I've posted a new manuscript titled "Uncertainty of prior and posterior model probability: Implications for interpreting Bayes factors." Here's a summary and examples to stimulate your interest.
Summary:
In most applications of Bayesian model comparison or Bayesian hypothesis testing, the results are reported in terms of the Bayes factor only, not in terms of the posterior probabilities of the models. Posterior model probabilities are not reported because researchers are reluctant to declare prior model probabilities, which in turn stems from uncertainty in the prior. Fortunately, Bayesian formalisms are designed to embrace prior uncertainty, not ignore it. This article provides
- novel formal derivations expressing the prior and posterior distribution of model probability
- a candidate decision rule that incorporates posterior uncertainty
- numerous illustrative examples
- benchmark BF’s using the uncertainty-based decision rule including benchmarks for a conventional uniform prior
- computational tools in R that are freely available at https://osf.io/36527/
I hope that this article provides both a conceptual framework and useful tools for better interpreting Bayes factors in all their many applications.
Examples:
Suppose you're doing a model comparison or hypothesis test, and you have a well-constructed Bayes factor of, say, BF=5. What do you conclude about the models or hypotheses? Your conclusion will depend on the posterior probabilities of the models, which in turn depend on the prior probabilities of the models. And what are the prior probabilities of the models? You're probably uncertain about the prior probabilities. Instead of pretending to have some specific point value for the prior model probabilities (as is usually done if it's done at all), we can represent the uncertainty as a distribution. The distribution of prior model probability becomes a distribution of posterior model probability, and we consider the entire distribution to decide about the models.
Notation: M1 is model 1, M2 is model 2. p(M1) is the prior probability of M1. BF is the Bayes factor for M1 relative to M2.
Figure 1, below, shows an example with a high-certainty (a.k.a., narrow, high-concentration) prior distribution at p(M1)=0.5. This prior distribution (see Panel A of Figure 1) represents a belief that the prior odds, p(M1)/p(M2), are almost certainly 50/50. When people assume any prior odds at all, this is the usual conventional for representing neutrality. Panel B shows the posterior distribution for BF=5 in favor of M1. Notice the probability of M1 has increased. Panel C shows the posterior distribution for BF=11.3, which is sufficient for the 95% HDI of the posterior distribution to exceed a decision criterion indicated by the vertical dashed line.
![Figure 1. Highly concentrated prior.](data:image/png;base64,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) 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Figure 1. A: High-certainty prior on p(M1). B: Posterior when BF=5. Posterior when BF=11.3.
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Figure 2, by contrast, shows an example with a very uncertain (a.k.a., broad, low-concentration) prior distribution. This prior distribution (see Panel A of Figure 2) represents a much more typical state of prior knowledge, or at least is a much better representation of neutrality between models. Panel B shows the posterior distribution for BF=5. Notice it is very spread out. Panel C shows the posterior distribution for BF=38.9, which is sufficient for the 95% HDI of the posterior distribution to exceed a decision criterion (again indicated by the vertical dashed line). This BF might be treated as a benchmark when assuming a more realistic "neutral" prior for the model probabilities.
![Figure 2. Uniform prior.](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA8AAAAVACAMAAACwaMFLAAABd1BMVEUAAAAAADoAAGYAALYAANsAAP8AK/8AOjoAOmYAOpAAOv8ATP8AZmYAZpAAZrYAZv8Aa/8AiP8ApP8Av/86AAA6ADo6AP86OgA6Ojo6OmY6OpA6Ov86ZmY6ZpA6ZrY6Zv86kJA6kLY6kNs6kP9mAABmADpmAP9mOgBmOjpmOv9mZgBmZjpmZpBmkJBmkLZmkNtmkP9mtttmtv+QAACQAP+QOgCQOv+QZjqQZmaQkDqQkGaQkLaQttuQtv+Q27aQ29uQ2/+2AAC2ZgC2Zjq2Zma2Zv+2kDq2kGa2kJC2kP+2ttu225C229u22/+2/9u2///bADrbANvbkDrbkGbbkP/btmbbtpDbtv/b25Db27bb29vb2//b/7bb/9vb////AAD/ADr/AGb/AJD/OgD/Ojr/Omb/OpD/ZgD/Zjr/Zmb/ZpD/Zrb/kDr/kGb/kJD/kLb/kNv/tmb/tpD/trb/ttv/tv//25D/27b/29v/2////7b//9v///8ZXwanAAAACXBIWXMAAB2HAAAdhwGP5fFlAAAgAElEQVR4nO29i38bx53g2dQtY8p7J2dGGEmexHYsc0UrznhG3KWczCljHbRyLpMwukUkOY8xoayoSLKteGBbEEXgj7+uqn4/qhtEdVdV4/v92CLQDXQXm79v17s6WAKAtwS2EwAAZweBATwGgQE8BoEBPAaBATwGgQE8BoEBPAaBATwGgQE8BoEBPAaBATwGgQE8BoEBPAaBATymQeD5KAiCC3V7x8H5o+XpbhCcuyffT5JXLRDfu5rftDioP5fmAA8uh4n8x6P231zl4AAu0yBwqGS9lDMZ4yLUo1hfV+DwAFu3234/OYBM4yrmr3JwAKfRCxxmiUFQF8nhTqGbFFh5t7bAYYZ/ftWcVKRx5S8BDAO9wKFQ535a50dkmxRYZYBrCxzdE1ZCCGw4+wXwBb3AoZHnH8T5q6wQ76c7x0pAJbDckQi8uBN+9I2PI+8ffijy6LcPxeuw2H3+P/aCYOdQCiz+kYeMXkxyMs6iU0cnDj+zdVsc7I0b8Veu5gSWJ3r71jJ/IpHOV5+Er8JDPRgFW+8f5c5w/guR2HeqUqc56CrXGKAztAILN66moZwXWOq0TAQWmXEssGz6CtmRNqs6auR4qMDOnqxXq+OOI/siV2e5PLxC4I+CpFCvDhAdPfxcVN4PgnePcicKT3FFJmjr0zvF6nL8qehExdQtaw+6/pUHMIBW4FCcMK7HcRk6L3DsWiSwCPdI4HiL+p46yKsDtW8WxJ9WisRHmQRJeTx3ioLAMfFpsgKPk70XltkTpduD5LOZM2QPWUzdsvagAE6gFVhZNQsqK6aRcjLU31d6RgJPZIgvPlOZ7jhpK46y2CDIlIAjY2Vev0x/KqoEfv9IZor7pSK0OPL5Q3mnEHvTEwkHL6hvhUebBIUzBFs3loux2lpMXf1BAZxAJ3CkRk2PSlz4lbtnMotSAsdG5VuX0jJytDE6rDqMyqZrvpMVWNwzZpUCjzMlggvZE42ztxV5rLzAcXFc3atKqas+KIAT6ASOi8zjqnboRLWkLrt1WwmcFIMnyfdOHn4ySgVW/qR5XPidWfzR3LkqBL5aepu5zSTCRi5ezbwvaF84Q2RqMXX1BwVwAp3AcZtUZRm6ILCQ6vxn8gtxE1ZcsRQtwEndM9Io+V6k+7hgm2JVgbPDSdITpQLH3dY5gc/dq/pSKnD1QQGcQCNw0gBb2WyTxHb0QpRQr1QJPBNv3771oEZgWYZO+3/7Fzg7BgWBwTM0AmdFLHecFHLguIk4W4ROPpfxJ83NMzqe+00yAqtS4ELpt20ROn9P0AucFKFzqas/KIATaASeBFmKGU9R4KiLJdOIpYgr0pM6gcXHryRSFQWOv9socEV7UzuBk0TkBK1txEJgcIl6gTNjjIUxpcbXcUFgVeKO23vfP1o+HL1zK9cSVi2wulFEG8vynz8Uw6daCJzp8cmfqEngINeNlE9d7UEBnKBe4Ex/y+IgqdymGXG2H/hq/IXCQI6oFHruUHYK1wgsvxfdKvL9wJkDNQucqbJHPrcVOK0klFJXe9DCsFIbjLVzOMZxq3n2N0p/9fCdLFoUZnCuNqET7FMv8CRTblav80Er6q5x6TJpQc4PpZTjDzOO7FcKLCWJAisenxkRfVcMX2wUODPqMfpqyzqwGp0ZV7YrCvhVB7Uv8EzbozVLB6ZEH8u+zgxbL8zgXGlCJ9inVuAo11WoMnT9WOi071R95eTOZTF94Zbc/DDUb+vdo2IzUK6FN46a+K4QI777xo0vDtoIHM87+K18vUIjljhJMpmhlLrqg1oXWD9xK9o7S8oO8aDQ6FefJe2ShRmcZ5nQCRZZY0mdsTYLWIF0wEdhNlL3+Fup1ZsW7U0aFgtTuzPrNBRuBGeZ0AkWWUPgMEiMyPYwM7hx3HP4+CNwYeJj4fZZs1cI/OORLCqEf60rkcCv9lKvS/fMvm+hsB5rCBzerNefVqeaVuLjhO/6LcB5JXB24mO5saBqrxD4J7vSyElw7hdB2mN/Obno+RmcxbfgOOusSjkzUA3Mt42aOOJKeCVwob28oF3VXrH5/QNxUwzvtmKkayTwzq108ZT8uJviW3CctZaV1XdktEJUzd64kb7pufjml8CZiY+TIHfta/bKcSqyYTn08kI0auX0wxtHmdWP8j13xbfgOKwL7QmFiY/jfFW1Zq/cPIsWTtjPzqXKC5w5FEuM+QUCe0J+1HZRs5q9ciyqbFgQrYPVAhdni1ZOHgVXQWBPyE98rBC4aq8UWDQ2/k5UhBF4gCCwJ+QnPhZXSanZq2aDhNv+aRQNxEHggYHAnnD2InTURL2PwEMEgT0hP/GxQuCqvUrg0+jZGQg8QBDYEwoTHytaoSv2ztIFs0MpqwWmFdprENgTCkM1KvqBK/ZGJetJEC/9WSMw/cDegsCeUJj4WJi2VbM3XccoHkNZFrgwKLPwFhwHgT2hMPGxPBa6am86hbI4kzIVuHArKE7oBLdBYE8oDvoszUbS7NXCbCSvQWBPKCqan8yp36tlXFSfErRPILAnFBXNT+bU79VRmMHZ+4ROWA8E9oTSvKnc1Ev93obj7te/BddBYE8oT3zMTubU79XAqpSeg8AAHoPAAB6DwAAeg8AAHoPAAB6DwAAeg8AAHoPAAB6DwAAeg8AAHoPAAB6DwAAeg8AAHoPAAB6DwAAeg8AAHoPAAB6DwAAeg8AAHoPAAB6DwAAeg8AAHlMvcAAAbnAGgW0nWc90ajsFMChcD6izCFxvvX2mU9spgEHhdkAhMIAWtwMKgQG0uB1QCAygxe2AQmAALW4HFAIDaHE7oBAYQIvbATU8gQE2CAQG8BgEBvAYBAbwGAQG8BgEBvAYBAbwmOEJ7Ha3HXiH2wGFwABa3A4oBPaUWTqj++pyOQ5/7Bc/ce7ecvLGzw6jt69+fjn+xCTck/wQB7qgO9PDvSDYuVU+9dZtE7+H+7gdUAjsKY0Cz0fhhkkQnD+SbxcHySceBErgxcGFZbPAk+QkhS0I7AII7CmzrFKhwMX8dzkW5k4Sz+ajSODFZ0EkcHiMffVDI3D4vRvC+Yyu401RV+F2QCGwpzQJLDPgUOAfj9TnJud+Kj8z3wt29iKBFwcye9YKPFHnmaSnWxxEX98Q3A4oBPaUCoFDs353JwjelrXesbRsEryvJA2Ly0ry8dbHXyQGTuSmVGBRzlZEBe9wi8pu56N4y/J0V1tlHhxuBxQCe0q1wL+IK6eRZWHGOZEGhhmyEvhPR5ksdD5StWCdwOqzp7tJtjsL3r0zCrY+PlpuBm4HFAJ7StqIJcyKBA7C+upiLHycJSXfuSxDT87dS4rZqcCnu0JUXRFafSJXbp4UHB86bgfU8ATeEKoFFq7KzFIVjoXAsqIrGpwrBFYF5BUFHgfvhIX0h6NcEQAsgcCeUlmEVvVV0UoctRSLtifxUjRpVQisPraiwBGZWjHYA4E9RSOwyH0zAovOIjFmo4XArerAy9JRwB4I7Cntc+DT3QtyyMYZBS61Qi9LRwF7ILCnVApcVQcWPUq/EZ3CZ6oDl/uB47x4tjGtWE6DwJ5SLfDWLfFvrhVavL6SNHQJVmmFrhiJNQ52DsMto/LgL+gfBPaUzFjoUMK4CH05bpZO+4HFa2lohcDFfuAqMmOhT3dlF/NeaXQ0WGN4ArvdbWeMaoE/vRME78iSbTwS66rMmeUYrLLAapCHXuDMbCQl8HJxZ1SYnzRo3A4oBB4EuUYsyXzUnEO2GQsNbgcUAg+CssBqNpKeNrORwO2AQuBBIOcD5wVW05F0tJsPvPG4HVAIPAgqBJYrcmhpuSLHpuN2QCEwgBa3AwqBAbS4HVAIDKDF7YBCYAAtbgfU8AQG2CAQGMBjEBjAYxAYwGMQGMBjEBjAYxAYwGOGJ7Db3XbgHW4HFAIDaHE7oBAYQIvbAYXAAFrcDigEBtDidkAhMIAWtwMKgQG0uB1QCAygxe2AQmAALW4H1PAEBtggEBjAYxAYwGMQGMBjEBjAYxAYwGMQGMBjhiew29124B1uBxQCA2hxO6AQGECL2wGFwABa3A4oBAbQ4nZAITCAFrcDCoE3k22B7UT4gdsB5ZzAF0tsA/hEOYQ79MUxgcu/OwKDZ1QFcWcOuyVw5a9u++8BsBKVUdyVwQgMYBYERmDwGARGYPAYBEZg8JgNFphWaPCfPv11TWDoCRlpthMB6zM8gd0eOAPe4XZAITCAFrcDCoEBtLgdUP0L/Pn17e03f1mz5fXdS+Hrffn6ZdQmcHu147t9vS1TuvhnvMibxOoBVQ7x+2FY/+hQvLqWtHXdM3L1exf4vkryB5VbXke/3luZ7QhsjtqLj8D1rBxQ5at8V20RGVNOYANXv2+BX18Sv8bnmTRnt9zdfu/P4Wu5JXxzpt8LgWspX/yzXuRNYtWAKl/l+9LdMKzTa31znRDP0rfA99WN6X56f8puufbmkXotsuCb4h61OghcS/nin/UibxKrBlT5KitbQ7PfKnzGwNU3IfDpcY4nuvPdVPec15eUqpVbot/02lvlr7cAgWupuNRnvMibxKoBVb7K1yJPb8Zb4n0trn6TXCYEXjybZvmLLj3xPedacu8pb1H3p5fb74kWrX85Kh1DDwLXUr7UZ73Im8TqAhevclSwTDPcKEtuc/Wb5DJThP56+pUmDVlKv0vFlrASkangv0lwmaJ8qbnI5ilf5SRPjra83I6rim2uvl4uQ3Xgp9OXujSktBD4ddyG9d6hrPl/UD4KnInyxecim6fyNvlLeZXjorTKgNtefa1chgRePNYWnFOaBY7aoGOyFTZYj/LFj+AiG6TiKt9UGe11taV4tZuuvlYuU63Q3z5vlwU31oHvbuf8pZ3UIBXNDYU9sD5VV/nXsqp7My45f1D9jTp0cvXdjdTUCn1z+83D4jeILUNUtEIne7jIpqi9ynE30s1i7+86V9+tfuDwV3mv0Pb+kgYWY5QvPhfZPOWrfFcVKuMtcRnbyNV3ayRWtnBxV+bFhRoxrEP54nORzVO+yi+3t8Or/Ovt2Ne499fE1Tcl8Kvnz46Pnzz/rvGE2YGi1+TvmNmSDBQVt6TrpSGlraAfuJ7yxT/jRd4k1hoLra7yzeyQ50wu1fLq6+QyI/D8cdLT/GVDYrJTNdRvl26JJ2dEPWNyZtIvNYeqBIE1lC/+2S7yJrHWbKTMVX4vaty5n8lw21x9vVxGBJ5PH31zcjKbfnXy7WP9QKweQGAwiuWAapDLiMBPp/8pfsxEh3P02h4IDEaxHFANchmZzBDdGE6nfxU3jL+eLaGmQGAwit2AapLLrMB/Sd9YA4HBKK4IXC2XkdlIj9VgzZk4/ByBbZOu35Jbs+XlpXiQ28vcSIKkUeWlmgSm+NG+6pu8tvE9xHYDqkkuI3Xgr6ePXi+Xr6bTr5avHreemNQRGy9wZv2W7Jotry+9dRS5mp+GWi1wPEcGgS0HVINcRgQO7xLTR+H/T8I8fqqdz98Dmy5wbv2Wu9kxG7cjHe/nR+4VBVa9kp9fVwYjsOWAapDLTD/w4sU0PEt4dzh98v1ZEwpmyK3fkpsRcy/651p+4EC1wKILUy7CtvEC20Yv1/DWhd50cuu3ZArLicB3C0Pn6wRWQ/4Q2G0QeGhkp6Nm12yJi9CvLxVG3tYJrI6EwG5jbCz0i+fHx8fPv3ltJFVwdrLrt2TXbIkbse4WjbyfNFsVBFblbQS2jk4u42Ohn6CwXbLrt+TWbHl9XTRvvQz/v38pO+sagd1GL5ehsdDTJ9+dCL59LBu9wSL59VsE2bnlN9+SZeZMRbi2CI3ALtAgl6Gx0F9VvgYr5NZvkaSN0WIMh9iT8ZQ6sNM0yGVyKGX5jQ02vR84IvMYgNwSgm8pJ3NPCaAVWocbQynLbxQIPDSy67eU1my5H5eKWwisprIi8PAFjodrSmbMRrJLdv2W0potcgxHqyL059fVyi8I7MZYaEmFXEbqwLPpo2iMyGI2bbvEe1dsusC59VsKa7aopquGRizGQuexHFANcpl6tErI8fGx+GF5Pr/t6+0A2fVbcmu2xGM4it1IlbORoi8hsO2A0stlaCDHyQvVWXX8N+udSLavNwwM6wGllWt4QymtX28YFm4HFAIDaHE7oBAYQIvbAWVcYOv9wABDpaN+4KZzAIAJ+hB4eWK9HRpgoJTlGl4dGGCDQGAAj2FFDgDHYUUOAG/ZtBU53O62A++w/nTCDVuRA4HBKNafTsiKHABnZ/gT+hEYBszwBWZFDhgwrMjRLwgMRmFFjn5BYDCK7YBiRQ6ANbAeUKzIAXB23A6o4QkMsEEgMIDHIDCAxyAwgMcgMIDHIDCAxyAwgMcMT2C3u+3AO9wOKFMCJ/MkmI0Ew8J+QOnkQmAALfYDqg+B0xVrba8Lbf96w6BwIKA0clEHBtDidkAhMIAWtwPK2LrQz58dHz95/p2RRK2F29cbvMPtgDK+LvSXhhJ2Zty+3uAdbgeUoXWhH31zcjKbfiWWrrX9cEK3rzd4h9sBZWhdaLnUx0ys2PPU+po6AMPh9DjHk+J+k8vKnoo18+a2V6UEGBCLZ9Msna4LLX9aH8gBMCi+1j7rxOS60DPh7hyBAUzyVLdSs5E68NfyoUuvpuGt4tVj289GAhgWi8eaPNGIwGEWPH0U/v8kLEBPS9VsAFiHb5/XZ8Fm+oEXL8L69aMw6z198v2qqQOAM8NQSgAtbgcUAgNocTugjI2FfvH8+Pj4+TfWn6zi+PUG77AfULqJBsbHQj+xrbD96w2DwnZA6ScaGBoLPX3y3Yng28eyR8kmtq83DAzLAdUw0cDQWOivKl9bAYHBKJYDqmGigcmhlOU3NkBgMIrdgGqaaIDAAFpcEbh6ooHJsdCSme3ZSAgMRrEbUE0TDYzUgWfTR9EArMVsqht5DQCr0TDRwEw30teijfv4+Fj8YD4/gDkaJhoYGshx8kJ1Vh3/zXY3MMCw0E80GN5QSoANAoEBPAaBATzGuMDW+4EBhkqXDzfTnKNf6AcGozgUUH0IzNMJYVi4FFA8nRBgRdwOKAQG0OJ2QLEiB4AW+wGlk4sVOQC02A4ovVysyAGgxfqKHFq5WJEDQIv1FTm0cjGhH0CLGxP6y28UwxMYYED0IbBbK3IADIgmuViRA8BlGuRiRQ4Ap9HLxYocAG6jlWt4QykBNghDAj+NepjntnuBAYbIrK5pyZDAsbhPbY/Dst1tB4PDhYBaPK7r3DFVhFbmupABu3C9YUC4EFCzR3+ryYJNCTyXDWRf28+AnbjeMCAcCKjF47+G/1XuMtaI9VQ+usV+BuzC9YYh4UBAiRpwTS3YmMAiC3YhA3bhesOQsB9QMvetyYLNdSM9DXN5BzJgB643DAr7ATVT9dPKLNicwPPpcxcyYAeuNwwK6wG1eCynMJxWNkQbHMhhfSawwvr1hmFhPaBm0QjKyizYoMDzYxcyYPvXG4aF7YBaPItW0pkff1ney1BKAI9BYACPMSjwq2fHx8dfOlGMBhgWtXKZE/hZtPQl84EBDFMvlzGBv1YLB7AiB4BpNHKZEjhZuoc1sQDMopPLlMDJenmsSglgFp1c5nJgVwS23W0HA8N+QOnkMlgH/ir6abkVy/71hkHhQEBp5DIm8MmL6ZPvT757Nv1KPMbFYmeSA9cbhoQDAaWRy1wdOIfFYrQD1xuGhP2A0sllrA78PEfFoM2+sH+9YVDYDyidXMMbSmn/esOgcDugEBhAi9sBhcAAWtwOKAQG0OJ2QA1PYIANAoEBPAaBATwGgQE8BoEBPAaBATwGgQE8ZngCu91tB97hdkAhMIAWtwMKgQG0uB1QCAygxe2AQmAALW4HFAIDaHE7oBAYQIvbAYXAAFrcDigEBtDidkANT2CADQKBATwGgQE8BoEBPAaBATwGgQE8BoEBPGZ4ArvdbQfe4XZAITCAFrcDCoEBtLgdUAgMoMXtgEJgAC1uBxQCA2hxO6AQGECL2wGFwABa3A4oBAbQ4nZADU9ggA0CgQE8BoEBPAaBATwGgQE8BoEBPAaBATxmeAK73W0H3uF2QCEwgBa3AwqBAbS4HVAIDKDF7YBCYAAtbgcUAgNocTugEBhAi9sBhcAAWtwOKAQG0OJ2QA1PYIANAoEBPAaBATwGgQE8BoEBPAaBATwGgQE8ZngCu91tB97hdkAhMIAWtwMKgQG0uB1QCAygxe2AQmAALW4HFAIDaHE7oBAYQIvbAYXAAFrcDigEBtDidkANT2CADQKBATwGgQE8BoEBPAaBATwGgQE8BoEBPGZ4ArvdbQfe4XZAITCAFrcDCoEBtLgdUAgMoMXtgEJgAC1uBxQCA2hxO6AQGECL2wF1NoFdZjq1nQIYFK4HFAIDaHA9oFYXuEucK56ToCZIUBOWEoTAAhLUBAlqAoEtQoKaIEFNILBFSFATJKgJBLYICWqCBDWBwBYhQU2QoCYQ2CIkqAkS1AQCW4QENUGCmkBgi5CgJkhQEwhsERLUBAlqAoEtQoKaIEFNILBFSFATJKgJBLYICWqCBDWxSQIDgBkQGMBjEBjAYxAYwGMQGMBjEBjAYxAYwGMQGMBjEBjAYxAYwGP6E/jhXhDs3NJv6ZXS6U/ujILgjRu20lNzPcZbty2kRVLxJ/swCLY+PrKUnooEPbhs9U8WMjl3L/u276DuTeCJWqD6qm5Lr5RO/2pXbbngSoKirdYErv2TnbdkcDlBY7sxFPIgyAnce1D3JfB8FNwQv20ajeUtvVI+/Th498/hllGw70iCBLPAmsBVf7KtG/JG58oVmgVbt8SfzNo9bvFZkBO4/6DuS+CJuilN0ntTeUuvlE5/uqsylomlLLjyesxHO3u2orOcoLEyd+bMFbIcQ8v5XrCzlxW4/wT1JPDiQIXhfBQXv8pbeqX+9PORlfCsTNDi4NzvDiwJXE5QfIuzRMUVSnyxUyRYjrc+/uIgI7CFoO5NYPVrnu7Gv255S6/Un97S7bwyQeOt2wt7AhcTFN7aFp/Ya8SquEJhmf7WcvlwZCWEQv50lKRKYiGoexI4vnmnv255S6/Unn5uKRqqEiRyFmsClxM0C36ya7ERq+oKhWXYkB1r7fSFALIQ1AicP/3cVhtWRYJkXdMpgQOV4dkpo1T9yX4/EgJvWexHQmCnBH4gWxFtUE6Qqkg5JbDVZouKP9kk2DmUdxRLdeDlxgjsRx14cSfYshUK5QRNkqc7O3KFYnEt3XPrY8jSHSWXhtyb4dWBvWiFXhzIG7odygmyLnAxQdYFrmsWt5SgZencw22Fdq8Pr3z60N93LXaT1FwPa0XocoLCCyTLJ7YyvIque6uZgCR/8xhsP7API7GsDQeoS5DEnsCVA59uWKxyVg2e2/l0ufzDnsW/XF7g4Y7Eyg4SjW6c7oyFlgk63Y1LrJZu5+UrJLAncEWC7jgzWlwlKCwTWB2cvcxWe+0EtY3ZSHF4