU3htW+bvKMz5LNnHN\nnT3jntbezce/r62t1aRJ0/TLnz2W8PiJkyv13stOz1HpkC7uHe8itt7k17iSKAMAcuZdF5+mmvEV\nWvuVe9XXG1ZJSZH+/ab3afaciZKkp7a06JXdnVKVtPOCfk3/R1A1O6MzZA/X9TpW6JSQgpODal/f\nrkhTRL3P9Cp8IKyKFRUKTghm6SdDtlgT0TnnLInbtnr1ap005wK1Hu1KeM6VH1us0tLiXBQPAOBR\nLA/lQqyj7F2dndGZgMvLy/NcEmQScR3qn0/t0VdvvFufveEdQyb7avjFft39+1dlnZx2/IsBTd0S\nVMWkIl114LUpv4btseq4p0N9z/VJkkyJUfkl5QrND2XkZxhLXN28XEYuJavvxtdM0Y2f+6O6OnuH\nnFM7e4J++NOPKFjEfKWFivdE7yK23uTX+o5E2YWMMT3BYDAUDofjtq9evVpr1qzJT6EAIE2dnb0q\nLx+atDY/163bFm/XnnP61ecsmVt62Oik50L6+K70un1Za9XzWI+6NnQdeyJduqRUpW8tlQlkftxy\nqtz8wSGXjDE9oVAo1NPTE7f9Rz/4i37zy8cTnvOlr7xHS86dn4viAQBG4Ob6jq7XLsWs1wDcLlGS\nLEXHM5cdCWjO/UE9d0GLiqqr1D3J6rmzevT8P1t18qnVKb+GMUalZ5cqOD2ojt90yHZYdT/cLQWl\nsrf4a1ISrzh8qE33/O+TCfed9JqpWvzWk3JcIgCAF5EouxizXgPwIhOQrKyenf2cdh/doxo7R+Or\n56o/ZHTLTS/p3StmaNm7pyqQxhPh4hOKVX1NtdrvapftsCo503UN23Dcefuj6u3tT7jvw9eck5UZ\nzgEA/kOiDAAoLEbafsJL2j19jySppfVl9fS2asqEBQoGi/X7X7+ql3d06MqPz1FZeeqTcwWqAqq6\nskqRtogCpYxfdaNX9xzRn+57JuG+1502SwvPOCHHJQIAeBWfFIAC0tTUpKampnwXAxlGXNPT8Jdn\n9OLsHXHburqbtX/fVk2eGm3ffXrLUa298Xnt3ZV41uNkTNAoWJOZma+Ja+797La/KRxOvE7YR3ia\n7BrcO95FbL3Jr3HlibJLWWu1efPmuG3Meu1++/fvlyRNnDgxzyVBJhHX9LS1D01+TcTo9MZTdF3D\nqfrVT3fr0U1NOnywR22tfZLGPtY4cjSijns7VH5huYLjU0ukiWtuDEw6unPHIW3a+FzCY858c51O\ned3MXBYLY8C9413E1pv8GlcSZZcKh8NasmToupLMeg3A7Za/9yw9f3ObnjnxWclIstIbX3i9JndN\nVigU0BXXzFbdiRXq6gqnNbFXMjZs1X5Xu8KvhtX2ozZVvLdCxSeyBm+huf3Wh5VsoY6PXHNObgsD\nAPA8EmWXKioq0gMPPBC3jVmv3W/BgvSWvoE7ENf0mIB0wv7ZCvWF9MTJT+mUxtdqxuHpUnk0SzLG\naPF5kzL3ggEpdHJIXfu6ZLut2u9sV+lbSlX6ltJhu/IS19wwxuiF5/bpsb/tSLj/3KUna+68yTku\nFcaCe8e7iK03+TWuJMouxqzXADzJyU2nN03TuMerVd5TLkmyiYemxolErPbt6dLM2eWpv5wxKl1c\nquCMoDr+t0O206r7oW71v9qviksqFChjOo98+8F3/5BweyBo9KGrqAsBAJlH7Q8AKCgmZtmngSRZ\nkpSk222shnsO6KYvPa8N9x04NrY1VcVzi1V9dbWCM6JjlPtf6lfbj9rUvy/xUkTIjXA4rO3PHUm4\n74ILX6cZs8bnuEQAAD8gUQYAFJRkvZ1HeqLc2dGvjX84oEhE+u0v9urH/7lT3V3htF47MC6gqg9X\nqWRRdJ3lSEtEbT9pU8+TPWldB5mU+A8iGAzoAx86K8dlAQD4BYkyAKCwJKmZbGT4J8TlFUX6/L+/\nRjNnR2fBfuLvLbr5357X/r1pLiFVZFR+YbnK31MeHaAUljrv6VTHvR2y/ek9pcbYRZLEfek7Fmjq\ntHE5Lg0AwC8Yo+xSLA/lTbt375bExGxeQ1zTEzuBVkQR9YR6JVkpKB3Yd1QRa2UkTZtRM+TcKdNK\n9fk1r9EvfrxL/9jcrAOv9mjtl1/QFStP0KKz0+uiW/KGEgWnBtVxV4ciRyLqfaJX4f1hVSyvULAm\nSFzzKBA0ev8VPE12K+4d7yK23uTXuJIouxTLQ3lTa2trvouALCCu6TExT5S7Srv14BkPHft+42Wb\nJEll5SH97/3XJjw/VBLQh//lBNWdVKG7frZHvT0R3fb9nXr5pQ5d8oGZChYln8l6sKJpRar6WJU6\n7+5U34t9Cu8Lq+NXHapaWUVc8+htS1+rGTOHNpTAHbh3vIvYepNf40qi7FLBYFAPPfRQ3Da/tfJ4\nUVlZWb6LgCwgrumJTZRNsp7OI0zUZYzRW5ZNVu2ccv3oe41qOdKnB/54UK80dupj187VuJrU10kO\nlAVUcVmFuh/uVvdfu1X+znIZY4hrnhgjXcbTZFfj3vEuYutNfo2rSXdWUOSfMaYnFAqFenqYXAaA\n93Q39+vHE5+XJHWWdOqBMx8ackxJaZF+9+fPpHS9tqN9uu2Wndr+bLskaVxNsa66dq5OfE1l2mWL\ntEYUqB779B4lJSXq7e3ttdaWjPliHmaM6TEmGHr7kpuObXvr+SfrhtUX5bFUAIBUubm+YzIvAEBB\niV0eKtmMx6ksFTWgalyxPnXDSVr27qmSpKMtffre17frwfsPpl22ZEkyjc65w0zXAIBcIFEGABSW\nmNw4WdfrdPPSYNDokg/M1DWfmavS0oAiYan5cO/oyxhblohVx10d6nmaXj7ZtvgtJ2lO3eR8FwMA\n4AOMUQYAFBQT14Sb+IlyZJRPcE87Y7ymzyzTxj8c0CUfmDmqawzW/ddu9T3fp77n+xTeG1bZBWUy\nwdQnDEPqPnDl2fkuAgDAJ3iiDAAoLCbhf+ONoavz1Bml+uDVJ6Q1+/VwiucXKzAuWp32PN6jttvb\nFGmNZOTakAKBgIqKgzrrzfN04vyp+S4OAMAneKLsUoyH86bt27dLkubPn5/nkiCTiGt64sYoJ3mr\nG+0T5ZG8vKNDtXPKFUzhiXBsXKuurlLH7zrUv6Nf4b1htd7aqopLK1Q8J/XZtZFYICDddufV6usL\n57soyBDeE72L2HqTX+NKouximzdvjvu+trZWs2fPzlNpkAl9fX35LgKygLimx8Q9UR77ZF6peqWx\nQ9/56nbVnVShqz41V1Xjhk9yY+MaKA+o8gOV6n4ouoSU7bRqv6NdZeeVqeRNJTKGrthjMXlKVb6L\ngAziPdG7iK03+TWuJMouFYlEtGTJkrhtq1ev1po1a/JTIGTExIkT810EZAFxTY9JYVBQNnrVPHj/\nQfX3WW1/tl03fel5Xf3pOs09qSLp8YPjagJGZeeWKTgjqM67O2W7rbo2dql/T78qLq6QKSFZHi0a\nhr2F90TvIrbe5Ne4so6yCw2so/zAAw/EbeeDAwAvCPdZ/XdomySpp7hXDWc/kPC4Pz70+cy+br/V\n7365Vw/8MbpsVDBotPxDs3TO0klpPxEOHwmrY32Hwgei3YUDEwKqXFGp4JSgJHevK5lLxpieYDAY\nCofju13TMAwA7uDm+o4nyi62ePHifBcBADLOpLA8lBR9qpzJLs3BIqNLr5ilOSdW6I51r6i3J6Jf\n/XS3dr7Uocuvmq1QSerzXwbHB1X10Sp1/qFTvU/3KtIcUettraq4qEKhU0MZK7MfBINBbdq0KW5b\nbW1tnkoDAPALEmUAQEFJpeu1JEUiNqVJt9K16OzxmjGrVLd+t1EH9vXo7w83a++uLl3zmTpNnpp6\ng7gpNip/T7mKZhWp80+dUp/U8duOY0+VkToahgEAucbyUACAwhL3RHmYRDiLI4emzyrTF75ysk47\no0aStHdXl9be+Lye2dqS1nWMMSpZVKKqD1fJVBuVLi4lUQYAwAVIlIEC0tfX59uZBb2MuKYn1e7U\nNpuZsqSy8qCu/vRcvfeDMxUISF2dYf33txt1z/pXFYnYtOJaNLNI1ddUq/Tc0qyWGXAD3hO9i9h6\nk1/jStdrl2ISNm8aWKduwYIFeS4JMom4joKRZIdZHkrRrtdZL4YxWvquqZo9t1y3fX+n2lr7df/v\n9uuVHR1609IelZaZlOMaKKdtejSo77yH90TvIrbe5Ne4UmsDAArOsXHKw+VIOcyf5p9SpRu+frLq\nnOWiWo/2K0hTMwAAnkU171KZnOkVhWPWrFn5LgKygLimzwSMbNgO/0Q5x08aayaE9OkbT9K96/fp\nzW+bqJKynpy+vl9R33kP74neRWy9ya9xJVEGCsi4cePyXQRkAXEdhVRyozx0yS0qCuiSy2c63zHe\nGBgN3hO9i9h6k1/jSqLsYps3b477vra2VrNnz85TaQAgc1Lpel1oQ1cP7u9WIGA0aUrqS0gBAIDC\nRKLsUuFwWEuWLInbtnr1aq1ZsyY/BQKADBrobVtIXa+H090d1rrvNKq1pU8f/sQcLXiDP1vfAQDw\nChJllwoGg9q0aVPcttra2jyVBgAyLOBMez2cwsmTtX1bm/bv7Za10g+/uUMXvm+63nHJNAUCjK8F\nAMCNSJRdbPHixfkuAjKstbVVklRdXZ3nkiCTiGv6jj1RtoX7RDk2rq9fVKNP3XCifnLLy2pv69d9\nv9mnl3d06MP/MkcVlVS1QCzeE72L2HqTX+PK8lAuxbqS3rR7927t3r0738VAhhHX9JlUaqc8vw8O\njuvJp1brhq+frBPmlUuStj3ZqrU3Pq/dL3fmq4ieQH3nPbwnehex9Sa/xpVEGQBQcFJJlAsxfxo/\nMaTPfnm+lpw/SZLUdKhX317zgh7Z1JTnkgEAgHTQH8ylWFfSm+bPn5/vIiALiOsoOO9xhTyZV7K4\nFhcHdPlVszX3xAr98rZd6uuzumPdK9r5UodWXDlLxcW0UaeD+s57eE/0LmLrTX6NK4kyUECKi4vz\nXQRkAXFNX9wTZavE6yrnOVEeKa5nv2WiZs4u063fbVTToV5tfuCw9rzcqas/XZejEgKFifdE7yK2\n3uTXuNKsDQAoPCb2v4mfKEYiOSrLGNTOKdcNXz9Zp54WnQDllcZO3fSl5/Kd4wMAgBGQKAMACs6Q\nJ8qJuCTbLK8o0qrPzdO7Lp0uY6TenojoTQwAQGGj6zUAoPDEZJIXPHqeBp4rL39sniYuKJUxUijk\nniosEDC68H3TdcK8cnW2h/XDO/NdInfZvHlz3Pe1tbWaPXt2nkoDAPAD93zKAHxg//79kqRp06bl\nuSTIJOKavtgnysXh42OjSoqLVVpaGGOlRhPXBW8Yl63ieFY4HNaSJUvitq1evVpr1qzJT4EwZrwn\nehex9Sa/xpVE2aVYV9KbmpqiS8j47Y3I64hr+pJ1TbaRwnnvI665EQgEtGnTprhttbW1eSoNMoF7\nx7uIrTf5Na4kykABKSrilvQi4pq+pOsoF06eTFxzaPHixfkuAjKIe8e7iK03+TWuhieT7mOM6QmF\nQqGenp58FwUAsuL2E15Q+66+IdtXPD5PUxaV5aFEmVVSUqLe3t5ea21JvstSyKjvAMDd3FzfMes1\nAKDgJJ0VmrZdAACQAyTKAICCk6zrdSGNUQYAAN7lzw7nHsFyGQA8K+aJ8lMn/lPhon5ZSfv/50WV\n3BOQjUif+Oz5mjipMm9FBAAA3kWi7FIslwHAy0zgeKa8f9IB9RVHxyvve/r4MR/9+Dm5LhYAAPAJ\nEmWXYrkMb9q5c6ckae7cuXkuCTKJuI5CsjHKMfLdDZu4AqPDveNdxNab/BpXEmUXY7kM7+ns7Mx3\nEZAFxDV9sWOUk87rlefhysQ1N1idw3u4d7yL2HqTX+NKouxSJumUsHCz6urqfBcBWUBc0xfb9Vo2\n8ftdvhMo4pob1Hfew73jXcTWm/waV9ZRdiHWlQTgdb9Y8KKOPBt9jztacVQRY2VkdG79TE09vUzG\nGNXOnqBQiTvbe928rmQuUd8BgLu5ub5z5ycMAICnxXa9Htcx7tj/T5g+SbPmM9M1AADILtZRBgAU\nnKS9bekEBQAAcoBEGQBQeAJJxiVHclwOAADgSyTKAICCk+yJcr6XhAIAAP5AouxSTMLmTdu2bdO2\nbdvyXQxkGHFNn0lWOxXQWx9xzQ3qO+/h3vEuYutNfo0riTIAoPAkfaKc22IAAAB/YtZrl2JdSW+a\nOnVqvouALCCu6YtdR7lxxsvqK+qTjNS/6YDG7QnJRqwuuuQ0TZ6av7UdiWtuUN95D/eOdxFbb/Jr\nXEmUgQIyadKkfBcBWUBc0xfb9frlGa+os6xLkvTi3yT9Lbr9TeeclNdEmbgCo8O9413E1pv8Gle6\nXgMACo9J+s0xTOwFAACyhSfKOWCMuU7SREk1kuokrbXWbshvqQCgcMV2vTZJ8mEmeSo81HcAAK8g\nUc4yY8xySROttdc73y+UtMUYM89a25jf0gFAYUplWCppcmGhvgMAeAldr7PvDEnLB76x1m51/rs0\nP8VBIevq6lJXV1e+i4EMI66jEFM7mQLtek1ch6C+Q0q4d7yL2HqTX+NKopx935C0bOAbp4VdksbU\nuk6XQ29qbGxUYyMPXryGuKYvpSfKeX4fJK5DUN8hJdw73kVsvcmvcTV+qICMMXWF0u3LGLNekqy1\nK8ZwDetcI1PFQoEIhUKSpN7e3jyXBJlEXNP3u7ft1N6/dEiSNi18WG0V7UOOWfu99+v1b5yd66Id\nM5a4lpSUqLe3t9daW5LJMlHfwQ14T/QuYutNhVjf5YKnxygbY5ZKqpe0QdKqYY5bqWgreLOkCZIa\nB8ZYZbAsaxXtflYjaVEmrw3vYL1QbyKuo5BCf6d8506FFFfqO7hJId07yCxi601+jasnE2VjTIOk\nFkn/UHTWzeGOrZdUZ62N7S5Wb4xpiN02VjGTmyyVtNMYc37M+C0AQIy4OtkmrqAj+c6UCwD1HQAA\n2eHJRHmgwjfG1Eham+w4Z/zUSknzBp2/yhhjjTErrbXrYo5vULQFfjjNgz6E1FhrW2KuvcEY0yjp\nVtHSDgAJmbjJvJIgT6a+AwAgS/w+mdcqSUoynmurpLhxVdbaZdbaRSN8DW6VP+KsKxmrWdEuaZ6w\na9curVmzRrt27SqIa6ZzbirHjnTMcPuT7cvG7yzTvB7XkY4jrrm5ZtJz4x4pJ5n1OskT5dHes6P9\ne3AJ6rsMKKT7J93zqO+SK6S4pnsucU3O63Ed6TivxjWnrLWe/VK0craS6pPs3yFpR5J966O/njGX\nYYuiXd0Gvq9zyrRyDNe0TtkKwsMPP2wl2YcffrggrpnOuakcO9Ixw+1Pti/Z9lAoZEOh0IjlzgWv\nx3Wk44hrbq6Z7Nzfv2OnvUXP2Fv0jL3stHr7jnO+OeTr8ccaR1WedOOXbN9Y4hoKhaykHkt9R303\nymume14h1XeF9J5obWHFNd1zCymu1hZWbL0e15GOK5S4Zrq+y+WXJ7tep6FO0Zb0RJqlaHc1O7ax\nVedL+qLTLW7gNVdYa+8awzUBwNtSWh4q+8XwEOo7AADS4NtEOaYizyobHa+V0RlF4V2WT/6eRFzT\nZwIjd72ORPL7e3VLXKnvUGjccu8gfcTWm/waV0+vo+x8ODgiaZ21dlWSfVuttUMmGXFmB10paZm1\ndkMuypuqgXUlR1JcXJx0OveBuA+3P9VzrbXq6+s79nqpXDuV/bHXTLds4XBYwWAw4bnplj32mETl\nHm7/4H0D+we/7uCfe2C9uuHKnmj/WH/nqZR9LK893M890vlS4r+J0cQs0bWT/a0k2zfwNxa7P9Hf\nkzHm2LqDsXHN1H2S7v6B7kTGmIxdezTvASOda/t1bLKuiLGyCWbuKioKJI3bcO8fyfan+/cwOK7p\n/N4GzrU2yZTeaaK+8299l+z6bqjvchGzVPZ7vb5L9W8l0X7qu+zXd6OJWewxw71/JPv5k10/2d9T\nIdV3ueTbJ8opGJjtszmvpRiDvr6+XK72Huzr6wsX0DWDkUgk1XNTeZ2Rjhluf7J9Sc8ZzYLuWVJw\ncU3j3FSPDUpKGrvh9iX5G3NFXJX85xr1NbMW1/hU6VjZR3i50d6zaf89jDKuQ1vD8of6Lj2F9L6Y\n7r1ccPVdASmkuKZ7bkpx1fB/K9R3aVwzV3FVamUf9p4c5hrJ9mU6roVU36XFt4mytbbFaQVJ1iVt\nYHtLkv1548YWGQBAflDfAQCQPr8vD9WiEdaJtImX0gAAwE2o7wAASIPfE+UNSt7CPkHJZwgFAMBN\nqO8AAEiD3xPleim6JEbsRmfik4UD+wEAcDnqOwAA0uCXRDlhdzNnds91ktYO2rVW0dlB12W7YAAA\nZBD1HQAAGeDJ5aGMMWsVbSE/Xce7mm2V1CipfvDyF8aY6yTNU3QMV52kRmsta0ECAAoa9R0AANnh\nyUQZyTkfks5wvq2RtLbQ1s3E6Bhj6iStl7SCSXncwxizXNJliiY2dZK+Ya1lvKgHcE/mF/Wdd3Fv\nuRP1nXd59Z707fJQfuR8aGi01t7sfL9UUoMxZhFvVO7lvDmtVbTiWajkE/agwDj34BettYtitu0w\nxizzUkXjN9yT+Ud9503cW+5FfedNXr8neaLsI8aYLZKuif2Q4GxrtNauyF/JkCnGGCuJD4IuYYxp\nkNQw8GHe2VYvqYXusN7APZkf1Hfex73lLtR33ufFe9Ivk3khqlnRcWyDt3mq9QdwkdMVbYWN1SJp\naR7KAngJ9R1QWKjv4DokyjnmdFHIC2vtsgQzmy4V62eOWT7jivwYa8ydZXlqFP2gEKtJ0bFbyAPu\n5cyhvvMm7hH/ob7zJu7lkTFGOUecsRn1kjZIWjXMcSslLXjktuwAAAl7SURBVFO05XuCsjgjqTOG\nq0XSN7JxfT8oxLgiu3IQ8xbx1CvnuJczpxB/l9R3Y1eIcUV2Ud95E/dy6kiUs8wZk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      "text/plain": [
       "<matplotlib.figure.Figure at 0x6527198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# approximation of Jungwiert et al. 2001\n",
    "def floss(td, C0, lam):\n",
    "    return C0*np.log(td/lam + 1.0) \n",
    "\n",
    "ltd = np.linspace(-2.5,1.3,100)\n",
    "td = 10.**ltd\n",
    "# Chabrier 03 IMF\n",
    "C0 = 0.046; lam = 2.76e5\n",
    "flch03 = floss(td*1.e9, C0, lam)\n",
    "rch03 = C0/lam/(1.+td*1.e9/lam) * 1.e9\n",