OjMbSSZoFlgWuOIKLa0KXJEgy5N/Sgla/EokyN70qJLAw52NBADmQWAAj0FgAI9BYACPQWAAj0FgAI9BYACPQWAAj0HgoSFH+M//4e2f/Xuy6eHPr6SDU2bRMKHTXVsDqsAgCDw05DrS81FmDpN4kwh8uhuP85tZnEULpkDggaEy2Plo63Li5yQzPPR0Lxmoa3MSHpgCgYdFZGUo8L/Gcw4WB1sfxQKLzDgZaW9reVgwCAIPi2hOZCjwv+0m0p7/TAm8uBMEO3uZ+b325kmAIRDYa0JRb7/aS5d6TZeE2Po01jMsVE+UwOHWf14cZNdUIAv2HQT2GlFUlgszBjuyPjuLyspC7HiBgnGwHwv8s8NlVmBbS+iCORDYa0SdVj0eSCk6juwUAkcLzYgF1iZpK3RW4HiNHPAXBPaaUOBzh9GL/YyRQuCoOC2aqmoEDn2nDO05COw182SRdelispKHEDjKjsUTyeoEnthcjAZMgMBeM0+erCldTN7KF7JCLJ2uE3hmZ8VaMAcCe03aDCVdTISUAkdLfYXuIvBgQWCv0QosS8+yHI3AgwWBvUZbhBb9vKolC4EHCwJ7TfowxYpGLJE//0Zm0TRiDRYE9pp51P8bPTkw140k334kO4roRhosCOw1YiCHeCDbg5FSMTYyKkuLeUj7y1qBGcjhPwjsNaGoH2UfJ5EdSinfqkpujcAMpfQfBPYaIWr2YR6ZyQzi5+muMrdGYCYz+A8Ce03aCh2xipNMJxwACOw1JYFXWWaDCf0DAIG9piTwClaypM4QQGCvKQusFrVrw8zao5nBHAjsNRUCn+62G5zBsrKDAIEBPAaBATwGgQE8BoEBPAaBATwGgQE8BoEBPAaBATwGgQE8BoEBPAaBATwGgQE8BoEBPAaBATwGgQE8BoEBPAaBATwGgQE8BoEBPAaBATwGgQE8RiPw6W4Qc+XjioUOy/szWypXJx7HO1nPFMAI7QQOgp3yGuDl/Q0Cp7sRGMAIbQWuELK8v0Fg8SxMBAYwSIPAyrRXe0FQXu+/vD/dUsmsumANAGellcBCPSGoyEL3NfvzAudyaPEYnjFZL4BZWgssDNQJLPbrBV4cBMGPwyO8fdjFLwKwibQS+I+7qvBbJ3C8Xy9wWgW+0cVvArCBtG3EqnhgVnl/ZktFZXeW7OS50gBmaCnwzq02+/UC//5KsBOWnh9U3w4AYHVadyO922J/XuBSI1bEOPcOAM5OuzrwXpCt/Nbub2iFjphRhgYwRLtWaPGyVOwt728ncL4pDADOTjuBRQ+QTuBov3Ygx+J/XhnJmjE5MIApOsyBCwjJZT5MHRjAFO2GUh5UtSuX9+uHUk7Eh45kKzQDsgCM0LoVunooZX6/XmCRBZcqxJvFWNuBJvfOMh3l6grHVzR8py5ceCHFYdLrf+XGUbQ9e5ctvE15cDn8zj829eStPlu0+NtEcLfuktYCC3F1Au8vGyczvNpNXd9IZk1zPa7Gw12uxlsyAkyCOoGDYOe2+kTu0k6qr/SknYErz0DnnREAACAASURBVBat+zoCd0k7gd94R45frhU42t8g8HLxq/De/0bV4gAbQSie5t4V7Z1l/BhnBZgFGoHVnvDvk83hC2/T87QaSLPybNE8zB3tB5bU6Y9qoQp7Z6mPUZ1DCTBJNmcFlvtkN/yFZekOUX3DEEdtM6tz5dmieZg72g8I3B1hDJ//4k6YE6nySWE6Zc1eIfCPR3GN5UoksHCoVmDppFR1krdmUiVRRuCHH4bHfPtWkpz/CM+yE88Va5otmvlYvhywrPhloSsQuDvCuN/ZS2v9YahnM8SavULgn+xKxSbBuV8ogaUll2sFll+K7M82EM4q2gtVDVicK2lUfPcok5zkC02zRTMfqxCYuaM9gcDdMctHdtmuqr1i8/vSUOHpZ4nAO7eqGrEy/fBxLTUzyK3wVpIKnDQTy6/Gybma/bJutmjmYxUCM3e0JxC4O4QTWzeWi7HyYpJvPKrZKzNT2X4cqnEhylpPP7xxVNkKXRgpJ35mFCu8TTfGxp4/VH34+5HAWdlWnS1a/t2TWwV0BwJ3R1ywjcapjfNxX7NXbpY9SuE/+/GHBC0Fzpyjsr0q3hgPiIty71lRy1Vni+Zh7mhPIHB3JIO+pStFm2r2CpH2Q1XOH43D/SsKLI6V9WVcoU90prjUHX8oeyZJ02zRqo+VR+gwbrZjELg7kkrvpEbgqr1S4PDdud8JTbsV+GrmuLOgUF9umi2a+ZhGYGaudAwCd0cSvFKRYvjX7FUihdv+aRR6JtqCWgicZKedCKydq9IgMHNHOwaBu+PsReioDWi/rcBJRr1WETqfVa44W7RwEuaO9gQCd0eslYr/CoGr9iqBZb4WRn5LgceZm0FLgSsasWoFbjNbtHwS5o72AQJ3R9QzE3cUVbRCV+ydpYMsQmdaCfzqk7hZaZVW6Ew3UjQGu07gdrNF8zB3tCcQuDsKQzUq+oEr9kYiTZQzTQIXap+r9AOnsztjn8sCp6w6Fpq5oz2BwN0hnPgoCX8hY2EkVtXeWZIhxmMo208nLI7WLLxVJNlyOpQyTo5G4BazRfNs/NzRnkDg7pBOPNyLpyuUx0JX7U0nDhQzvVqBt96+FeXshXtE4a2iNJnht2lysp9bfbZo4TybPXe0LxC4O4pOlGYjafbqiASuoM1sJBgUCNwdRUXno6xP+r066gUeF+8JFGCHDgJ3R1FRMb6qfn37/F4dtQLLEZi1b2GIIHB3lKqVs+yoJP1eHbUCF47Q+oDgLwjcHeVRSNlVKfV7ddQJ3HZVShgQCAzgMQgM4DEIDOAxCAzgMQgM4DEIDOAxCAzgMQgM4DEIDOAxCAzgMQgM4DEIDOAxCAzgMQgM4DEIDOAxCAzgMQgM4DEIDOAxCAzgMQgM4DEIDOAxCAzgMfUCBwDgBmcQ2HaS9UyntlMAg8L1gDqLwPXW22c6tZ0CGBRuBxQCA2hxO6AQGECL2wGFwABa3A4oBAbQ4nZAITCAFrcDCoEBtLgdUMMTGGCDQGAAj0FgAI9BYACPQWAAj0FgAI9BYACPGZ7AbnfbgXe4HVAIDKDF7YBCYOiaWTr5/OpyOQ5/7Bc/ce7ecvLGzw6jt69+fjn+xCTcE7I4uJA50JUbR+k+sfGC7vQP94Jg51Z2y4PLQfDGDfly8atRELx9WHqdwe2AQmDomkaB56NwwyQIzksvQ1uTTzwIqgSOPplu1Ak8Sc4cM063iFMFUYKyr7O4HVAIDF0zy9oT6lM0ZDkWPoaibd2Wb+ejyKLFZ0FBYHmgRZinSoNn6mMzncDhwW6IG0F0bPnxrVvhlpHYMgt2DsVpxFmyr7O4HVAIDF3TJLDMgEOBfzxSn5uc+6n8zHwv2NmrEHi5PN2N8szIY43AE/WdSZqGzJbFgfJ6HP7Ivs7hdkAhMHRNhcCLg3O/uxNXOMdS0knw/kFcMlaSj7c+/uKgUuDY2Yn8XCpwXApOSuOJlvNRvCUVOLmRxB8qvla4HVAIDF1TLfAvhGdCltPdSMarE+lOmCErgf90JD5XKfDprvRxPlKbdQKrA5zuJiXj+UgUoR+Okg2LO2kWnn0d4XZAITB0Tdr2JJyJBA7CquliLGyZJUXauSxDT87dS4rZdQJH25XHuiJ0ZHpyIEFYNA/ZiTJaUeN+/6j8OsHtgBqewOAa1QILF2W+GJVlQ4FlnVa42lZgVd5dVeDfj2Tmr/qRlvMrV4LgnaPSa09AYOiayiJ02mIUtRqJqql4KZq02gqsvruiwBPR2hwWoTN14HGmDD3W9yq7BgJD12gEFrlvRmDRLySGZzQKHHtZELhNHTjekmnWytaQc689AIGha9rnwKe7F6SqjQLHzrYQuNgKXVWornvtAQgMXVMpcFUdWPQo/UZ0CjcJfLqrtGyuA5f7gePvCqXj3Lb42sRv3RMIDF1TLfDWLfFvrhVavL6SNHQJKgUWI7GUss2t0BUjscbBzqfL5R/21LjOqD5ceO0PCAxdkxkLHfoWF6Evx83SaT+wHGIl3tQKXCghF/uBq8iMhVaZb1zOFseIX18ovPaH4QnsdrfdJlIt8Kd34h6beCTWVSmRHIOlF/jtW9GR1cgPvcCZ2UhR6XnxKzEb6WNVExYzkLIzk6LXGdwOKASGfsk1Yknmo8ZCqxK4vLV5LPT6uB1QCAz9UhZYzUbSUi1wm9lI6+N2QCEw9IucD5wXWE1H0lEpcLv5wGvjdkAhMPRLhcByRQ4tlQK3XJFjXdwOKAQGD6guQveD2wGFwABa3A4oBAbQ4nZAITCAFrcDangCA2wQCAzgMQgM4DEIDOAxCAzgMQgM4DEIDOAxwxPY7W478A63AwqBAbS4HVAIDKDF7YBCYAAtbgcUAgNocTugEBhAi9sBhcAAWtwOKAQG0OJ2QCEwgBa3A2p4AgNsEAgM4DEIDOAxCAzgMQgM4DEIDOAxCAzgMcMT2O1uO/AOtwMKgQG0uB1QCAygxe2AQmAALW4HFAIDaHE7oBAYQIvbAYXAAFrWDahtgZmkVIDAAFrWDKjtCEOpKYLAAFoQGGBj2d7u1mAEBugQBAbwGAQG8BgEBvAZGrEA/OUiAgP4y0Vl8MWLHR1/eALTDwxGWS+gLsaYSk4BBAbQslZAde0vAgPoQeB+QWAwigGBf7jttMCnx381lp71QWAwyvoC/9329j1jySlgRODp9NH3xlK0LggMRlknoKL8132Bp9MvXxtL03ogMBhlTYH//gfbP/iB6wL/ZfF4Ov3KWKLWAoHBKGsK/F+3f3hxDYFPj3M8Ke43JPByOQtz4ScnZ02mQRAYjLJGQIkC9N+H/68h8OLZNMtfivuNCbxcvBAnePLN966UpQEsE/chrVWE/lpbtjUncMirZ5U3CYDNxIjAy6fTl/U7jQoccvLt8y/bJw1gwCSjOG6uJfDisSZPNC0wAEQYEnj57fP6LBiBATrClMA6hjeUEsAN0nHQCAzgHV4J/OrF8+Pj4+ff2O9Doh8YjHLmgDImsBxecfLi+ZcV4yzMCDx/nPQ0P7GtMAKDUc4aUJmZhGsJLIdILefSrnKPsBGBw4M/+e5E8O3j6SPLBiMwGMWAwOsQynX8ePr88aPvT0KVS83RRgR+mrkzPLU9JhqBwSiWBX46/U8xGkuqO5uWJu4a70ay3qeEwGCUMwaUIX+VT5FVFXIhMICW4Qu8eJwpmlfk8v2CwGAUuwIruWaqaWneTRFaHD5akWNRVc/uFwQGo5wtoIytZvf19NF3306PhbqhzP9Z3G2mG+lr0cR9fHwsfpRO0TMIDEaxLLBYK2P66GWo2LHoTipiaCDHyQvVE3z8N9vdwAAuYEzg5fKVHB8lpttXTPRjKCWAeQz6qweBAczjncDujIUGsI95gU/LC9oJhjcWGsA6HWTANQMshjcWGsA65gROlpV9LPt5OllW1q2x0AC2uWhQ4LRw2/GyslVvbEA/MBjlDAFlsgS9eDz9RvzssAiNwDBgLAsshkmJAZQdCsxYaBgwqweU6SasuWhY6rIRi7HQMFzsCywHQXcpMGOhYbg4ILB4QtJxlwK7NBYagcEoKwdUJ6OwZjXPLBreUEoEBqO4IfDyVfUzixAYQMuqAWWwE7gFCAyg5cwCd5OcAsYFtt4PDGCVDgXuaE2spnMAbA5dZsB9CLw8sd4ODWCPTkvQZbmGVwcGsEi/TVgIDGCUnv1lRQ4Ak3QhsE4uVuQAMEcH/urlGt6KHPQDg1FWCijzAjfINbwVORAYjLJKQHXQhNUgFxP6AbScSWBjZ2+SC4EBtKwQUB1kwH0IzIocMGDOIrC5szfJxYocAFrsCtwkFytyAGhpH1DdDOLQy8WKHABabAusl2t4QykRGIzSOqD6HgYtGZ7AAHaw4S8CA5jBSgaMwABmsOIvAgMYwU4GjMAARrDjLwIDmMBSBozAACaw5O8ABaYfGIzSKqBsZcDGBE7mSTAbCYbFagJ3kQKdXAgMoKVNQHWbAfchcLpire11oREYjLKSwN0kQSMXdWAALS0CyloNGIEBGlhF4B6SU8DYutDPnx0fP3n+nZFErQUCg1GaA8piBmx+XejKpxD3CQKDUVYQuI/kFDC0LvSjb05OZtOvxNK1th9OiMBglMaAspkBm1oXWi71MRMr9jy1vqYOQK9024V0nONJcb/JZWVPxZp5c9urUgL0SrcZ8OLZNEun60LLn9YHcgD0StcF6K+1zzoxuS70TLg7R2DYJLqvAT/VrdRspA78tXzo0qtpeKt49dj2s5EAeqSHFqzFY02eaETgMAuePgr/fxIWoKelajbAcOmjCfrb5/VZsJl+4MWLsH79KMx6T598v2rqAPzFaheSgKGUAFq0AYXAxkFgMIouoKz7a24s9Ivnx8fHz7+x/mQVBAaztBK40xToJhoYHwv9xLbCCAxG0QRULxmwfqKBobHQ0yffnQi+fSx7lGyCwGCU+oDqx1/9RANDY6G/qnxtBQQGo1gWuGGigcmhlOU3NkBgMEptQPXib9NEAwQG0FIXUBd7Frh6ooHJsdCSme3ZSAgMRmkWuMuzN000MFIHnk0fRQOwFrOpbuQ1wFDoqwu4YaKBmW6kr0Ub9/HxsfjBfH7YAPopQC8bJxoYGshx8kJ1Vh3/zXY3MEAf9DcGSz/RYHhDKQG6x/4YyggEBliZ3grQjSAwwMo44695ga33AwN0jS1/u3y4meYc/UI/MBilHFDWCtB9CMzTCWFY6ATuOy08nRBgRUoB5U4FeInAAA0UA8qdFmgBK3IAaCkElAV/dXKxIgeAllqBezq/Xi5W5ADQkg+o3jPgBrlYkQNASy6g+i9AN8jFhH4ALdmA6t/fJrmGJzBAZ/TfgNWHwG6tyAHQFRZaoJvkYkUOgJZY6QFukIsVOQDaYWkEh14uVuQAaIW1EVhauYY3lBKgCy5aE1iLIYGfRj3Mc9u9wADdYNffWV3TkiGBY3Gf2h6HRT8wGEYFlF1/F4/rOndMFaGVuS5kwAgMRpEBZbn8PHv0t5os2JTAc9lA9rX9DBiBwSwioCz7u3j81/C/yl3GGrGeyke32M+AERjMEgaU7fYrUQOuqQUbE1hkwS5kwAgMZplObTdAy9y3Jgs21430NMzlHciAERjMkhPYSgpmqn5amQWbE3g+fe5CBozAYJaswFYSsHgspzCcVjZEGxzIYX0msAKBwSQXMwLbScEsGkFZmQUbFHh+7EIGjMBgkosZge2kYPEsWklnfvxleS9DKQHqsd1+1QgCA9TivL8mBX717Pj4+EsnitEAJnDH31q5zAn8LFr6kvnAMBDc8bdeLmMCf60WDmBFDhgK7virkcuUwMnSPayJBcPAHX91cpkSOFkvj1UpYRC4469WLnM5sCsC0w8MBkjttR9QOrkM1oG/in5absWyf73Be7LZrwMBpZHLmMAnL6ZPvj/57tn0K/EYF4udSQ5cb/Cci44JrJHLXB04h8VitAPXG/wm568DAaWTy1gd+HmOikGbfWH/eoPf5P11IKB0cg1vKKX96w1eU/DX8YBCYIAMF4v+Oh5QCAyQUvbX8YBCYICEsr6uB9TwBAY4IxXZr/MgMIDCR38RGEBy0Ut/ERhA4Km/CAyw9LT4LEBgAF+z3yUCA1z02N8BCux2tx04R5O+bgcUAsNG05z9uh1QCAybTIvSs9sBhcCwubSq/bodUAgMm0pR35rWK7cDCoFhM2mpr+sBhcCwkbTvO3I7oBAYNpDW2e/S9YBCYNg4VtHX9YAansAAWkr6+jX0qgACw0YxLH0RGDaJsr2e64vAsDkMUF8Ehk2hQt8B+IvAsBEMVF8Ehg2gyt5h6DtEgd3utttU7l/a3v7RoXz5cltxW7wON+9HW29nPx5tDTd/kH7jR/tHcuO1N49WOPW6+rodUAgMPXBXGSitvJ8K/PrSW0eRq9feyn6+WuDtbWXuCgJX2rta7ut2QCEwdM996e7nl2QuezfNa+VLqeP97Xv5L+QF/kC++fy6MritwNX2rlp4djugEBi656byMcxw5Zt76fZ70T/XPsh9oVrg8GNyezuBjdi7dD2gEBi651rk7E1hXqawnAh8N58B1wr8clt8uYXAZjJfidsBhcDQPbFxwtWX2+/dvbS9/S9iS1yEfn1pP/+FOoHVkZoErrH3jA3PbgcUAkP33FTV3teXQoHvZ9qj4kasu0Uj7yfNVgWBVXlbJ3CdvWfuN3I7oBAYuif08ZeyEUuWlt87lK+FlK+vi+atl+H/9y9tv3mY/cKZBDZu79L1gEJg6IGbKtO9nlZ1X19KLbz5liwzZyrCtUVojcC18q45aMPtgBqewOAiv5bV3psZ89LGaDGGQ+zJeLpyHbgre50HgaE3VDdSRCqwaJYWTmZ2r9QKrZF34PYuERj64G48BuuDpEvp5XZs4f24VNxC4GuyNSwjsE7eDdAXgaEPXm5vH4bFaNGGFcr8pmrEinuO5BiOVkXoz6/LDDgWWC/vJti7RGDohZvp/IXl9aR1WaKarhoasUpjoRvk3RB7lwgM/SDGbrx3mL5+85fRjngMR7EbqXI2kvrSxe0fYG8MAoNHNGW8G2bvcogCu91tB2fGlrxuBxQCg/u0cLe7rNftgEJgcJlW6nZbbnY7oBAYHKWlu51Xet0OKAR2g8+vZ1pmE+LFK9K915IelXvFDw+Gtub2IK/AWEDd7+JvhsBOcD/fN5puvV3YO2yBV1C3v+ZmUwH1eSd/MwR2gddyXNLn27mVGWX35+3qvTe394vH8JqVzO1RXoGhgPp1NzddBHaB+yrvvZ/Lgl9fevO6dLa8934xr/aWVc210M9rJKBeX89NpjQHArtAsmJFdprNze17antpb/5zXrK6uFbkFRgJqLtiMiUCD5X4T3st8ycWDVixwIW9/hagz+atNXfN8eej3HKc5kBgF8gu+hYhRwPfzM2ei/emM/F84eze+q9uCgIPlrLAauZ6tcC+ZMBraTsodRUIPFhKAke13EqB3a4Br23tENVVIPBgKdVyM6sy3ivuda4J2oyzQ1ZXgcCDpdTOXBA4t/dmvrfYBkaVHb65EQg8WCr7gZexq4W9qz1c0wxdGLs55kYgcCt87AeuHokVC5zfq5q3OqVLXf0T11hAIXArfBQ4Nxb6WqrxzdJYaNNV4H5c9dHbBATuFy8Fzs5GKgucm6t0/0ydSP2L6ru3CQjcL34KvD62Da3E9kUxgdsBhcAeUGHGNnhEh7GBwP1jImuzHZKwCh0GEwKvhgn5TGA7