    "\n",
    "# Salpeter 1955 IMF\n",
    "C0 = 0.032; lam = 5.13e5\n",
    "fls55 = floss(td*1.e9, C0, lam)\n",
    "rs55 = C0/lam/(1.+td*1.e9/lam) * 1.e9\n",
    "\n",
    "# plot\n",
    "fig, ax = plt.subplots(1, 2, figsize=(6,3))\n",
    "ax[0].set_xscale('log'); ax[0].set_yscale('log')\n",
    "ax[0].set_xlabel(r'$t\\ \\rm(Gyr)$'); \n",
    "ax[0].set_ylabel(r'$\\dot{f}_*\\ (1\\mathrm{\\,M_\\odot/Gyr})$')\n",
    "ax[0].set_xlim(0.01,13.5); ax[0].set_ylim(0.001,20.)\n",
    "ax[0].plot(t, mlratech, c='darkviolet', lw=2.5, label=r'$\\rm Chabrier\\ 03$')\n",
    "ax[0].plot(t, mlrates, '-.', c='darkslateblue', lw=2.5, label=r'$\\rm Salpeter$')\n",
    "ax[0].plot(td, rch03, '--',  c='violet', lw=1, label=r'$\\rm Jungwiert\\ et\\ al.\\  01\\ approx$')\n",
    "ax[0].plot(td, rs55, '--',  c='slateblue', lw=1, label=r'$\\rm Jungwiert\\ et\\ al.\\  01\\ approx$')\n",
    "ax[0].grid(linestyle='dotted', c='lightgray')\n",
    "\n",
    "ax[1].set_xscale('log'); ax[1].set_yscale('log')\n",
    "ax[1].set_xlabel(r'$t\\ \\rm(Gyr)$'); \n",
    "ax[1].set_ylabel(r'$f_{\\rm loss}$')\n",
    "ax[1].yaxis.set_label_position('right')\n",
    "ax[1].set_xlim(0.01,13.5); ax[1].set_ylim(0.001,3.)\n",
    "ax[1].plot(t, mlcumch,  c='darkviolet', lw=2.5, label=r'$\\rm Chabrier\\ 03$')\n",
    "ax[1].plot(td, flch03, '--',  c='violet', lw=1, label=r'$\\mathrm{J01};\\ C_0= 0.046;\\ \\lambda= 0.276\\ \\rm Myr$')\n",
    "ax[1].plot(t, mlcums, '-.', c='darkslateblue', lw=2.5, label=r'$\\rm Salpeter$')\n",
    "ax[1].plot(td, fls55, '--', c='slateblue', lw=1, label=r'$\\mathrm{J01};\\ C_0= 0.032;\\ \\lambda= 0.513\\ \\rm Myr$')\n",
    "ax[1].grid(linestyle='dotted', c='lightgray')\n",
    "\n",
    "ax[1].legend(frameon=False, loc='upper left', fontsize=7)\n",
    "#plt.savefig('fig/mass_loss.png', bbox_inches='tight')\n",
    "plt.show()\n"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}