JGEVOgzIIQicD+3p1I5S/WI7JGEVOgx+5wReO7QRGFyjQ18cE9i2F95gOyRhFTrzxTWBbWvhD7ZDElahK1+WCOwrtkMSVqErX5YI7AtdXXHwHAS2QlcXEDYNBF6Zrn55gNVxS+AzG9xZggCcxjGBDeD+UErwCrcDCoEBtLgdUAgMoMXtgEJgAC1uBxQCA2hxO6AQGECL2wGFwABa3A6oswnsMtOp7RTAoHA9oBAYQIPrAbW6wF3iXPGcBDVBgpqwlCAEFpCgJkhQEwhsERLUBAlqAoEtQoKaIEFNILBFSFATJKgJBLYICWqCBDWBwBYhQU2QoCYQ2CIkqAkS1AQCW4QENUGCmkBgi5CgJkhQEwhsERLUBAlqAoEtQoKaIEFNILBFSFATJKiJTRIYAMyAwAAeg8AAHoPAAB6DwAAeg8AAHoPAAB6DwAAeg8AAHoPAAB7Tn8AP94Jg55Z+S6+UTn9yZxQEb9ywlZ6a6zHeum0hLZKKP9mHQbD18ZGl9FQk6MFlq3+ykMm5e9m3fQd1bwJP1ALVV3VbeqV0+le7assFVxIUbbUmcO2f7Lwlg8sJGtuNoZAHQU7g3oO6L4Hno+CG+G3TaCxv6ZXy6cfBu38Ot4yCfUcSJJgF1gSu+pNt3ZA3Oleu0CzYuiX+ZNbucYvPgpzA/Qd1XwJP1E1pkt6bylt6pXT6012VsUwsZcGV12M+2tmzFZ3lBI2VuTNnrpDlGFrO94KdvazA/SeoJ4EXByoM56O4+FXe0iv1p5+PrIRnZYIWB+d+d2BJ4HKC4lucJSquUOKLnSLBcrz18RcHGYEtBHVvAqtf83Q3/nXLW3ql/vSWbueVCRpv3V7YE7iYoPDWtvjEXiNWxRUKy/S3lsuHIyshFPKnoyRVEgtB3ZPA8c07/XXLW3ql9vRzS9FQlSCRs1gTuJygWfCTXYuNWFVXKCzDhuxYa6cvBJCFoEbg/OnnttqwKhIk65pOCRyoDM9OGaXqT/b7kRB4y2I/EgI7JfAD2Ypog3KCVEXKKYGtNltU/Mkmwc6hvKNYqgMvN0ZgP+rAizvBlq1QKCdokjzd2ZErFItr6Z5bH0OW7ii5NOTeDK8O7EUr9OJA3tDtUE6QdYGLCbIucF2zuKUELUvnHm4rtHt9eOXTh/6+a7GbpOZ6WCtClxMUXiBZPrGV4VV03VvNBCT5m8dg+4F9GIllbThAXYIk9gSuHPh0w2KVs2rw3M6ny+Uf9iz+5fICD3ckVnaQaHTjdGcstEzQ6W5cYrV0Oy9fIYE9gSsSdMeZ0eIqQWGZwOrg7GW22msnqG3MRorD05nZSDJBs8CywBVXaGlV4IoEWZ78U0rQ4lciQfamR5UEHu5sJAAwDwIDeAwCA3gMAgN4DAIDeAwCA3gMAgN4DAIDeAwCDwA5qH/+D2//7N+TTQ9/fiUdjzKLRgapwf/x8KUguCJW8VM7bA2ugjVB4AEgl46ejzLTlsSbRODT3RqB0zF/M4szamEdENh/VAY7H21dTjScZEaEnu4FRYHV28UfP4n32JyQB+uAwN4TyRcK/K/xNIPFwdZHscAiM64WeJlZNt7WUrGwJgjsPdE0yFDgf9tNpD3/mRJ4cScIdvZqBQ5fX4he2JszAWuAwL4Rinr71V66umu6CsTWpwdJfnp1ogQOt/5zYmxZ4GSdK2vr2cN6ILBviKKyXIsx2JHV1llUVhZix2sSjIP9WOCfHS51Ap/Gz0mxtZwurAcC+4ao06onAilFx5GOQuBobRmxptokbYXWCZy2aB3QEO0jCOwbocDnDqMX+xnxhMBRcVq0SLUUOPT/QuEF+AQC+8Y8WVddKpcs3iEEjrJj8RCylQWe2FyYBs4KAvvGPHmYplQueStfyAqxdHplgWd2Vq+F9UBg30hbm6RyiXdS4Gh1r9DTVevACOwnCOwbWoFl6VmWo1sKnLRCI7CfILBvaIvQojtXtWS1FDjVFoG9BIF9I31+YkUjlsiffyOz6HYCJyOxaMTyFAT2jXnU/xsNosp1I8m3H0kn2wk8SZ8hQDeSlyCwb4iBHOIZbA9GyrhYvKgsLeYh7S9bCbz444fpMwQYyOEnCOwboagfZZ8gkR1KKd+quqxW4IStf04PSxXYRxDYN4So2ed3ZCYziJ+nu8rcNgJfyTyThMkMfoLAvpG2Qke0Vy9+nm4FTCf0FAT2jZLA7VfT0AjMhH5PQWDfKAncXr56gVlSx1cQ2DfKAqtF7VpQL/AsOzwaPAKBfaNCYE3RuN3nWFbWWxAYwGMQGMBjEBjAYxAYwGMQGMBjEBjAYxAYwGMQGMBjEBjAYxAYwGMQGMBjEBjAYxAYwGMQGMBjEBjAYxAYwGMQGMBjEBjAYxAYwGMQGMBjEBjAYxoEPvnV5SAI3vi4ejHDV5+MguDtW9G7cfzEjqvL5eKTIHhHfmmSX7D0dDd5ntZEPcVHbIme9HFDnWYWBJ09JiBz/tW/s/jVLztIEsDZ0Qs8SR6CdaNi72yUCLvMing1klmsYXq6m18xXCdwEOxIb10V+OEeD/ADx9AKPE7Vqoj6+Si3L/s2fH1VPXq2+NQAvcDqwXquCRwhfkEEBrfQCSzy361bYcnxTqxWjrHc+2ov1S5xNXy9L/4vP3W2WmC55Y/hkeQhEBigJRqBRaxH2k5UNpsLYfGUSqFbvHGcMUPIG27fD3cWngWgEVgeUeXaeYEXd0ZxPTxOU5K2xQNRSY/r4ZlPlt69+lDUBOKzLWTlfuud3+ZSlz1amIrz/yEe43movjOJH8qLyOAOGoFnacH59L+98+/LgsCxCtFPYd+PRZvW4TKTA0+K2Z1O4PiMBYHjsvlOlM+L20b8HPrTvajsfeGo+MnCu6jC/n+qsyXfy6Uvd7TwTDt7suiBwOAsGoHHpZJsSeA4B76QrQLfWCZ14NPdYllYK3B0yLzAaR1ZZuYyVdE5sw+bv1r8ZN27uJHt/aPlq4PcmfJHmyUvERicpV5gEc7aZ06OZeO0jPpQkVkS/EKJqBW6/ODLXJNVUWBxLHWojFaq+L74LMpzhT7/10Fa7xa55cORfJ//ZPld9EmlpDzD/Mo/HaZpyx9tFt2MkhQiLriHXmDtQ+9SZcXnfn8lrC0ulw/Uu6gfeFyK+JUFjqva8c84J5QHHkdJnOz8338ufLL8Tn5yluSp75Z+t9zR4sL6EoHBYdYQOO0lzn5unMm3S01YZxBY7N6PziaPpgq6F+LPX1hWf7L8LunsuhodpVyO5gAAHhRJREFUY+fjPxd/4UyBIW0CQGBwljWK0HJkQ7Dz27zoWftEE9Z8LzcKRFsHrhI4rVvHyRFb1P58n1D+k/l3ySejF/EYlK3MGLNCD9MszuYRGNylXSPW4uCdW3UfixuzIjJhLpqwlEf7uU+v1IhVFngSBHkbKz+pF1h2X0t2knsUAoN/tOtGilt9q4gKpf/zyuhC9K3YPtGENQnOhVl0vpy7UjdSUhTOni/6QE0RuubdhTS1gsX/+2GQFMaXpaNlUoHA4CytBnLIKmMpdh9cuSx2q5wqKXBn6sCiCWsclonHmSK2VuBxxUCOglZJX0/cp6Rao0Vrcv6T5XeqgSrIZrN/2M0W/3NHQ2DwgTZDKV8dBFXtWSq/FGEt9kX9NA+y2fa5e6E4QuBzVeXUosCvPgmqhlKKA78vOndUKV68vRFrOFMJE+Xh8Bv5T5bfieSpbqTlH//1H+QZxlnL80crCSybrle7ugAd03Yyg+o2HRWLpQqxLR0FEds6USMm2uTA+Vpu3UCOOBs8fxQPuswMvQhPkf9k7bvwrVBVdHo9zP1C+aNVChzXrlvlxGNtK/446T3PnCYtHoTvkuJPfiRKNOtycVAsmVRXcuTo0H/Udicsc9fnimrYy16xuupTyokYtrpzK3on55luvZtr5C9MPgUztJxOqOb5FUI3P53w1W5G9aVqwlq2rAPnT1MzlFL23KalbBXWubao3Cer3537qTx/2gNWOZRy515FEVrdz9oLPNNOm5hlhntdjbdk0jMJ6gSOL9MkP1Cu8Dbd3MrA3G1UXsyVBI6vtSqhJG382QTlowUM0WpC/9u31A28GLpyfsA78VgmOT8gnfs/k3HXrhVa/bnj0xQnM5zcuSz3LjMNa+PoqGr6QbwUQOaTpXeihL717lE05+JEM5lBHa0ssJyV9Y9tBQ7F08ypivbOMn6Ms/E9CzQCqz1hOrI5fOFtep6G3vxl8jvmhV1F4HxhLO0AyHRDFiafgiG6W1InGoVV6AfeHKqFKuydpXEeFeBVeE/S8M8InJ91WbhDVN8wim2AdaQ31qgJYKWJl+LXuCHLYHFzyPtHyYQTRWHyKRiCNbFMIaYffiFqglGRZJyL/5q9IvJ/PIrzrStBrpO6WuBk1qUwJOvmpErVjMAPPwySOmg6VzL6XL4zr1bgcjkgOvTlC8ukTBW15otTJwcoTj4FQyCwKeLph5Fd8XwJ/V4h8E92AxX9534RpK1ll2sFTuoRs3xuNqvI3CZJZTRpoXv3KJOc5Av5wxe691JqBI4YJzlwLHDd5FMwBQKbYpaP7LJdVXvF5velocLTzxKBd25VNWLlB6wVx7iUhrwsswKnPQoXMsm5mv2yevPHzNFXE/hBNEhG5LKqCJ3vPsxMPgVTILAphBNieuU4iNu5s1Xgmr0yM5Xtx2GEX4iy1tMPbxxVtkLnh4zny6ilt+nG2Njzh6pLf3+ZmSsZkTPz/FF+SyvjZCuVXFdB9bYH+abI/ORTMAUCmyIu2J6qppxxPu5r9srNs6hrej8zeLWtwJlzVLZXxRvjUWbpcPP8Z3O9VLcKW1oJHN0iJA9GRX8Lk0/BFAhsiqTbSbpStKlmrxyHGqoiRrts3V5R4GQCc8S4wo3oTOmMk3Gy/EIut853I727rBFYU4TOdGPfiT+RPUXl5FNYFwQ2RVLpndQIXLVXChy+O/e7A7mASZcCX80cN51qFZGpA++pfavXgePVT1SnUrKGSkzV5FNYFwQ2RZLHTnLzF/V7lUjhtn8ahZ6lU6W0AifZaScCx6X8M7RCV62FUnEAGrEMgsCmOHsROip97rcVODsc7exF6Pyoj3IGv0KHz+Lnqh9YHTz5YlV6sr8iGACBTRFrpeK/QuCqvUpgma+FQrUUeJy5GbQUuKIRq1ZgXQ5cTb5VLb5Z5Edx5iafgjEQ2BRRz0zcUVTRCl2xd5YOsghjvZXAyazLlVqhM91IVWvnZ4dSHgSFUnczooHq3SM5Vlz9ckG0Hmh6gPzkUzAFApuiMFSjoh+4Ym8k0iRI1tZuMxsps85C237gzFTJyqfX5FuhVx0LnX47ncASpzMaPJmf7wCmQGBTCCc+SsJfxG1hJFbV3lk6O/Jq3pnm6YTF0ZqFt4okW06HUsbJ0Qi8v1xx0GPyFAzZEZwbyBGPfmY6YScgsCmkE6KrRE1XKI+FrtqbThwoZnq1AiezLov3iMJbRWkyw2/T5GQ/lxH4jSSJK8hWeA5VZkJ/Mn0hP/kUzIDApig6UZqNpNmrIxK4gjazkWDgILApiorOR9VrXFbt1VEv8Lh4T+jsoazgLAhsiqKiYnzVvZZ7ddQKLEdg1r6FzQCBTVGqVs6yDa76vTpqBS4cofUBYUggsClKiuZWpdTv1VEncNtVKWHQIDCAxyAwgMcgMIDHIDCAxyAwgMcgMIDHIDCAxyAwgMcgMIDHIDCAxyAwgMcgMIDHIDCAxyAwgMcgMIDHIDCAxyAwgMcgMIDHIDCAxyAwgMcgMIDHIDCAx9QLHACAG5xBYNtJ1jOd2k4BDArXA+osAtdbb5/p1HYKYFC4HVAIDKDF7YBCYAAtbgcUAgNocTugEBhAi9sBhcAAWtwOKAQG0OJ2QA1PYIANAoEBPAaBATwGgQE8BoEBPAaBATwGgQE8ZngCu91tB97hdkAhMIAWtwMKgcE/Zul09qvL5Tj8sV/8xLl7y8kbPzuM3r76+eX4E5NwT8ji4ELmQFduHKX7xMYL6aHKAfVwLwh2bmW3/H4UBG+Lk53uxgkTh4oOv3XbwO9cAwKDfzQKPB+FGyZBcF56GdqafOJBUCVw9Ml0o07gSXLmmLHacqMo8ASBVweBh88sa0+oTzH/XY6Fj5NEnfkoEnjxWVAQWB5oEeap0uCZ+thMJ3B4sBviRpBqOQm2wi0PR+mW8I4hDjTuUl0FAoN/NAksM+DQqx+P1Ocm534qPzPfC3b2KgSWOee+3Bp5rBF4or4zSdIQ2Rqe9UL+M4sDda4uQWDwjwqBQ1l+dyeqiC7HUpxJ8P5BXDIeRznix18cVAocOzuRn0sFFoXvTBlbblHZ6nwUbzndjQ8Zb4n2ne5m7gMdgcDgH9UC/yKub0bihNngRMoWZshK4D8dJbliUeDTXemcykX1AqsDxNomX00z3DhLngXv3hkFWx8fdXIRFAgM/pG2PQllIoFFI9JiLNSbJYXcuSxDT87dS4rZdQJH25WMuiJ0SddMnhxtmUW2Twrud8HwBIbhUy2wcFHmi6ocLASWpVrhaluBlYw5gQuUBRaNWLdEI1bSPhadbBy8cyi3X608khEQGPyjsgitskHR8Bs1/oqWJPFSNGm1FVh9d0WBo3J23D6W1o4VxfdGQWDwD43AIvfNCCz6hcTwjEaBYy8LArepA4fbfiWqul8cxCXnfI7baWM0AoN/tM+BT3cvSFUbBY6dbSFwsRU6JupGij+QgMAAOSoFrqoDix6l34hO4SaBT3eVdc114HI/cHzwaEuclyd59KzLViwEBv+oFnjrlvg31wotXl9JGroElQKLkVhK2YpW6CLlkViz4NyhGOQV+xp/eRzsHIafHJVHipkDgcE/MmOhQ9/iIvTluFk67QeWQ6zEm1qBCyXkYj9wFZmx0CrjjsrZkdFp1ny6Vxo1bZzhCUw/8PCpFvjTO0HwjmqJikZiXU1HJesFfvtWdGQ18kM7lDI7GykqeS/ujALZZSQPkWa4cnt+3pJpEBh8J9eIJZmPGjM9JXB5a/NYaLdAYPCdssBqNpKWaoHbzEZyCwQG35HzgfMCq+lIOioFbjcf2CkQGHynQmC5IoeWSoFbrsjhEggMG0l1EboKtwMKgQG0uB1QCAygxe2AQmAALW4H1PAEBtggEBjAYxAYwGMQGMBjEBjAYxAYwGMQGMBjhiew29124B1uBxQCA2hxO6AQGECL2wGFwABa3A4oBAbQ4nZAITCAFrcDCoEBtLgdUAgMoMXtgEJgAC1uB9TwBAbYIBAYwGMQGMBjEBjAYxAYwGMQGMBjEBjAY4YnsNvdduAdbgcUAgNocTugEBhAi9sBhcAAWtwOKAQG0OJ2QCEwgBa3AwqBAbSsG1DbAjNJqQCBAbSsGVDbEYZSUwSBAbQgMMDGsr3drcEIDNAhCAzgMQgM4DEIDOAzNGIBeAwCA3jMRanvxYsdHX54AtMPDEZZM6AuRhhKTREEBtCCwP2CwGAUBO4XBAajGBD4h9SB24PAYJT1Bf47GrFWAIHBKGsL/ENaoVcBgcEoawbU3/9g+wc/QOD2IDAYZc2A+q/bP7yIwCuAwGCUdXPgsBKMwACechGBAfzFkMCvnh8/+aZiOwIDdMmaAp9O/yJ+fD0VPHpZ2o/AAF1iRODZ9NH3JydfTx+9Lu5HYIAuMSHw4vFU5r1fT78q7kdggC4xIXBUjl7Oo58ZEBigS0wKfLoJAtMPDEYxMJlh7TrwU1X5nU//WtyPwABabAs8nR4/fyErv4unm1AHRmAwiuX5wN+9OBY9SLIgXS5BIzCAHgcm9C++e/FXIfCX5V0IDKDFAYE1IDCAFgTuFwQGo6wXUBcNCPzq+bPj4yfPv6vah8AAWmwLPH88jaEODLAqlgWeTx99c3Iym3518u3jDluhX714fnx8/Pyb0mBrgE1m7Qz46fQ/xY+ZGA0dvc5iRuBMLv8EhQES1hU4HUX51+5GYs1Db787EYS5fHnGE8DGYk7gv3Q3Fjo7wqtitBfAxrKuwPFMwplwt6PZSLn7QsVNAmBjWbsOrGbxv5qGGeOrx92MhUZggBrWFjjMgqePwv+fiLHQT0q7TQgc5/KSWbmeDbCxrD+OY/FCrIYVZr2nT74v7zVSBxYr9kQnm02n5YW3eoV+YDCKmX5gU6kpYqYbSa6Zd3ws5z2Veqp6BoHBKJsg8PLkheoJPv6b9U4kBAajbITADoHAYBSHBGZNLIBVQeB+QWAwikMCL082YGF3BAajuCRwGQQG0ILA/YLAYBT7Auvm6g5PYACHWF9g/VxdBAbokPVX1NHP1UVggA4xsCKHdq6uKYGTHipmIwGkmJrQX36jQGCADvFF4LSLudzXDLCxmFqRQ1IxV5c6MEB3XFy7DtwwV3d4AtMPDEZZK6DWF7hhrq6xdaE1T3/oFwQGo9gWWD9X1/i60BVPf+gXBAajGBHYWGqKGFoXWvv0h35BYDDKBgjc8PSHfkFgMMrwBW56+kO/IDAYZZMErn76Q78gMBhl+AI3Pf2hXxAYjDJ8gZue/tAvCAxG2QCBG57+ALCp+CFww9MfADYVTwQGgCqMCKyb6ofAAN3hjcC6dbcANhUzRWjNXF3jY6Er1t0C2FT8qAM3rLsFsKn4IXDDulv9Qj8wGGX4/cBNy/b0CwKDURC4XxAYjDJ8gZvW3eoXBAaj2BX49DhHaZyjkTpww7pb/YLAYJR1Amr9FXUWz6ZZOuoH1q+71S8IDEaxK7CQS9csbGggh3bdrX5BYDCKCYHXSsBTXaF2eEMpERiMYl3gxWNNuzACA2ixLvDy2+f1WfDwBAZwhs57kcwLbL0fGMAZEBjAYzwUmKcTAsSYEVj33CLqwACdYUJg/XOLEBigMwwI3PDcIlbkAOgMAwI3PLdoeCty0A8MRrHbD9z03KLhrciBwGAUVwSufm4RK3IAaLErcNNzi5jQD6DF8lDKhucWITCAFssCNzy3iBU5ALSsEVAmpgM3PLeIFTkAtNgWWA8rcgBoMSCwwdQUYUUOAC0bITAAlDAtcHcPN3saDd+Y2+4FBnAHfwSOxX1qexwWgDsYL0J39XTC2FwyYIAUj+rAc9n6/DUZMECCRwIvn8qx1mTAAAmGBNbN1TUmsMiCyYABMhgRWD9X11w30tO/Lh67kAHTDwxGsdwP3DBX15zA8+lzJzJgBAajWBa4Ya6uwYEc1mcCKxAYjGJX4KapfgYFnh+7kAEjMJjl7AFlYi5DjwI7AgKDUewK3DRXF4EBtNgVuGmurkGBXz07Pj7+0noxGoHBKOsLvN759XN1zQn8LOqrYj4wDArbAuvn6hoT+GuV07MiBwwM6wJrMSVwUte2viYWgCMYFHhWly+aEjhp4La+KiWAI5gTOMwfa/JFczkwAgPkMCfw7NHfarJgg3Xgr6KftluxANzAmMCLx38N/6vcZUzgkxfTJ9+ffPds+pUYd229MwnAOsYEFjXgmlqwuTpwDorRAKYElrlvTRZsrA78PEfFo8QBNgsjA7EEM7XcTWUWzFBKAC1nDihTAkcNxKeVDdEIDKDFusCzqF24MgtGYAAtawu85vkXz6KVdObHFTVTBAbQYltgPQgMoAWB+wWBwShOCFw7VxeBAbS4IHD9XF0EBtDigMCauboIDKDFvsC6ubrDExjADYwJrJuri8AAnWBsJKV2ri4CA3SCOYF1c3URGKATDAqsmauLwACdYM5f3VxdBAboBIMrYmnm6iIwQCf0MpJygALTDwxGOWtAIfDZQGAwCgL3CwKDURC4XxAYjHLGgDLYi6QDgQG0IHC/IDAYBYH7BYHBKGsKbDg1RRAYQAsC9wsCg1EQGGDzQGAAf+mpDQuBAboAgQE8BoEBPKYnfxEYoAsQGMBjEPis0A8MRjlbQCHwWUFgMMqZAqqvNiwEBtCDwP2CwGAUBO4XBAajrCWw8dQUQWAALQjcLwgMRkHgfkFgMMpZAqq3KjACA+hBYIANA4EBPKY3fxEYwDwIDOAv/ZWgERjAOAgM4DEIDOAx/fk7QIHpBwajnCGgEHgNEBiMsnpA9ViCRmAAPQjcLwgMRjm7wF2kpggCA9Rx/9L29o/+HxlQL7cVt8XrcPP+Um29nf242nrx4t9t/1D8o/jR/pHce+3Now6SiMAANdxVBv438fp+KvDrS28dRa5eeyv7+WqBt7eVuQjcDgQGM9yX+eznl/6LyGXvpnmtfCl1vL99L/+FvMAfyK2fX1cGI3A7EBjMcFP5+L8vvSXf3Eu334v+ufZB7gvVAocfk9sRuB0IDGa4ppx99D+EeZnCciLw3XwGHAl8sSTwy23xZQQG6JPYOOHqy+337l7a3v4XsSUuQr++tJ//Qp3A6kgIDNAnN1W19/WlUOD7mfaouBHrbtHI+0mzVUFgVd5GYIAeCX38pWjE2pal5fcO5Wsh5evronnrZfj//Uvbbx5mv5AR+CUCA9jkpsp0r6dV3deXUgtvviXLzJmKsCxCX4yL0AgMYJdfy2rvzYx5aWO0GMMh9mQ8rRWYOjCALV5fyozWSAUWzdLCycxuIfDFWOCM2bRCA/TPXdWte1+IGHUpvdyOLbwfl4pbCHxNtoYhcDvoBwYzvNzePgyL0dv/xz0h85uqESvuOZJjOMpF6ItlgT+/LjNgBG4JAoMhVCPWf/nv4vV11bocy6qarsqNWInA6fQHxkKvBgKDKcTYjffUbCT5+s1fRjviMRzFbqQqgX8UfQmB24HAYJRVAqrPqfwKBAbQskJAXUTg9UFgMAoC9wsCg1HaB5QFfxEYNo7Pr2eaoyRy6ZzD8t7MkjptaBC4MP3fDAgMG8b9fIfQMlk6Z7+4N7ukTgsa/P18G4EB1uW1HIzx+Xa6RE68dI5a7yrdm93eggZ/f72NwABrc1/lrvezc4Vk3ivHRGb3Zrc3c1Er8OvruVlN5kBg2CySafrJuIponLMcGJndm93eiN7fsDT+L0c3ERhgXWKNrqXzijJL52T3Zrc3cbFB4D8ftTvOyiAwbBZlLbNL5+RlTrc30ORv4YwGQWDYLMoCZ5fOye7NbtfTyl8EBlifioJxZumc3N7ykjqVXGznLwK3g35g0FGuA2eXzsnvldv/v/+hb8Rq6y8CtwOBQUe5FTpCdhdV7P3f2m6ki639ReB2IDDoKPcDZ5fOye6Ntv+v7Q+qjiO4eHEFfxG4HQgMOsojseKlc4Rf2b3ZJXUqKNrbOIUBgVuBwKAlO9pZLTd3M330b25vdkmdPGV5m/1F4HYgMOjJzDdSAqulcypmI2WX1ImpdLeNvwjcDgQGo8QBVWtuO307AoEBahFqTrfXpsMUIjCANntF4OGgL0XBMEHgVbD91wIogMDtsf23AiiBwK2x/acCKIPArbH9pwIog8Ctsf2nAiiDwK2x/acCKNJVrBtieAJPpyaOAhtHXVC6PbDALYFNGNyxwJ396uAoCNwvbl9v8A63AwqBAbS4HVAIDKDF7YBCYAAtbgcUAgNocTugziawy0yntlMAg8L1gEJgAA2uB9TqAneJc8VzEtQECWrCUoIQWECCmiBBTSCwRUhQEySoCQS2CAlqggQ1gcAWIUFNkKAmENgiJKgJEtQEAluEBDVBgppAYIuQoCZIUBMIbBES1AQJagKBLUKCmiBBTSCwRUhQEySoCQS2CAlqggQ1gcAWIUFNkKAmNklgADADAgN4DAIDeAwCA3gMAgN4DAIDeAwCA3gMAgN4DAIDeAwCA3hMfwI/3AuCnVv6Lb1SOv3JnVEQvHHDVnpqrsd467aFtEgq/mQfBsHWx0eW0lORoAeXrf7JQibn7mXf9h3UvQk8UQtUX9Vt6ZXS6V/tqi0XXElQtNWawLV/svOWDC4naGw3hkIeBDmBew/qvgSej4Ib4rdNo7G8pVfKpx8H7/453DIK9h1JkGAWWBO46k+2dUPe6Fy5QrNg65b4k1m7xy0+C3IC9x/UfQk8UTelSXpvKm/pldLpT3dVxjKxlAVXXo/5aGfPVnSWEzRW5s6cuUKWY2g53wt29rIC95+gngReHKgwnI/i4ld5S6/Un34+shKelQlaHJz73YElgcsJim9xlqi4QokvdooEy/HWx18cZAS2ENS9Cax+zdPd+Nctb+mV+tNbup1XJmi8dXthT+BigsJb2+ITe41YFVcoLNPfWi4fjqyEUMifjpJUSSwEdU8Cxzfv9Nctb+mV2tPPLUVDVYJEzmJN4HKCZsFPdi02YlVdobAMG7JjrZ2+EEAWghqB86ef22rDqkiQrGs6JXCgMjw7ZZSqP9nvR0LgLYv9SAjslMAPZCuiDcoJUhUppwS22mxR8SebBDuH8o5iqQ683BiB/agDL+4EW7ZCoZygSfJ0Z0euUCyupXtufQxZuqPk0pB7M7w6sBet0IsDeUO3QzlB1gUuJsi6wHXN4pYStCyde7it0O714ZVPH/r7rsVukprrYa0IXU5QeIFk+cRWhlfRdW81E5Dkbx6D7Qf2YSSWteEAdQmS2BO4cuDTDYtVzqrBczufLpd/2LP4l8sLPNyRWNlBotGN052x0DJBp7txidXS7bx8hQT2BK5I0B1nRourBIVlAquDs5fZaq+doLYxGykOT2dmI8kEzQLLAldcoaVVgSsSZHnyTylBi1+JBNmbHlUSeLizkQDAPAgM4DEIDOAxCAzgMQgM4DEIDOAxCAzgMQgM4DEIPADkoP75P7z9s39PNj38+ZV0PMosGhmkBv/Hw5eC4IpYxU/tsDW4CtYEgQeAXDp6PspMWxJvEoFPd2sETsf8zSzOqIV1QGD/URnsfLR1OdFwkhkReroXFAVWbxd//CTeY3NCHqwDAntPJF8o8L/G0wwWB1sfxQKLzLha4GVm2XhbS8XCmiCw90TTIEOB/203kfb8Z0rgxZ0g2NmrFTh8fSF6YW/OBKwBAvtGKOrtV3vp6q7pKhBbnx4k+enViRI43PrPibFlgZN1rqytZw/rgcC+IYrKci3GYEdWW2dRWVmIHa9JMA72Y4F/drjUCXwaPyfF1nK6sB4I7BuiTqueCKQUHUc6CoGjtWXEmmqTtBVaJ3DaonVAQ7SPILBvhAKfO4xe7GfEEwJHxWnRItVS4ND/C4UX4BMI7BvzZF11qVyyeIcQOMqOxUPIVhZ4YnNhGjgrCOwb8+RhmlK55K18ISvE0umVBZ7ZWb0W1gOBfSNtbZLKJd5JgaPVvUJPV60DI7CfILBvaAWWpWdZjm4pcNIKjcB+gsC+oS1Ci+5c1ZLVUuBUWwT2EgT2jfT5iRWNWCJ//o3MotsJnIzEohHLUxDYN+ZR/280iCrXjSTffiSdbCfwJH2GAN1IXoLAviEGcohnsD0YKeNi8aKytJiHtL9sJfDijx+mzxBgIIefILBvhKJ+lH2CRHYopXyr6rJagRO2/jk9LFVgH0Fg3xCiZp/fkZnMIH6e7ipz2wh8JfNMEiYz+AkC+0baCh3RXr34eboVMJ3QUxDYN0oCt19NQyMwE/o9BYF9oyRwe/nqBWZJHV9BYN8oC6wWtWtBvcCz7PBo8AgE9o0KgTVF43afY1lZb0FgAI9BYACPQWAAj0FgAI9BYACPQWAAj/n/AaFdinv6DXyjAAAAAElFTkSuQmCC) 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Figure 2. A: Broad, uncertain prior on p(M1). B: Posterior when BF=5. C: Posterior when BF=38.9.
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All the details are in the manuscript at https://osf.io/36527/. Please send me an email if you have comments!